.I 1
.T
experimental investigation of the aerodynamics of a
wing in a slipstream .
.A
brenckman,m.
.B
j. ae. scs. 25, 1958, 324.
.W
experimental investigation of the aerodynamics of a
wing in a slipstream .
an experimental study of a wing in a propeller slipstream was
made in order to determine the spanwise distribution of the lift
increase due to slipstream at different angles of attack of the wing
and at different free stream to slipstream velocity ratios . the
results were intended in part as an evaluation basis for different
theoretical treatments of this problem .
the comparative span loading curves, together with
supporting evidence, showed that a substantial part of the lift increment
produced by the slipstream was due to a /destalling/ or
boundary-layer-control effect . the integrated remaining lift
increment, after subtracting this destalling lift, was found to agree
well with a potential flow theory .
an empirical evaluation of the destalling effects was made for
the specific configuration of the experiment .
.I 2
.T
simple shear flow past a flat plate in an incompressible fluid of small
viscosity .
.A
ting-yili
.B
department of aeronautical engineering, rensselaer polytechnic
institute
troy, n.y.
.W
simple shear flow past a flat plate in an incompressible fluid of small
viscosity .
in the study of high-speed viscous flow past a two-dimensional body it
is usually necessary to consider a curved shock wave emitting from the
nose or leading edge of the body . consequently, there exists an
inviscid rotational flow region between the shock wave and the boundary
layer . such a situation arises, for instance, in the study of the
hypersonic viscous flow past a flat plate . the situation is somewhat
different from prandtl's classical boundary-layer problem . in prandtl's
original problem the inviscid free stream outside the boundary layer is
irrotational while in a hypersonic boundary-layer problem the inviscid
free stream must be considered as rotational . the possible effects of
vorticity have been recently discussed by ferri and libby . in the
present paper, the simple shear flow past a flat plate in a fluid of small
viscosity is investigated . it can be shown that this problem can again
be treated by the boundary-layer approximation, the only novel feature
being that the free stream has a constant vorticity . the discussion
here is restricted to two-dimensional incompressible steady flow .
.I 3
.T
the boundary layer in simple shear flow past a flat plate .
.A
m. b. glauert
.B
department of mathematics, university of manchester, manchester,
england
.W
the boundary layer in simple shear flow past a flat plate .
the boundary-layer equations are presented for steady
incompressible flow with no pressure gradient .
.I 4
.T
approximate solutions of the incompressible laminar
boundary layer equations for a plate in shear flow .
.A
yen,k.t.
.B
j. ae. scs. 22, 1955, 728.
.W
approximate solutions of the incompressible laminar
boundary layer equations for a plate in shear flow .
the two-dimensional steady boundary-layer
problem for a flat plate in a
shear flow of incompressible fluid is considered .
solutions for the boundary-
layer thickness, skin friction, and the velocity
distribution in the boundary
layer are obtained by the karman-pohlhausen
technique . comparison with
the boundary layer of a uniform flow has also
been made to show the effect of
vorticity .
.I 5
.T
one-dimensional transient heat conduction into a double-layer
slab subjected to a linear heat input for a small time
internal .
.A
wasserman,b.
.B
j. ae. scs. 24, 1957, 924.
.W
one-dimensional transient heat conduction into a double-layer
slab subjected to a linear heat input for a small time
internal .
analytic solutions are presented for the transient heat
conduction in composite slabs exposed at one surface to a
triangular heat rate . this type of heating rate may occur, for
example, during aerodynamic heating .
.I 6
.T
one-dimensional transient heat flow in a multilayer
slab .
.A
campbell,w.f.
.B
j. ae. scs. 25, 1958, 340.
.W
one-dimensional transient heat flow in a multilayer
slab .
in a recent contribution to the readers'
forum wassermann gave analytic
solutions for the temperature in a double
layer slab, with a triangular heat
rate input at one face, insulated at the other,
and with no thermal resistance
at the interface . his solutions were for the
three particular cases..
i propose here to give the general solution
to this problem, to indicate
briefly how it is obtained using the method of
reference 2, and to point out
that the solutions given by wassermann are
incomplete for times longer
than the duration of the heat input .
.I 7
.T
the effect of controlled three-dimensional roughness
on boundary layer transition at supersonic speeds .
.A
van driest,e.r. and mccauley,w.d.
.B
j. ae. scs. 27, 1960, 261.
.W
the effect of controlled three-dimensional roughness
on boundary layer transition at supersonic speeds .
experiments were performed in the 12-in. supersonic wind
tunnel of the jet propulsion laboratory of the california
institute of technology to investigate the effect of three-dimensional
roughness elements (spheres) on boundary-layer transition on a
tained at local mach numbers of 1.90, 2.71, and 3.67 by varying
trip size, position, spacing, and reynolds number per inch .
the results indicate that (1) transition from laminar to turbulent
flow induced by three-dimensional roughness elements begins
when the double row of spiral vortices trailing each element
contaminates and breaks down the surrounding field of vorticity, (2)
transition appears rather suddenly, becoming more violent with
increasing roughness height relative to the boundary-layer
thickness, (3) after the breakdown of the vorticity field, the strength
of the spiral vortices may still persist in the sublayer of the
ensuing turbulent flow, (4) lateral spacing of roughness elements has
little effect upon the initial breakdown (contamination) of the
laminar flow, and (5) the trip reynolds number where u
and v are the velocity and kinematic viscosity at the outer edge of
the boundary layer and k is roughness height, such that transition
occurs at the roughness position, varies as the position reynolds
number to the one-fourth power, viz., where x is
trip position .
.I 8
.T
measurements of the effect of two-dimensional and three-dimensional
roughness elements on boundary layer transition .
.A
klebanoff,p.s.
.B
j. ae. scs. 22, 1955, 803.
.W
measurements of the effect of two-dimensional and three-dimensional
roughness elements on boundary layer transition .
in his study of the effect of roughness on transition, h. l.
dryden found, on the basis of available data, that the effect
of a two-dimensional roughness element such as a /trip wire/
could be represented reasonably well in terms of a functional
relation between and, where is the reynolds number
of transition based on distance from the leading edge, is the
height of the roughness element, and is the boundary-layer
displacement thickness at the position of the element . at his
suggestion some additional data were obtained, primarily to
extend the range to higher values of, during the course of an
investigation of transition on a flat plate conducted at the
national bureau of standards . after the results on the two-
dimensional roughness elements were obtained, it appeared to be
desirable to see whether a row of three-dimensional roughness
elements would behave in the same way .
.I 9
.T
transition studies and skin friction measurements on
an insulated flat plate at a mach number of 5.8 .
.A
korkegi,r.h.
.B
j. ae. scs. 23, 1956, 97.
.W
transition studies and skin friction measurements on
an insulated flat plate at a mach number of 5.8 .
an investigation of transition and skin friction on an insulated
flat plate, 5 by 26 in., was made in the galcit 5 by 5 in.
hypersonic wind tunnel at a nominal mach number of 5.8 .
the phosphorescent lacquer technique was used for transition
detection and was found to be in good agreement with total-head
rake measurements along the plate surface and pitot boundary-
layer surveys . it was found that the boundary layer was
laminar at reynolds numbers of at least 5 x 10 . transverse
contamination caused by the turbulent boundary layer on the
tunnel sidewall originated far downstream of the flat plate leading
edge at reynolds numbers of 1.5 to 2 x 10, and spread at a
uniform angle of 5 compared to 9 degree in low-speed flow .
the effect of two-dimensional and local disturbances was
investigated . the technique of air injection into the boundary
layer as a means of hastening transition was extensively used .
although the onset of transition occurred at reynolds numbers
as low as 10, a fully developed turbulent boundary layer was
not obtained at reynolds numbers much below 2 x 10
regardless of the amount of air injected .
a qualitative discussion of these results is given with emphasis
on the possibility of a greater stability of the laminar boundary
layer in hypersonic flow than at lower speeds .
direct skin-friction measurements were made by means of the
floating element technique, over a range of reynolds numbers
verified as being laminar over the complete range . with air
injection, turbulent shear was obtained only for reynolds
numbers greater than 2 x 10, this value being in good agreement with
earlier results of this investigation . the turbulent skin-friction
coefficient was found to be approximately 0.40 of that for
incompressible flow for a constant value of r, and 0.46 for an effective
reynolds number between 5 and 6 x 10 .
.I 10
.T
the theory of the impact tube at low pressure .
.A
chambre,p.l. and schaaf,s.a.
.B
j. ae. scs. 15, 1948, 735.
.W
the theory of the impact tube at low pressure .
a theoretical analysis has been made for an impact tube of the
relation between free-stream mach number and the impact and
free-stream pressures and densities for extremely low pressures .
it is shown that the results differ appreciably from the
corresponding continuum relations .
.I 11
.T
similar solutions in compressible laminar free mixing
problems .
.A
napolitano,l.
.B
j. ae. scs. 23, 1956, 389.
.W
similar solutions in compressible laminar free mixing
problems .
there are in supersonic aerodynamics many situations of
practical interest wherein streams of different velocities and,
in general, different stagnation pressures mix with one another .
in the majority of these problems the interaction between the
two streams takes place in the presence of an axial pressure
gradient . its effect on the characteristics of the mixing may
influence significantly the performances of the devices wherein
the phenomena cited above occur . a theoretical and
experimental program of research to study mixing in the presence of
axial pressure gradients is being carried on at the polytechnic
institute of brooklyn .
.I 12
.T
some structural and aerelastic considerations of high
speed flight .
.A
bisplinghoff,r.l.
.B
j. ae. scs. 23, 1956, 289.
.W
some structural and aerelastic considerations of high
speed flight .
the dominating factors in structural design of high-speed
aircraft are thermal and aeroelastic in origin . the subject
matter is concerned largely with a discussion of these factors and
their interrelation with one another . a summary is presented
of some of the analytical and experimental tools available to
aeronautical engineers to meet the demands of high-speed flight
upon aircraft structures . the state of the art with respect to
heat transfer from the boundary layer into the structure, modes
of failure under combined load as well as thermal inputs and
acrothermoelasticity is discussed . methods of attacking and
alleviating structural and aeroelastic problems of high-speed
flight are summarized . finally, some avenues of fundamental
research are suggested .
.I 13
.T
similarity laws for stressing heated wings .
.A
tsien,h.s.
.B
j. ae. scs. 20, 1953, 1.
.W
similarity laws for stressing heated wings .
it will be shown that the differential equations for a heated
plate with large temperature gradient and for a similar plate at
constant temperature can be made the same by a proper
modification of the thickness and the loading for the isothermal plate .
this fact leads to the result that the stresses in the heated plate
can be calculated from measured strains on the unheated plate by
a series of relations, called the /similarity laws ./ the
application of this analog theory to solid wings under aerodynamic
heating is discussed in detail . the loading on the unheated analog
wing is, however, complicated and involves the novel concept
of feedback and /body force/ loading . the problem of stressing
a heated box-wing structure can be solved by the same analog
method and is briefly discussed .
.I 14
.T
piston theory - a new aerodynamic tool for the
aeroelastician .
.A
ashley,h. and zartarian,g.
.B
j. ae. scs. 23, 1956, 1109.
.W
piston theory - a new aerodynamic tool for the
aeroelastician .
representative applications are described which illustrate the
extent to which simplifications in the solutions of high-speed
unsteady aeroelastic problems can be achieved through the use of
certain aerodynamic techniques known collectively as /piston
theory ./ based on a physical model originally proposed by
hayes and lighthill, piston theory for airfoils and finite wings
has been systematically developed by landahl, utilizing
expansions in powers of the thickness ratio and the inverse of the
flight mach number m . when contributions of orders and
are negligible, the theory predicts a point-function
relationship between the local pressure on the surface of a wing and the
normal component of fluid velocity produced by the wing's
motion . the computation of generalized forces in aeroelastic
equations, such as the flutter determinant, is then always
reduced to elementary integrations of the assumed modes of motion .
essentially closed-form solutions are given for the bending-
torsion and control-surface flutter properties of typical section
airfoils at high mach numbers . these agree well with results of
more exact theories wherever comparisons can be fairly made .
moreover, they demonstrate the increasingly important influence
of thickness and profile shape as m grows larger, a discovery that
would be almost impossible using other available aerodynamic
tools . the complexity of more practical flutter analyses-e.g., on
three-dimensional wings and panels-is shown to be substantially
reduced by piston theory . an iterative procedure is outlined, by
which improved flutter eigenvalues can be found through the
successive introduction of higher-order terms in and .
other applications to unsteady supersonic problems are
reviewed, including gust response and rapid maneuvers of elastic
aircraft . steady-state aeroelastic calculations are also discussed,
but for them piston theory amounts only to a slight modification
of ackeret's formulas .
suggestions are made regarding future research based on the
new aerodynamic method, with particular emphasis on areas where
computational labor can be reduced with a minimum loss of
precision . it is pointed out that a mach number zone exists where
thermal effects are appreciable but nonlinear viscous interactions
may be neglected, and that in this zone piston theory is the logical
way of estimating air loads when analyzing aerodynamic-
thermoelastic interaction problems .
.I 15
.T
on two-dimensional panel flutter .
.A
fung,y.c.
.B
j. ae. scs. 25, 1958, 145.
.W
on two-dimensional panel flutter .
theory and experiments of the flutter of a buckled plate are
discussed . it is shown that an increase in the initial deviation
from flatness or a static pressure differential across the plate
raises the critical value of the /reduced velocity ./
the applicability of the galerkin method to the linearized
problem of flutter of an unbuckled plate has been questioned by
several authors . in this paper the flutter condition was
formulated in the form of an integral equation and solved numerically
by the method of iteration and the method of matrix
approximations, thus avoiding the constraint of assumed modes . for a
plate (with finite bending rigidity) the results confirm those
given by the galerkin method .
an approximate analysis of the limiting form and amplitude of
the flutter motion for a buckled plate is presented .
.I 16
.T
transformation of the compressible turbulent boundary
layer .
.A
mager,a.
.B
j. ae. scs. 25, 1958, 305.
.W
transformation of the compressible turbulent boundary
layer .
the transformation of the compressible turbulent boundary-
layer equations to their incompressible equivalent is
demonstrated analytically . the transformation is essentially the same
as that for the laminar layer, first given by stewartson, except
that the explicit relation between the viscosity and temperature
is not required . a key point in the analysis is the modification
of the stream function to include a mean of the fluctuating
components and the postulate that the apparent turbulent shear,
associated with an elemental mass, remains invariant in the
transformation .
the values of the incompressible friction coefficients and of
pressure rise causing separation thus transformed show good
agreement with the experimentally measured and independently
reported results . an application of the transformation to the
self-preserving boundary layers and to the computations of
general boundary-layer flow is shown .
.I 17
.T
remarks on the eddy viscosity in compressible mixing flows .
.A
lu ting and paul a. libby
.B
polytechnic institute of brooklyn, and general applied science
laboratories, inc.
.W
remarks on the eddy viscosity in compressible mixing flows .
in connection with a study of the wakes behind bodies in hypersonic flow
carried out for the missile and space vehicle division of the general
electric company, it was desired to estimate the eddy viscosity in
axisymmetric, compressible wakes . because of the lack of applicable
experimental data, it was found necessary to make such an estimate by
rationally extending the few available data for incompressible flows to
the compressible case . this suggested the application and extension of
the transformations applied to turbulent boundary layers in reference
infinitesimal mass are invariant with transformation, mager showed that
the partial differential equations for the compressible turbulent
boundary layer can be transformed to incompressible form . the validity of
this assumption and of the transformations was established for several
boundary-layer flows by comparison with experiment .
.I 18
.T
the flow field in the diffuser of a radial compressor .
.A
rhyming,i.l.
.B
j. ae. scs. 27, 1960, 798.
.W
the flow field in the diffuser of a radial compressor .
this note discusses the two-dimensional diffuser flow field
in a radial compressor outside the impeller wheel . it is
assumed that the diffuser has guide vanes arranged in a circular
row at a radius . the impeller wheel has the radius (see
fig. 1) . the flow in the diffuser starts at the circle with the
radius . the velocity components, and in the r and
directions of the velocity vector on this circle are prescribed
together with the thermal state of the gas . the flow so prescribed
on the radius will, if no disturbances are present (i.e., no
boundary conditions in the flow other than zero velocity at
infinity are to be fulfilled), develop in a spiral flow .
.I 19
.T
an investigation of the pressure distribution on conical bodies in
hypersonic flows .
.A
victor zakkay
.B
aerodynamics laboratory, polytechnic institute of brooklyn, freeport,
n.y.
.W
an investigation of the pressure distribution on conical bodies in
hypersonic flows .
a large amount of work on conical flow fields without axial symmetry
at supersonic speed is presently available . however, no apparent
hypersonic approximation has yet been derived . in this note,
experimental data on two elliptical cones at m = 6 are presented and a
hypersonic approach obtained from physical considerations is suggested .
.I 20
.T
generalised-newtonian theory .
.A
love,e.s.
.B
j. ae. scs. 26, 1959, 314.
.W
generalised-newtonian theory .
author generalizes lees's (amr 10(1957), rev. 2601)
modification of newtonian theory for blunt-nose bodies to apply to pointed-
nose bodies as well . the result is expressed by
sin where is the local inclination of the body
surface and the subscript /max/ refers to the maximum local
inclination and pressure coefficient . for blunt-nose bodies
and the generalized theory reverts to lees's blunt-nose
modification with given by normal shock relations . author shows,
by comparison of newtonian and generalized-newtonian theory
with exact solutions, the superiority of generalized-newtonian
theory . he also shows that both two-dimensional and
axisymmetric shapes are correlated by this generalization . results are
presented in two figures that support author's generalization and
indicate the independence of the correlation from variations in
both the hypersonic similarity parameter k = m(d1) and the ratio
of specific heats y .
reviewer believes this generalization should be of interest to
those engaged in development of hypersonic hardware as well as
theory .
.I 21
.T
on heat transfer in slip flow .
.A
stephen h. maslen
.B
lewis flight propulsion laboratory, naca, cleveland, ohio
.W
on heat transfer in slip flow .
a number of authors have considered the effect of slip on the heat
transfer and skin friction in a laminar boundary layer over a flat plate .
reference 1 considers this by a perturbation on the usual laminar
boundary-layer analysis while some other studies.dash e.g., reference
the impulsive motion of an infinite plate .
.I 22
.T
on slip-flow heat transfer to a flat plate .
.A
oman,r.a. and scheuing,r.a.
.B
j. ae. scs. 26, 1959, 126.
.W
on slip-flow heat transfer to a flat plate .
assuming that continuum flow energy equation in a boundary
layer remains valid well into slip region and taking account of the
temperature jump in a moving rarefied gas and for influence of
large mean free path through appropriate boundary conditions, a
solution is found for the temperature gradient in the slip region .
then from maslen expression (j. aero. sci. 25, 6, 400-401, june
slipping fluid to a flat plate, and behavior confirms results for
small values of knudsen number .
.I 23
.T
skin-friction and heat transfer characteristics of
a laminar boundary layer on a cylinder in axial incompressible
flow .
.A
seban,r.a. and bond,r.
.B
j. ae. scs. 18, 1951, 671.
.W
skin-friction and heat transfer characteristics of
a laminar boundary layer on a cylinder in axial incompressible
flow .
a solution is given for the case of the laminar boundary layer
of an incompressible fluid of constant properties on the exterior
of a cylinder with flow parallel to the cylinder axis . this case
differs from the blasius solution for flow along a flat plate by
considering the effect of the curvature in a plane transverse to
the flow direction . the local skin-friction and heat-transfer
coefficients for a prandtl number of 0.715 are evaluated and
compared to the similar magnitudes for flat plate flow, and the
effect of the curvature is shown to be significant in some practical
cases . recovery factors are evaluated, and this quantity is
found to be insensitive to the effect of curvature of the boundary .
.I 24
.T
theory of stagnation point heat transfer in dissociated
air .
.A
fay,j.a. and riddell,f.r.
.B
j. ae. scs. 25, 1958, 73.
.W
theory of stagnation point heat transfer in dissociated
air .
the boundary-layer equations are developed in general for the
case of very high speed flight where the external flow is in a
dissociated state . in particular the effects of diffusion and of atom
recombination in the boundary layer are included . it is shown
that at the stagnation point the equations can be reduced exactly
to a set of nonlinear ordinary differential equations even when the
chemical reactions proceed so slowly that the boundary layer is
not in thermochemical equilibrium .
two methods of numerical solution of these stagnation point
equations are presented, one for the equilibrium case and the
other for the nonequilibrium case . numerical results are
correlated in terms of the parameters entering the numerical
formulation so as not to depend critically on the physical assumptions
made .
for the nonequilibrium boundary layer, both catalytic (to
atom recombination) and noncatalytic wall surfaces are
considered . a solution is represented which shows the transition
from the /frozen/ boundary layer (very slow recombination
rates) to the equilibrium boundary layer (fast recombination rates) .
a recombination rate parameter is introduced to interpret the
nonequilibrium results, and it is shown that a scale factor is
involved in relating the equilibrium state of a boundary layer on
bodies of different sizes .
it is concluded that the heat transfer through the equilibrium
stagnation point boundary layer can be computed accurately by
a simple correlation formula and that the heat
transfer is almost unaffected by a nonequilibrium state of the
boundary layer provided the wall is catalytic and the lewis
number near unity .
.I 25
.T
inviscid hypersonic flow over blunt-nosed slender bodies .
.A
lees,l. and kubota,t.
.B
j. ae. scs. 24, 1957, 195.
.W
inviscid hypersonic flow over blunt-nosed slender bodies .
at hypersonic speeds the drag area of a blunt nose is much
larger than the drag area of a slender afterbody, and the energy
contained in the flow field in a plane at right angles to the flight
direction is nearly constant over a downstream distance many
times greater than the characteristic nose dimension . the
transverse flow field exhibits certain similarity properties directly
analogous to the flow similarity behind an intense blast wave
found by g. i. taylor, s. c. lin, and a. sakurai . a comparison
with the experiments of hammitt, vas, and bogdonoff on a
flat plate with a blunt leading edge at in helium shows
that the shock-wave shape is predicted very accurately by this
similarity analysis . the predicted surface pressure distribution
is somewhat less satisfactory . experimental results on a
hemisphere-cylinder obtained at in the galcit air tunnel
indicate that not only the shock-wave shape but also the surface
pressures for this body are given very closely by the similarity
theory, except near the hemisphere-cylinder junction .
energy considerations combined with a detailed study of the
equations of motion show that flow similarity is also possible for
a class of bodies of the form, provided that,
where for a two-dimensional body and for a
body of revolution . when the shock shape is not
similar to the body shape, and the entire flow field some
distance from the nose must depend to some extent on the details
of the nose geometry .
by again utilizing energy and drag considerations one finds
that at hypersonic speeds the inviscid surface pressures
generated by a blunt leading edge are larger than the pressures
induced by boundary-layer growth on an insulated flat surface
for an insulated blunt-nosed slender body of revolution the
corresponding distance is given by . (here
is free-stream reynolds number based on leading-edge
thickness, or nose diameter .) in free flight these constants are
replaced by 1,700 and 20, respectively, so that viscous
interaction effects are important over the forward portion of a blunt-
nosed slender body only for relatively low values of .
however, /far downstream/ of the nose the inviscid over-pressure is
small and viscous interaction phenomena will have to be taken
into account .
.I 26
.T
inviscid leading-edge effect in hypersonic flow .
.A
cheng,h.k. and pallone,a.j.
.B
j. ae. scs. 23, 1956, 700.
.W
inviscid leading-edge effect in hypersonic flow .
current interest in the problem of inviscid-viscous
interaction has led to the realization of the significant effect of
the leading-edge thickness in hypersonic flow . the purpose
of this note is to give an account of the downstream influence
of the blunt leading edge on the basis of the hypersonic small
perturbation theory .
.I 27
.T
newtonian flow theory for slender bodies .
.A
cole,j.d.
.B
j. ae. scs. 24, 1957, 448.
.W
newtonian flow theory for slender bodies .
as an aid to the aerodynamieist in the design of air frames for
hypersonic speeds (speeds faster than about mach 5), newtonian
flow theory is examined from the point of view of gas dynamics
and hypersonic small-disturbance theory . the usual theory is
shown to result as the first approximation of an expansion valid
for small . a basic similarity parameter
is introduced . a general solution
of the first approximation for the flow past slender bodies (bodies
which cause only a small disturbance to the stream) at zero angle
of attack is given . an important condition which limits the
application of the theory is noted-namely, that the pressure
coefficient on the surface not fall to zero . the theory is then
applied to cones and to bodies whose shape is .
.I 28
.T
a note on the explosion solution of sedov with application
to the newtonian theory of unsteady hypersonic flow .
.A
freeman,n.c.
.B
j. ae. scs. 27, 1960, 77.
.W
a note on the explosion solution of sedov with application
to the newtonian theory of unsteady hypersonic flow .
an exact analytical solution of the equations of inviscid
compressible unsteady flow has been given by sedov (reference
to the solution may be made through hayes and probstein) .
this solution is the similarity solution for a constant-energy point
explosion . in view of the recent work on problems of hypersonic
flow in the limiting form of the ratio of specific heats near 1
solution in this limit and inquire what form such a solution would
take . einbinder, in a recent note, has examined the solution for
various but does not mention the interesting case of .
it may be shown that the convergence to the limit is nonuniform
over the flow field . it is also not difficult to show that the non-
uniform behavior exhibited here is that which one would expect
from the newtonian formulation as derived in reference 3 .
.I 29
.T
a simple model study of transient temperature and thermal
stress distribution due to aerodynamic heating .
.A
isakson,g.
.B
j. ae. scs. 24, 1957, 611.
.W
a simple model study of transient temperature and thermal
stress distribution due to aerodynamic heating .
the present work is concerned with the determination of
transient temperatures and thermal stresses in simple models intended
to simulate parts or the whole of an aircraft structure of the built-
up variety subjected to aerodynamic heating .
the first case considered is that of convective heat transfer
into one side of a flat plate, representing a thick skin, and the
effect of the resulting temperature distribution in inducing
thermal stresses associated with bending restraint at the plate edges .
numerical results are presented for the transient temperature
differentials in the plate when the environment temperature first
increases linearly with time and then remains constant, the
period of linear increase representing the time of acceleration of
the aircraft . corresponding thermal stress information is
presented .
the second case is that of the wide-flanged i-beam with
convective heat transfer into the outer faces of the flanges . numerical
results are presented for transient temperature differentials for a
wide range of values of the applicable parameters and for an
environment temperature variation as described above .
corresponding thermal stresses in a beam of infinite length are
determined . a theoretical analysis of the stress distribution in a beam
of finite length is carried out and numerical results obtained for
one case . an experimental investigation of temperatures and
stresses in such a beam is described, and results are presented
which indicate good agreement with corresponding theoretical
results .
.I 30
.T
photo-thermoelastic investigation of transient thermal
stresses in a multiweb wing structure .
.A
gerard,g. and tramposch,h.
.B
j. ae. scs. 26, 1959, 783.
.W
photo-thermoelastic investigation of transient thermal
stresses in a multiweb wing structure .
photothermoelastic experiments were performed on a long
multiweb wing model for which a theoretical analysis is available in
the literature . the experimental procedures utilized to simulate
the conditions prescribed in the theory are fully described .
correlation of theory and experiment in terms of dimensionless
temperature, stress, time, and biot number revealed that the
theory predicted values higher than the experimentally observed
maximum thermal stresses at the center of the web . detailed
temperature measurements in the flange suggested that the major
source of this discrepancy can be traced to the one-dimensional
heat conduction analysis of the flange employed in the theory .
.I 31
.T
thermal buckling of supersonic wing panels .
.A
hoff,n.j.
.B
j. ae. scs. 23, 1956, 1019.
.W
thermal buckling of supersonic wing panels .
the temperature and thermal stress distributions are analyzed
in multicellular supersonic wing structures . a buckling criterion
is established for the panels of cover plates subjected to thermal
stresses .
.I 32
.T
the dynamic motion of a missile descending through
the atmosphere .
.A
friedrich,h.r. and dore,f.j.
.B
j. ae. scs. 22, 1955, 628.
.W
the dynamic motion of a missile descending through
the atmosphere .
a method is presented for computing rapidly, yet accurately,
the dynamic motion of a ballistic-type missile descending through
the atmosphere . the equations of motion are separated into a
set of /static/ trajectory equations (zero angle of attack) and a
set of /rotational/ equations describing the oscillatory motion
of the missile about its center of gravity . a transformation
allows the rotational equations to be written in a manner
analogous to the equation for an undamped oscillating spring mass
system with the mass equal to unity and a time variable spring
constant . for given initial conditions this equation can be
solved to obtain the envelope of maximum angle of attack . an
additional transformation allows the calculation of the complete
oscillatory motion at any time during the trajectory as a function
of the maximum angle of attack at that time .
this solution shows that the maximum angle of attack of a
missile descending through the atmosphere at relatively constant
speed is reduced even when the aerodynamic damping is neglected .
.I 33
.T
the prospects for magneto-aerodynamics .
.A
resler,e.j. and sears,w.r.
.B
j. ae. scs. 25, 1958, 235.
.W
the prospects for magneto-aerodynamics .
the equations describing the flow of an electrically conducting
fluid in the presence of electric and magnetic fields are written
down with the aid of certain simplifications appropriate to
aeronautical applications . in order to estimate the probable
significance of magneto-aerodynamic effects, some data on
conductivity of pure and /seeded/ air are first examined .
dimensionless quantities representing the ratios of forces and of
currents are then formed and their values studied for conditions
of flight in the atmosphere .
some examples of magneto-hydrodynamic and magneto-
gasdynamic effects in simple flows are given . these include
two cases of poiscuille flow of conducting liquids with applied
magnetic fields and the case of quasi-one-dimensional gas flow
with applied electrical and magnetic fields . in the last case,
attractive possibilities are found for controlled acceleration or
deceleration of gas at subsonic and supersonic speeds, even in
constant-area channels . the behavior of the flow is
characteristically different in different regimes of mach number and flow
speed relative to certain /significant speeds/ that are dependent
on the ratio of electrical to magnetic field strengths . these
are studied, and a chart is constructed to relate the length to
the speed ratio of a maximum-acceleration constant-area channel .
it is concluded that the advantages that may accrue from
magneto-aerodynamic methods are sufficiently attractive to
justify the considerable research and engineering development
that will be required . among the unsolved engineering problems
are the reduction of surface resistance of electrodes in contact
with a conducting gas, development of techniques for seeding,
and provision of the required magnetic fields in flight .
.I 34
.T
constant-temperature magneto-gasdynamic channel flow .
.A
kerrebrock,j.p. and marble,f.e.
.B
j. ae. scs. 27, 1960, 78.
.W
constant-temperature magneto-gasdynamic channel flow .
in the course of investigating boundary-layer flow in
continuous plasma accelerators with crossed electric and
magnetic fields, it was found advantageous to have at hand simple
closed-form solutions for the magneto-gasdynamic flow in the
duct which could serve as free-stream conditions for the boundary
layers . nontrivial solutions of this sort are not available at
present, and in fact, as in the work of resler and sears, the
variation of conditions along the flow axis must be obtained
through numerical integration .
consequently, some simple solutions of magneto-gasdynamic
channel flow were sought, possessing sufficient algebraic simplicity
to serve as free-stream boundary conditions for analytic
investigations of the boundary layer in a physically reasonable accelerator .
in particular, since the cooling of the accelerator tube is likely to
be an important physical problem because of the high gas
temperatures required to provide sufficient gaseous conductivity,
channel flow with constant temperature appears interesting .
some simple algebraic solutions for the case of a constant
temperature plasma are developed in the following paragraphs .
.I 35
.T
stagnation point of a blunt body in hypersonic flow .
.A
li,t.y. and geiger,r.e.
.B
j. ae. scs. 24, 1957, 25.
.W
stagnation point of a blunt body in hypersonic flow .
the purpose of this paper is to present a method of calculation
devised to yield all the important information on the symmetric
inviscid hypersonic flow in the stagnation point region of a blunt
body . the problem is the same as that considered by hayes
who used a slightly different approach . it is demonstrated that
hayes' results are valid in the stagnation point region and can
hence be considered a basis for constructing less restricted
solutions .
equations are presented giving velocity, pressure, detachment
distance, and vorticity . the values of shock detachment
distance and body pressure coefficient are compared with
experimental data for spheres . the pressure comparison shows that
the results of hayes and the theory presented herein represent a
better approximation than the newtonian impact theory for
hypersonic mach numbers .
in conclusion, the possibility of refinements to this analysis is
discussed .
.I 36
.T
supersonic flow around blunt bodies .
.A
serbin,h.
.B
j. ae. scs. 25, 1958, 58.
.W
supersonic flow around blunt bodies .
the newtonian theory of impact has been shown to be
useful for pressure calculations on the forward facing part
of bodies moving at high speed . it is now a familiar practice
to use this information to calculate nonviscous velocities at the
wall and then to estimate rates of heat transfer . this
procedure is perhaps open to question,. heat-transfer rates depend
on velocity gradients which are not given by the newtonian
analysis . nor can one obtain information on boundary-layer
stability or all the body stability derivatives . it seems,
therefore, inevitable that, as design proceeds with these hypersonic
missiles, there will be a greater need for more accurate
aerodynamic theories either to predict what will happen in unfamiliar
flight conditions or to effect an extrapolation from a known test
result to the design condition .
.I 37
.T
a new technique for investigating heat transfer and
surface phenomena under hypersonic flow conditions .
.A
ferri,a. and libby,p.a.
.B
j. ae. scs. 24, 1957, 464.
.W
a new technique for investigating heat transfer and
surface phenomena under hypersonic flow conditions .
on the forebody of many practically interesting hypersonic
vehicles, there is little interaction between the inviscid
flow field and the boundary layer . therefore, inviscid flow theory
can be used to determine, independent of surface phenomena,
the physically interesting quantities such as shock shape, shock
detachment distance, sonic line shape, and pressure distribution .
furthermore, the pressure distribution so determined can then be
used for the study of heat transfer, materials behavior, and other
surface phenomena . thus, for these bodies, the prandtl
boundary-layer concept can be utilized for the calculation of both the
inviscid flow and the boundary-layer behavior .
it is the purpose of this note to point out that this concept can
also be applied experimentally in order to provide, in
conjunction with a conventional hypersonic wind-tunnel air supply, a
means for investigating hypersonic heat transfer and surface
phenomena under conditions of flight reynolds numbers .
.I 38
.T
on the prediction of mixed subsonic/supersonic pressure
distributions .
.A
sinnott,c.s.
.B
j. ae. scs. 27, 1960, 767.
.W
on the prediction of mixed subsonic/supersonic pressure
distributions .
high-speed wind-tunnel results are analyzed to derive a
semiempirical scheme for the prediction of transonic pressure
distributions . the supersonic and subsonic parts of the flow are
treated separately, and then linked by an empirical shock
pressure rise relation . the significance of the empirical results is
considered in relation to the physical mechanism of transonic
flows . it is also shown that theoretical solutions can be
improved by introducing the empirical shock relation .
.I 39
.T
on the flow of a sonic stream past an airfoil surface .
.A
sinnott,c.s.
.B
j.ae.scs. 26, 1959, 169.
.W
on the flow of a sonic stream past an airfoil surface .
this study of the flow about an airfoil in a near-sonic stream
indicates the important factors determining the pressure
distribution on the airfoil . analysis of the mach wave pattern
suggests that the supersonic domain of the flow can be derived
from two simple-wave flows, one arising from the mach waves
reflected at the sonic line and the other from the changes in
airfoil surface slope . the compressive effect of the reflected mach
waves is determined quantitatively as a function of airfoil
leading-edge geometry from an analysis of measured pressure
distributions for uncambered airfoils,. and it is shown how this can
be superimposed on the wave system from the curved surface to
give an equivalent simple-wave flow over the airfoil .
an application of this scheme to the calculation of the pressure
distribution over an airfoil in a sonic stream gives results in good
agreement with experiment .
.I 40
.T
experiments on boundary layer transition at
supersonic speeds .
.A
van driest,e.r. and boison,j.c.
.B
j. ae. scs. 24, 1957, 885.
.W
experiments on boundary layer transition at
supersonic speeds .
tests were conducted in the 12-in. continuous supersonic wind
tunnel of the jet propulsion laboratory, california institute of
technology, to determine the effects of surface cooling on
boundary-layer transition at supersonic speeds . the effects of
cooling were investigated at test section mach numbers of 1.97,
smooth cone in the presence of three levels of supply-stream
turbulence (0.4, 2, and 9 per cent) and several single-element
roughnesses at fixed axial location . transition data were obtained
optically by means of a magnified-schlieren system . the results,
for the range of mach number investigated, indicate that (1)
transition on a smooth cone can definitely be delayed by surface
cooling, (2) transition promoted by either supply-stream
turbulence or surface roughness can also be delayed by surface cooling
depending upon degree of turbulence or relative roughness
respectively, and (3) the adverse effects of increased turbulence and
roughness decrease with increasing mach number .
.I 41
.T
on transition experiments at moderate supersonic speeds .
.A
morkovin,m.v.
.B
j. ae. scs. 24, 1957, 480.
.W
on transition experiments at moderate supersonic speeds .
studies of transition over a flat plate at mach number 1.76
were carried out using a hot-wire anemometer as one of the
principal tools . the nature and measurements of free-stream
disturbances at supersonic speeds are analyzed . the
experimental results are interpreted in the light of present overall
information on transition at supersonic speeds and conclusions as
to further fruitful experiments are drawn .
.I 42
.T
the gyroscopic effect of a rigid rotating propeller
on engine and wing vibration modes .
.A
scanlan,r.h. and truman,j.c.
.B
j. ae. scs. 17, 1950, 653.
.W
the gyroscopic effect of a rigid rotating propeller
on engine and wing vibration modes .
in many wing vibration analyses it is found necessary to take
into account the effect of flexibly mounted engines . hence,
it is reasonable to ask what vibratory gyroscopic effect this
flexibility may give rise to when propellers are whirling . an engine
mount may be thought of as a horizontal beam cantilevered
from the wing, having both horizontal and vertical flexibility .
if this beam were infinitely rigid horizontally, then, when it
vibrated, the gyroscopic moments induced in the propeller due
to the resultant pitching motion of its axis would not produce
propeller axis yaw . however, engine-mount lateral stiffness
tical stiffness, so that gyroscopic effects will play a role as the
propeller axis undergoes pitching vibrations at the tip of the
cantilever engine mount . the purpose of this paper is to
investigate this role under the assumption that the propeller itself
is a rigid disc .
the paper is divided into four parts . part (1) deals briefly
with classical gyroscope theory . part (2) presents engine
vibration mode studies-experimental photographic techniques on a
model gyroscope mounted at the ends of two different cantilever
beams . part (3) presents the theory of the coupled motion of
an elastic wing upon which a gyroscope is mounted to simulate
an engine-propeller system on an airplane . part (4) consists
of an example of the theory of part (3), in which, by taking
what are thought to be reasonable parameters, results are
obtained showing how the whirling of a rigid propeller may
materially affect wing normal mode shapes and frequencies .
.I 43
.T
the relation between wall temperature and the effect
of roughness on boundary layer transition .
.A
potter,j.l. and whitfield,j.d.
.B
j. ae. scs. 28, 1961, 663.
.W
the relation between wall temperature and the effect
of roughness on boundary layer transition .
the experimentally demonstrated rise and subsequent
fall of transition reynolds number with decreasing wall-
to-ambient temperature ratio has been the subject of two recent
notes . in both cases it was argued that the increased
effectiveness of roughness due to wall cooling was not sufficient to
explain the transition-reversal phenomenon on nominally smooth
bodies . in one case, the criterion for transition reversal was
taken to be and in the other values of as low as
eter is a reynolds number formed from velocity and
kinematic viscosity based on calculated conditions at the height of
roughness element k in the undisturbed, laminar boundary layer
at the station of roughness location . the present note is
submitted to show that another method for evaluating the effect
of roughness on transition leads to an opposite conclusion .
.I 44
.T
tip-bluntness effects on cone pressures at m=6.85 .
.A
bertram,m.h.
.B
j.ae.scs. 23, 1956,898.
.W
tip-bluntness effects on cone pressures at m=6.85 .
there is, at present, considerable interest in the
characteristies of blunted bodies from both an aerodynamic and a
heat-transfer standpoint . the use of blunt shapes is
contemplated to reduce the heat-transfer problem at body noses, but
there are also applications for blunt noses which occur from
mainly aerodynamic considerations . an actual reduction in
drag may be the beneficial result of blunting the nose of a cone
or a similar slender shape under certain conditions . although
the sphere has received considerable treatment, the nose shapes
are not necessarily tangent spheres . in the case, let us say, of a
total head tube situated in the nose of a given body, the blunting
may be quite flat, and nose sections blunter than spherical shape
may conceivably be desirable, in some cases, from the heat-
transfer standpoint .
the purpose of the present investigation is to examine the
aerodynamic effect of a simple type of nose blunting on a basic
body .
the incompressible flow of an electrically conducting fluid
past a porous plate y = 0 with constant suction velocity in
the presence of a transverse uniform strength has recently
been investigated by gupta . in this note, the problem is
generalized to take into account the effect of free convection, when a
body force g per unit mass is acting in the negative x-direction
parallel to the wall . the fluid is assumed to be semi-
incompressible as usual . in addition to the obvious practical
significance, this problem is also interesting in the sense that it
provides another exact solution of the magnetohydrodynamic
equations, since the only electromagnetic assumptions involved
are constant properties and freedom from excessive charges .
.I 45
.T
an investigation of separated flows, part ii: flow
in the cavity and heat transfer .
.A
charwat,a.f.
.B
j. ae. scs. 28, 1961, 513.
.W
an investigation of separated flows, part ii: flow
in the cavity and heat transfer .
the first portion of this paper describes studies of the internal
structure of the separated flow in a notch at a free-stream mach
number of 3 . observations include.. flow visualization, spark-
schlieren pictures of the fluctuations of the free shear layer, and
studies of the diffusion of heat from sources placed in the
separated region . the second part describes measurements of local
heat transfer to the wall .
the external mach number, the length-to-depth ratio of the
cavity, the ratio of the oncoming boundary layer thickness to the
notch depth (in the turbulent flow region), the thermal
to-momentum thickness ratio of the boundary layer and, finally,
the geometry of the internal boundary of the separated region
are varied as systematically as possible . on the basis of these
observations, a simple model of the flow in and the heat transfer
across the separated region is formulated .
.I 46
.T
some comments on the inversion of certain large matrices .
.A
bertram klein
.B
convair, a division of general dynamics corp., san diego, calif.
.W
some comments on the inversion of certain large matrices .
the subject of matric structural analysis has been treated in two
recently published papers in the journal . the authors of these papers
have made a number of statements about the inversion of certain large
matrices . it is the purpose of this note to bring to the attention of
the reader certain facts that shed new light on this important problem .
it is shown here that the situation is not as hopeless as the above-
mentioned authors intimate .
.I 47
.T
analysis of low-aspect-ratio aircraft structures .
.A
samson,s.h. and bergmann,h.w.
.B
j. ae. scs. 27, 1960, 679.
.W
analysis of low-aspect-ratio aircraft structures .
two methods are presented for the analysis of complex low-
aspect-ratio aircraft structures . both methods provide for
arbitrary external loading, are general with respect to the
orientation of structural members, and permit arbitrary boundary
conditions . for purposes of analysis a structure is idealized as a
network of flexural members with interconnected torsion boxes .
in the first method, sets of linear equations are obtained by
expressing boundary conditions, member deflection equations,
equilibrium requirements, and slope-compatibility relationships
in terms of deflections and internal forces . the solution for
deflections and internal forces is then formed as the product of an
inverse structural matrix and a column matrix of load functions .
in the second method, the conditions at a given boundary are
assembled as a column matrix and are transferred in a step
by-step fashion over the entire structure to an opposite boundary .
the transfer is accomplished by successive multiplications of
square matrices composed independently for the different
transfer ranges . the final operation is the inversion of a relatively
small matrix and provides the solution for the unknown boundary
conditions .
comparisons of theoretical results with experimental data and
electric-analog solutions are favorable .
.I 48
.T
supersonic flow at the surface of a circular cone at
angle of attack .
.A
willett,j.e.
.B
j. ae. scs. 27, 1960, 907.
.W
supersonic flow at the surface of a circular cone at
angle of attack .
formulas for the inviscid flow properties on the surface of a
cone at angle of attack are derived for use in conjunction with
the m.i.t. cone tables . these formulas are based upon an
entropy distribution on the cone surface which is uniform and
equal to that of the shocked fluid in the windward meridian
plane . they predict values for the flow variables which may
differ significantly from the corresponding values obtained
directly from the cone tables . the differences in the magnitudes
of the flow variables computed by the two methods tend to
increase with increasing free-stream mach number, cone angle
and angle of attack .
.I 49
.T
temperature and velocity profiles in the compressible
laminar boundary layer with arbitrary distribution
of surface temperature .
.A
chapman,d. and rubesin,m.
.B
j. ae. scs. 16, 1949, 547.
.W
temperature and velocity profiles in the compressible
laminar boundary layer with arbitrary distribution
of surface temperature .
an analysis is presented which enables the temperature
profiles, veiocity profiles, heat transfer, and skin friction to be
calculated for laminar flow over a two-dimensional or axially
symmetric surface without pressure gradient but with an arbitrary
analytic distribution of surface temperature . the general theory is
applicable to a gas of any prandtl number, although the
numerical results given herein have been computed for air .
the predictions of the theory for the special case of constant
surface temperature are compared with the calculations of crocco .
on the basis of this comparison, it is inferred that the present
theory enables heat-transfer and skin-friction calculations
accurate to within about 5 per cent to be made for flight conditions
up to mach numbers near 5 and to within about 1 or 2 per cent
for supersonic wind-tunnel conditions up to considerably higher
mach numbers .
a particular effort has been made to present the results, which
are simple considering their generality, in a form that can be used
readily in practical applications . from the mathematical point
of view, the theory is applicable to an arbitrary analytic
distribution of surface temperature, but in any given practical case it is
necessary that the surface-temperature distribution be
approximated by a polynomial . the only unknowns in the final
equations developed are the coefficients of this polynomial, so that the
work involved in applying the theory in any given case depends
entirely on the work involved in approximating a given surface-
temperature distribution by a polynomial .
an example is worked out in detail which illustrates some of the
principal effects of variable surface temperature . it is shown
that both positively infinite and negatively infinite heat-transfer
coefficients can occur . the anomaly of infinite and negative
heat-transfer coefficients is discussed and attributed to the
customary definition of the heat-transfer coefficient, which is shown
to be fundamentally inappropriate for flows with variable surface
temperature . in the particular example considered, a
conventional method for calculating the net heat transferred yields
completely incorrect results . a brief qualitative discussion of the
possible effects of the heat transfer on flow separation is given .
in order to facilitate the use of the results, all of the principal
equations developed are collected and summarized in the section
entitled /practical use of results ./
.I 50
.T
investigation of laminar boundary layer in compressible
fluids using the crocco method .
.A
van driest,e.r.
.B
naca tn.2597, 1952.
.W
investigation of laminar boundary layer in compressible
fluids using the crocco method .
in the present investigation of the flow of air in a thin laminar
boundary layer on a flat plate, the crocco method has been used to solve
the simultaneous differential equations of momentum and energy involved
in such flow . the crocco method was used because it gave accurate
results for arbitrary prandtl number near unity . the prandtl number
was taken at 0.75, the specific heat was held constant, and the
sutherland law of viscosity-temperature variation was assumed to
represent the viscosity data starting with an initial ambient
temperature of -67.6 f . the main results presented here are the
skin-friction and heat-transfer coefficients as functions of reynolds number,
mach number, and wall-to-free-stream temperature ratio . variations of
shear, velocity, temperature, and mach number across the boundary layer
are included . the crocco method is discussed in detail .
.I 51
.T
theory of aircraft structural models subjected to aerodynamic
heating and external loads .
.A
o'sullivan,w.j.
.B
naca tn.4115, 1957.
.W
theory of aircraft structural models subjected to aerodynamic
heating and external loads .
the problem of investigating the simultaneous effects of transient
aerodynamic heating and external loads on aircraft structures for the
purpose of determining the ability of the structure to withstand flight
to supersonic speeds is studied . by dimensional analyses it is shown
that ..
constructed of the same materials as the aircraft will be thermally
similar to the aircraft with respect to
the flow of heat through the structure
will be similar to those of the aircraft when the structural model is
constructed at the same temperature as the aircraft .
external loads will be similar to those of the aircraft .
subjected to heating and cooling that correctly simulate the aerodynamic
heating of the aircraft, except with respect to angular velocities and
angular accelerations, without requiring determination of the heat flux
at each point on the surface and its variation with time .
acting on the aerodynamically heated structural model to those acting
on the aircraft is determined for the case of zero angular velocity and
zero angular acceleration, so that the structural model may be subjected
to the external loads required for simultaneous simulation of stresses
and deformations due to external loads .
.I 52
.T
procedure for calculating flutter at high supersonic
speed including camber deflections, and comparison
with experimental results .
.A
morgan,h.g.
.B
naca tn.4335, 1958.
.W
procedure for calculating flutter at high supersonic
speed including camber deflections, and comparison
with experimental results .
a method which may be used at high supersonic mach numbers is
described for calculating the flutter speed of wings having camber in
their deflection modes . the normal coupled vibration modes of the wing
are used to derive the equations of motion . chord deflections of the
vibration modes are approximated by polynomials . the wing may have a
control surface and may carry external stores although no aerodynamic
forces on the stores are presented . the aerodynamic forces that are
assumed to be acting on the wing are obtained from piston theory and
also from a quasi-steady form of a theory for two-dimensional steady
flow . airfoil shape and thickness effects are taken account of in the
analysis .
the method is used to calculate the flutter speed of some wings
which had been previously tested at mach numbers of 1.3 to 3.0 .
comparison of the calculations and experiment is made for flat-plate 60
and 45 delta wings and also for an untapered 45 sweptback wing .
.I 53
.T
transition reynolds numbers of separated flows at
supersonic speeds .
.A
larson,h.k. and keating,s.j.
.B
nasa tn.d349, 1960.
.W
transition reynolds numbers of separated flows at
supersonic speeds .
experimental research has been conducted on the effects of wall
cooling, mach number, and unit reynolds
number on the transition reynolds
number of cylindrical separated boundary
layers on an ogive-cylinder model .
results were obtained from pressure and temperature measurements and
shadowgraph observations . the maximum
scope of measurements encompassed
mach numbers between 2.06 and 4.24, reynolds numbers (based on length of
separation) between 60,000 and 400,000,
and ratios of wall temperature to
adiabatic wall temperature between 0.35 and 1.0 .
within the range of the
present tests, the transition reynolds number was observed to decrease
with increasing wall cooling, increase with increasing mach number, and
increase with increasing unit reynolds number . the wall-cooling effect
was found to be four times as great when the attached boundary layer
upstream of separation was cooled in conjunction with cooling of the
separated boundary layer as when only the separated boundary layer was
cooled . wall cooling of both the
attached and separated flow regions also
caused, in some cases, reattachment in the otherwise separated region .
cavity resonance present in the separated region for some model
configurations was accompanied by a large decrease in transition reynolds
number at the lower test mach numbers .
.I 54
.T
method for calculation of compressible laminar boundary
layer characteristics in axial pressure gradient with
zero heat transfer .
.A
morduchow,m. and clarke,j.h.
.B
naca tn.2784, 1952.
.W
method for calculation of compressible laminar boundary
layer characteristics in axial pressure gradient with
zero heat transfer .
the karman-pohlhausen method is extended primarily to sixth-degree
velocity profiles for determining
the characteristics of the compressible
laminar boundary layer over an adiabatic
wall in the presence of an axial
pressure gradient . it is assumed that the prandtl number is unity and
that the coefficient of viscosity varies linearly with the temperature .
a general approximate solution which permits a rapid determination of
the boundary-layer characteristics for any given free-stream mach number
and given velocity distribution at the outer edge of the boundary layer
is obtained . numerical examples indicate that this solution will in
practice lead to results of satisfactory
accuracy, including the critical
reynolds number for stability . for the special purpose of calculating
the location of the separation point in an adverse pressure gradient, a
short and simple method, based on the use of a seventh-degree velocity
profile, is derived . the numerical example given here indicates that
this method should in practice lead to sufficiently accurate results .
for the special case of flow near a forward stagnation point it is shown
that the karman-pohlhausen method with the usual fourth-degree profiles
leads to results of adequate accuracy, even for the critical reynolds
number .
.I 55
.T
separation, stability and other properties of compressible
laminar boundary layer with pressure gradient and heat
transfer .
.A
morduchow,m. and grape,r.g.
.B
naca tn.3296, 1955.
.W
separation, stability and other properties of compressible
laminar boundary layer with pressure gradient and heat
transfer .
a theoretical study is made of the effect of pressure gradient,
wall temperature, and mach number on laminar boundary-layer
characteristics and, in particular, on the skin-friction and heat-transfer
coefficients, on the separation point in an adverse pressure gradient,
on the wall temperature required for complete stabilization of the
laminar boundary layer, and on the minimum critical reynolds number for
laminar stability . the prandtl number is assumed to be unity and the
coefficient of viscosity is assumed to be proportional to the
temperature, with a factor arising from the sutherland relation . a simple and
accurate method of locating the separation point in a compressible flow
with heat transfer is developed . numerical examples to illustrate the
results in detail are given throughout .
.I 56
.T
an analysis of the applicability of the hypersonic
similarity law to the study of the flow about bodies
of revolution at zero angle of attack .
.A
ehret,d.m.
.B
naca tn.2250, 1950.
.W
an analysis of the applicability of the hypersonic
similarity law to the study of the flow about bodies
of revolution at zero angle of attack .
the hypersonic similarity law as derived by tsien has been
investigated by comparing the pressure distributions along bodies of
revolution at zero angle of attack . in making
these comparisons, particular
attention was given to determining the limits of mach number and fineness
ratio for which the similarity law applies . for the purpose of this
investigation, pressure distributions
determined by the method of
characteristics for ogive cylinders for
values of mach numbers and fineness
ratios varying from 1.5 to 12 were compared .
pressures on various cones
and on cone cylinders were also compared in this study .
the pressure distributions presented demonstrate that the hypersonic
similarity law is applicable over a
wider range of values of mach numbers
and fineness ratios than might be expected from the assumptions made in
the derivation . this is significant since within the range of
applicability of the law a single pressure
distribution exists for all similarly
shaped bodies for which the ratio of
free-stream mach number to fineness
ratio is constant . charts are presented
for rapid determination of
pressure distributions over ogive cylinders for any combination of mach
number and fineness ratio within defined limits .
.I 57
.T
applicability of the hypersonic similarity rule to
pressure distributions which include the effects of
rotation for bodies of revolution at zero angle of
attack .
.A
rossow,v.j.
.B
naca tn.2399, 1951.
.W
applicability of the hypersonic similarity rule to
pressure distributions which include the effects of
rotation for bodies of revolution at zero angle of
attack .
the analysis of technical note 2250, 1950, is extended to include
the effects of flow rotation . it is
found that the theoretical pressure
distributions over ogive cylinders can be related by the hypersonic
similarity rule with sufficient accuracy for most engineering purposes .
the error introduced into pressure distributions and drag of ogive
cylinders by ignoring the rotation term in the characteristic equations
is investigated . it is found that
the influence of the rotation term on
pressure distribution and drag depends only upon the similarity
parameter k (mach number divided by fineness ratio) .
although the error in
drag, due to neglect of the rotation term, is negligible at k=0.5, the
error is about 30 percent at k=2.0 .
charts are presented for the rapid determination of pressure
distributions for rotational flow over
ogive cylinders for all values of
the similarity parameter between 0.5 and
of mach number and fineness ratio .
.I 58
.T
pressure measurements on sharp and blunt 5 and 15 half-angle
cones at mach number 3.86 and angles of attack to
100 .
.A
amick,j.l.
.B
nasa tn.d753, 1961.
.W
pressure measurements on sharp and blunt 5 and 15 half-angle
cones at mach number 3.86 and angles of attack to
100 .
measured pressure distributions on cones are compared with modified
newtonian theory . deviations as large as 14 percent of the stagnation
pressure behind a normal shock are found .
by combining empirical results
for cylinders normal to the flow with
newtonian concepts, a method of
calculating pressures on cones at high angles
of attack is developed .
calculations by this method differ from the
experimental results on sharp cones
by only 2 percent of the stagnation
pressure behind a normal shock . for
blunted cones, additional deviations
up to 8 percent are noted near the
nose .
schlieren pictures of the flow show an attached shock on the sharp
of attack . detachment of the shock
appears to be associated with the
attainment of sonic speed immediately
behind the shock .
an orifice size effect is found which can increase the indicated
pressure above the true value, if
the orifice width is greater than
one-tenth the local radius of curvature .
.I 59
.T
tables of exact laminar-boundary layer solutions when
the wall is porous and fluid properties are variable .
.A
brown,w.d. and donoughe,p.l.
.B
naca tn.2479, 1951.
.W
tables of exact laminar-boundary layer solutions when
the wall is porous and fluid properties are variable .
the three partial differential equations of the laminar boundary
layer for two-dimensional steady-state compressible flow have been
transformed into two ordinary differential equations by the method of
pohlhausen, falkner, and skan . the ordinary equations include
parameters for expressing the simultaneous effects of pressure gradient in
the main-stream flow through a porous wall and property changes in the
fluid due to large temperature differences between the wall and the
free stream .
a total of 58 cases have been solved numerically by the method of
picard . the euler number (nondimensional pressure-gradient parameter)
ranges in value from 1 (stagnation-point value) to the negative values
found at the laminar separation points . three rates of flow through
the porous wall were considered (including the impermeable case where
the flow rate is 0) . five temperature ratios (stream temperature
divided by wall temperature) were used .. the uncooled and unheated
case (temperature ratio of 1), two cooled cases (temperature ratios of
ture ratios of and ) . velocity, weight-flow, and temperature
distributions are tabulated as are the dimensionless stream function of
falkner and skan and its derivatives and the dimensionless temperature
function of pohlhausen and its derivatives .
for each case, displacement, momentum, and convection thicknesses,
as well as nusselt number and coefficient of friction at the wall, were
computed .
.I 60
.T
estimation forces and moments due to rolling for several
slender tail configurations at supersonic speeds .
.A
bobbitt,p.j. and malvestuto,f.s.
.B
naca tn.2955, 1953.
.W
estimation forces and moments due to rolling for several
slender tail configurations at supersonic speeds .
the velocity potentials, span loadings, and corresponding force
and moment derivatives have been theoretically evaluated for a number
of slender-tail arrangements performing a steady rolling motion at
supersonic speeds .
the method of analysis is based upon an application of
conformal-transformation techniques . the utilization of these techniques allows
the simple determination of the complex potentials for various types
of two-dimensional boundary-value problems .
in addition, two simple and often-used approximations to the
rolling derivatives have been compared with the corresponding exact
values determined by the method presented in this report .
in order to show the importance of wing-tail interference, the
effect of the flow field behind a rolling wing on the tail
characteristics has been illustrated for a simple wing-tail arrangement .
.I 61
.T
on flow of electrically conducting fluids over a flat
plate in the presence of a transverse magnetic field .
.A
rossow,v.j.
.B
naca tn.3971, 1957.
.W
on flow of electrically conducting fluids over a flat
plate in the presence of a transverse magnetic field .
the use of a magnetic field to control the motion of electrically
conducting fluids is studied . the boundary-layer solutions are found
for flow over a flat plate when the magnetic field is fixed relative to
the plate or to the fluid . the
equations are integrated numerically for
the effect of the transverse magnetic
field on the velocity and temperature
profiles, and hence, the skin friction and rate of heat transfer .
it is concluded that the skin friction and the heat-transfer rate are
reduced when the transverse magnetic
field is fixed relative to the plate
and increased when fixed relative to the fluid . the total drag is
increased in all the cases studied .
.I 62
.T
similar solutions for the compressible laminar boundary
layer with heat transfer and pressure gradient .
.A
cohen,c.b. and reshotko,e.
.B
naca tn.3325, 1955.
.W
similar solutions for the compressible laminar boundary
layer with heat transfer and pressure gradient .
stewartson's transformation is applied to the laminar compressible
boundary-layer equations and the
requirement of similarity is introduced,
resulting in a set of ordinary nonlinear differential equations
previously quoted by stewartson, but unsolved . the requirements of the
system are .. prandtl number of 1.0, linear viscosity-temperature
relation across the boundary layer, an
isothermal surface, and the particular
distributions of free-stream velocity
consistent with similar solutions .
this system admits axial pressure
gradients of arbitrary magnitude, heat
flux normal to the surface, and arbitrary mach numbers .
the system of differential equations is transformed to an integral
system, with the velocity ratio as
the independent variable . for this
system, solutions are found for pressure gradients varying from that
causing separation to the infinitely favorable gradient and for wall
temperatures from absolute zero to twice the free-stream stagnation
temperature . some solutions for separated flows are also presented .
for favorable pressure gradients, the solutions are unique . for
adverse pressure gradients, where the solutions are not unique, two
solutions of the infinite family of possible solutions are identified as
essentially viscid at the outer edge of the boundary layer and the
remainder essentially inviscid . for
the case of favorable pressure gradients
with heated walls, the velocity within
a portion of the boundary layer is
shown to exceed the local external velocity .
the variation of a reynolds
analogy parameter, which indicates the ratio of skin friction to heat
transfer, is from zero to 7.4 for a surface of temperature twice the
free-stream stagnation temperature, and from zero to 2.8 for a surface
held at absolute zero where the value 2 applies to a flat plate .
.I 63
.T
hypersonic viscous flow over slender cones .
.A
talbot,l.
.B
naca tn.4327, 1958.
.W
hypersonic viscous flow over slender cones .
viscous self-induced pressures on 3 -semivertex-angle cones were
measured over the range 3.7 free-stream mach number 5.8 and 0.5
viscous-interaction parameter 2.3 . the data were found to be in good
agreement with results obtained by talbot on 5 cones in the range
rameter 3.5 . all these data were correlated reasonably well by the
viscous-interaction parameter, which is defined as
where and are the mach number and reynolds number based on
ideal taylor-maccoll flow conditions and c is the chapman-rubesin
factor .
a new method for calculating self-induced pressures is presented
which takes into account the interaction between boundary-layer growth
and the inviscid-flow field at the outer edge of the boundary layer .
pressures calculated by this method were only 10 to 20 percent higher
than the measured values .
.I 64
.T
unsteady oblique interaction of a shock wave with plane
disturbances .
.A
moore,f.k.
.B
naca tn.2879, 1953.
.W
unsteady oblique interaction of a shock wave with plane
disturbances .
analysis is made of the flow field produced by oblique impingement
of weak plane disturbances of arbitrary
profile on a plane normal shock .
three types of disturbance are considered ..
moves . the sound wave refracts either
as a simple isentropic sound wave
or as an attenuating isentropic pressure wave, depending on the angle
between the shock and the incident
sound wave . a stationary vorticity
wave of constant pressure appears behind the shock .
reflects as a sound wave, and a stationary vorticity wave is produced .
the shock . the incident wave refracts as a stationary vorticity wave,
and either a sound wave or attenuating pressure wave is also produced .
computations are presented for the first two types of incident wave,
over the range of incidence angles, for shock mach numbers of 1, 1.5,
and .
.I 65
.T
convection of a pattern of vorticity through a shock
wave .
.A
ribner,h.s.
.B
naca tn.2864, 1953.
.W
convection of a pattern of vorticity through a shock
wave .
an arbitrary weak spatial distribution of vorticity can be
represented in terms of plane sinusoidal shear waves of all orientations and
wave lengths (fourier integral) . the analysis treats the passage of a
single representative weak shear wave through a plane shock and shows
refraction and modification of the shear wave with simultaneous
generation of an acoustically intense sound
wave . applications to turbulence
and to noise in supersonic wind tunnels are indicated .
.I 66
.T
some effects of joint conductivity on the temperature
and thermal stresses in aerodynamically heated skin-stiffener
combinations .
.A
griffith,g.e. and miltonberger,g.h.
.B
naca tn.3609, 1956.
.W
some effects of joint conductivity on the temperature
and thermal stresses in aerodynamically heated skin-stiffener
combinations .
temperatures and thermal stresses in typical skin-stiffener
combinations of winglike structures subjected to aerodynamic heating have
been obtained with the aid of an electronic differential analyzer .
variations were made in an aerodynamic
heat-transfer parameter, in a joint
conductivity parameter, and in the ratio
of skin width to skin thickness .
the results, which are presented in nondimensional form, indicate that
decreasing the joint conductivity parameter lowers both the interior
and the average temperature ratios, increases the peak thermal stress
ratios in the skin, and may considerably increase the peak stiffener
stress ratios,. increasing the aerodynamic heat-transfer parameter
decreases the interior and average temperature ratios, increases the
peak skin stress ratios somewhat,
but greatly increases the peak
stiffener stress ratios,. and increasing the ratio of skin width to skin
thickness produces only moderate decreases in the peak skin stress
ratios while moderately increasing the peak stiffener stress ratios .
.I 67
.T
dynamic stability of vehicles traversing ascending
or descending paths through the atmosphere .
.A
tobak and allen.
.B
naca tn.4275, 1958.
.W
dynamic stability of vehicles traversing ascending
or descending paths through the atmosphere .
an analysis is given of the oscillatory motions of vehicles which
traverse ascending and descending paths through the atmosphere at high
speed . the specific case of a skip path is examined in detail, and
this leads to a form of solution for the oscillatory motion which should
recur over any trajectory . the distinguishing feature of this form is
the appearance of the bessel rather than the trigonometric function as
the characteristic mode of oscillation .
.I 68
.T
some aspects of air-helium simulation and hypersonic
approximations .
.A
love,e.s.
.B
nasa tn.d49, 1959.
.W
some aspects of air-helium simulation and hypersonic
approximations .
some illustrations of the differences that may be expected between
results obtained in hypersonic wind tunnels that employ air and results
obtained in those that employ helium as the test medium (imperfect-gas
effects are not considered) are compiled and presented herein . simple
expressions are presented that demonstrate the possibility of simulating
air results in helium tests and of transforming helium data to
equivalent air data . nonviscous and viscous simulations are considered . in
most cases, the methods and the general forms of the expressions for
simulation that are derived are applicable to any two ideal gases having
different ratios of specific heats .
.I 69
.T
predicted shock envelopes about two types of vehicles
at large angles of attack .
.A
kaattari,g.e.
.B
nasa tn.d860, 1961.
.W
predicted shock envelopes about two types of vehicles
at large angles of attack .
methods based on oblique- and normal-shock relationships and the
continuity of mass flow through suitably chosen volume elements between
the shock and body were developed to predict shock envelopes about two
types of vehicles being considered for atmosphere entry . one type is a
high-drag capsule shape . the other type is essentially a slender
triangular wing capable of providing high lift or high drag, depending on
the angle of attack . predicted and measured shock envelopes were
compared for a mach number range of 3 to 15 for vehicles at high angles of
attack,. good agreement was found . most of the available experimental
data were in a speed and temperature range in which no important
real-gas effects occurred .
.I 70
.T
a study of flow changes associated with airfoil section
drag rise at supercritical speeds .
.A
nitzburg,g.e. and crandall,s.
.B
naca tn.1813, 1949.
.W
a study of flow changes associated with airfoil section
drag rise at supercritical speeds .
a study of experimental pressure distributions and section
characteristics for several moderately thick airfoil sections was made . a
correlation appears to exist between the drag-divergence mach number
and the free-stream mach number for which sonic velocity occurs at the
airfoil crest, the chordwise station at which the airfoil surface is
tangent to the free-stream direction . it was found that, since the
mach number for which sonic velocity occurs at the airfoil crest can be
estimated satisfactorily by means of the prandtl-glauert rule, a method
is provided whereby the drag-divergence mach number of an airfoil
section at a given angle of attack can be estimated from the low-speed
pressure distribution and the airfoil profile . this method was used
to predict with a reasonable degree of accuracy the drag-divergence
mach number of a considerable number of airfoil sections having diverse
shapes and a wide range of thickness-chord ratios .
the pressure distributions and section force characteristics of
several moderately thick airfoil sections at mach numbers above the
drag-divergence mach number were analyzed . some of the characteristics
of the flow over these airfoils at supercritical mach numbers are
discussed .
.I 71
.T
laminar boundary layer behind shock advancing into
stationary fluid .
.A
mirels,h.
.B
naca tn.3401, 1955.
.W
laminar boundary layer behind shock advancing into
stationary fluid .
a study was made of the laminar compressible boundary layer induced
by a shock wave advancing into a stationary fluid bounded by a wall .
for weak shock waves, the boundary layer is identical with that which
occurs when an infinite wall is impulsively set into uniform motion
shocks .
velocity and temperature profiles, recovery factors, and
skin-friction and heat-transfer coefficients are tabulated for a wide range
of shock strengths .
.I 72
.T
boundary layer behind shock or thin expansion wave
moving into stationary fluid .
.A
mirels,h.
.B
naca tn.3712, 1956.
.W
boundary layer behind shock or thin expansion wave
moving into stationary fluid .
the boundary layer behind a shock or thin expansion wave advancing
into a stationary fluid has been determined . laminar and turbulent
boundary layers were considered . the wall surface temperature behind
the wave was also investigated . the assumption of a thin expansion
wave is valid for weak expansions but becomes progressively less
accurate for strong expansion waves .
the laminar-boundary-layer problem was solved by numerical
integration except for the weak wave case,
which can be solved analytically .
integral (karman-pohlhausen type)
solutions were also obtained to provide
a guide for determining expressions
which accurately represent the
numerical data . analytical expressions
for various boundary-layer parameters
are presented which agree with the
numerical integrations within 1 percent .
the turbulent-boundary-layer problem was solved using integral
methods similar to those employed for the
solution of turbulent compressible
flow over a semi-infinite flat plate .
the fluid velocity, relative to
the wall, was assumed to have a
seventh-power profile . the blasius
equation, relating turbulent skin friction
and boundary-layer thickness, was
utilized in a form which accounted for compressibility .
consideration of the heat transfer to the wall permitted the wall
surface temperature, behind the wave,
to be determined . the wall
thickness was assumed to be greater than the
wall thermal-boundary-layer
thickness . it was found that the wall
temperature was uniform (as a
function of distance behind the wave)
for the laminar-boundary-layer case
but varied with distance for the turbulent-boundary-layer case .
.I 73
.T
investigation of the stability of the laminar boundary
layer in a compressible fluid .
.A
lees,l. and lin,c.c.
.B
naca tn.1115, 1946.
.W
investigation of the stability of the laminar boundary
layer in a compressible fluid .
in the present report the stability of two-dimensional laminar
flows of a gas is investigated by the method of small perturbations .
the chief emphasis is placed on the case of the laminar boundary layer .
part 1 of the present report deals with the general mathematical
theory . the general equations governing one normal mode of the small
velocity and temperature disturbances are derived and studied in great
detail . it is found that for reynolds numbers of the order of those
encountered in most aerodynamic problems, the temperature disturbances
have only a negligible effect on those particular velocity solutions
which depend primarily on the viscosity coefficient (/viscous
solutions/) . indeed, the latter are actually of the same form in the
compressible fluid as in the incompressible fluid, at least to the first
approximation . because of this fact, the mathematical analysis is
greatly simplified . the final equation determining the characteristic
values of the stability problem depends on the /inviscid solutions/ and
the function of tietjens in a manner very similar to the case of the
incompressible fluid . the second viscosity coefficient and the
coefficient of heat conductivity do not enter the problem,. only the
ordinary coefficient of viscosity near the solid surface is involved .
part 2 deals with the limiting case of infinite reynolds numbers .
the study of energy relations is very much emphasized . it is shown
that the disturbance will gain energy from the main flow if the gradient
of the product of mean density and mean vorticity near the solid surface
has a sign opposite to that near the outer edge of the boundary layer .
a general stability criterion has been obtained in terms of the
gradient of the product of density and vorticity, analogous to the
rayleigh-tollmien criterion for the case of an incompressible fluid .
if this gradient vanishes for some value of the velocity ratio of the
main flow exceeding 1-1/m (where m is the free stream mach number) .
.I 74
.T
an experimental study of the turbulen coundary layer
on a shock tube wall .
.A
gooderum,p.n.
.B
naca tn.4243, 1958.
.W
an experimental study of the turbulen coundary layer
on a shock tube wall .
interferometric measurements were made of the density profiles of
an unsteady turbulent boundary layer on the flat wall of a shock tube .
the investigation included both subsonic and supersonic flow (mach
numbers of 0.50 and 1.77) with no pressure gradient and with heat transfer
to a cold wall . velocity profiles and average skin-friction
coefficients were calculated . effects on the velocity profile of
surface roughness and flow length are examined .
.I 75
.T
studies of structural failure due to acoustic loading .
.A
hess,n.w.
.B
naca tn.4050, 1957.
.W
studies of structural failure due to acoustic loading .
some discussion of the acoustic fatigue problem of aircraft
structures is given along with data pertaining to the acoustic inputs from
some powerplants in common use . comparisons are given for results of
some fatigue tests of flat panels and cantilever beams exposed to both
random- and discrete-type inputs . in this regard it appears that both
the stress level of the test and the type of model are significant,.
hence, no generalization can be made at this time . with regard to
increasing the fatigue life, it was noted that increased stiffening of
a panel due to curvature and pressure differential is particularly
beneficial .
.I 76
.T
flight measurement of wall pressure fluctuations and
boundary-layer turbulence .
.A
mull,h.r. and algranti,j.s.
.B
nasa tn.d280, 1960.
.W
flight measurement of wall pressure fluctuations and
boundary-layer turbulence .
the results are presented for a flight test program using a fighter
type jet aircraft flying at pressure altitudes of 10,000, 20,000, and
apparatus was used to measure and record the output of microphones and
hot-wire anemometers mounted on the forward-fuselage section and wing of
the airplane . mean-velocity profiles in the boundary layers were
obtained from total-pressure measurements .
the ratio of the root-mean-square fluctuating wall pressure to the
free-stream dynamic pressure is presented as a function of reynolds
number and mach number . the longitudinal
component of the turbulent-velocity
fluctuations was measured, and the turbulence-intensity profiles are
presented for the wing and forward-fuselage section .
in general, the results are in agreement with wind-tunnel
measurements which have been reported in the literature . for example, the
variation of (is the root mean square of the wall-pressure
fluctuation, and q is the free-stream dynamic pressure) with reynolds
number was found to be essentially constant for the forward
fuselage-section boundary layer, while variations at the wing station were
probably unduly affected by the microphone diameter, which was
large compared with the boundary-layer thickness .
.I 77
.T
a comparative analysis of the performance of long range
hypervelocity vehicles .
.A
eggers,a.j.
.B
naca tn.4046, 1957.
.W
a comparative analysis of the performance of long range
hypervelocity vehicles .
long-range hypervelocity vehicles are studied in terms of their
motion in powered flight, and their motion and aerodynamic heating in
unpowered flight . powered flight is
analyzed for an idealized propulsion
system which rather closely approaches
present-day rocket motors .
unpowered flight is characterized by a return
to earth along a ballistic, skip,
or glide trajectory . only those
trajectories are treated which yield the
maximum range for a given velocity at the end of powered flight .
aerodynamic heating is treated in a manner
similar to that employed previously
by the senior authors in studying ballistic missiles (naca tn 4047),
with the exception that radiant as well as convective heat transfer is
considered in connection with glide and skip vehicles .
the ballistic vehicle is found to be the least efficient of the
several types studied in the sense
that it generally requires the highest
velocity at the end of powered flight in order to attain a given range .
this disadvantage may be offset, however, by reducing convective heat
transfer to the re-entry body through
the artifice of increasing pressure
drag in relation to friction drag - that
is, by using a blunt body . thus
the kinetic energy required by the vehicle at the end of powered flight
may be reduced by minimizing the mass of coolant material involved .
the glide vehicle developing lift-drag ratios in the neighborhood
of and greater than 4 is far superior
to the ballistic vehicle in ability
to convert velocity into range . it has the disadvantage of having far
more heat convected to it,. however, it has the compensating advantage
that this heat can in the main be radiated
back to the atmosphere .
consequently, the mass of coolant material may be kept relatively low .
the skip vehicle developing lift-drag ratios from about 1 to 4 is
found to be superior to comparable ballistic and glide vehicles in
converting velocity into range . at
lift-drag ratios below 1 it is found to
be about equal to comparable ballistic
vehicles while at lift-drag ratios
.I 78
.T
an analytical treatment of aircraft propeller precession
instability .
.A
reed,w.h. and bland,s.r.
.B
nasa tn.d659, 1961.
.W
an analytical treatment of aircraft propeller precession
instability .
an analytical investigation is made of a precession-type instability
which can occur in a flexibly supported aircraft-engine-propeller
combination . by means of an idealized
mathematical model which is comprised
of a rigid power-plant system flexibly
mounted in pitch and yaw to a fixed
backup structure, the conditions required for neutral stability are
determined . the paper also examines the sensitivity of the stability
boundaries to changes in such parameters
as stiffness, damping, and
asymmetries in the engine mount, propeller
speed, airspeed, mach number,
propeller thrust, and location of pitch and yaw axes . stability is found
to depend strongly on the damping and stiffness in the system .
with the use of nondimensional charts theoretical stability
boundaries are compared with experimental results obtained in wind-tunnel
tests of an aeroelastic airplane model . in general, the theoretical
results, which do not account for wing response, show the same trends
as observed experimentally,. however,
for a given set of conditions
calculated airspeeds for neutral stability
are consistently lower than the
measured values . evidently, this result is due to the fact that wing
response tends to add damping to the system .
.I 79
.T
effects of extreme surface cooling on boundary layer
transition .
.A
jack,j.r.
.B
naca tn.4094, 1957.
.W
effects of extreme surface cooling on boundary layer
transition .
an investigation was made to determine the combined effects of
surface cooling, pressure gradients, nose blunting, and surface finish on
boundary-layer transition . data were obtained for various body shapes
at a mach number of 3.12 and reynolds
numbers per foot as high as 15x10 .
previous transition studies, with moderate cooling, have shown
agreement with the predictions of stability theory . for surface roughnesses
ranging from 4 to 1250 microinches the location of transition was
unaffected with moderate cooling . with extreme cooling, an adverse effect
was observed for each of the parameters investigated . in general, the
transition reynolds number decreased with
decreasing surface temperature .
in particular, the beneficial effects of a favorable pressure gradient
obtained with moderate cooling disappear with extreme cooling, and a
transition reynolds number lower than
that observed on a cone is obtained .
further, an increase in the nose bluntness decreased the transition
reynolds number under conditions of extreme cooling .
.I 80
.T
effect of distributed three-dimensional roughness and
surface cooling on boundary layer transition and lateral
spread of turbulence at supersonic speeds .
.A
braslow,a.l.
.B
nasa tn.d53, 1959.
.W
effect of distributed three-dimensional roughness and
surface cooling on boundary layer transition and lateral
spread of turbulence at supersonic speeds .
an investigation was made in the langley 4 by 4-foot supersonic
pressure tunnel at mach numbers of 1.61 and 2.01 to determine (1) the
effect of distributed roughness on boundary-layer transition with the
model surface at adiabatic wall temperature and cooled and (2) the
effect of surface cooling on the lateral spread of turbulence . both
distributed granular-type and single spherical roughness particles were
used, and transition of the boundary layer was determined by hot-wire
anemometers . the transition-triggering mechanism of the
three-dimensional roughness at supersonic speeds appeared to be the same as
that previously observed at subsonic speeds . in fact, the critical
value of the roughness reynolds number parameter (that is,
the value at which turbulent spots are initiated by the roughness) was
found to be approximately the same at supersonic and subsonic speeds
when complete local conditions at the top of the roughness, including
density and viscosity, were considered in the formulation of the
roughness reynolds number . for three-dimensional roughness at a reynolds
number less than its critical value, the roughness introduced no
disturbances of sufficient magnitude to influence transition . surface
cooling, although providing a theoretical increase in stability to small
disturbances, did not increase to any important extent the value of the
critical roughness reynolds number for three-dimensional roughness
particles . cooling, therefore, because of its effect on the
boundary-layer thickness, density, and viscosity actually promoted transition due
to existing three-dimensional surface roughness for given mach and
reynolds numbers . the measured lateral spread of turbulence in the
boundary layer appeared to be unaffected by the increased laminar
stability derived from the surface cooling .
.I 81
.T
compressible laminar flow and heat transfer about a
rotating isothermal disk .
.A
ostrach,s. and thornton,p.
.B
naca tn.4320, 1958.
.W
compressible laminar flow and heat transfer about a
rotating isothermal disk .
the flow and heat transfer about a rotating isothermal disk are
re-examined to include the effects of compressibility and property
variations . if viscous dissipation is neglected,
the compressible problem is
correlated to the incompressible problem by assuming linear variations
of viscosity and thermal conductivity with temperature . certain
inaccuracies in several previous incompressible solutions are noted and
corrected herein . the effect of compressibility appears as a
distortion of the normal coordinate and normal velocity component and as
a multiplicative factor in the heat-transfer coefficient, the nusselt
number, and in the expressions for the skin-friction components and
torque required to rotate the disk .
.I 82
.T
theoretical investigation of the ablation of a glass-type
heat protection shield of varied material properties
at the stagnation point of a re-entering irbm .
.A
adams,e.w.
.B
nasa tn.d564, 1961.
.W
theoretical investigation of the ablation of a glass-type
heat protection shield of varied material properties
at the stagnation point of a re-entering irbm .
the melting-type heat protection at the stagnation point of a
re-entering irbm is treated by employing homogeneous, opaque, and
nondecomposing glass shields which do not exceed a temperature of
some effects due to variations of the glass properties . the ballistic
re-entry vehicle has a nose diameter of 0.635 m, a ballistic factor
of 3.5 x 10, a re-entry angle of 124.9 (from the
vertical) at an altitude of 100 km, and a re-entry speed of 4.5 .
the performance of 36 different glass shields with assumed
combinations of material properties is investigated by employing a
calculation method which yields practically exact, transient solutions
for the problem . as a corollary, results for a certain steady flight
state are also given . the discussions made it possible to derive
under realistic flight conditions some thermal characteristics for the
employment of thin, or light-weight, glass shields .
investigation of these hypothetical glass shields leads to the
conclusion that a low thermal conductivity and a high specific heat,
and thus, a small thermal diffusivity are most desirable . a small
thermal diffusivity yields high surface temperatures, causing a high
radiative heat transfer out of the shield,. and steep temperature
profiles normal to the surface, causing a small thermal penetration across
the shield with little total ablation of the shield . results show that
for the assumed irbm re-entry, the necessary thickness of the employed
glass shields increases monotonically with thermal diffusivity which is
the only material parameter affecting this thickness .
a high viscosity level and a high emissivity constant of the
surface of the supposedly opaque shield are also desirable,. although,
these two properties exert a comparatively small influence on the
overall performance when disregarding glass shields with an extremely
low viscosity level .
.I 83
.T
discussion of solar proton events and manned space
flights .
.A
anderson,k. and sinchtel,c.d.
.B
nasa tn.d671, 1961.
.W
discussion of solar proton events and manned space
flights .
as a result of studies made during the
international geophysical year (igy) and the
international geophysical cooperation (igc),
it is known that a considerable fraction of
large solar flares give rise to almost pure
streams of protons which reach the earth and
continue to arrive for as long as 11 days .
the energies of these particles lie within a
very steep spectrum extending from 20 to
least 500 mev . because of the frequency
of large flares during times of high solar
activity, and owing to the long duration of each
solar proton emission, these particles were
present in detectable intensity near the top
of the earth's atmosphere for about 15 percent
of the time from 1957 to 1960 . the number
of large flares that accelerated and released
these particles during this three-year period was about 30 .
the event that began on august 22, 1958
contributed greatly toward the understanding
of the solar and terrestrial sequence of events,
and in addition provided the first
identification of the emitted particles . a flare on may
of protons in the neighborhood of the earth that
this phenomenon was recognized as an
additional radiation hazard to manned vehicles
in the high atmosphere and in most parts
of the solar system . the three very intense
events that occurred in july, 1959 further
supported this conclusion, and the possibility
of predicting such events became an
important consideration . in addition to its value
in the protection of human beings, effective
forecasting clearly would be of great value in
the detailed scientific study of this
phenomenon .
this paper presents a preliminary
discussion of some aspects of predicting the
arrival of protons at the earth following the
appearance of solar activity features and,
equally important, of forecasting the periods
when this penetrating radiation is unlikely
to occur .
.I 84
.T
experimental investigation of the downstream influence
of stagnation point mass transfer .
.A
libby,pa. and cresci,r.j.
.B
j. ae. scs. 28, 1961, 51.
.W
experimental investigation of the downstream influence
of stagnation point mass transfer .
this report presents the results of an experimental
investigation of the downstream influence of localized mass transfer in the
stagnation region of a blunt body under hypersonic flow
conditions . the coolant is injected through a porous plug coaxial
with the centerline of symmetry of the model . the tests were
carried out in a wind tunnel with a mach number of 6.0,
stagnation temperatures of approximately 1,600 r., and a stagnation
pressure of approximately 600 psia . four different gases were
injected over a range of mass flows . the heat transfer on the
impermeable section was measured under isothermal wall
conditions,. for the higher rates of mass flow, adiabatic surface
temperatures were also determined . the theoretical analysis of the
boundary-layer flow is investigated in order to establish the
similarity parameters for the flow system . these parameters permit
the extrapolation of the test results to other flow conditions,
provided that laminar flow prevails . helium is found to be the
most efficacious coolant .
.I 85
.T
on trails of axisymmetric hypersonic blunt bodies flying
through the atmosphere .
.A
feldman,s.
.B
j. ae. scs. 28, 1961, 433.
.W
on trails of axisymmetric hypersonic blunt bodies flying
through the atmosphere .
the trail left in the atmosphere by a body moving at hypersonic
speeds is the subject of theoretical treatment . the times
required for ionization and dissociation (and their inverse processes)
to go to completion, when compared to the flow times of a gas
particle, are important in determining the observable effects of
hypersonic trails-i.e., emitted thermal radiation and reflection
of electromagnetic waves from the trail .
in order to simplify the theoretical treatment, the trail is
divided into two regions .. (1) the expansion-controlled trail,
which treats the behavior of the wake behind the body up to a
point, along the direction of flight, where the pressure decays to
the free-stream value and cooling is controlled principally by the
expansion of the flow, and (2) the conduction-controlled trail,
where the trail cools mainly by diffusion of heat away from the
high-temperature core .
the influence of the details of the body shape on the
observables are discussed and a simple computational procedure for
the behavior of the conduction-controlled trail is developed based
on integral methods . results of calculations that assume
thermodynamic equilibrium of the flow field give the values of the
thermodynamic variables in the trail of a sphere, axial
distributions of emitted thermal radiation, and maps of electron density
distribution . it is shown that the cooling of the
conduction-controlled trail is essentially due to conduction of heat and that
viscous effects are not important . it is found that this portion
of the trail does not widen as one proceeds downstream . flight
velocities considered vary between 15,000 and 35,000 ft sec and
altitudes range between 100,000 and 250,000 ft .
.I 86
.T
inviscid-incompressible flow theory of static peripheral
jets in proximity to the ground .
.A
strand,t.
.B
j. ae. scs. 1961, 27.
.W
inviscid-incompressible flow theory of static peripheral
jets in proximity to the ground .
an /exact/ flow theory of peripheral jets issuing
symmetrically from a hovering aerial-ground vehicle is presented . the
theory is exact insofar as no simplifying assumptions have been
made in obtaining a solution of the governing inviscid,
two-dimensional hydrodynamical flow equations . the results are
valid for all jet thickness vehicle height ratios . the limit of
applicability of existing theories (very low thickness height
ratios) are defined . jet reaction, lift, and power coefficients for
static conditions are introduced and computed . lift
augmentation and lift power ratios are also calculated .
applications to three-dimensional vehicles with rotational
symmetry are indicated .
.I 87
.T
free-convection magnetohydrodynamic flow past a porous flat plate .
.A
pau-chang lu
.B
graduate assistant, department of mechanical engineering, case
institute of technology, cleveland, ohio
.W
free-convection magnetohydrodynamic flow past a porous flat plate .
the incompressible flow of an electrically conducting fluid past a
porous plate with constant suction velocity in the presence of a
transverse uniform strength has recently been investigated by gupta . in
this note, the problem is generalized to take into account the effect of
free convection, when a body force is acting parallel to the wall . the
fluid is assumed to be semi-incompressible as usual . in addition to
the obvious practical significance, this problem is also interesting in
the sense that it provides another exact solution of the
magnetohydrodynamic equations, since the only electromagnetic assumptions involved
are constant properties and freedom from excessive charges .
.I 88
.T
magnetohydrodynamic free-convection pipe flow .
.A
cramer,k.r.
.B
j. ae. scs. 28, 1961, 736.
.W
magnetohydrodynamic free-convection pipe flow .
it has been shown that transverse magnetic fields of practical
strengths exert considerable influence on liquid-metal,
free-convection, vertical, flat-plate and parallel-plate flow fields .
the extent of influence was determined by the magnitude of a
nondimensional parameter a which is the ratio of the hartmann
number to the fourth root of the grashof number, and is a
measure of the relative influence of the magnetic and buoyant
forces . in this note the steady, fully developed, laminar,
free-convection flow of a fluid of electrical conductivity through
a fully submerged, open-ended, constant-temperature, vertical
pipe located in a transverse magnetic field of strength is
analyzed in terms of the same parameter . the magnitude of
its influence on the velocity and temperature profiles, the surface
shear and heat transfer, and the volumetric flow rate is
determined .
.I 89
.T
an investigation of separated flows, part i: the pressure
field .
.A
charwat,a.f.
.B
j. ae. scs. 28, 1961, 457.
.W
an investigation of separated flows, part i: the pressure
field .
the present article describes an investigation of several types of
separated regions such as blunt-base wakes and cavities formed
in cutouts in the boundaries and ahead of or behind two
dimensional steps in supersonic (mach numbers 2 to 4) and
subsonic flow . the conditions for the existence, the geometry,
and the pressure field are described in this paper .
a second article (to be published) will describe investigations of
the internal flow and the heat transfer across such separated
regions .
it is found that there is a maximum (critical) ratio of the length
of the separated free-shear layer to the depth of the depression
in the boundary beyond which the cavity collapses, leaving
mutually independent separated regions at each protrusion .
this critical length changes greatly upon laminar-turbulent
transition in the oncoming boundary layer,. in either laminar or
turbulent flow it is approximately independent of mach and
reynolds numbers . a semiempirical correlation predicting the
conditions under which the flow will span a depression of arbitrary
depth is proposed .
detailed pressure distributions along the boundaries of a
cavity (in turbulent flow) are presented as a function of the ratio
of the cavity length to the critical length, which is found to be
the pertinent similarity parameter . for short notches
the impact pressure due to the reversal of the inner portion
of the shear layer at recompression tends to thicken the shear
layer and a type of boundary layer-free stream interaction
governs the pressure field . the pressure in the cavity is nearly
constant and can be higher than free-stream . in long notches
the shear layer bends inward at separation and
curves back gradually ahead of the recompression point . the
floor-pressure variation is pronounced and the recovery pressure
at reattachment is small . the variation of the drag coefficient
with mach number reflects the change from one to the other
mechanism of recompression .
detailed surveys of the mach-number distributions in a
blunt-body wake and the mixing region behind its throat, as
well as in the shear layer spanning a cutout in a wall, are presented
and analyzed . it is found that, in general, the assumptions of
the simple supersonic-wake models which rely on a principle of
steady flow with mass conservation in the cavity are not adequate
for cavities in which there is recompression against a boundary .
results showing the influence of the thickness of the initial
boundary layer (in the range of 0.3 to 3 times the notch depth)
and of the geometry of the notch are also presented .
.I 90
.T
periodic temperature distributions in a two-layer composite
slab .
.A
stonecypher,t.e.
.B
j. ae. scs. 27, 1960, 152.
.W
periodic temperature distributions in a two-layer composite
slab .
an investigation to determine the feasibility of using an
insulating thermal barrier to protect exposed solid
propellant motors from atmospheric or environmental temperature
variations has recently been completed . in one portion of this
study, a solution was developed for the periodic temperature
distribution in a two-layer composite slab . one exposed surface of
this composite slab was adiabatic, and the other exposed surface
was subjected to a sinusoidal temperature variation . the
technique used in the analysis was similar to that of grober . in this
note, pertinent features of the development of the solution are
given .
.I 91
.T
periodic temperature distribution in a two-layer composite slab .
.A
w. f. campbell
.B
national aeronautical establishment, ottawa, ont., canada
.W
periodic temperature distribution in a two-layer composite slab .
in a recent contribution to the reader's forum, under the above title,
stonecypher outlined a method for finding the periodic temperature
distribution in a two-layer composite slab, one exposed surface of the slab
being insulated and the other subject to a sinusoidal temperature
variation . perfect thermal contact between the two layers, and constant
thermal properties were assumed .
two years ago i drew attention in these pages to a method for
determining the transient temperature in such a two-layer slab resulting from a
triangular heat-input pulse . i should like to point out that this same
method also is applicable to the case where one external face is given
a sinusoidal temperature variation with time . the method is based on
the analogy between one-dimensional heat flow and the flow of an
electric current in a simple transmission line having only series resistance
and parallel capacitance .
.I 92
.T
the analysis of redundant structures by the use of
high-speed digital computers .
.A
chrichlow,w.j. and haggenmacher,g.w.
.B
j. ae. scs. 27, 1960, 595.
.W
the analysis of redundant structures by the use of
high-speed digital computers .
large-scale redundant structure analyses are currently
feasible by the use of modern high-speed digital computers .
this capability opportunely meets the urgent need to solve
complex problems which otherwise would be hopelessly beyond
the capacity of the hand desk computer . however, the difficulties
have now shifted from tedious hand computations to the problems
of adequately representing the structure by a model and
of the peculiarities of irregular geometrical configurations .
a wide scope of problem types can be handled by a generalized
program approach . matrix formulation is used for the organization
of input data and for handling data transfer in the large
complex of subroutines, including the formation of equilibrium
and continuity conditions to the final loads and deflections .
simultaneous treatment of thermal expansions and plasticity
is included .
the use of minimum-size redundant systems is emphasized,
starting from the philosophy of cutting members to provide a
statically determinate structure . improved numerical accuracy
and problem size capacity is gained for a given computer .
examples are discussed ranging from simple plane-load diffusion
problems to pressurized fuselage cutouts and complex
wing-fuselage-shell intersection-type problems .
.I 93
.T
the supersonic blunt body problem - review and extensions .
.A
van dyke,m.d.
.B
j. ae. scs. 25, 1958, 485.
.W
the supersonic blunt body problem - review and extensions .
a survey of existing analytical treatments of the supersonic or
hypersonic blunt-body problem indicates that none is adequate
for predicting the details of the flow field . reasons are given for
the failure of various plausible approximations . a numerical
method, which is simpler than others proposed, is set forth for
solving the full inviscid equations using a medium-sized electronic
computer . results are shown from a number of solutions for
bodies that support detached shock waves described by conic
sections .
.I 94
.T
the transverse curvature effect in compressible axially
symmetric laminar boundary layer flow .
.A
probstein,r.f. and elliott,d.
.B
j. ae.scs. 28, 1956, 206.
.W
the transverse curvature effect in compressible axially
symmetric laminar boundary layer flow .
the viscous transverse curvature effect in compressible axially
symmetric laminar boundary-layer flow has been investigated,
and it is found that the effect is characterized by the parameter
which is essentially the ratio of the boundary-layer thickness
to body radius . it is shown that the busemann and crocco
integrals of the two-dimensional energy equation for are
still valid for axially symmetric flow in which the transverse
curvature effects are considered . by a generalization of
mangler's transformation it is then shown that the boundary-layer
equations are reducible to an almost two-dimensional form,
making the analysis simpler for two asymptotic flow regions
characterized by and less than or of the order of unity .
it is with the latter region that the present paper is primarily
concerned, and for this case it is shown that the additional term
in the momentum and energy equations, which differentiates them
from the two-dimensional form, behaves like an external
favorable pressure gradient .
except for certain special cases it is necessary to obtain the
of the order of unity by means of asymptotic expansions in
ascending powers of a parameter that is small compared to unity
but proportional to . it is shown how the asymptotic
solutions can be found for (1) the velocity and temperature
distributions for the compressible zero pressure gradient case when the
body shapes are given by and and (2) the
velocity distribution for incompressible flow with an external
velocity of the form past a body given by . the
zeroth approximation is the mangler result . for the cases of a
linear external velocity distribution, similar profiles can be found
for all values of . more generally it is shown that similar
profiles exist if the exponents n and m satisfy the condition that .
here, similar is used in the restricted meaning
that the distributions are derivable from ordinary differential
equations .
in the case of the cone and cylinder with zero pressure gradient
where the equations have been numerically integrated for,
the first-order correction to the mangler formulation shows that
the effect on both the skin-friction coefficient and heat-transfer
rate can become appreciable in the range where is less than
or of the order of unity . at a constant, the effects are
increased in magnitude when either the ratio of wall to free-stream
temperature, or mach number, is increased . also, all other
conditions being equal, for the same value of the skin-friction
coefficient and heat-transfer increase on the cylinder is greater
than that on the cone .
for flows with pressure gradient, the transverse curvature term
behaves again like a favorable pressure gradient and tends to
delay both separation and transition when compared with axially
symmetric flows in which the transverse curvature effect is
neglected .
.I 95
.T
temperature distribution and thermal stresses in a
model of a supersonic wing .
.A
pohle,f.v. and oliver,h.
.B
j. ae. scs. 21, 1954, 8.
.W
temperature distribution and thermal stresses in a
model of a supersonic wing .
the transient temperature distribution and the thermal
stresses in an idealized wing structure considered by hoff and
torda in reference 1 are determined . only the effects of
aerodynamic heating and of heat conduction are included,. radiation
and convection effects are neglected . the present work differs
from that of reference 1 in that the conduction from the cap to
the web is considered when the temperature of the cap is
calculated, and the spar cap temperature is assumed to be a function
of both space and time . graphs of temperature and thermal
stress distributions are presented, and the results are compared
with those of reference 1 .
.I 96
.T
review of published data on the effect of roughness on transition from
laminar to turbulent flow .
.A
hugh l. dryden
.B
national advisory committee for aeronautics
.W
review of published data on the effect of roughness on transition from
laminar to turbulent flow .
a review is presented of the published data on the effect of roughness,
especially single roughness elements, on transition from laminar to
turbulent flow, in which an attempt is made to reanalyze and correlate the
available information . the reanalysis shows that the transition
reynolds number of a flat plate with zero pressure gradient is a
function of the ratio of the height of the roughness element to the
displacement thickness of the boundary layer at the element, this functional
relation being a better representation of the data than a constant
critical reynolds number of the roughness element . other data show that the
effects of roghness are similar in streams of different initial
turbulence and that a plot of the ratio of transition reynolds number of the
rough plate to that for the smooth plate against the ratio of the height
of the roughness element to displacement thickness of the boundary layer
at the element gives good correlation of all the data for a given shape
when transition occurs downstream from the
roughness element . at a certain value of the height-thickness ratio
dependent on the stream speed, location of roughness element, and
airstream turbulence, the transition position reaches the element and
remains there as the height or the stream speed is further increased .
the paper also discusses available data on the effect of distributed
roughness on transition on a flat plate, as well as some of the
published data on roughness effects on transition on air-foils .
.I 97
.T
a mixing theory for the interaction between dissipative
flows and nearly isentropic streams .
.A
crocco,l. and lees,l.
.B
j. ae. scs. 19, 1952, 649.
.W
a mixing theory for the interaction between dissipative
flows and nearly isentropic streams .
by means of a simplified theoretical /model,/ the present paper
treats the general class of flow problems characterized by the
interaction between a viscous or dissipative flow near the surface
of a solid body, or in its wake, and an /outer/ nearly isentropic
stream . for the present, the external flow is taken to be a plane,
steady, supersonic flow, which makes a small angle with a plane
surface or plane of symmetry, although the methods used can be
extended to curved surfaces, to axially symmetric supersonic
flows, and also to subsonic flows . the internal dissipative flow
is regarded as quasi-one-dimensional and parallel to the surface
on the average, with a properly defined mean velocity and mean
temperature . the nonuniformity of the actual velocity
distribution is taken into account only approximately by means of a
relation between mean temperature and mean velocity .
mixing, or the transport of momentum from outer stream to
dissipative flow, is considered to be the fundamental physical process
determining the pressure rise that can be supported by the flow .
with the aid of this concept, a large number of flow problems is
shown to be basically similar, such as boundary-layer
shockwave interaction, wake flow behind blunt-based bodies (base
pressure problem), flow separation in overexpanded supersonic
nozzles, separation on wings and bodies, etc .
.I 98
.T
heat transfer by laminar flow to a rotating plate .
.A
millsaps,k. and pohlhausen,k.
.B
j. ae. scs. 19, 1952, 120.
.W
heat transfer by laminar flow to a rotating plate .
an exact solution of the heat-transfer problem for the von
karman example of the laminar flow of a viscous fluid over a
rotating plate is given in dimensionless form and physically
discussed . the solution is explicitly given for a constant
temperature on the plate with viscous dissipation included . the
numerical results are given for prandtl numbers from 0.5 to 10 .
.I 99
.T
the fundamentals of the statistical theory of turbulence .
.A
th. von karman
.B
california institute of technology
.W
the fundamentals of the statistical theory of turbulence .
statistical theory in general considers mean values of certain
quantities . in the case of the turbulent motion one is interested in mean
values of velocities and of their derivatives, and in mean values of
squares and products of velocities and their derivatives . it was o.
reynolds who first expressed the so-called apparent or turbulent
stresses by the mean values of the products of the velocity components . the
different theories suggested so far have as their common objective the
establishment of relations between certain mean values, e.g. between the
turbulent shear stresses given by the mean products of velocity
fluctuations and the derivatives of the mean velocities, i.e. the measured mean
velocity gradients . in this sort of investigations the conception of
the /correlation/ is of paramount importance . the late a. friedman
tried to introduce the correlations as unknown variables in the
hydrodynamic equations., however, he could not carry his investigations to
practical results, i.e., to results which can be compared with the
experimental evidence . recently, g. i. taylor had success in his
analysis of /isotropic/ turbulence by means of correlation calculations, and
was able to discuss, theoretically, the problem of the decay of
turbulence in a windstream behind a turbulence producing device . his theory
raised considerable interest because it is concerned with the important
problem of wind-tunnel turbulence and its results could be compared
directly with experimental work done by dryden in this country and by
fage, townend and simmons in england .
the present paper is concerned with two fundamental problems.. with
uniform isotropic turbulence and with the turbulent friction in a
parallel stream . first, the general theory of isotropic turbulence is
developed . this general theory includes taylor's consideration as a
special case . however, it
.I 100
.T
vibration isolation of aircraft power plants .
.A
taylor,e.s. and browne,k.a.
.B
j. ae. scs. 6, 1938, 43.
.W
vibration isolation of aircraft power plants .
vibration in aircraft structure can almost
always be traced to vibratory forces originating
from the power plant . these forces are transmitted
to the aircraft in two ways .. (1) by the action of air
forces upon the surfaces of the aircraft in, or adjacent
to, the slip stream of the propeller, and (2) by direct
transmission of unbalanced forces from the power
plant through the engine mounting . the latter has
always caused the preponderance of disturbance .
vibratory stresses induced in the engine mounting
structure occasionally produce fatigue failures in the
associated parts, and always shorten the useful life
of the entire aircraft structure . more important,
however, are the psychological and physiological
effects of continuous vibration and its attendant noise
on the passengers and crew . this may very likely
be the major source of the rapid fatigue which is so
intimately associated with flying . the importance
and desirability of drastically reducing vibration can
hardly be questioned .
this paper is limited to a consideration of the
directly transmitted forces and, further, considers the
power plants as rigid bodies attached by flexible means
to the aircraft which is also considered as a rigid body
of relatively large mass . it is also limited to the case
of engines and engine supporting structures having
axial symmetry (radial engines), although the methods
employed could easily be extended to other cases .
.I 101
.T
laminar heat transfer over blunt-nosed bodies at hypersonic flight
speeds .
.A
lester lees
.B
the ramo-wooldridge corporation, los angles, and california institute
of technology, pasadena, california
.W
laminar heat transfer over blunt-nosed bodies at hypersonic flight
speeds .
this paper deals with two limiting cases of laminar heat transfer over
blunt-nosed bodies at hypersonic flight speeds, or high stagnation
temperatures.. (a) thermodynamic equilibrium, in which the chemical
reaction rates are regarded as /very fast/ compared to the rates of diffusion
across streamlines., (b) diffusion as rate-governing, in which the
volume recombination rates within the boundary layer are /very slow/
compared to diffusion across streamlines . in either case the gas density
near the surface of a blunt-nosed body is much higher than the density
just outside the boundary layer, and the velocity and stagnation
enthalpy profiles are much less sensitive to pressure gradient than in the
more familiar case of moderate temperature differences . in fact, in
case (a), the nondimensionalized enthalpy gradient at the surface is
represented very accurately by the /classical/ zero pressure gradient
value, and the surface heat-transfer rate distribution is obtained
directly in terms of the surface pressure distribution . in order to
illustrate the method, this solution is applied to the special cases
of an unyawed hemisphere and an unyawed, blunt cone capped by a
spherical segment .
in the opposite limiting case where diffusion is rate-controlling the
diffusion equation for each species is reduced to the same form as the
low-speed energy equation, except that the prandtl number is replaced
by the schmidt number . the simplifications introduced in case (a) are
also applicable here, and the expression for surface heat transfer rate
is similar., the maximum value of the ratio between the rate of heat
transfer by diffusion alone and by heat conduction alone in the case of
thermodynamic equilibrium is given by.. (prandtl no./schmidt no .)
when the diffusion coefficient is estimated by taking a reasonable value
of atom-molecule collision cross section this ratio is 1.30 .
additional theoretical and (especially) experimental studies are clearly
required before these simple results are accepted .
.I 102
.T
advantages and limitations of models .
.A
sobey,a.j.
.B
j. r. ae. s. 63, 1959, 646.
.W
advantages and limitations of models .
summary .. the use of models for structural test investigations in the
presence of kinetic heating effects is examined . the principal
features of the complex process to be
represented are discussed under the classifications
external air flow, internal heat transfer,
elastic response . of these the second is found
to influence most model design, and an
analysis of a typical structure is included to
illustrate the various contributions to
internal heat transfer .
.I 103
.T
theory of mixing and chemical reaction in the opposed
jet diffusion flame .
.A
spalding,d.b.
.B
a.r.s. jnl. 31, 1961, 763.
.W
theory of mixing and chemical reaction in the opposed
jet diffusion flame .
an idealization of the flow system used by potter
and butler is analyzed . the differential
equation of mixing is solved exactly, to give the location
of, and burning rate in, the flame . the solutions
to the chemical kinetic differential equation
are discussed, relations being derived between the jet
flow rate at extinction, the chemical kinetic
constants and the laminar flame speed in premixed
gases . it is shown that the jet flow rate at
extinction is independent of the transport properties .
comparison is made with the experimental
data of potter, heimel and butler . it is argued that
experiments must be carried out at higher
reynolds numbers if the measurements are to be
quantitatively analyzable .
.I 104
.T
similar solutions of a free convection boundary layer
equation for an electrically conducting fluid .
.A
reeves,b.l.
.B
a.r.s. jnl. 31, 1961, 517.
.W
similar solutions of a free convection boundary layer
equation for an electrically conducting fluid .
author investigates the existence of a class of similar solutions
for free convection from a vertical flat plate, such as are known for
free convection in a nonconducting fluid . the magnetic field acts
transversely to the fluid motion and is assumed to remain constant
in the direction perpendicular to the plate . this introduces into
the momentum equation a retarding force which is a function only
of x, the distance along the plate length . for similarity it is
found that the magnetic inductance must vary as . if
the plate temperature is constant . if n = 0, the magnetic
inductance is constant while the plate temperature increases linearly
with x .
.I 105
.T
the asymptotic boundary layer on a circular cylinder
in axial incompressible flow .
.A
stewartson,k.
.B
q.app.math. 13, 1955, 113.
.W
the asymptotic boundary layer on a circular cylinder
in axial incompressible flow .
in this paper the incompressible boundary layer over a
circular cylinder in an axial flow is investigated far from the
leading edge . if u and v are the velocity components in the
x and r direction respectively and a stream function is
introduced by and, then
for a constant free-stream velocity has the
following asymptotic form ..
where the p's are determined successively, first for s=1 and
all t, then s=2 and all t, etc., from ordinary differential
equations . here and log c=euler's
constant . it is shown that the effect of the curvature of the
body (in planes perpendicular to the flow) is to increase
the skin friction . also the case in which the free-stream
velocity is proportional to (at the
method breaks down), is studied . it is concluded that the
effect of the curvature of the cylinder, when the boundary
layer has a thickness comparable with its radius of
curvature, is to delay separation .
.I 106
.T
the transverse potential flow past a body of revolution .
.A
campbell,i.j.
.B
q.j.mech.app.math. 9, 1956, 140.
.W
the transverse potential flow past a body of revolution .
it is shown that in the potential flow of
an incompressible inviscid fluid past a
body of revolution set with its axis at right
angles to the stream, the velocity
components at the surface along and perpendicular
to the meridians vary with azimuthal
angle round the body in a simple manner .
this is shown by entirely elementary
considerations .
.I 107
.T
on the mixing of two parallel streams .
.A
ting,lu.
.B
j.math.phys. 38, 1959, 153.
.W
on the mixing of two parallel streams .
using the techniques of boundary-layer theory, the proper third
boundary condition for the mixing of two parallel streams is
derived from the compatibility condition of the higher order
approximation . it is shown that the commonly adopted third boundary
condition of balancing of transverse momentum is correct only for
the mixing problem of two semi-infinite incompressible streams .
for the fulfillment of the proper third boundary condition, the
possibility of introducing the similar solution of blasius type is
examined for various cases .
.I 108
.T
properties of the confluent hypergeometric function .
.A
a. d. macdonald
.B
.W
properties of the confluent hypergeometric function .
the confluent hypergeometric functions have proved useful in many
branches of physics . they have been used in such problems involving
diffusion and sedimentation, as isotope separation and protein molecular
weight determinations in the ultracentrifuge . the solution of the
equation for the velocity distribution of electrons in high frequency
gas discharges may frequently be expressed in terms of these functions .
the high frequency breakdown electric field may then be predicted
theoretically for gases by the use of such solutions together with kinetic
theory .
this report presents some of the properties of the confluent
hypergeometric functions together with six-figure tables of the functions .
.I 109
.T
the production of uniform shear flow in a wind tunnel .
.A
owen,p.r. and zienkiewicz,h.k.
.B
j.fluid mech. 2, 1957, 521.
.W
the production of uniform shear flow in a wind tunnel .
a nearly uniform shear flow was obtained in the working
section of a wind tunnel by inserting a grid of parallel rods with
varying spacing .
the function of such a grid is to impose a resistance to the
flow, so graded across the working section as to produce a linear
variation in the total pressure at large distances downstream
without introducing an appreciable gradient in static pressure near
the grid . a method of calculating a suitable arrangement of the
rods is described . although this method is strictly applicable
only to weakly sheared flows, an experiment made with a grid
designed for a shear parameter as large as 0.45 gave results in
close agreement with the theory . there was no evidence from
the experiment of any large-scale secondary flow accompanying
the shear--a danger inherent in an empirical attempt to grade the
resistance of the grid--nor was any tendency observed for the
shear to decay with increasing distance from the grid .
.I 110
.T
dynamics of a dissociating gas .
.A
lighthill,m.j.
.B
j.fluid mech. 2, 1957, 1.
.W
dynamics of a dissociating gas .
this is a lucid introduction to the effects of dissociation
in gas dynamics . the problem in view is that of air flow
past a bluff body at speeds somewhat above 2 km sec .
thermodynamic equilibrium is assumed,. theories of near
equilibrium for transport properties and of large
departures from equilibrium being promised in parts 2 and 3 .
following a survey of the equilibrium statistical
thermodynamics of a pure dissociating diatomic gas, a
new model is introduced . this /ideal dissociating gas/ is
characterized by only three constants, the characteristic
temperature, density and internal energy for dissociation .
physically, it may be regarded as having its vibrational
modes always just half excited (so that at low
temperatures the ratio of specific heats approaches 4 3 rather
then 7 5) . thermodynamic properties of the ideal gas
are derived, and the oblique shock wave relations
deduced in the /strong-shock/ approximation (including an
elegant relation between the principal curvatures of any
bow shock and the subsequent vorticity) . useful relations
are given for the isentropic changes that take place along
streamlines between shocks .
various of these results are applied to the problem
typified by a sphere flying at high mach number . the
newtonian impact theory and its empirical modification
are dismissed as lacking theoretical basis, in favor of the
limit for large values of both mach number and density
ratio across the shock . it is suggested that the zero
surface pressure sometimes predicted by the latter theory
corresponds to separation not of the flow but of the shock
wave from the surface . an estimate is given for the
subsequent shape of the shock . finally, another
approximation is applied to the region near the stagnation
streamline . the fluid is assumed incompressible, but rotational
in accord with the shock relations,. and it is shown that a
spherical shock corresponds to a concentric spherical body .
the resulting surface pressure is within 1 per cent of that
predicted by freeman's second approximation based on
the newtonian-plus-centrifugal solution (same j. 1 (1956),
.I 111
.T
the laminar boundary layer equation: a method of solution
by means of an automatic computer .
.A
leigh,d.c.f.
.B
proc. cam. phil. s. 51, 1955, 320.
.W
the laminar boundary layer equation: a method of solution
by means of an automatic computer .
a method, very suitable for use with an automatic computer,
of solving the hartree-womersley approximation to the
incompressible boundary-layer equation is developed .
it is based on an iterative process and the choleski method
of solving a simultaneous set of linear algebraic equations .
the programming of this method for an automatic computer is
discussed . tables of a solution of the boundary-layer
equation in a region upstream of the separation point are
given . in the upstream neighbourhood of separation
this solution is compared with goldstein's
asymptotic solution and
the agreement is good .
.I 112
.T
steady motion of conducting fluids in pipes under transverse
magnetic fields .
.A
shercliff,j.a.
.B
proc. cam. phil.s. 49, 1953, 136.
.W
steady motion of conducting fluids in pipes under transverse
magnetic fields .
this paper studies the steady
motion of an electrically conducting, viscous fluid
along channels in the presence of an imposed
transverse magnetic field when the walls do not
conduct currents . the equations which determine
the velocity profile, induced currents and
field are derived and solved exactly in the case
of a rectangular channel . when the imposed
field is sufficiently strong the velocity profile is
found to degenerate into a core of uniform flow
surrounded by boundary layers on each wall .
the layers on the walls parallel to the imposed
field are of a novel character . an analogous
degenerate solution for channels of any symmetrical
shape is developed . the predicted pressure
gradients for given volumes of flow at various field
strengths are finally compared with experimental results for square and
circular pipes .
.I 113
.T
acoustical signal detection in turbulent airflow .
.A
smith,m.w. and lambert,r.f.
.B
j.acous.s.am. 32, 1960, 858.
.W
acoustical signal detection in turbulent airflow .
improvement in detected signal-to-noise ratio is obtained
for a periodic signal masked by additive noise
and turbulent noise backgrounds . comparisons are made
between autocorrelation, crosscorrelation, and a
combination of frequency filtering and crosscorrelation .
although the latter method provided the greatest
improvement, the crosscorrelation technique was the
most successful single method . it turned out that
the maximum improvement obtainable was limited by
the dynamic range of the correlator computer and
not by errors due to finite averaging time and scanning
the delay . the improvement for signals masked by
turbulent noise was found to be about 5 db less than that
obtained for additive noise .
.I 114
.T
response of plates to a decaying and convecting randon
pressure field .
.A
dyer,i.
.B
j.acous.s.am. 31, 1959, 922.
.W
response of plates to a decaying and convecting randon
pressure field .
following the methods of lyon, an analysis of the
vibratory response of a plate to a random pressure
field is given . the pressure correlation of the random
field is assumed to have a scale small compared to
the plate size, to decay exponentially, and to convect
with constant speed over the plate . two cases are
considered, one in which the convection speed is much
less than the speed of free flexural waves in the plate,
the other in which the convection speed is the same
order as the flexural wave speed . the mean square plate
displacement is shown to be relatively independent
of convection for speeds much less than the flexural
wave speed, and to increase significantly for speeds in
the order of the flexural wave speed . it is shown that
damping is usually, but not always, an effective means
of vibration reduction . in the case of convection
speeds much smaller than the flexural speed, the use of
hysteretic damping for reduction of the displacement
response is shown to be limited by the decay of the
assumed random pressure field .
.I 115
.T
on turbulent lubrication .
.A
constantinescu,v.n.
.B
proc.inst.mech.e. 173, 1959, 881.
.W
on turbulent lubrication .
the paper concerns the hydrodynamic turbulent
motion in the lubricant layer . proceeding
from the reynolds equations and introducing
the approximations currently used in
lubrication problems, owing to the lubricant film
thickness, the general motion equations for
turbulent lubrication are written .
using the prandtl mixing length hypothesis,
exact and approximate solutions are
obtained for the velocity distribution into the
lubricant layer . the results are discussed by
pointing out the pressure gradient and the
reynolds number influence on the velocity
distributions, as well as the differences with
respect to the laminar flow .
in order to obtain simple formulae, the
exact dependence of the rate of flow on the
pressure gradient into a dimensionless form
is replaced by a linear relation, the slope of
which depends on the reynolds number .
this approximation allows the obtainment of
the pressure differential equation under a
simple form . the pressure equation is integrated
in case of journal bearings, by assuming a
constant or a variable viscosity of the lubricant .
the results are compared to the experimental
data obtained by m. i. smith and d. d.
fuller and the good qualitative agreement is pointed out .
.I 116
.T
the elliptic cylinder in a shear flow with hyperbolic
velocity profile .
.A
jones,e.e.
.B
q.j.mech.app.math. 12, 1959, 191.
.W
the elliptic cylinder in a shear flow with hyperbolic
velocity profile .
the stream function for the shear flow with hyperbolic
velocity profile past an elliptic cylinder has been determined
as an infinite series of mathieu functions . it is found that
the stagnation streamline of the flow is displaced towards
a region of higher velocity, this displacement increasing
the main stream, (2) as the stream becomes progressively
non-uniform, (3) with increase of minor axis length when
the major axis length remains invariant . in each case the
displacement reaches a limiting value as the cylinder moves away
from the axis of symmetry of the stream . these limiting
values are reached at critical distances from the axis of symmetry,
which decrease as the stream becomes progressively non-uniform,
but these distances are approximately independent of incidence .
the pressure coefficients and the resultant force and moment
coefficients associated with the cylinder have also been obtained,
and investigated numerically for the flat plate type of cylinder .
.I 117
.T
the motion of a viscous liquid past a paraboloid .
.A
mather,d.j.
.B
q.j.mech.app.math. 14, 1961, 423.
.W
the motion of a viscous liquid past a paraboloid .
an approximate solution for the steady
flow of incompressible viscous liquid past
a paraboloid of revolution is described .
an assumption is made for the form of the
stokes stream function and substituted
into the navier-stokes equations using
paraboloidal coordinates . after making
suitable approximations, a non-linear
differential equation for a function f is
deduced . the solutions of this equation
depend on the reynolds number of the
flow considered . examples found by
numerical integration are given to illustrate
the properties of the function f for
reynolds numbers varying from 0.0001 to
is found, and it is shown that this approximate
solution tends to the perfect fluid
flow away from the boundary, allowance
being made for the displacement effect of
what may be called the boundary layer .
.I 118
.T
the transonic flow of a compressible fluid through
an axially symmetrical nozzle .
.A
tomotika,s. and hasimoto,z.
.B
j.math.phys. 29, 1950, 105.
.W
the transonic flow of a compressible fluid through
an axially symmetrical nozzle .
by a method similar to that developed by s. tomotika
and k. tamada (quart. appl. math. 7, 381-397 (1950),.
these rev. 11, 275) for computing two-dimensional mixed
isentropic flows in the sonic region, the flow in the vicinity
of the throat of an axially symmetrical nozzle is studied .
several exact solutions to von karman's equation for axially
symmetrical transonic flows are obtained and the one that
gives flows through a converging and diverging nozzle is
considered in detail . this solution consists of four branches
of which two are rejected because of singularities . of the
remaining two branches, one gives pure supersonic flow and
the other gives taylor's type of flow with a local supersonic
region in the throat . by varying a parameter, the latter
branch approaches two asymptotes which yield meyer's
type of asymmetrical flows .
.I 119
.T
conduction of fluctuating heat flow in a wall consisting
of many layers .
.A
vodicka,v.
.B
app.sc.res. 5, 1955, 108.
.W
conduction of fluctuating heat flow in a wall consisting
of many layers .
van gorcum has pointed to interesting and important analogies
between the theory of a passive four-pole and the conduction of heat
waves through stratiform bodies . this paper generalizes in certain
regards van gorcum's ideas and draws their consequences for the case of
a solid, bounded by two infinite parallel planes and consisting of any
number of layers made from different materials .
.I 120
.T
measurement of convective heat transfer by means of
the reynolds analogy .
.A
granville,r.a. and boxall,g.
.B
brit.j.app.phys. 11, 1960, 471.
.W
measurement of convective heat transfer by means of
the reynolds analogy .
preston's method for measuring skin friction in pipes has
been extended to include non-uniform flow, with and
without pressure gradients, over flat surfaces . by means of a
modified form of the reynolds analogy, the local
convective heat transfer coefficient can be related to the skin
friction, and it is proposed that the method be used in
aerodynamic models of furnaces and in heat transfer plant
of simple geometry . more investigations are required of
the effects of fluid turbulence, surface roughness and
surface curvature on convective heat transfer and skin
friction .
.I 121
.T
a theory for base pressures in transonic and supersonic
flow .
.A
korst,h.h.
.B
j.app.mech. 23, 1956, 593.
.W
a theory for base pressures in transonic and supersonic
flow .
a physical flow model is devised based on the concepts of
interaction between the dissipative shear flow and the
adjacent free stream and the conservation of mass in the
wake . four flow components are integrated in the model,.
namely, the flow approaching the trailing edge, the
expansion around the trailing edge, the mixing within the
free-jet boundary, and the recompression at the end of the
wake . a unique and stable solution results for the base
pressure . theoretical results obtained for thin
approaching boundary layer do not require empirical information
and are, therefore, best suited to evaluate the merits of the
theory . here emphasized is the case of isoenergetic
constant-pressure mixing in the turbulent free-jet boundary
and agreement is found between theory and experimental
data .
.I 122
.T
a simplified approximate method for the calculation of the pressure
around conical bodies of arbitrary shape in supersonic and hypersonic
flow .
.A
willi f. jacobs
.B
lockheed aircraft corporation, georgia division
.W
a simplified approximate method for the calculation of the pressure
around conical bodies of arbitrary shape in supersonic and hypersonic
flow .
exact conical-flow solutions are available only for circular cones at
zero angle of attack . for nonaxisymmetric cones or cones at angle of
attack, only approximate methods exist . these methods are generally
quite complicated and further limited to certain body shapes or certain
mach-number ranges . a great need was therefore felt for a simple
approximate method applicable to any arbitrarily shaped conical body at
zero incidence as well as at angle of attack .
such a method has been developed recently at lockheed and is presented
here in abbreviated form . the method is based on the /equivalent-cone/
theory . this theory determines the pressure on a conical body
utilizing information for a symmetric cone at zero angle of attack with the
same normal component of the free stream with respect to the surface as
the local element of the body considered . this method works relatively
well at high mach numbers . however, it is quite inconsistent at lower
mach numbers, especially for bodies which deviate considerably from
circular cones . the equivalent-cone method does not give satisfactory
results, mainly due to the fact that it considers only the local surface
element on the body independent of the other body elements in the
newtonian-theory manner .
.I 123
.T
the downstream influence of mass transfer at the nose
of a slender cone .
.A
cresci,r.j. and libby,p.a.
.B
j.aer.scs. 29, 1962, 815.
.W
the downstream influence of mass transfer at the nose
of a slender cone .
the influence of localized mass transfer at the nose of a slender
cone under hypersonic flow conditions has been studied by
experimental and theoretical means . two gaseous coolants, nitrogen
and helium, are injected through a porous plug subtending a
half angle of 30 . the effect of the mass transfer on the shock
shape, pressure distribution, heat transfer, and transition are
investigated . the experimental work involved tests in the
mach-number-8.0 tunnel at pibal . the theoretical analysis involved
a study of the effect of mass transfer on the shock stand-off
distance and leads to an inviscid-flow parameter permitting the
experimentally determined shock shape and pressure distribution
to be extrapolated to other than test conditions and to other
coolant gases . there is obtained the maximum value of this
parameter resulting in no significant alteration of the pressure
distribution on the cone and thus defining the flows in which
boundary-layer-type similarity applies .
significant reductions in heat transfer are obtained with
injection . indeed, with small amounts of helium injection the
peak heating is found to occur downstream on the cone and to be
an order of magnitude less than would occur at the stagnation
point without mass transfer . with nitrogen early transition is
found to occur, so that local heating rates are actually increased
over those prevailing at the same reynolds number without
injection .
.I 124
.T
a summary of the supersonic pressure drag of bodies
of revolution .
.A
morris,d.n.
.B
j.aero.scs. 28, 1961, 563.
.W
a summary of the supersonic pressure drag of bodies
of revolution .
a number of approximate theories for supersonic and
hypersonic flow over bodies of revolution at zero angle of attack are
appraised by a critical comparison with characteristics and
second-order results, with the use of hypersonic similarity as a
basis for the comparison . most of the approximate theories
are inadequate except over very limited ranges of fineness ratio
and mach number . the combination of second-order
supersonic theory and second-order shock-expansion theory provides
consistently good results throughout the supersonic speed range .
on the basis of exact (or nearly exact) supersonic solutions and
a limited amount of test data and theory in the transonic region,
summary design curves are developed that give the pressure
drag of conical and ogive noses and conical and ogive boattails
over the complete range of transonic, supersonic, and hypersonic
mach numbers . other shapes can be analyzed in the same
manner, provided that an equivalent amount of data is available .
the analysis is made with the assumption of inviscid flow,
so that the effects of boundary-layer growth, shock
boundary-layer interaction, and flow separation are not included . the
present correlations provide a sound basis of inviscid-flow results
from which these additional viscous effects can be evaluated .
.I 125
.T
measurements of skin friction of the compressible turbulent
boundary layer on a cone with foreign gas injection .
.A
pappas,c.c. and okuno,a.f.
.B
j.aero.scs. 27, 1960, 321.
.W
measurements of skin friction of the compressible turbulent
boundary layer on a cone with foreign gas injection .
measurements of average skin friction of the turbulent
boundary layer have been made on a 15 total included angle cone with
foreign gas injection . measurements of total skin-friction drag
were obtained at free-stream mach numbers of 0.3, 0.7, 3.5, and
x 10 with injection of helium, air, and freon-12
through the porous wall . substantial reductions in skin
friction are realized with gas injection within the range of mach
numbers of this test . the relative reduction in skin friction is
in accordance with theory--that is, the light gases are most
effective when compared on a mass flow basis . there is a marked
effect of mach number on the reduction of average skin friction,.
this effect is not shown by the available theories . limited
transition location measurements indicate that the boundary layer
does not fully trip with gas injection but that the transition point
approaches a forward limit with increasing injection . the
variation of the skin-friction coefficient, for the lower injection rates
with natural transition, is dependent on the flow reynolds
number and type of injected gas,. and at the high injection rates the
skin friction is in fair agreement with the turbulent
boundary-layer results .
.I 126
.T
an investigation of two-dimensional supersonic base
pressures .
.A
charwat,a.f. and yakura,j.k.
.B
j.aero.scs. 25, 1958, 122.
.W
an investigation of two-dimensional supersonic base
pressures .
an investigation of the base pressure behind wedges at mach
numbers 2 and 3 in the laminar and the transitional regime is
reported . temperature and velocity traverses through the
mixing zone are shown and exploratory investigations of the
wake vortex by use of hot wires and flow-visualization techniques
are described . it is found that the laminar two-dimensional base
pressure agrees well with chapman's theoretical predictions .
the shear layer exhibits gross velocity distributions
characteristic of the free jet mixing zone, but also shows disturbances that
originate in the expansion-turning of the oncoming boundary
layer . an interesting trailing vortex is observed, which is
explained in terms of nonuniform mixing rate in the wake .
.I 127
.T
supersonic axially symmetric nozzles .
.A
clippinger,r.f.
.B
b. r. l. r794, 1951.
.W
supersonic axially symmetric nozzles .
at each of twenty-one exit mach numbers, ranging
from 1.008 to 8.238, ten supersonic axially symmetric
nozzle shapes with plane sonic surfaces have been computed
on the eniac by the method of characteristics . the
boundary of the shortest of each group of ten has a
sharp edge at the sonic plane, while the others have
smooth boundaries . this report describes the computational
procedures and presents a sample of the results for twenty
nozzles .
more extensive and elaborate tables of the results of the
entire computations are available at the ballistic
research laboratories . nozzle contours can be obtained
accurately from them by interpolation for exit mach numbers
between 1.479 and 8.238 for a wide range of ratios of nozzle
length to throat diameter .
.I 128
.T
effects of free stream vorticity on the behaviour of
a viscous boundary layer .
.A
li,t-y.
.B
j.aero.scs. 23, 1956, 1128.
.W
effects of free stream vorticity on the behaviour of
a viscous boundary layer .
theoretical investigation is considered of the two-dimensional
steady flow field at large distance from a finite object set in a
viscous incompressible fluid . study is made of coordinate-type
expansions for pressure and velocity for large r, uniformly in, for
fixed reynolds number, assuming exact boundary conditions at
infinity and regularity of flow with zero net mass flow across a
simple curve enclosing the object .
mathematical nature of the distinction between parameter and
coordinate-type expansions is discussed with description of inner
and outer expansions and matching techniques .
a feature of the expansion procedure is the introduction of an
artificial parameter . inner and outer expansions are matched with
the aid of known solutions of the navier-stokes equations .
analysis requires simple consideration of the heat and laplace
equations without resort to special methods .
paper is worth studying by those interested in asymptotic
expansion procedures .
.I 129
.T
an investigation of the noise produced by a subsonic air jet .
.A
j. h. gerrard
.B
university of manchester
.W
an investigation of the noise produced by a subsonic air jet .
to investigate the theoretical predictions of lighthill on aerodynamic
sound, measurements have been made of the sound field of a 1 in. air jet
issuing from a long pipe . the measurements have been made over a wide
frequency band (30 to 10,000 cycles/sec.) and in one-third octave bands
in this frequency range . the mean mach number at the pipe orifice was
varied from 0.3 to 1.0 .
the dependence of the apparent position of the noise sources on
frequency and jet speed was investigated . at a given frequency a source is
situated farther from the jet orifice the higher the jet speed . lower
frequency sources appear farther downstream than ones of higher
frequency, consistent with their association with larger eddies . the
directional characteristics of the sound field at different frequencies
and jet speeds are illustrated by means of scale diagrams showing lines
of constant sound intensity . these sound fields are analyzed in terms
of the moving quadrupole sources of lighthill's theory and good
agreement obtained . it is shown that the apparent spread of the sources at
low frequencies is due to the doppler effect . at low frequency
relative to the frequency of maximum power output) the radiation is
predominantly that of three mutually orthogonal longitudinal quadrupoles
which, except for the effect of convection upon it, has a sound field
like a monopole source . at higher frequencies the sound fields of
lateral and longitudinal quadrupoles predominate .
.I 130
.T
the behaviour of non-linear systems .
.A
clauser,f.h.
.B
j.aero. scs. 23, 1958, 411.
.W
the behaviour of non-linear systems .
many of the phenomena that occur in the world around us are
governed by nonlinear relationships . in the development of the
mathematical sciences, the difficulties of nonlinear analysis have
hindered the formulation of nonlinear concepts that would
permit us to understand such phenomena . in the present article,
our progress in understanding the behavior of nonlinear systems
is reviewed and an attempt is made to present the resulting
concepts in such a way that they may be applied with some
generality to other problems .
.I 131
.T
two-dimensional jet mixing of a compressible fluid .
.A
pai,s.i.
.B
j.aero.scs. 16, 1949, 463.
.W
two-dimensional jet mixing of a compressible fluid .
the mixing and divergence of a supersonic jet exhausting into
a supersonic stream are investigated theoretically .
in the first part of this paper, the flow is assumed to be laminar .
when the velocity and temperature in the jet are different
slightly from those of the surrounding stream, by the method of
small perturbations and under ordinary boundary layer
assumptions, the equation of motion of two-dimensional flow will be
reduced to a form of the well-known equation of heat conduction,
whose solution is known for any given boundary conditions . it
has also been shown that the exact solution of the two
dimensional jet mixing of viscous compressible fluids can be obtained
by successive approximations starting with the solution of small
perturbations .
velocity and temperature distributions for two cases--one is
the mixing of two-uniform flows and the other is the mixing of a
jet of compressible fluid from a two-dimensional nozzle with full
expansion exhausting into a supersonic stream--have been
calculated . the properties of the jet mixing depend mainly on the
momentum of the jet regardless of whether the change of
momentum is due to the change of velocity or the change of
temperature--i.e., the change of density . compressibility has a
considerable effect on the properties of the jet .
in the second part, the cases of turbulent flow are investigated .
by means of reichardt's theory of free turbulence, the turbulent
shearing stress may be expressed as
it has been shown in this paper that
where is a constant that can be determined experimentally .
the value of n lies between 0 and 1 . the exact value of n
depends on the condition of mixing .
when the expression of turbulent shearing stress given above
is used instead of the viscous stress in the equation of motion,
by suitable transformation of variables, it has been shown that
the equation of two-dimensional turbulent jet mixing is identical
to that of the laminar case . hence, the solution of the first part
of this paper can be applied to the turbulent case, provided that
the characteristic constants and n have been properly chosen .
.I 132
.T
viscosity effects in sound waves of finite amplitude:
in survey in mechanics .
.A
lighthill,m.j.
.B
ed. by g.k.batchelor and r.m.davies. c.u.p. 1956.
.W
viscosity effects in sound waves of finite amplitude:
in survey in mechanics .
this article has as its subject /the conflicting influence on
sound propagation of convection on the one hand, and of diffusion
and relaxation on the other/, whose importance in the
determination of the structure of shock waves was first appreciated clearly
by sir geoffrey taylor . as an essential introduction to the main
topics, author gives an exceptionally clear and valuable account
of the physical mechanisms of viscosity, thermal conductivity, and
other diffusion effects, including relaxation . the classical theory
of shock-wave formation is then discussed, and some extensions
are made .
the remainder of the article is based on the demonstration that
the nonlinear equation for plane progressive sound waves, in which
convection and diffusion are taken into account to a first
approximation, can be transformed into burgers's equation, the general
solution of which was given by hopf and cole . this approach, in
which all flows are continuous (they become discontinuous at
shock waves in the limit as viscosity, etc., tend to zero), allows
the author to re-derive and extend whitham's theory of the
formation and decay of weak plane shock waves, and to derive many
new results, such as the velocity distributions during the union
of two shock waves and during the formation of a shock wave .
the application of the same idea to non-plane shock waves is
also discussed, but more briefly,. in these cases, burgers's
equation is not quite such a good approximation as before .
the article concludes with sections on sound waves whose
reynolds numbers based on the length scale of the flow and the
velocity amplitude are comparable with unity, and on the effects
of relaxation on the properties of shock waves . the whole is
much more than a survey, and represents a very substantial
advance in the theory of sound waves . it is the finest possible
tribute to sir geoffrey taylor that he should be able to inspire
articles such as this and the others in this volume .
.I 133
.T
some effects of surface curvature on laminar boundary
layer flow .
.A
murphy,j.s.
.B
j.aero.scs. 20, 1953, 338.
.W
some effects of surface curvature on laminar boundary
layer flow .
the laminar flow of a viscous incompressible fluid over a
two-dimensional curved surface is investigated for two cases, one in
which the curvature is /large/ and the other in which it is
cases are obtained as approximations from the exact equations of
motion by an order-of-magnitude analysis . these equations are
solved for flow over a particular surface with zero surface pressure
gradient . in this analysis, the pressure gradient normal to the
surface is included, and the outer boundary conditions are
modified in accordance with the requirements of flow over a curved
surface .
the results indicate that for equal reynolds numbers, the
stress on convex surfaces is less than the flat-plate value, while
the stress on concave surfaces is greater than for a flat plate . the
most important effect of surface curvature, for the cases
considered, is the modification of the shape of the velocity profile
near the /outer edge/ of the boundary layer . the requirement
that a smooth transition exist between the viscous flow and the
potential flow at the outer edge of the layer causes the profile to
have a negative slope near the outer edge for convex surface
curvature and a positive slope for concave surface curvature .
.I 134
.T
note on an interaction between the boundary layer and the inviscid
flow .
.A
antonio ferri and paul a. libby
.B
department of aeronautical engineering and applied mechanics,
polytechnic institute of brooklyn, brooklyn, n.y.
.W
note on an interaction between the boundary layer and the inviscid
flow .
according to the classical boundary-layer theory the flow about bodies
at reynolds numbers of aeronautical interest can be considered as
composed of two regimes.. an outside inviscid flow and a thin
boundary-layer region adjacent to the body . this point of view leads to the
approximation that, on a slightly curved surface, throughout the layer
is negligibly small . the additional assumption that the inviscid flow
is irrotational leads to the requirement that is zero at the outer edge
of the boundary layer . in this theory any interaction between the two
regimes is accountable by a simple correction to the body shape based on
the boundary-layer displacement thickness .
recently, in connection with hypersonic laminar boundary layers, this
classical point of view has been modified., an interaction between the
two flow regimes leading to a self-induced axial pressure gradient has
been considered . it is the purpose of the present note to point out
another type of interaction which may be of practical importance and of
fundamental interest even at mach numbers below those considered in the
hypersonic boundary-layer theory and which may have to be considered in
that theory .
.I 135
.T
the calculation of wall shearing stress from heat-transfer measurements
in compressible flows .
.A
nick s. diaconis
.B
lewis flight propulsion laboratory, naca, cleveland, ohio
.W
the calculation of wall shearing stress from heat-transfer measurements
in compressible flows .
it has been shown by ludwieg that the wall shearing stress of a laminar
or turbulent boundary layer in an incompressible flow can be determined
from a heat-transfer measurement at the surface . the instrument
used in that investigation was essentially a small, locally insulated,
heating element embedded in the test surface . the size of the
instrument was restricted by the condition that the thermal boundary layer
generated by the heating element be contained locally within the laminar
sublayer . in the present analysis ludweig's theory for such an
instrument is extended to compressible flow over an insulated flat plate .
with the same limitations on the design and operation of the instrument
as mentioned above, it can also be assumed for compressible laminar
and turbulent boundary layers that only the flow in the immediate
vicinity of the wall or the laminar sublayer will be affected in the region
of the heated element . this assumption then permits the use of the
laminar boundary-layer equations as the governing equations for this
analysis for both laminar and turbulent boundary layers .
.I 136
.T
recent developments in rocket nozzle configurations .
.A
roa,g.v.r.
.B
a.r.s.jnl. 31, 1961,1488.
.W
recent developments in rocket nozzle configurations .
existing configurations of supersonic portion of rocket nozzles
are described and compared . survey covers bell-type conical and
contoured nozzles, annular nozzles, plug nozzles, and the author's
own /e-d/ (expansion-deflection) nozzle . the latter is a
bell-type nozzle in which the gases are first deflected radially outward
by a small central plug, then expanded radially inward around the
base of the plug, and finally deflected back to a nearly axial
direction by the nozzle wall, in compressive turning .
.I 137
.T
the generation of sound by aerodynamic means .
.A
curle,n.
.B
j.roy.ae.s. 65, 1961, 724.
.W
the generation of sound by aerodynamic means .
a summary is given of some of the more important experimental results
relating to the noise radiated from a cold subsonic turbulent jet .
these are then related to the predictions of lighthill's general theory
of aerodynamic noise .
.I 138
.T
wakes in axial compressors .
.A
pearson,h. and mckenzie,a.b.
.B
j.roy.ae.s.63, 1959, 415.
.W
wakes in axial compressors .
the tendency in the past has been to assume that
when wakes or non-uniform total head profiles are
fed into an axial compressor then substantially constant
static pressure prevails at the entry, the variations in total
head appearing as variations in velocity . this variation
in velocity causes variation in incidence on the early stage
blade rows and thus can give rise to excitation of blade
vibration . this assumption is implicit, for instance, in
references 1 and 2, but we think has been a common
assumption by most of the people working in this field .
where the compressor is fed by a duct of substantially
parallel walls for a reasonable length ahead, such an
assumption appeared justifiable . such a duct when given
an air flow test with its outlet discharging, for instance,
to atmosphere instead of to the compressor, then the
distribution assumed would normally be obtained and in fact
many surveys of such ducts have been represented in this
fashion . the object of this note is to show that, in fact,
this distribution will not normally occur when the
compressor is present and we may normally expect much more
nearly a constant velocity into the compressor with
attendant static pressure distributions to match with the total
head variations ahead of the intake, with of course, the
attendant curved flow to support the static pressure
gradients .
.I 139
.T
viscous effects on pitot tubes at low speeds .
.A
mcmillan,f.a.
.B
j.roy.ae.s.58, 1954, 570.
.W
viscous effects on pitot tubes at low speeds .
measurements were made of the pressure in a blunt-nosed pitot
tube, in an air stream at reynolds numbers from about 15 to 1000 .
the results are expressed in terms of a pressure coefficient
density of the fluid, and p and v are the static pressure and
velocity in the undisturbed stream . as found in previous
investigations, becomes greater than 1 at low reynolds numbers, the
increase being about at a reynolds number of 50 (based
on external tube radius) . in disagreement with the work of hurd,
chesky, and shapiro, no decrease of below 1 was found at any
reynolds number .
when the values of found by various experiments are
plotted against reynolds numbers based on internal tube radius,
it is found that the curves are in closer agreement than when the
external radius is used .
.I 140
.T
the determination of turbulent skin friction by means
of pitot tubes .
.A
preston,j.h.
.B
j.roy.ae.s. 58, 1954, 109.
.W
the determination of turbulent skin friction by means
of pitot tubes .
a simple method of determining
local turbulent skin friction on a smooth
surface has been developed which utilises a
round pitot tube resting on the surface .
assuming the existence of a region near the
surface in which conditions are functions
only of the skin friction, the relevant physical
constants of the fluid and a suitable length,
a universal non-dimensional relation is
obtained for the difference between the total
pressure recorded by the tube and the static
pressure at the wall, in terms of the skin
friction . this relation, on this assumption,
is independent of the pressure gradient .
the truth and form of the relation were first
established, to a considerable degree of
accuracy, in a pipe using four geometrically
similar round pitot tubes--the diameter
being taken as representative length . these four
pitot tubes were then used to determine
the local skin friction coefficient at three stations
on a wind tunnel wall, under varying
conditions of pressure gradient . at each station,
within the limits of experimental
accuracy, the deduced skin friction coefficient was
found to be the same for each pitot
tube, thus confirming the basic assumption and
leaving little doubt as to the correctness
of the skin friction so found . pitot traverses
were then made in the pipe and in the
boundary layer on the wind tunnel wall . the results
were plotted in two non-dimensional
forms on the basis already suggested and they
fell close together in a region whose
outer limit represented the breakdown of the
basic assumption, but close to the wall
the results spread out, due to the unknown
displacement of the effective centre of a
pitot tube near a wall . this again provides
further evidence of the existence of a
region of local dynamical similarity and of the
correctness of the skin friction deduced
from measurements with round pitot tubes on
the wind tunnel wall . the extent of the
region in which the local dynamical similarity
may be expected to hold appears to vary
from about to of the boundary-layer
thickness for conditions remote from,
and close to, separation respectively .
.I 141
.T
free-flight techniques for high speed aerodynamic research .
.A
hamilton,j.a. and hufton,p.a.
.B
j.roy.ae.s. 60, 1956, 151.
.W
free-flight techniques for high speed aerodynamic research .
the development rocket-borne and rocket-launched high-speed
airplane model test is described . details of airborne components,
telemetering units, tracking, and their calibration are also discussed .
tests on controls, drag measurements, longitudinal stability
evaluations, lift measurements, pressure measurements, aeroelastic
estimations, and sonic bang recordings are effected . the reynolds numbers
involved are much higher than are usual in the wind tunnel, and
extensions of mach numbers are obtained beyond the tunnel limits, both free
of the tunnel wall interference .
.I 142
.T
the problem of aerodynamic heating .
.A
van driest,e.r.
.B
aero.eng.rev. 15, 1956.
.W
the problem of aerodynamic heating .
paper is a good review of knowledge to date on convective heat
transfer to objects moving through air at low and high speeds .
theoretical and experimental information is given on recovery
factors and heat-transfer coefficients for isothermal surfaces of
unswept flat plates, wedges and cones with attached shock waves,
and stagnation points of blunt bodies of revolution, for both
laminar and turbulent boundary layers . a convenient nomograph for
calculating flat plate turbulent boundary-layer heat-transfer
coefficients is given . effects of surface cooling, surface roughness,
and supply stream turbulence on transition are discussed and
shown graphically .
.I 143
.T
interplanetary orbits .
.A
vertregt,m.
.B
j.brit.inter.s. 16, 1958, 326.
.W
interplanetary orbits .
the basic equations under simplified
conditions for interplanetary flight are derived .
for a voyage from planet to planet an
unlimited number of orbits is possible . in
order to give a clear survey of these possible
orbits a diagram is developed from which the
approximate energy-requirement, the duration,
and other particulars of a voyage can be
easily found .
.I 144
.T
heat flow in composite slabs .
.A
mayer,e.
.B
j.am.r.s. 22, 1952, 150.
.W
heat flow in composite slabs .
this paper presents the solution of the heat flow
problem in composite walls under heat transfer conditions
which are typical of uncooled rocket engine walls .
analytic expressions in the form of fourier sums are obtained
for the temperature distribution in a composite wall
consisting of an inner (refractory) medium and an outer
metallic) medium under newtonian heat transfer into the
first medium with negligible heat transfer from the
second medium to the exterior . the expressions obtained
are based on a plane parallel composite slab as a
representative model for relatively thin cylindrical walls, with
thickness-to-radius ratio not exceeding 0.2 . the general
results for the composite slab are simplified for the limiting
cases of a thin refractory shield with a thick shielded
medium and a thick refractory shield with a thin shielded
medium .
.I 145
.T
skin friction in the laminar boundary layer in compressible
flow .
.A
young,a.d.
.B
aero.quart. 1, 1949, 137.
.W
skin friction in the laminar boundary layer in compressible
flow .
from an analysis of the work of
crocco and others, semi-empirical formulae
are derived for the skin friction on a
flat plate at zero incidence with a laminar
boundary layer . these formulae are
for the general case of heat transfer, and
when there is no heat transfer .
the problem of heat transfer and
the effect of radiation are discussed in the
light of these formulae . the second
formula is then utilised in the development of
an approximate method for solving the
momentum equation of the boundary layer
on a cylinder without heat transfer .
the method indicates that with increase of
mach number there is a marked forward
movement of separation from a flat plate
in the presence of a constant adverse velocity gradient .
.I 146
.T
supersonic flow past slender bodies with discontinuous
profile slope .
.A
fraenkel and portnoy.
.B
aero.quart. 6, 1955, 114.
.W
supersonic flow past slender bodies with discontinuous
profile slope .
ward's slender-body theory is extended to derive first
approximations to the external forces on slender
bodies of general cross section
with discontinuous profile slope . two
classes of body are considered ..
bodies whose profile (typified by the local
radius) is continuous between the
nose and base, and certain bodies whose
profile is discontinuous, such as
bodies with annular or side air intakes and
wing-bodies on which the wing
has an unswept leading edge . (where air
intakes are concerned, it is
assumed that they are sharp-edged and that
there is no /spillage/ of the
internal flow) .
the following conclusions apply to
the former class of bodies . the
variation of drag with mach number is
found to depend only on the
discontinuities in the longitudinal rate of change
of the cross-sectional area, and is
thus independent of cross-sectional shape .
the drag itself is unchanged if
the direction of the flow is reversed . the
expressions for lift and moment
assume the same forms as for smooth pointed
bodies, the lift depending only
on conditions at the base of the body .
the general theory is applied to
winged bodies of revolution with an
unswept wing leading edge .. the results
bear a marked resemblance to those
obtained by ward . the results for wings
alone are seen to be applicable,
with one modification, to subsonic as well as to supersonic speeds .
.I 147
.T
supersonic flow past slender pointed wings with ?similar?
cross sections at zero lift .
.A
lord,w.t. and brebner,g.g.
.B
aero.quart. 10, 1959, 79.
.W
supersonic flow past slender pointed wings with ?similar?
cross sections at zero lift .
some recent theoretical work on slender pointed wings at zero lift is
co-ordinated and extended . the wings
considered may have any pointed plan
form shape, provided that the trailing
edge is straight and unswept . the root
section profile and cross-section shapes
are arbitrary, provided that, on any
one wing, the latter are /descriptively
similar/ (diamond or parabolic biconvex
for instance), though not necessarily
geometrically similar . the chief aim of
the work is to find wings with simple
geometry, low wave drag and pressure
distributions which are unlikely to be
seriously affected by viscous effects .
wave drag and pressure distributions
are calculated by slender-wing theory .
general formulae, which are both simple
and instructive, are given for the wave
drag and the overall pressure distribution,
with particular emphasis on the root
pressure distribution . results for a number
of wings of special interest are
presented and discussed .
.I 148
.T
on displacement thickness .
.A
lighthill,m.j.
.B
j.fluid mech. 4, 1958, 383.
.W
on displacement thickness .
four alternative theoretical treatments of 'displacement
thickness', and, generally, of the influence of boundary layers
and wakes on the flow outside them, are set out, first for
two-dimensional, and then for three-dimensional, laminar or turbulent,
incompressible flow . they may be called the methods of 'flow
reduction', 'equivalent sources', 'velocity comparison' and
the principal expression obtained for the displacement
thickness in three-dimensional flow may be written
if, as orthogonal coordinates (x,y) specifying position on the
surface, we choose x as the velocity potential of the external
flow, and y as a coordinate, constant along the external-flow
streamlines, such that h dy is the distance between (x,y) and
z is the distance from the surface, u and v are the x and y components
of velocity, and u takes the value u just outside the boundary layer .
.I 149
.T
expansions at small reynolds number for the flow past
a sphere and a circular cylinder .
.A
proudman,i. and pearson,j.r.a.
.B
j.fluid mech. 2, 1957, 237.
.W
expansions at small reynolds number for the flow past
a sphere and a circular cylinder .
this paper is concerned with the problem of obtaining higher
approximations to the flow past a sphere and a circular cylinder
than those represented by the well-known solutions of stokes
and oseen . since the perturbation theory arising from the
consideration of small non-zero reynolds numbers is a singular
one, the problem is largely that of devising suitable techniques for
taking this singularity into account when expanding the solution
for small reynolds numbers .
the technique adopted is as follows . separate, locally valid
the regions close to, and far from, the obstacle . reasons are
presented for believing that these 'stokes' and 'oseen' expansions
are, respectively, of the forms
where are spherical or cylindrical polar coordinates made
dimensionless with the radius of the obstacle, r is the reynolds
number, and and vanish with r . substitution
of these expansions in the navier-stokes equation then yields a
set of differential equations for the coefficients and, but
only one set of physical boundary conditions is applicable to each
expansion (the no-slip conditions for the stokes expansion, and
the uniform-stream condition for the oseen expansion) so that
unique solutions cannot be derived immediately . however, the
fact that the two expansions are (in principle) both derived from
the same exact solution leads to a 'matching' procedure which
yields further boundary conditions for each expansion . it is thus
possible to determine alternately successive terms in each
expansion .
the leading terms of the expansions are shown to be closely
related to the original solutions of stokes and oseen, and detailed
results for some further terms are obtained .
.I 150
.T
integration of the boundary layer equations .
.A
meksyn,d.
.B
proc.roy.s.a. 237 1956, 543.
.W
integration of the boundary layer equations .
the equations of the boundary layer
are integrated by an expression of the form
where f(x) is a positive function with x=0
as the stationary point,. (x) is slowly varying,.
the integral contains an unknown parameter
which is found from the condition .
the integral is evaluated by the method of
steepest descent . the expressions obtained are
usually divergent, except in few cases which
include blasius's equation,. the divergent
expressions are summed by euler's transformation .
to check the procedure it is applied to falkner
and skan's equation . the results obtained
are very striking,. few terms in the expansions
are sufficient to obtain close agreement with
hartree's laborious numerical computations .
the method is also applied to the general
boundary-layer equation for the case of flow past
an elliptic cylinder, measured by schubauer .
the results obtained are in close agreement
with schubauer's measurements for the velocities,
almost up to separation, for the position of
the separation point,. and in satisfactory agreement downstream of
separation .
.I 151
.T
the generation of noise by isotropic turbulence .
.A
proudman,j.
.B
proc.roy.s.a 214,1952,119.
.W
the generation of noise by isotropic turbulence .
a finite region, with fixed boundaries, of an
infinite expanse of compressible fluid is in
turbulent motion . this motion generates noise
and radiates it into the surrounding fluid .
the acoustic properties of the system are studied
in the special case in which the turbulent
region consists of decaying isotropic turbulence .
it is assumed that the reynolds number
of the turbulence is large, and that the mach number is small .
the noise appears to be generated mainly
by those eddies of the turbulence whose
contribution to the rate of dissipation of kinetic
energy by viscosity is negligible .
it is shown that the intensity of sound at large
distances from the turbulence is the same
as that due to a volume distribution of simple acoustic
sources occupying the turbulent region .
in this analogy, the whole fluid is to be regarded
as a stationary and uniform acoustic
medium . the local value of the acoustic power output
p per mass of turbulent fluid is given
approximately by the formula
where a is a numerical constant, u is the
mean-square velocity fluctuation, is the time, and
c is the velocity of sound in the fluid . the
constant a is expressed in terms of the well-known
velocity correlation function f(r) by
assuming the joint probability distribution of the
turbulent velocities and their first two
time-derivatives at two points in space to be
gaussian . the numerical value is
then obtained by substituting the form of f(r)
corresponding to heisenberg's theoretical
spectrum of isotropic turbulence .
it is found that the effects of decay make
only a small contribution to the value of a, and
that the order of magnitude of a is not changed
when widely differing forms of the function
f(r) are used .
.I 152
.T
on the flow of compressible fluid past an obstacle .
.A
lord rayleigh, o.m., f.r.s.
.B
.W
on the flow of compressible fluid past an obstacle .
it is well known that according to classical hydrodynamics a steady
stream of frictionless incompressible fluid exercises no resultant
force upon an obstacle, such as a rigid sphere, immersed in it . the
development of a /resistance/ is usually attributed to viscosity, or
when there is a sharp edge to the negative pressure which may accompany
it (helmholtz) . in either case it would seem that resistance involves
something of the nature of a wake, extending behind the obstacle to an
infinite distance . when the system of disturbed velocities, although
it may mathematically extend to infinity, remains as it were attached to
the obstacle, there can be no resistance .
the absence of resistance is asserted for an incompressible fluid., but
it can hardly be supposed that a small degree of compressibility, as in
water, would affect the conclusion . on the other hand, high relative
velocities, exceeding that of sound in the fluid, must entirely alter
the conditions . it seems worth while to examine this question more
closely, especially as the first effects of compressibility are amenable
to mathematical treatment .
.I 153
.T
on the steady motion of viscous, incompressible fluids,
with particular reference to a variation principle .
.A
millikan,c.b.
.B
phil.mag. 7, 1929, 641.
.W
on the steady motion of viscous, incompressible fluids,
with particular reference to a variation principle .
except in exceptional cases, it is not possible to represent the
motion of a viscous incompressible liquid by means of a variation
principle, but all cases of such motion that have yet been discovered
belong to this class of /exceptional cases ./ the appropriate functions
are given .
.I 154
.T
velocity and temperature distributions in the turbulent
wake behind a heated body of revolution .
.A
hall,a.a. and hislop,g.s.
.B
proc.cam.phil.s. 34, 1938, 345.
.W
velocity and temperature distributions in the turbulent
wake behind a heated body of revolution .
recently (see abstract 954 (1938)) goldstein made calculations based
on theories of vorticity transfer, of the distributions of velocity and
temperature in the turbulent wake behind a heated body of revolution,
and the present authors now record an experimental determination of
these distributions in a low-turbulence wind tunnel . difficulty was
experienced in obtaining a truly symmetrical wake and observations
have been reduced to mean values, curves of which are given .
.I 155
.T
on the solution of the laminar boundary layer equations .
.A
howarth,l.
.B
proc.roy.s.a, 164, 1938, 547.
.W
on the solution of the laminar boundary layer equations .
the problem of the flow along a flat plate
placed edgewise to a steady stream,
when a retarding pressure gradient
varying linearly as the distance x
from the leading edge of the plate
is superposed is discussed . if y denotes
distance measured perpendicular to
the plate, a solution is obtained in the
form of a power series in x where
coefficients are functions of .
differential equations are obtained for these
coefficients . seven of the coefficients
have been obtained with reasonable
accuracy, and the eighth and ninth
roughly . unfortunately it appears
that about eight more terms are
required to carry the solution to
the point of separation,. the work
involved in their determination is
prohibitive . two approximate methods
have been developed for determining
the error when the first seven terms
of the series are used as an approximation .
these methods lead to the
determination of the point of separation
and are in agreement as to its
position . if is the velocity at the
edge of the boundary layer at the
leading edge of the plate and is the
velocity gradient, separation is found
when . a method is
developed for the solution of the
boundary layer equations in any retarded region .
it is obtained by
replacing the velocity distribution at the edge
of the boundary layer by a
circumscribing polygon of infinitesimal sides and
applying the preceding solution
to each of these sides, making the
momentum integral continuous at each
vortex . the problem is thereby
reduced to the solution of a first order
differential equation .
.I 156
.T
the effect of shallow water on wave resistance .
.A
havelock,t.h.
.B
proc.roy.s.a, 100,1922,499.
.W
the effect of shallow water on wave resistance .
the general character of experimental
results dealing with the effect of
shallow water on ship resistance may be
stated briefly as follows ..--at low
velocities the resistance in shallow
water is greater than in deep water, the
speed at which the excess is first
appreciable varying with the type of vessel .
as the speed increases, the excess
resistance increases up to a maximum at a
certain critical velocity, and then
diminishes . with still further increase of
speed, the resistance in shallow
water ultimately becomes, and remains, less
than that in deep water at the same speed .
the maximum effect is the more
pronounced the shallower the water .
for further details and references one
may refer to standard treatises, but one
quotation may be made in regard to
the critical velocity .. /this maximum
appears to be at about a speed such
that a trochoidal wave travelling at this
speed in water of the same depth is
about times as long as the vessel .
it was at one time supposed
that the speed for maximum increase
in resistance was that of the wave of
translation . this, however, holds only
for water whose depth is less than
for greater depths the speed of the
wave of translation rapidly becomes
greater than the speed of maximum
increase of resistance ./ in a recent
analysis of the data, h. m. weitbrecht
expresses a similar conclusion by stating
that for each depth of water there is
a critical velocity, but that the critical
velocity does not vary as the square
root of the corresponding depth .
.I 157
.T
the hodographic transformation in transonic flow .
.A
lighthill,m.j.
.B
proc. roy.s. a, 191, 1947, 323.
.W
the hodographic transformation in transonic flow .
the author studies the problem of finding the shape of a
symmetrical nozzle with the velocity along the axis (x-axis)
specified . the velocity along each streamline is assumed to
increase steadily . the singularity at the sonic velocity and
to the axis of the nozzle) is first studied in the physical
plane by using a power series in . in the hodograph plane,
the two characteristics of the hodograph differential
equation passing through the sonic point and are lines
of branch points . the region between these lines is a
region of triple-valuedness for the stream function .
outside this region is single-valued . there are also
singularities at the sonic point and the point corresponding to
the specified condition at the exit of the nozzle . the author
then proposes to construct in the hodograph plane by
at the exit velocity and (3) a finite sum regular throughout ..
sin, where r is the square of the velocity
and the are hypergeometric functions . the a's are
fixed by the required approximation to the specified velocity
distribution along the axis . this solution is single-valued,
convergent and represents except a region near the sonic
point in the nozzle . for this excluded region, the author
inverts the solution to obtain a power series in for 0 . this
is shown to be convergent for the region of interest . the
type of solution considered by the author gives a nozzle
having an infinitely long supersonic part .
.I 158
.T
temperature charts for induction and constant temperature
heating .
.A
heisler,m.p.
.B
a.s.m.e.trans. 14, 1947, 227.
.W
temperature charts for induction and constant temperature
heating .
charts are presented for determining complete
temperature historics in spheres, cylinders, and plates . it
is shown that for values of the dimensionless time ratio
x greater than 0.2 the heating equations reduce to such
a simple form that for each shape two charts which give
temperatures at any position within the heated or cooled
bodies can be plotted . it is also shown that the usual
simple heating and cooling charts can also be used for the
determination of temperatures and heating times in
bodies heated by a constant rate of heat generation at
the surface (induction heating) . finally, a two
dimensional chart is given for finding heating times in short
cylinders, thereby eliminating the trial-and-error
solution that is necessary when heating times are found from
the present one-dimensional charts .
.I 159
.T
numerical methods for transient heat flow .
.A
dusinberre,g.m.
.B
a.s.m.e.trans. 12, 1945, 703.
.W
numerical methods for transient heat flow .
this paper deals with the application of numerical
methods for the solution of heat-conduction problems,
their generality being extended in the following ways ..
may proceed most rapidly to a solution, or may proceed
more slowly and with greater precision,. (b) criteria are
developed for the choice of modulus to insure convergence .
this is most important at a convective surface,. (c) a
method is developed for handling k and c when these
properties vary independently with temperature . a
comprehensive appendix gives the derivations, and the use of
equations and charts is demonstrated by typical
examples .
.I 160
.T
approximate analytical solutions for hypersonic flow
past slender power-law bodies .
.A
mirels,h.
.B
nasa r-15, 1959.
.W
approximate analytical solutions for hypersonic flow
past slender power-law bodies .
approximate analytical solutions are presented
for two-dimensional and axisymmetric
hypersonic flow over blunt-nosed slender bodies whose
shapes follow a power law variation . in particular,
the body shape is given by where is the
transverse body ordinate, is the streamwise distance
from the nose, and m is a constant in the range .
both zero-order
solutions and first-order (small but nonvanishing values
of solutions are presented, where m is the
free-stream mach number and is a characteristic
body or streamline slope . the zero-order shock shape
is similar to the body shape for these flows . the
solutions are found within the framework of
hypersonic-slender-body theory .
the limiting case m=1 corresponds to a wedge
or cone flow . the limiting case
corresponds to a constant-energy flow .
the latter cases are included
so that the present study may be applied to all flows
wherein the zero-order shock shape is given by
with m in the range . flow
fields associated with shock shapes having values of m
outside this range are also discussed . for all values
of, except m=1, certain portions of the flow field
riolate the hypersonic-slender-body approximations,
while other portions are consistent with these
approximations . for m=1, all portions of the flow field
are consistent with the approximations .
the approximate solutions are found as follows .
the asymptotic form of the flow in the vicinity of the
body surface is used as a guide to write approximate
expressions for the dependent variables . these
expressions exactly satisfy the continuity and
energy equations and contain arbitrary constants
which are evaluated so as to satisfy boundary
conditions at the shock . the approximate solutions do
not satisfy the lateral momentum equation except at
the shock and (for the first-order problem) at the body
surface .
the results of the approximate solutions are
compared with numerical integrations of the
equations of motion for various values of m and (ratio
of specific heats) . good agreement is noted,
particularly when m and are both near one . the
shock is relatively close to the body for the latter
cases . sufficient results are presented to evaluate
the accuracy of the approximate method for various
values of m and .
.I 161
.T
supersonic flow past a family of blunt symmetric bodies .
.A
van dyke,m.d. and gordon,h.d.
.B
nasa r-1, 1959.
.W
supersonic flow past a family of blunt symmetric bodies .
some 100 numerical computations have been
carried out for unyawed bodies of revolution with
detached bow waves . the gas is assumed perfect
with . free-stream mach numbers
are taken as 1.2, 1.5, 2, 3, 4, 6, 10, and . the
results are summarized with emphasis on the sphere
and paraboloid .
.I 162
.T
nearly circular transfer trajectories for descending
satellites .
.A
low,g.m.
.B
nasa r-3, 1959.
.W
nearly circular transfer trajectories for descending
satellites .
simplified expressions describing the transfer
from a satellite orbit to the point of atmospheric
entry are derived . the expressions are limited to
altitude changes that are small compared with the
earth's radius, and velocity changes small compared
with satellite velocity . they are further restricted
to motion about a spherical, nonrotating earth .
the transfer orbit resulting from the application
of thrust in any direction at any point in an elliptic
orbit is considered . expressions for the errors in
distance (miss distance) and entry angle due to an
initial misalinement and magnitude error of the
deflecting thrust are presented .
the largest potential contributing factor towards
a miss distance stems from the misalinement of the
retrovelocity increment . if this velocity increment is
pointed in direct opposition to the flight path, a 1
misalinement leads to a miss distance of 34.5 miles .
however, it is shown that this error can be avoided
by applying the velocity increment at an angle
between 120 and 150 below the flight-path direction .
the guidance and accuracy requirements to
establish a circular orbit, in addition to the corrections
applied to transform elliptic orbits into circular
ones, are also discussed .
.I 163
.T
an analysis of the corridor and guidance requirements
for supercircular entry planetary atmospheres .
.A
chapman,d.r.
.B
nasa r-55, 1959.
.W
an analysis of the corridor and guidance requirements
for supercircular entry planetary atmospheres .
an analysis is presented of supercircular entry
into a planet's atmosphere giving particular attention
to the corridor through which spacecraft must be
guided in order to accomplish various maneuvers .
a dimensionless parameter based on conditions at
the conic perigee altitude is introduced for
characterizing supercircular entries and conveniently
prescribing corridor widths associated with elliptic,
parabolic, or hyperbolic approach trajectories . the
analysis applies to vehicles of arbitrary weight, shape,
and size . illustrative calculations are made for
venus, earth, mars, jupiter, and titan .
for nonlifting vehicles having fixed aerodynamic
coefficients, curves are presented of dimensionless
parameters from which can be calculated the maximum
deceleration, maximum rate of laminar convective
heating, and total laminar heat absorbed during
single-pass entry at velocities up to twice circular
velocity . for lifting vehicles, curves are presented of
the maximum deceleration and overshoot boundary
of an entry corridor,. equations are presented for
estimating laminar aerodynamic heating from the
maximum deceleration . it is shown that the corridor
width is independent of vehicle weight, dimensions,
and drag coefficient, provided these are the same at
the overshoot boundary as at undershoot . the
corridors of certain planets can be broadened
markedly by the application of aerodynamic lift,. for
example, the 10-earth-g corridor width for
single-pass, nonlifting, parabolic entry is increased from
to 52, 51, and 52 miles, respectively, by employing a
lift-drag ratio of 1 . the use of aerodynamic lift
does not increase appreciably the corridors of mars
and titan . all corridor widths decrease rapidly
as the entry velocity is increased .
terminal guidance requirements on accuracy of
velocity and flight path angle for successfully entering
various corridors are compared with analogous
requirements for putting a satellite into orbit, for
hitting the moon from the earth, and for achieving
icbm accuracy . consideration is given to the
terminal guidance problem involved in using a
planet's atmosphere--rather than rocket fuel--to
effect orbital transfers from heliocentric to
planeto-centric motion, thereby converting a hyperbolic
approach trajectory to an elliptic orbit about the
target planet . this fuel saving maneuver appears
technologically feasible for certain planetary voyages,
and implies the possibility of achieving a large
reduction in required earth lift-off weight of chemical
propulsion systems .
.I 164
.T
an approximate analytical method for studying entry
into planetary atmospheres .
.A
chapman,d.r.
.B
nasa r-11, 1959.
.W
an approximate analytical method for studying entry
into planetary atmospheres .
the pair of motion equations for entry into a
planetary atmosphere is reduced to a single, ordinary,
nonlinear differential equation of second order by
disregarding two relatively small terms and by
introduring a certain mathematical transformation . the
reduced equation includes various terms, certain of
which represent the gravity force, the centrifugal
acceleration, and the lift force . if these particular
terms are disregarded, the differential equation is
linear and yields precisely the solution of allen and
eggers applicable to ballistic entry at relatively steep
angles of descent . if all the other terms in the basic
equation are disregarded (corresponding to negligible
vertical acceleration and negligible vertical component
of drag force), the resulting truncated differential
equation yields the solution of sanger for equilibrium
flight of glide vehicles with relatively large lift-drag
ratios .
a number of solutions for lifting and nonlifting
vehicles entering at various initial angles also have
been obtained from the complete nonlinear equation .
these solutions are universal in the sense that a
single solution determines the motion and heating
of a vehicle of arbitrary weight, dimensions, and
shape entering an arbitrary planetary atmosphere .
one solution is required for each lift-drag ratio .
these solutions are used to study the deceleration,
heating rate, and total heat absorbed for entry into
venus, earth, mars, and jupiter . from the
equations developed for heating rates, and from
available information on human tolerance limits
to acceleration stress, approximate conditions for
minimizing the aerodynamic heating of a trimmed
vehicle with constant lift-drag ratio are established
for several types of manned entry . a brief study
is included of the process of atmosphere braking for
slowing a vehicle from near escape velocity to near
satellite velocity .
.I 165
.T
skin-friction measurements in incompressible flow .
.A
smith, d.w. and walker, j. h.
.B
naca report r-26
.W
skin-friction measurements in incompressible flow .
experiments have been conducted to measure in
incompressible flow the local surface-shear stress
and the average skin-friction coefficient for a turbulent
boundary-layer on a smooth flat plate having zero pressure gradient .
the local surface-shear stress was measured by a floating-element
skin-friction balance and also by a calibrated total head
tube located on the surface of the test wall . the
average skin-friction coefficient was obtained from
boundary-layer velocity profiles . the
boundary-layer profiles were also used to determine the location
of the virtual origin of the turbulent boundary layer .
data were obtainec for a range of reynolds numbers
from 1 million to about 45 million with an attendant
change in mach number from 0.11 to 0.32 .
the measured local skin-friction coefficients
obtained with the floating-element balance agree
well with those of schultz-grunow and kempf
for reynolds numbers up to 45 million . the
measured average skin-friction coefficients agree
with those given by the schoenherr curve in the
ranges of reynolds numbers from 1 to 3 million
and 30 to 45 million . in the range of reynolds
numbers from 3 to 30 million the measured values
are less than those predicted by the schoenherr curve .
the results show that the /univeral skin-friction constants/
proposed by coles appraoch asymptotically
a constant value at reynolds numbers exceeding
mentioned constants and the limited reynolds
number range of the present investigation, there is some doubt
as to the validity of any turbulent
skin-friction law written on the basis of the present
results . hence, no new friction law is proposed .
the frictional resistance of a flat plate was
calculated by means of the momentum method and
also the integrated measured local surface shear .
for reynolds numbers from 14 million to 45 million
both methods give about the same result,. whereas
at lower values of reynolds number the momentum
method based on velocity profiles uncorrected for
the effects of turbulence results in a frictional
resistance as much as 4 percent higher than that
of the integrated shear .
the measurement of local surface shear by a
calibrated preston tube appears to be accurate
and inexpensive . the calibration as given by
preston must be modified slighlty, however, to yield the
results obtained from the floating-element
skin-friction balance .
.I 166
.T
flow of chemically reacting gas mixtures .
.A
clarke,j.f.
.B
coa r117, 1961.
.W
flow of chemically reacting gas mixtures .
suitable forms of the equations
for the flow of an inviscid,
non-heat-conducting gas in which chemical
reactions are occurring are derived .
the effects of mass diffusion and
non-equilibrium amongst the internal
modes of the molecules are neglected .
special attention is given to
the speeds of sound in such a gas
mixture and a general expression for
the ratio of frozen to equilibrium
sound speeds is deduced . an example
is given for the ideal dissociating
gas . the significance of the velocity
defined by the ratio of the convective
derivatives of pressure and density is
explained . it is the velocity
which exists at the throat of a
convergent-divergent duct under maximum
mass flow conditions, and it is shown that
this velocity depends on the
nozzle geometry as well as on the 'reservoir' conditions .
as an illustration the phenomena of
sound absorption and dispersion are
discussed for the ideal dissociating gas .
the results can be concisely
expressed in terms of the frozen and
equilibrium sound speeds, the
frequency of the (harmonic) sound
vibration and a characteristic time for
the rate of progress of the reaction .
.I 167
.T
linearized flow of a dissociating gas .
.A
clarke,j.f.
.B
j.fluid mech. 7, 1960, 577.
.W
linearized flow of a dissociating gas .
the equations for planar two-dimensional
steady flow of an ideal dissociating gas
are linearized, assuming small disturbances
to a free stream in chemical
equilibrium .
as an example of their solution, the
flow past a sharp corner in a supersonic
stream is evaluated and the variations
of flow properties in the relaxation zone
are found . numerical illustrations are
provided using an 'oxygen-like' ideal gas
and comparisons made with a characteristics
solution . the flow past a sharp
corner can be studied in a conventional
shock tube and it may be possible to
verify the present theory experimentally .
in particular it may prove feasible to
use the results to obtain a measure of the
reaction rates in the gas mixture .
.I 168
.T
heat conduction through a gas with one inert internal
model .
.A
clarke,j.f.
.B
coa n102, 1960.
.W
heat conduction through a gas with one inert internal
model .
the rate of energy transfer between
parallel flat plates is evaluated
when the (stagnant) gas between them is
polyatomic with one inert internal
mode . deviations of the thermal
conductivity from the complete equilibrium
of the inert mode relaxation time
and the effectiveness of the walls in
exciting or de-exciting this mode .
the results are obtained via a linear
theory consistent with small
temperature differences between the plates .
it is found that the eucken-value
of conductivity could be exceeded
if the relaxation times are non-zero and
the plates very effective in
exciting the inert mode . when relaxation
times are very short the effect
of the walls on the energy transfer rate
is small, but the walls make
their presence felt by distorting the
temperature profiles in /boundary
layers/ adjacent to the walls which are
of order in thickness
time) . this result is
analogous to hirschfelder's (1956) for the
case of chemical reactions .
for experimental measurement of
conductivity in a hot wire cell type
of apparatus it is shown that extrapolation
of measured reciprocal
conductivities to zero reciprocal pressure
should load to the full eucken
value . it is also shown that the slope of
reciprocal apparent (measured)
conductivity versus reciprocal pressure
curves is a function of relaxation
time as well as of the accommodation
coefficients . it is quite possible
that the relaxation effect here is
comparable with the temperature jump
effects, even for rotation in diatomic molecules .
.I 169
.T
on the sudden contact between a hot gas and a cold solid .
.A
j. f. clarke, b.sc., ph.d., a.f.r.ae.s.
.B
.W
on the sudden contact between a hot gas and a cold solid .
the flow induced by the sudden contact between a semi-infinite expanse
of gas and a solid, initially at different temperatures, is examined on
the basis of a linear continuum theory . for times large compared with
the mean time between molecular collisions in the gas, the velocity
and pressure disturbances are found to be concentrated around a wave
front propagating out from the interface at the ambient isentropic sound
speed, whilst, near to the interface, these disturbances are small and
the gas temperatures are nearly equal to those predicted by the
classical constant pressure heat conduction theory .
the possible significance of these results in connection with
reflected shock wave techniques to measure high temperature gas properties is
commented upon .
.I 170
.T
the interaction of a reflected shock wave with the
boundary layer in a shock tube .
.A
mark,h.
.B
naca tm.1418.
.W
the interaction of a reflected shock wave with the
boundary layer in a shock tube .
ideally, the reflection of a shock
from the closed end of a shock
tube provides, for laboratory study,
a quantity of stationary gas at
extremely high temperature . because
of the action of viscosity, however,
the flow in the real case is not
one-dimensional, and a boundary layer
grows in the fluid following the initial shock wave .
in this paper simplifying assumptions
are made to allow an analysis
of the interaction of the shock reflected
from the closed end with the
boundary layer of the initial shock
afterflow . the analysis predicts
that interactions of several different
types will exist in different
ranges of initial shock mach number .
it is shown that the cooling
effect of the wall on the afterflow
boundary layer accounts for the change
in interaction type .
an experiment is carried out which
verifies the existence of the
several interaction regions and shows
that they are satisfactorily
predicted by the theory . along with these
results, sufficient information
is obtained from the experiments to make
possible a model for the
interaction in the most complicated case .
this model is further verified
by measurements made during the experiment .
the case of interaction with a
turbulent boundary layer is also
considered . identifying the type of
interaction with the state of
turbulence of the interacting boundary
layer allows for an estimate of the
state of turbulence of the boundary
layer based on an experimental
investigation of the type of interaction .
.I 171
.T
a low density wind tunnel study of shock wave structure
and relaxation phenomena in gases .
.A
sherman,f.s.
.B
naca tn.3298.
.W
a low density wind tunnel study of shock wave structure
and relaxation phenomena in gases .
the profiles and thicknesses
of normal shock waves of moderate
strength have been determined
experimentally in terms of the variation
of the equilibrium temperature
of an insulated transverse cylinder in
free-molecule flow . the shock
waves were produced in a steady state in
the jet of a low-density wind
tunnel, at initial mach numbers of 1.72
and 1.82 in helium and 1.78,
the shock thickness, determined
from the maximum slope of the cylinder
temperature profile, varied from
mean free path in the supersonic
stream . a comparison between the
experimental shock profiles and various
theoretical predictions leads to the
tentative conclusions that .. (1)
the navier-stokes equations are adequate
for the description of the shock
transition for initial mach numbers up
to 2, and (2) the effects of
rotational relaxation times in air can be
accounted for by the introduction
of a /second/ or /bulk/ viscosity
coefficient equal to about two-thirds
of the ordinary shear viscosity .
.I 172
.T
some aerodynamic considerations of nozzle afterbody
combination .
.A
cortright,e.m.
.B
aero. eng. rev. 15, 1956, 59.
.W
some aerodynamic considerations of nozzle afterbody
combination .
the aerodynamic problems associated with
propulsion-system installations have assumed a role
of vital importance in the development of supersonic
aircraft . although air-induction systems have received
moderate attention in the literature, considerably less
information can be found on the design and installation
of turbojet exit nozzles . this condition should not be
interpreted to indicate a lack of problems in jet-exit
design .
as flight speeds reach supersonic levels, it becomes
increasingly difficult to achieve nozzle installations
which are efficient over the entire speed range . the
difficulties largely stem from the fact that the goals of
high jet thrust and low afterbody drag are not always
compatible . in many of the compromise solutions, it
is generally unsatisfactory to examine isolated nozzle
and afterbody performance . rather they must be
treated as a unit, and the complex effects of jet
interaction with the external stream must be taken into
account . to accomplish this, the nozzle and air-frame
designers must closely coordinate their efforts .
some of the aerodynamic problems of nozzle
afterbody combinations are outlined in this report .
particular attention is devoted to the influence of the
jet-stream interaction on both nozzle thrust and
after-body drag . for this purpose, use is made of shock-
boundary-layer-interaction concepts . this approach,
although not precise, correctly predicts many trends
and is generally enlightening .
.I 173
.T
the effect of a central jet on the base pressure of
a cylindrical afterbody in a supersonic stream .
.A
reid,j. and hastings,r.c.
.B
arc r + m.3224, 1962.
.W
the effect of a central jet on the base pressure of
a cylindrical afterbody in a supersonic stream .
this report describes an experimental investigation
of the factors affecting the base flow and
jet structure behind a cylindrical after-body with a central nozzle .
seven interchangeable nozzles were tested .
six of these were convergent-divergent, with a design mach
number of 2.0, jet base diameter ratios ranging
from 0.2 to 0.8 and nozzle divergence angles ranging from
convergent with a jet base diameter ratio of 0.6 .
in the main experimental programme the free-stream
mach number was 2.0 and the boundary layer was
turbulent both on the after-body and in the nozzle .
measurements were made of the base pressure, the surface
pressure distribution inside the nozzle, the overall thrust
and the nozzle mass flow, over a range of jet pressures .
this programme was supplemented by comparative
tests with the jet exhausting into still air (static tests) .
readings were taken of the internal nozzle pressures
and the jet thrust at different jet pressures . schlieren
photography was used extensively throughout .
the results of the tests with external flow are
presented in the form of curves showing the separate effects
of jet pressure ratio, jet base diameter ratio, nozzle
design mach number and nozzle divergence angle on the
base pressure and overall thrust . the special case
of base bleed is discussed separately . similar curves are
included for the static tests . these show the effect
of jet pressure ratio and nozzle geometry on the jet thrust .
a general method of correlating data on annular
base pressures is proposed and discussed . essentially, this
method compares the pressure on an annular
base with the calculated pressure on the corresponding
two-dimensional base . it correlates the present
results reasonably well, but is less successful when applied
to more extensive data .
.I 174
.T
investigation at supersonic speeds of the effects of
jet mach number and divergence angle of the nozzle
upon the pressure of the base annulus of a body of
revolution .
.A
bromm,a.f. and o'donnel,r.m.
.B
naca rm l54i16, 1954.
.W
investigation at supersonic speeds of the effects of
jet mach number and divergence angle of the nozzle
upon the pressure of the base annulus of a body of
revolution .
an investigation has been conducted
in the langley 9-inch supersonic
tunnel to determine the jet effects for
varying jet mach number and
nozzle divergence angle upon the pressure
on the base annulus of a model with
a cylindrical afterbody . the tests
were conducted over a wide range of
jet static pressure ratios and at a
reynolds number of approximately
free-stream mach numbers of 1.62, 1.94,
and 2.41 . all testing was conducted
with an artificially induced
turbulent boundary layer along the model .
in the lower range of jet static
pressure ratios, jet flow from a
sonic or supersonic nozzle affected
the pressure acting on the base
annulus in essentially the same manner
as shown in naca rm e53h25 which covers
jet static pressure ratios up to about
present results showed that the base
pressure tends to level off with
increasing jet static pressure ratio,
and at the extreme static pressure
ratios reached in tests with sonic
nozzles the base pressure began to
decrease . except in the lower range
of jet static pressure ratios,
nozzle divergence angle generally had a
larger effect on the base pressures
than nozzle mach number,. the increase
in base pressure for a change in
divergence angle from 0 to 10 was
small compared to the increase when
the divergence angle was changed from
and other data indicates that the effects
of divergence angle were reduced
when the ratio of jet exit diameter to base
diameter was decreased . jet
mach number effects increased with increase in stream mach number .
.I 175
.T
experiments with static tubes in a supersonic airstream .
.A
holder,d.w., north,r.j. and chinneck,a.
.B
arc r + m 2782, 1953.
.W
experiments with static tubes in a supersonic airstream .
systematic tests have been made at a mach
number of 1.6 on a family of static tubes . the variables
which have been investigated are the shape of the nose, the
distance of the holes downstream, and the inclination of
the tube to the flow . pressure measurements have also been
made in the vicinity of a shock wave and close to a wall .
.I 176
.T
base pressure at subsonic speeds in the presence of
a supersonic jet .
.A
craven,a.h.
.B
coa r129, 1960.
.W
base pressure at subsonic speeds in the presence of
a supersonic jet .
this paper presents the results of an experimental investigation
into the effect of supersonic jets upon the base pressure of a bluff
cylinder in a uniform subsonic flow . the ratio of jet diameter to base
diameter was 0.1875 .
jet stagnation pressures giving slight under-expansion of the jet
cause an increase in the base pressure but for larger jet stagnation
pressures the base pressure is again reduced .
a simple theory, based on a momentum integral, shows the dependence
of the base drag upon the jet and free stream speeds and upon the
dimensions of the jet and the base .
.I 177
.T
the mixing of free axially-symmetrical jets of mach number 1.40 .
.A
n. h. johannesen
.B
department of the mechanics of fluids, university of manchester
communicated by the director-general of scientific research (air),
ministry of supply
.W
the mixing of free axially-symmetrical jets of mach number 1.40 .
axially-symmetrical, supersonic, fully-expanded jets of diameter
about 0.75 in. and of mach number 1.40 issuing into an atmosphere
at rest were investigated by schlieren and shadow photography and
by pressure traversing . the development of the jets was found to
depend critically on the strength of the shock waves in the core of the
jet at the nozzle exit . with strong shock waves present the jet spread
very rapidly and was very unsteady . the jet did in some cases break up
into large eddies of the same size as the diameter of the jet . when
no disturbances were present in the core of the jet the spreading
was far more gradual and the jet showed only slight unsteadiness .
the turbulent mixing region of the first part of the jet with strong
shock waves was investigated in detail by pitot tubes . the first
inch was found to correspond to a two-dimensional half-jet . the
velocity profiles were similar and well represented by the error
integral . the rate of spreading was only half the value for
low-speed flow . by integrations across the mixing region the
entrainment and the loss of kinetic energy were determined .
these quantities were found to agree well with the values estimated by
assuming an error-integral velocity profile .
.I 178
.T
on full dispersed shock waves in carbon dioxide .
.A
griffith,w.c. and kenny,a.
.B
j.fluid mech. 3, 1957, 286.
.W
on full dispersed shock waves in carbon dioxide .
it is pointed out that, for shock mach numbers between 1 and
that the adjustments in the energy in all the degrees of freedom
proceed slowly and in parallel and occur over a distance large
compared with the mean free path . theoretical velocity profiles
for such shock waves are given and found to be in excellent
agreement with interferometric shock-tube observations .
.I 179
.T
an analysis of base pressure at supersonic speeds and
comparison with experiment .
.A
chapman,d.
.B
naca tn.2137, 1950.
.W
an analysis of base pressure at supersonic speeds and
comparison with experiment .
in the first part of the
investigation an analysis is made of base
pressure in an inviscid fluid,
both for two-dimensional and
axially-symmetric flow . it is shown that
for two-dimensional flow, and also for
the flow over a body of revolution
with a cylindrical sting attached to
the base, there are an infinite
number of possible solutions satisfying
all necessary boundary conditions
at any given free-stream mach number .
for the particular case of a body
having no sting attached only one
solution is possible in an inviscid
flow, but it corresponds to zero
base drag . accordingly, it is concluded
that a strictly inviscid-fluid
theory cannot be satisfactory for practical applications .
since the exact inviscid-fluid
theory does not adequately describe
the conditions of a real fluid flow,
an approximate semi-empirical theory
for base pressure in a viscous fluid
is developed in a second part of the
investigation . the semi-empirical
theory is based partly on
inviscid-flow calculations, and is restricted
to airfoils and bodies without
boat-tailing . in this theory an attempt
is made to allow for the effects of
mach number, reynolds number, profile
shape, and type of boundary-layer
flow . the results of some recent
experimental measurements of base
pressure in two-dimensional and
axially-symmetric flow are presented for
purposes of comparison . some
experimental results also are presented
concerning the support interference
effect of a cylindrical sting, and
the interference effect of a reflected
bow wave on measurements of base
pressure in a supersonic wind tunnel .
.I 180
.T
boundary layer over a flat plate in presence of shear
flow .
.A
ting,l.
.B
phys. fluids, 13, 1960, 78.
.W
boundary layer over a flat plate in presence of shear
flow .
the governing equations of an incompressible
boundary layer over a flat plate in the presence of a
shear flow with finite vorticity are derived . for large
vorticity, a similarity solution is obtained . for
moderate vorticity, one of the governing equations
is replaced by an approximate one for which
similarity solutions exist .
.I 181
.T
some problems on heat conduction in stratiform bodies .
.A
vodicka,v.
.B
j. phys. soc. japan, 14, 1959, 216.
.W
some problems on heat conduction in stratiform bodies .
problems on heat conduction in multilayer bodies lead usually to
complicated calculations . the present paper gives an idea of specific
difficulties arising in the case of infinite composite solides .
general deductions are applied to a special class of questions .
.I 182
.T
effect of roughness on transition in supersonic flow .
.A
van driest,e.r. and blumer,c.b.
.B
agard r255, 1960.
.W
effect of roughness on transition in supersonic flow .
further experiments carried out in the 12-inch supersonic wind tunnel
of the jet propulsion laboratory of
the california institute of technology
to investigate the effect of
three-dimensional roughness elements (spheres)
on boundary-layer transition on a 10
transfer are reported herein . the
local mach number for these tests was
minimum (effective) size of trip
required to bring transition to its
lowest reynolds number varies as the
one-fourth power of the distance from
the apex of the cone to the trip .
use of available data at other mach
numbers indicates that the mach
number influence for effective tripping
is taken into account by the
simple expression .
.I 183
.T
properties of impact pressure probes in free molecule
flow .
.A
harris,e.l. and patterson,g.n.
.B
utia r52, 1958.
.W
properties of impact pressure probes in free molecule
flow .
an expression has been derived for the mass flow through
a circular tube in free molecule flow when the tube and gas are in
relative motion . the gas entering the tube is assumed to have a
maxwellian distribution function and the molecular reflection process
at the wall is assumed to be diffuse .
the theory has been used to determine the pressure read
by an impact probe in free molecule flow . although the general
expressions derived apply to any value of gas velocity and tube size,
the detailed calculations for the pressure probe are difficult except
for the case of low speeds and long tubes .
an experimental check of the theory has been carried out
using impact probes in a whirling arm apparatus and in the utia low
density wind tunnel . agreement between theory and experiment is
quite satisfactory .
.I 184
.T
scale models for thermo-aeroelastic research .
.A
molyneux,w.g.
.B
rae tn.struct.294, 1961.
.W
scale models for thermo-aeroelastic research .
an investigation is made of the
parameters to be satisfied for
thermo-aeroelastic similarity . it is concluded
that complete similarity obtains
only when aircraft and model are identical
in all respects, including size .
by limiting consideration to
conduction effects, by assuming the major
load carrying parts of the structure
are in regions where the flow is either
entirely laminar, or entirely turbulent,
and by assuming a specific
relationship between reynolds number and nusselt
number, an approach to similarity can
be achieved for small scale models .
experimental and analytical work is
required to check on the validity of these assumptions .
it appears that existing hot wind
tunnels will not be completely
adequate for thermo-aeroelastic work, and
accordingly a possible layout for
the type of tunnel required is described .
automatic programmed control of
the tunnel would appear to be necessary .
.I 185
.T
some possibilities of using gas mixtures other than in
aerodynamic research .
.A
dean r. chapman
.B
.W
some possibilities of using gas mixtures other than in
aerodynamic research .
a study is made of the advantages that can be realized in
compressible-flow research by employing a substitute heavy gas in place of air .
most heavy gases considered in previous investigations are either toxic,
chemically active, or (as in the case of the freons) have a ratio of
specific heats greatly different from air . the present report is based
on the idea that by properly mixing a heavy monatomic gas with a
suitable heavy polyatomic gas, it is possible to obtain a heavy gas
mixture which has the correct ratio of specific heats and which is
nontoxic, nonflammable, thermally stable, chemically inert, and
comprised of commercially available components .
calculations were made of wind-tunnel characteristics for 63 gas pairs
comprising 21 different polyatomic gases properly mixed with each of
three monatomic gases (argon, krypton, and xenon) . for a given
mach number, reynolds number, and tunnel pressure, a gas-mixture
wind tunnel having the same specific-heat ratio as air would be
appreciably smaller and would require much less power than a
corresponding air wind tunnel . analogous though different advantages
can be realized in compressor research and in firing-range research .
the most significant applications, perhaps, arise through selecting and
proportioning a gas mixture so as to have at ordinary wind-tunnel
temperatures certain dimensionless characteristics which air at
flight temperatures possesses but which air at ordinary wind-tunnel
temperatures does not possess . characteristics which involve the
relaxation time (or bulk viscosity), the variation of viscosity with
temperature, and the variation of specific heat with temperature fall
within this category . other applications arise in heat-transfer
research since certain gas mixtures can be concocted to have any prandtl
number in the range at least between 0.2 and 0.8 .
.I 186
.T
base pressure in supersonic flow .
.A
gadd,g.e., holder,d.w. and regan,j.d.
.B
arc cp271, 1956.
.W
base pressure in supersonic flow .
the problem of accurately predicting the pressure and wake
configuration at the base of bodies in supersonic flow is an
extremely important one inasmuch as a sizeable portion of the total
drag of a given body may be attributable to the low pressure in
this region . although a great deal of theoretical and experimental
work has been done in this field, there does not yet exist a
satisfactory method for accurate predictions .
this paper represents an excellent effort to experimentally
confirm analytically deduced concepts . a large amount of
experimental data on body shapes such as wedges, cones, and
cone-cylinders has been obtained over a range of mach numbers up to 4 .
the data are thoroughly discussed with respect to analytical
deductions . on the basis of the evidence accumulated it is
concluded that the boundary-layer thickness has only a small effect
on the base pressure for axisymmetric bodies and for
two-dimensional bodies when the base height-to-chord ratios are of
the order .
reviewer believes this report is a significant contribution in the
field of base pressure and wake flow phenomena .
.I 187
.T
investigation of separated flows in supersonic and subsonic
streams with emphasis on the effect of transition .
.A
chapman, d.r., kuehn, d. m. and larson, h. k.
.B
naca report 1356
.W
investigation of separated flows in supersonic and subsonic
streams with emphasis on the effect of transition .
experimental and theoretical research has been conducted on
flow separation associated with steps, bases, compression corners,
curved surfaces, shock-wave boundary-layer reflections, and
configurations producing leading-edge separation . results were
obtained from pressure-distribution measurements,
shadow-graph observations, high-speed motion pictures, and oil-film
optics . the maximum scope of measurement encompassed
mach numbers between 0.4 and 3.6, and length reynolds
numbers between 4000 and 5000000 .
the principal variable controlling pressure distribution in
the separated flows was found to be the location of transition
relative to the reattachment and separation positions .
classification is made of each separated flow into one of three regimes ..
and /turbulent/ with transition upstream of separation .
by this means of classificaiton it is possible to state rather
literal results regarding the steadiness of flow and the influence
of reynolds number within each regime .
for certain pure laminar separations a theory for calculating
dead-air pressure is advanced which agrees well with subsonic
and supersonic experiments . this theory involves no empirical
information and provides an explanation of why transition
location relative to reattachment is important . a simple analysis
of the equations for interaction of boundary-layer and external
flow near either laminar or turbulent separation indicates the
pressure rise to vary as the square root of the wall shear stress
at the beginning of interaction . various experiments substantiate tnis
variation for most test conditions . an incidental
observation is that the stability of a separated laminar mixing
layer increases markedly with an increase in mach number .
the possible significance of this observation is discussed .
.I 188
.T
an analysis of base pressure at supersonic velocities and
comparison with experiment .
.A
chapman, dean r .
.B
naca report 1051
.W
an analysis of base pressure at supersonic velocities and
comparison with experiment .
in the first part of the investigation an analysis is made of
base pressure in an inviscid fluid, both for two-dimensional and
axially symmetric flow . it is shown that for two-dimensional
flow, and also for the flow over a body of revolution with a
cylindrical sting attached to the base, there are an infinite
number of possible solutions satisfying all necessary boundary
conditions at anh given free-stream mach numger . for the
particular case of a body having no sting attached only one
solution is possible in an inviscid flow, but it corresponds to
zero base drag . accordingly, it is concluded that a strictly
inviscid-flow theory cannot be satisfactory for practical
applications .
an approximate semi-empirical analysis for base pressure
in a viscous fluid is developed in a second part of the
investigation . the semi-empirical analysis is based partly on
inviscid-flow calculations . in this theory an attempt is made to allow
for the effects of mach number, reynolds number, profile shape,
and type of boundary-layer flow . some measurements of base
pressure in two-dimensional and axially symmetric flow are
presented for purposes of comparison . experimental results
then are presented concerning the support interference effect
of a cylindrical sting, and the interference effect of a reflected
air wave on measurements of base pressure in a supersonic wind tunnel .
.I 189
.T
experimental investigation of base pressure on blunt-trailing-edge
wings of supersonic velocities .
.A
chapman,d.r., wimbrow,w.r. and kester,r.h.
.B
naca r1109.
.W
experimental investigation of base pressure on blunt-trailing-edge
wings of supersonic velocities .
measurements of base pressure are presented for 29
blunt-trailing-edge wings having an aspect ratio of 3.0 and various
airfoil profiles . the different profiles comprised thickness
ratios between 0.05 and 0.10, boattail angles between --2.9
and 20, and ratios of trailing-edge thickness to airfoil thickness
between 0.2 and 1.0 . the tests were conducted at mach numbers
of 1.25, 1.5, 2.0, and 3.1 . for each mach number, the reynolds
number and angle of attack were varied . the lowest reynolds
number investigated was 0.2 x 10 and the highest was 3.5 x 10 .
measurements on each wing were obtained separately with
turbulent flow and laminar flow in the boundary layer .
span-wise surveys of the base pressure were conducted on several
wings .
the results with turbulent boundary-layer flow showed only
small effects on base pressure of variations in reynolds number,
airfoil profile shape, boattail angle, and angle of attack . the
principal variable affecting the base pressure for turbulent flow
was the mach number . at the highest mach number
investigated (3.1), the ratio of boundary-layer thickness to
trailing-edge thickness also affected the base pressure significantly .
the results obtained with laminar boundary-layer flow to
the trailing edge showed that the effect of reynolds number on
base pressure was large . in all but a few exceptional cases
the effects on base pressure of variations in angle of attack and
in profile shape upstream of the base were appreciable though
not large . the principal variable affecting the base pressure
for laminar flow was the ratio of boundary-layer thickness to
trailing-edge thickness .
for a few exceptional cases involving laminar flow to the
trailing edge, the effects on base pressure of variations in profile
shape, boattail angle, and angle of attack were found to be
unusually large . in such cases the variation of base pressure
with angle of attack was discontinuous and exhibited a
hysteresis . stroboscopic schlieren observations at a mach number
of 1.5 indicated that these apparently special phenomena were
associated with a vortex trail of relatively high frequency .
.I 190
.T
on magnetohydrodynamic shock waves .
.A
kanwal,r.
.B
j.math.mech. 9, 1960, 681.
.W
on magnetohydrodynamic shock waves .
in the earlier attempts at finding the jump conditions
across a hydromagnetic shock wave (1, 2, 3)
various simplifying assumptions
regarding the shape of the shock and the
dimensions and the character of the
motion are made . from that analysis it
is possible to write down the jump
conditions in a higher degree of generality (4) .
the shock conditions for magnetohydrodynamic
flows can, however, be
derived in their full generality with the help
of the transport equation as used by
thomas (5) in the derivation of shock conditions
in conventional gas dynamics .
the purposes of this paper are ..
cover the present more general case .
that every flow and field quantity
downstream from the shock wave is
expressible separately in terms of
the known values of these quantities
upstream from the shock wave .
in this rearranged form of the equations,
various effects of the shock
wave can be easily read off .
the shock conditions along the same
lines as in conventional gas dynamics .
.I 191
.T
a theory for the core of a leading edge vortex .
.A
hall,m.g.
.B
rae r.aero.2644, 1960.
.W
a theory for the core of a leading edge vortex .
in the flow past a slender delta wing
at incidence can be observed a
roughly axially symmetric core of spiralling
fluid, formed by the rolling up
of the shear layer that separates from a
leading edge . the aim in this
report is to predict the flow field within
this vortex core, given
appropriate conditions at its outside edge .
the basic assumptions are
core .
in addition it is assumed that the flow
is axially symmetric and incompressible .
together, these admit outer and inner
solutions for the core from the equations
of motion .
for the outer solution the sub-core
is ignored, and the flow is taken to
be inviscid (but rotational) and conical .
the resulting solution consists of
simple expressions for the velocity components
and pressure . for the inner
solution, which applies to the diffusive
sub-core, the flow is taken to be
laminar, and approximations, some based on
the boundary conditions and some
analogous to those of boundary layer theory,
are made . the solution obtained
in this case is a first approximation, and is
presented in tabular form .
a sample calculation yields results
which are in good qualitative and
fair quantitative agreement with experimental measurements .
.I 192
.T
on the hypersonic viscous flow past slender bodies
of revolution .
.A
yashura,m.
.B
j.phys.soc. japan, 11, 1956, 878.
.W
on the hypersonic viscous flow past slender bodies
of revolution .
a similar solution of the hypersonic viscous flow past slender bodies
of revolution is deduced for a special case when the radial coordinate
of the body surface at section x is proportional to x, where the radial
coordinate have the comparable order value with the thickness of the
boundary layer . here, /similar/ is used in the direct meaning that
distributions in the boundary layer keep the similar form lengthwise .
calculations are accomplished for the region of strong interaction
between the boundary layer and the shock wave . from several calculations
it may be expected that if the thickness of the body becomes small, the
thickness of the layer in which the longitudinal velocity component u is
rapidly decreased also becomes small, and in the major part of the
boundary layer, only the normal component v is increased . further if
the thickness of the body is increased, then, the height of the shock
wave, the pressure on the wall, and the shear stress at the wall are
also increased while the boundary layer thickness is decreased . the
nose region is excluded by the reason that the ordinary boundary layer
theory will be invalid there .
.I 193
.T
a study of inviscid flow about air foils at high supersonic
speeds .
.A
eggers, a.j., syvertson, c.a., and krqus, s.
.B
naca report 1123
.W
a study of inviscid flow about air foils at high supersonic
speeds .
steady flow about curved airfoils at high supersonic speeds is
investigated analyticially . with the assumption that air behaves
as a diatomic gas, it is found the the shock-expansion
method may be used to predict the flow about curved airfoils up to
extremely high mach numbers, provided the flow deflection
angles are not too close to those corresponding to shock
detachment . this result applies not only to the determination of the
surface pressure distribution, but also to the determination of the
whole flow field about an airfoil . verification of this observation
is obtained with the aid of the method of characteristics by
extensive calculations of the pressure gradient and shock-wave
curvature at the leading edge, and by calculations of the pressure
distribution on a 10-percent-thick biconvex airfoil at 0 angle of
attack .
an approximation to the shock-expansion method for thin
airfoils at high mach numbers is also investigated and is found
to yield pressures in error by less than 10 percent at mach
numbers above three and flow deflection angles up to 25 . this
slender-airfoil method is relatively simple in form and thus may
prove useful for some engineering purposes .
effects of caloric imperfections of air manifest in disturbed
flow fields at high mach numbers are investigated, particular
attention being given to the reduction of the ratio of specific
heats . so long as this ratio does not decrease appreciably below
to include the effects of these imperfections, should be substantially
as accurate as for ideal-gas flows . this observation is
verfied with the aid of a generalized shock-expansion method and a
generalized method of characteristics employed in forms applicable
for local air temperatures up to about 5000 rankine .
the slender-airfoil method is modified to employ an average
value of the ratio of specific heats for a particular flow field .
this simplified method has essentially the same accuracy for
imperfect-gas flows as its counterpart has for ideal-gas flows .
an approximate flow analysis is made at extremely high mach
numbers where it is indicated that the ratio of specific heats may
approach close to 1 . in this case, it is found that the
shock-expansion method may be in considerable error,. however, the
busemann method for the limit of infinite free-stream mach
number and specific-heat ratio of 1 appears to apply with
reasonable accuracy .
.I 194
.T
general theory of airfoil sections having arbitrary
shape or pressure distribution .
.A
allen,h.j.
.B
naca r833, 1945.
.W
general theory of airfoil sections having arbitrary
shape or pressure distribution .
in this report a theory of thin airfoils of small camber is
developed which permits either the velocity distribution
corresponding to a given airfoil shape, or the airfoil shape
corresponding to a given velocity distribution to be calculated . the
procedures to be employed in these calculations are outlined and
illustrated with suitable examples .
.I 195
.T
correlation of theoretical and photo-thermoelastic
results on thermal stresses in idealized wing structure .
.A
tramposch,h. and gerard,g.
.B
j.app.mech. 27, 1960.
.W
correlation of theoretical and photo-thermoelastic
results on thermal stresses in idealized wing structure .
after a rather complete exploratory program
described in previous papers, the
photo-thermoelastic method was applied to the
experimental evaluation of the thermal-stress
theories . the new technique was correlated
with several theories which analyzed the
transient thermal stresses in idealized wing
structures of high-speed aircraft . various
theories were investigated which represented
the same idealized wing models and
differed from each other only in the simplifying
assumptions regarding the temperature
distributions in skin and webs . the theories
were evaluated by duplicating the boundary
and initial conditions on plastic models and
then by correlating the theories with the
observed fringe orders in nondimensional form .
a significant general conclusion was
reached after correlating the available theories
and experimental results . owing to
simplifying assumptions concerning the thermal
behavior in the flanges, thermal
stresses predicted by the available theories are all
higher than the experimental
observation . in some cases the discrepancy is as great as 30 per cent .
.I 196
.T
pressure distributions . axially symmetric bodies in
oblique flow .
.A
campbell,i.j. and lewis,r.g.
.B
arc cp213, 1955.
.W
pressure distributions . axially symmetric bodies in
oblique flow .
a simple picture, known from the work of i. lotz, of the flow over
the forward part of a body of revolution in oblique flow is derived
here from entirely elementary considerations . the pressure at any
point of the (forward part of the) body at any angle of incidence
depends on three parameters whose values vary along the body . the
variation of these parameters along the body can be determined from a
relatively small number of wind tunnel or water tunnel measurements .
the necessary water tunnel measurements have been made for four axially
symmetric head shapes . additional measurements have been made to
illustrate the theoretical conclusions . the data for each head shape
are adequate for a determination of the pressure coefficient at any
point on the head shapes at any angle of incidence (up to 6, say) .
in particular they can be used to determine the peak suction at any
angle of incidence and so the conditions for the onset of cavitation
on the head .
.I 197
.T
pressure distributions on three bodies of revolution
to determine the effect of reynolds number up to and
including the transonic speed range .
.A
swihart,j.m. and whitcomb,c.f.
.B
naca rm l53h04, 1953.
.W
pressure distributions on three bodies of revolution
to determine the effect of reynolds number up to and
including the transonic speed range .
this paper presents the results of an investigation conducted in
the langley 16-foot transonic tunnel to determine the effects of varying
reynolds number on the pressure distribution on a transonic body of
revolution at angles of attack through the transonic speed range . the
effect of a change in sting cone angle on the pressure distributions
and a comparison of experimental incremental pressures with theory is
also included .
the models were tested through a mach number range from 0.60 to 1.09 .
the reynolds number range based on body length was from 9 x 10 to 39 x
diameter was 1.3 x 10 to 4.53 x 10 for the model at 8 angle of attack .
an increase in reynolds number from 9 x 10 to 39 x 10 affected
the longitudinal pressure distributions very slightly . these effects
were of such a nature as to cause an increase of 0.05 in the
normal-force coefficient of the body when tested in the subcritical cross-flow
reynolds number range . this increase is in agreement with theoretical
approximations .
a comparison between experimental and theoretical values of the
incremental pressure coefficient due to angle of attack indicated good
agreement except at angles where separated flow areas existed over the
body .
the effect of a change in sting-cone angle from 5 to 9 on the
pressure distribution of the 120-inch model was negligible up to a
mach number of 1.05 . at this mach number the effect was to cause a
small increase in the velocity over the rear of the body .
.I 198
.T
investigation of a systematic group of naca 1 - series
cowlings with and without spinners .
.A
nichols,m.r. and keith,a.l.
.B
naca r950, 1949.
.W
investigation of a systematic group of naca 1 - series
cowlings with and without spinners .
an investigation has been conducted in the langley
propeller-research tunnel to study cowling-spinner combinations based
on the naca 1-series nose inlets and to obtain systematic
design data for one family of approximately ellipsoidal spinners .
in the main part of the investigation, 11 of the related spinners
were tested in various combinations with 9 naca open-nose
cowlings, which were also tested without spinners . the effects
of location and shape of the spinner, shape of the inner surface
of the cowling lip, and operation of a propeller having
approximately oval shanks were investigated briefly . in addition, a
study was conducted to determine the correct procedure for
extrapolating design conditions determined from the low-speed
test data to the design conditions at the actual flight mach
number .
the design conditions for the naca 1-series cowlings and
cowling-spinner combinations are presented in the form of
charts from which, for wide ranges of spinner proportions and
rates of internal flow, cowlings with near-maximum pressure
recovery can be selected for critical mach numbers ranging from
spinners and the effects of the spinners and the propeller on
the cowling design conditions are presented separately to
provide initial quantitative data for use in a general design
procedure through which naca 1-series cowlings can be
selected for use with spinners of other shapes . by use of this
general design procedure, correlation curves established from
the test data, and derived compressible-flow equations relating
the inlet-velocity ratio to the surface pressures on the cowling
and spinner, naca 1-series cowlings and cowling-spinner
combinations can be designed for critical mach numbers as
high as 0.90 .
.I 199
.T
measurement of two dimensional derivatives on a wing-aileron-tab
system .
.A
wight,k.c.
.B
part i, arc r + m 2934, 1955. part ii arc r + m 3029, 1958.
.W
measurement of two dimensional derivatives on a wing-aileron-tab
system .
measurements have been made of the direct
two-dimensional damping and stiffness derivatives for a
in incompressible flow .
corrections arising from the apparatus are discussed and
reference is made to an attempt to measure the direct
tab derivatives .
the effects are shown of frequency parameter, amplitude of
oscillation, reynolds number, aileron angle and position
of transition on the wing .
variation with frequency parameter is substantially the
same as for vortex-sheet theory and variation of amplitude
produces little change in both derivatives . at the lowest
reynolds number there is little change in both derivatives
with variation of aileron angle for the condition of natural
transition, but at higher reynolds numbers the stiffness
derivatives increase at .
a forward movement of transition reduces the stiffness
derivatives at the smaller aileron angles, but at,
at the lowest reynolds number, an increase results .
similar trends are observed for the damping derivatives above .
comparison with vortex-sheet theory shows that the
measured values of the stiffness and damping
derivatives are approximately 0.6 of the theoretical values .
measurements have been made of the direct
tab derivatives and cross aileron-tab derivatives for a
per cent aileron and 4 per cent (approx.) tab . in addition
some measurements of the direct aileron derivatives have been
made for comparison with earlier results together with a
number of static derivatives for the wing and controls .
the influence is shown of frequency parameter, reynolds
number, position of transition, mean tab angle and sealing
of the control hinge gaps . some tests have been made with
the ailcron set at minus 8 deg and the tab at plus 12 deg
for which condition the hinge moment on the aileron was zero .
reasonable agreement with the values given by the /equivalent
profile/ theory is shown for both direct damping
derivatives and for the direct tab stiffness derivative . the direct
aileron stiffness derivative shows some departure from
the theoretical value when .
at and the natural transition, comparison
with the values given by flat-plate theory gives the
following approximate factors, where suffix denotes the
theoretical values ..
.I 200
.T
calculation of derivatives for a cropped delta wing
with subsonic leading edges oscillating in a supersonic
airstream .
.A
watson,j.
.B
arc r + m 3060, 1958.
.W
calculation of derivatives for a cropped delta wing
with subsonic leading edges oscillating in a supersonic
airstream .
the lift, pitching moment and full-span
constant-chord control hinge-moment are derived for a cropped
delta wing describing harmonic plunging and pitching
oscillations of small amplitude and low-frequency parameter in
a supersonic air stream . it is assumed that (a) the wing
has subsonic leading edges, (b) the wing is sufficiently thin
and the mach number sufficiently supersonic to permit the
use of linearised theory .
expressions for the various derivative coefficients are
obtained for a particular delta wing of aspect ratio 1.8 and
taper ratio these are avaluated and tabulated for mach
numbers 1.1, 1.15, 1.2, 1.3, 1.4, 1.5, 1.6 and 1.944 .
.I 201
.T
supersonic flow past oscillating airfoils including
nonlinear thickness effects .
.A
van dyke,m.d.
.B
naca r1183, 1954.
.W
supersonic flow past oscillating airfoils including
nonlinear thickness effects .
a solution to second order in thickness is derived for
harmonically oscillating two-dimensional airfoils in supersonic
flow . for slow oscillations of an arbitrary profile, the result is
found as a series including the third power of frequency . for
arbitrary frequencies, the method of solution for any specific
profile is indicated, and the explicit solution derived for a single
wedge .
nonlinear thickness effects are found generally to reduce the
torsional damping, and so to enlarge the range of mach numbers
within which torsional instability is possible . this
destabilizing effect varies only slightly with frequency in the range
involved in dynamic stability analysis, but may reverse to a
stabilizing effect at high flutter frequencies . comparison with
a previous solution exact in thickness suggests that nonlinear
effects of higher than second order are practically negligible .
the analysis utilizes a smoothing technique that replaces
the actural problem by one involving no kinked streamlines .
this stratagem eliminates all consideration of shock waves
from the analysis, yet yields the correct solution for problems
that actually contain shock waves .
.I 202
.T
aircraft flutter .
.A
williams,j.
.B
arc r + m 2492, 1951.
.W
aircraft flutter .
the term flutter is used here to denote maintained or
violent oscillations of a structure due to aerodynamic forces
acting in conjunction with both elastic and inertial forces .
attention is restricted to this particular branch of the more
general field of aeroelasticity, which embraces buffeting,
divergence, and reversal of control, as well as flutter,. airscrew
flutter is not specifically considered . the monograph is
divided into three main parts, each of which has been made
self-contained for the convenience of readers .
in the first part, general methods for the investigation
of aircraft flutter, by theoretical analysis and by experiments
on flutter models, are set out and discussed . a detailed
account of the aerodynamic theory of wings in non-uniform
motion is not included, since this has already been provided
elsewhere, but methods for the evaluation of the aerodynamic
forces required in a theoretical flutter analysis are logically
developed, and a bibliography of researches on the
aerodynamic theory is given in the appendix . investigations
on specific types of aircraft flutter--namely wing flutter,
control surface flutter, and tab flutter--are discussed in part
these various types of flutter are considered, but the practical
details of flutter-prevention devices are omitted . finally,
in part 3, methods for the experimental determination of
airloads on oscillating aerofoil systems are described, and
available airload measurements are analysed and compared
with theoretical results .
an attempt has been made to refer in the text to all relevant
british work reported by the early part of 1947 . foreign
work has been mentioned in parts 1 and 2 only where necessary
for the sake of completeness, but in part 3 and the
appendix all relevant foreign references known to the author have
been included .
matrix notation has been used for the theoretical treatment in
part 1, but otherwise its use has been avoided .
.I 203
.T
calculated velocity distributions and force derivatives
for a series of high-speed aerofoils .
.A
sinott,c.s.
.B
arc r + m 3045.
.W
calculated velocity distributions and force derivatives
for a series of high-speed aerofoils .
the polygon method of woods is used to
calculate the velocity distribution over a number of
two-dimensional aerofoils at low incidence, subcritical flows only
being considered . lift slopes and aerodynamic centres
at zero lift are also calculated .
some comparisons with experimental results are made, and
these show good agreement at zero incidence .
.I 204
.T
a study of the application of airfoil section data
to the estimation of the high subsonic speed characteristics
of swept wings .
.A
hunton,l.w.
.B
naca rm a55c23, 1955.
.W
a study of the application of airfoil section data
to the estimation of the high subsonic speed characteristics
of swept wings .
estimates of the variation with
mach number of the aerodynamic
characteristics of swept wings are made
on the basis of airfoil section
data combined with span-loading theory .
the analysis deals with
examinations of some 26 wings and wing-body
combinations ranging in sweep
angle from 30 to 60 and for mach
numbers between 0.6 and 1.0 .
results of the study indicate
that the two-dimensional section data
afford good qualitative information
for such high-speed aerodynamic
characteristics as the variation with
mach number of drag, zero-lift
pitching-moment coefficient, and lift
coefficient for flow separation .
quantitative estimates of the force
and moment divergence mach numbers
could not be made with any degree of
certainty from the airfoil data
alone . somewhat improved quantitative
estimates for a given
configuration were obtainable by basing the
estimates on the measured
characteristics for a wing of similar plan form
but different section, and
adjusting for the effects of differences in
section on the basis of section data .
.I 205
.T
a correlation of airfoil section data with the aerodynamic
loads measured on a 45 sweptback wing at subsonic mach
numbers .
.A
walker,h.j. and maillard,w.c.
.B
naca rm a55c08, 1955.
.W
a correlation of airfoil section data with the aerodynamic
loads measured on a 45 sweptback wing at subsonic mach
numbers .
an investigation has been made of the possibility of correlating
airfoil section data with measured pressure distributions over a 45
sweptback wing in the mach number range from 0.50 to 0.95 at a
free-stream reynolds number of approximately 2 million .
the wing had an aspect ratio
of 5.5, a taper ratio of 0.53, naca 64a010 sections normal to the
quarterchord line, and was mounted on a slender body of revolution .
at mach numbers of 0.85 and below, and for wing normal-force
coefficients below the maximum normal-force coefficient for an
infinite-aspect-ratio wing yawed 45 to the flow (derived from airfoil section
data by simple sweep relations), good correlation was obtained over most
of the wing between wing-section and two-dimensional-airfoil pressure
distributions . for greater normal-force coefficients lateral
boundary-layer flow permitted the inboard wing sections to rise to high maximum
section normal-force coefficients . the effectiveness of this lateral
boundary-layer flow disappeared towards the tip . for all mach numbers,
the influence of plan-form effects on the pressure distributions limited
the quality of the correlation at the 20- and 95-percent-semispan
stations . above a mach number of about 0.85 the shock waves
originating at the juncture of the body and the wing trailing edge spread over
the span, preventing further application of two-dimensional data .
the spanwise load distributions at moderate normal-force coefficients
could be predicted from span-loading theory for the entire mach number
range of the tests .
.I 206
.T
the applications of the polygon method to the calculation
of the compressible subsonic flow round two-dimensional
profiles .
.A
woods,l.c.
.B
arc cp115, 1953.
.W
the applications of the polygon method to the calculation
of the compressible subsonic flow round two-dimensional
profiles .
this paper sets out the method now used by the author of
applying the polygon method to the calculation of the compressible
subsonic flow round two-dimensional aerofoils . tables have been
constructed which can be used for all aerofoil shapes, putting the
polygon method on the same footing numerically as goldstein's
method has the advantage over approximation 3 that it can be applied in
the following cases which are beyond the scope of goldstein's method ..
conventional aerofoils, (b) the low-speed flow about very thick
aerofoils, e.g., in reference 3 it is applied to circular cylinders, (c)
the flow about symmetric aerofoils between either straight or constant
pressure walls, (d) flow in asymmetric channels,
and (e) more difficult problems
of the flow about aerofoils in the presence
of one or two constraining
walls (to be published) . a method of
calculating lift and moment
coefficients, and their rates of change
with incidence (a) is also
given in the paper .
as an example the velocity distribution and the rates of
change of the lift and moment coefficients with a are calculated for
the aerofoil r.a.e.104 at values of m (mach number at infinity) of 0,
and 0.7, for various values of the incidence, a . the velocity
distributions for zero incidence are found to be in fair agreement with
the corresponding experimental results . the results at incidence are
in satisfactory agreement with the experimental results, not for the
same incidence, but for the same lift coefficient . it is found, for
example, that at m = 0.7 the theory for a = 0.8 agrees best
with experiment for a = 1.0, when the lift coefficients are
approximately the same .
.I 207
.T
laminar boundary layer oscillations and transition
on a flat plate .
.A
schubauer,g.b. and skramstad,h.k.
.B
naca r909, 1948.
.W
laminar boundary layer oscillations and transition
on a flat plate .
this is an account of an investigation in which oscillations
were discovered in the laminar boundary layer along a flat plate .
these oscillations were found during the course of an experiment
in which transition from laminar to turbulent flow was being
studied on the plate as the turbulence in the wind stream was
being reduced to unusually low values by means of damping
screens . the first part of the paper deals with experimental
methods and apparatus, measurements of turbulence and
sound, and studies of transition . a description is then given
of the manner in which oscillations were discovered and how
they were found to be related to transition, and then how
controlled oscillations were produced and studied in detail . the
oscillations are shown to be the velocity variations
accompanying a wave motion in the boundary layer, this wave motion having
all the characteristics predicted by a stability theory based on
the exponential growth of small disturbances . a review of this
theory is given . the work is thus experimental confirmation
of a mathematical theory of stability which had been in the
process of development for a period of approximately 40 years,
mainly by german investigators .
.I 208
.T
the hall effect in the viscous flow of ionized gas
between parallel plates under transverse magnetic field .
.A
sato,h.
.B
j.phys.soc. japan, 16, 1961, 1427.
.W
the hall effect in the viscous flow of ionized gas
between parallel plates under transverse magnetic field .
the electrical conductivity of an ionized
gas is anisotropic in the
presence of magnetic field (hall effect) .
the conductivity is expressed by
a tensor in the same form for both fully
and partially ionized gases . by
the use of modified ohm's law and
conventional magnetohydrodynamical
equations the incompressible viscous
flow between parallel plates under
the transverse magnetic field is analyzed
and an exact solution is obtained
when the magnetic reynolds number
is small . the numerical results
reveal a remarkable effect of anisotropy
of conductivity . the acceleration
and deceleration of viscous ionized
gas under combined electric and
magnetic fields are also calculated .
.I 209
.T
boundary layer induced noise in the interior of aircraft .
.A
ribner,h.s.
.B
utia r37, 1956.
.W
boundary layer induced noise in the interior of aircraft .
at high speeds the turbulent boundary layer washing the
airplane fuselage excites appreciable skin vibration, promoting strong
noise in the interior . the fluctuating exciting pressure distribution
can be represented as a pattern of moving waves (fourier integral) .
a running ripple in the skin follows underneath each wave, and the noise
is ultimately due to these ripples .
the acoustic effects of the running ripples are calculated
for an infinite sheet,. this is considered the main result of the
paper . supersonically moving ripples radiate strong sound in the form
of mach waves,. subsonically moving ripples radiate no sound . formulas
for the mean square surface pressure and the energy flux are obtained
for an assumed idealized turbulent pressure spectrum .
the results are adapted to provide a tentative estimate of
the noise generated at subsonic speeds in a practical fuselage . the
running ripples are almost noise-free, but multiple reflections at the
frames and stringers promote standing waves . an assumption is used
to link the two kinds of waves, and this leads to provisional
calculations of noise level .. on this basis the noise level is
predicted to vary as for thin boundary layers, changing
progressively to for thick layers ( = external air
density, = speed, = layer thickness, = panel thickness) . some
comparisons are made with experiment . finally, an idea for
minimizing the noise is presented .
.I 210
.T
propeller in yaw .
.A
ribner,h.s.
.B
naca r820, 1945.
.W
propeller in yaw .
it was realized as early as 1909 that a propeller in yaw
develops a side force like that of a fin . in 1917, r. g. harris
expressed this force in terms of the torque coefficient for the
unyawed propeller . of several attempts to express the side
force directly in terms of the shape of the blades, however, none
has been completely satisfactory . an analysis that
incorporates induction effects not adequately covered in previous work
and that gives good agreement with experiment over a wide
range of operating conditions is presented herein . the present
analysis shows that the fin analogy may be extended to the form
of the side-force expression and that the effective fin area may
be taken as the projected side area of the propeller . the
effective aspect ratio is of the order of 8 and the appropriate dynamic
pressure is roughly that at the propeller disk as augmented by
the inflow . the variation of the inflow velocity, for a
fixed-pitch propeller, accounts for most of the variation of side force
with advance-diameter ratio v nd .
the propeller forces due to an angular velocity of pitch are
also analyzed and are shown to be very small for the pitching
velocities that may actually be realized in maneuvers, with the
exception of the spin .
further conclusions are .. a dual-rotating propeller in yaw
develops up to one-third more side force than a single-rotating
propeller . a yawed single-rotating propeller experiences a
pitching moment in addition to the side force . the pitching
moment is of the order of the moment produced by a force equal
to the side force, acting at the end of a lever arm equal to the
propeller radius . this cross-coupling between pitch and yaw
is small but possibly not negligible .
the formulas for propellers in yaw derived herein (with the
exception of the compressibility correction) and a series of
charts of the side-force derivative calculated therefrom have been
presented without derivation in an earlier report .
.I 211
.T
effect of slight blunting of leading edge of an immersed
body on the flow around it at hypersonic speed .
.A
chernyi,g.g.
.B
nasa tt f-35, 1960.
.W
effect of slight blunting of leading edge of an immersed
body on the flow around it at hypersonic speed .
manufacturing and maintainance of ideally sharp leading edges
and noses is practically impossible, hence a discrepancy arises
between the theory established for sharp edges and actual flow
around slightly blunted edges, where a detached shock is formed
with a subsonic adjacent region . semi-empirical method is worked
out showing that the pressure distribution in the vicinity of the
leading edge is the same for different thin profiles having the same
shape of bluntness on their edges or noses . the data for a flat
plate can be used for all of them . for moderate supersonic speed
the pressure on the remaining body is practically unaffected by the
nose bluntness, and can be computed from a sharp-edge theory .
for high supersonic speed a slight blunting of the edge can
considerably alter the pattern of flow over a large region . the method
consists in replacing blunted edge by action of concentrated
forces on the flow,. it is applied to blunted wedge where it shows
doubling of the drag computed by classic theory, and to cones,
where the drag of a blunted cone may become smaller than that of
a sharp one .
.I 212
.T
theory and tunnel tests of rotor blade for supersonic
turbines .
.A
stratford,b.s. and sansome,g.e.
.B
arc r + m 3275, 1960.
.W
theory and tunnel tests of rotor blade for supersonic
turbines .
in special circumstances where a large work
output is required from a turbine in a single stage
it is necessary to use high pressure ratios across the
nozzle blades, thus producing supersonic velocities at
inlet to the rotor . as part of an investigation into such
turbines, several designs for the inter-blade passages of
the rotor have been tested in a two-dimensional tunnel,
a design theory being developed concurrently .
the first design, featuring constant passage width
and curvature as in steam-turbine practice, but having
thin leading and trailing edges, was found to suffer from
focusing of the compression waves from the concave
surface, with consequent flow separation from the
opposite convex surface . it gave a velocity coefficient of
measured at an inlet mach number of 1.90 and turning
angle of 140 deg . the measured value compares favourably
with values from previous steam tests, where the
results have been in the range from 0.65 to 0.92 .
from theoretical reasoning, and from additional test
observations, a subsequent passage was designed
having an inlet transition length of small curvature, leading
to a free-vortex passage of double the transition
curvature,. a small amount of contraction was incorporated .
schlieren photographs showed the flow in this
passage to be almost shock free . a thin region of low-energy
air existed close to the convex surface, but
liquid-injection tests located only one small bubble of reversed flow .
pressure traverses at exit indicated a velocity
coefficient of 0.952, based on the area-mean total pressure .
when allowance is made for turning angle and
reynolds number this result appears to compare quite favourably
with previous work .
it would seem that the optimum blade pitching in a turbine
would be about 20 to 30 per cent closer than in a
two-dimensional cascade . however, the resultant pitching
tends to become very close, except at very large
turning angles, with the result that in some applications
difficulties could arise in the practical design and
manufacture .
several uncertainties remain and the present design must be regarded
as still experimental .
.I 213
.T
the performance of supersonic turbine nozzles .
.A
stratford,b.s. and sansome,g.e.
.B
arc r + m 3273, 1959.
.W
the performance of supersonic turbine nozzles .
an investigation has been conducted
at the national gas turbine establishment into the
performance of turbines having high pressure ratios
per stage . the present report discusses the mode of
operation of supersonic nozzles for such turbines,
and describes a cascade experiment . both theory and
experiment demonstrate that the conditions imposed
upon the supersonic flow immediately downstream
of the nozzles (e.g., by a following row of rotor blades)
exert an overriding influence upon the nozzle outlet
flow angle, and hence upon the maximum pressure
ratio obtainable across the nozzle--providing that the
axial component of velocity is subsonic . this is an
important difference from the more familiar flow of
subsonic turbine nozzles, where, for example, the
downstream gas angle is controlled predominantly by the
nozzle blade shape and spacing . a suitable test technique
using a closed-jet tunnel is demonstrated .
the particular nozzles tested, of convergent-divergent
form, had a straight-sided divergent portion of
to axial direction) and a design mach number of 2 .
the flow was found to be well behaved as regards shock
pattern, losses, and starting over the range of pressure
ratios tested--between 9 1 and 19 1 . in particular the
efficiency at the design pressure ratio of 16.6 1 was
high, the velocity coefficient calculated from traverses of
pitot and static tubes being 0.98 .
for the conversion of pitot to total pressure at a mach
number of 2.5 a high accuracy is important in the
measurement of the static pressure,. nevertheless readings
from a conventional four-hole instrument appear to
be reliable .
.I 214
.T
on the testing of supersonic compressor cascades .
.A
staniforth,r.
.B
ngte r212, 1957.
.W
on the testing of supersonic compressor cascades .
to facilitate the development of high speed axial-flow compressors,
an investigation was made into the possibility of measuring blade
performance in a stationary cascade at supersonic speeds . a suitable
technique was developed and the losses in a variety of cascades were
measured, but these losses were too high for the blading to have any
possible application . it was concluded that if a useful compressor is
to result, it is essential to test the cascades at mach numbers close to
the existing technique was suitable only for zero incidence tests, and
thus a new approach is necessary .
some of the fundamentals of this cascade testing at low supersonic
speeds are discussed in the light of the current understanding of the
mode of operation of supersonic compressors at transonic speeds .
.I 215
.T
the test performance of highly loaded turbine stages
designed for high pressure ratio .
.A
johnston,i.h. and dransfield,d.c.
.B
ngte r235, 1959.
.W
the test performance of highly loaded turbine stages
designed for high pressure ratio .
a blade design for a highly loaded two-stage
turbine is described and the test performance of
the turbine is presented .
some of the factors affecting the performance and matching
of turbine blade rows operating at supersonic
gas velocity are discussed and investigated by means of tests
on a three-dimensional nozzle cascade tunnel
and on a variety of single-stage turbine builds .
.I 216
.T
the supersonic axial flow compressor .
.A
kantrowitz,a.
.B
naca r974, 1950.
.W
the supersonic axial flow compressor .
an investigation has been made to explore the possibilities of
axial-flow compressors operating with supersonic velocities into
the blade rows . preliminary calculations showed that very
high pressure ratios across a stage, together with somewhat
increased mass flows, were apparently possible with
compressors which decelerated air through the speed of sound in their
blading . the first phase of this investigation, which has been
reported in naca acr l5d20, was the development of efficient
supersonic diffusers to decelerate air through the speed of sound .
the present report is largely a general discussion of some of the
essential aerodynamics of single-stage supersonic axial-flow
compressors . in the supersonic flow about isolated bodies,
large energy losses usually occur due to wave systems which
extend far from the bodies . supersonic flow entering a cascade
is considered and, in this case, the possibility of entirely
eliminating this extended wave system is demonstrated,. thus, no
reason for supersonic compressors to be necessarily inefficient
is apparent . the conditions that occur as the flow through the
compressor is being started are discussed and a hypothesis as
to the type of transonic flow which will be encountered is
proposed .
as an approach to the study of supersonic compressors, three
possible velocity diagrams are discussed briefly . because of
the encouraging results of this study, an experimental
single-stage supersonic compressor has been constructed and tested in
freon-12 . in this compressor, air decelerates through the
speed of sound in the rotor blading and enters the stators at
subsonic speeds . a pressure ratio of about 1.8 at an efficiency
of about 80 percent has been obtained .
.I 217
.T
flow pattern in a converging-diverging nozzle .
.A
oswatitsch,k. and rothstein,w.
.B
naca tm.1215.
.W
flow pattern in a converging-diverging nozzle .
the present report describes a new method for the prediction
of the flow pattern of a gas in the two-dimensional and axially
symmetrical case . it is assumed that the expansion of the gas is
adiabatic and the flow stationary . the several assumptions
necessary on the nozzle shape effect, in general, no essential
limitation on the conventional nozzles . the method is applicable
throughout the entire speed range,. the velocity of sound itself
plays no singular part . the principal weight is placed on the
treatment of the flow near the throat of a converging-diverging
nozzle . for slender nozzles formulas are derived for the
calculation of the velocity components as function of the location .
.I 218
.T
intensity, scale and spectra of turbulence in mixing
region of free subsonic jet .
.A
laurence,j.
.B
naca r1292, 1956.
.W
intensity, scale and spectra of turbulence in mixing
region of free subsonic jet .
the intensity of turbulence, the longitudinal and lateral
correlation coefficients, and the spectra of turbulence in a 3.5
inch-diameter free jet were measured with hot-wire anemometers at
exit mach numbers from 0.2 to 0.7 and reynolds numbers from
the results of these measurements show the following .. (1)
near the nozzle (distances less than 4 or 5 jet diam downstream
of the nozzle) the intensity of turbulence, expressed as percent
of core velocity, is a maximum at a distance of approximately
increasing mach and or reynolds number . at distances greater
than 8 jet diameters downstream of the nozzle, however, the
maximum intensity moves out and decreases in magnitude until
the turbulence-intensity profiles are quite flat and approaching
similarity . (2) the lateral and longitudinal scales of
turbulence are nearly independent of mach and or reynolds number
and in the mixing zone near the jet vary proportionally with
distance from the jet nozzle . (3) farther downstream of the
jet the longitudinal scale reaches a maximum and then decreases
approximately linearly with distance . (4) near the nozzle the
lateral scale is much smaller than the longitudinal and does not
vary with distance from the centerline, while the longitudinal
scale is a maximum at a distance from the centerline of about
mum moves out from the centerline . (6) a statistical analysis
of the correlograms and spectra yields a /scale/ which, although
different in magnitude from the conventional, varies similarly
to the ordinary scale and is easier to evaluate .
.I 219
.T
on the strength distribution of noise sources along
a jet .
.A
ribner,h.s.
.B
utia r51, 1958.
.W
on the strength distribution of noise sources along
a jet .
the spatial distribution of noise sources along a jet is
investigated by application of lighthill's
theory to regions of 'similar'
profiles . the analysis refers to the
noise power emitted by a 'slice' of
jet (section between two adjacent planes
normal to the axis) as a function
of distance x of the slice from the nozzle .
it is found that this power
is essentially constant with x in the initial
mixing region (x law), then
further downstream (say 8 or 10 diameters
from the nozzle) falls off
extremely fast (x law or faster) in the
fully developed jet . because
of this striking attenuation of strength
with distance, it is concluded that
the mixing region produces the bulk of
the noise and must dominate in
muffler behavior,. conversely, the 'fat'
part of the jet must contribute
much less to the total noise power than is commonly supposed .
powell's experiments on the effects of nozzle velocity
profile on total noise power are interpreted
qualitatively . the behavior of
multiple-nozzle or corrugated mufflers,
both as to overall quieting and
frequency-shifting, is also interpreted
in the light of the results . the
possibility emerges that such mufflers
may be improved without serious
thrust loss by the addition of a sound-attenuating shroud .
.I 220
.T
a general purpose analogue correlator for the analysis of
random noise signals .
.A
g. a. allcock, a.m.i.e.e., a.m.brit.i.r.e.
p. l. tanner, m.sc. (eng), grad. i.e.e.
k. r. mclachlan, a.m.brit. i.r.e.
.B
.W
a general purpose analogue correlator for the analysis of
random noise signals .
a large proportion of the current research programme of the
department of aeronautics and astronautics is concerned with the
study of jet noise and boundary layer pressure fluctuations and
their effect on aircraft structures . early in the work it was
decided that for a complete description of the random processes
involved it would be necessary in the experimental programme to
make correlation measurements in addition to the more standard
spectrum and amplitude distribution measurements . it was also
felt that it would be desirable from the university point of view
to construct a general purpose correlator which could later be
used on other types of work . to this end it was decided to give
the correlator a wider bandwidth than might strictly have been
necessary for the problems on hand . subsequent development work
has amply justified this decision .
.I 221
.T
a theoretical study of annular supersonic nozzles .
.A
lord,w.t.
.B
arc r + m 3227, 1961.
.W
a theoretical study of annular supersonic nozzles .
this paper is concerned with the design
of annular supersonic nozzles to produce uniform
flow in supersonic wind tunnels which are axi-symmetrical
and which have an internal coaxial circular cylinder
throughout . symmetrical two-dimensional and conventional
axi-symmetrical nozzles are special cases of
annular nozzles .
proposals are made for design criteria sufficient to
ensure that the flow inside a nozzle is free from limit
lines and shock waves,. the criteria for (symmetrical)
two-dimensional and (conventional) axi-symmetrical
nozzles are new . the two outstanding procedures for
designing two-dimensional and axi-symmetrical nozzles
are generalised to apply to annular nozzles . one of the
design procedures is mainly analytical and the other is
mainly numerical,. the analytical expressions in both
procedures are made much more complicated by the
presence of the internal cylinder but the numerical process
criteria and the mainly numerical design procedure are
successfully applied to the design of a particular
annular nozzle .
.I 222
.T
the flow over delta wings at low speeds with leading
edge separation .
.A
marsden,d.j., simpson,r.w. and rainbird,w.j.
.B
coa r114, 1957.
.W
the flow over delta wings at low speeds with leading
edge separation .
a low speed investigation of the flow over a 40 apex angle delta
wing with sharp leading edges has been made in order to ascertain
details of the flow in the viscous region near the leading edge of the
suction surface of the wing . a physical picture of the flow was
obtained from the surface flow and a smoke
technique of flow visualization,
combined with detailed measurements of total
head, dynamic pressure, flow
directions and vortex core positions in the flow above the wing .
surface pressure distributions were also measured and integrated
to give normal force coefficients .
the results of this investigation were compared with those of other
experimental investigations and also with various theoretical results .
in particular, the normal force coefficients, vortex core positions and
attachment line positions were compared with the theoretical results of
mangler and smith, reference 19 . it was found that ..
exist on the upper surface of the wing outboard of and below
the main vortices . these secondary vortices are formed as a
result of separation of the boundary layers developing outboard
of the top surface attachment lines .
.I 223
.T
a note on the theory of the stanton tube .
.A
gadd,g.e.
.B
arc r + m 3147, 1958.
.W
a note on the theory of the stanton tube .
existing theories for the stanton tube are
critically reviewed, and the paper then outlines a
simple method which predicts the calibration function
at high reynolds numbers to the right order of
magnitude .
.I 224
.T
quasi-cylindrical surfaces with prescribed loadings
in the linearised theory of supersonic flow .
.A
jones,j.g.
.B
rae tn.aero.2769.
.W
quasi-cylindrical surfaces with prescribed loadings
in the linearised theory of supersonic flow .
a formula for the velocity field in terms of a given surface
distribution of vorticity is applied to points
lying on the surface . an equation
giving the shape of a quasi
circular-cylindrical surface in terms of a
prescribed loading is derived . as an
example a half ring wing with prescribed
loading is discussed .
.I 225
.T
elliptic cones alone and with wings at supersonic speeds .
.A
jorgensen,l.h.
.B
naca tn4045,1957
.W
elliptic cones alone and with wings at supersonic speeds .
to help fill the gap in the knowledge
of aerodynamics of shapes
intermediate between bodies of revolution
and flat triangular wings, force
and moment characteristics for elliptic
cones have been experimentally
determined for mach numbers of 1.97 and
sectional axis ratios from 1 through 6
and with lengths and base areas
equal to circular cones of fineness
ratios 3.67 and 5 have been studied
for angles of bank of 0 and 90 .
elliptic and circular cones in
combination with triangular wings of aspect
ratios 1 and 1.5 also have been
considered . the angle-of-attack range
was from 0 to about 16, and the
reynolds number was 8x10, based on
model length . in addition to the
forces and moments at angle of attack,
pressure distributions for elliptic
cones at zero angle of attack have been determined .
the results of this investigation
indicate that there are distinct
aerodynamic advantages to the use of
elliptic cones . with their major
cross-sectional axes horizontal, they
develop greater lift and have higher
lift-drag ratios than circular cones
of the same fineness ratio and volume .
in combination with triangular wings
of low aspect ratio, they also develop
higher lift-drag ratios than circular
cones with the same wings . for
winged elliptic cones, this increase
in lift-drag ratio results both from
lower zero-lift drag and drag due to
lift . visual-flow studies indicate
that, because of better streamlining
in the crossflow plane, vortex flow
is inhibited more for an elliptic cone
with major axis in the plane of the
wing than for a circular cone with the
same wing . as a result, vortex
drag resulting from lift is reduced .
shifts in center of pressure with
changes in angle of attack and mach
number are small and about the same
as for circular cones .
comparisons of theoretical and
experimental force and moment
characteristics for elliptic cones indicate
that simple linearized (flat plate)
wing theory is generally adequate even
for relatively thick cones .
zero-lift pressure distributions and drag
can be computed using van dyke's
second-order slender-body theory .
for winged circular cones, a
modification of the slender-body theory of
naca rep. 962 results in good agreement
of theory with experiment .
.I 226
.T
aerofoil theory of a flat delta wing at supersonic
speeds .
.A
robinson,a.
.B
rae r.aero.2151, 1946.
.W
aerofoil theory of a flat delta wing at supersonic
speeds .
lift, drag, and pressure distribution of a triangular
flat plate moving at a small incidence at supersonic
speeds are given for arbitrary mach number and aspect ratio .
the values obtained for lift and drag are compared with
the corresponding values obtained by strip theory . the
possibility of further applications of the analysis leading up
to the above results is indicated .
.I 227
.T
a technique for improving the predictions of linearised
theory on the drag of straight edge wings .
.A
randall,d.g.
.B
arc cp394, 1957.
.W
a technique for improving the predictions of linearised
theory on the drag of straight edge wings .
the curve of drag against mach number for straight-edged wings,
calculated by using the linearised theory of supersonic flow, displays
discontinuities in slope at the various mach numbers for which the edges
are sonic . these features, which are not observed in practice, are due
to the fact that linearised theory predicts an infinite pressure along
a subsonic or sonic edge . it is shown that if the linearised equation
of supersonic flow is used to determine the flow over straight-edged
wings, but the linearised boundary condition is replaced by the full
placed by plausible values . on this basis a simple method is derived
for improving the linearised predictions of the drag of straight-edged
wings which exhibits satisfactory agreement with experimental results .
while the technique is not directly applicable to ridge lines, an
artifice renders them amenable to similar treatment .
.I 228
.T
navier-stokes solutions at large distances from a finite body .
.A
i-dee chang
.B
.W
navier-stokes solutions at large distances from a finite body .
this paper is concerned with a theoretical investigation of the flow
field at large distances from an object moving through a viscous fluid .
the discussion will be restricted to the case of two-dimensional
stationary incompressible flow . the object will be assumed to be of
finite size . the domain of the fluid is infinite and it is assumed
that there are no other boundaries for the fluid except that of the
given object . the reynolds number will be assumed to have a fixed
value., thus we shall not consider the limiting cases of the reynolds
number tending to zero or to infinity .
.I 229
.T
interference between the wings and tail surfaces of
a combination of slender body, cruciform wings and
cruciform tail set at both incidence and yaw .
.A
owen,p.r. and anderson,r.g.
.B
rae r.aero.2471, 1952.
.W
interference between the wings and tail surfaces of
a combination of slender body, cruciform wings and
cruciform tail set at both incidence and yaw .
the interference between the wings and the tail surfaces of a
combination of circular body, low aspect ratio cruciform wings and
cruciform tail in an inviscid flow is analysed using the slender body
theory . the system may be subjected to both incidence and yaw and,
in general, the tail fins may be staggered angularly with respect to
the main wings .
the method is a development of that used by owen and maskell in
r.a.e. report no. aero.2441 to analyse similar effects on a system set
at zero yaw .
simple expressions to determine the strengths and positions of
the trailing vortices (supposed to be rolled-up) downstream of the main
wings are given, and from them the forces on the tail are deduced .
when the tail surfaces are triangular and of low aspect ratio an exact
solution is obtained from slender body theory .. but for rectangular
tail surfaces of moderate or high aspect ratio, it is suggested that the
changes in lift and sideforce on the tail caused by the wing vortex
field can be estimated approximately from the mean upwash and sidewash
angles evaluated over the respective tail spans . formulae for these
means angles are presented .
.I 230
.T
interference between the wings and tail plane of a
slender wing-body tailplane combination .
.A
owen,p.r. and maskell,e.c.
.B
rae r.aero.2441, 1951.
.W
interference between the wings and tail plane of a
slender wing-body tailplane combination .
an approximate method of predicting the interference between
the wings and the tailplane of a slender wing-body-tailplane
combination in an inviscid flow is developed, in order to explain the change
in centre of pressure position with incidence which has been found to
occur in wind tunnel and flight tests on guided weapons . incidence
changes in one plane only, normal to the plane containing the wings
and the tail surfaces, have been considered .
the method is based on slender body theory and the assumption
that the wing trailing vortices roll-up completely before they reach
the tailplane,. it is, therefore, applicable to weapons equipped with
low aspect ratio wings far separated from the tail surfaces . when
the tail surfaces are triangular and of low aspect ratio, an
analytical solution is given for the effect of the wing downwash field on
the tail lift . for high aspect ratio, rectangular tail surfaces it
is suggested by comparison with experimental data, that the tail lift
may be estimated approximately from the value of the mean downwash
angle across the tail span .
a summary of the method is given in para.5 which, in conjunction
with the introduction, may be read independently of the rest of the
report .
.I 231
.T
practical calculation of second-order supersonic flow
past non-lifting bodies of revolution .
.A
van dyke,m.d.
.B
naca tn.2744.
.W
practical calculation of second-order supersonic flow
past non-lifting bodies of revolution .
calculation of second-order supersonic flow past bodies of
revolution at zero angle of attack is described in detail, and reduced to
routine computation . use of an approximate tangency condition is shown
to increase the accuracy for bodies with corners . tables of basic
functions and standard computing forms are presented . the procedure is
summarized so that one can apply it without necessarily understanding
the details of the theory . a sample calculation is given, and several
examples are compared with solutions calculated by the method of
characteristics .
.I 232
.T
accuracy of approximate methods for predicting pressure
on pointed non-lifting bodies of revolution in supersonic
flow .
.A
ehret,d.m.
.B
naca tn.2764.
.W
accuracy of approximate methods for predicting pressure
on pointed non-lifting bodies of revolution in supersonic
flow .
the accuracy and range of applicability of the linearized theory,
second-order theory, tangent-cone method, conical-shock-expansion theory
and newtonian theory for predicting pressure distributions on pointed
bodies of revolution at zero angle of
attack are investigated . pressure
distributions and integrated pressure
drag obtained by these methods are
compared with standard values obtained
by the method of characteristics
and the theory of taylor and maccoll .
three shapes, cone, ogive, and a
modified optimum body, are investigated
over a wide range of fineness
ratios and mach numbers .
it is found that the linearized
theory is accurate only at low values
of the hypersonic similarity parameter
number to body fineness ratio) and that
second-order theory appreciably
extends the range of accurate application .
the second-order theory gives
good results on ogives when the ratio of
the tangent of maximum surface
angle to the tangent of the mach angle
is less than 0.9 . tangent-cone
method cannot be widely applied with
good accuracy . in general, the
conical-shock-expansion theory predicts
pressure and drag within
engineering accuracy when the hypersonic similarity
parameter is greater than 1.2 .
although newtonian theory gives good accuracy,
except for cones, at the
highest values of the hypersonic similarity
parameter investigated, it is
less accurate than the conical-shock-expansion theory .
.I 233
.T
the theoretical wave drag of some bodies of revolution .
.A
fraenkel,l.e.
.B
rae r.aero.2420.
.W
the theoretical wave drag of some bodies of revolution .
this report investigates the wave drag of bodies
of revolution with pointed or open-nose forebodies
and pointed or truncated afterbodies . the 'quasi-cylinder'
and 'slender-body' theories are reviewed, a reversibility
theorem is established, and the concept of the interference
effect of a forebody on an afterbody is introduced .
the theories are applied to bodies whose profiles are either
straight or parabolic arcs, formulae and curves being
given for forebody and afterbody drag, and for the interference
drag . the results of the two theories are compared
and are seen to agree well in the region of geometries where both
theories are applicable .
.I 234
.T
a second order shock-expansion method applicable to
bodies of revolution near zero lift .
.A
syvertson,c.a. and denis,d.h.
.B
naca tn.3527.
.W
a second order shock-expansion method applicable to
bodies of revolution near zero lift .
a second-order shock-expansion
method applicable to bodies of
revolution near zero lift is developed .
expressions defining the pressures on
noninclined bodies are derived by the
use of characteristics theory in
combination with properties of the flow
predicted by the generalized
shock-expansion method . this result is
extended to inclined bodies to
obtain expressions for the normal-force
and pitching-moment derivatives
at zero angle of attack . the method is
intended for application under
conditions between the ranges of applicability
of the second-order
potential theory and the generalized shock-expansion
mehtod - namely, when the
ratio of free-stream mach number to nose fineness
ratio is in the
neighborhood of 1 .
for noninclined bodies, the pressure
distributions predicted by the
second-order shock-expansion method are
compared with existing experimental
results and with predictions of other
theories . for inclined bodies, the
normal-force derivatives and locations
of the center of pressure at zero
angle of attack predicted by the method
are compared with experimental
results for mach numbers from 3.00 to 6.28 .
fineness ratio 7, 5, and 3
cones and tangent ogives were tested alone
and with cylindrical afterbodies
up to 10 diameters long . in general, the
predictions of the present method
are found to be in good agreement with the
experimental results . for
non-inclined bodies, pressure distributions
predicted with the method are in
good agreement with existing experimental
results and with distributions
obtained with the method of characteristics .
for inclined bodies, the
normal-force derivatives per radian (for
normal-force coefficients
referenced to body base area) are predicted
within 0.2 and the locations of
the center of pressure are predicted
within 0.2 body diameters . on the
basis of these results, the
second-order shock-expansion method appears
applicable for values of the ratio
of free-stream mach number to nose
fineness ratio from 0.4 to 2 .
.I 235
.T
on the minimisation and numerical evaluation of wave
drag .
.A
eminton,e.
.B
rae r.aero.2564.
.W
on the minimisation and numerical evaluation of wave
drag .
a fourier analysis of the linearised theory expression for the
zero-lift wave drag of a smooth, slender body in terms of its
cross-sectional area distribution is used
to derive the area distribution which
minimises the expression for given
length, volume, nose area, base area
and n intermediate areas . another
minimal deduced from this by relaxing
the restriction on volume is used to
evolve a method for the numerical
evaluation of the original expression .
two practical applications of these
results are discussed . the first
is in the design of wing-body combinations
to have small drag rise at
transonic speeds . the second is in the
calculation of the wave drag of
wing-body combinations at zero lift,.
an example is constructed to
illustrate the method and to give an indication of its accuracy .
.I 236
.T
criteria for thermodynamic equilibrium in gas flow .
.A
rudin,m.
.B
phys.fluids, 1, 1958.
.W
criteria for thermodynamic equilibrium in gas flow .
when gases flow at high velocity, the rates
of internal processes may not be fast enough to
maintain thermodynamic equilibrium . by defining
quasi-equilibrium in flow as the condition in which
the temperature, pressure, density, and velocity
deviate by less than a fixed, small percentage from
what they would be if the flowing gas could actually
be in thermodynamic equilibrium, criteria are
derived for determining whether quasi-equilibrium
is a stable condition in the flow . by use of
excitation of molecular vibration as an example, the
general properties of criteria curves are discussed and
interpreted . a discussion is given of how to use
these results to determine definitely whether a flow
is or is not in thermodynamic equilibrium .
applications to dissociating gases, to mixtures, and to
the phenomenon of /choking/ in a laval nozzle
are given special consideration . for cases when
application of the criteria predict nonequilibrium,
equations are provided in a form useful for
numerical forward integration along streamlines .
.I 237
.T
a compressor routine test code .
.A
n. a. dimmock
.B
communicated by the deputy controller aircraft (research and
development), ministry of aviation
.W
a compressor routine test code .
the routine testing of aircraft-type compressors.dash in the main,
axial-flow, multi-stage compressors.dash requires a compromise between
research accuracy and the practical considerations . this test code
is the outcome of a survey of compressor testing techniques and
instrumentation, initiated and subsequently discussed and endorsed
by the aerodynamics sub-committee of the gas turbine collaboration
committee .
the code aims at defining methods of measurement and weighting whereby
compressor performance can be obtained sufficiently accurately
for a realistic and direct comparison to be made between one compressor
and another . the measurement of a quantity at a point in the fluid
flow, and the averaging and weighting of such measurements have been
treated separately as far as is possible .
the recommendations are given in the main text, whilst additional
discussion on these is put into the appendices .
.I 238
.T
on a determination of the pitot-static tube factor
at low reynolds numbers, with special reference to
the measurement of low air speeds .
.A
ower,e. and johansen,f.c.
.B
arc r + m 1437, 1931.
.W
on a determination of the pitot-static tube factor
at low reynolds numbers, with special reference to
the measurement of low air speeds .
reasons for enquiry--to provide a standard instrument for
the calibration of low speed anemometers .
.I 239
.T
design and calibration at low speeds of a static tube
and a pitot-static tube with semi-ellipsoidal nose
shapes .
.A
kettle,d.j.
.B
rae tn.aero.2247, 1953.
.W
design and calibration at low speeds of a static tube
and a pitot-static tube with semi-ellipsoidal nose
shapes .
a new static tube and a new pitot-static tube have been designed and
calibrated in the no.1 and the no.2 11 ft x 8 ft wind tunnels of the
r.a.e., using a long static tube, the error of which is believed to be
very small, as a standard for comparison .
the results show that the static pressure measured by these tubes
is in error due to the supporting strut and to the nose shape of the
tube by an amount which may be calculated for positions of the static
slot, or holes, greater than 10 tube diameters ahead of the strut . the
readings show no measurable scale effect in the speed range 100-230 ft
sec . the static tube is insensitive to yaw in the range 1 with a
square-edged slot and is even less sensitive to yaw when the slot edges
are rounded . the turbulence of the tunnel has an effect on the static
pressure reading .
.I 240
.T
a theoretical analysis of heat transfer in regions of separated flow .
.A
dean r. chapman
.B
naca technote 3792
.W
a theoretical analysis of heat transfer in regions of separated flow .
the flow field analyzed consists of a thin, constant pressure
viscous mixing layer separated from a solid surface by an enclosed
region of low-velocity air (/dead air/) . the law of conservation of
energy is employed to relate calculated conditions within the
separated mixing layer to the rate of heat transfer at the solid
surface . this physical speed is app ied to alminar separations in
compressible flow for various prandtl numbers, including consideration
of the case where air is injected into the separated region .
.A
application to turbulent separations is made for a prandtl number of
.B
unity in low-speed flow without injection .
all calculations are for the case of zero boundary-layer thickness at
the position of separation .
for alminar separations the differential equations for viscous flow
at arbitrary mach number are solved for the enthalpy and velocity
profiles within the thin layer where mixing with dead air takes place .
results are presented in tabular form for prandtl numbers between 0.1
and 10 . the rate of heat transfer to a separated laminar region in air
laminar boundary layer having the same constant pressure . injection
of gas into the separated region is calculated to have a powerful effect
in reducing the rate of heat transfn to the wall . it is calculated
that a moderate quantity of gas injection reduces to zero the heat
transfer in a laminar separated flow .
.I 241
.T
laminar mixing of a non-uniform stream with a fluid
at rest .
.A
nash,j.f.
.B
arc 22245, 1960.
.W
laminar mixing of a non-uniform stream with a fluid
at rest .
a theoretical analysis is made of the constant pressure
laminar mixing process between a stream having an initial boundary layer
velocity profile, and a fluid at rest .
the present theory follows the methods of w. tollmien and
s. i. pai with certain modifications .
the results apply to incompressible
flow, but can be extended to the compressible case without difficulty .
.I 242
.T
an approximate theory of base pressure in two dimensional
flow at supersonic speeds .
.A
kirk,f.n.
.B
rae tn.aero.2377, 1954.
.W
an approximate theory of base pressure in two dimensional
flow at supersonic speeds .
an approximate theory of the base pressure in two-dimensional flow
at supersonic speeds is presented using asimplified representation of
the flow and some of the findings of tollmien's work on turbulent mixing
in incompressible flow . good qualitative predictions of the effects of
a boundary layer, of bleed air and of boat-tailing are obtained .
.I 243
.T
investigation with an interferometer of the turbulent
mixing of a free supersonic jet .
.A
gooderum,p.b., wood,g.p. and brevoort,m.
.B
naca r963, 1950.
.W
investigation with an interferometer of the turbulent
mixing of a free supersonic jet .
the free turbulent mixing of a supersonic jet of mach number
of which a description is given, was used for the investigation .
density and velocity distributions through the mixing zone
have been obtained . it was found that there was similarity
in distribution at the cross sections investigated and that, in
the subsonic portion of the mixing zone, the velocity
distribution fitted the theoretical distribution for incompressible flow .
it was found that the rates of spread of the mixing zone both
into the jet and into the ambient air were less than those of
subsonic jets .
.I 244
.T
an improved smoke generator for use in the visualisation
of airflow, particularly boundary layer flow at high
reynolds numbers .
.A
preston,j.h. and sweeting,n.e.
.B
arc r + m 2023, 1943.
.W
an improved smoke generator for use in the visualisation
of airflow, particularly boundary layer flow at high
reynolds numbers .
and rapid method by which boundary
layer flow was rendered visible has been
previously described in the journal of the royal
aeronautical society . it gave promise of
being useful at the highest tunnel speeds provided
a denser smoke could be obtained, which at
the same time was free from the troublesome deposits
associated with the wood smoke .
of the aerodynamics division attempts were made
by the fuel research station to improve the
density of the wood smoke and to reduce the
deposits . these they showed were conflicting
requirements, and whilst some improvement
was effected, it was not sufficient for observation
in the new tunnels at high speeds .
the staff of the director-general of scientific
research and development, ministry of supply,
was then approached and it was decided to
develop an oil smoke generator from a simple
generator of this type which was demonstrated
to us . this has been done successfully .
the final apparatus in contrast to the wood smoke
generator is light and compact . it takes
only a few minutes to start and can be run as long as desired .
improvement on the wood smoke both as regards
density and freedom from deposits, which cause
premature transition . the density and quality
of the smoke are now under control . smokes
ranging from a light smoke of bluish white colour
to a heavy smoke dense white in appearance
can be obtained . the oil smoke retains the
advantages of the wood smoke in that it is
non-corrosive and non-irritant, and the smell can be
tolerated even when it is present in a considerable
concentration . a certain amount of condensation
is inevitable with oil smokes, but with suitable
precautions troubles arising from this can be
avoided . a dry solid smoke made by melting a
hard wax was successfully generated with the
same apparatus . unfortunately because of its
flocculent nature this smoke gave rise to solid
deposits when passed through bore tubing,
leading eventually to complete blockage . this
seems to be a feature of solid smokes .
the apparatus has been used to determine
transition and laminar separation points on model
wings in a number of the national physical
laboratory tunnels . smoke filaments have been
maintained in the laminar state up to wind
speeds of 180 ft. sec. in the new tunnels .
there is much to be said for making a standard
practice of visualising boundary layer flow on
models, particularly as the technique is simple and
rapid . it would greatly assist the
interpretation of force measurements and the more detailed
explorations of the boundary layer by total
head tubes and hot wires .
the use of oil smoke is not limited to
boundary layer flow visualisation . the apparatus
described in this report would seem to be
particularly suited for educational work in small
demonstration tunnels .
.I 245
.T
the ground effect on the jet flap in two dimensions .
.A
huggett,d.j.
.B
arc 19,713, 1957.
.W
the ground effect on the jet flap in two dimensions .
this paper presents the results of the first part of an
experimental investigation of the ground effect on simple jet flap
aerofoils . in this part of the work an aerofoil having a 58.1 deg jet
flap was tested under two-dimensional conditions .
the pressure lift on the aerofoil was measured, with the ground
at fixed positions, for varying jet momentum coefficients . it was
found that the effect of the ground on the pressure lift was very small
up to a certain critical jet coefficient . on increasing the jet
coefficient beyond the critical value a marked loss of pressure lift was
observed . this critical value referred to is approximately the same as
the jet coefficient at which the jet first hits the ground .
some significant, though highly tentative comments, are made
regarding the practical application of this work to the take-off
characteristics of a jet flapped aircraft .
.I 246
.T
the design of minimum drag tip fins . with an appendix
- on the conformal transformation of a wing with a
fin .
.A
falkner,v.m.
.B
arc r + m 2279, 1945.
.W
the design of minimum drag tip fins . with an appendix
- on the conformal transformation of a wing with a
fin .
the report describes an investigation into
the design of minimum drag tip fins by lifting line theory . the
work is based on an exact solution of the conformal
transformation which is applicable to this problem following the
method of trefitz . three types of solution are treated,
corresponding to symmetrical upper and lower fins, single
upper or lower fins, and unequal upper and lower fins .
a representative range of solutions for circulation distribution
along wing and fins has been calculated for each of the
three cases by the use of elliptic and theta functions .
a detailed account is given, with examples, of the
procedure for calculating the plan of wing and fins, the lift and
induced drag, and the setting of the fins .
.I 247
.T
the calculation of the pressure distribution on thick
wings of small aspect ratio at zero lift in subsonic
flow .
.A
weber,j.
.B
arc r + m 2993.
.W
the calculation of the pressure distribution on thick
wings of small aspect ratio at zero lift in subsonic
flow .
the method of expressing the velocity increment
over aerofoils directly in terms of the section ordinates
wings of finite aspect ratio . the wings considered are
untapered in plan-form but may be tapered in thickness .
the section can be of any given shape so that in this sense
the analysis is more general than that of refs. 3 to 6 which
deal with wings of biconvex section .
the coefficients required in the calculation are tabulated
for the centre-section of straight and swept-back wings
of aspect ratios 0.5,. 1,. 2,. and 4, the wing of infinite
aspect ratio having been
treated in ref. 1 . the remaining calculations can be made
very quickly .
since wings of very small aspect ratio can be treated also by
the method of slender-body theory, the relations between
linear theory, slender-body theory, and linearised slender-body
theory are discussed . for the special case of ellipsoids,
the results obtained from the various methods are compared
with the exact solution .
.I 248
.T
the application of lighthill formula for numerical
calculation of pressure distributions on bodies of
revolution at supersonic speed and zero angle of attack .
.A
ohman,l.
.B
saab tn.45, 1960.
.W
the application of lighthill formula for numerical
calculation of pressure distributions on bodies of
revolution at supersonic speed and zero angle of attack .
an integral expression, given by lighthill and based
on linearized theory, for the external
supersonic flow over the surface of slender pointed
or ducted bodies of revolution at zero
angle of attack is shown to give a good approximation
of the exact flow for a much wider mach
number and thickness range than could be expected from
linearized theory . a numerical method,
based on this expression, is developed and applied for
digital computing . some results from
applying the digital computing procedure for determining
the pressure distribution and wave
drag for various bodies of revolution are given .
.I 249
.T
formulae for the computation of the functions employed
for calculating the velocity distribution about a given
aerofoil .
.A
watson,e.j.
.B
arc r + m 2176.
.W
formulae for the computation of the functions employed
for calculating the velocity distribution about a given
aerofoil .
in order to determine the velocity distribution
about an arbitrary aerofoil, it is necessary to evaluate
the functions and (in the notation of aerofoil theory)
when is given numerically . if the values of are specified
at 2n points equally spaced about the circle into which the
aerofoil is transformed, the formulae obtained here may be
used to calculate these functions at the same points .
formulae are also given for calculating the integrals of or,
since these have application to the design of aerofoils by
thwaites's numerical method .
the simplicity of the formulae for and enables
the effect on the velocity distribution of a local change of shape
readily to be determined by making n large . this is
discussed in 3 .
the formulae are collected in the appendix, and a table
of the coefficients for the case n = 20 is given .
.I 250
.T
pressure distributions at zero lift for delta wings
with rhombic cross sections .
.A
eminton,e.
.B
arc cp.525, 1960.
.W
pressure distributions at zero lift for delta wings
with rhombic cross sections .
the linearised theory of thin wings is used to calculate pressure
distributions over delta wings with rhombic cross sections . a deuce
programme has been written for the calculation and some of the results
are compared with those of slender thin wing theory .
.I 251
.T
a collection of longitudinal stability derivatives
of wings at supersonic speeds .
.A
naysmith,a.
.B
rae tn.aero.2423, 1956.
.W
a collection of longitudinal stability derivatives
of wings at supersonic speeds .
a collection has been made of
theoretical data, for wings alone, on
those stability derivatives that govern
the short-period oscillation of
aircraft travelling at supersonic speeds .
all the derivatives available
have been obtained by means of the linear
theory, and so the information
given is subject to the usual limitations .
the information has been
presented in what is hoped is the most
convenient form to show its extent,
and to expose the parts of the field
where experimental investigation is
most needed .
.I 252
.T
an investigation of interference effects on similar models of
different size in various transonic tunnels in the u.k. .
.A
f. o/hara and l. c. squire, r.a.e.
.B
and a. b. haines, a.r.a.
.W
an investigation of interference effects on similar models of
different size in various transonic tunnels in the u.k. .
details are given of a programme of tests being made on similar
swept-wing models in transonic tunnels of different types . force measurement
results at subsonic speeds in the r.a.e. 3 ft. by 3 ft. slotted tunnel
show only small interference effects for models of moderate blockage
at low incidence., at higher incidences, the interference effect on
lift becomes appreciably greater than estimated by theory, and
significant pitching moment differences occur, apparently due to wall
interference on the wing flow field . comparable but smaller effects
are evident in the results from the a.r.a. 9 ft. by 8 ft. perforated
tunnel . at speeds just above m = 1, the force fluctuates as speed
is increased, because of wave reflection interference . the magnitude
of the fluctuations diminishes as speed is further increased and this
reduction is more marked in the perforated tunnel . pressure
measurements along the top of the body at zero incidence show delay in
shock movements at high subsonic speeds indicating a blockage effect
on speed., the effect is larger in the perforated tunnel though
smaller than predicted by theory . above m = 1, both expansion and
shock waves are strongly reflected in the slotted tunnel but
considerable alleviation, particularly of shock waves, is achieved
in the perforated tunnel, for which an analysis of the effects is
given, showing for example, the effect of the open-area distribution of
the walls .
.I 253
.T
on the ground level disturbance from large aircraft
flying at supersonic speeds .
.A
lilley,g.m. and spillman,j.j.
.B
coa n103.
.W
on the ground level disturbance from large aircraft
flying at supersonic speeds .
the whitham-walkden theory for the estimation of the strength
of shock waves at ground level from aircraft flying at supersonic
speeds is applied to the case of a typical projected supersonic civil
transport aeroplane .
if a figure of 2 lb sq.ft. (including a factor of 2 for ground
reflection) is taken as an upper limit for the acceptable strength of
the bow wave from such an aircraft it is shown that restrictions on
the climb and flight plan will be involved . the advantage of the
employment of larger engines with or without afterburning is discussed,
with reference also to the penalties involved owing to the increase in
weight of the aircraft and its direct operating costs .
finally it is suggested that an aircraft of given volume could be
designed, by suitable choice of thickness and lift distribution, to
minimise the strength of the shock waves in the far field .
.I 254
.T
boundary layers with suction and injection . a review
of published work on skin friction .
.A
craven,a.h.
.B
coa r136.
.W
boundary layers with suction and injection . a review
of published work on skin friction .
available data on the effects of suction and injection on skin
friction are summarised and compared .
it is shown that injection into a turbulent boundary layer can
produce a skin friction coefficient lower than the laminar value at the
same reynolds number on an impermeable plate .
.I 255
.T
an approximate solution of the turbulent boundary layer
equations in incompressible and compressible .
.A
lilley,g.m.
.B
coa r134, 1960.
.W
an approximate solution of the turbulent boundary layer
equations in incompressible and compressible .
if over the 'outer region' of the boundary layer, where the mean
velocity varies but little from its value outside the shear layer, a
virtual eddy viscosity is defined, which is constant over the outer
region but varies in the direction of the mainstream, a solution of the
turbulent boundary layer equations can be found which satisfies the
appropriate boundary conditions . the solution leads to a compatibility
condition for the virtual eddy viscosity in terms of the wall shear
stress, the boundary layer momentum thickness and the mainstream
velocity, at least for the case of a constant external velocity . this
compatibility condition, which can be expressed as
for moderate to high reynolds numbers, where is the shear velocity,
is the boundary layer thickness and is the virtual eddy (kinematic)
viscosity, is just the condition townsend (1956) found for the
equilibrium of the large eddies . the numerical value of the constant
derived by townsend agrees with ours for reynolds numbers (based on x)
of about . with this relation for an equation, analoguous to the
momentum integral equation solution, can be found for as a function of
local freestream velocity, with one disposable parameter .
.I 256
.T
an experimental study of the glancing interaction between
a shock wave and a turbulent boundary layer .
.A
stanbrook,a.
.B
arc cp.555, 1960.
.W
an experimental study of the glancing interaction between
a shock wave and a turbulent boundary layer .
an experimental study has been made at mach numbers from 1.6 to 2.0 of
the interaction between the turbulent
boundary layer on a side wall of a wind
tunnel and the shock wave produced by
a plate mounted on the wall . under
these conditions the shock wave boundary
layer interaction was three
dimensional at least over the region
investigated (up to 10 boundary layer
thicknesses from the plate) . it was
found that the boundary layer was
separated by a shock wave of strength
type occur on the sides of fuselages at
the wing fuselage junction and may
therefore be important with regard to the
design of waisted shapes .
.I 257
.T
on turbulen flow between parallel plates .
.A
pai,s.i.
.B
j.app.mech. 20, 1953, 109.
.W
on turbulen flow between parallel plates .
the reynolds equations of motion of turbulent flow of
incompressible fluid have been studied for turbulent
flow between parallel plates . the number of these
equations is finally reduced to two . one of these consists of
mean velocity and correlation between transverse and
longitudinal turbulent-velocity fluctuations only .
the other consists of the mean pressure and transverse
turbulent-velocity intensity . some conclusions about
the mean pressure distribution and turbulent fluctuations
are drawn . these equations are applied to two special
cases .. one is poiseuille flow in which both plates are
at rest and the other is couette flow in which one plate is at
rest and the other is moving with constant velocity . the
mean velocity distribution and the correlation can
be expressed in a form of polynomial of the co-ordinate in
the direction perpendicular to the plates, with the ratio
of shearing stress on the plate to that of the corresponding
laminar flow of the same maximum velocity as a
parameter . these expressions hold true all the way across the
plates, i.e., both the turbulent region and viscous layer
including the laminar sublayer . these expressions for
poiseuille flow have been checked with experimental data
of laufer fairly well . it also shows that the logarithmic
mean velocity distribution is not a rigorous solution of
reynolds equations .
.I 258
.T
the effect of turbulence on slider bearing lubrication .
.A
chou,y.t. and saibei,e.
.B
j.app.mech. 25, 1959, 122.
.W
the effect of turbulence on slider bearing lubrication .
based on prandtl's mixing-length mechanism, the pressure
equation for turbulent flow in
slider-bearing lubrication is derived . an analytical
solution is given and compared with
the one for laminar flow . it is found that the turbulent
effect increases the pressure and
consequently, the load-carrying capacity . however, the
power loss also increases .
.I 259
.T
second order theory for unsteady supersonic flow
past slender pointed bodies of revolution .
.A
revell, j. d.
.B
j. ae. scs.1960, 730.
.W
second order theory for unsteady supersonic flow
past slender pointed bodies of revolution .
the thermodynamic properties (z = pv rt, e rt, h rt, s r,
and pressure) are given for equilibrium mixtures of dissociated and
ionized molecules and atoms of the elements nitrogen and oxygen
having the low temperature composition of .78847 n and .21153 o .
the tabulated properties of this mixture (a close approximation to
the properties of air) are given at close intervals from 2000 to
and 10 times the normal density . the results are based on
chemical equilibria between the species o, o, n, n, no, no, no,
no, o, o, o, o, n, n, n and electrons . the method of
presentation permits later corrections for the effect of argon and co
and the contribution of intermolecular forces . the calculations are
based on 9.758 e.v. as the dissociation energy of molecular nitrogen
and 1.45 e.v. as the electron affinity of atomic oxygen .
.I 260
.T
a critical review of skin friction and heat transfer
solutions of the laminar boundary layer of a flat plate .
.A
rubesin,m.w. and johnson,h.a.
.B
asme trans. 1949.
.W
a critical review of skin friction and heat transfer
solutions of the laminar boundary layer of a flat plate .
a review is made of existing literature concerned with
the analytical investigation of the velocity and
temperature distributions in the boundary layers of a heated (or
cooled) flat plate . the plate is postulated infinitely thin
and is parallel to a uniform fluid stream . the more
recent solutions include the combined effects of frictional
dissipation and variable fluid properties . only the results
pertaining to the transfer phenomena occurring at the
plate surface are included, i.e., skin drag and over-all
heat transfer,. the individual temperature and velocity
distributions leading to these results are omitted .
.I 261
.T
experiments on axi-symmetric boundary layers along
a long cylinder in incompressible flow .
.A
yashura,m.
.B
trans. japan soc.ae.sc. 2, 1959.
.W
experiments on axi-symmetric boundary layers along
a long cylinder in incompressible flow .
experiments on axi-symmetric boundary
layers along a long cylinder were made
especially to investigate the effect of transverse
curvature on the velocity profile . laminar
velocity profiles were measured and compared
with theoretical ones with good accuracy .
a representative profile was plotted to see the
effect of transverse curvature, which showed
small, but obvious effect accompanied by
increasing skin friction .
the transition of the flow from laminar to
turbulent was observed, and its reynolds
number was estimated to occur at 1.2 1.8x10
in the present experiment . the turbulent
profile was also measured and plotted by using
the coordinates to express the wall law
deduced by richmond, from which it was
estimated that, as the ratio of the momentum
thickness to body radius increases, the profile
near the outer layer tends to bend down
relative to the line of logarithmic wall law .
.I 262
.T
the formation of a blast wave by a very intense explosion .
.A
taylor,g.i.
.B
proc. roy. soc. a, 201, 1950, 159.
.W
the formation of a blast wave by a very intense explosion .
this paper was written early in 1941
and circulated to the civil defence research
committee of the ministry of home security
in june of that year . the present writer
had been told that it might be possible
to produce a bomb in which a very large
amount of energy would be released by
nuclear fission--the name atomic bomb had
not then been used--and the work here
described represents his first attempt to form
an idea of what mechanical effects might
be expected if such an explosion could occur .
in the then common explosive bomb mechanical
effects were produced by the sudden
generation of a large amount of gas at a high
temperature in a confined space . the
practical question which required an answer
was .. would similar effects be produced
if energy could be released in a highly
concentrated form unaccompanied by the
generation of gas .qm this paper has now
been declassified, and though it has been
superseded by more complete calculations,
it seems appropriate to publish it as it was
first written, without alteration, except for
the omission of a few lines, the addition of
this summary, and a comparison with some
more recent experimental work, so that
the writings of later workers in this field may be appreciated .
an ideal problem is here discussed . a finite
amount of energy is suddenly released
in an infinitely concentrated form . the motion
and pressure of the surrounding air is
calculated . it is found that a spherical shock
wave is propagated outwards whose
radius r is related to the time t since the explosion
started by the equation
where is the atmospheric density, e is
the energy released and s a calculated
function of, the ratio of the specific heats of air .
the effect of the explosion is to force most
of the air within the shock front into a
thin shell just inside that front . as the front
expands, the maximum pressure
decreases till, at about 10 atm., the analysis ceases
to be accurate . at 20 atm. 45 of
the energy has been degraded into heat which is
not available for doing work and used
up in expanding against atmospheric pressure .
this leads to the prediction that an
atomic bomb would be only half as efficient, as
a blast-producer, as a high explosive
releasing the same amount of energy .
in the ideal problem the maximum pressure is
proportional to r, and comparison
with the measured pressures near high explosives,
in the range of radii where the two
might be expected to be comparable, shows that
these conclusions are borne out by
experiment .
.I 263
.T
cylindrical shock waves produced by instantaneous energy
release .
.A
lin,s.c.
.B
j.app.phys. 25, 1954, 54.
.W
cylindrical shock waves produced by instantaneous energy
release .
taylor's analysis of the intense spherical explosion
has been extended to the cylindrical case . it is found
that the radius r of a strong cylindrical shock wave
produced by a sudden release of energy e per unit length
grows with time t according to the equation
where is the atmospheric density and
is a calculated function of the specific
heat ratio . for is found to be approximately
unity . for this case, the pressure behind the
shock wave decays with radius r according to the relation .
applying the results of this analysis
to the case of hypersonic flight, it can be shown that
the shock envelope behind a meteor or a high-speed
missile is approximately a paraboloid given by
where d and v denote the total
drag and the velocity of the missile, respectively,
and x is the distance behind the missile .
.I 264
.T
asymptotic solution of the two dimensional oscillating
aerofoil problem for high subsonic mach numbers .
.A
eckhaus,w.
.B
proc. 9th int. con. app.mech. 1956.
.W
asymptotic solution of the two dimensional oscillating
aerofoil problem for high subsonic mach numbers .
a new method has been given, for obtaining asymptotic solutions of a
boundary value problem for the wave equation . the method is simpler
than the method previously given by burger, and leads to a result
identical with burger's result .
.I 265
.T
some instabilities arising from the interaction between
shock waves and boundary layer .
.A
lambourne,n.c.
.B
npl aero.348, 1958.
.W
some instabilities arising from the interaction between
shock waves and boundary layer .
a brief review is made of the available information concerning
the flow fluctuations and instabilities arising from shock-induced
separation in the flow over aerofoils and wings . the influence this
phenomenon has on the oscillatory behaviour of aerofoils and control
surfaces is also briefly discussed .
a more detailed consideration is devoted to a recent investigation
at the n.p.l. into the part played by shock-induced separation in the
instability of a control surface .
.I 266
.T
exact solution of the neumann problem . calculation
for non- circulatory plane and axially symmetric flows
about or within arbitrary boundaries .
.A
smith,a.n.c. and pierce,j.
.B
3rd nat. con. app. mech. 1958.
.W
exact solution of the neumann problem . calculation
for non- circulatory plane and axially symmetric flows
about or within arbitrary boundaries .
an exact general method of solving
the neumann or second boundary-value
problem has been developed and has been
applied to the calculation of
low-speed flows about or within bodies of
almost any shape, provided the flow is
either plane or has axial symmetry .
solid-body, inlet, and purely internal
flow problems can be solved . the
method is capable of dealing with several
bodies at once in the presence of
one another, and consequently interference
problems can be treated with ease .
boundaries need not be solid, that is,
flows involving area suction can be
calculated . velocities can be computed
not only for points on the surface of
the body but for the entire flow field .
a surface source distribution is
used as a basis for solution . this
leads to a fredholm integral equation
of the second kind, which is solved as
a set of linear algebraic equations,
usually by a modified seidel method .
at the present time the solution is
programed on the ibm 704 edpm to solve
the flow about any body that has the
previously mentioned characteristics
and whose profile can be defined
satisfactorily by no more than 300
coordinate points . a number of solutions
are presented, to show both the scope
of the method and its accuracy .
computations require from three minutes
to two hours, depending upon the
shape of the body and the number of points
used to define it .
.I 267
.T
steady and transient free convection of an electrically
conducting fluid from a vertical plate in the presence
of a magnetic field .
.A
gupta,s.
.B
app. sc. res. 9, 1959.
.W
steady and transient free convection of an electrically
conducting fluid from a vertical plate in the presence
of a magnetic field .
an analysis is made for the laminar
free convection and heat transfer of
a viscous electrically conducting fluid
from a hot vertical plate in the case
when the induced field is negligible
compared to the imposed magnetic field .
it is found that similar solutions for
velocity and temperature exist when
the imposed magnetic field (acting
perpendicular to the plate) varies inversely
as the fourth root of the distance from
the lowest end of the plate . explicit
expressions for velocity, temperature,
boundary layer thickness and nusselt
number are obtained and the effect
of a magnetic field on them is studied .
it is found that the effect of the
magnetic field is to decrease the rate of
heat transfer from the wall . in the
second part, the method of characteristics
is employed to obtain solutions of
the time-dependent hydromagnetic free
convection equations (hyperbolic) of
momentum and energy put into integral
form . the results yield the time required
for the steady flow to be established,
and the effect of the magnetic field on this time is studied .
.I 268
.T
several magnetohydrodynamic free-convection solutions .
.A
cramer,k.r.
.B
5th nat. heat transfer con. 1962.
.W
several magnetohydrodynamic free-convection solutions .
the influence of transverse magnetic fields on
the laminar free-convection flow of liquid
metals over a vertical flat plate and between
vertical parallel plates is examined for
specific wall temperature variations and
prandtl numbers . the extent of influence on
the flow and temperature fields is determined
by the magnitude of a nondimensional
influence parameter which is the ratio of the
magnetic force to the buoyant force . in
general, increasing the magnetic field strength
decreases the magnitude of the velocity, wall
shear, and surfaces heat transfer and
increases the temperature throughout the fluid .
analytical results demonstrate that magnetic
fields of practical strengths exert
considerable influence on liquid metal free-convection flow fields .
.I 269
.T
on a laminar free-convection flow and heat transfer
of electrically conducting fluid on a vertical flat
plate in the presence of a transverse magnetic field .
.A
mori,y.
.B
trans. japan soc. ae. sc. 2, 1959.
.W
on a laminar free-convection flow and heat transfer
of electrically conducting fluid on a vertical flat
plate in the presence of a transverse magnetic field .
the free-convection flow and heat transfer of an
electrically conducting fluid on a
vertical plate in the presence of a transverse magnetic
field is analysed for a magnetic field
fixed to the electrically non-conducting wall . the
boundary layer equations for
self-preserving flows are integrated numerically for the
prandtl number of unity, and the effect
of the transverse magnetic field on the velocity
profile, temperature profile and rate of
heat transfer is discussed . it is concluded that
the heat transfer rate is reduced as the
magnetic field intensity is increased .
.I 270
.T
on combined free and forced convection laminar magnetohydrodynamic
flow and heat transfer in channels with transverse
magnetic field .
.A
mori,y.
.B
int. devel. in heat transfer,1961.
.W
on combined free and forced convection laminar magnetohydrodynamic
flow and heat transfer in channels with transverse
magnetic field .
combined free and forced convective heat
transfer in vertical channels has been studied by many
researchers . due to the need for engineering design
information there have been many papers concerning
cases of fully developed flow with varying wall
temperature . forced flows in a channel of electrically
conducting fluid with a transverse magnetic field
have been studied and the large effects of a magnetic
field on the flow pattern have been established .
flows of combined free and forced convection in
electrically conducting fluids in vertical channels
with a transverse magnetic field are expected to
attract attention in future engineering applications, for
example, in a magneto-hydrodynamic generator or in
plasma studies . however, except for a report by
gershuni and zhukhovitskii (1) concerning a
particular case, no general study has been published .
this paper is a general treatment of fully
developed, free and forced convective, laminar,
magneto-hydrodynamic flow in a vertical channel with a
transverse magnetic field . it includes combined free and
forced convective flows in channels without a
magnetic field reported by ostrach (2), tao (3), etc. as
special cases . hartmann flow (4) is included in the
other limit .
.I 271
.T
an experimental test of compressibility transformation
for turbulent boundary layer .
.A
squire,w.
.B
j. ae. sc. 29, 1962.
.W
an experimental test of compressibility transformation
for turbulent boundary layer .
discussion of various turbulent-boundary-layer theories, in
the light of experimental measurements by matting and co-workers .
the application of (1) the mager insulated-wall transformation, and
and illustrated graphically .
.I 272
.T
oscillatory aerodynamic coefficients for a unified supersonic
hypersonic strip theory .
.A
rodden, w. +. and revell, j.d.
.B
j. ae. scs. 1960, 451.
.W
oscillatory aerodynamic coefficients for a unified supersonic
hypersonic strip theory .
the shock tube is shown to be a feasible research tool for
conducting boundary-layer transition experiments . the use of the
shock tube permits the study of transition with highly cooled
boundary layers, as may be encountered on hypersonic vehicles .
boundary-layer transition investigations have been made on
optically polished pyrex hemisphere-cylinder and ellipse-cylinder
models with stagnation-to-wall enthalpy ratios between 4.5 and
roughness estimated to be less than 1 microinch (rms) .
transition was detected by measurements of the heat-transfer rates on
the model surface .
the shock tube experiments indicated that a characteristic
feature of transition of a highly cooled boundary layer on a
hemisphere was the simultaneous occurrence of transition over the
entire supersonic portion of the hemisphere . this implies that
transition first occurred in the sonic region . the transition
reynolds number (based on local fluid properties at the outer
edge of the boundary layer and the momentum thickness) in the
sonic region increased from about 225 to 325 as the stagnation-
to-wall enthalpy ratio increased from about 9.5 to 29.5 . transition
occurred along the cylindrical portion of the hemisphere-cylinder
model at a nearly constant momentum thickness reynolds
number, increasing from about 400 to 625 as the stagnation-
to-wall enthalpy ratio increased from about 9.5 to 29.5 .
the highly cooled boundary layers obtained on the cylindrical
portion of the shock tube hemisphere-cylinder model provided an
extension of nasa transition results obtained on a cooled
hemisphere-cone-cylinder model in a wind tunnel . the transition
reynolds numbers obtained from these shock tube data were of
the same order of magnitude as the minimum transition
reynolds numbers obtained in the wind-tunnel experiments . the
results indicate that, for practical purposes, boundary-layer
cooling is not a critical transition parameter for blunt bodies with
a highly cooled boundary layer resulting from a stagnation-
to-wall enthalpy ratio of about 3 to 30 . that is, the transition
reynolds number did not vary significantly with boundary-
layer cooling in this cooling range, but transition always occurred
at a low reynolds number (between about 350,000 and 750,000
based on local external properties and a distance along the body
surface from the stagnation point) .
the boundary-layer history (body shape history) appeared to
be an important parameter affecting the magnitude of the
reynolds number for transition and the amount of increase in the
transition reynolds number with increased boundary-layer
cooling . that is, transition occurred at a lower reynolds
number on the ellipse-cylinder configuration than on the
hemisphere-cylinder . also, the increase in transition reynolds number with
an increase in boundary-layer cooling was even less significant
for the ellipse-cylinder than the hemisphere-cylinder .
.I 273
.T
flow past slender blunt bodies - a review and extension .
.A
capiaux,r. and karchmar,l.
.B
paper 61-201-1904, nat. ias-ars joint meeting, 1961.
.W
flow past slender blunt bodies - a review and extension .
a numerical solution of the inviscid flow field about slender blunt
bodies of revolution has been developed through a combination of two
methods .. the van dyke solution in the subsonic flow
region at the nose, and the method of
characteristics in the supersonic region .
the results are compared with
second-order blast wave theory and with experimental
data,. and the respective merits and
deficiencies of the two theoretical methods
are pointed out . the results of the
numerical solution are further used in a
discussion of the entropy layer, to
propose a possible criterion of entropy layer thickness .
.I 274
.T
analysis of quartz and teflon shields for a particular
re-entry mission .
.A
adams,e.w.
.B
heat transfer and fluid mech. inst. 1961, 222.
.W
analysis of quartz and teflon shields for a particular
re-entry mission .
the transient performance of
ablation type heat protection shields is
treated herein for the surface of
a vehicle returning from outer space to the
earth . the vehicle weighs 8640 kg,
has a ballistic factor of 500 lb ft,
re-enters with a speed of 11 km sec at
ratio of 0.5, and is subjected to a
maximum deceleration of 7.7 times the
gravity constant .
by use of well known equations
for the heat transfer and the mass
transfer at a heated surface, a numerical
calculation method is derived which, for
the investigated ablation processes,
yields exact transient solutions of the
fundamental system of partial differential
equations . the method is applied
to various quartz shields and to one
teflon shield, which all evaporate so
readily under the conditions of the
problem at hand that practically no flow
of molten shield material exists .
the solutions also show comparatively small
temperature changes parallel to the surface .
the results show that the nose
of the vehicle is cooled predominantly by
the evaporation of the quartz or the
teflon,. the rest of the vehicle's surface
is cooled by radiation of the quartz
or evaporation of the teflon . the large
mass transfer effects on the nose of
the vehicle are detrimental since the
resulting low surface temperatures prevent
the radiative heat transfer out of
the shield, which does not involve any
mass loss, from being the desirable
governing cooling factor .
.I 275
.T
the effect of lift on entry corridor depth and guidance
requirements for the return lunar flight .
.A
wong,t. and slye,r.
.B
nasa r-80, 1960.
.W
the effect of lift on entry corridor depth and guidance
requirements for the return lunar flight .
corridors for manned vehicles are
defined consistent with requirements
for avoiding radiation exposure and for
limiting values of peak
deceleration . use of lift increases the depth
of the entry corridor . mid-course
guidance requirements appear to be critical
only for the flight-path angle .
increasing the energy of the transfer orbit
increases the required guidance
accuracy for the flight-path angle .
corrective thrust applied essentially
parallel to the local horizontal
produces the maximum change in perigee
altitude for a given increment of
velocity . energy required to effect a
given change in perigee altitude
varies inversely with range measured
from the center of the earth .
.I 276
.T
reaction tests of turbine nozzles for supersonic velocities .
.A
keenan,j.h.
.B
asme trans. 1949, 773.
.W
reaction tests of turbine nozzles for supersonic velocities .
a machine for testing turbine nozzles by the reaction
method, which was described in a previous paper, was
used to test a series of convergent-divergent turbine
nozzles . the results of these tests, along with the test
of a convergent turbine nozzle, are compared with each
other and with analytical values . two kinds of analytical
values are employed, namely, the usual values obtained
from an assumed isentropic expansion from inlet state to
exhaust pressure, and the values obtained from the
assumption that the processes in the nozzle are isentropic
except for a normal shock which takes up a position in the
nozzle such as to cause the stream to fill the exit area at
the exhaust pressure whenever possible . this latter kind
of analytical value involves no shock when the exit area can
be filled at the exhaust pressure by means of isentropic
processes only, or when the exhaust pressure is lowered
so far that the shock has passed out of the passage . the
agreement of the test results with the calculated results
of this latter kind is good, and the disagreement which
exists can be attributed largely to separation at the shock
and to transmission of exhaust-pressure effects upstream
through the boundary layer .
.I 277
.T
study of flow conditions and deflection angle at exit
of two-dimensional cascade of turbine rotor blades
at critical and supercritical pressure ratios .
.A
hauser,c.h., plohr,h.w. and sonder,g.
.B
naca rm e9k25, 1950.
.W
study of flow conditions and deflection angle at exit
of two-dimensional cascade of turbine rotor blades
at critical and supercritical pressure ratios .
an analysis was made of the flow conditions downstream of a
cascade of turbine rotor blades at critical and supercritical
pressure ratios . the results of five theoretical methods for
determining the deflection angle are compared with those of an experimental
method using the conservation-of-momentum principle and
static-pressure surveys, and also are compared with an analysis of
schlieren photographs of the flow downstream of the blades . a two-
dimensional cascade of six blades with an axial width of 1.80 inches
was used for the static-pressure surveys and for some of the
schlieren photographs . in order to determine the flow conditions several
blade chords downstream of the cascade, schlieren photographs were
taken of the flow through a cascade of 18 blades having an axial
width of 0.60 inch .
for the blade design studied, even at static-to-total pressure
ratios considerably lower than that required to give critical
velocity at the throat section, the flow was deflected in the tangential
direction as predicted for the incompressible case . as the pressure
ratio was lowered further, the aerodynamic loading of the rear
portion of the blade reached a maximum value and remained constant .
after this condition was attained, the expansion downstream of the
cascade took place with a constant tangential velocity so that no
further increase in the amount of turning across the blade row and
no further increase in the loading of the blade was available .
.I 278
.T
on source and vortex distributions in the linearised
theory of steady supersonic flow .
.A
robinson,a.
.B
q.j.mech.app.math. 1948.
.W
on source and vortex distributions in the linearised
theory of steady supersonic flow .
the hyperbolic character of the differential
equation satisfied by the velocity
potential in linearized supersonic flow entails
the presence of fractional infinities
in the fundamental solutions of the equation .
difficulties arising from this fact can
be overcome by the introduction of hadamard's
finite part of an infinite integral .
together with the definition of certain counterparts
of the familiar vector operators
this leads to a natural development of the analogy
between incompressible flow
and linearized supersonic flow . in particular, formulae
are derived for the field of
flow due to an arbitrary distribution of supersonic
sources and vortices .
applications to aerofoil theory, including the
calculation of the downwash in the
wake of an aerofoil, are given in a separate report (ref. 9) .
.I 279
.T
supersonic drag calculations for a cylindrical shell
wing of semicircular cross section combined with a
central body of revolution .
.A
beane,b.j. and ryna,b.m.
.B
douglas sm22627, 1956.
.W
supersonic drag calculations for a cylindrical shell
wing of semicircular cross section combined with a
central body of revolution .
a semi-circular ring wing with a body of revolution on
the axis is studied to find the wave and the vortex drag for
various chordwise lift distributions and for three values of
a parameter describing the wing geometry . using the
wave drag obtained from the chordwise loading that gives the
least drag, together with the vortex and skin friction drags,
the maximum lift to drag ratio for each wing geometry is
computed . compared to the estimates made by lomax and
heaslet, somewhat lower drags are found .
.I 280
.T
the surface oil flow technique as used in high speed
wind tunnels in the united kingdom .
.A
stanbrook,a.
.B
rae tn.aero.2712, 1960.
.W
the surface oil flow technique as used in high speed
wind tunnels in the united kingdom .
an examination has been made of the
various versions of the surface oil
flow technique used in different high speed
wind tunnels . to provide
background information for this investigation
some systematic tests were made on
a simple model in a small supersonic tunnel .
the experience gained made it
possible to explain many of the variations
in terms of the different operating
conditions of the tunnels .
the time taken to form a pattern
on a typical model is, to a first
approximation, directly proportional to
the value of the parameter,
the factor being 36,000 12,000 . the
time taken appears to be independent
of the initial thickness of the oil sheet .
a general procedure for the development
of oil mixtures for any purpose
is suggested .
.I 281
.T
higher order approximations for relaxation oscillations .
.A
.B
.W
higher order approximations for relaxation oscillations .
the problem of solving asymptotic developments for all quantities
involved in relaxation oscillations has been solved by haag . this
paper indicates how one can carry out such developments in a case
which is simple enough to be treated explicitly .
.I 282
.T
jet effects on base pressure of conical afterbodies
at mach 1. 91 and 3. 12 .
.A
baughman,l.e. and kochendorfer,f.d.
.B
naca rm e57e06.
.W
jet effects on base pressure of conical afterbodies
at mach 1. 91 and 3. 12 .
data are presented which show the effect of a jet on base pressure
for a series of conical afterbody-jet-nozzle combinations having
boat-tail angles that varied from 0 to 11 and base-to-jet diameter ratios
that varied from 1.11 to 2.67 . the jet nozzles had exit angles from 0
to 20 and were designed for exit mach numbers from 1.0 to 3.2 .
pressure ratios up to 30 were tested for both a cold (air) and a hot
numbers of 1.91 and 3.12 .
in general, base pressure increased for increasing values of
boat-tail angle, nozzle angle, jet temperature, and jet total pressure and
for decreasing values of base-to-jet diameter ratio, jet mach number,
and free-stream mach number . the addition of tail surfaces produced
only small changes in base pressure .
for all variables, base pressure is governed by the maximum
pressure rise that can be supported by the wake fluid in the region of the
trailing shock . the wake pressure ratio is in turn governed by the jet
and free-stream mach numbers adjacent to the wake region and by the
state of the boundary layer on the boattail and on the nozzle .
values of wake pressure ratio computed using the theory of korst,
page, and childs were in good agreement with experimental values for
convergent nozzles .
.I 283
.T
laminar heat transfer around blunt bodies in dissociated
air .
.A
kemp,n.h., rose,p.h. and detra,r.w.
.B
j.ae.sc. 26, 1959.
.W
laminar heat transfer around blunt bodies in dissociated
air .
a method of predicting laminar heat-transfer rates to blunt,
highly cooled bodies with constant wall temperature in dissociated
air flow is developed . attention is restricted to the case of
axisymmetric bodies at zero incidence, although two-dimensional
bodies could be treated the same way . the method is based on
the use of the /local similarity/ concept and an extension of the
ideas used by fay and riddell . a simple formula is given for
predicting the ratio of local heat-transfer rate to stagnation-point
rate . it depends on wall conditions and pressure distribution,
but not on the thermodynamic or transport properties of the hot
external flow, except at the stagnation point .
experimental heat-transfer rates obtained with correct
stagnation-point simulation and high wall cooling in shock tubes are
also presented and compared with the theoretical predictions .
on the whole, the agreement is good, although in regions of
rapidly varying pressure there is evidence that the local similarity
assumption breaks down, and the theory underestimates the
actual heat-transfer rate by up to 25 per cent .
.I 284
.T
the divergence of supersonic wings including chordwise
bending .
.A
biot,m.a.
.B
j. ae. scs. 23, 1956.
.W
the divergence of supersonic wings including chordwise
bending .
the static aeroelastic stability or divergence problem is
investigated for thin supersonic wings when not only the spanwise
bending and twist are taken into account but also the chordwise
bending . the problem is treated in successive phases of
increasing complexity from the two-dimensional curling-up of the
leading edge to the three-dimensional stability of the cantilever
wing . several methods of approach are developed including
the nonlinear aspects of the structure and the aerodynamics .
results indicate a strong dependence of stability on poisson's
ratio and the magnitude of the deformation .
.I 285
.T
on the flutter of panels at high mach numbers .
.A
hedgepeth,j.m.
.B
j.ae.scs. 23, 1956.
.W
on the flutter of panels at high mach numbers .
there have recently arisen some questions as to the
possibility of panel flutter at high dynamic pressures and
mach numbers . in addition, some doubts have been raised
about the convergence of the galerkin method when applied to
such problems . this note is intended to shed light on these
matters .
.I 286
.T
effect of roll on dynamic instability of symmetric
missiles .
.A
murphy,c.h.
.B
j. ae. scs. 21, 1954.
.W
effect of roll on dynamic instability of symmetric
missiles .
this note attempts to extend the discussion by stating a
slightly neater form of generalized stability conditions and
describing certain experimental results on dynamic instability .
.I 287
.T
some theoretical low-speed loading characteristics
of swept wings in roll and sideslip .
.A
bird,j.d.
.B
naca r969, 1950.
.W
some theoretical low-speed loading characteristics
of swept wings in roll and sideslip .
the weissinger method for determining additional span
loading for incompressible flow is used to find the damping in
roll, the lateral center of pressure of the rolling load, and the
span loading coefficients caused by rolling for wing plan forms
of various aspect ratios, taper ratios, and sweep angles . in
addition, the applicability of the method to the determination
of certain other aerodynamic derivatives is investigated, and
corrections for the first-order effects of compressibility are
indicated .
the agreement obtained between experimentally and
theoretically determined values for the aerodynamic coefficients
indicates that the method of weissinger is well suited to the
calculation of the additional span loading caused by rolling
and for the calculation of such resulting aerodynamic
derivatives of wings as do not involve considerations of tip suction .
.I 288
.T
the rolling up of the trailing vortex sheet and its
effect on the downwash behind wings .
.A
spreiter,j.r. and sacks,a.h.
.B
j. ae. scs. 18, 1951.
.W
the rolling up of the trailing vortex sheet and its
effect on the downwash behind wings .
the motion of the trailing vortices associated with a lifting wing
is investigated by theoretical and visual-flow methods for the
purpose of determining the proper vortex distribution to be used
for downwash calculations . both subsonic and supersonic speeds
are considered in the analysis .
it is found that the degree to which the vortices are rolled up
depends upon the distance behind the wing and upon the lift
coefficient, span loading, and aspect ratio of the wing . while the
rolling up of the trailing vortices associated with high
aspect-ratio wings is of little practical importance, it is shown that, with
low-aspect-ratio wings, the trailing vortex sheet may become
essentially rolled up into two trailing vortex cores within a chord
length of the trailing edge .
the downwash fields associated with the two limiting cases of
the flat vortex sheet and the fully rolled-up vortices are
investigated in detail for both subsonic and supersonic speeds . the
intermediate case in which the rolling-up process is only partially
completed at the tail position is also discussed .
.I 289
.T
a theoretical study of the aerodynamics of slender
cruciform-wing arrangements and their wakes .
.A
spreiter,j.r. and sacks,a.h.
.B
naca r1296, 1957.
.W
a theoretical study of the aerodynamics of slender
cruciform-wing arrangements and their wakes .
a theoretical study is made of some cruciform-wing
arrangements and their wakes by means of slender-body theory . the
basic ideas of this theory are reviewed and equations are
developed for the pressures, loadings, and forces on slender
cruciform wings and wing-body combinations . the rolling-up of
the vortex sheet behind a slender cruciform wing is considered
at length and a numerical analysis is carried out using 40
vortices to calculate the wake shape at various distances behind
an equal-span cruciform wing at 45 bank . analytical
expressions are developed for the corresponding positions of
the rolled-up vortex sheets using a 4-vortex approximation to
the wake, and these positions are compared with the positions
of the centroids of vorticity resulting from the numerical analysis .
the agreement is found to be remarkably good at all distances
behind the wing .
photographs of the wake as observed in a water tank are
presented for various distances behind a cruciform wing at 0
and 45 bank . for 45 bank, the distance behind the wing
at which the upper two vortices pass between the lower two is
measured experimentally and is found to agree well with the
the calculation of loads on cruciform tails is considered in
some detail by the method of reverse flow, and equations are
developed for the tail loads in terms of the vortex positions
calculated in the earlier analyses .
.I 290
.T
dynamic stability of a missile in rolling flight .
.A
bolz,r.e.
.B
j. ae. scs. 19, 1952.
.W
dynamic stability of a missile in rolling flight .
the paper sets down the equations of motion for a symmetric
rolling missile with respect to axes attached to the missile . the
missile may be jet (or rocket) propelled or coasting under
accelerating or decelerating conditions, respectively, wherein the
variable rolling velocity is derived from intentionally or
unintentionally /canted/ fins and or wings .
the equations contain a force and moment system that
includes, in addition to the usual forces and moments, those due to
magnus effects, misaligned surfaces, canted surfaces, jet
misalignment, and the linear accelerations in the plane normal to the
missile axis .
the results present general stability criteria for a rolling missile
which are summarized in the /discussion of stability ./
.I 291
.T
sweepback effects in the turbulent boundary-layer shock-wave
interaction .
.A
stalker,r.j.
.B
j. ae. scs. 27, 1960.
.W
sweepback effects in the turbulent boundary-layer shock-wave
interaction .
experiments are reported on the interaction of turbulent
boundary layers and shock waves with sweptback configurations .
they show that the peak pressure rise at separation, the
upstream influence ahead of separation, and the pressure rise at
reattachment for moderate sweep angles can all be understood by
simple extensions of available two-dimensional theories .
.I 292
.T
rapid laminar boundary layer calculations by piece-wise
application of similar solutions .
.A
smith,a.m.o.
.B
j. ae. scs. 23, 1956.
.W
rapid laminar boundary layer calculations by piece-wise
application of similar solutions .
a method is presented for the rapid calculation of the
incompressible laminar boundary layer in an arbitrary flow around
either a two-dimensional or a rotationally-symmetrical body .
the solution is obtained without recourse to von karman's
momentum equation by means of a coarse step-by-step procedure
in which each segment of the velocity distribution is
approximated by one of the falkner-skan family of similar flows .
solutions have at least as much accuracy as those of any other
one-parameter approximate method, and in certain cases the
solutions become exact . in regions of accelerating velocity, the
accuracy appears to be very high . in decelerating flows,
separation is predicted somewhat early compared with exact solutions
that is, the method is conservative in contrast to the von
karman-pohlhausen procedure which sometimes fails to predict
separation that actually exists .
the method is the most rapid hand procedure known to the
author, provided the full history of the boundary layer is
required . if only a thickness such as is needed at one point on a
surface, then it is about equal in speed to the quadrature method .
but, if several values of or other properties along a surface are
required, it is appreciably faster than the quadrature method .
characteristically, only four steps are needed between the forward
stagnation point and the pressure peak . once the
velocity-distribution data are available, each step in a two-dimensional
calculation requires about 5 minutes, using a slide rule .
.I 293
.T
recent studies on the effect of cooling on boundary
layer transition at mach 4.
.A
wisniewski,r.j. and jack,j.r.
.B
j. ae. scs. 28, 1961.
.W
recent studies on the effect of cooling on boundary
layer transition at mach 4.
the advent of high-speed flight has necessitated the study of
boundary-layer transition on highly cooled bodies .
investigations such as those of references 1-4 have concentrated
on this problem and have indicated, contrary to the trends
predicted by small-disturbance theory, that premature transition
can be found with cooling . this phenomenon, commonly called
detail in references 2-5 .
the purpose of this note is to report some recent transition
data obtained on a cooled cone in a mach 4 wind tunnel . the
model, a sharp-tip cone (included angle 13.5), was cooled by
liquid nitrogen to a temperature of -340 f . the cooling
method and the data analysis are similar to that described in
reference 3 .
.I 294
.T
an investigation of laminar transitional and turbulent
heat transfer on blunt-nosed bodies in hypersonic flow .
.A
cresci,r.j. and mackenzie,d.a.
.B
j. ae. scs. 27, 1960.
.W
an investigation of laminar transitional and turbulent
heat transfer on blunt-nosed bodies in hypersonic flow .
laminar, transitional, and turbulent heating rates have been
measured by means of the shrouded model technique . the
reynolds number was varied over a ninefold range,. the enthalpy
ratio (stagnation to wall) varied from 2.3 to approximately 1.5 .
two different pressure distributions were imposed on the model
which consisted of a spherically capped cone .
the experimental data are compared to the laminar hypersonic
boundary-layer theory and shown to be in good agreement on the
conical portion of the model . on the spherical portion the data
are approximately 20 per cent higher than the theoretical
prediction . some of this discrepancy can be attributed to radiation to
the nose of the model .
the fully developed turbulent heat-transfer data are compared
to two theories .. (1) a relatively simple turbulent theory which is
based on recent theoretical work and which takes into account
the upstream history of the boundary layer, and (2) the flat-plate
reference-enthalpy theory, which depends on only /local/
conditions . although both theories are in reasonable agreement with
the data, the latter method is simpler and somewhat more
accurate .
for transitional flow the theory mentioned first can be readily
modified in order to permit reasonable estimates of transitional
heat transfer to be obtained . on this basis it is possible to
estimate laminar, transitional, and fully developed turbulent heat
transfer under hypersonic blunt-body conditions .
the behavior of transition reynolds number based on
momentum thickness is also discussed and shown to be in quantitative
agreement with recent shock-tube measurements .
.I 295
.T
a note on transitional heat transfer under hypersonic conditions .
.A
constantino economos and paul a. libby
.B
research assistant and professor of aeronautical engineering,
respectively
polytechnic institute of brooklyn, brooklyn, n.y.
.W
a note on transitional heat transfer under hypersonic conditions .
in references 1 and 2 there were presented experimental data on
transitional heat transfer on a blunt body under hypersonic-flow
conditions obtained by the shroud technique . the data were compared
with a theoretical prediction of transitional heat transfer based
on a suggestion of persh . the agreement between theory and experiment
in the transitional region was found to be 'qualitatively good and
quantitatively fair' .
it is the purpose of this note to present some additional transitional
data obtained in conventional wind-tunnel tests and to indicate a
means for improving somewhat the agreement between transitional
theory and experiment .
.I 296
.T
notes on waves through gases at pressures small compared
with the magnetic pressure, with applications to upper
atmosphere aerodynamics .
.A
lighthill,m.j.
.B
j. fluid mech. 9, 1960, 465.
.W
notes on waves through gases at pressures small compared
with the magnetic pressure, with applications to upper
atmosphere aerodynamics .
most treatments of magnetohydrodynamic
waves have confined physical
interpretation to cases when the alfven velocity a
is small compared with the sound
velocity a . here we consider the 'low-beta
situation', in which a is much
larger than a . then, except for two modes with
wave velocity a the only possible
waves are longitudinal ones, propagated
unidirectionally along lines of magnetic
force with velocity a . these can be
interpreted as sound waves, confined to
effectively rigid magnetic tubes of force .
hall-current effects do not alter these
conclusions (in contrast to the high-beta
situation), and finite conductivity
introduces only small dissipation .
an application is made to the flow pattern
around a body moving through the
f layer of the ionosphere, where, although
neutral particles have a very large
mean free path, charged particles interact
electrostatically and, it is argued, may
be regarded as forming a continuous fluid
whose movement is independent of
that of the neutral particles . a body moving
at satellite speed or below would
then excite the above-mentioned unidirectional
sound waves, but no waves at
much faster alfven velocity . these considerations
suggest that its movement
would be accompanied by a v-shaped pattern of
electron density (figure 2),
which might be in part responsible for some
anomalous radar echoes that have
been reported .
.I 297
.T
compressibility effects in magneto-aerodynamic flows
past thin bodies .
.A
mccune,j.e. and resler,e.l.
.B
j. ae. scs. 27, 1960.
.W
compressibility effects in magneto-aerodynamic flows
past thin bodies .
the effects of compressibility on the steady motion of a highly
conducting fluid past thin cylindrical bodies in the presence of a
magnetic field are studied . procedures are developed for the
solution of this class of magnetoaerodynamic problems over the
entire mach number range and for all ratios of magnetic to
fluid-dynamic pressure . the results obtained are analogous either to
the ackeret theory or the prandtl-glauert rule of conventional
aerodynamics, depending on the relative values of the flow speed
and the appropriate speed of propagation of magnetoacoustic
disturbances . the methods used and the physical interpretation
of the solutions obtained vary according to the orientation of the
magnetic field with respect to the flow direction .
the results of the theory are explained in terms of the
anisotropic propagation of magnetoacoustic pulses studied previously
by several authors .
.I 298
.T
incompressible wedge flows of an electrically conducting
viscous fluid in the presence of a magnetic field .
.A
yen,k.t.
.B
j. ae. scs. 27, 1960.
.W
incompressible wedge flows of an electrically conducting
viscous fluid in the presence of a magnetic field .
the purpose of this note is to discuss the two-dimensional
flow of an electrically conducting viscous fluid past a wedge
in the presence of a magnetic field . the governing differential
equations and boundary conditions are given and analyzed .
.I 299
.T
magnetohydrodynamic flow past a semi-infinite plate .
.A
meksyn,d.
.B
j. ae.scs. 29, 1962.
.W
magnetohydrodynamic flow past a semi-infinite plate .
the flow of viscous electrically conducting fluid
past a semi-infinite plate is considered . the
applied constant magnetic field and the constant
on-coming velocity of the fluid are in the direction parallel
to the plate .
in addition to reynolds number the flow in the
boundary layer depends on two parameters
and . the two simultaneous
ordinary nonlinear differential equations are solved by
the asymptotic method for the cases when
and respectively .
the main results obtained are as follows . the
equations can be solved exactly for and .
the perturbation effect from infinity when k is large
depends on, whereas the perturbation effect from
zero when k is small depends on . for large k,
including there is no solution for . it is
assumed that the fluid is incompressible with constant
physical properties .
.I 300
.T
on a particular class of similar solutions of the equations
of motion and energy of a viscous fluid .
.A
reeves,b.l. and kippenhan,c.j.
.B
j. ae. scs. 29, 1962.
.W
on a particular class of similar solutions of the equations
of motion and energy of a viscous fluid .
by introducing the similarity concept to the two-dimensional,
incompressible navier-stokes equations and energy equation, a
particular class of solutions is found . two general types of flows
are considered .. (1) laminar free convection--i.e., flows which
take place due to a body force--and (2) laminar forced
convection .
for free convection on vertical plates, similar solutions are
obtained for two different power-law surface temperature
variations, and it is shown that one of these solutions constitutes a
new type of boundary problem . results of numerical
integrations of the equations are compared with solutions of the similar
boundary-layer equations for free convection, and it is
demonstrated that a range of surface temperature variations exists for
which the boundary layer equations are no longer valid .
for forced convection, it is shown that the use of similarity
transformations provides an alternate method of deriving the
ordinary differential equations for some well-known solutions,
such as couette and stagnation point flows . solutions are
obtained for radial converging or diverging flows between plane
surfaces when the temperatures of the surfaces vary as arbitrary
powers of the distance from the orgin . results of numerical
integrations of the ordinary differential equations are presented
for prandtl numbers of 0.01 and 1.0 and for linear surface
temperature variations . some rather surprising results are obtained
for diverging flows when separation occurs and some revealing
comparisons with results from boundary-layer theory are made .
.I 301
.T
approximate design of sharp-cornered supersonic nozzles .
.A
m. a. rahman
.B
nack and sunderland consulting mech. and elec. engineers
.W
approximate design of sharp-cornered supersonic nozzles .
a modified parabolic curve appears to be in close proximity to that
obtained by either the method of characteristics or the wave method .
thus an attempt has been made to use analytic geometry to determine
approximately the contour of a two-dimensional, sharp-cornered
supersonic nozzle in a very short time .
.I 302
.T
approximations for the thermodynamic and transport properties of high
temperature air .
.A
hansen, c. f.
.B
nasa tr r 50, 1959 .
.W
approximations for the thermodynamic and transport properties of high
temperature air .
the thermodynamic and transport properties of high-temperature air are
found in closed form starting from approximate partition functions for
the major components in air and neglecting all minor components . the
compressibility, enthalpy, entropy, the specific heats, the speed of
sound, the coefficients of viscosity and of thermal conductivity, and
the prandtl numbers for air are tabulated from 500degree to 15,000degree
k over a range of pressure from 0.0001 to 100 atmospheres . the energy
of air and the mol fractions of the major components of air can be found
from the tabulated values for compressibility and enthalpy . it is
predicted that the prandtl number for fully ionized air, which is in
complete equilibrium, will become small compared to unity, the order of
transparent to heat flux .
.I 303
.T
effect of variable heat recombination on stagnation
point heat transfer .
.A
fenster,s.j. and neyman,r.j.
.B
j. ae. scs. 29, 1962.
.W
effect of variable heat recombination on stagnation
point heat transfer .
earlier studies assume an average heat of formation of atoms
based upon external flow conditions . it is shown that equilibrium
heat transfer decreases by 35 for a typical mach number 24 case
when allowance is made for the proportions of air components .
the variable recombination energy also results in atom mass
fractions which are realistically less for equilibrium than frozen
situations throughout the cold-wall boundary layer .
.I 304
.T
first-order approach to a strong interaction problem
in hypersonic flow over an insulated flat plate .
.A
oguchi,h.
.B
univ. tokyo aero.res r330, 1958.
.W
first-order approach to a strong interaction problem
in hypersonic flow over an insulated flat plate .
the present paper concerns with
the strong interaction phenomenon over an
insulated semi-infinite flat plate with a sharp
leading edge . in particular the main interest
is in the consistent treatment in which the
boundary-layer solution may be joined
continuously with the inviscid solution regarding
flow variables including pressure, normal
velocity, temperature (or streamwise velocity) and density .
it is shown that the behavior of the inviscid
solution may be consistent with that of the
boundary-layer solution to at least first-order
approximation that is correct to the order of,
where m is the mach
number of undisturbed flow, r the reynolds
number based on the distance from leading
edge and the ratio of specific heats . then
the first-order boundary-layer problem is
formulated under such an external circumstance
and an attempt is made for arriving at the solution .
actual calculations are carried out for both
cases of air and helium . from the solution
it is found that the region in which the viscous
effect plays a significant role is ranged over
from 0 to a certain finite value of n, say n, in
terms of the similarity coordinate n in the
corresponding incompressible boundary layer .
the numerical results moreover indicate
that the induced pressure is considerably smaller
than the estimate of lees (7) obtained by
his approximate method in which the effect
of the first-order induced pressure on the
boundary layer is ignored and no survey of the
first-order boundary-layer equation is made .
the present results are also found to be in
excellent agreement with experimental data
recently obtained in helium flow by erickson (15) .
.I 305
.T
hypersonic strong viscous interaction on a flat plate
with surface mass transfer .
.A
li,t.y. and gross,j.f.
.B
heat transfer and fluid mech. inst. 1961, 146.
.W
hypersonic strong viscous interaction on a flat plate
with surface mass transfer .
the present report gives an account of
the development of an
approximate theory to the problem of hypersonic
strong viscous interaction
on a flat plate with mass-transfer at the
plate surface . the disturbance
flow region is divided into inviscid and
viscous flow regions . the
hypersonic small perturbation theory is applied
to the solution of the inviscid
flow region . the method of similar solutions
of compressible laminar
boundary layer equations is applied to the
treatment of the viscous flow
region . the law of surface mass-transfer
for similar solutions is derived .
the pressure and the normal velocity are
matched between the inviscid and
viscous flow solutions . formulas for induced
surface pressure, boundary
layer thickness, skin friction coefficient,
and heat transfer coefficient
are obtained . numerical results and their
significance are discussed .
future improvements are indicated .
.I 306
.T
second approximation to laminar compressible boundary
layer on flat plate in slip flow .
.A
maslen,s.h.
.B
naca tn.2818, 1952.
.W
second approximation to laminar compressible boundary
layer on flat plate in slip flow .
the first-order solution for the laminar compressible boundary-layer
flow over a flat plate at constant wall temperature is given . the
effect of slip at the wall as well as the interaction between the
boundary-layer flow and the outer stream flow are taken into
consideration . the solution is obtained explicitly in terms of the known zero
order, or continuum, solution . no
assumptions regarding the prandtl
number or viscosity-temperature law need be made . it is found that the
first-order solution gives a decrease in heat transfer and, for
supersonic flow, an increase in skin friction .
for subsonic flow there is no
first-order shear effect . the change in heat transfer is due to slip
and the change in friction is due to the interaction of the zero- and
first-order velocities at the outer edge of the boundary layer .
.I 307
.T
an approximate solution of hypersonic laminar boundary
layer equations and its application .
.A
nagakura,t. and naruse,h.
.B
j. phys. soc. japan, 12, 1957, 1298.
.W
an approximate solution of hypersonic laminar boundary
layer equations and its application .
approximate formulae of the displacement thickness and the skin
friction of the hypersonic laminar boundary layer are derived by use of
von karman's integral method, assuming the heat-insulated wall, the
prandtl number of unity and chapman and rubesin's formula for the
variation of viscosity with temperature .
the results obtained are
compared with some exact solutions .
because of the good agreement, it
seems that these formulae are very useful .
these formulae, together with the tangent-wedge-approximation, are
applied to the viscous flow over
slender bodies with a sufficiently sharp
leading edge . as an example, the
pressure distribution over a flat plate
is calculated numerically over the
entire region of the surface .
comparison with other author's theoretical
results as well as experimental
values is made .
.I 308
.T
on the hypersonic viscous flow past a flat plate with
suction or injection .
.A
yasuhara,m.
.B
j. phys. soc. japan, 12, 1957, 177.
.W
on the hypersonic viscous flow past a flat plate with
suction or injection .
the hypersonic viscous flow past a flat
plate with suction or injection
is dealt with by karman-pohlhausen's
method in special cases when
suction or injection velocity proportional
to, especially
for the region of strong interaction between
the shock wave and the
boundary layer, were p is the pressure on
the plate and x is the
distance measured along the plate from its leading edge .
several numerical examples are given,
which shows similar effects of
injection to those in the case of incompressible
flow that the injection
makes all the height of the shock wave,
the thickness of the boundary
layer and the pressure on the plate larger
than those in the case of no
injection . on the contrary, in the case of
suction no remarkable change
both in the height of the shock wave and
the pressure on the plate can
be seen and only the velocity profile in
the boundary layer is affected
by the suction .
.I 309
.T
on the motion of a flat plate at high speed in a viscous
compressible fluid, ii, steady motion .
.A
stewartson,k.
.B
j. ae. scs. 22, 1955, 303.
.W
on the motion of a flat plate at high speed in a viscous
compressible fluid, ii, steady motion .
the theory of the steady flow of a viscous compressible fluid
past a flat plate at high mach number due to lees and
probstein is extended by a more complete discussion of the flow in
the inviscid layer between the shock wave and the boundary layer .
it is shown that similar solutions exist in this layer, analogously
to those found by li and nagamatsu in the boundary layer, and
that the two may be joined to give, allowing one minor
assumption, a full account of the flow . it is shown that the
boundary-layer equations may be reduced to those for an incompressible
fluid and that the von karman-pohlhausen method describes
the flow in it with good accuracy . the tangent wedge
approximation for the pressure on the plate, used by lees and his
collaborators, is found to be in deficit
by 10 per cent for air . finally,
it is shown that the theory for weak interaction cannot be
extended further without a complete knowledge of the flow .
.I 310
.T
hypersonic viscous flow over a flat plate .
.A
lees, l. and probstein, r. f.
.B
princeton univ. aero eng. r195, 1952
(abstract by e.m.keen)
.W
hypersonic viscous flow over a flat plate .
in dealing with the steady laminar viscous flow over a
semi-infinite flat plate some of the following topics are discussed .
the streamline in the boundary layer over a leading edge of given
thickness . the rate of growth of the boundary layer in the main stream, and
causes of pressure variations .
asymptotic solutions for thn downstream flow region, including the
joining interaction of shock waves at the leading edge .
pressure variations in the interanl viscous flow layer and in external
inviscid flow considered as prandtl meyer flow . in cases of streamline
deflection, the free stream mach number, zero pressure gradient, and
surface pressure distribution . asymptotic solutions for cases of
fluid injection of a cool gas . prandtl heat transfer . the joining
interaction between the external inviscid flow and the internal viscous
flow layer . steady laminar hpyersonic viscous flow over a flat wedge
and a cone .
.I 311
.T
a method for predicting the onset of buffeting and other separation
effects from wind tunnel tests on rigid models .
.A
pearcey, h. h.
.B
n.p.l. aero. 358, fm 2763. dec. 1958 .
.W
a method for predicting the onset of buffeting and other separation
effects from wind tunnel tests on rigid models .
the method is based on the observation of the divergence that occurs in
the variation of mean static pressure at the trailing edge of an
aircraft wing at the critical stage in the development of boundary-layer
separation when its influence first spreads to the trailing edge and
thereby to the overall flow .
the significance of the trailing-edge pressure variations and their
connection with the effects that separation has on the mean and unsteady
loads is discussed for various types of separation . good prediction
can be obtained from wind-tunnel tests, or warning provided in flight,
for low-speed separations and for shock-induced ones up to the stage at
which the shock wave reaches the trailing edge . related divergences in
wake width, lift coefficient, or shock position can also be used .
pressure measurements at other isolated points often indicate the type
of separation .
certain special considerations apply for swept wings .
the various flow changes that are considered are illustrated by
schlieren photographs and described in an appendix .
.I 312
.T
chordwise pressure distributions over several naca
16 series airfoils at transonic mach numbers up to
1.25 .
.A
ladson,c.l.
.B
nasa memo 6-1-59l, 1959.
.W
chordwise pressure distributions over several naca
16 series airfoils at transonic mach numbers up to
1.25 .
a two-dimensional wind-tunnel
investigation of the pressure
distributions over several naca 16-series
airfoils with thicknesses of
and design lift coefficients of
the langley airfoil test apparatus
at transonic mach numbers from 0.7 to
number from 2.4 x 10 to 2.8 x 10 and
in angle of attack from -10 to
and schlieren flow photographs
are presented without analysis .
.I 313
.T
on alternative forms for the basic equations of transonic
flow theory .
.A
spreiter,j.r.
.B
j. ae. scs. 21, 1954.
.W
on alternative forms for the basic equations of transonic
flow theory .
attention has been called by numerous authors to the
possibility of certain alternative forms for the equations for
transonic flow about thin wings . it is the purpose of this note
to contribute to this discussion and to indicate some reasons for
the selection of one form of these in preference to another more
widely used form .
.I 314
.T
simplified method for determination of the critical
height of distributed roughness particles for boundary
layer transition at mach numbers from 0 to 5.
.A
braslow,a.l. and knox,e.c.
.B
naca tn.4363, 1958.
.W
simplified method for determination of the critical
height of distributed roughness particles for boundary
layer transition at mach numbers from 0 to 5.
a simplified method has been devised for determination of the
critical height of three-dimensional roughness particles required to
promote premature transition of a laminar boundary layer on models of
airplanes or airplane components in a wind tunnel with zero heat
transfer . a single equation is derived which relates the roughness height
to a reynolds number based on the roughness height and on local flow
conditions at the height of the roughness, and charts are presented
from which the critical roughness height can be easily obtained for
mach numbers from 0 to 5 . a discussion of the use of these charts is
presented with consideration of various model configurations .
the method has been applied to various types of configurations in
several wind-tunnel investigations conducted by the national advisory
committee for aeronautics at mach numbers up to 4, and in all cases
the calculated roughness height caused premature boundary-layer
transition for the range of test conditions .
.I 315
.T
scale effects at high subsonic and transonic speeds
and methods for fixing transition in model experiments .
.A
haines,a.b., holder,d.w. and pearcey,h.h.
.B
arc r + m3012, 1954.
.W
scale effects at high subsonic and transonic speeds
and methods for fixing transition in model experiments .
the major scale effects at high subsonic and transonic
speeds arise from differences between the conditions
under which laminar and turbulent boundary layers separate, and in
how they behave after separation . for turbulent
boundary layers, these conditions and behaviour do not vary greatly
as the reynolds number is changed and in many
examples, it has been shown that they are similar for the turbulent
layers that occur naturally at high reynolds number
and for boundary layers in which transition to turbulent flow is fixed
artificially . the scale effects arising in wind-tunnel
tests made at low reynolds number may, therefore, often be
minimised by fixing transition to turbulent flow by
introducing an artificial disturbance such as that produced by
excrescences attached to the surface . the fact that the
effects of separation are often less severe for laminar layers than
for the turbulent layers that are likely to be encountered
at full scale, makes it all the more important to do this whenever
possible .
several methods which can be used to fix transition are described,
and the results obtained by using them are compared .
in general, in experiments in two-dimensional flow, good agreement
is found, and explanations can be advanced for
cases in which discrepancies occur . several uncertainties and
difficulties that arise in fixing transition are discussed
and illustrated by examples . in particular, special care is needed
in interpreting the results obtained with transition
fixed at very low reynolds numbers (say, less than about r = 1 x 10
based on local chord for wings of about 0.1
thickness chord ratio and possibly higher reynolds numbers for thinner
wings) .
the difficulties of fixing transition satisfactorily are increased
for three-dimensional wings, particularly if they are
swept-back or highly tapered (i.e., small chord and reynolds
number near the tip) and if the tests cover a large range
of incidence including high incidences for which the flow may
separate from very close to the leading edge . under
these circumstances, it is frequently necessary to place the
excrescences at different chordwise positions for low and
high angles of incidence, and this is inconvenient in practice .
more research is needed before sound recommendations
can be made as to how and where transition should be fixed
on such models, particularly since in routine testing, it is
often not possible to check the effects of transition-fixing fully .
in the sections dealing with three-dimensional tests, examples
are given of the spurious results that have been avoided
successfully by fixing transition, of the conditions where even
at low reynolds numbers artificial fixing of transition
may not be necessary to give a turbulent boundary layer ahead
of the shock, and of the conditions under which there
are some doubts whether the methods used for fixing transition
have been satisfactory .
.I 316
.T
the occurrence and development of boundary layer separations at high
incidences and high speeds .
.A
pearcey, h. h.
.B
r + m 3109, arc 17901, september 1955 .
.W
the occurrence and development of boundary layer separations at high
incidences and high speeds .
this note describes the manner in which the onset of the effects of
boundary-layer separation varies with mach number for two-dimensional
aerofoils, and discusses the influence of section shape as far as it is
known . a brief qualitative description is given of the mechanism
underlying the development of the separated flow and its effects,
followed by a discussion of some of the ways in which this is likely to
differ for swept-back wings at high speeds . finally, the need is
emphasized for continued work in a broadening field .
.I 317
.T
non-equilibrium flow of an ideal dissociating gas .
.A
freeman, n. c.
.B
j. fluid mech. v. 4, 1958 .
.W
non-equilibrium flow of an ideal dissociating gas .
the theory of an'ideal dissociating'gas developed by lighthill/1957/for
conditions of thermodynamic equilibrium is extended to non-equilibrium
conditions by postulating a simple rate equation for the dissociation
process/including the effects of recombination/ . this equation contains
the'equilibrium'parameters of the lighthill theory plus a further
dissociation phenomena .
the behaviour of this gas is investigated in flow through a strong
normal shock wave and past a bluff body . the assumption is made that
the gas receives complete excitation of its rotational and vibrational
degrees of freedom in an infinitesimally thin region according to the
familiar rankine-hugoniot shock wave relations before dissociation
begins . the variation of the relevant thermodynamic variables
down-stream of this region is then computed in a few particular cases . the
method used in the latter case is an extension of the'newtonian'theory
of hypersonic inviscid flow . in particular, the case of a sphere is
treated in some detail . the variation of the shock shape and the
sphere diameter to the length scale of the dissociation process, is
exhibited for conditions extending from completely undissociated flow
to dissociated flow in thermal equilibrium . results would indicate
that significant and observable changes from the undissociated values
occur, although values for the non-equilibrium parameter are not, at
present, available .
.I 318
.T
inviscid hypersonic flow past blunt bodies .
.A
maslen,s.h. and moeckel,w.e.
.B
j. ae. scs. 24, 1957.
.W
inviscid hypersonic flow past blunt bodies .
two methods are shown for the calculation of the flow field
between a blunt body and the shock associated with it for the
case of hypersonic flow . real gas effects are included . the
solutions consider only symmetric flows--that is, symmetric
bodies at zero incidence .
one method consists in tracing successive stream tubes around
the body and leads to iterations on the initially assumed position
of the shock . the second is an integral method closely analogous
to the karman-pohlhausen procedure for boundary layers . a
distinction is made between round-nosed and flat-nosed bodies,
and both cases are discussed .
a specific example corresponding to a re-entry missile situation
is calculated,. the two methods agree within a few per cent .
comparison is also made with other known solutions in the
stagnation region .
.I 319
.T
propagation of weak disturbances in a gas subject to
relaxation effects .
.A
moore,f.k. and gibson,w.e.
.B
j. ae. scs. 27, 1960.
.W
propagation of weak disturbances in a gas subject to
relaxation effects .
a generalized wave equation is derived for sound disturbances
in a gas when relaxation effects connected with, for example,
molecular vibration or dissociation are important . solutions
involving discontinuous wave fronts are presented, and it is shown
that, under certain assumptions, the complete wave equation
reduces to a variant of the telegraph equation . detailed solutions
are presented for disturbance fields produced by a wavy wall in
subsonic and supersonic flow and a simple wedge in supersonic
flow . this study is viewed as a step in the development of a
theory of small disturbances of a high-temperature gas, as is found
behind the shock in hypersonic flight .
.I 320
.T
comment on improved numerical solution of the blasius problem with
three-point boundary conditions .
.A
leigh, d. c.
.B
j. aero. sc. v. 29, may 1962 .
.W
comment on improved numerical solution of the blasius problem with
three-point boundary conditions .
attention is drawn to a previous accurate solution to the problem .
.I 321
.T
improved numerical solution of the blasius problem with three-point
boundary conditions .
.A
christian, w. j.
.B
j. aero. sc. v. 28, november, 1961 .
.W
improved numerical solution of the blasius problem with three-point
boundary conditions .
the blasius equation describes the velocity distribution resulting from
laminar, constant-pressure mixing of a stationary fluid layer and a
moving stream . in connection with a numerical procedure for the univac
based on analytic continuation of the function f' . high-speed computers
now make it feasible to use analytic continuation for numerical
integration of single-point boundary-value problems such that, within
the limits of taylor's expansion, truncation error may be made
arbitrarily small . a brief description of the application of the
routine is given .
.I 322
.T
on the numerical solution of the blasius problem with three-point
boundary conditions .
.A
toba, k.
.B
j. aero. sc. v. 29, p480-1, april, 1962 .
.W
on the numerical solution of the blasius problem with three-point
boundary conditions .
relates to a technique for approximate determination of the initial
parameters . the technique is an application of the asymptotic
integration method introduced by meksyn and has been applied to the computation
of the skin friction for shock-generated boundary-layer flow .
.I 323
.T
vorticity interaction at an axisymmetric stagnation
point in a viscous incompressible fluid .
.A
kemp,n.h.
.B
j. ae. scs. 26, 1959.
.W
vorticity interaction at an axisymmetric stagnation
point in a viscous incompressible fluid .
the purpose of the present note is to give an exact solution of
the incompressible navier-stokes equations at an axisymmetric
stagnation point with vorticity in the oncoming flow which varies
linearly with distance from the axis . this solution has application
to the hypersonic axisymmetric blunt body problem, for which
lighthill has shown the vorticity in the inviscid shock layer is
very nearly of this form .
.I 324
.T
vorticity effect on the stagnation point flow of a viscous
incompressible fluid .
.A
rott, n. and lenard, m.
.B
j. aero. sc. v. 26, august, 1959 .
.W
vorticity effect on the stagnation point flow of a viscous
incompressible fluid .
the effect of vorticity on axisymmetric stagnation point boundary layer
calculations is investigated by calculating a perturbation to the
stagnation point flow . the shear caused by the vorticity effect is
found to be surprisingly large,.the slope of the shear curve /at zero
vorticity/ as calculated by kemp agrees perfectly with the value deduced
in this note .
.I 325
.T
heat transfer to constant property laminar boundary
layer flows with power function free stream velocity
and wall temperature variation .
.A
levy,s.
.B
j.ae.scs. 19, 1952.
.W
heat transfer to constant property laminar boundary
layer flows with power function free stream velocity
and wall temperature variation .
numerical computations have been performed for the
boundary-layer form of the energy equation for incompressible flows
with power-function variation of free-stream velocity (u =
cx) and of wall temperature (t = ax), the pertinent solutions
of the momentum equation in this case being those of hartree .
the numerical computations given herein are to some extent a
repetition of those given by schuh and by chapman and rubesin,
the object of the present computations being the resolution of
discrepancies appearing in the previous solutions and an extension of
their range . ibm machine calculations were employed in the
finite difference calculation presently utilized, the results thereof
covering a range of wall-temperature function exponents from
values of m(4, 1, 0, -0.0904) . the accuracy of the numerical
computations is examined in detail, and the accuracy of the
computed functions at the wall, which determine the heat-transfer
rate, is estimated to be within 2 per cent .
examination of the results reveals that the results of schuh
for the flat plate are in error . for the range of the calculations,
it was found that the local heat-transfer coefficient can, with the
exception of large negative values, be expressed within 5
per cent as
where the exponent of the prandtl number varies from 0.254
to 0.367 for -0.0904 and where the function
can be approximated by the equation
.I 326
.T
forst-order slip effects on the compressible laminar
boundary layer over a slender body of revolution in
axial flow .
.A
shen,s.f. and solomon,j.m.
.B
j.ae.scs. 28, 1961.
.W
forst-order slip effects on the compressible laminar
boundary layer over a slender body of revolution in
axial flow .
analysis of the
compressible boundary layer with transverse curvature in first
order slip flow . no boundary-layer interaction effects are considered
and only the zero pressure-gradient case is examined .
.I 327
.T
on local flat plate similarity in the hypersonic boundary
layer .
.A
moore,f.k.
.B
j. ae. scs. 28, 1961.
.W
on local flat plate similarity in the hypersonic boundary
layer .
a study is made of lees' /local flat-plate similarity/ rule for
the hypersonic laminar boundary layer . it is shown that this
rule is exact under assumptions commonly invoked in the
inviscid theory of hypersonic flow .
beginning from this theoretical basis, a modified local
flat-plate similarity scheme is derived, involving separate rules for
velocity and enthalpy profiles, and is compared with exact
similarity solutions and with the existing theory of hypersonic
leading-edge interaction .
.I 328
.T
the boundary layer near the stagnation point in hypersonic
flow past a sphere .
.A
herring,t.r.
.B
j. fluid mech. 7, 1960, 257.
.W
the boundary layer near the stagnation point in hypersonic
flow past a sphere .
flow properties behind shock waves caused by bluff bodies
traveling at supersonic speeds are of major importance in missile
and high-speed aircraft design . paper presents a mathematical
solution for the laminar boundary layer near the stagnation point of a
sphere . surface temperature is free-stream static and shock is
strong . air is assumed calorically and thermally perfect with a
prandtl number of 0.72 and a dynamic viscosity directly
proportional to temperature .
based on work of homann (zamm 16, p. 153, 1936) and lighthill
simultaneous differential equations for the velocity and
temperature profiles . these are solved by numerical integration along a
normal to the surface using a digital computer . results are
presented as functions of free-stream mach number, reynolds
number, and specific heat ratio . as increases,
boundary-layer thickness is shown to decrease while shock stand-off
distance increases . stand-off distance also decreases with increasing
and decreasing specific heat . for constant and specific
heat ratio, the product of skin-friction coefficient and the square
root of decreases with increasing only approaching a
constant value at greater than 10,000 .
reviewer's comment is concerned with the perfect gas
assumption for air . author suggests that the effects of dissociation on
flow properties are accounted for by a proper choice of specific
heat ratio . a consideration of the kinetics of chemical reaction in
the cooled boundary layer emphasizes the oversimplification of
this approach . the effect on transport properties could have been
approximated in present analysis by changing the prandtl number
to one more representative of the existing pressures and
temperatures .
.I 329
.T
various aerodynamic characteristics in hypersonic rarefied
gas flow .
.A
probstein,r.f. and kemp,n.h.
.B
j. ae. scs. 27, 1960.
.W
various aerodynamic characteristics in hypersonic rarefied
gas flow .
this paper considers the problem of calculating viscous
aerodynamic characteristics of blunt bodies at hypersonic speeds and
at sufficiently high altitudes where the appropriate mean free
path becomes too large for the use of familiar boundary-layer
theory but not so large that free molecule concepts apply .
results of an order-of-magnitude analysis are presented to
define the regimes of rarefied gas flow and the limits of
continuum theory . based on theoretical and experimental
evidence, the complete navier-stokes equations are used as a
model, except /very close/ to the free molecule condition . this
model may not necessarily give the shock wave structure in
detail but satisfies overall conservation laws and should give a
reasonably accurate picture of all mean aerodynamic quantities .
in this /intermediate/ regime there are two fundamental classes
of problems .. a /viscous layer/ class and a /merged layer/
class, the latter corresponding to a larger degree of rarefaction .
for the viscous layer class there is a thin shock wave, but the
shock layer region between the shock and the body is fully
viscous, although the viscous stresses and conductive heat transfer
are small at the shock wave boundary . here, the use of the
navier-stokes equations with outer boundary conditions given
by the hugoniot relations is justified . for the merged layer
class, the shock wave is no longer thin, and the navier-stokes
equations can be used to give a solution which includes the shock
structure and has free-stream conditions as outer boundary
conditions . a simpler procedure is presented for /incipient merged/
conditions where the shock may no longer be considered an
infinitesimally thin discontinuity but where it has not thickened
sufficiently to entail the /fully merged layer/ analysis . in this
case we approximate the shock by a discontinuity obeying
conservation laws which include curvature effects, viscous stresses,
and heat conduction .
for a sphere and cylinder it is shown that the navier-stokes
equations can be reduced to ordinary differential equations for
both the viscous and merged layer class of problems . solutions
of these equations, when used in connection with hypersonic flow
problems, are in general only valid in the stagnation region . to
illustrate the viscous layer solutions, numerical calculations
have been performed for a sphere and cylinder with the
assumption of constant density in the shock layer, which is a useful
approximation at hypersonic speeds . to illustrate the merged
layer solution, calculations have been carried out for a sphere
using the incipient merged layer approximation .
results are presented for detachment distance, surface shear,
and heat-transfer rate in the stagnation region of a highly cooled
sphere flying at hypersonic speed . with decreasing reynolds
number, the shear and heat transfer are shown to increase above
the extrapolated boundary-layer values in the viscous layer
regime and then to begin falling in the incipient merged regime .
as the reynolds number decreases in the incipient merged
regime, the density in the shock layer increases, and the static
and stagnation enthalpy behind the shock decrease .
calculations performed for an insulated sphere show that, with
decreasing reynolds number in the incipient merged regime,
the density in the shock layer decreases,. the total enthalpy
behind the shock and at the stagnation point increase so that they
are higher than the free-stream total enthalpy,. and the
stagnation-point pressure behaves like the total enthalpy .
for the highly cooled cylinder in the viscous layer regime, the
same quantities are presented as for the sphere . the increase
found in shear and heat transfer above extrapolated
boundary-layer theory is small, in agreement with vorticity interaction
theory .
a discussion is given of the behavior of available experimental
data for viscous flow quantities in the intermediate regime and
the behavior predicted by the results of the present calculations .
qualitative agreement is indicated .
.I 330
.T
taylor instability of finite surface waves .
.A
emmons,h.w., chang,c.r. and watson,b.c.
.B
j. fluid mech. 7, 1960.
.W
taylor instability of finite surface waves .
the instability of the accelerated interface
between a liquid (methanol or carbon
tetrachloride) and air has been investigated
experimentally for approximate
sinusoidal disturbances of wave-number range
from well below to well above the
cut-off . the growth rates are measured and
compared with theoretical results .
a third-order theory shows the phenomena
of overstability which is found in the
experimental results . some measurements
of later stages of growth agree
moderately well with the available theory
and disclose some additional
phenomena of bubble competition, helmholtz
instability with transition to turbulence,
and jet instability with production of drops .
.I 331
.T
effects of surface tension and viscosity on taylor
instability .
.A
bellman,r. and pennington,r.h.
.B
q. app. math. 12, 1954.
.W
effects of surface tension and viscosity on taylor
instability .
the model used is that of two
fluids of infinite depth, with the interface
initially in the form of a sine wave with
amplitude small compared to wave length .
the fluids are considered incompressible,
and only the linear terms in the equations of
hydrodynamics are used . the first four
sections discuss the effects of surface tension
and viscosity . the fifth gives a few numerical
results to illustrate the main points of
the preceding sections .
.I 332
.T
similitude of hypersonic real-gas flows over slender
bodies with blunted noses .
.A
cheng,h.k.
.B
j. ae. scs. 26, 1959, 575.
.W
similitude of hypersonic real-gas flows over slender
bodies with blunted noses .
on the basis of the hypersonic small-perturbation theory, the
laws of similitude for hypersonic inviscid flow fields over thin or
slender bodies are examined, and the restrictions to ideal gases
with constant specific heats and to bodies with pointed noses are
removed . only steady plane or axisymmetric flows are
considered .
inspection of the governing system of equations shows that a
similitude law exists for flow fields, under local thermal
equilibrium, having the same free-stream atmosphere . for flows of
ideal gas with constant specific heats, the requirement of the same
free-stream atmosphere--i.e., the same composition, pressure, and
density--can be replaced by the requirement of the same ratio of
specific heats .
for flows over blunted wedges or cones, special laws of
similitude can be obtained .
application of the similarity rules is examined for the case of
hypersonic flows of an ideal gas with over flat plates
with blunt leading edges, and for the case of equilibrium air
flows over wedges . the possibility of simulating nonequilibrium
flows over slender or thin bodies is also pointed out .
.I 333
.T
boundary-layer interaction on a yawed infinite wing in hypersonic
flow .
.A
robert j. whalen
.B
principal scientist, flight sciences laboratory, inc.,
buffalo, n.y.
.W
boundary-layer interaction on a yawed infinite wing in hypersonic
flow .
the equations are given for the laminar boundary-layer
equations on a yawed infinite wing for constant
wall temperature, under the combined howorth and
mangler transformation . diagrams show the relatively
small influence of yaw, the increase of boundary-layer
secondary flow, and the variation of the local heat
transfer rate with yaw .
.I 334
.T
influence of the leading-edge shock wave on the laminar boundary layer
at hypersonic speeds .
.A
lester lees
.B
california institute of technology
.W
influence of the leading-edge shock wave on the laminar boundary layer
at hypersonic speeds .
in order to bring out the importance of the leading-edge region at
hypersonic speeds, the influence of the leading-edge shock wave on
the laminar boundary layer is investigated in two simple cases of
steady flow over a semi-infinite, insulated flat plate.. (1) sharp
leading edge., (2) blunt leading edge, as approximated by a normal
shock wave . the streamlines that enter the boundary layer over a large
region of the plate surface has previously crossed the shock wave
very near the leading-edge, where the shock is strong and highly
curved . consequently, the temperature at the outer edge of the
boundary layer is appreciably higher than free-stream temperature,
and the vorticity there is not zero . the effects of this shock-wave
larger than the usual /errors/ made in the boundary-layer theory,
and an estimate of these effects can therefore be obtained within the
framework of that theory . the numerical magnitude of the shock-wave
influence is found to be appreciable . for the case of the blunt
leading edge the slope of the curve of induced pressures plotted against
the hypersonic interaction parameter closely approaches the experimental
data of hammitt and bogdonoff obtained in helium at large values of this
parameter . these approximate results show that the influence of the
leading-edge region at hypersonic speeds requires careful theoretical
and experimental study .
.I 335
.T
the interaction between boundary layer and shock waves in transonic
flow .
.A
liepmann, h. w.
.B
j. aero. sc. v. 13, december, 1946 .
.W
the interaction between boundary layer and shock waves in transonic
flow .
experiments of transonic flow past a circular arc profile show that the
shock-wave pattern and the pressure distribution are strongly dependent
upon the state of the boundary layer . a change from laminar to
turbulent boundary layer at a given mach number changes the flow pattern
considerably .
shock waves can interact with the boundary layer in a manner similar to
a reflection from a free jet boundary . these shock waves are not
distinctly discernible from pressure distribution measurements .
.I 336
.T
simplified laminar boundary layer calculations for
bodies of revolution and for yawed wings .
.A
rott,n. and crabtree,l.f.
.B
j. ae. scs. 19, 1962.
.W
simplified laminar boundary layer calculations for
bodies of revolution and for yawed wings .
since the introduction of momentum methods in
boundary-layer calculations by von karman and pohlhausen, many
improvements have been proposed . an especially simple solution
reduces the problem to a quadrature . here, it is proposed to
extend these methods to elementary three-dimensional cases and to
compressible laminar boundary-layer calculations . for
comparison, the corresponding problems for the turbulent boundary
layer are also discussed briefly .
.I 337
.T
boundary layer transition with gas injection .
.A
scott,c.j. and anderson,g.e.
.B
j. ae. scs. 25, 1958.
.W
boundary layer transition with gas injection .
the mass-injection process has been proposed as a method
of cooling aerodynamic surfaces, and, since the amount of
coolant required to maintain practical wall temperatures is
considerably larger for turbulent than for laminar boundary layers,
knowledge of the effect of the cooling method on the transition
process is certainly important . exploratory studies reported
here were conducted at mach number 3.7 to ascertain the
effects of gas injection on the stability of the laminar boundary
layer on a conical surface .
.I 338
.T
mass transfer cooling at mach number 4. 8.
.A
leadon,b.m., scott,c.j. and anderson,g.e.
.B
j. ae. scs. 25, 1958.
.W
mass transfer cooling at mach number 4. 8.
mass-transfer experiments on a 5 mil wire porous cone
of 20 total angle have been conducted at using
air and helium injection . details of the experimental technique
are described in references 1 and 2 . in the laminar boundary
layer the recovery factors and heat-transfer coefficients measured
with zero injection agreed within per cent with theory .
transition reynolds numbers observed on the porous cone with
zero injection were half as large as observed on a smooth,
impermeable model of identical geometry in the same channel, but
injection of large amounts of air or helium did not cause
transition to move forward from its zero-injection position on the
porous cone . distributed roughness of this type apparently does
not disturb impermeable wall theory, but it masks whatever
effective roughness may be caused by discrete pore injection .
.I 339
.T
experimental evaluation of heat transfer with transpiration
cooling in a turbulent boundary layer at m=3 .2.
.A
bartle,e.r. and leadon,b.h.
.B
j. ae. scs. 27, 1960.
.W
experimental evaluation of heat transfer with transpiration
cooling in a turbulent boundary layer at m=3 .2.
it is found that for prescribed velocity field, electrical field and
conductivity, the current can be calculated by integration . work is
related to analytic investigation of the boundary layer in a
physically reasonable accelerator .
.I 340
.T
analysis of effects of diffusion of a foreign gas into
the laminar boundary layer of a supersonic flow of
air in a tube .
.A
radbill,j.r. and kaye,j.
.B
j.ae.scs. 26, 1959.
.W
analysis of effects of diffusion of a foreign gas into
the laminar boundary layer of a supersonic flow of
air in a tube .
adiabatic wall temperatures and recovery factors are calculated
for pipe flows with an entrance mach number of 5 and with uniform
injection of helium . predicted values of the recovery factor
increase slowly with increasing injection rate and with increasing
distance from the tube entrance .
.I 341
.T
the analytical design of an axially symmetric laval
nozzle for a parallel and uniform jet .
.A
foelsch,k.
.B
j. ae. scs. 16, 1949.
.W
the analytical design of an axially symmetric laval
nozzle for a parallel and uniform jet .
the equations for the nozzle's contours are derived by
integration of the characteristic equations of the axially symmetric flow .
since it is not possible to integrate these equations
mathematically in an exact form, it was necessary to find a way to
approximate the calculations . the approximation offers itself by
considering and comparing the conditions of the flow in a cone with
those in a nozzle, as a linearization of the characteristic equations .
the first part of the report deals with equations for the
transition curve by which the conical source flow is converted into a
parallel stream of uniform velocity . the equations are derived
by integration along a mach line of the flow in the region where
the conversion takes place . a factor f is introduced expressing a
relation between the direction and the velocity of the flow along
a certain mach line . f remains undetermined and is not involved
in the final equations .
in the second part of the report, the spherical sonic flow
section is converted into a plane circular section of the throat .
the nozzle's contour adjacent to the throat is formed by the arc
of a circle connected with the transition curve by a straight line .
the gas dynamic properties of the boundary mach line are
calculated in table 1, the use of which shortens the calculations
considerably .
.I 342
.T
effect of diffusion fields on the laminar boundary
layer .
.A
smith,j.w.
.B
j.ze.scs. 21, 1954.
.W
effect of diffusion fields on the laminar boundary
layer .
a theory is developed which describes the effect of a general
diffusion field on the dynamic and thermal characteristics of a
laminar boundary layer on a flat plate in steady compressible
flow . fluid properties are considered as functions of
temperature and local concentration of the foreign gas . the diffusion
field is described by a differential equation that relates
convective and diffusion transfer and which considers diffusion currents
arising from gradients of concentration and temperature . by
means of the usual transformations the system is reduced to a set
of ordinary differential equations, which in turn are transformed
into a set of integral equations . the latter is amenable to
solution by the method of successive approximations .
the theory and results have bearing on the problem of control
and reduction of aerodynamic heating at hypersonic speeds .
the special feature of this approach lies in the utilization of
diffusion fields for the purpose of reducing the detrimental effects
of viscous dissipation . although the theory is adapted to a
fuller investigation of this problem, the numerical examples
considered involve mainly diffusion fields of helium, with which
good results have been achieved at mach numbers 8 and 12 .
whereas at the higher mach number the influx of heat was
practically eliminated, a reversal in the direction of heat flow has
been effected at the lower mach number .
.I 343
.T
transpiration cooling experiments in a turbulent boundary
layer at m=3 .
.A
leadon,b.m. and scott,c.j.
.B
j. ae. scs. 23, 1956.
.W
transpiration cooling experiments in a turbulent boundary
layer at m=3 .
turbulent recovery factor and heat-transfer measurements have been
made on a porous flat wall section at a nominal mach number of 3.0 and a
reynolds number of approximately 4 x 10 using both air and helium as the
transpired gas . measured heat-transfer
coefficients correlate well with the
compressible theory of rubesin for air
and qualitatively with simple film
theory for either coolant, indicating that
the heat transfer from a turbulent
boundary layer can be reduced by transpiration
cooling to well below that of
the uncooled boundary layer at the same reynolds number .
.I 344
.T
some experimental techniques in mass transfer cooling .
.A
leadon,b.m.
.B
aero/space eng. 18, 1959.
.W
some experimental techniques in mass transfer cooling .
author introduces his survey by a brief review of the history of
investigations dealing with boundary layers on impermeable solid
surfaces, and notes that no true theory exists for turbulent
boundary layers, the success of studies in this area having been due to
the introduction of artificial, if ingenious, assumptions which
permitted empirical correlations fd data . the terminology introduced
by the author for distinguishing the different situations involving
mass transfer from the wall to the stream may give rise to some
objections . for instance, /film cooling/ need not refer only to
the injection of a liquid, since applications involving gas film
cooling exist . also, his restriction of the term /transpiration
cooling/ to refer to the injection through a porous surface of a gas
only of the same composition as the exterior stream does not enjoy
universal usage . the influence of mass transfer on heat transfer
through laminar boundary layers and on the transition from laminar
to turbulent flow is described, with consideration given to the
question of the net effect of the stabilizing influence of surface
cooling and the destabilizing influence of injection .
reviewer suggests that author's inaccurate statement to the
effect that /thus far the higher energy conditions do not threaten
to involve turbulent injection, so turbulent boundary-layer research
enjoys a fairly academic serenity broken only by its own
frustrations/ be excused on grounds of poetic license, although it
ignores the efforts being devoted to the pressing practical problems
of erosive burning of solid propellants (possibly the most common
example of a complete /aerothermochemical/ problem involving
distributed surface heat and mass transfer with chemical reaction
in a flow system) and of effusion cooling of rocket nozzles, both
of which involve turbulent boundary-layer conditions . author
emphasizes the tedious experimental problems involved in research
on boundary layers with blowing, and notes the desirability of
velocity distribution measurements, especially in turbulent injection
layers . the observation that no good data on concentration
profiles in the case of the diffusion boundary layer have been
published may be an overstatement, since author's bibliography
overlooks the work of j. berger (/contribution a l'etude de l'injection
parietale,/ doctor's thesis, university of paris, memorial des
poudres 38 (annex), p. 1,. paris, imprimerie nationale, 1956) .
.I 345
.T
the interaction of shock waves with boundary layer
on a flat surface .
.A
barry,f.w., shapiro,a.h. and neumann,e.p.
.B
j. ae. scs. 18, 1951, 229.
.W
the interaction of shock waves with boundary layer
on a flat surface .
the development of supersonic compressors, supersonic
diffusers, and high-speed aircraft points to the increasing
importance of the interaction between shock waves and boundary
layers .
the experimental work reported here is intended to (1)
provide a better understanding of the nature of the shock
boundary-layer interaction, (2) serve as a guide and stimulus to theoretical
work, and (3) develop an empirical method for predicting the
effects of the interaction .
experiments were performed on the reflection of an oblique
shock from a boundary layer on a flat surface at a mach number
of 2.05 . the effects of shock strength and boundary-layer regime
were explored .
the results are in the form of schlieren photographs,
constant-density contours found from interferometer photographs, and
static pressure distributions at the plate surface .
.I 346
.T
measurements of turbulent friction on a smooth flat plate in supersonic .
.A
.B
.W
measurements of turbulent friction on a smooth flat plate in supersonic .
direct measurements of supersonic local skin friction, using the
floating-element technique, are presented for mach numbers from
bulent flow and transition are emphasized, although some
measurements in the laminar regime are included . the observed effect
of compressibility is to reduce the magnitude of turbulent skin
friction by a factor of two at a mach number of 4.5 and a
reynolds number of about 10 .
the boundary-layer momentum-integral equation for constant
pressure is verified within a few per cent by two experimental
methods . typical static pressure measurements are presented to
show that transition can be detected by observing disturbances
in pressure associated with changes in displacement thickness
of the boundary layer .
it is found that the turbulent boundary layer cannot be defined
experimentally for values of less than about 2,000, where
is the momentum thickness . for larger values of there is a
unique relationship between local friction coefficient and
momentum-thickness reynolds number at a fixed mach number . the
appendix compares the present measurements at m = 2.5 with
experimental data from other sources .
.I 347
.T
boundary layer measurements in hypersonic flow .
.A
hill,f.k.
.B
j. ae. scs. 21, 1954, 433.
.W
boundary layer measurements in hypersonic flow .
experimental data are presented on boundary-layer formation,
heat transfer, and skin-friction coefficient at mach numbers of
the wall of a conical nozzle in the presence of a favorable pressure
gradient and several rates of heat transfer . the reynolds
number based on momentum thickness varied from 1,500 to 3,500 .
comparison is made with data at lower mach numbers and with
the semiempirical theory of von karman . the existing data up
to mach numbers of nine indicate agreement to within 5 per
cent when compared with a form of the wilson theory, but it is
clear that the effects of heat transfer and pressure gradients
present problems which require extensive study and experiment in
the future .
.I 348
.T
turbulent boundary layer in compressible fluids .
.A
van driest,e.r.
.B
j.ae.scs. 18, 1951, 145.
.W
turbulent boundary layer in compressible fluids .
the continuity, momentum, and energy differential equations
for turbulent flow of a compressible fluid are derived, and the
apparent turbulent stresses and dissipation function are
identified . a general formula for skin friction, including heat
transfer to a flat plate, is developed for a thin turbulent boundary
layer in compressible fluids with zero pressure gradient . curves
are presented giving skin-friction coefficients and heat-transfer
coefficients for air for various wall-to-free-stream temperature
ratios and free-stream mach numbers .
in the special case when the boundary layer is insulated, this
general formula yields skin-friction coefficients higher than those
given by the von karman wall-property compressible-fluid
formula but lower than those given by the von karman
incompressible-fluid formula . heat transfer from the boundary layer
to the plate generally increases the friction and heat-transfer
coefficients .
.I 349
.T
numerical solution of the boundary layer equations
without similarity assumptions .
.A
kramer,r.f. and lieberstein,h.
.B
j. ae. scs. 26, 1959, 508.
.W
numerical solution of the boundary layer equations
without similarity assumptions .
the crocco transformation combined with a mangler
transformation is used to carry the boundary-layer problem for axially
symmetric blunt bodies into a form suitable for direct numerical
computation without introduction of similarity assumptions .
conditions which in the original problem appear at infinity now
are brought to a finite straight line, and the body is transformed
to a parallel line . data can be generated on the stagnation line
the equations are a parabolic system of two second-order
equations, the boundary-value problem is analogous to the slab
problem for the heat equation . an implicit difference equation is
used to reduce stability difficulties . special techniques in
forming the difference equation result in a linear system of algebraic
equations to be solved on any given line of integration, and these
solutions are computed from recursion relations generated by
back substitution . for bluntnosed bodies with approach flow
mach numbers greater than 8 (approximately), large
temperature gradients occur across a thin boundary layer of dissociated
gas, and it is necessary to use real-gas effects, approximated here
by certain fits to the gas tables . a case is computed, however,
for a lower mach number approach flow using perfect-gas theory
to provide a standard against which similarity solutions may be
tested .
.I 350
.T
laminar jet mixing of two compressible fluids with heat release .
.A
s. i. pai
.B
university of maryland
.W
laminar jet mixing of two compressible fluids with heat release .
the laminar jet mixing problems with heat release have been formulated .
a general discussion of the solution of these problems is also given .
the important parameters of these problems are brought out . some
specific cases of the jet mixing problem, such as jet mixing of one
compressible fluid, isothermal jet mixing of two compressible fluids,
and isovel jet mixing of two compressible fluids with heat release, are
discussed in detail.
.I 351
.T
thermal distributions in jeffrey-hamel flows between nonparallel plane
walls .
.A
millsaps, k. and pohlhausen, k.
.B
j. aero. sc. v. 20. march 1953, pp 187-196 .
.W
thermal distributions in jeffrey-hamel flows between nonparallel plane
walls .
the authors give the exact solution for the thermal distributions for
the steady laminar flow of a viscous incompressible fluid between
non-parallel plane walls held at a constant temperature . the velocity
profiles are determined with the aid of jacobian elliptic functions by
using the jeffery-hamel solution of the hydrodynamic problem . it is
shown that in this special case the energy equation giving the
temperature profiles can be reduced to an ordinary linear differential
equation with variable coefficients . after the introduction of
dimensionless parameters, numerical solutions are given for diverging and
converging channels with total openings of 10degree for the possible
combinations of three reynolds numbers and five prandtl numbers .
.I 352
.T
on heat transfer over a sweat-cooled surface in laminar
compressible flow with a pressure gradient .
.A
murduchow,m.
.B
j. ae. scs. 19, 1952, 705.
.W
on heat transfer over a sweat-cooled surface in laminar
compressible flow with a pressure gradient .
a simple expression is derived for the normal injection velocity
distribution theoretically required to maintain a given uniform
temperature along a porous surface in the laminar
boundary-layer region of a compressible flow with a given velocity
distribution outside of the boundary layer . this expression is valid for
any given free-stream mach number but is based on a prandtl
number of unity and on the assumption that the viscosity
coefficient varies linearly with the temperature . by using the
dorodnitsyn type of transformation, the variation of fluid
properties even in the case of zero mach number is taken into
account . this study is of particular practical interest in
connection with the sweat-cooling of turbine blades and of airfoil surfaces
in high speed flow . the method of analysis consists of applying
the karman-pohlhausen method to both the momentum and
energy boundary-layer equations and of using an additional heat
balance equation, involving the coolant temperature . a
closed-form approximate solution of the equations is then derived .
numerical examples for flow in the immediate vicinity of a
stagnation point and for a typical type of flow over a turbine blade are
given .
.I 353
.T
the effect of helium injection at an axially symmetric stagnation
point .
.A
h. hoshizaki and h. j. smith
.B
missile and space division, lockheed aircraft corporation,
sunnyvale, calif.
.W
the effect of helium injection at an axially symmetric stagnation
point .
an effective means of protecting the surface of a hypersonic re-entry
vehicle is to inject small quantities of a lightweight gas into the
boundary layer through a porous wall . this process, which is known
as mass-transfer cooling, protects the surface in two ways . first
of all, as the injected gas or coolant passes from the reservoir through
the wall to the surface, a considerable quantity of heat is absorbed as
its temperature is raised from the reservoir temperature to the wall
surface temperature . characteristically, lightweight gases have
relatively high specific heats .
secondly, the transfer of mass and enthalpy by convection and diffusion
normal to the surface alters the characteristics of the boundary
layer in such a manner as to reduce the temperature gradient at the
wall, and, hence, the conductive heat transfer at the wall . this is
sometimes referred to as the blowing effect .
.I 354
.T
laminar heat-transfer and pressure measurements over blunt-nosed
cones at large angle of attack .
.A
victor zakkay
.B
research associate, polytechnic institute of brooklyn, freeport, n.y.
.W
laminar heat-transfer and pressure measurements over blunt-nosed
cones at large angle of attack .
tests have been conducted at a mach number of 6, in the pibal hypersonic
facility, in order to determine the heat-transfer and pressure
distributions over a slender blunted cone at angles of attack of
erature ratio, stagnation to wall, was approximately 2.3 . the model
tested has a sperical nose diameter of 1.0 in., a base diameter of 3.75
in., and a cone half-angle of 20 degrees . the measurements were made
at 5 peripheral stations on the model .
in this note the experimental results at a 15 degree angle of attack
are presented . a more detailed analysis of the results for all
angles of attack is presented in reference 1 .
.I 355
.T
the injection of air into the dissociated hypersonic laminar boundary
layer .
.A
sinclaire m. scala
.B
research engineer
missile and ordnance systems department, general electric company,
philadelphia, pa.
.W
the injection of air into the dissociated hypersonic laminar boundary
layer .
in first approximation, dissociated air may be treated as a binary
mixture of air atoms and air molecules . in order to include the
effects of mass transfer into the boundary layer, it becomes necessary
to introduce a third chemical species and hence a second diffusion
equation . we have avoided this complexity by considering the injection
of air molecules into the boundary layer, and hence the theoretical
treatment is accomplished within the framework of a binary mixture gas .
.I 356
.T
on optimum nose curves for missiles in the super-aerodynamic
regime .
.A
tan,h.s.
.B
j. ae. scs. 25, 1958, 56.
.W
on optimum nose curves for missiles in the super-aerodynamic
regime .
author shows that the differential equations defining the
minimum drag body shapes for free molecule flow that were developed
and numerically integrated by w. j. carter (amr 11 (1958), rev.
realized, however, that numerical or analytical integration of the
second-order differential equation is unnecessary since, for the
flow conditions considered, the first integral to the euler equation
can be written prior to the substitution of the expression defining
the pressure coefficient .
.I 357
.T
optimum nose shapes for missiles in the super-aerodynamic
region .
.A
carter,w.j.
.B
j. ae. scs. 24, 1957, 527.
.W
optimum nose shapes for missiles in the super-aerodynamic
region .
the mechanics of the kinetic theory of gases is employed to
describe the drag force on the nose of a missile moving in the
super-aerodynamic region of the atmosphere . three separate cases are
considered--ideal specular reflection, specular-type reflection
from a slightly rough surface, and surface absorption followed by
random emission of the striking molecules . the calculus of
variations is employed to obtain the differential equation of the nose
shape which minimizes the drag force for each of the three cases .
the resulting differential equations are then solved by a numerical
procedure . the drag coefficients for the optimum nose shapes are
likewise determined and these are compared with the drag
coefficients given by other nose shapes . it is further shown that
the drag coefficients arising when specular-type reflections occur
are significantly dependent on the nose shape . when surface
absorption followed by random emission occurs, the drag
coefficient is not strongly dependent on either the missile nose shape
or the fineness ratio of the nose .
.I 358
.T
on the model of the free shock separation, turbulent
boundary layer .
.A
mager,a.
.B
j. ae. scs. 1956, 181.
.W
on the model of the free shock separation, turbulent
boundary layer .
by free shock-separated boundary layers, one means that type of
separation where the flow downstream of the separation region is free to
adjust to any direction that may result from the shock-boundary-layer
interaction process . a detailed model of the free shock-separated
turbulent boundary layer is postulated, and the pressure rise following
from this model is estimated and compared with experiments . the
results are applied to the prediction of separation in an overexpanded
nozzle .
.I 359
.T
note on the hypersonic similarity law for an unyawed
cone .
.A
lees,l.
.B
j. ae. scs. 18, 1951.
.W
note on the hypersonic similarity law for an unyawed
cone .
it is now known that the hypersonic similarity law derived for
slender cones and ogival bodies under the assumption, is
applicable for mach numbers as low as 3 . this note makes use of
a series development to infer the hypersonic similarity law for
unyawed cones from the taylor-maccoll differential equations and
associated boundary conditions . a simple approximate formula
for the function of the similarity law is obtained,
and the drag function computed with this formula is compared
with kopal's numerical results and, for very slender cones, with
von karman's linearized formula .
.I 360
.T
lift on inclined bodies of revolution in hypersonic flow .
.A
grimminger, g., williams, e. p., and young, g.
.B
j. aero. sc. v. 17, november, 1950 .
.W
lift on inclined bodies of revolution in hypersonic flow .
the importance of body lift lies in the fact that at moderate angles of
attack and high mach number it can constitute an appreciable part of
the total lift of a winged missile . in this paper an attempt has been
made to analyze body lift in hypersonic flow by an approximate method
and, together with a correlation of existing experimental data, to
indicate the probable variation of body lift over a wide range of mach
numbers extending from low supersonic to hypersonic . the method of
analysis of hypersonic flow over inclined bodies of revolution employed
herein has been denoted as the hypersonic approximation . it is an
improvement on the newtonian corpuscular theory of aerodynamics, since it
considers the centrifugal forces resulting from the curved paths of the
air particles in addition to the impact /newtonian/ forces .
.I 361
.T
the flow of a viscous liquid past a flat plate at small
reynolds number .
.A
tomotika,s. and yosinobu,h.
.B
j. math.phys. 35, 1956.
.W
the flow of a viscous liquid past a flat plate at small
reynolds number .
the authors repeat the earlier calculations of piercy
and winny (proc. roy. soc. london. ser. a. 140 (1933),
earlier works were known to be different from each other .
the careful analysis of the present authors shows that the
skin-friction coefficient up to the second approximation
agrees perfectly with that of piercy and winny .
.I 362
.T
three-dimensional effect of flutter in a real fluid .
.A
wen-hwa chu
.B
senior research engineer, department of mechanical sciences,
southwest research institute, 8500 culebra road, san antonio 6, texas
.W
three-dimensional effect of flutter in a real fluid .
in ref. 1, an alternative semi-empirical formulation for flutter in a
real fluid is given . for more accurate determination of the empirical
coefficients, the three-dimensional effect of finite span should be
taken into account . following reissner's approximation for
large-aspect-ratio rectangular wings, the boundary-value problem governing the
downwash w and the vorticity distribution .
.I 363
.T
an alternative formulation of the problem of flutter
in real fluids .
.A
chu,w.h. and abramson,h.n.
.B
j. ae. scs. 26, 1959.
.W
an alternative formulation of the problem of flutter
in real fluids .
it is well known, in steady flow, that the actual lift curve
slope is somewhat less than that predicted by inviscid flow
theory, even at small angles of attack . as the stall angle is
approached, the lift curve slope continually decreases and thus
deviates even more from the theoretical value . pinkerton
employed the measured circulation to determine the pressure
distribution and found that the resulting prediction of the moment
is considerably improved over that given by the classical theory .
this amounts to replacing the conventional kutta-joukowski
condition with the condition that the total lift should agree with
the measured value, and this, in turn, completely determines the
flow pattern . practically, this is accomplished by giving a
fictitious camber to the profile . since potential flow theory is
valid outside of the boundary layer, once the boundary-layer
thickness is known, the potential flow may be corrected for the
displacement thickness and the viscous wake by appropriate
source distributions . the boundary layer cannot be evaluated,
of course, until the potential flow is known and the circulation is
applied . a criterion to determine the circulation, by
generalizing the kutta-joukowski condition, was proposed by preston
and spence by assuming that the pressure at the trailing edge
shall have the same value when determined from the
potential-flow values above and below the airfoil . this procedure gives
qualitative information concerning viscous effects in steady
flow .
.I 364
.T
a method for analysing the insulating properties of
the laminar compressible boundary layer .
.A
libby,pa. and pallone,a.
.B
j. ae. scs. 21, 1954.
.W
a method for analysing the insulating properties of
the laminar compressible boundary layer .
in some cooling problems associated with high energy flows
it may be convenient to localize strongly the cooling, as for
example by injecting a coolant through an upstream porous strip,
and to depend on the insulating properties of the boundary layer
to reduce, or to eliminate completely the need for further cooling
on the surface downstream of the highly cooled section . this
upstream cooling technique may be of interest in connection with
optical windows in hypersonic wind tunnels, and on radomes,
wings, and bodies of high-speed aircraft and missiles .
in this paper a method for investigating the insulating
properties of a laminar compressible boundary layer on a two-
dimensional surface with zero heat transfer is presented . the physical
situation considered thus corresponds to the case in which the
heat transfer downstream of the strongly cooled section is
completely eliminated . of practical concern is how the
temperature of the uncooled surface varies in the downstream direction
from its low initial value and thus how the low energy layer
established by the upstream cooling insulates the downstream
surface .
the karman integral method extended to both the momentum
and energy partial differential equations of the boundary layer
has been used . the station, at which cooling and or injection
ceases, corresponds to a discontinuity in boundary conditions
and thus in solutions . at this point the flux of mass, momentum,
and energy within the boundary layer has been made continuous
by the introduction of three additional parameters in the velocity
and stagnation enthalpy profiles . thus the velocity and
stagnation enthalpy profiles have both been taken as sixth degree
polynomials . the resulting two integral-differential equations
are then solved for two unknown functions of the distance along
the wall . these two functions are related to the boundary-layer
thickness and to the wall temperature . initial conditions
corresponding to a given initial wall temperature and an initial
boundary-layer thickness are prescribed . exact closed-form solutions
for the case of zero axial pressure gradient are obtained . for
flows with significant pressure gradients, numerical solutions
are required in general . several numerical examples of practical
interest are presented .
.I 365
.T
the homogeneous boundary layer at an axisymmetric stagnation
point with large rates of injection .
.A
libby,p.a.
.B
j. ae. scs. 29, 1962.
.W
the homogeneous boundary layer at an axisymmetric stagnation
point with large rates of injection .
this report presents a theoretical analysis of the boundary
layer at an axisymmetric stagnation point with large rates of
air injection . the results of a previous investigation indicated
that for localized mass transfer in the stagnation region, the
rates of injection are considerably greater than those usually
treated . the exact stagnation-point boundary-layer equations
are integrated numerically for an approximate representation
of the gas properties . the two-point boundary conditions are
treated in a new manner which is useful for various
boundary-layer and mixing problems . the exact solutions indicate that
for large rates of injection the boundary layer is closely
represented by an inner isothermal shear flow and by and exterior,
relatively thin region, in which the flow variables change to their
free-stream values . an integral method based on profiles
suggested by the exact solutions is developed and shown to lead
to accurate predictions of the integral thicknesses which are
of interest for a study of the downstream influence of the
stagnation-point mass transfer .
.I 366
.T
helium injection into the boundary layer at an axisymmetric
stagnation point .
.A
fox,h. and libby,p.a.
.B
j. ae. scs. 1962, 921.
.W
helium injection into the boundary layer at an axisymmetric
stagnation point .
this report presents a theoretical analysis of the boundary
layer at an axisymmetric stagnation point with large rates of
helium injection . the exact stagnation-point boundary-layer
equations are integrated numerically with approximate
representations of the gas properties . the treatment of the
two-point boundary-value problem employed herein is shown to be
useful for various boundary-layer and mixing problems . the
exact solutions indicate that for large rates of injection the
boundary layer can be represented by a thick, inner layer of
constant shear, temperature, and composition and by a relatively
thin outer region in which the flow variables adjust to their
free-stream values . an inviscid-flow model is shown to lead to
accurate predictions of this shear layer and will thus provide
sufficiently accurate profiles for use in the study of the downstream
influence of stagnation-point mass transfer . the heat transfer
to the stagnation point is also considered . tabulations of the
eigenvalues for a variety of wall conditions and injection rates
are given .
.I 367
.T
control system and analysis and design via the second method of
lyapunov .
.A
kalman, r. e. and bertram, j. e.
.B
trans. asme. series d, v. 82, june 1960 .
.W
control system and analysis and design via the second method of
lyapunov .
the/second method/of lyapunov is the most general approach currently in
the theory of stability of dynamic systems . after a rigorous exposition
of the fundamental concepts of this theory, applications are made to/a/
stability of linear stationary, linear nonslationary, and nonlinear
systems,./b/estimation of transient behavior,./c/control-system
optimization,./d/design of relay servos . the discussion is essentially
self-contained, with emphasis on the thorough development of the
principal ideas and mathematical tools . only systems governed by
differential equations are treated here . systems governed by difference
equations are the subject of a companion paper .
.I 368
.T
some problems of polar missile control .
.A
best,d.
.B
j.roy.ae.soc., 64, 1960.
.W
some problems of polar missile control .
a polar-controlled missile is one in which manoeuvre
is carried out by rotations about roll and pitch axes,
that is, in the manner of a conventional aeroplane . this
paper discusses some problems in the application of this
form of control to homing missiles .
in comparison with the alternative cartesian
configuration, this method presents some special design
problems . in the former case, it is often possible to
resolve the motion into two planes and consider the
pitch and yaw control systems as independent
two-dimensional problems . this simplification is not
possible in the case of polar control and it is usually
necessary to consider the whole three-dimensional
system . the equations of motion which result are, in
general, not susceptible to analysis . because of this,
the design of control systems requires extensive use of
simulators .
.I 369
.T
an approximate solution of the supersonic blunt body
problem for prescribed arbitrary axisymmetric shapes .
.A
traugott,s.
.B
j. ae. scs. 27, 1960, 361.
.W
an approximate solution of the supersonic blunt body
problem for prescribed arbitrary axisymmetric shapes .
the integral method of belotserkovskii has been carried out to
the first approximation for arbitrary blunt axisymmetric bodies
in supersonic or hypersonic flight . this method is direct, in
that it gives the surface-pressure distribution and shock shape for
a prescribed body . results obtained by numerical integration
for several body shapes at several mach numbers are compared
to experimental results with good agreement . it is also shown
that the method can be successfully applied to pointed bodies
with attached shock . in the stagnation region, simple
relationships are found from the equations of the first approximation
which connect the surface-velocity gradient, shock curvature,
shock-detachment distance, and body curvature . these
relations are also correlated with experiment for a variety of shapes
as a function of mach number . the correlations permit a rapid
estimate of the stagnation-point velocity gradient, important for
heat-transfer calculations, for any blunt body from the shock
stand-off distance . a method for a higher approximation is
described, for which, in contrast to the higher approximations of
belotserkovskii, a large number of simultaneous total differential
equations with unknown parameters does not occur . one form
of this method has been studied numerically . results are given
which, though only partially successful, indicate the amount of
improvement to be expected from a higher approximation .
.I 370
.T
theoretical pressure distribution on a hemisphere-cylinder
combination .
.A
anthony casaccio
.B
research assistant, aerodynamics laboratory, polytechnic institute
of brooklyn, freeport, n.y.
.W
theoretical pressure distribution on a hemisphere-cylinder
combination .
in recent years great use has been made of approximate methods for
the determination of the pressure distribution on blunt-nosed bodies
and afterbodies at high mach numbers . for quasi-spherical bodies
it has been suggested that modified newtonian theory in combination
with a prandtl-meyer expansion be used on the nose portion, the two
laws being matched at the point where the pressure gradients are equal .
no simple approximation, however, has been found for flat-nosed bodies .
as for the pressure distribution on the afterbody, the blast-wave
analogy has been suggested for general nose shapes but particular
afterbody profiles .
the purpose of the present note is to compare these approximate
estimates with a more accurate determination of the flow field about
a hemisphere-cylinder in an ideal gas flow . it was felt that since
experimental investigations in air at this mach number are scarce
and very difficult to obtain, the comparison would be of interest . the
basis of comparison is the flow field as it results from a numerical
integration of the exact equations governing the motion of the ideal
fluid .
.I 371
.T
note on tip-bluntness effects in the supersonic and
hypersonic regimes .
.A
bennett,f.d.
.B
j. ae. scs. 24, 1957, 314.
.W
note on tip-bluntness effects in the supersonic and
hypersonic regimes .
in a recent letter, m. h. bertram presents some data on
flows at m = 6.85 around 10 half-angle cones with blunted
tips . since the demarcation between the supersonic and
hypersonic regimes is not sharp and since one expects hypersonic flows
to be generally similar to those at lower mach numbers--
especially where viscous effects do not predominate throughout the
entire field of interest--it is of some value to compare bertram's
results with those obtained by giese and bergdolt for 15
half-angle cones at m = 2.45 . following the observation by charters
and stein that drag coefficient measurements on blunted cones
imply a reynolds number effect, giese and bergdolt study the
convergence to conical flow of the perturbed flow about a cone
with truncated tip . they employ the mach-zehnder
interferometer and the conical flow criterion as analytical tools .
.I 372
.T
an experimental investigation of flow about simple
blunt bodies at a nominal mach number of 5. 8.
.A
oliver,r.e.
.B
j. ae. scs.23, 1956, 177.
.W
an experimental investigation of flow about simple
blunt bodies at a nominal mach number of 5. 8.
an experimental investigation was
conducted in the galcit hypersonic
wind tunnel to determine flow characteristics
for a series of blunt bodies at a
nominal mach number of 5.8 and free-stream
reynolds numbers per in. of
measured values for the pressure
coefficient distributions are compared with
a modified newtonian
expression . the agreement is very good for the
three-dimensional bodies and is
fair for the circular cylinder transverse to the
free-stream flow direction . a
complete report of the investigation is given in
a galcit hypersonic wind
tunnel memorandum .
.I 373
.T
the generalized expansion method and its application
to bodies travelling at high supersonic airspeeds .
.A
eggers,a.j., savin,r.c. and syvertson,c.a.
.B
j.ae.scs. 22, 1955, 231.
.W
the generalized expansion method and its application
to bodies travelling at high supersonic airspeeds .
it is demonstrated that the shock-expansion method can be
generalized to treat a large class of hypersonic flows, only one of
which is flow about airfoils . this generalized method predicts
the whole flow field, including shock-wave curvatures and
resulting vorticity, providing that (1) disturbances originating on
the surface of an object are largely absorbed in shock waves with
which they interact and (2) disturbances associated with the
divergence of stream lines in tangent planes to the surface are of
secondary importance compared to those associated with the
curvature of stream lines in planes normal to the surface . it is
shown that these conditions may be met in three-dimensional as
well as two-dimensional hypersonic flows . when they are met,
surface streamlines may be taken as geodesics, which, in turn,
may be related to the geometry of the surface .
the validity of the generalized shock-expansion method for
three-dimensional hypersonic flows is checked by comparing
predictions of theory with experiment for the surface pressures and
bow shock waves of bodies of revolution . the bodies treated
are two ogives having fineness ratios of 3 and 5 . tests were
conducted at mach numbers from 2.7 to 6.3 and angles of attack up
to 15 degrees in the 10- by 14-in. supersonic wind tunnel of the
ames aeronautical laboratory . at the lower angles of attack,
theory and experiment approach agreement when the ratio of
mach number to fineness ratio--that is, the hypersonic
similarity parameter--exceeds 1 . at the larger angles of attack, theory
tends to break down, as would be expected, on the leeward sides
of the bodies .
as a final point, it is inquired if the two-dimensionality of
inviscid hypersonic flows has any counterpart in hypersonic
boundary-layer flows . the question is answered in the
affirmative, and results of experiment are employed to provide a partial
check of this conclusion .
.I 374
.T
an investigation of optimum zoom climb techniques .
.A
kelly,h.j.
.B
j. ae.scs. 26, 1959, 794.
.W
an investigation of optimum zoom climb techniques .
the problem of optimal zoom climb maneuvering of a turbojet
aircraft has been investigated using the mayer formulation of the
calculus of variations . the euler-lagrange equations governing
optimum symmetric flight have been integrated numerically by
digital computation .
discontinuities in thrust arising from turbojet afterburner
blowout have been treated, and conditions which must be
satisfied across the interface generated by the discontinuity have been
derived .
arbitrary control techniques have been compared with the
optimum, and it has been found that performance is relatively
insensitive to piloting technique unless a time limitation is
imposed which requires high maneuvering load factors .
.I 375
.T
steady flow in the laminar boundary layer of a gas .
.A
illingworth,c.r.
.B
proc. roy. soc. a, 199, 1949.
.W
steady flow in the laminar boundary layer of a gas .
if the boundary-layer equations for a gas are
transformed by mises's transformation, as
was done by karman tsion for the flow
along a flat plate of a gas with unit prandtl
number, the computation of solutions is
simplified, and use may be made of previously
computed solutions for an incompressible fluid .
for any value of the prandtl number, and
any variation of the viscosity with the temperature
t, after the method has been applied
to flow along a flat plate (a problem otherwise treated
by crocco), the flow near the forward
stagnation point of a cylinder is calculated with
dissipation neglected, both with the effect of
gravity on the flow neglected and with this effect
retained for vertical flow past a horizontal
cylinder . the approximations involved by the neglect
of gravity are considered generally,
and the cross-drift is calculated when a horizontal
stream flows past a vertical surface .
when, and the boundary is heat-insulated,
it is shown that the boundary-layer
equations for a gas may be made identical, whatever be
the main stream, with the
boundary-layer equations for an incompressible fluid with a certain,
determinable, main stream . the
method is also applied to free convection at a flat plate
variation with altitude of the state of the surrounding
fluid neglected) and to laminar flow in
plane wakes, but for plane jets the conditions,
previously imposed by howarth,
are also imposed here in order to obtain simple solutions .
.I 376
.T
transformation between compressible and incompressible
boundary layer equations .
.A
van le,n.
.B
j. ae. scs. 20, 1953.
.W
transformation between compressible and incompressible
boundary layer equations .
it is proposed to show that the boundary-layer equation of
compressible flow can be reduced to that of incompressible
flow . such work was initiated by stewartson and by rott and
crabtree . in the following some of the restrictions imposed by
references 1 and 2 will be removed, and it will be shown that the
transformation from compressible boundary layer to
incompressible boundary layer can be applied to the laminar, as well as
turbulent, case . a direct method will be used for this purpose .
.I 377
.T
a turbulent analog of the stewartson-illingworth transformation .
.A
culick,f.e. and hill,j.
.B
j. ae. scs. 25, 1958.
.W
a turbulent analog of the stewartson-illingworth transformation .
the stewartson-illingworth transformation is applied to the
integral momentum equation for compressible boundary-layer
flow, leaving the x-coordinate transformation unspecified,
however . it is shown that the transformed equation is the integral
momentum equation for incompressible flow if (a) the effect of
compressibility on the boundary-layer shape parameter h can be
represented by
and (b) the x-coordinate transformation is chosen to be suitably
related to the ratio of skin-friction coefficients in compressible
and incompressible flows .
experimental evidence is presented which shows that
condition (a) is satisfied for turbulent boundary layers up to m = 5 .
an x-transformation is chosen according to (b) and an equation is
presented which gives the turbulent boundary-layer growth in
compressible flow in terms of a simple quadrature . the
predictions of this equation are then compared with some
measurements on wind-tunnel nozzles .
.I 378
.T
engineering relations for friction and heat transfer to surfaces in high
velocity flow .
.A
eckert, e.
.B
j. aero. sc. v.22, august 1955, pp 585-587
.W
engineering relations for friction and heat transfer to surfaces in high
velocity flow .
in calculations of thermodynamic heating for high speed missiles
parameters have been used based on relationships which hold for
constant-property fluids . the validity of this procedure has been verified
recently in a survey of heat transfer in which a relationship for the
reference temperature was developed . a calculation procedure for
laminar and turbulent boundary layers, based on this relationship, is
given .
.I 379
.T
reverse flow and variational theorems for lifting surfaces
in nonstationary compressible flow .
.A
flax,a.h.
.B
j. ae. scs. 20, 1953.
.W
reverse flow and variational theorems for lifting surfaces
in nonstationary compressible flow .
a reverse-flow theorem for compressible nonsteady flow, valid
within the limits of linearized theory, is derived . this theorem
gives a general class of relations between linearized solutions for
lifting surfaces in direct and reverse flow . based on the same
considerations used to establish the theorem, an adjoint variational
principle, which may be useful in approximate solutions of
non-steady lifting surface problems, is obtained . to illustrate the
uses of the reverse-flow theorem, it is applied to the determination
of relations between aerodynamic coefficients in direct and
reverse flow and to the obtaining of influence functions for total
lift, pitching moment, and rolling moment for a wing oscillating
with arbitrary motion and surface deformation, in terms of the
pressure distributions for simpler cases in reverse flow .
.I 380
.T
effect of quasi-steady air forces on incompressible
bending-torsion flutter .
.A
dugundi,j.
.B
j. ae. scs. 1958.
.W
effect of quasi-steady air forces on incompressible
bending-torsion flutter .
explicit solutions are obtained for the bending-torsion flutter
of a two-dimensional airfoil in incompressible flow under the
assumptions that the theodorsen function, c(k) is set equal to a
real constant, and the diagonal virtual mass terms are negligible .
for the case of small bending to torsion frequency ratio, a
comparison is made of these quasi-steady solutions with an
earlier empirical expression suggested by theodorsen and garrick
for the nonsteady case, and the effect of the c(k) function is
indicated . the importance of the c.g. location for these small
cases is re-emphasized, and the possibility of flutter at zero
air speed is indicated .
.I 381
.T
the axisymmetric boundary layer on a long thin cylinder .
.A
glauert,m.b. and lighthill,m.j.
.B
proc. roy. soc. a, 230, 1955, 188.
.W
the axisymmetric boundary layer on a long thin cylinder .
the laminar boundary layer in axial flow about
a long thin cylinder is investigated by two
methods . one (2) is a pohlhausen method,
based on a velocity profile chosen to represent
conditions near the surface as accurately as
possible . the other (3) is an asymptotic series
solution, valid far enough downstream from
the nose for the boundary-layer thickness to
have become large compared with the cylinder
radius . another series solution (due to seban,
bond and kelly) is known, valid near enough
to the nose for the boundary layer to be thin
compared with the cylinder radius . the
pohlhausen solution shows good agreement with
both series, near and far from the nose, and
enables an interpolation to be made (4) between
them in the extensive range of distances from
the nose for which neither is applicable . the
final recommended curves, for the variation
along the cylinder of skin friction,
boundary-layer displacement area and momentum defect
area, are displayed in graphical and tabular
form (figure 1 and table 1) and are expected to
be correct to within about 2 .
the velocity near the wall is closely proportional
to the logarithm of the distance from the
axis,. this is the profile used in the pohlhausen
method . the analogy with the distribution
of mean velocity in turbulent flow over a flat
plate is discussed at the end of 2 .
.I 382
.T
a note on the laminar boundary layer on a circular cylinder in
axial incompressible flow .
.A
howard r. kelly
.B
u.s. naval ordnance test station, inyokern, china lake, calif.
.W
a note on the laminar boundary layer on a circular cylinder in
axial incompressible flow .
a correction is made for the equation to compute the ratio
of the displacement thickness on a cylinder to the corresponding
thickness on a flat plate .
.I 383
.T
integration of the boundary layer equations for a plane in compressible
flow with heat transfer .
.A
meksyn, d.
.B
proc. roy. soc. series a. v. 231, 1955. pp 274-180 .
.W
integration of the boundary layer equations for a plane in compressible
flow with heat transfer .
the equations of motion of compressible viscous flow with vanishing
pressure gradient past a plane are integrated in semi-convergent
expressions, for the case when the physical constants depend on
temperature and the prandtl number is close to unity .
simple expressions are obtained for the temperature and velocity
distributions in the boundary layer, the drag coefficient, and their
dependence on the physical constants,.they contain the well-known results
and several new ones .
for the case when the temperature of the boundary is either above, or
not much below, the temperature of the main flow, the results obtained
closely agree with crocco's numerical computations .
.I 384
.T
application of second-order shock-expansion theory
to several types of bodies of revolution .
.A
lavender,r.e. and deep,r.a.
.B
j. ae. scs. 23, 1956, 1052.
.W
application of second-order shock-expansion theory
to several types of bodies of revolution .
second-order shock-expansion theory is utilized to obtain equations
for the initial normal force curve slope, initial pitching moment curve
slope, and zero-lift wave drag for several type bodies of revolution .
bodies considered are the cone-cylinder, cone-cylinder-frustum,
cone-cylinder-frustum-booster, cone-frustum, and cone-frustum booster .
.I 385
.T
on a generalised porous-wall ?couette type? flow .
.A
lilley,g.m.
.B
j. ae. scs. 26,1959, 685.
.W
on a generalised porous-wall ?couette type? flow .
in a recent paper, the problem of a /couette-type/ flow in
which the fixed wall is porous has been considered . the
results quoted in the above reference can be obtained rigorously
by the method stated below in which a different interpretation to
one of the parameters is made .
.I 386
.T
a generalised porous-wall ?couette type? flow .
.A
cramer,k.r.
.B
j. ae. scs. 26, 1959, 121.
.W
a generalised porous-wall ?couette type? flow .
recently, it was observed that the two existing
boundary-layer texts (references 1 and 2) did not contain a solution
for the case of couette flow with a constant, uniformly
distributed suction or blowing . thus, the following analysis
considers a /couette-type/ flow between a stationary flat surface and
a slightly inclined flat plate moving at a constant velocity . in
addition, the flow is subjected to a constant, uniformly distributed
suction or blowing at the fixed surface .
.I 387
.T
heat transfer for laminar flow in an annulus with porous
wall .
.A
inman,r.m.
.B
j. ae. scs. 26, 1959, 532.
.W
heat transfer for laminar flow in an annulus with porous
wall .
temperature profiles and heat-transfer rates of established
incompressible flow through an annulus channel with porous walls
of constant temperatures are determined at different injection rates .
axial conduction and viscous dissipation are, as usual, neglected .
injecting fluid is tacitly assumed to have the same temperature as
the porous wall .
.I 388
.T
the pressure gradient induced by shear flow past a
flat plate .
.A
glauert,m.b.
.B
j. ae. scs. 1962, 540.
.W
the pressure gradient induced by shear flow past a
flat plate .
article is a continuation of an earlier note on papers by li
on a semiinfinite plate in a uniform shear flow . li had deduced
from the form of his equations that stream vorticity caused an
induced pressure gradient in the flow . later papers by li and
murray (amr 15(1962), rev. 7157) support the induced pressure
gradient theory . the author notes, however, that the mathematics used
by li and murray are not acceptable and the problem thus not
resolved . the present note sets up simple models of complete flows
examinable by elementary means . author holds that analyses
demonstrate conclusively that no pressure gradient is induced in
the boundary layer on a flat plate in a limited region of shear flow .
he notes that the original question in the case of unbounded shear
remains obscure--and anyway an unlimited shear layer is not of
great practical importance .
.I 389
.T
simple shear flow past a flat plate in a compressible
viscous fluid .
.A
li,t.y.
.B
j. ae. scs. 22, 1955, 724.
.W
simple shear flow past a flat plate in a compressible
viscous fluid .
by transformation of variables, the problem of a simple shear flow of
a compressible fluid over a flat plate is reduced to the corresponding
problem for an incompressible fluid . the prandtl number of the
compressible fluid is assumed to be unity and its viscosity to be a linear
function of temperature .
.I 390
.T
some panel-flutter studies using piston theory .
.A
johns,d.j.
.B
j. ae. scs. 25, 1958.
.W
some panel-flutter studies using piston theory .
the use of piston theory was recently advocated for
supersonic aeroelastic analyses, including the problem of panel flutter,
and this has stimulated the investigation reported here .
linear piston theory is mainly considered, but some effects of
introducing higher order terms are discussed .
flutter of rectangular simply supported panels and of
elliptically shaped clamped-edge panels is considered, and some
justification is provided for the use of /static/ aerodynamic forces
and the neglect of aerodynamic damping . hence, it is concluded
that ackeret loading gives more exact results than piston theory .
solution of the flutter equations is made by applying galerkin's
method to a rayleigh-type analysis using assumed modes of
deformation .
.I 391
.T
flutter of rectangular simply supported panels at high
supersonic speeds .
.A
hedgepeth,j.m.
.B
j. ae. scs. 24, 1957.
.W
flutter of rectangular simply supported panels at high
supersonic speeds .
the problem of panel flutter of rectangular simply supported
plates subjected to supersonic flow over one surface is treated
theoretically . the assumption is made, and subsequently
verified, that the /static/ approximation to the aerodynamic flutter
forces yields flutter boundaries with satisfactory accuracy for
mach numbers greater than about 2 . two panel flutter analyses
are performed using this static approximation in conjunction with
thin-plate theory--one employs aerodynamic strip theory, the
other aerodynamic surface theory . the influence of mach
number, dynamic pressure, panel aspect ratio, and midplane
stress on the panel thickness required to prevent flutter is
determined for extensive ranges of these parameters .
.I 392
.T
natural frequencies of rectangular plates with edges
elastically restrained against rotation .
.A
jogarao,v. and lakshmikantham,c.
.B
j. ae. scs. 1957.
.W
natural frequencies of rectangular plates with edges
elastically restrained against rotation .
plates with attachments to heavier members along the
edges can be described as having edges elastically restrained
against rotation, in many cases uniformly along each edge . at
the edges, setting slope, when is the edge bending
moment with always positive, the elastic restraint can be
analytically defined with describing respectively,
clamped and simply supported edges . in this note natural
frequencies of such plates are calculated mainly following the
nomenclature of dana young .
.I 393
.T
the shear flow along a flat plate with uniform suction .
.A
sakurai,t.
.B
j.ae.scs. 24, 1957.
.W
the shear flow along a flat plate with uniform suction .
recently, several authors have investigated the boundary
layer in a shear flow . in this note, an exact solution of the
navier-stokes equations will be presented, which represents the
boundary layer along an infinite flat plate with uniform suction
situated in a shear flow .
.I 394
.T
the viscous flow near a stagnation point when the external flow has
uniform vorticity .
.A
j. t. stuart
.B
national physical laboratory, teddington, middlesex, england
.W
the viscous flow near a stagnation point when the external flow has
uniform vorticity .
in view of the recent controversy between li and glauert on the nature
of the solution of the boundary-layer equations when the external
flow is rotational, it seems worthwhile to draw attention to a certain
exact solution of the navier-stokes equations which lends support to
glauert's point of view .
.I 395
.T
new methods in heat flow analysis with application
to flight structures .
.A
biot,m.a.
.B
j. ae. scs. 24, 1957.
.W
new methods in heat flow analysis with application
to flight structures .
new methods are presented for the analysis of transient heat
flow in complex structures, leading to drastic simplifications in
the calculation and the possibility of including nonlinear and
surface effects . these methods are in part a direct application of
some general variational principles developed earlier for linear
thermodynamics . they are further developed in the
particular case of purely thermal problems to include surface and
boundary-layer heat transfer, nonlinear systems with
temperature-dependent parameters, and radiation . the concepts of
thermal potential, dissipation function, and generalized thermal
force are introduced, leading to ordinary differential equations
of the lagrangian type for the thermal flow field . because of the
particular nature of heat flow phenomena, compared with
dynamics, suitable procedures must be developed in order to formulate
each problem in the simplest way . this is done by treating a
number of examples . the concepts of penetration depth and
transit time are introduced and discussed in connection with
one-dimensional flow . application of the general method to the
heating of a slab, with temperature-dependent heat capacity,
shows a substantial difference between the heating and cooling
processes . an example of heat flow analysis of a supersonic wing
structure by the present method is also given and requires only
extremely simple calculations . the results are found to be in
good agreement with those obtained by the classical and much
more elaborate procedures .
.I 396
.T
variational and lagrangian thermodynamics of thermal
convection-fundamental shortcomings of the heat transfer
coefficient .
.A
biot,m.a.
.B
j. ae. scs. 29, 1962.
.W
variational and lagrangian thermodynamics of thermal
convection-fundamental shortcomings of the heat transfer
coefficient .
extension of previous analyses, indicating the possibility of
extending the thermodynamics of irreversible processes to systems
which are not in the vicinity of an equilibrium state and for which
onsager's relations are not verified . this involves generalizations
beyond the narrow field of heat transfer and to principles of wider
range than those of current nonequilibrium thermodynamics .
.I 397
.T
a sublayer for fluid injection into the incompressible
turbulent boundary layer .
.A
turcotte,d.l.
.B
j. ae. scs. 27, 1960.
.W
a sublayer for fluid injection into the incompressible
turbulent boundary layer .
a sublayer region is introduced in which the intensity of
turbulence grows at a prescribed rate . the decrease in wall shear
stress due to fluid injection into the boundary layer is found under
the hypothesis that the effect of injection is restricted to the
sublayer region . experimental measurements of the velocity
profiles with fluid injection substantiate this hypothesis . the
theoretical decrease in wall shear stress is in good agreement
with experiment,. the solution is particularly simple and for small
values of the injection parameter it contains no arbitrary
parameters . the theory provides a similarity parameter which differs
from the one in general use .
.I 398
.T
heat transfer in turbulent shear flow .
.A
rannie,w.d.
.B
j. ae. scs. 23, 1956.
.W
heat transfer in turbulent shear flow .
the problems of heat transfer in turbulent shear flow along a
smooth wall are discussed from the point of view of von karman's
well-known 1939 paper on the analogy between fluid friction and
heat transfer . methods for extending the analysis to higher
prandtl numbers are suggested .
.I 399
.T
conduction of heat in composite slabs .
.A
jaeger, j. c.
.B
quart. appl. math. v. 8 july, 1950 . pp 187-198
.W
conduction of heat in composite slabs .
a method of calculating the total quantity of heat that passes through a
unit area from zero time to time t is developed . allowance is made for
surface resistance by regarding each contact resistance as an
additional layer of the appropriate thermal resistance and zero heat
capacity
.I 400
.T
buckling stress of clamped rectangular plates in shear .
.A
budiansky,b. and connor,r.w.
.B
naca tn.1559, 1948.
.W
buckling stress of clamped rectangular plates in shear .
by consideration of antisymmetrical, as well as symmetrical,
buckling configurations, the theoretical shear buckling stresses of
clamped rectangular flat plates are evaluated more correctly than in
previous work . the results given, which represent the average of upper
and lower-limit solutions obtained by the lagrangian multiplier method,
are within percent of the true buckling stresses .
.I 401
.T
inviscid hypersonic airflows with coupled non-equilibrium
processes .
.A
hall,j.g., eschenroeder,a.w. and marrone,p.v.
.B
ias paper 62-67, 1962.
.W
inviscid hypersonic airflows with coupled non-equilibrium
processes .
analyses have been made of the effects of coupled chemical rate
processes in external inviscid hypersonic airflows at high enthalpy
levels . exact (numerical) solutions have been obtained by the
inverse method for inviscid airflow over a near-spherical nose
under flight conditions where substantial nonequilibrium prevails
through the nose region . typical conditions considered include
nose radii of the order of 1 ft at an altitude of 250,000 ft and
velocities of 15,000 and 23,000 ft per sec .
the results illustrate the general importance of the coupling
among the reactions considered . these included
dissociation-recombination, bimolecular-exchange, and ionization reactions .
the exact solutions show the bimolecular, no exchange reactions
to be important in blunt-nose flow for the kinetics of no and n,
as they are in the case of a plane shock wave . an important
difference between blunt-nose flow and plane shock flow,
however, is the gasdynamic expansion in the curved shock layer of the
former . this expansion reduces post-shock reaction rates . as a
consequence, in the regime studied the oxygen and nitrogen-atom
concentrations tend to freeze in the nose region at levels below
those for infinite-rate equilibrium . the reduction below the
equilibrium dissociation level can be large, particularly for
nitrogen dissociation at higher velocities .
in the regime considered, the chemical kinetics are dominated
by two-body collision processes . the inviscid nose flow,
including coupled nonequilibrium phenomena, is thus amenable to
binary scaling for a given velocity . the binary scaling is
demonstrated for a range of altitude and scale by correlation of the
exact solutions for given velocity and a constant product of
ambient density and nose radius . this similitude, which can
also scale viscous nonequilibrium and radiation phenomena in the
shock layer, provides a useful flexibility for hypersonic testing
where it is applicable .
the afterbody inviscid-flow problem is briefly discussed in the
light of the results for the nose flow .
.I 402
.T
magnetohydrodynamics shocks .
.A
de hoffman,f. and teller,e.
.B
phys. rev. 80, 1950, 693.
.W
magnetohydrodynamics shocks .
a mathematical treatment of the coupled motion of
hydrodynamic flow and electromagnetic fields is
given . two simplifying assumptions are introduced .. first,
the conductivity of the medium is infinite, and
second, the motion is described by a plane shock wave .
various orientations of the plane of the shock and
the magnetic field are discussed separately, and the
extreme relativistic and unrelativistic behavior is
examined . special consideration is given to the behavior
of weak shocks, that is, of sound waves . it is
interesting to note that the waves degenerate into common
sound waves and into common electromagnetic
waves in the extreme cases of very weak and very strong
magnetic fields .
.I 403
.T
magnetohydrodynamic shock waves .
.A
helger,l.
.B
astrophys. j. 117, 1953, 177.
.W
magnetohydrodynamic shock waves .
an interpretation of the de hoffman-teller shock-wave
equations for an infinitely conducting
medium is given analogous to the classical interpretation of
the ordinary hydrodynamic shock-wave
equations of rankine and hugoniot . two cases of interest
are considered as a consequence of this theory .
it is shown that weak magnetic fields in interstellar clouds
will be amplified, and, if external mechanisms
are available to reduce the compressional effects of shock
waves, the field will reach a value,
where p is the pressure . also, some aspects of the internal
motions of prominences are considered ,. it is
shown that gauss will yield results in accord with
the observational material .
.I 404
.T
two dimensional transonic flow past airfoils .
.A
kuo,y.a.
.B
naca tn.2356.
.W
two dimensional transonic flow past airfoils .
this report concerns the problem of constructing solutions for
transonic flows over symmetric airfoils . the aspect of the problem
emphasized is, of necessity, not how to form a solution for compressible
flow but how to simplify the initial phase of the problem, namely, the
mapping of the incompressible flow . in the case of the symmetric
joukowski airfoil without circulation, the mapping is relatively simple,
but the coefficients in the power series are difficult to evaluate . as
a result, the problem requires simplification . instead of the exact
incompressible flow past the airfoil, an approximate flow is used, which
is derived from a combination of source and sink . this flow differs
only slightly from the exact one when the thickness is small . by the
same method, the flow with circulation is also considered .
after the incompressible-flow functions are approximated in this
fashion, the numerical calculation of the corresponding compressible
flow, by the hodograph theory, does not present any
essential difficulty .
.I 405
.T
tables of thermal properties of gases .
.A
joseph hilsenrath, chalres beckett, william bendict, liila fano, harold
hoge, joseph masi, ralph nuttall, yeram touloukian, harold woolley
.B
nbs circular 564 (1955)
.W
tables of thermal properties of gases .
tables of thermodynamic and transport properties
of air, argon, carbon dioxide, carbon monoxide, hydrogen,
nitrogen, oxygen, and steam .
.I 406
.T
on the behaviour of boundary layers at supersonic speeds .
.A
.B
.W
on the behaviour of boundary layers at supersonic speeds .
this paper considers the implications of recent advances in knowledge of
the behaviour of boundary layers in supersonic flow . only the simplest
case is considered-dashthat of the two-dimensional boundary layer on a
flat plate, with nominal zero longitudinal pressure and temperature
gradients .
it is shown that the empirical/intermediate enthalpy/used with success
in approximations for skin friction, etc., of laminar boundary layers is
closely the same as the mean enthalpy with respect to velocity .
furthermore, the mean enthalpics of laminar and turbulent boundary
layers may be the same . a nonrigorous approach is made to the problems
of self-induced pressure gradients, and the indications are that their
effects on laminar skin friction, etc., may become noticeable at mach
numbers greater than 5 and they increase as the surface temperature
builds up towards zero heat-transfer conditions . the effects with
turbulent boundary layers may not be so severe .
finally, the results are applied to give an idea of the magnitude of the
drag and aerodynamic heating problems up to m 10, and one result is
that, if there is any conflict at the higher mach numbers between
surface conditions required for high radiative emissivity and those
which may be thought necessary for preserving a laminar boundary layer,
then it may be better to choose the former .
.I 407
.T
stationary convection flow of an electrically conducting
liquid between parallel plates in a magnetic field .
.A
gershuni,g.z. and shukhovitskii,e.m.
.B
soviet physics,34, 1958.
.W
stationary convection flow of an electrically conducting
liquid between parallel plates in a magnetic field .
a study is made of the stationary convection
of an electrically conducting liquid in the space
between two parallel plates, heated to different
temperatures, in the presence of a magnetic
field . the distribution of velocity, temperature,
and induced fields are found, and the convective
heat flow is calculated .
.I 408
.T
on convective motion of a conducting fluid between
parallel vertical plates in a magnetic field .
.A
regirer,s.a.
.B
soviet physics, 37, 1960.
.W
on convective motion of a conducting fluid between
parallel vertical plates in a magnetic field .
stationary convective motion of a conducting fluid
between vertical parallel plates in a
magnetic field is considered . an exact solution of the
magnetohydrodynamic equations is
obtained for the case of a constant vertical temperature
gradient . the critical value of
grasshof's number is determined for the case when the
temperature of both plates is the same .
.I 409
.T
on the base pressure resulting from the interaction of a supersonic
external stream with a sonic or subsonic jet .
.A
chow, w. l.
.B
j. aero. sc. march, 1959 . p. 176-180 .
.W
on the base pressure resulting from the interaction of a supersonic
external stream with a sonic or subsonic jet .
it is shown that the two-dimensional base pressure problems relating to
base bleed into the wake of blunt-trailing-edge airfoils, or the
interaction between an external supersonic or sonic slipstream with a
sonic or subsonic jet stream of a jet engine, can be calculated by
theoretical considerations . constant-pressure, isoenergetic, turbulent
mixing between the streams and the stagnant fluid in the wake is
assumed . the theoretical calculations are in good agreement with the
experimental results .
.I 410
.T
the supersonic flow about a blunt body of revolution
for gases at chemical equilibrium .
.A
gravalos,f.g., edelflet,i.h. and emmons,h.
.B
9th int. astro. fed. 1958.
.W
the supersonic flow about a blunt body of revolution
for gases at chemical equilibrium .
the supersonic flow about a blunt body of
revolution for gases at chemical
equilibrium . a method to determine the shock
wave, and its location, about a body
of revolution moving at supersonic speeds is given .
the method provides also the means
to compute the flow characteristics in the shock layer .
the fluid in which the motion
takes place is assumed to be in chemical equilibrium
within the shock layer ,. its
thermochemical properties must be known . the essential
new features of the method are ..
a) it solves the direct problem, i. e., the initial data
are the conditions upstream and
the body shape ,. b) the integration of the fundamental
equations is done in the physical
plane and the difficulties inherent to other, less direct,
mathematical formulations
of the problem are avoided . a physical interpretation of
the method is made which
is in accord with the analytical definition of the problem .
.I 411
.T
data on shape and location of detached shock waves
in cones and sphere .
.A
herberle,j.w., wood,g.p. and gooderum,p.b.
.B
naca tn.2000, 1950.
.W
data on shape and location of detached shock waves
in cones and sphere .
accurate experimental data are given on the shape and the location
of detached shock waves on cones and spheres at mach numbers from 1.17
to 1.81 . the data are correlated to obtain equations that describe the
shock waves . this knowledge of the shock waves should be useful in
calculations of the pressure distribution and the pressure drag of the
fore part of cones and spheres . the experimental data on shock waves
are compared with theory .
.I 412
.T
critical combinations of shear and transverse direct
stress for an infinitely long flat plate with
edges elastically restrained against rotation .
.A
batdorf,s.b. and houbolt,j.c.
.B
.W
critical combinations of shear and transverse direct
stress for an infinitely long flat plate with
edges elastically restrained against rotation .
an exact solution and a closely concurring approximate
energy solution are given for the buckling of an infinitely long
flat plate under combined shear and transverse direct stress
with edges elastically restrained against rotation . it was found
that an appreciable fraction of the critical stress in pure shear
may be applied to the plate without any reduction in the
transverse compressive stress necessary to produce buckling . an
interaction formula in general use was shown to be decidedly
conservative for the range in which it is supposed to apply .
.I 413
.T
turbulent skin friction at high mach numbers and reynolds
numbers in air and helium . nasa r82, 1960 .
.A
matting,f.w., chapman,d.r., nyholm,j.r. and thomas,a.g.
.B
naca r847, 1946.
.W
turbulent skin friction at high mach numbers and reynolds
numbers in air and helium . nasa r82, 1960 .
results are given of local skin-friction measurements in turbulent
boundary layers over an equivalent air mach number range from 0.2 to 9.9
and an over-all reynolds number variation of 2x10 to 100x10 . direct
force measurements were made by means of a floating element . flows
were two-dimensional over a smooth flat surface with essentially zero
pressure gradient and with adiabatic conditions at the wall . air and
helium were used as working fluids . an equivalence parameter for
comparing boundary layers in different working fluids is derived and
the experimental verification of the parameter is demonstrated .
experimental results are compared with the results obtained by several
methods of calculating skin friction in the turbulent boundary layer .
.I 414
.T
the problem of resistance in compressible fluids .
.A
von karman,t.
.B
5th volta cong. 1955,226.
.W
the problem of resistance in compressible fluids .
this report is restricted to the
resistance of bodies of revolution and
of cylindrical bodies of infinite length
moving with uniform velocity in
a compressible fluid . in the case of bodies
of revolution it will be assumed
that the direction of the movement is
parallel to the axis of symmetry .
it will be assumed that the fluid satisfies
the equation of state of perfect
gases, i. e. const., where p denotes
the pressure, the density and
t the absolute temperature . in addition
to obeying this equation the
fluid is characterized by the statement
that the intrinsic energy of the
unit mass amounts to where for
simplicity's sake the specific heat
will be expressed in work rather
than heat units . the ratio between
the specific heat at constant pressure
and the specific heat at constant
volume will be denoted by . it is
known that the value of x depends
upon the number of degrees of freedom
of the molecules,. if this number
is denoted by n . for air
the value x = 1.4 will be used .
the limiting case x = 1 will
be referred to as that of a
assumed that in the range
considered and are independent of
the temperature .
.I 415
.T
the aerodynamic design of section shapes for swept wings .
.A
pearcey, h.h.
.B
2nd inter. congr. of int. council of aero. sc. september, 1960 .
.W
the aerodynamic design of section shapes for swept wings .
an extension of work of lock and rogers and the result of cooperation by
n.p.l., r.a.e. and members of the british aircraft industry to achieve a
satisfactory design for an aircraft cruising at low supersonic speeds .
knowledge of shock-wave prediction, onset of wave drag and
shock-induced separation allows the basic design to be generalized for a wide
range of parameters . unpublished work by bagley on the relation of
aerodynamic coefficients and geometry is used . the role of upper
surface velocity distribution is noted and methods for predicting pressure
distributions with shock waves are reviewed for both subsonic and
transonic flows .
.I 416
.T
methods of boundary-layer control for postponing and alleviating
buffeting and other effects of shock-induced separation .
.A
pearcey, h.h. and stuart, c.m.
.B
smf fund paper, no. f.f. -dash 22, 1959 .
.W
methods of boundary-layer control for postponing and alleviating
buffeting and other effects of shock-induced separation .
the use of boundary-layer control to increase the separation-free
margins of mach number and lift coefficient beyond the cruise point of
high-speed aircraft may often be preferred to design changes that impair
the cruising performance or the landing and take-off characteristics .
the factors that influence the choice of method and details of its
application are discussed, emphasising particularly the need to maintain
effectiveness over most of the chord to cover the wide range of
separation positions encountered as the shock moves over the wing with
changing flight conditions .
research at the national physical laboratory that has embraced
high-velocity blowing, vane and air-jet vortex generators, and, in a
preliminary way, distributed suction, is briefly described . the
relative merits of the various methods are discussed, and some results
achieved in their application are given .
for vortex generators, the importance is stressed of the vortex paths
determined by the interactions of neighbouring vortices and their
images . thus, systems of counter-rotating vortices always leave the
surface in pairs and lose their effectiveness . co-rotating systems are
therefore preferred for many applications . blowing, which in
wind-tunnel tests gives results as good as or better than vortex generators
and does not have the disadvantage of a drag penalty at cruise, has not
yet been assessed in flight . air-jet vortex generators, which would
also avoid the drag penalty, show promise of producing significant
effects with relatively small blowing pressures and quantities .
.I 417
.T
on the stability of two dimensional parallel flows .
.A
lin,c.c.
.B
pt.iii - stability in a viscous fluid. q. app. math. 3, 1945, 273.
.W
on the stability of two dimensional parallel flows .
this is the last part of the author's theory of the stability
of plane laminar motion . (for parts 1 and 2, cf. the same
quart. 3, 117-142, 218-234 (1945),. these rev. 7,225,226 .)
the stability character of a viscous fluid is considered in
detail . the author proceeds first to give a proof of a criterion
of stability due to heisenberg .. if a velocity profile has an
number and phase velocity, the disturbance with the same
wave number is unstable in the real fluid when the reynolds
number is sufficiently large . this destabilizing effect of
viscosity is one of the most interesting phenomena in the
general stability theory,. its physical and mathematical
significance is carefully discussed .
the author then discusses the behavior of the so-called
neutral curve for the two characteristic types of
velocity distribution, the boundary layer type profile and
the symmetrical profile . the asymptotic behavior of the
neutral curve is discussed first . the main difference between
profiles with and without a point of inflection is that the two
branches of the neutral curve approach and for
profiles with a flex, but both converge to for the profile
without a flex . the most important results are as follows .
for sufficiently large reynolds number r . (2) there always
exists a minimum r below which the motion is stable . a
similar result was obtained by synge from energy
considerations . synge found a limiting curve below which the
motion is necessarily stable . the author's discussion of the
asymptotic behavior of the curves shows further
that there always exists a maximum value of a beyond
which the motion is stable for all reynolds numbers . hence
the qualitative shape of the curve is determined .
the author proceeds to show that simple approximate
expressions for the stability limit can be obtained from his
general analysis for a given velocity profile . these
approximate stability limits for plane poiseuille flow and blasius
flow are found to be r=5906 and r=502 . the reynolds
numbers are based on the width of the channel and the
displacement thickness, respectively . finally, the method
for computing the complete instability curve is presented
and the plane poiseuille case and the blasius problem worked
out in detail . the stability limit for blasius flow had been
given before by tollmien and schlichting . the present more
exact computations agree well with tollmien's result as far
as the minimum critical reynolds number is concerned .
the value found here is r=420 . the neutral curve for
poiseuille motion had not been obtained before . the
minimum critical number here is found to be r=5314 . the
agreement with the estimate from the simple criterion
mentioned above is thus very good .
a discussion of the physical significance of the viscous
effects and of future developments concludes the paper .
.I 418
.T
transition form laminar to turbulent shear flow .
.A
morkovin,m.v.
.B
asme trans, 80, 1958,1121.
.W
transition form laminar to turbulent shear flow .
recent experimental studies of transition from laminar to
turbulent shear flows are reviewed . certain common features
are emphasized and related to the stability theories of viscous
shear layers . the three-dimensional character, the
unsteadiness, and the nonlinear and random behavior of the latter stages
of the transition process are also examined .
.I 419
.T
the design of intermediate vertical stiffeners on web
plates subjected to shear .
.A
rockey,k.c.
.B
aero. quart. 1956, 275.
.W
the design of intermediate vertical stiffeners on web
plates subjected to shear .
the correct design of intermediate vertical stiffeners on web plates
subjected to shear becomes very important when
the web plates are designed
to operate at loads close to their buckling loads .
this paper presents details
of an extensive series of tests conducted on
stiffened web plates subjected to
shear . from the analysis of the results obtained
from these tests, new empirical
relationships between the flexural rigidity and
spacing of the intermediate
stiffeners and the buckling stress of the stiffened
web plate have been obtained .
one interesting and important feature of
these new relationships is that
they define more clearly than hitherto the difference
in the behaviour of
single-and double-sided stiffeners .
.I 420
.T
an experimental study of the flow field about swept and delta wings
with sharp leading edges .
.A
jaszlics, i. and trilling, l.
.B
j. aero. sc. august 1959 . p 487 - 494, 544 .
.W
an experimental study of the flow field about swept and delta wings
with sharp leading edges .
a series of experiments was performed to define the flow field on the
upper surface of high aspect ratio swept wings and narrow delta wings at
high angles of attack .
it was found that near the root section of either type of wing the flow
is conical . the edge of the vortex sheet which originates at the
leading edge is a straight line whose position relative to the leading edge
depends only on incidence . on swept wings, the vortex edge turns
down-stream as soon as the vortex sheet covers the front half of the wing
chord, and the flow under the vortex sheet outboard of that turning
point is uniform and parallel to the leading edge of the wing . on
narrow delta wings, the conical symmetry persists almost to the trailing
edge .
.I 421
.T
analytic study of induced pressure on long bodies of
revolution with varying nose bluntness at hypersonic
speeds .
.A
van hise,v.
.B
nasa r78, 1960.
.W
analytic study of induced pressure on long bodies of
revolution with varying nose bluntness at hypersonic
speeds .
a systematic study of induced pressures on a series
of bodies of revolution with varying nose bluntness
has been made by using the method of characteristics
for a perfect gas . the fluid mediums investigated
were air and helium and the mach number range
was from 5 to 40 . a study of representative shock
shapes was also made . flow parameters obtained
from the blast-wave analogy gave good correlations of
induced pressures and shock shapes . the
induced-pressure correlations yielded empirical equations for
air and helium which cover the complete range of
nose bluntness considered . (nose fineness ratios
varied from 0.4 to 4.) available experimental
results were in good agreement with the characteristics
solutions . properties connected with the concept of
hypersonic similitude enabled correlations of the
calculations to be made with respect to nose shape,
mach number, and ratio of specific heats .
.I 422
.T
bending of a square plate with two adjacent edges free
and the others clamped or simply supported .
.A
leissa,a.w. and niedenfuhr,f.w.
.B
a.i.a.a. jnl. 1, 1963, 116.
.W
bending of a square plate with two adjacent edges free
and the others clamped or simply supported .
the title problems were solved for the two cases .. (1) uniform
transverse loading, (2) a concentrated force at the free corner . a
function is chosen to exactly satisfy the biharmonic equation
while the boundary conditions are enforced at a number of points
plied at discrete points around the boundary for each of the four
problems and the resulting 35 simultaneous equations were solved
on an ibm 704 . tables listing the values of deflection and
bending moments are presented . this paper provides useful information
on the solution of these problems which are intractable by
analytical methods .
.I 423
.T
an experimental investigation of the flow over blunt-nosed
cones at a mach number of 5. 8.
.A
machell,r.m. and o'bryant,w.t.
.B
guggenheim aero. lab. memo 32, 1956.
.W
an experimental investigation of the flow over blunt-nosed
cones at a mach number of 5. 8.
shock shapes were observed and static pressures were measured
on spherically-blunted cones at a nominal mach number of 5.8 over a
range of reynolds numbers per inch from 97,000 to 238,000, for angles
of yaw from 0 to 8 . six combinations of the bluntness ratios 0.4, 0.8,
and 1.064 with the cone half angles 10, 20, and 40 were used in
determining the significant parameters governing pressure distribution .
the pressure distribution on the spherical nose for both yawed
and unyawed bodies is predicted quite accurately by the modified
newtonian theory given by, where is the angle between the
normal to a surface element and the flow direction ahead of the bow
shock . cone half angle was found to be the significant parameter in
determining the pressure distribution near the nose-cone junction and
over the conical afterbody . on the 40 spherical nosed cone models
the flow overexpanded with respect to the taylor-maccoll pressure in
the region of the spherical-conical juncture, after which the pressure
returned rapidly to the taylor-maccoll value . for models with smaller
cone angles the region of minimum pressure occurred farther back on
the conical portion of the model, and the taylor-maccoll pressure was
approached more gradually . the shape of the pressure distributions
as described in nondimensional coordinates was independent of the
radius of the spherical nose and of the reynolds number over the range
of reynolds number per inch between .97 x 10 and 2.38 x 10 .
integrated results for the pressure foredrag of the models at zero
yaw compared very closely with the predictions of the modified newtonian
approximation, except for models with large cone angles and small nose
radii, where the drag approaches the value given by the taylor-maccoll
theory for sharp cones .
.I 424
.T
cantilever plate with concentrated edge load .
.A
holl,d.l.
.B
j.app.mech. 1937, 8.
.W
cantilever plate with concentrated edge load .
the author gives, by the method of finite differences, an
approximate solution of the problem of a finite length
of a cantilever plate which bears a concentrated load at
the longitudinal free edge . all the boundary conditions
are taken into account, and the plate action is
determined approximately at all points of the plate . the
author points out that a secondary maximum transverse
stress occurs at the clamped edge nearest the loading
point, and that the longitudinal stress is greatest directly
under the loading point .
.I 425
.T
the solution of elastic plate problems by electrical analogies .
.A
r. h. macneal,
.B
pasadena, calif.
.W
the solution of elastic plate problems by electrical analogies .
a dynamic-analogy method for the solution of elastic plate problems is
described in this paper . the electrical circuits developed here can be
set-up and studied on an electric-analog computer . problems involving
deflections under constant load, transient vibrations, or normal
modes can be solved in this way . the method of applying boundary
conditions to plates with irregular edges is given, together with
a detailed description of the representation of the boundary conditions
for a rectangular variable-thickness plate . solutions that have been
obtained on the cal tech electric-analog computer are presented for
the static deflections and normal modes of a rectangular cantilever
plate .
.I 426
.T
preliminary analysis of axial flow compressors having
supersonic velocity at the entrance of the stator .
.A
ferri,a.
.B
naca rm l9g06, 1949.
.W
preliminary analysis of axial flow compressors having
supersonic velocity at the entrance of the stator .
a supersonic compressor design having supersonic velocity at the
entrance of the stator is analyzed on the assumption of two-dimensional
flow . the rotor and stator losses assumed in the analysis are based on
the results of preliminary supersonic cascade tests . the results of
the analysis show that compression ratios per stage of 6 to 10 can be
obtained with adiabatic efficiency between 70 and 80 percent .
consideration is also given in the analysis to the starting,
stability, and range of efficient performance of this type of
compressor . the desirability of employing variable-geometry stators
and adjustable inlet guide vanes is indicated . although either
supersonic or subsonic axial component of velocity at the stator
entrance can be used, the cascade test results suggest that higher
pressure recovery can be obtained if the axial component is supersonic .
.I 427
.T
flow of gas through turbine lattices .
.A
deich,m.e.
.B
naca tm.1393, 1956.
.W
flow of gas through turbine lattices .
paper is a translation of chap. 7 of the book /technical
gas-dynamics/ (see amr 9, rev 1869) . the topics treated are best
shown by the list of paragraph headings . they are .. 7-1 .
geometrical and gasdynamical parameters of the lattices,.
fundamentals of flow through lattices,. 7-2 . theoretical methods of
investigation or plane potential flow of incompressible fluid through a
lattice,. 7-3 . electro-hydrodynamic analogy,. 7-4 . forces acting
on an airfoil in a lattice,. theorem of joukowsky for lattices,. 7-5 .
fundamental characteristics of lattices,. 7-6 . friction losses in
plane lattice at subsonic velocities,. 7-7 . edge losses in plane
lattice at subsonic velocities,. 7-8 . several results of
experimental investigations of plane lattices at small subsonic
velocities,. 7-9 . flow of gas through lattice at large subsonic
velocities,. critical mach number for lattice,. 7-10 . profile losses in
lattices at large subsonic velocities,. 7-11 . flow of a gas through
reaction lattices at supersonic pressure drops,. 7-12 . impulse
lattices in supersonic flow,. 7-13 . losses in lattices at near sonic
and supersonic velocities,. 7-14 . computation of angle of
deflection of flow in overhang section of a reaction lattice at supersonic
pressure drops,. 7-15 . characteristic features of three-dimensional
flow in lattices .
.I 428
.T
the quasi-cylinder of specified thickness and shell
loading in supersonic flow .
.A
portnoy,j.
.B
aero. quart. 11, 1960, 387.
.W
the quasi-cylinder of specified thickness and shell
loading in supersonic flow .
the methods of the operational
calculus are used to obtain a linear
approximation to the shape of the mean camber
surface of a quasi-cylinder in a
supersonic flow in terms of its shell thickness
and loading distributions . the
analysis deals with a generalised quasi-cylinder ,.
that is one which, although lying
close to a mean cylinder, need not possess
axial symmetry . the quasi-cylinder
is also permitted to be within the small
disturbance field of other separate
components, e.g. a centre-body . because
the linearised theory is inadmissable
for internal duct flows close to and beyond
the first reflected characteristic cone,
the present solution is likewise invalid close
to and beyond the position where
this characteristic meets the mean cylinder .
the work given here enables the
camber shapes of /ring-wings/, which have
been used theoretically to reduce or
even nullify the wave-drag of a central slender-body,
to be found . an example
illustrates the general method .
.I 429
.T
a description of the r. a. e. high speed supersonic
tunnel .
.A
poole,j.a.
.B
rae tn.aero.2678,1960
.W
a description of the r. a. e. high speed supersonic
tunnel .
an account is given of the high supersonic speed tunnel now nearing
completion . the design philosophy is reviewed, the principal features
are described and some of the more interesting development problems
are noted .
.I 430
.T
calibration of the flow in the mach 4 working section
of the 4ft . x 3ft . high supersonic speed wind tunnel
at rae bedford .
.A
andrews,d.r. and brown,c.s.
.B
rae tn.aero.2820, 1962.
.W
calibration of the flow in the mach 4 working section
of the 4ft . x 3ft . high supersonic speed wind tunnel
at rae bedford .
mach number and flow angle distributions in the working section of
the mach 4 nozzle of the 4 ft x 3 ft high-supersonic-speed wind tunnel
are presented for a range of total pressure and humidity .
.I 431
.T
free-flight measurements of the zero-lift drag and
base pressure on a wind tunnel interference model (m=0 .
8 - 1. 5) .
.A
greenwood,g.h.
.B
rae tn.aero.2725, 1960.
.W
free-flight measurements of the zero-lift drag and
base pressure on a wind tunnel interference model (m=0 .
8 - 1. 5) .
five free-flight models were flown to measure the zero-lift drag and
body base pressure on a standard wind tunnel interference model over a
mach number range of 0.84 to 1.48 .
roughness bands on the wings and body of the model are shown to
produce a small but definite increase in the zero-lift drag at all mach
numbers .
the measured drag is in fair agreement with corresponding measurements
made in various transonic tunnels with differences that could plausibly
be explained as the effects of tunnel interference .
the effect of a simulated wind tunnel support sting is shown to
increase the base pressure . the discrepancy between models with and
without a sting is greatest at subsonic speeds and progressively
decreases with increasing mach number until at m = 1.4 the sting has no
effect on base pressure .
.I 432
.T
theoretical damping in roll and rolling moment due
to differential wing incidence for slender cruciform
wings and wing-body combinations .
.A
adams,g.j. and dugan,d.w.
.B
naca r1088, 1952.
.W
theoretical damping in roll and rolling moment due
to differential wing incidence for slender cruciform
wings and wing-body combinations .
a method of analysis based on slender-wing theory is developed
to investigate the characteristics in roll of slender cruciform wings
and wing-body combinations . the method makes use of the
conformal mapping processes of classical hydrodynamics which
transform the region outside a circle and the region outside
an arbitrary arrangement of line segments intersecting at the
origin . the method of analysis may be utilized to solve other
slender cruciform wing-body problems involving arbitrarily
assigned boundary conditions .
in the present report, the application of the method has
shown ..
differential incidence of both pairs of opposite surfaces of the
cruciform wing-body combinations are practically independent
of the body-diameter-maximum-span ratio up to a value of this
ratio of 0.3 .
arrangement is only 62 percent greater than that for a
corresponding planar wing-body combination .
dence of both pairs of the opposing surfaces of the cruciform
wing-body arrangement, is only 52 percent greater than that
for a corresponding planar wing-body combination .
unit surface deflection) of the cruciform wing-body arrangement
having four equally deflected panels is therefore 94 percent of
the corresponding planar wing-body combination .
.I 433
.T
application of two dimensional vortex theory to the
prediction of flow fields behind wings of wing-body
combinations at subsonic and supersonic speeds .
.A
rogers,a.w.
.B
naca tn.3227, 1954.
.W
application of two dimensional vortex theory to the
prediction of flow fields behind wings of wing-body
combinations at subsonic and supersonic speeds .
a theoretical investigation has been made of a general method for
predicting the flow field behind the wings of plane and cruciform wing
and body combinations at transonic or supersonic speeds and slender
configurations at subsonic speeds . the wing trailing-vortex wake is
represented initially by line vortices distributed to approximate the
spanwise distribution of circulation along the trailing edge of the
exposed wing panels . the afterbody is represented by corresponding
image vortices within the body . two-dimensional line-vortex theory is
then used to compute the induced velocities at each vortex and the
resulting displacement of each vortex is determined by means of a
numerical stepwise integration procedure . the method was applied to the
calculation of the position of the vortex wake and the estimation of
downwash at chosen tail locations behind triangular-wing and
cylindrical-body combinations at supersonic speeds . the effects of
such geometric parameters as aspect ratio, angle of attack and
incidence, ratio of body radius to wing semi-span, and angle of bank on
the vortex wake behind wings of wing-body combinations were studied .
the relative importance of wing vortices, the corresponding image
vortices within the body, and body crossflow indetermining the the total
downwash was assessed at a possible tail location .
it was found that the line-vortex method of this report permitted
the calculation of vortex paths behind wings of wing-body combinations
with reasonable facility and accuracy . a calculated sample wake shape
agreed qualitatively with one observed experimentally, and sample
results of the line-vortex method compared well with an available exact
crossflow-plane solution . an empirical formula was derived to estimate
the number of vortices required per wing panel for a satisfactory
computation of downwash at tail locations . it was found that the shape
of the vortex wake and the ultimate number of rolled-up vortices behind
a wing depend on the circulation distribution along the wing trailing
edge . for the low-aspect-ratio plane wing and body combinations
considered, it appeared that downwash at horizontal tail locations is
largely determined except near the tail-body juncture by the wing
vortices alone for small ratios of body radius to wing semispan, and by
the body upwash alone for large values of that ratio .
.I 434
.T
contributions of the wing panels to the forces and
moments of supersonic wing-body combinations at combined
angles .
.A
spahr,j.r.
.B
naca tn.4146, 1958.
.W
contributions of the wing panels to the forces and
moments of supersonic wing-body combinations at combined
angles .
a wind-tunnel investigation was
conducted at a mach number of 1.96
and at reynolds numbers (based on the
mean aerodynamic chord of the
exposed wing) of 0.36 and 1.03 million
to determine the normal forces,
pitching moments, and rolling moments
contributed by each wing panel of
a cruciform-wing and body combination
over a wide range of combined
angles of pitch and roll . the wings
were triangular of aspect ratio 2,
and the body was an ogive-cylinder
combination . the effects of forebody
length and roughness and of the
presence of the adjacent panels on these
panel contributions were determined .
the results of the investigation
show that large changes in the panel
forces and moments can occur as the
result of combined angles . a general
theoretical method based on slender-body
and strip theories was found to
yield results in good agreement with the
wind-tunnel measurements . these
comparisons indicate that the changes in
the panel characteristics due to
combined angles are caused primarily by
a cross coupling between the
side-wash velocities due to angle of attack
and sideslip and by the presence
of forebody vortices due to crossflow
separation . it was found that an
increase in forebody length increases
the effect of the forebody vortices
because of the dependence of the strength
of these vortices on the forebody
length .
.I 435
.T
application of similar solutions to calculations of
laminar heat transfer on bodies with yaw and large
pressure gradients in high speed flow .
.A
beckwith,i.e. and cohen,n.b.
.B
nada tn.d625, 1961.
.W
application of similar solutions to calculations of
laminar heat transfer on bodies with yaw and large
pressure gradients in high speed flow .
an integral method for the rapid calculation of heat-transfer
distributions on yawed cylinders of arbitrary cross-sectional shape
and on bodies of revolution in high-speed flows is developed for
laminar boundary layers . the method involves the quadrature of a
function of the pressure distribution (assumed given) and satisfies
the integral energy equation with the assumption of local similarity,
wherein the actual boundary-layer profiles at every station are
replaced by corresponding profiles from a family of similar solutions .
the method is compared with other local similarity methods and
with experimental heat-transfer data on a circular cylinder and on a
body of revolution designed for large axial pressure gradients . good
agreement between theory and data is obtained and it is shown that the
present integral method, in both its complete and simplified form, gives
generally better agreement with the data than certain other local
similarity methods .
numerical examples are presented showing that the effect of sweep
and gas properties on heat-transfer distribution is small .
.I 436
.T
heat transfer in planetary atmospheres at super-satellite speeds .
.A
hoshizaki, h.
.B
ars prep. 2173-61, august 1961 .
.W
heat transfer in planetary atmospheres at super-satellite speeds .
the main purpose of this investigation is to examine the dependence of
heat transfer in planetary atmospheres on the total enthalpy up to
flight velocities of 50,000 ft/sec where a large proportion of the atoms
are ionized . the /total thermodynamic and transport property/ concept
discussed by hirshfelder /j.chem.phys.,26/2/,feb.,1957/ is used .
.I 437
.T
hypervelocity stagnation point heat transfer .
.A
scala, s. m. and warren, w. r.
.B
arsj. jan. 1962 .
.W
hypervelocity stagnation point heat transfer .
this analysis includes the specific contributions of atoms, molecules,
tions are .. /i/ partially ionized air can be approximated as a
four-component gas including n2, n, n and e,. /ii/ the gas is in local
thermochemical equilibrium,. /iii/ there is no charge separation,. /iv/
thermal diffusion is neglected,. /v/ no electrical or magnetic fields,.
low re effects are neglected .
.I 438
.T
stagnation point heat transfer measurements at super
satellite speeds .
.A
offenhartz,e., wisblatt,h. and flagg, r.f.
.B
j. roy. aero. soc., 66, 1962.
.W
stagnation point heat transfer measurements at super
satellite speeds .
brief description of experiments performed by using shock tube
techniques for measurement of the stagnation point heating of a blunt
body over a stagnation enthalpy range of 650 to 900,
corresponding to velocities between 32,000 ft. per sec. and 39,000
ft per sec., respectively . data thus provided are used for
comparison with theory .
.I 439
.T
a factor affecting transonic leading edge flow separation .
.A
wood,g.p. and gooderum,p.b.
.B
naca tn.3804, 1956.
.W
a factor affecting transonic leading edge flow separation .
a change in flow pattern that was observed as the free-stream mach
number was increased in the vicinity of 0.8 was described in naca
technical note 1211 by lindsey, daley, and humphreys . the flow on the
upper surface behind the leading edge of an airfoil at an angle of
attack changed abruptly from detached flow with an extensive region of
separation to attached supersonic flow terminated by a shock wave . in
the present paper, the consequences of shock-wave--boundary-layer
interaction are proposed as a factor that may be important in determining the
conditions under which the change in flow pattern occurs . when the
mach number is high enough, the attached-flow pattern exists because
then the shock wave is far enough behind the leading edge to keep the
influence of the high pressure behind the shock wave from extending
through the boundary layer to the immediate vicinity of the leading edge
and affecting the flow there . some experimental evidence in support of
the importance of shock-wave--boundary-layer interaction is presented .
.I 440
.T
compilation of information on the transonic attachment
of flows at the leading edge of airfoils .
.A
lindsey,w.f. and landrum,e.
.B
naca tn.4204, 1958.
.W
compilation of information on the transonic attachment
of flows at the leading edge of airfoils .
schlieren photographs have been compiled of the two-dimensional flow
at transonic speeds past 37 airfoils having variously shaped profiles,
some of which are related and vary in thickness and camber . the data
for these airfoils were analyzed to provide basic information on the
flow changes involved and to determine factors affecting transonic-flow
attachment, which is a transition from separated to unseparated flow at
the leading edges of two-dimensional airfoils at fixed angles of attack
as the subsonic mach number is increased .
.I 441
.T
evaluation of high angle-of-attack aerodynamic derivative
data and stall-flutter prediction techniques .
.A
halfman,r.l., johnson,h.c. and haley,s.m.
.B
naca tn.2533, 1951.
.W
evaluation of high angle-of-attack aerodynamic derivative
data and stall-flutter prediction techniques .
the problem of stall flutter is approached in two ways . first,
using the m.i.t.-naca airfoil oscillator, the aerodynamic reactions on
wings oscillating harmonically in pitch and translation in the stall
range have been measured, evaluated, and correlated where possible with
available published data, with the purpose of providing empirical
information where no aerodynamic theory exists . the major effects of
reynolds number, airfoil shape, and reduced frequency on the aerodynamic
reactions have been reaffirmed . no instances of negative damping were
observed in pure translatory motion and the ranges of negative damping
occurring in pure pitch had the same general trends noted by other
experimenters . data on the time-average values in the stall range of
both lift and moment are presented for the first time .
second, the results of numerous experimental observations of stall
flutter have been reviewed and the various known attempts at its
prediction have been examined, compared, and extended . the sharp drop in
critical speed and change to a predominantly torsional oscillation
usually associated with the transition from classical to stall flutter
is apparently primarily but not entirely caused by the marked changes
in moment due to pitch . fairly good stall-flutter predictions have
been reported only when adequate empirical data for this aerodynamic
reaction happened to be available for the desired airfoil shape,
reynolds number range, and reduced-frequency range . a semiempirical
method of predicting the variations of moment in pitch with airfoil
shape, reduced frequency, initial angle of attack, and amplitude of
oscillation has been presented .
.I 442
.T
some effects of variations in several parameters including
fluid density on the flutter speed of light uniform
cantilever wings .
.A
woolston,d.c. and castile,g.e.
.B
naca tn.2558, 1951.
.W
some effects of variations in several parameters including
fluid density on the flutter speed of light uniform
cantilever wings .
an experimental investigation has been made of some effects of
variations in several parameters, including fluid density, on the
flutter characteristics of light uniform cantilever wings . the
assortment of wings tested covered a variety of positions of the elastic axis
and center of gravity and values of the aspect ratio of 8, 6, and 4 .
the relative-density parameter (where k is representative of the
ratio of fluid density to wing mass) was varied over a range of values
from 1.2 to nearly 14 . special emphasis has been placed on the lower
values .
the experimental investigation has been supplemented by an
analytical investigation based on the two-dimensional aerodynamic theory for
incompressible flow . in a few instances corrections for the effects of
finite span have been made . in general, the theoretical results
followed the trends indicated by experiment except at very low values of
the relative-density parameter . for these low values
the analytical considerations employed indicated a freedom from flutter
not found experimentally . at higher values of the flutter-speed
coefficient is shown to decrease with decreasing values of and
to be nearly proportional to the inverse of the square root of the air
density .
.I 443
.T
calculated and measured pressure distributions over the midspan section
of the naca 4412 airfoil .
.A
pinkerton, r. m.
.B
naca r. 563, 1936 .
.W
calculated and measured pressure distributions over the midspan section
of the naca 4412 airfoil .
pressures were simultaneously measured in the variable-density tunnel
at 54 orifices distributed over the midspan section of a 5 by 30 inch
rectangular model of the n.a.c.a. 4412 airfoil at 17 angles of attack
ranging from -dash 20degree to 30degree at a reynolds number of
approximately 3,000,000 . accurate data were thus obtained for studying the
deviations of the results of potential-flow theory from measured results
technique are presented .
it is shown that theoretical calculations made either at the effective
angle of attack or at a given actual lift do not accurately describe the
observed pressure distribution over an airfoil section . there is
therefore developed a modified theoretical calculation that agrees
reasonably well with the measured results of the tests of the n.a.c.a. 4412
section and that consists of making the calculations and evaluating the
circulation by means of the experimentally obtained lift at the
effective angle of attack,. i.e., the angle that the chord of the model makes
with the direction of the flow in the region of the section under
consideration . in the course of the computations the shape parameter
is modified, thus leading to a modified or an effective profile shape
that differs slightly from the specified shape .
.I 444
.T
an approach to the flutter problem in real fluids .
.A
rott,n. and george,m.b.t.
.B
inst. aero. scs. perp.509, 1955.
.W
an approach to the flutter problem in real fluids .
an approximate theory of airfoils in unsteady motion in a viscous
fluid is proposed, in which viscous effects are accounted for by
relaxing the kutta condition and replacing it by a relation derived from
experiments in steady flow . applications here, are limited to moderate
viscous effects below the stall . the possibility of one-degree-
of-freedom flutter is discussed under this assumption . the discussion is
partly extrapolated to the domain of stall flutter . some possibilities
of further development of this theory for the stalled case are
indicated .
.I 445
.T
on the application of mathieu functions in the theory
of subsonic compressible flow past oscillating airfoils .
.A
reissner,e.
.B
naca tn.1961.
.W
on the application of mathieu functions in the theory
of subsonic compressible flow past oscillating airfoils .
an account is given of explicit solutions in terms of mathieu function
functions of the problem of two-dimensional subsonic compressible
flow past oscillating airfoils . the results are applied to the
calculation of three-dimensional corrections for the two-dimensional
theory and the effect of the incorporation of the three-dimensional
effects on the mathieu function solution of the two-dimensional
problem is shown . the developments are formal and must be
supplemented by an appreciable amount of numerical calculations before the
theory can be applied to specific problems .
.I 446
.T
wake of a satellite traversing the ionosphere .
.A
rand,s.
.B
phys. fluids, 3, 1960.
.W
wake of a satellite traversing the ionosphere .
the particle treatment is applied to a study of the
structure of the wake behind a charged body
moving supersonically through a low-density plasma .
for the case of a body whose dimensions are
considerably smaller than a debye length, a solution is obtained
which is very similar in structure to the
solution obtained by using the linearized fluid dynamics equation .
for the case of a disk whose radial
dimensions are much larger than a debye length, two
conical regions are found in the wake . at the
surface of each of these cones, over thicknesses of
the order of a debye length, the ion and electron
densities are increased over their ambient values .
formulae for the electrohydrodynamic drag on a
wire, and on a large disk are obtained .
.I 447
.T
motion of thin bodies in a highly rarefied plasma .
.A
yoshira,h.
.B
phys.fluids,4, 1961.
.W
motion of thin bodies in a highly rarefied plasma .
magnetic effects are considered negligible,
and the velocity of the body is in a range between the
electron and positive ion thermal speeds .
the self-consistent field approach is used in which the
electron distribution is assumed to be maxwellian,
while the positive ion distribution function is given
by the /collision-free/ boltzmann equation .
it is assumed that the ion reflection at the body surface
is specular, and the body is sufficiently thin so
that the ion distribution function is a small perturbation
of a maxwellian distribution . the solution for
the simple case of a dielectric body with a given surface
charge, as well as some general properties to
be expected for a conducting body are given .
.I 448
.T
induction drag on a large negatively charged satellite
moving in a magnetic-field-free ionosphere .
.A
wyatt,p.j.
.B
j. geophys. rev. 65, 1960.
.W
induction drag on a large negatively charged satellite
moving in a magnetic-field-free ionosphere .
an induction drag, experienced by a
charged satellite during its traversal of the
ionosphere, has been theoretically postulated by
several authors . previous 'exact' treatments
of the problem are inapplicable to large systems, and
the semiempirical approach of jastrow
and pearse may yield somewhat questionable results .
the present description initially
considers the satellite as a completely permeable spherical
shell of charge, thus avoiding the
difficult boundary conditions introduced by the 'exact'
linearized treatment . the effects of
permeability are then shown to be approximately removable
by means of an iterative process . a
final result, apparently valid to within an order of
magnitude, is obtained for the drag force
arising solely from electrical effects . its magnitude
is considerably less than that obtained by
jastrow and pearse .
.I 449
.T
interaction of a charged satellite with the ionosphere .
.A
davis,a.h. and harris,i.
.B
nasa tn. d704, 1961.
.W
interaction of a charged satellite with the ionosphere .
the problem of the ion density distribution around a
charged satellite has been treated by a numerical method
which does not require linearization of the equations or
restriction to infinitesimal objects . however, magnetic field
effects were not considered, and a number of other
simplifying assumptions were required . some sample calculations
for spherical satellites are presented, illustrating the
general character of the satellite wake . calculations of the
so-called /charge drag/ were also made, yielding results
qualitatively similar to those previously obtained by jastrow and pearse .
.I 450
.T
some physical interpretations of magnetohydrodynamic duct flows .
.A
fujihiko sakao
.B
university of tokyo, tokyo, japan
.W
some physical interpretations of magnetohydrodynamic duct flows .
this note presents some physical interpretations of magnetohydrodynamic
duct flows with various boundary conditions viewed in the light of the
effects of conducting walls on the pattern of electric current, taking
examples from published results on rectangular ducts . the current
patterns are illustrated in fig. 1 for rectangular ducts having
various combinations of conducting and nonconducting walls, a uniform
magnetic field being applied in the horizontal direction .
.I 451
.T
liapunov's methods in automatic control theory .
.A
parks, p. c.
.B
control, november and december 1962 .
.W
liapunov's methods in automatic control theory .
the work of a. m. liapunov and his theory of stability is discussed .
the second method of liapunov is shown to have applications for linear
equations with real constant coefficients, for a proof of the
routh-hurwitz criterion, and linear equations with periodic coefficients .
practical examples include non-linear stability problems of control, and
the functions have uses in other areas of control systems .
.I 452
.T
symmetric joukowsky airfoils in shear flow .
.A
tsien,h.s.
.B
q. app. math. 1, 1943, 130.
.W
symmetric joukowsky airfoils in shear flow .
the velocity components of the fluid far from the airfoil
are given by where c is the chord of
the airfoil, and k are constants, u and v are velocity
components in the directions of the coordinates x and y .
the solution is sought in the form of the stream function
and satisfies laplace's equation . a general expression for
for vanishing disturbance velocities at points far from
the origin is written, and the flows due to a source, a vortex
and a solid circular cylinder in shear flow are considered
as examples . typical streamline patterns are shown for
these cases . from the eulerian equations of motion the
author obtains the expression for in terms of the
parameter and derivatives of . the general form
of is introduced and the appropriate solution for the
pressure p is obtained . by integration around a contour
enclosing the body, expressions are obtained, analogous to
the blasius formulae, for the force and couple on any
cylinder in this type of flow . these formulae are applied to
the case of a symmetrical joukowsky airfoil . the method of
conformal transformation is employed in the determination
of . the boundary condition of tangential flow at the
airfoil surface must be satisfied by the total flow in the airfoil
plane, but this condition leads to a boundary condition for
in the transformed plane . the kutta-joukowsky
condition of finite velocity at the trailing edge also leads to a
condition on in this plane . from these conditions and the
general expression for the circulation and the strengths
of the doublets and quadruplets required for the force and
moment are determined . hence, the formulae for lift and
moment coefficient are obtained . these involve, in addition
to the usual (potential-flow) terms, terms proportional to .
the ten functions that appear in the expressions for the
lift and moment coefficients are tabulated for values of the
thickness ratio between 0 and 1 . the aerodynamic-center
position and the coefficient of the moment about the
aerodynamic center are also calculated and are presented
graphically as functions of .
.I 453
.T
the influence of two-dimensional stream shear on airfoil maximum lift .
.A
.B
.W
the influence of two-dimensional stream shear on airfoil maximum lift .
the cornell aeronautical laboratory is conducting a program of
theoretical and experimental research on low-speed aerodynamics as
applied to stol and vtol aircraft . the objective of this program is to
re-examine certain aspects of classical aerodynamic information, in the
light of low-speed flight requirements, with the aim of seeking
aerodynamic processes which might be exploited to enhance law-speed
performance .
one aspect of propeller-driven aircraft which has recently received
increasing attention is the existence of strong gradients of
longitudinal velocity, or shear, in the propeller slipstream . this
slipstream shear interacts with a wing surface and can alter the wing
characteristics . in theoretical treatments of a wing interacting with
a propeller slipstream, the first important simplification is the
replacement of the slipstream with an ideal uniform
jet, free of all velocity
gradients . the application of these theories requires that one equate
the actual slipstream to an effective uniform jet . one method
employed is to assume the uniform jet has a momentum flux equal to the
average in the propeller slipstream . these and similar procedures
are well founded on momentum considerations., however, the implicit
assumption is that the flow nonuniformity, the shear, does not influence
the wing characteristics .
.I 454
.T
several approximate analyses of the bending of a rectangular
cantilever plate by uniform normal pressure .
.A
nash,w.a.
.B
j.app.mech. 1952, 33.
.W
several approximate analyses of the bending of a rectangular
cantilever plate by uniform normal pressure .
three methods of approximating the deflections and
moments occurring in a rectangular cantilever plate
subjected to uniform normal pressure over its entire surface
are presented in this paper . the first is the application of
the well-known finite-difference procedure . the second
and third are collocation methods, one based upon
polynomial solutions of the lagrange equation, the other
employing /mixed/ hyperbolic-trigonometric terms
satisfying this equation . in the last two methods the boundary
conditions are satisfied exactly along the clamped edge and
at a finite number of points along the free edges of the plate .
the results obtained for the particular case of a cantilever
plate with uniform normal load indicate that the use of a
relatively small number of points in the collocation
method yields values of deflections and moments that are
in substantial agreement with those given by the
finite-difference procedure . it cannot be concluded from these
results that the collocation method using the assumed
functions will give satisfactory results with fewer points
than the finite-difference method for cantilever plates with
loading different from the one investigated .
.I 455
.T
modified cross-lees mixing theory for supersonic separated
and reattaching flows .
.A
glick,h.s.
.B
galcit hyp. res. proj. memo 53, 1960.
.W
modified cross-lees mixing theory for supersonic separated
and reattaching flows .
re-examination of the crocco-lees method has shown that the
previous quantitative disagreement between theory and
experiment in the region of flow up to separation was caused primarily
by the improper c(k) relation assumed . a new c(k) correlation,
based on low-speed theoretical and experimental data and on
supersonic experimental results has been developed and found to
be satisfactory for accurate calculation of two-dimensional,
laminar, supersonic flows up to separation .
a physical model which incorporates the concept of the /dividing/
streamline and the results of experiment . according to this
physical model, viscous momentum transport is the essential
mechanism in the zone between separation and the beginning of
reattachment, while the reattachment process is, on the contrary,
an essentially inviscid process . this physical model has been
translated into crocco-lees languages using a semiempirical
approach, and approximate c(k) and f(k) relations have been
determined for the separated and reattaching regions . the
results of this analysis have been applied to the problem of
shockwave, laminar-boundary-layer interaction, and satisfactory
a study of separated and reattaching regions of flow has led to
quantitative agreement with experiment has been achieved .
.I 456
.T
a study of flow fields about some typical blunt-nosed
slender bodies .
.A
vaglio-laurin,r. and trella,m.
.B
pibal r.623, 1960.
.W
a study of flow fields about some typical blunt-nosed
slender bodies .
complete inviscid flow fields about three model axisymmetric
configurations have been determined numerically . configurations
decreasing bluntness) and flight conditions have been selected so
as to indicate separately effects of nose shape, drag coefficient,
flight mach number, and thermodynamic behavior of the gas (either
ideal calorically perfect gas or air in equilibrium dissociation) .
results are presented for thirteen cases . particular attention is
devoted to interpretation and, when possible, correlation of
pressure distributions on, and shock shapes about, the cylindrical
afterbodies . it is found that .. (a) the correlation of pressure
distributions on bodies having nonspherical noses involves interpretive
modifications of the law suggested by blast wave analogy . also
shocks about these bodies are not described by parabolae,. (b) for
all configurations there is substantial influence of gas behavior
on shock shape,. this, however, can be correlated in terms of the
gas conditions along a generally defined streamline,. (c) the shock
layer can generally be divided into two regions (the first bound by
the body and the aforementioned streamline, the second delimited
by this streamline and the shock) wherein flow properties can
either be approximated by simple laws or correlated .. (d) for each
configuration knowledge of the complete flow field in one flight
condition (even pertaining to ideal gas flow) can be used to
estimate features of flows under general flight conditions including
those where equilibrium dissociation is encountered .
.I 457
.T
on laminar boundary-layer flow near a position of separation .
.A
goldstein,s.
.B
q. j. mech.app. mech. 1, 1948, 43.
.W
on laminar boundary-layer flow near a position of separation .
singularities are considered in the solution of
the laminar boundary-layer
equations at a position of separation . a singularity of
the type here considered occurred
in a careful numerical computation by hartree
for a linearly decreasing velocity
distribution outside the boundary layer ,. it may
occur generally . whenever it does
occur, the boundary-layer equations cease to be
valid at and near separation on the
upstream side, and also downstream of separation .
the work suggests that
singularities may arise in the solution of non-linear
parabolic equations due to their
non-linearity . the formulae found may help
computers of laminar boundary layers,
who desire more than a rough solution, to have
an end-point at which to aim .
.I 458
.T
a new series for calculation of steady laminar boundary
layer flows .
.A
gortler,h.
.B
j. math. mech. 6, 1957, 1.
.W
a new series for calculation of steady laminar boundary
layer flows .
a new and general method for solving
problems of plane and steady laminar
boundary layer flows in incompressible
fluids with arbitrary outer pressure
distribution is developed . this method
is based on the introduction of the
dimensionless quantities
as new independent spatial variables .
ordinates, u(x) the given outer velocity
distribution, v the kinematic viscosity .)
the solution of the boundary layer problem
is then given as a power series in e
with coefficient functions depending on n .
this series is a formally exact solution
of the boundary layer problem .
the new series solution has the following qualities ..
have the significance only of cartesian
coordinates, the influence of wall
curvature being neglected in boundary
layer theory, the new coordinates
are adjusted to the data of the special
problem in any case of application .
the new variables represent a logical
development of former efforts in
the field of boundary-layer flow calculation .
with other series solutions known for
some special cases is that the leading
term of the new series satisfies
exactly the outer boundary condition
at all cross-sections along the wall .
therefore, the succeeding terms give
corrections only in the inner part of
the boundary layer . accordingly,
taking also no. 1 into account, the zero
order term by itself gives a good
approximation for the boundary layer flow .
.I 459
.T
on the solution of the laminar boundary layer equations .
.A
tani,i.
.B
j.phys.soc.japan, 4, 1949, 149.
.W
on the solution of the laminar boundary layer equations .
the theory of the laminar boundary layer
offers a means of determining the skin friction
under the assumption of a given velocity
distribution outside the boundary layer . owing to the
mathematical difficulties, however, exact solutions
are possible only when the velocity distribution
is expressed as a simple function of the distance
along the surface . more complicated velocity
distributions necessitate recourse to the method of
expansion in series or that of step-by-step
calculations, but the labor involved is too great for the
methods to be of practical use . approximate
method due to pohlhausen (1921), which had long
been recommended for general use, gives a
reasonably accurate solution in a region of accelerated
flow, but recently its adequacy in a region of
retarded flow has been questioned . separation of
flow may actually occur where the solution of
pohlhausen fails to give it . more recently howarth
solution, which gives fairly reasonable results in
a region of retarded flow .
howarth's solution essentially consists in
solving the boundary layer equations for the particular
case in which the velocity u outside the boundary
layer decreases linearly with the distance x
measured along the surface, and utilizing the solution
by replacing the actual distribution of u by a
circumscribing polygon of infinitesimal sides .
therefore, it is assumed that the velocity
distribution at any section depends on the velocity
gradient du/dx at that section only, being affected
by the conditions upstream only in so far as this
affects the momentum thickness 0 . in other words,
the velocity distribution across the boundary layer
is determined by a parameter .
.I 460
.T
correlated incompressible and compressible boundary
layers .
.A
stewartson,k.
.B
proc. roy. soc. a, 200, 1949, 84.
.W
correlated incompressible and compressible boundary
layers .
the boundary-layer equations for a compressible
fluid are transformed into those for an
incompressible fluid, assuming that the boundary
is thermally insulating, that the viscosity is
proportional to the absolute temperature, and
that the prandtl number is unity . various
results in the theory of incompressible boundary
layers are then taken over into the
compressible theory . in particular, the existence of
method for retarded flows is applied to determine
the point of separation for a uniformly
retarded main stream velocity . a comparison with
an exact solution is used to show that this
method gives a closer approximation than does pohlhausen's .
.I 461
.T
approximate methods fore predicting separation properties
of laminar boundary layers .
.A
curle,n. and skan,s.w.
.B
aero. quart. 8, 1957, 257.
.W
approximate methods fore predicting separation properties
of laminar boundary layers .
some new solutions for steady incompressible laminar boundary
layer flow, obtained by gortler, have been used to test the accuracy of
two methods which are commonly used to predict separation . a
modification of stratford's criterion for separation is given in this
paper and is probably the most accurate and the simplest of all methods
at present in use . modified numerical functions are also given for
thwaites's method of predicting the main characteristics of the boundary
layer over the whole surface, which improve the accuracy of the method .
.I 462
.T
photo-thermoelasticity .
.A
gerard,g and gilbert,a.c.
.B
j.app.mech. 24, 1957.
.W
photo-thermoelasticity .
this paper summarizes the optical and physical
properties of the photoelastic model material paraplex p-43 over
the temperature range from room temperature to -40 f .
descriptions are presented of techniques and equipment
developed to obtain the modulus of elasticity, the material
fringe value, and the thermal-expansion coefficient as a
function of temperature . experimental investigations
were conducted into the plane-stress problems of a disk
contracting upon an elastic inclusion and the transient
thermal-stress field produced by a temperature differential
suddenly applied to the upper edge of a long beam . the
data are correlated with theory using the material
properties obtained in the calibration phase . also included are
photographic results of an exploratory investigation of the
thermal-shock phenomenon produced by the sudden
application of a temperature differential upon plastic beams
of various length-depth ratios .
.I 463
.T
physical properties of plastics for photo-thermoelastic
investigation .
.A
tramposch,h. and gerard,g.
.B
j.app. mech. 25, 1958.
.W
physical properties of plastics for photo-thermoelastic
investigation .
the optical and physical properties of
paraplex p43, castolite, and epoxy resin
hysol 6000-op, which are potentially of
interest in photothermoelastic investigations,
were investigated over a temperature range
from +100 to -60 f . results on the
thermal-expansion coefficient, the material
fringe value, and the modulus of elasticity
as functions of temperature are presented .
also evaluated were thermal properties of
importance in heat conduction . photothermoelastic
figures of merit, which rate the
optical sensitivity of materials in photothermoelastic
applications, as well as a new
method to determine this figure in a relative manner are presented .
.I 464
.T
flow studies on flat plate delta wings at supersonic
speeds .
.A
michael,w.h.
.B
naca tn.3472, 1955.
.W
flow studies on flat plate delta wings at supersonic
speeds .
an experimental study has been made to investigate some aspects
of the nature of the flow around delta wings . vapor-screen,
pressure-distribution, and ink-flow studies were made at a mach number of 1.9 on
a series of semispan delta-wing models with slender wedge airfoil
sections and very sharp leading edges . the models had semiapex angles
ranging from 5 to 31.75 .
separated regions of vorticity existed along the chords of all
the wings in the series tested . concentrated vortex cores were found
only on wings of very small semiapex angles . for wings with medium
and large semiapex angles, the separated vorticity was concentrated in
a region extending over the outboard part of the span and lying close
to the wing upper surface .
the results show that theoretical aerodynamic calculations, such
as those in naca tn 3430, utilizing a single, separated vortex pair
above the wing upper surface to represent the separated vorticity can
be applied at supersonic speeds for very slender wings .
.I 465
.T
slender delta wings with sharp edges at zero lift .
.A
weber,j.
.B
rae tn.aero.2508.
.W
slender delta wings with sharp edges at zero lift .
several slender wings of delta planform with sharp edges have been
investigated theoretically at zero lift at subsonic and at supersonic
speeds . most of the wings have diamond-shaped cross sections and are
intended to lead to a type of flow with leading-edge separation in the
lifting condition . the pressure distributions and overall
normal-pressure drags resulting from various theoretical methods are compared
with one another and some discussion is included concerning the
possibility of achieving the results, calculated for an inviscid stream,
in a real flow in the presence of a viscous layer around the body .
.I 466
.T
development of the vapour screen method of flow
visualization in the 3ft tunnel at rae bedford.
.A
mcgregor,i.
.B
.W
development of the vapour screen method of flow
visualization in the 3ft tunnel at rae bedford.
the vapour screen method of flow visualisation in supersonic wind
tunnels is outlined, and the development of a suitable technique for use
in the 3 ft tunnel described, together with the associated optical and
photographic equipment .
the results of tests to determine the humidity required to produce an
optimum density of fog in the working section over the mach number range
temperature discussed . numerous vapour screen photographs of the flow
over and behind delta wings are included and some comparisons made with
the corresponding surface oil-flow patterns .
the process of condensation, the physical and optical properties of
the resulting fog, and the formation of the vapour screen picture are
all considered in some detail .
the effects of humidity on the mach number and static pressure in the
working section were investigated and the results are compared with
theoretical estimates at a nominal mach number of 2.0 . it is shown
that the adverse effects of condensation on the flow at high mach
numbers may be alleviated by the use of liquids with a lower latent heat
of evaporation than water, and some results obtained at a mach number of
the possibility of extending the vapour screen technique to transonic
and subsonic speeds is also considered, and some results obtained at a
mach number of 0.85 are included .
.I 467
.T
thin airfoil theory based on approximate solution of the transonic flow
equation .
.A
spreiter, j. r. and alksne, a. y.
.B
naca tn 3970, may, 1957 .
.W
thin airfoil theory based on approximate solution of the transonic flow
equation .
the present paper describes a method for the approximate solution of the
nonlinear equations of transonic small disturbance theory . although
the solutions are nonlinear, the analysis is sufficiently simple that
results are obtained in closed analytic form for a large and significant
class of nonlifting airfoils . application to two-dimensional flows
with free-stream mach number near 1 leads, for instance, to general
expressions for the determination of the pressure distribution on an
airfoil of specified geometry and for the shape of an airfoil having a
prescribed pressure distribution and gives, furthermore, the correct
variation of pressure with mach number at mach number 1 . for flows that
are subsonic everywhere, the method yields a pressure-correction
formula that is more accurate than the prandtl-glauert rule and compares
favorably with existing higher approximations . for flows that are
supersonic everywhere, the method yields the equivalent, in transonic
approximation, of simple wave theory . results obtained by application
of these general expressions are shown to correspond closely to existing
solutions and to experimental data for a wide variety of airfoils .
.I 468
.T
a refinement of the linearised transonic flow theory .
.A
hosowaka,a.
.B
j.phys.soc. japan, 15, 1960.
.W
a refinement of the linearised transonic flow theory .
a new method is proposed to calculate the velocity and pressure
distributions around a thin symmetrical aerofoil or a slender body of
revolution flying at transonic speed . it is essentially a refinement
of the linearized transonic flow theory due to oswatitsch and maeder,
such that a correction term is introduced to take account of the
nonlinear character of the transonic flow . as examples of application,
a symmetrical circular-arc aerofoil and a circular-arc body of
revolution in the sonic flow are dealt with, and the results are found
to be in good agreement with experiments, except for the rear portion in
the latter case .
.I 469
.T
linearised transonic flow about slender bodies at zero
angle of attack .
.A
maeder,p.f. and thommen,h.u.
.B
asme trans. j.app.mech. 28, 1961.
.W
linearised transonic flow about slender bodies at zero
angle of attack .
the simple linearized transonic flow theory
as originally proposed by oswatitsch and
keune(1) and by the present authors (2)
is improved by considering and partially
correcting its error . in this manner a theory
which is easy to apply and which should
be valid for a great number of smooth bodies
is obtained . this improved theory
predicts shock waves in the lower transonic regions .
it is applied to a number of significant
body and airfoil shapes and its predictions are
compared with experiments and results
of other theoretical investigations .
.I 470
.T
some notes for the small disturbance linear theory
of the method of local linearisation of the flow over
an airfoil at mach number of unity .
.A
miyai,y.
.B
proc. 10th japan nat. cong. app. mech. iii-4, 1960, 207.
.W
some notes for the small disturbance linear theory
of the method of local linearisation of the flow over
an airfoil at mach number of unity .
in this paper, the pressure
distribution at the surface of a symmetrical
non-lifting aerofoil with free stream
mach number of unity has been
investigated by means of the small-disturbance
linear theory or the method of local
linearization . and by comparing with
the calculated results based on an
hodograph method, the accuracy of these
approximate methods has been
evaluated . moreover, when these approximate
methods are used for the calculation
of the pressure coefficient, some notes
necessary to obtain more correct
results have been discussed .
.I 471
.T
.A
.B
.W
.I 472
.T
waves in supersonic flow .
.A
.B
.W
waves in supersonic flow .
in this chapter we shall mainly consider problems of steady, two-
dimensional (plane) supersonic flow . using the fact that in this case
there is a steady wave system, we shall find solutions by an indirect
approach . that is, we shall first study the conditions under which
simple stationary waves may exist in the flow, and then find the flow
boundaries to which they correspond or which may be fitted to
them . in this procedure the limited upstream influence in a supersonic
field is very helpful, for it allows flows to be analyzed or
constructed step by step, which is a method that is not possible in
the subsonic case .
.I 473
.T
freeman method .
.A
.B
.W
freeman method .
the freeman method (ref. 26) is similar to
chester's method in that the newtonian-plus-centrifugal solution (eq.
with the von mises transformation . a method of successive
approximations is applied to both plane and axially symmetric blunt-nosed bodies
for small and infinite free-stream mach number .
formulas for the streamlines, shock shape, and pressure distribution are
determined to this approximation . a number of special shapes are
treated in ref. 26, and in certain cases the theory has a singular point
where the first approximation to the pressure vanishes., that is,
for a sphere (see eq. 7-113) . as in chester's method, the theory is
not applicable where the pressure becomes too small .
.I 474
.T
laminar mixing of a compressible fluid .
.A
dean r. chapman
.B
.W
laminar mixing of a compressible fluid .
a theoretical investigation of the velocity profiles for laminar
mixing of a high-velocity stream with a region of fluid at rest
has been made assuming that the prandtl number is unity . a method
which involves only quadratures is presented for calculating the
velocity profile in the mixing layer for an arbitrary value of the
free-stream mach number .
detailed velocity profiles have been calculated for free-stream mach
numbers of 0, 1, 2, 3, and 5 . for each mach number, velocity profiles
are presented for both a linear and a 0.76-power variation of viscosity
with absolute temperature . the calculations for a linear variation are
much simpler than those for a 0.76-power variation . it is shown that
by selecting the constant of proportionality in the linear approximation
such that it gives the correct value for the viscosity in the
high-temperature part of the mixing layer, the resulting velocity profiles
are in excellent agreement with those calculated by a 0.76-power
variation .
.I 475
.T
the velocity distribution in the laminar boundary layer
between parallel streams .
.A
lock,r.c.
.B
q. j. mech. app. math. 4, 1951, 42.
.W
the velocity distribution in the laminar boundary layer
between parallel streams .
a method is given for obtaining the solution of the laminar boundary
layer equations for the steady flow of a stream of viscous
incompressible fluid over a parallel stream of different density and
viscosity . an approximate solution is also obtained by means of the
momentum equation . it is shown that the solutions depend only on the
ratio of the velocities of the two streams and on the product of the
corresponding density and viscosity ratios . numerical results are
given, in the case where the lower fluid is at rest, for four values of
and also when for one non-zero value of the velocity ratio .
.I 476
.T
the blasius equation with three-point boundary conditions .
.A
napolitano, i. g.
.B
quart. appl. math. v. 16, no. 4, pp 397-408, 1958 .
.W
the blasius equation with three-point boundary conditions .
the blasius equation subject to three-point boundary conditions,
describing the interaction between two parallel streams, is solved by way
of a series in terms of ascending powers of the ratio equals /u1 -dash
u2//u1, where the u1's are the outer streams' velocities .
the first three terms of the series are analytically expressed in terms
of the repeated integrals of the complementary error function /im erfc /
and of the repeated integrals of the square of the successive integrals
of the complementary error function /jmin erfc n/ . these functions
often appear in problems leading to extended heat-conduction type of
equations . a recurrence formula for jmin erfc n is established and
formulae relating the functions in erfc /-dashn/ and jmjn erfc to
available tabulated values of the functions in erfc /n/ are derived .
the first three approximations to the blasius function and to its first
two derivatives are also presented in tabulated form with four
significant figures . test on the convergence of the series has been made by
comparison with some exact solutions obtained by high speed computing
machine . the comparison, extended to the physically essential
quantities, shows that ..
second and first derivatives .
yield extremely accurate results . the errors in the first two
derivatives of the blasius functions are always contained within less than one
per cent .
.I 477
.T
laminar boundary layers at the interface of co-current
parallel streams .
.A
potter,o.e.
.B
q. j. mech. app. math. 10, 1957, 302.
.W
laminar boundary layers at the interface of co-current
parallel streams .
the approximate solution of keulegan(1) for the steady flow of a
stream of viscous incompressible fluid over another at rest is extended
to the case where both fluids are moving co-current but at different
velocities . this solution utilizes a sextic polynomial for the
velocity distribution in the boundary layers . the solutions depend
only on the ratio of the velocities of the two streams and on the
product of the corresponding viscosity and density ratios . numerical
results are given for seven values of at one value of . lock(2) has
published an exact solution with a numerical result for and the sextic
polynomial solution is evaluated f40umerical result for and the sextic
indicates that in general the sextic polynomial is more accurate than
the quartic polynomial but that the advantage is not great .
.I 478
.T
tabulation of the blasius function with blowing and
suction .
.A
emmons,h.w. and leigh,d.c.
.B
arc cp.1913, 1953.
.W
tabulation of the blasius function with blowing and
suction .
authors tabulate solutions of f''' + ff'' = 0 for the velocity
distribution in a boundary layer . for each solution f'(0) = 0,
the third boundary condition is the specification
of f(0) . f(n) and its first three derivatives are tabulated to 5d
in gaps of 0.1 in n for f(0) = -1.23849, -1.2(0.05) 0.5 (0.1) 1.5,
introduction gives method of solution and
physical meaning of boundary conditions, etc . lock's (amr
cussed .
.I 479
.T
on an equation occurring in falkner and skan's approximate
treatment of the equation of the boundary layer .
.A
hartree,d.r.
.B
proc. cam. phil. s. 33, 1937, 223.
.W
on an equation occurring in falkner and skan's approximate
treatment of the equation of the boundary layer .
the differential analyser
has been used to evaluate solutions of the equation y''' = -yy'' +
with boundary conditions y = y' = 0 at x = 0, as
which occurs in falkner and skan's approximate treatment of the
laminar boundary layer (see abstract 1081 (1932)) . a numerical
iterative method has been used to improve the accuracy of the solutions,
and the results show that the accuracy of the machine solutions is about
insufficient to specify a unique solution for negative values of,.
a discussion of this situation is given, and it is shown that for the
application to be made of the solution the appropriate condition is that
from below, and as rapidly as possible, as . the condition that
from below can be satisfied only for values of greater than a limiting
value whose value is approximately -0.199, and which is related to the
point at which the laminar boundary layer breaks away from the
boundary .
.I 480
.T
adiabatic wall temperature due to mass transfer cooling with a
combustible gas .
.A
d. b. spalding
.B
imperial college, london, england
.W
adiabatic wall temperature due to mass transfer cooling with a
combustible gas .
a recent technical note by sutton (1), with the above title, discusses
the influence of the burning of a transpiration coolant on the quantity
of coolant necessary to maintain a given wall temperature . the present
note discusses the same problem in a way which has been found useful
in calculating the burning rates of solid and liquid fuels (2) .
consider the transpiration cooling of a porous surface in a gas stream .
then a simple modification of the general mass .
.I 481
.T
mass transfer cooling of a laminary boundary layer
by injection of a light weight foreign gas .
.A
eckert,e., schneider,p., hayday,a. and larson,r.
.B
jet prop. 1958, 34.
.W
mass transfer cooling of a laminary boundary layer
by injection of a light weight foreign gas .
analytical predictions are given for the development of
the velocity, temperature and concentration fields in a
laminar air boundary layer on a flat plate in high-speed
dissipative flow, the plate being considered porous and
cooled by injection of hydrogen from its surface . the
admixture of hydrogen, having a low density and high
thermal capacity relative to air, is shown to greatly
diminish the skin friction and to markedly relieve the
adverse thermal effects of intense aerodynamic heating under
conditions of hypersonic flow .
.I 482
.T
a re-examination of the use of the simple concepts
for prediction the shape and location of detached shock
waves .
.A
love,e.s.
.B
naca tn.4170, 1957.
.W
a re-examination of the use of the simple concepts
for prediction the shape and location of detached shock
waves .
a reexamination has been made of the use of simple concepts for
predicting the shape and location of detached shock waves . the results
show that simple concepts and modifications of existing methods can
yield good predictions for many nose shapes and for a wide range of mach
numbers .
.I 483
.T
stagnation point shock detachment distance for flow
around spheres and cylinder .
.A
ambrosio,a. and wortman,a.
.B
ars j. 32, 1962.
.W
stagnation point shock detachment distance for flow
around spheres and cylinder .
development of an analytical relation between shock detachment
distance and free-stream mach numbers . results are presented
graphically for shock detachment distance of cylinders and spheres
in air .
.I 484
.T
the influence of two-dimensional stream shear for airfoil
maximum lift .
.A
vidal,r.j.
.B
j. ae. scs. 29, 1962, 889.
.W
the influence of two-dimensional stream shear for airfoil
maximum lift .
the effects of stream velocity gradients on airfoil maximum
lift are defined with experimental data obtained in a simulated
two-dimensional slipstream . the experimental results show
that when positioned near the slipstream plane of symmetry, the
airfoil maximum lift varies markedly with location in the
slipstream . in moving the airfoil from above to below the
slipstream plane of symmetry through a total distance corresponding
to the airfoil thickness, force data and boundary-layer
observations show that boundary-layer separation is delayed to higher
angles of attack, and the airfoil maximum lift is doubled .
it is concluded that the destalling effect observed in the
non-uniform slipstream is not associated with slipstream boundary
interference, but stems from the influence of the large local
slipstream shear on airfoil characteristics . the effects of uniform
and nonuniform shear on airfoil lift and pressure distribution are
discussed, within the framework of existing first-order,
small-shear theory, to show that these effects of shear tend to promote
stall . a pohlhausen calculation of the laminar boundary layer
in a stream with shear is used to identify and to assess the effects
of stream shear on boundary-layer separation criteria . it is
demonstrated that these effects are negligibly small, and that the
uniform-flow criterion applies . it is concluded on the basis of
the experimental data that the observed destalling phenomenon
stems from a shear effect of higher order than those treated in the
inviscid theories . it is hypothesized that it is a second-order
effect, fixed by the product of the stream shear and the derivative
of the shear, which was large in the present experiments .
.I 485
.T
linear heat flow in a composite slab .
.A
reid,w.p.
.B
j.ae.scs. 29, 1962.
.W
linear heat flow in a composite slab .
the temperature is determined as a function of position and
time in the case of linear heat conduction in a composite slab of
ture throughout, and the two external surface temperatures are
considered to be prescribed functions .
.I 486
.T
similarity laws for aerothermoelastic testing .
.A
dugundji,j.
.B
j.ae.scs. 29, 1962, 935.
.W
similarity laws for aerothermoelastic testing .
the similarity laws for aerothermoelastic testing are presented
in the range . these are obtained by
making nondimensional the appropriate governing equations of
the individual external aerodynamic flow, heat conduction to
the interior, and stress-deflection problems which make up the
combined aerothermoelastic problem .
for the general aerothermoelastic model, where the model is
placed in a high-stagnation-temperature wind tunnel, similitude
is shown to be very difficult to achieve for a scale ratio other
than unity . the primary conflict occurs between the
free-stream mach number reynolds number aeroelastic
parameter heat conduction parameter and
thermal expansion parameter .
means of dealing with this basic conflict are presented . these
include (1) looking at more specialized situations, such as the
behavior of wing structures and of thin solid plate lifting surfaces,
and panel flutter, where the aerothermoelastic similarity
parameters assume less restrictive forms, (2) the use of /incomplete
aerothermoelastic/ testing in which the pressure and/or heating
rates are estimated in advance and applied artificially to the
model, and (3) the use of /restricted purpose/ models
investigating separately one or another facet of the complete
aerothermoelastic problem .
some numerical examples of modeling for the general
aerothermoelastic case as well as for the specialized situations
mentioned in (1) above are given .
finally, extension of the aerothermoelastic similarity laws to
higher speeds and temperatures is discussed .
.I 487
.T
theory for supersonic two-dimensional, laminar, base-type
flows using the crocco-lees mixing concepts .
.A
rom,j.
.B
j.ae.scs. 29, 1962, 963.
.W
theory for supersonic two-dimensional, laminar, base-type
flows using the crocco-lees mixing concepts .
a separated flow field, in which the incoming boundary layer
is undisturbed up to the separation point, is defined as a /
base-type/ flow . examples are the flows over a blunt base and over
a backward-facing step . the crocco-lees theory is applied to
the supersonic, two-dimensional, laminar, base-type flows
defined above . the separated flow is divided into a mixing region
and a recompression (or reattachment) region . calculations of
base pressure show its dependence on the mach number and on
two reynolds-number-dependent variables, and .
it is shown that existing base-pressure data can be explained
by these results .
.I 488
.T
a reaction-rate parameter for gasdynamics of a chemically
reacting gas mixture .
.A
leonard,m.
.B
j.ae.scs. 29, 1962, 995.
.W
a reaction-rate parameter for gasdynamics of a chemically
reacting gas mixture .
presented note proposes a linearized reaction rate parameter
which is applicable to any reacting gas mixture provided all the
pertinent reactions and their rate constants are known at the
thermodynamic conditions under consideration . linearizing is
achieved by expanding equation of rate of chemical reaction in a
taylor series and neglecting higher-order terms . author
announces that tables of linearized reaction rate parameters for
dissociated and slightly ionized air are now in preparation at the
space sciences laboratory, general electric co., msvo .
comparison of preliminary results with exact calculations
published by hall, i. g., et.al., /inviscid hypersonic air-flows with
coupled non-equilibrium processes/ (ias paper 62-67, 30th
annual meeting, new york, jan. 1962) indicates good agreement .
.I 489
.T
on calculation of the laminar separation point and
results of certain flows .
.A
morduchow,m.
.B
j.ae.scs. 29, 1962, 996.
.W
on calculation of the laminar separation point and
results of certain flows .
paper studies compressible laminar boundary layer in adverse
pressure gradient . after mentioning mathematical instabilities in
howarth's and like solutions, authors quote equation from one of
the references, based on the assumptions that zero
heat transfer and y = 1.4 . thence authors compute nondimensional
distances to separation, comparing with solutions by other
workers .
results are interesting, though reviewer feels rather unhappy
about approximations leading to eq. (4),. more detailed
justifications should have been given . thus we have the statement
ber, as ./ surely a fuller discussion of effects
of letting is warranted .
typography in eqs. (2) and (3) is rather confusing and there is
a typographical error in heading to table 2 .
.I 490
.T
normal-shock relations in magnetohydrodynamics .
.A
gundersen,r.m.
.B
j.ae.scs.29, 1962, 997.
.W
normal-shock relations in magnetohydrodynamics .
the magnetic-field vector is perpendicular to the flow direction,.
thus for normal shocks there is no change of flow direction through
the shock front . this class of shocks is included in
investigations by several authors (five are referred to here), but the
presentation here is thought to be especially convenient . all
downstream quantities are given in terms of upstream flow conditions,
including the upstream ratio of alfven speed to sound speed, and
the shock strength (density ratio) .
.I 491
.T
on the close relationship between turbulent plane-couette
and pressure flows .
.A
burton,r.a.
.B
j. ae. scs. 29, 1962, 1004.
.W
on the close relationship between turbulent plane-couette
and pressure flows .
author studies the velocity profiles measured by others in plane
and turbulent couette flow, such as is induced in parallel
channels of which one of the walls moves in its own plane . he finds
these profiles to be satisfactorily describable in terms of the
seventh-power law, which was originally set up for plane and
turbulent pressure flow in channels where both walls are stationary .
further, he finds the shear law for pressure flow,
to be applicable also to the couette flow, in a similar range of
reynolds number, r . no attempt is made in this concise
contribution to put these findings on a firmer basis through a theoretical
explanation .
.I 492
.T
prediction of ogive-forebody pressures at angles of attack .
.A
earl r. keener
.B
aerodynamicist, nasa flight research center, edwards, calif.
.W
prediction of ogive-forebody pressures at angles of attack .
various approximations are being suggested for obtaining surface
pressures on arbitrary bodies at angle of attack . this not presents
a method for obtaining an approximate pressure distribution over
the lower surface of an ogive forebody at angle of attack by utilizing
the calculated pressures for zero angle of attack .
.I 493
.T
real-gas laminar boundary layer skin friction and heat
transfer .
.A
wilson,r.e.
.B
j. ae. scs. 29, 1962, 640.
.W
real-gas laminar boundary layer skin friction and heat
transfer .
the laminar-boundary-layer equations have been integrated
for the case of a flat plate over a wide range of free-stream
enthalpies and velocities and over a wide range of enthalpies of
the gas at the wall . the range of free-stream velocities extended
up to 25,000 ft sec at low free-stream enthalpies, corresponding
to local conditions on a slender body traveling at high speeds .
at low free-stream velocities, the range of free-stream enthalpies
extended up to 400,000 btu slug, corresponding to the local
conditions on a blunt body traveling at speeds up to 25,000 ft sec .
the gas was assumed to be in thermodynamic equilibrium at each
point in the boundary layer and diffusion effects were neglected .
the solutions to the boundary-layer equations were carried out
on a high-speed digital computing machine, both skin-friction and
heat-transfer coefficients being obtained from the computations .
before presenting the results, the t' method of rubesin and
johnson for computing skin-friction coefficients for the
perfect-gas case is reviewed . for the real-gas case, the average
temperature, t', is replaced by the average enthalpy, h', and the h'
method is then used to compute skin-friction coefficients . these
values are in excellent agreement with the computing-machine
results . it was found that the recovery factor for the real-gas
case can be approximated by, the best results for the
cases considered being obtained if a value of pr corresponding to
the enthalpy, h', is used . using this recovery factor and
reynolds analogy, heat-transfer rates can be computed which,
with a few exceptions, are within 5 percent of values obtained
from computing-machine results .
.I 494
.T
axisymmetric viscous flow plast very slender bodies
of revolution .
.A
yashura,m.
.B
j. ae. scs. 29, 1962, 667.
.W
axisymmetric viscous flow plast very slender bodies
of revolution .
axisymmetric viscous flow past unyawed very slender bodies
of revolution is treated within the category of the perfect gas .
attention is paid especially to the effect of transverse curvature
of the body . from the transformed equations, the similarity
conditions are deduced, and the parameter characterizing the
effect of transverse curvature is obtained . several numerical
solutions of similarity equations for hypersonic flows are
presented, and upon the basis of these results, the effect of the
transverse-curvature parameter is discussed . a method of
applying the local-similarity approximation to obtain the
approximate solution for nonsimilar cases is described, as are
practical applications to incompressible flow past a long cylinder and
to hypersonic flow past a very slender cone . comparison with
experimental results shows fair agreement with calculations using
the local-similarity approximation in the present range of
experimental flow conditions .
.I 495
.T
on similar solutions for strong blast waves and their
application to steady hypersonic flow .
.A
borcher,e.f.
.B
j. ae. scs. 29, 1962, 694.
.W
on similar solutions for strong blast waves and their
application to steady hypersonic flow .
the general solution of the strong blast wave is found in the
newtonian approximation--i.e., neglecting terms of order
the expressions obtained for the pressure, temperature, density,
and velocity profiles are simple . the results are applied to
power-law bodies in hypersonic flow using the equivalence
principle .
higher-order approximations for strong blast waves are
investigated for the cases in which the shock layer is thin . a
simple pressure formula is found, which constitutes an
improvement upon the newton-busemann formula, and some of its
applications are shown .
.I 496
.T
a theory of transonic aileron buzz, neglecting viscous
effects .
.A
eckhaus,w.
.B
j. ae. scs. 29, 1962, 712.
.W
a theory of transonic aileron buzz, neglecting viscous
effects .
usaf-sponsored analysis of the unsteady perturbations of
two-dimensional transonic flow around an airfoil, where local supersonic
regions terminated by shock waves are present in the vicinity of the
airfoil . viscous effects are neglected, and a linearized theory of
the perturbations due to harmonic oscillations of an aileron is
developed . a series solution for the pressure distribution is obtained,
and numerical results for the nonsteady hinge moment, from the
first approximation to the solution, are presented . as a result of
flutter analysis a stability boundary for transonic aileron buzz is
obtained . comparison of the theoretical results with experimental
observations shows satisfactory agreement .
.I 497
.T
theoretical and experimental investigation of thermal
stresses in hypersonic aircraft wing structures .
.A
tramposch,h.
.B
j. ae. scs. 29, 1962.
.W
theoretical and experimental investigation of thermal
stresses in hypersonic aircraft wing structures .
a simple and relatively accurate analytic approximation is
developed to determine the temperature and thermal-stress
distribution in aircraft wing structures . theoretical investigations
show that the results of the existing thermal-stress theories
which neglect the temperature gradient through the skin
thickness may exceed, in the range of higher biot numbers, the true
values by more than 30 percent .
refined photothermoelastic experiments verify these results
and add another significant conclusion . they indicate that
thermal stresses in wing structures generated by a variable
heat-transfer coefficient coincide with the theoretical predictions
which are based on a constant heat-transfer coefficient, as long
as the latter represents the arithmetic average over the heating
cycle and the variation is in the order of 10 percent .
however, even much greater variations in the order of 100 percent
produce only relatively small differences .
.I 498
.T
calculation of potential flow about bodies of revolution
having axes perpendicular to the free-stream direction .
.A
hess,j.l.
.B
j. ae. scs. 29, 1962.
.W
calculation of potential flow about bodies of revolution
having axes perpendicular to the free-stream direction .
a general method is described for calculating, with the aid of
an electronic computer, the potential flow about arbitrary bodies
of revolution whose axes are perpendicular to the free-stream
direction . when combined with the solution for the
axisymmetric flow about these bodies, this method makes it possible to
calculate the pressure distribution on any body of revolution at
angle of attack forward of any separated region of the flow, and
also to calculate the flow at points off the body surface . after
the basic equations of the method have been derived, its accuracy
is exhibited by comparison with analytic solutions for ellipsoids
of revolution . calculated pressure distributions are then
compared with experimental data for a variety of bodies . the
agreement is quite satisfactory in all cases . the calculated
velocities for other selected bodies are presented to exhibit
certain properties of this type of flow .
.I 499
.T
a closed-form solution for the oscillations of a vehicle
entering a planetary atmosphere .
.A
greensite,a.l.
.B
j. ae. scs. 29, 1962, 745.
.W
a closed-form solution for the oscillations of a vehicle
entering a planetary atmosphere .
author considers the equation of the yawing motion of a missile,
derived with a series of customary assumptions and with the
distance traveled as the independent variable . his assumptions
include the linearity of the aerodynamic forces, the constancy of the
aerodynamic coefficients with respect to mach number, the
absence of spin, and the absence of gravity . if to these assumptions
one could add the common ballistic assumption of a constant air
density, the coefficients of this equation would have been
con-damped sinusoids . in ballistics any slow variation of these
coefstant, and the solution would have been simply the
exponentially-ficients is usually treated by adding an approximate correction
term to the damping rate (which is spoken of as the wkb
perturbation) . however, with a body entering the planetary atmosphere the
variation of the air density is apparently of greater essence (this
is a point not stated explicitly in this brief communication), and
the equation is of the type .
the author shows that with a series of further transformations
the equation can be reduced to the form
the solutions of which are confluent
hypergeometric functions . these functions are defined as series
involving gamma functions, and with a series of further assumptions
can be reduced to laguerre polynomials and bessel functions .
it is certainly nice to have an exact solution to a problem which
has heretofore been extensively treated by approximations and by
the numerical approach . this reviewer is puzzled, however, as to
the practical significance of the proposed approach . an
idealization is of value in that it facilitates our understanding,. and the
numerical approach, in that it allows refinements of the problem,
freeing us from the necessity of idealizing . but the proposed
solution is certainly more difficult to refine than the original
problem,. and it is certainly not simple (the solution of the original
equation is not the value of z, but the various /reverse/
transformations of z) . an evaluation of a series in practice must compete
with the numerical approach,. and the equation suggested is of the
zero) . viewing the problem /afresh/ (in the light of the /
computer revolution/ and without the constraints imposed by the prior
art), it seems at least equally easy to /standardize/ the
solutions of the original equation .
.I 500
.T
joule heating in magnetohydrodynamic free-convection
flows .
.A
cramer,k.r.
.B
j.ae.scs., 29, 1962, 746.
.W
joule heating in magnetohydrodynamic free-convection
flows .
the steady, fully developed, laminar, free-convection flow of an
electrically conducting fluid between two fully submerged
open-ended, constant-temperature vertical plates located in a constant,
uniformly distributed, transverse magnetic field has been analyzed
with the joule heating term retained in the energy equation .
analytic results are obtained . such analytic results are useful in
estimating the actual magnitude of the influence of joule heating as
well as a qualitative description of the manner in which it alters
the temperature and flow fields . the present result confirms the
usual practice that the influence of joule heating is negligibly
small .
.I 501
.T
stagnation-point shock detachment of blunt bodies in
supersonic flow .
.A
ridyard,h.w.
.B
j. ae. scs. 29, 1962, 751.
.W
stagnation-point shock detachment of blunt bodies in
supersonic flow .
presentation of stagnation-point shock-detachment distances
determined by the exact numerical method of gravalos, edelfelt,
and emmons . the results are compared with those from the
previously published methods of van dyke and gordon, li and geiger,
and serbin, and with experimental data .
.I 502
.T
on squire's test of the compressibility transformation .
.A
mager,a.
.B
j. ae. scs. 29, 1962,752.
.W
on squire's test of the compressibility transformation .
discussion of a previous application, by squire, of the author's
compressibility transformation to the correlation of high-speed
boundary-layer data for air and helium . squire's suggestion that
the compressibility transformation is invalid is shown to be
incorrect .
.I 503
.T
theoretical prediction of the transonic characteristics
of airfoils .
.A
sinnott,c.s.
.B
j. ae. scs. 29, 1962, 275.
.W
theoretical prediction of the transonic characteristics
of airfoils .
it is shown that the author's transonic-flow airfoil theory
can be used to estimate transonic drag-rise and onset-of-
separation-effects mach numbers without reference to experimental
results . a simple comparative method is applied to a series of
airfoils, and the results are analyzed to determine some of the
design features of importance in transonic flow . an
improvement to this scheme is shown to give results in good agreement
with experiment for both the first appearance of shock waves
and the onset of separation effects . application to finite swept
wings is briefly considered and illustrated .
.I 504
.T
stability of compressible boundary layers induced by
a moving wave .
.A
ostrach,s.
.B
j. ae. scs. 29, 1962, 289.
.W
stability of compressible boundary layers induced by
a moving wave .
the problem of determining the stability of compressible
viscous flows with nonzero surface velocities is formulated and is
shown to be identical to that for conventional boundary layers,
with only a redefinition of the mach and reynolds numbers
required . specific consideration is given to the wall boundary
layer behind a moving shock wave, and the minimum critical
reynolds numbers are obtained for various shock velocities .
the entire stability map is determined for the limiting case of a
weak wave, which is analogous to the rayleigh problem .
the minimum critical reynolds number is found to increase
monotonically with shock velocity--i.e., with increasing surface
cooling and stream mach number combined . for the ratio of
wall to stream velocity of 2.92 with (shock mach number
of 2.18) the flow is found to be infinitely stable to two-dimensional
disturbances .
experimental transition data do not follow the trends predicted
by the theory . in fact, the transition reynolds numbers are
orders of magnitude below the computed minimum critical
reynolds numbers . the lack of correlation between theory and
experiment is attributed to disturbances which are external to
the boundary layer .
.I 505
.T
transition measurements on cones in free flight ballistics
range tests .
.A
lyons,w.c.
.B
j. ae. scs. 29, 1962, 352.
.W
transition measurements on cones in free flight ballistics
range tests .
navy-sponsored experimental investigation of the location of
boundary-layer transition on sharp-nosed cones having 10 total
angles . the ambient temperature in a portion of the aeroballistics
range is varied so as to obtain different adiabatic recovery
temperatures at a constant nominal mach number of 3.1 . the location
of transition is expressed as a transition reynolds number, and
results are presented graphically as a function of the ratio between
the wall temperature and the adiabatic recovery temperature .
.I 506
.T
a note on havelock's shallow-water wave-resistance
curves .
.A
brandmaier,h.e.
.B
j. ae. scs. 29, 1962, 257.
.W
a note on havelock's shallow-water wave-resistance
curves .
in the continuous quest for improved means of
transportation, attention is currently focused on the ground-effect
machine . as there is no physical contact between the vehicle
and the terrain over which it operates, its performance should
be similar over land and water . however, over water there is
an additional resistance to motion due to the gravity-wave
system generated by the supporting or /cushion/ pressure acting
on the water surface . estimates of this component can be made
using the analysis of t. h. havelock . it is the purpose of this
note to present an ibm 650 digital-computer solution of his
equations . as shown below, these results differ from havelock's
original results .
.I 507
.T
energy equation approximations in fluid mechanics .
.A
goldstein,a.w.
.B
j. ae. scs. 29, 1962,358
.W
energy equation approximations in fluid mechanics .
discussion of several forms of the energy equation and of their
use for the study of the flow of nearly incompressible fluids .
.I 508
.T
a correlation of nose-bluntness induced pressures on
cylindrical and conical after-bodies at hypersonic
speeds .
.A
greenberg,r.a.
.B
j. ae. scs. 29, 1962, 359.
.W
a correlation of nose-bluntness induced pressures on
cylindrical and conical after-bodies at hypersonic
speeds .
van hise, in his detailed study of the nose-bluntness-induced
pressures on cylindrical afterbodies, shows that, starting
a few nose diameters aft of the nose-afterbody junction, these
pressures are correlated with the parameter
as predicted by the blast-wave analogy . chernyi developed a
modified form of the blast-wave analogy which takes into account
the addition of energy to the flow by a thin afterbody . he
showed that for thin afterbodies and hypersonic speeds, the
pressure distribution, plotted as should correlate with
the parameter . the purpose of this note
is to show that the above correlation techniques may be
combined into a form such that pressures on cylindrical and conical
afterbodies are correlated by one parameter .
.I 509
.T
a graphical approximation for temperatures and sublimation rates at
surfaces subjected to small net and large gross heat transfer rates .
.A
adams, e. w.
.B
j. aero. sc. v. 29, march 1962, pp. 360-1 .
.W
a graphical approximation for temperatures and sublimation rates at
surfaces subjected to small net and large gross heat transfer rates .
considers a material, acted upon by heat of conduction, which changes
its state by sublimation at the heated surface . the derived method is
most suitable under conditions of severe heating such as space vehicle
re-entry .
.I 510
.T
manoeuvring technique for changing the plane of circular
orbits with minimum fuel expenditure .
.A
weiss,d.c.
.B
j. ae. scs. 29, 1962, 368.
.W
manoeuvring technique for changing the plane of circular
orbits with minimum fuel expenditure .
usaf-supported discussion of the use of an intermediate
elliptic orbit for changing the plane of a circular orbit . values of the
perigee and apogee velocities are calculated for the following cases ..
the braking impulse supplied by grazing of the atmosphere,. and (3)
re-orbit with 90 of the braking impulse supplied in this manner .
.I 511
.T
tunnel tests on a double cascade to determine the interaction
between the rotor and the nozzles of a supersonic turbine .
.A
stratford,b.s.
.B
ngte m359.
.W
tunnel tests on a double cascade to determine the interaction
between the rotor and the nozzles of a supersonic turbine .
experimental confirmation has been required that in a supersonic
turbine the leading edges of the rotor governs the rotor incidence and,
hence, the gas exit angle from the nozzles . evidence has also been
required that, once the rotor incidence has been allowed for, there is
no adverse effect of the rotors on the nozzle flow, even when the rotors
have a large turning angle .
the present test cascade represented the stationary configuration
of a turbine of 2.5 nozzle mach number and 74 swirl angle, the rotors
being designed to operate at 1.9 relative mach number and to provide a
turning angle of 140 . in the tests, fully supersonic flow could be
established through the system, but the losses were fairly high and an
increase in loss of about 25 per cent would have caused choking in the
rotor .
.I 512
.T
quasi-cylindrical surfaces with prescribed thickness
distributions .
.A
moore,k.c.
.B
rae tn.aero.2815, 1962.
.W
quasi-cylindrical surfaces with prescribed thickness
distributions .
a formula for the supersonic velocity field in terms of a given
surface distribution of sources is applied to points lying in the
surface . an equation giving the camber shape of a quasi
circular-cylindrical surface in terms of a prescribed thickness distribution
is derived and the half ring wing with prescribed thickness distribution
is discussed as an example .
.I 513
.T
pressure measurements at supersonic speeds on three
uncambered conical wings of unit aspect ratio .
.A
britton,j.w.
.B
rae tn.aero.2821, 1962.
.W
pressure measurements at supersonic speeds on three
uncambered conical wings of unit aspect ratio .
pressure measurements were made at mach numbers between 1.3 and 2.8
over a range of incidences on three simple models representing thick
conical uncambered wings with sharp leading edges . these tests form
part of an investigation into the effects of thickness and camber on
slender wings .
the aspect ratio of the models was unity in each case, and the
spanwise cross sections were bounded
by .. the measured pressure distributions are presented, along with overall
lift and drag (excluding skin friction and base drag) obtained by
integration .
.I 514
.T
pressure distributions and flow patterns on some conical
shapes with sharp edges and symmetrical cross-sections
at m=4 .0.
.A
squire,l.c.
.B
rae tn.aero.2823, 1962.
.W
pressure distributions and flow patterns on some conical
shapes with sharp edges and symmetrical cross-sections
at m=4 .0.
results are given of a wind tunnel programme made to study the
pressure distributions and flow patterns over a series of simple,
conical shapes at a mach number of 4.0 . the results have been compared
with various approximate theories and the limitations of these theories
are discussed .
it is found that at this mach number leading edge separations still
have an influence on the suction surface pressure, and that this surface
still makes a significant contribution to the overall forces .
.I 515
.T
self sustained oscillations of a system with non-linear
damping of a particular type .
.A
neumark,s.
.B
rae tn.aero.2839, 1962.
.W
self sustained oscillations of a system with non-linear
damping of a particular type .
the paper deals with self-sustained
oscillations of a dynamic system
of single degree of freedom, with linear
restoring force and non-linear
damping force . the latter is supposed
to be a function of velocity
representable by a simple /polygonal/
graph, such that the damping is
negative at small velocities but becomes
positive at velocities above a
certain value . on these assumptions,
a rigorous solution is presented,
including the equations of motion,
amplitude, maximum velocity and period .
a very simple solution is obtained
for the limiting case of vanishingly
small damping . an approximate solution
by series in powers of damping
ratio is worked out which
gives a satisfactory accuracy for
quite large values of .
.I 516
.T
free-flight measurements of the dynamic longitudinal
stability characteristics of a wind tunnel interference
model (m=0 .92 to 1. 35) .
.A
greenwood,g.h.
.B
rae tn.aero.2798, 1961.
.W
free-flight measurements of the dynamic longitudinal
stability characteristics of a wind tunnel interference
model (m=0 .92 to 1. 35) .
the dynamic longitudinal-stability characteristics of a standard
wind tunnel interference model have been investigated in free flight
over a mach number range of 0.92 to 1.35 .
measurements of lift-curve slope and manoeuvre margin were
obtained, and are compared with results from transonic-tunnel tests
under low blockage conditions .
the analysis was extended to obtain damping derivatives to allow
comparison to be made with possible future dynamic tests in wind tunnels
on the standard shape .
.I 517
.T
reaction-resisted shock fronts .
.A
clarke,j.f.
.B
coa r.150, 1961.
.W
reaction-resisted shock fronts .
it is shown that shock waves whose
structure is determined solely by the effects
of chemical reactions (reaction-resisted
shock fronts) are possible and completely
analogous to relaxation - resisted waves .
a single dissociation reaction is considered
and numerical results indicate that such
waves could be observed experimentally .
bulk viscosities equivalent to reaction
effects are possibly 10 or more times shear
viscosity values . (examples are based on
lighthill's ideal dissociating gas) .
.I 518
.T
heat conduction through a polyatomic gas .
.A
clarke,j.f.
.B
coa r.149, 1961.
.W
heat conduction through a polyatomic gas .
a heat conduction problem is set up
which, in essence, simulates the conditions
arising when a plane shock wave reflects
from a co-planar solid boundary . the gas
is assumed to be polyatomic, with one
the quantity of primary interest is
the temperature of the solid at the interface,
since this can be observed experimentally
without much difficulty . solutions are
obtained for this quantity which cover a
range of practically plausible relaxation times
and 'wall effect' parameters . it is essential
to include proper temperature jump
boundary conditions for both active and
relaxing (or inert) energy modes . thus it is
necessary to know accommodation coefficients
for these modes of energy storage .
the temperature jump effects are found to
dominate the (interface) solid's temperature
time history, with relaxation effects playing
a very secondary role .
the theoretical results are compared
with some experimental observations and
encouraging agreement is found . as a
result of this agreement it proves possible to
estimate the accommodation coefficient
for the active modes (in this case for the
combination platinum air), the pressure
being about 15 atmospheres . the pressure
sensitivity of accommodation effects is commented on .
.I 519
.T
base pressure at supersonic speeds in the presence
of a supersonic jet .
.A
craven,a.h.
.B
coa r.144, 1960.
.W
base pressure at supersonic speeds in the presence
of a supersonic jet .
the effects on base pressure of jet mach number, free stream
reynolds number and jet to base diameter ratio have been investigated
experimentally .
it was found that, for jet stagnation pressures greater than that
required for the nozzle to reach its design mach number, an increase
of jet mach number reduced the base pressure . similarly the base
pressure increased with increase of the ratio of jet diameter to base
diameter and, at high jet stagnation pressures, base pressures higher
than free stream static pressure were found . the base pressure was
independent of free stream reynolds numbers greater than 2 x 10 per
foot but increased with reduction of reynolds number below 2 x 10 per
foot .
unsteady wave patterns were found when the jet mach number did
not differ markedly from the free stream mach number and the jet had
just reached its design conditions .
.I 520
.T
wing-tail interference as a cause of 'magnus' effects
on a finned missile .
.A
benton,e.r.
.B
j. ae. scs. 29, 1962, 1358.
.W
wing-tail interference as a cause of 'magnus' effects
on a finned missile .
wing-tail interference is shown to cause large /magnus/ effects
on a finned missile whose wings are deflected into an aileron
setting . a simple experimental method with water as the
working medium is used to obtain low-speed magnus data on a rolling
missile . the missile is a slender cruciform configuration with
all-movable wings and fixed tail fins . magnus data are
presented for angles of attack up to 15 and for the one (high) roll
rate which accompanies a 30 aileron deflection angle of the
wings . tests conducted at zero roll rate but with the wing
deflection maintained, revealed large forces in the magnus direction,
thereby providing the basis for understanding magnus effects due
to wing-tail interference .
a semiempirical theory is proposed to explain the experimental
data . a simplified model of the wake behind the wings is
introduced to predict tail-interference factors . good agreement with
the data is obtained .
this magnus effect is opposite in direction to the classical
magnus lift on a spinning cylinder ,. it is much larger than either
that effect or the one on a missile with only one set of fins .
wing-tail interference is the predominant source of the effect ,. roll rate
only modifies the basic interference mechanism .
.I 521
.T
a note on application of transonic linearization to
an airfoil with a round leading edge .
.A
hosokawa,i.
.B
j. ae. scs. 29, 1962, 1395.
.W
a note on application of transonic linearization to
an airfoil with a round leading edge .
the profile of a symmetric airfoil of unit length with a round
leading edge can be expressed, in general, as
where p(x) has a finite slope at x = 0 . it is well known that
the conventional sub- and supersonic linear theories of
compressible flow break down in the neighborhood of such a round
leading edge due to the failure of the small-disturbance
assumption . the linearized transonic flow theory has the same
short-coming, but if the determination of the sonic point on the airfoil
plays an important role in any more advanced theory--e.g.,
spreiter's local-linearization method or hosokawa's method of
refinement--this theoretical barrier will become more serious
because the sonic point is usually located in a flow region near
the leading edge that may be greatly affected by the roundness .
.I 522
.T
laminar, transitional and turbulent heat transfer to
a cone-cylinder-flare body at mach 8. 0.
.A
zakkay,v. and callahan,c.j.
.B
j. ae. scs. 29, 1962, 1403.
.W
laminar, transitional and turbulent heat transfer to
a cone-cylinder-flare body at mach 8. 0.
an experimental investigation of the laminar, transitional, and
turbulent heat transfer rates over a conical cylindrical flared
body is presented . regions of favorable, zero, and adverse
pressure gradient on the body are investigated . the experimental
results are compared with the theories available in the literature .
the model chosen for this investigation is a cone-cylinder-flare
configuration consisting of a 20 semivertex conical nose portion
smoothly blended by a shoulder radius into a long cylindrical body
and terminated by a smooth large radius flare .
the model was tested at a free stream mach number of 8, over
a range of reynolds number from 0.3 x 10 to 1.6 x 10 per inch
based on free stream conditions . various stagnation-to-wall
temperature ratios were obtained by cooling the model prior to
the test with liquid nitrogen . the stagnation-to-wall
temperature ratios were 10 and 3.3 .
the theoretical predictions gave good results for the heat
transfer rates in the laminar region, and fair prediction in the
transitional and turbulent regimes extending over the shoulder
and forward portion of the cylindrical body . over the aft portion
of the cylinder and over the flare the predictions are only
qualitatively correct, and underestimate the heating rate by a factor as
high as 3 . conversely, the /flat plate reference enthalpy/
over the aft portion of the body, but to increasingly overestimate
the heating rates over the forward portion of the cylinder .
a modified equation for the heat transfer coefficient in the
transitional and fully turbulent region based on the f.p.r.e.
method is then presented . this method gives good agreement
with the experimental results presented over the entire range of
transitional and turbulent flow .
from the results the following is concluded .. cooling the wall
delayed transition . by expanding the flow rapidly between the
cone and the cylinder, the transition reynolds number is reached
very rapidly . by making a smooth transition between the
cylinder and the flare, no separation occurred at the cylindrical flare
junction . the transitional and turbulent heat transfer in the
presence of an adverse pressure gradient may be predicted with
sufficient accuracy by the f.p.r.e. method .
.I 523
.T
approximate determination of position of the sonic
line for a blunt body in hypersonic flow .
.A
rahman,m.a.
.B
j. ae. scs. 29, 1962.
.W
approximate determination of position of the sonic
line for a blunt body in hypersonic flow .
the detached shock in front of a blunt body in hypersonic
flow tends to acquire the shape of the frontal curvature of the
body . thus the curvature of the shock can be assumed to be the
same as that of the body, at least up to the sonic point (point a,
fig. 1) . if the equation of curvature of the body is known, the
equation of curvature of the shock is also known . in this paper,
with this assumption, a method is described to determine the
approximate position of the sonic line (ao'b, fig. 1) . the
shock-detachment distance is assumed known .
the method is, of course, general . this can be applied to
any detached shock provided its equation of curvature is known
corresponding to that of the body . for simplicity the detached
shock is assumed to be circular in this paper and the procedure is
outlined below with the assumption that the sonic line ao'b is
parabolic .
.I 524
.T
stagnation point heat transfer in partially ionized
air .
.A
rozycki,r.c. and fenster,s.j.
.B
j. ae. scs. 29, 1962.
.W
stagnation point heat transfer in partially ionized
air .
comparison of heat-transfer rates, obtained by using transport
properties recently reported by peng and pindroh, with rates based
on hansen's thermodynamic and transport properties . it is shown
that the heat-transfer rates based on the peng and pindroh data
are 20 to 30 lower for the velocity range of 25,000 to 40,000
ft sec .
.I 525
.T
on hypersonic viscous flow over an insulated flat plate
with surface mass transfer .
.A
tien,c.l.
.B
j. ae. scs. 29, 1962, 1024.
.W
on hypersonic viscous flow over an insulated flat plate
with surface mass transfer .
hypersonic viscous flow over an insulated flat plate with
surface mass transfer is studied . the tangent-wedge approximation
is used in the inviscid-flow region, and the integral method is
applied to the treatment of the laminar boundary layer . the law
of surface mass transfer for the present analysis is derived . a
continuous transition of the pressure variation is achieved from
the strong to the weak pressure-interaction region . first-order
formulas for the induced surface pressure and the skin-friction
coefficient are obtained for both the strong and weak
pressure-interaction regions . results are compared with those calculated
from other analyses .
.I 526
.T
leading edge attachment in transonic flow with laminar
or turbulent boundary layers .
.A
mabey,d.g.
.B
j. ae. scs. 29, 1962.
.W
leading edge attachment in transonic flow with laminar
or turbulent boundary layers .
the transonic flow round a two-dimensional airfoil at
incidence is often determined by the type of flow in the leading-edge
region . if the flow separates at the leading edge at low speeds it
is liable to attach as the speed increases, often quite suddenly .
a review of this change with laminar or with turbulent boundary
layers re-emphasizes the importance of fixing transition when
making model tests at transonic speeds in order to obtain flows
closest to full-scale conditions .
it is shown that similar airfoils with attached leading-edge
flow show transonic similarity upstream of the terminal shock .
.I 527
.T
note on the three-point boundary layer problem for
the blasius equations .
.A
martin,e.d.
.B
j. ae. scs. 29, 1962.
.W
note on the three-point boundary layer problem for
the blasius equations .
in a recent paper a method was presented for obtaining
higher accuracy in the numerical solution of the blasius
equation with three-point boundary conditions . the
well-known blasius equation was previously developed in an
investigation of the steady two-dimensional incompressible
boundary-layer flow over a flat plate, but it has been extensively used in
investigating other fluid flow problems . the three-point
boundary-value problem is encountered in the theory of laminar
mixing and in approximate analyses of separated and wake
flows as noted in ref. 1 .
.I 528
.T
first-order slip effects on the laminar boundary layer over a slender
body of revolution with zero pressure gradient .
.A
jay m. solomon
.B
research aerospace engineer, u. s. naval ordnance laboratory,
white oak, silver spring, md.
.W
first-order slip effects on the laminar boundary layer over a slender
body of revolution with zero pressure gradient .
in reference 1, the analysis given by probstein and elliott for the
zero-pressure-gradient, constant-wall-temperature, compressible,
laminar boundary layer with transverse curvature was extended to
first-order slip flow . this extension was based on a double asymptotic
expansion in a transverse-curvature parameter and a slip parameter .
the expansion in ref. 1, however, was carried out with the parameter
held constant . for and a constant wall temperature, is constant and
e varies with x due to the dependence of the local body radius on x .
thus, for arbitrary body shapes, e will not be constant . in the
present note, the analysis of ref. 1 is re-examined taking into account
the variation of e .
.I 529
.T
some effects of injection of foreign gases in a decelerating
laminar boundary layer in supersonic flow .
.A
gouse,s.w., brown,g.a. and kaye,j.
.B
j. ae. scs. 29, 1962, 1250.
.W
some effects of injection of foreign gases in a decelerating
laminar boundary layer in supersonic flow .
the purpose of this research program was to investigate the
effects of a diffusion field on a laminar boundary layer in a
supersonic flow . specifically, helium, nitrogen, and argon were
uniformly injected into the laminar boundary layer of a
high-speed flow in a tube with the objective of determining the effects
of such injection on the pressure, temperature, and recovery
factor distribution along and downstream of the injection region .
a continuously operating axially-symmetric wind tunnel has
been designed, constructed, and operated . this tunnel consists
of an air supply system, a flowmeter, an upstream stagnation
tank, a supersonic nozzle (throat diameter 0.262 and exit
diameter 1.400), a test section of variable length (zero to 81 diameters,
test section diameter of 1.400), a downstream stagnation tank,
an exhaust system, a foreign gas supply system, and all necessary
instrumentation . the overall performance of this apparatus in
terms of the design specifications was excellent .
the tunnel was instrumented with 109 thermocouples . all
temperatures except ambient temperatures were automatically
measured and recorded by means of a self-balancing recording
potentiometer . there was 29 pressure taps distributed along the
tunnel, 23 along the test section itself . pressures were measured
by means of an interconnected micromanometer and a vacuum
referenced manometer system with overlapping ranges .
for all of the results reported herein, the overall test section
was 41 diameters in length,. composed of a porous test section
approximately 7.2 diameters in length (leading edge
approximately 1.8 diameters from the nozzle exit plane) and four nylon
test sections of 8 diameters each .
.I 530
.T
an aerodynamic analysis for flutter in oseen-type viscous
flow .
.A
chu,wen-hwa.
.B
j. ae. scs. 29, 1962, 781.
.W
an aerodynamic analysis for flutter in oseen-type viscous
flow .
oseen's equations for unsteady flow are employed to obtain
a linearized solution based on a discontinuous-wake model .
the analysis is employed to estimate the viscous correction to
unsteady lift and moment at large reynolds number . if the
asymptotic solution is not too slowly convergent, the correction
is of the order of the ratio of the logarithm of reynolds number
to the reynolds number . the theory is preliminary in nature
as it is limited by the accuracy of oseen's equations and is
restricted to small angle of attack . however, it also shows that
the generalized trailing-edge condition for potential flow is
reasonable and might predict the essential correction in a real
fluid .
.I 531
.T
the flow about a moving body in the upper ionosphere .
.A
bird,g.a.
.B
j. ae. scs. 29, 1962.
.W
the flow about a moving body in the upper ionosphere .
a particle approach is used to study the flow pattern around a
body moving in the upper layers of the ionosphere . the effects
of distant encounters between charged particles (dynamic
friction) and of the earth's magnetic field are taken into account .
it is shown that, when the magnetic lines of force are parallel
to the direction of motion of the body, there may be a marked
concentration of charged particles in the vicinity of the body
and a considerable fraction of the reflected or deflected charged
particles may reimpinge on the body surface . a numerical
example is given for the size and shape of the charged-
particle-density contours in the flow field surrounding a circular disc,
and these are compared with the corresponding neutral-particle
contours .
.I 532
.T
pitch-yaw stability of a missile oscillating in roll
via the second method of lyapunov .
.A
parks,p.c.
.B
j. ae. scs. 29, 1962, 874.
.W
pitch-yaw stability of a missile oscillating in roll
via the second method of lyapunov .
the stability theory of a. m. lyapunov, a popular topic in
the u.s.s.r., is receiving increasing attention elsewhere .
this note describes lyapunov's /second method/ very briefly
and applies it to an aeronautical stability problem .
.I 533
.T
stagnation-point shock-detachment distance for flow
around spheres and cylinders in air .
.A
ambrosio,a. and wortman,a.
.B
j. ae. scs. 29, 1962.
.W
stagnation-point shock-detachment distance for flow
around spheres and cylinders in air .
author discusses the problem of deflection of a cantilevered
bar, initially in the shape of a circular arc, subjected to an
arbitrarily inclined end load .
.I 534
.T
consideration of energy separation for laminar slip
flow in a circular tube .
.A
inman,r.m.
.B
j. ae. scs. 29, 1962, 1014.
.W
consideration of energy separation for laminar slip
flow in a circular tube .
the energy separation for laminar low-density-nonunity prandtl
number flow in circular cross-section tubes is the topic of this
note . a conclusion is reached as to the effect of prandtl number
on the velocity profiles for these flows . however, in order to
reach valid quantitative conclusions the reviewer feels that more
detailed analysis is in order, and that the analysis as presented
here is of qualitative value only .
.I 535
.T
shroud design for simulating hypersonic flow over the nose of a
hemisphere .
.A
roger dunlap
.B
associate research engineer, dept, of aeronautical and
astronautical engineering, ann arbor, mich.
.W
shroud design for simulating hypersonic flow over the nose of a
hemisphere .
following is an analytical method for designing a shroud which will
generate the hypersonic pressure distribution on a hemisphere . the
method was found to be successful throughout the region of subsonic
flow . this shroud was designed as part of a low-turbulence wind tunnel
used for investigating the effects of cooling on boundary-layer
transition on a hemisphere .
the design of the shroud contour was carried out in two steps . first,
an approximate solution for the incompressible, irrotational flow
field was found in the region, and, second, the resulting contour
was corrected for compressibility near the sonic region, assuming
one-dimensional flow .
.I 536
.T
transition in the viscous wakes of blunt bodies at
hypersonic speeds .
.A
hidalgo,h., taylor,r.l. and keck,j.c.
.B
j. ae. scs. 29, 1962.
.W
transition in the viscous wakes of blunt bodies at
hypersonic speeds .
transition from laminar to turbulent flow in the hypersonic
wakes of spheres was detected in laboratory measurements of the
radiation from the flow field . a hypervelocity gun facility was
used to fire models, 0.22-in. in diameter, into a range at velocities
from 10,000 to 17,000 ft sec . experiments were performed by
changing .. (a) the material of the projectile ,. (b) the ambient
gas in the range ,. and (c) the pressure in the range . three
optical techniques were used to observe the wake radiation ..
which show a turbulent viscous wake as the pressure in the
range is decreased from one atmosphere to about 20 cm hg .
which show the luminous flow field at pressures between 30 and
ence of short luminous streaks, which disappear suddenly as the
pressure is decreased below 3 cm hg for air, and below 0.8 cm
hg for argon .
both air and argon, which show the main features of the flow
field . above the transition pressure, the intensity of radiation
from the wake is always associated with fluctuations that appear
to be the same phenomenon as the drum-camera streaks .
the appearance of the streaks in the drum camera and
photo-multiplier data is interpreted as transition from laminar to
turbulent flow in the viscous wake, because experimental evidence
shows that their appearance is not controlled by chemical,
radiative, or ablative processes, but depends on aerodynamic
effects . this conclusion is supported by other experiments based
on optical and schlieren techniques . the transition in the wake
at positions very close to the body is given by a local reynolds
number of 10 for air, and 3 x 10 for argon . the results indicate
a possible local-mach-number effect .
.I 537
.T
stagnation point viscous hypersonic flow .
.A
stoddard,f.j.
.B
j. ae. scs. 29, 1962, 1138.
.W
stagnation point viscous hypersonic flow .
several methods have been developed for computing the
hypersonic, low reynolds number flow in the stagnation
region of a blunt body . in general, these methods involve
complicated numerical solutions . simultaneous iterations on several
parameters are usually required in view of the boundary-value
nature of the problem .
the purpose of this note is to present an approximate
closed-form solution to axisymmetric stagnation point hypersonic flow
in the viscous layer regime .
.I 538
.T
the conpressibility transformation and the turbulent
boundary layer equations .
.A
burgraf,o.r.
.B
j. ae. scs. 19, 1962.
.W
the conpressibility transformation and the turbulent
boundary layer equations .
the compressibility transformation first introduced by
dorod-nitzyn has been applied in this paper to the equations of the
turbulent boundary layer on a flat plate, considering heat transfer
and arbitrary prandtl numbers . assuming the shear
distribution to be invariant under the transformation, the stream
function and the momentum equation take the proper form for
incompressible flow, allowing the use of incompressible velocity
profiles in the transformed coordinates . application of crocco's
method to the transformed energy equation permits integration
of the energy equation resulting in a formulism remarkably
similar to that proposed by eckert . finally, the reference
condition was chosen to correspond to the edge of the sublayer from
considerations of the assumptions made regarding the
shear-stress distribution . with this choice, the reference enthalpy is in
good agreement with eckert's formula over the ordinary range of
test conditions . in view of these results, the analysis may be
considered to provide a theoretical basis for the
reference-enthalpy method .
.I 539
.T
local heat transfer to a yawed, infite, circular cylinder
in laminar compressible flow .
.A
weiss,d.
.B
j. ae. scs. 29, 1962.
.W
local heat transfer to a yawed, infite, circular cylinder
in laminar compressible flow .
this note presents a simplification of a method for
calculating the ratio of local to stagnation-line heat-transfer
coefficients on a yawed, infinite, circular cylinder in laminar
compressible flow . a brief description of the method of ref. 1 is
presented, followed by a discussion of the assumptions and
mathematical procedure which lead to a considerable simplification .
.I 540
.T
use of local similarity concepts in hypersonic viscous
interaction problems .
.A
forbes dewey,c.
.B
a.i.a.a. j. 1963, 20.
.W
use of local similarity concepts in hypersonic viscous
interaction problems .
the problem of predicting the characteristics
of a hypersonic laminar boundary layer that
interacts with the external flow field is approached
using the tangent wedge formulation for
the inviscid flow field and the method of similar
solutions for the viscous flow . it is shown
that the concept of local similarity which allows
the pressure gradient parameter to vary in
the streamwise direction leads to an explicit
relation between the viscous and inviscid flows
for all values of the hypersonic interaction
parameter . the conditions of /strong/ and
limits of the general relations . the present theory
is compared with three independent experimental
investigations . in each case, the
agreement is found to be excellent over the range of
investigated . it is shown, using asymptotic
solutions to the exact boundary layer equations,
that the present theory is applicable to a wide
variety of viscous interaction problems .
a large number of solutions to the laminar
boundary layer similarity equations for a perfect
gas with cross flow and surface mass transfer are
given . these numerical results, when combined
with the solutions of previous authors, are
sufficient to describe the range of conditions with high precision .
.I 541
.T
similitude of hypersonic flows over slender bodies
in non-equilibrium dissociated gases .
.A
inger,g.r.
.B
a.i.a.a. j. 1963, 46.
.W
similitude of hypersonic flows over slender bodies
in non-equilibrium dissociated gases .
this paper is concerned with the similitude laws
governing inviscid, nonequilibrium gas flows
around blunt or sharp-nosed slender bodies at
zero angle of attack, based on the hypersonic
small disturbance flow theory . some related
features of the interaction between the effects of
nose bluntness and nonequilibrium dissociation
and vibration and the influence of a
dissociated freestream are also discussed . the
hypersonic equivalence principle and the related
similitude for affinely related bodies are set
forth for nonequilibrium flows in either diatomic
gases or a gas mixture such as air . for a family
of diatomic gases, as opposed to a given gas
such as air, a generalized ambient gas state
scaling condition is obtained, whereby the
ambient density and temperature need not be
simulated . a detailed discussion is given of
blunted cylinders and slabs or sharp-nosed
cones and wedges, including example
nonequilibrium flow field correlations of numerical
solutions available in the literature . low density
nonequilibrium flows with a negligible shock
layer atom recombination rate are also
examined ,. as expected, a less restrictive small
disturbance similitude law is obtained in this
case .
.I 542
.T
biot's variational principle in heat conduction .
.A
lardner,t.j.
.B
a.i.a.a. j. 1963, 196.
.W
biot's variational principle in heat conduction .
biot's variational principle is applied to a number of different
one-dimensional heat conduction problems . these problems
show the applicability of the variational principle to problems
involving prescribed heat flux boundary conditions and to those
with temperature-dependent material properties .
a method is introduced for including boundary conditions
when these are expressed as prescribed heat fluxes . the idea
behind this is overall energy balance within the body, which is a
constraint condition to be satisfied by the time histories of the
generalized coordinates .
the variational principle is then applied to the well-known
problem of constant surface heat flux in order to present the
technique and provide a basis for the remaining sections . the
equivalence of the result obtained in applying the variational
principle for a prescribed surface temperature history to that
obtained for a prescribed heat flux is also pointed out . radiation
cooling due to fourth power radiation from semi-infinite solids
and finite slabs together with radiation according to newton's
law of cooling is then treated . finally, the introduction of
temperature-dependent material properties is discussed and the
determination of the temperature distribution in a semi-infinite
solid with variable properties is investigated .
.I 543
.T
the stacking of compressor stage characteristics to
give an overall compressor performance map .
.A
doyle,m.d.c.
.B
aero. aquart. 13, 1962.
.W
the stacking of compressor stage characteristics to
give an overall compressor performance map .
a method of calculation is developed to compute the overall
performance of a multi-stage axial compressor, from a knowledge of the
individual stage characteristics, by a /stacking/ technique .
compressor models are designed and their overall performance
calculated . these results are compared to show, qualitatively, the
effect of alterations in design and stage performance on overall
performance and to find how compressors should be designed
for optimum performance .
.I 544
.T
a theoretical and experimental study of oscillating wedge shaped
aerofoils in hypersonic flow .
.A
r. a. east
.B
.W
a theoretical and experimental study of oscillating wedge shaped
aerofoils in hypersonic flow .
aerodynamic stiffness and damping derivatives have been measured
in a /hypersonic gun/ wind tunnel for sharp and blunt-nosed two
dimensional single wedge shapes oscillating in the pitching mode in
hypersonic flow . the results, which have been compared with
theoretical prediction, modified to account for leading edge bluntness,
show that this may increase the damping by up to 50 percent for certain
axis positions . details of the experimental technique designed to
measure the derivatives in the short running times available are
described .
.I 545
.T
calculation of sideslip derivatives and pressure distribution
in asymmetric flight conditions on a slender wing-fin
configuration .
.A
sells,c.c.l.
.B
rae tn.aero.2805, 1962.
.W
calculation of sideslip derivatives and pressure distribution
in asymmetric flight conditions on a slender wing-fin
configuration .
the flow around slender wing-fin
configurations having curved leading
edges, whose shape is defined by polynomials,
is considered . a general
expression for the pressure distribution
on such a configuration in
asymmetric flow is derived and the
derivatives due to the particular case
of sideslipping motion are also given .
no numerical results are given for
wing-fin load distribution, but the
sideslip derivatives have been
evaluated in a number of cases for
gothic and ogee wings .
.I 546
.T
measurements of aerodynamic heating on a 15 cone of
graded wall thickness at a mach number of 6. 8.
.A
woodley,j.g.
.B
rae tn.aero.2847, 1962.
.W
measurements of aerodynamic heating on a 15 cone of
graded wall thickness at a mach number of 6. 8.
this note describes transient wall
temperature measurements made on a
in an airstream of mach number 6.8 .
the skin of the model was
sufficiently thin to allow it to reach zero
heat transfer conditions within a
running time of one minute .
in order to reduce effects
of longitudinal heat conduction during a
run the electroformed-nickel skin
of the model was made with graded
thickness, and as a result fairly
uniform temperature distributions along
the surface were obtained at all
times in both the laminar and turbulent
regions .
values of heat transfer, calculated from the wall temperature-time
histories using the thin-wall
temperature are compared to theoretical
estimates using the intermediate
enthalpy method 10, 11 .
.I 547
.T
boundary layer characteristics of caret wings .
.A
catherall,d.
.B
rae tn.aero.2835, 1962.
.W
boundary layer characteristics of caret wings .
the theory of laminar boundary
layers along flat surfaces has been
used in conjunction with eckert's
approximations to the displacement
thickness, skin friction and temperature
profiles on the undersurface of a
caret wing configuration . to a first
approximation it has been assumed
that parallel flow exits behind the shock
outside the boundary layer, and the
displacement of the shock by the boundary
layer near the leading edge is neglected .
conduction of heat within the
body and along the surface is neglected
but radiation is included, so that
are found . examples are given for
various altitudes and configurations and
the effect of the skin friction on
the lift drag ratio calculated, assuming
the undersurfaces to be plane .
.I 548
.T
the contraction of satellite orbits under the influence
of air drag . pt .iv with scale height dependent on
altitude .
.A
king-hele,d.g., and cook,g.e.
.B
rae tn.space 18, 1962.
.W
the contraction of satellite orbits under the influence
of air drag . pt .iv with scale height dependent on
altitude .
the effect of air drag on satellite
orbits of small eccentricity e
was studied in part i (tech. note
gw 533), on the assumption that
atmospheric density varies exponentially
with distance r from the earth's
centre, so that the 'density scale height'
h, defined as, is
constant . in practice h varies with height
in an approximately linear
manner, and in the present note the theory
is developed for an atmosphere
in which h varies linearly with r . equations
are derived which show how
perigee distance and orbital period vary
with eccentricity, and how
eccentricity varies with time . expressions
are also obtained for the
life-time and air density at perigee in terms
of the rate of change of orbital
period . the results are also presented
graphically .
the results are formulated in two
ways . the first is to specify the
extra terms to be added to the constant-h
equations of part i . the second
the best constant value of h for
use with the equations of part i . for
example, it is found that the
constant-h equations connecting perigee
distance (or orbital period) and
eccentricity can be used unchanged without
loss in accuracy, if h is taken
as the value of the variable h at a height
above the mean perigee height
during the time interval being considered,
where, and
decreases from to 0 as e decreases
from 0.02 to 0 . similarly the
constant-h equations for air density at
perigee can still be used if h is
evaluated at a height above perigee,
where, and
decreases to zero as e decreases from
constant-h equations can still be used
if h is evaluated at the scale height
below the initial height . variation of
h with altitude has a small effect
on the lifetime - about 3 - and on the
e-versus-time curve .
.I 549
.T
experimental study of the velocity and temperature
distribution in a high-velocity vortex-type flow .
.A
hartnett,j.p. and eckert,e.r.g.
.B
asme trans. 70, 1957.
.W
experimental study of the velocity and temperature
distribution in a high-velocity vortex-type flow .
the vortex tube represents a simple device in which a
particular type of vortex motion may be studied in the
laboratory in an attempt to obtain a better understanding
of such flows . such an investigation has been pursued in
the heat transfer laboratory of the university of
minnesota . the present paper summarizes the major results of
this vortex-tube investigation .
.I 550
.T
laminar heat transfer in tubes under slip-flow conditions .
.A
sparrow,e.m. and lin,s.h.
.B
asme paper 61-wa-165.
.W
laminar heat transfer in tubes under slip-flow conditions .
the effects of low-density phenomena on the
fully developed heat-transfer characteristics
for laminar flow in tubes has been studied
analytically . consideration is given to the
slip-flow regime wherein the major rarefaction
effects are manifested as velocity and
temperature jumps at the tube wall . the
analysis is carried out for both uniform wall
temperature and uniform wall heat flux .
in both cases, the slip-flow nusselt numbers
are lower than those for continuum flow
and decrease with increasing mean free path .
extension of the results is made to include
the effects of shear work at the wall,
temperature jump modifications for a moving fluid,
and thermal creep .
.I 551
.T
analysis of a loaded cantilever plate by finite difference
methods .
.A
livesley,r.k. and birchall,p.c.
.B
rae tn. ms26, 1956.
.W
analysis of a loaded cantilever plate by finite difference
methods .
the various difference patterns necessary for finite difference
solution of rectangular plate problems, with various boundary conditions
and under various transverse loads, are developed . the solution of
one particular problem on deuce is also described .
.I 552
.T
chemical kinetics of high temperature air .
.A
wray,k.l.
.B
hypersonic flow research, p 181, academic press, new york, 1962.
.W
chemical kinetics of high temperature air .
when a hypersonic object enters earth's atmosphere, a shock
wave is formed in front of it, and the air passing through this
shock wave is heated to high temperatures . the shock heated
molecules equilibrate their translational and rotational
degrees of freedom within a distance of a few mean free paths .
to achieve equilibrium, it is necessary to excite vibration,
dissociate molecules, produce new molecules and produce ions
and electrons . the problem is complex, since all these
phenomena occur simultaneously and because the reaction rates depend
on the temperature, density and composition which are changing
during the relaxation toward equilibrium .
the experimental techniques used to investigate these
reactions are briefly discussed along with the resulting rate
expressions obtained by the various investigators . a compilation
of the rate expressions for these reactions representing the
author's evaluation of all the available data is presented .
several pertinent problems which are not yet completely
understood and which still require theoretical and experimental
investigation are outlined . computed concentration, temperature
and density time histories are shown for three different shock
speeds in air . the time rate of change of concentration for
each chemical reaction is also shown and regimes of importance
for the various processes are discussed .
.I 553
.T
ablation of glassy materials around blunt bodies of
revolution .
.A
hidalgo,h.
.B
ars j. 30, 1960.
.W
ablation of glassy materials around blunt bodies of
revolution .
the steady-state equations of motion for a
thin layer of an incompressible glassy material on the
surface of an ablating and radiating blunt
body are reduced to a first-order ordinary differential
equation which is integrated numerically .
this solution is coupled with the solution of the air
boundary layer for both laminar and turbulent
heat transfer with or without mass vaporization of
the ablating material . the distribution of the
effective energy of ablation around the body is thus
obtained for a cone cylinder with a hemispherical
cap that re-enters the atmosphere at hypersonic
flight speeds, and has quartz as the ablating
material . it is found that the ablation process from
turbulent heating is more efficient than from
the laminar case because of increased vaporization .
this solution of the equations of motion at the
stagnation point has been verified by are wind tunnel
experiments . the present state of development
of the are wind tunnel does not permit its use for
experimental investigations of ablation around
blunt bodies under turbulent heating .
.I 554
.T
generalized heat transfer formulas and graphs .
.A
detra,r.w. and kidalgo,h.
.B
ars j. 1961.
.W
generalized heat transfer formulas and graphs .
utilizing the research results of previously
reported investigations of the laminar, turbulent and
radiative heat transfer in dissociated air, some
generalized formulas for calculating heat transfer
are given . graphs for determining the laminar
heat transfer, momentum thickness reynolds
number, and turbulent heat transfer distributions
around an axisymmetric body are also given .
these heat transfer correlations are valid for velocities
between 6000 and 26,000 fps and for altitudes
up to 250,000 ft . this range of velocities and
altitudes covers the important re-entry regime of
practical re-entry trajectories having interest today .
in the last section of this report these
generalized results are specialized for icbm nose cone re-entry
applications . these formulas and graphs
may be found useful for making rapid engineering
estimates and preliminary design evaluations
of the heating problems associated with re-entry
into earth's atmosphere .
.I 555
.T
closing reply to comments on generalized heat transfer
formulas and graphs for nose cone re-entry into the
atmosphere .
.A
hidalgo,h.
.B
ars j. 1962.
.W
closing reply to comments on generalized heat transfer
formulas and graphs for nose cone re-entry into the
atmosphere .
in a recent paper (1), detra and hidalgo have shown
that, when the boundary layer is turbulent, the heat
flux per unit area at the sonic point of a nose cone may exceed
the corresponding laminar heat flux per unit area at the
stagnation point . the ratio of turbulent sonic-point to
laminar stagnation-point heat flux per unit area has been
estimated (2) to vary from about 1.0 to 10 for a hemispherical
nose as the reynolds number (based on nose diameter)
increases from 10 to 10 . since for an axisymmetric body
the surface area in the vicinity of the sonic point greatly
exceeds the area in the vicinity of the stagnation point, the
ratio of turbulent to laminar heat fluxes to the entire body
will be much greater than the above quoted ratios of heat
fluxes per unit area .
.I 556
.T
numerical comparison between exact and approximate
theories of hypersonic inviscid flow past slender blunt
nosed bodies .
.A
feldman,s.
.B
ars j. 30, 1960.
.W
numerical comparison between exact and approximate
theories of hypersonic inviscid flow past slender blunt
nosed bodies .
this paper presents numerical results of
exact calculations of the inviscid equilibrium flow about
a long hemisphere-cylinder in motion
at hypersonic velocity . a comparison is made with blast
wave as well as free layer theories of hypersonic
flow . as a result of the comparison, it is concluded
that the second-order blast wave theory can
be used for the purpose of finding the shock shape and
the body pressure distribution . however,
this procedure is definitely empirical and cannot be
justified on rational or theoretical grounds .
we show that the presently calculated radial distribution
of energy is radically different than that
given by blast wave theory . if body shapes other than
those considered here are of interest, the
only reliable approach at the present time is to carry out
numerical calculations . it was found
that for certain flight velocities the pressure on the body
does not decay to free stream pressure
monotonically but overexpands .
.I 557
.T
a numerical comparison between exact and approximate
theories of hypersonic inviscid flow past slender blunt
nosed bodies .
.A
cheng,k.h. and chang,a.l.
.B
ars j. 31, 1961.
.W
a numerical comparison between exact and approximate
theories of hypersonic inviscid flow past slender blunt
nosed bodies .
this note refers to paper of same title by feldman in ars j. 30,
validity of blast wave theory cannot be justified on rational or
theoretical grounds because of different values of energy in cross
flow field as calculated by this theory and by method of
characteristics . present note questions this conclusion, shows reasonably
good agreement when energy is calculated for points where shock
location, streamline pattern, and velocity, temperature, and
pressure profiles are adequately defined, and still better agreement
when energy is calculated from flow quantities provided by-
characteristics method . results are checked using data from
independent source . conclusion is reached that blast wave theory is
still valid .
.I 558
.T
experimental measurements of turbulent transition motion,
statistics and gross radial growth behind hypervelocity object.
.A
slattery,r.e. and clay,w.g.
.B
.W
experimental measurements of turbulent transition motion,
statistics and gross radial growth behind hypervelocity object.
the laminar-turbulent transition behind 0.500-in.-diameter
spheres at 8500 ft sec and behind
measured as a function of pressure . schlieren
motion-picture techniques were used to analyze the
turbulent motion and the results are described .
autocorrelation functions of the density fluctuations
of the turbulence have been measured . from
these values has been calculated and the results
are given for several positions in the turbulent
trail at 30 mm hg downstream air pressure . in addition
the authors' previous measurements of the
gross radial growth of the turbulent wake have been
extended to pressures of 10 mm hg for the case
of 0.500-in.-diameter spheres and to the trail behind
.I 559
.T
heat transfer at the forward stagnation point of blunt
bodies .
.A
reshotko,e. and cohen,c.b.
.B
naca tn.3513, 1955.
.W
heat transfer at the forward stagnation point of blunt
bodies .
relations are presented for the calculation of heat transfer at
the forward stagnation point of both two-dimensional and axially
symmetric blunt bodies . the relations for the heat transfer, which were
obtained from exact solutions to the equations of the laminar boundary
layer, are presented in terms of the local velocity gradient at the
stagnation point . these exact solutions include effects of variation
of fluid properties, prandtl number, and transpiration cooling .
examples illustrating the calculation procedure are also included .
.I 560
.T
a theoretical study of the effect of upstream
transpiration-cooling on the heat transfer and skin friction characteristics
of a compressible laminar boundary layer .
.A
rubesin,m.w. and inouye,m.
.B
naca tn.3969, 1957.
.W
a theoretical study of the effect of upstream
transpiration-cooling on the heat transfer and skin friction characteristics
of a compressible laminar boundary layer .
an analysis is presented which predicts
the skin-friction and
heat-transfer characteristics of a compressible,
laminar boundary layer on a
solid flat plate preceded by a porous
section that is transpiration cooled .
the analysis is restricted to a prandtl
number of unity and linear
variation of viscosity with temperature .
the local skin friction has been
found to have a low value in the
region of transpiration cooling and then
to increase until it approaches
the value for a completely nonporous surface
asymptotically . the initial
increase in local skin friction is rapid
as half of the ultimate increase
occurs in a distance beyond the porous
region that is about 20 percent of
the length of the porous region for all rates
of injection . when the
total coolant flow rate is kept constant
and the porous length is varied,
it is found that the average skin friction
on a partially porous plate is
slightly lower than that on a fully porous plate .
the local heat transfer behaves in
a manner similar to that of the
local skin friction . it is found, in
an example, that the temperature
at the end of a partially porous plate
could be maintained at about the
same temperature as a fully porous plate
by doubling the total rate of
coolant flow .
.I 561
.T
a geometric problem related to the optimum distribution
of lift on a planar wing in supersonic flow .
.A
graham,e.w.
.B
j. ae. scs. 1958, 771.
.W
a geometric problem related to the optimum distribution
of lift on a planar wing in supersonic flow .
the problem studied may be regarded as a problem of
geometry . its simplest form (loosely stated) is then as follows .. a
mountain rises up from the x-y plane . determine the exact
shape of the mountain knowing only the cross-sectional area of
every possible cut which can be made through the mountain with
a vertical plane . in a more complicated version of the problem,
the given information might be restricted to the cross-sectional
area of every cut which can be made by a vertical plane inclined
less than 45 to the y-axis .
this latter case has direct applications to certain minimum
drag problems in supersonic flow . the shape of the mountain
corresponds to the (unknown) shape of the optimum lift
distribution on a planar wing . the cross-sectional area of a cut is
the integrated value of the lift along a straight line crossing the
wing plan form . for a restricted range of line inclinations, these
optimum integrated lift values can sometimes be determined
directly . here it is assumed that they are given .
the problem in its simplest form was originally solved by
radon, who found solutions for a large class of such problems .
the derivation presented here may perhaps be more readily
understood .
.I 562
.T
concerning the effect of compressibility on laminar
boundary layers and their separation .
.A
howarth,l.
.B
proc. roy. soc. a, 194, 1948.
.W
concerning the effect of compressibility on laminar
boundary layers and their separation .
the theory of compressible flow in a laminar
boundary layer has been developed for the
case when the viscosity is assumed to be
proportional to the absolute temperature and the
prandtl number is unity . (these assumptions
may be compared with the empirical relations
suggested by cope .)
it is shown that a transformation of the ordinate
normal to the layer can lead to a simplified
form of equation of motion very similar to the
ordinary incompressible equation but modified
by a multiplicative factor g in the pressure
term . this factor is greater than unity at the
boundary and tends to one at the outside of
the layer .
several particular solutions are considered
including accelerated flow with a linearly
increasing velocity and retarded flow along a
flat plate with a linearly decreasing velocity .
the general implications of the theory are
discussed and qualitative conclusions are drawn
when the mainstream velocity starts from
a stagnation point, rises to a maximum and
subsequently falls . it is concluded that for
such a velocity distribution increasing
compressibility will reduce the skin friction, increase
the boundary layer thickness and cause
earlier separation as compared with the incompressible
flow with the same mainstream velocity
distribution and the kinematic viscosity corresponding
to conditions at the stagnation point .
.I 563
.T
the law of the wake in the turbulent boundary layer .
.A
coles,d.
.B
j. fluid mech. 1, 1956,191.
.W
the law of the wake in the turbulent boundary layer .
after an extensive survey of mean-velocity profile measurements
in various two-dimensional incompressible turbulent
boundary-layer flows, it is proposed to represent the profile by a linear
combination of two universal functions . one is the well-known
law of the wall . the other, called the law of the wake, is
characterized by the profile at a point of separation or reattachment .
these functions are considered to be established empirically, by
a study of the mean-velocity profile, without reference to any
hypothetical mechanism of turbulence . using the resulting
complete analytic representation for the mean-velocity field,
the shearing-stress field for several flows is computed from the
boundary-layer equations and compared with experimental data .
the development of a turbulent boundary layer is ultimately
interpreted in terms of an equivalent wake profile, which supposedly
represents the large-eddy structure and is a consequence of the
constraint provided by inertia . this equivalent wake profile is
modified by the presence of a wall, at which a further constraint is
provided by viscosity . the wall constraint, although it penetrates
the entire boundary layer, is manifested chiefly in the sublayer flow
and in the logarithmic profile near the wall .
finally, it is suggested that yawed or three-dimensional flows
may be usefully represented by the same two universal functions,
considered as vector rather than scalar quantities . if the wall
component is defined to be in the direction of the surface shearing
stress, then the wake component, at least in the few cases studied,
is found to be very nearly parallel to the gradient of the pressure .
.I 564
.T
local heat transfer and recovery temperature on a yawed
cylinder at a mach number of 4. 15 and high reynolds
numbers .
.A
beckwith,i.e. and gallagher,j.j.
.B
nasa memo 2-27-59l, 1959.
.W
local heat transfer and recovery temperature on a yawed
cylinder at a mach number of 4. 15 and high reynolds
numbers .
local heat transfer, equilibrium temperatures,
and wall static pressures have been measured on a
circular cylinder at yaw angles of 0, 10, 20, 40,
and 60 . the reynolds number range of the tests
was from 1x10 to 4x10 based on cylinder
diameter .
increasing the yaw angle from 0 to 40 increased
the stagnation-line heat-transfer coefficients by 100
to 180 percent . a further increase in yaw angle to
heat-transfer coefficients .
at zero yaw angle the boundary layer over the
entire front half of the cylinder was laminar but at
yaw angles of 40 and 60 it was evidently completely
turbulent, including the stagnation line, as
determined by comparison of local heat-transfer coefficients
with theoretical predictions . the level of heating
rates and the nature of the chordwise distribution
of heat transfer indicated that a flow mechanism
different from the conventional transitional boundary
layer may have existed at the intermediate yaw angles
of 10 and 20 . at all yaw angles the peak
heat-transfer coefficient occurred at the stagnation line
and the chordwise distribution of heat-transfer
coefficient decreased monotonically from this peak .
the average heat-transfer coefficients over the
front half of the cylinder are in agreement with
previous data for a comparable reynolds number
range .
the theoretical heat-transfer distributions for
both laminar and turbulent boundary layers are
calculated directly from simple quadrature formulas
derived in the present report .
.I 565
.T
similar solutions for the compressible boundary layer
on a yawed cylinder with transpiration cooling .
.A
beckwith,i.e.
.B
naca tn.4345, 1958.
.W
similar solutions for the compressible boundary layer
on a yawed cylinder with transpiration cooling .
heat-transfer and skin-friction
parameters obtained from exact
numerical solutions to the laminar
compressible-boundary-layer equations
for the infinite cylinder in yaw are
presented . the chordwise flow in
the transformed plane is of the
falkner-skan type . solutions are given
for chordwise stagnation flow with
both a porous and a nonporous wall .
the effect of a linear
viscosity-temperature relation is compared with
the effect of the sutherland
viscosity-temperature relation at the
stagnation line of the cylinder for a
prandtl number of 0.7 . the effects of
pressure gradient, mach number, yaw
angle, and wall temperature are
investigated for a linear viscosity-temperature
relation and a prandtl number
of 1.0 with a nonporous wall .
the results indicate that compressibility
effects become important
at large mach numbers and yaw angles,
with larger percentage effects on
the skin friction than on the heat
transfer . the use of the two different
viscosity relations gives about the
same results except when large changes
in temperature occur across the boundary
layer, as for a highly cooled
wall . the present solutions predict that
a larger amount of coolant would
be required at a given large mach number
and yaw angle than would be
predicted from solutions of the corresponding
incompressible-boundary-layer
equations .
.I 566
.T
investigation of local heat transfer and pressure drag
characteristics of a yawed circular cylinder at supersonic
speeds .
.A
goodwin,g., creager,m.o. and winkler,e.l.
.B
naca rm.a55h31, 1956.
.W
investigation of local heat transfer and pressure drag
characteristics of a yawed circular cylinder at supersonic
speeds .
local heat-transfer coefficients,
temperature recovery factors, and
pressure distributions were measured
on a circular cylinder at a nominal
mach number of 3.9 over a range of
free-stream reynolds numbers from
from 0 to 44 .
it was found that yawing the
cylinder reduced the local heat-transfer
coefficients, the average heat-transfer
coefficients, and the pressure
drag coefficients over the front side
of the cylinder . for example, at
is reduced by 34 percent and the
pressure drag by 60 percent . the
amount of reduction may be predicted by
a theory presented herein . local
temperature recovery factors were also
reduced by yaw, but the amount of
reduction is small compared to the
reduction in heat-transfer coefficients .
a comparison of these data with
other data obtained under widely
different conditions of body and stream
temperature, mach number, and
reynolds number indicates that these
factors have little effect upon the
dropoff of heat transfer due to yaw .
.I 567
.T
aerodynamic characteristics of a circular cylinder
at mach number of 6. 86 and angles of attack up to
90 .
.A
penland,j.a.
.B
naca tn.3861, 1957.
.W
aerodynamic characteristics of a circular cylinder
at mach number of 6. 86 and angles of attack up to
90 .
pressure-distribution and force
tests of a circular cylinder have
been made in the langley 11-inch
hypersonic tunnel at a mach number of
based on diameter, and angles of
attack up to 90 . the results are
compared with the hypersonic
approximation of grimminger, williams, and
young and with a simple modification
of the newtonian flow theory . the
comparison of experimental results
shows that either theory gives adequate
general aerodynamic
characteristics but that the modified newtonian
theory gives a more accurate
prediction of the pressure distribution .
the calculated crossflow drag
coefficients plotted as a function
of crossflow mach number were found
to be in reasonable agreement with
similar results obtained from other
investigations at lower supersonic
mach numbers . comparison of the
results of this investigation with
data obtained at a lower mach number
indicates that the drag coefficient
of a cylinder normal to the flow is
relatively constant for mach numbers
above about 4 .
.I 568
.T
shock wave effects on the laminar skin friction of
an insulated flat plate at hypersonic speeds .
.A
li,t.y. and nagamatsu,h.t.
.B
j. ae. scs. 20, 1953, 345.
.W
shock wave effects on the laminar skin friction of
an insulated flat plate at hypersonic speeds .
an approximate theory on the phenomena of interaction
between the shock wave and the laminar boundary layer on an
insulated flat plate at hypersonic speeds has been formulated .
results on the rate of growth of the boundary-layer thickness and
the rate of decay of the shock-wave strength have been found
that hold for . a new set of formulas
for the average skin-friction coefficient, over an insulated
flat plate at hypersonic speeds has been obtained . calculations
on the basis of the new formulas yield the data shown in figs.
steady decrease in as increases, the present results indicate
that may increase with at hypersonic mach
numbers .
.I 569
.T
an experimental investigation of leading edge shock wave boundary layer
interaction at mach 5.8 .
.A
kendall, j. m.
.B
j. aero. sc. v. 24, pp 47-56, 1957 .
.W
an experimental investigation of leading edge shock wave boundary layer
interaction at mach 5.8 .
the boundary layer on a slender body tends to be very thick at
hypersonic speeds . it interacts with the external flow by producing larger
flow deflections near the leading edge than those due to the body alone
flow around the boundary layer gives rise to an induced pressure with a
negative gradient which thins the boundary layer and increases the skin
friction with respect to the zero pressure gradient value .
experiments on a flat plate with a sharp leading edge have been
performed in the galcit 5-dash by 5-dash in. mach 5.8 hypersonic wind
tunnel . the induced pressure was measured by means of orifices in the
plate surface . profiles of mach number, velocity, mass flow, pressure,
and momentum deficiency were calculated from impact pressure surveys
normal to the plate surface made at various distances from the leading
edge .
the results are as follows . /1/ the induced pressures are 25 per cent
higher than the weak interaction theory . /2/ the boundary layer and the
external flow are distinctly separate for as low as 6,000 . /3/ the
shock wave location is in good agreement with that predicted by the
friedrichs theory for a body shape equivalent to the observed
boundary-layer displacement thickness . /4/ expansion waves reflected from the
shock are weak . /5/ the average skin-friction coefficient tends toward
and nearly matches the zero pressure gradient value downstream, but
increases to approximately twice that value as the leading edge is
approached .
.I 570
.T
on the boundary layer equations in hypersonic flow
and their approximate solutions .
.A
lees,l.
.B
j. ae. scs. 20, 1953, 143.
.W
on the boundary layer equations in hypersonic flow
and their approximate solutions .
analytical solutions of the prandtl boundary-layer equations are
obtained for the problem of the /strong/ interaction between the
leading-edge shock and the viscous layer over a flat plate at hypersonic
velocities . as the mach number increases and the interaction region
spreads downstream over the plate, the local skin-friction coefficient
increases rapidly over its conventional value . the local heat-transfer
coefficient at first remains practically unaffected but then also begins
to increase with mach number .
.I 571
.T
heat transfer to flat plate in high temperature rarefied
ultra-high mach number flow .
.A
nagamatsu,h.t., weil,h.a. and sheet,r.e.
.B
ars j. 32, 1962, 533.
.W
heat transfer to flat plate in high temperature rarefied
ultra-high mach number flow .
an investigation was conducted in a hypersonic
shock tunnel to determine the local heat transfer
rates for a sharp leading edge flat plate . the free
stream mach number range was 7.95 to 25.1 with
stagnation temperatures of approximately 2550
and 6500 r . for these temperature and mach
number conditions, the strong interaction parameter,
varied from 2.35 to 826 . the
corresponding knudsen numbers, based on the
ratio of the free stream mean free path and the
leading edge thickness, varied from 0.38 to 85.5 .
for free stream mach numbers greater than 10,
knudsen numbers of approximately unity, and
perfect gas conditions, the calculated heat transfer
coefficients were found to vary as as predicted
by the noninsulated flat plate theory of li
and nagamatsu . for the case of,
the leading edge slip phenomenon
drastically reduced the local heat transfer coefficients
as compared to the theoretical values predicted
with no slip at the surface . for the extreme case of and,
the measured local
heat transfer rate was an order of magnitude
less than the analytical value . both the knudsen
number and the free stream mach number are
important physical parameters that determine the
extent of the slip-flow region .
.I 572
.T
boundary layer displacement and leading edge bluntness effects in high
temperature hypersonic flow .
.A
cheng, h.k., hall,j.g., golian, t.c. and hertzberg, a.
.B
j. aero. sc. v. 28, pp 353-381, 410. 1961 .
.W
boundary layer displacement and leading edge bluntness effects in high
temperature hypersonic flow .
two important features of hypersonic flow over slender or thin bodies
are the displacement effect of the boundary layer and the large
down-stream influence of leading-edge bluntness . the present paper
contributes new theoretical and experimental results on this problem .
the interaction of the two effects is treated theoretically by extending
the basic shock-layer concept . in the outer inviscid flow, a model
consisting of a detached shock layer and an entropy layer is introduced
to account for bluntness . in the boundary layer, the approximate
solution is found to be governed by a local flat-plate similarity . under
the assumption of a strong bow shock and a specific heat ratio close to
unity, a theory is developed for an arbitrary thin body . for flat-plate
afterbodies, the theory yields a solution agreeing with blast-wave
theory at one limit and strong-interaction theory at the other . within
the framework of the present theory, the problems involving angle of
attack are also analyzed . complementary to the above study, a
hypersonic similitude involving strong shocks, but not requiring close to one
a natural comparison with experimental data correlated on the basis of
this similitude .
flat-plate experiments in air, conducted in the c.a.l. 11 x 15-dashin.
hypersonic shock tunnel under cold-wall conditions, included measurement
of surface heat-transfer distributions and schlieren studies for zero
and nonzero angle of attack . steady laminar heat-transfer rates were
measured by means of thin-film resistance thermometers at air test-flow
mach numbers around 12, free-stream reynolds numbers from 1.4 x 10 to 1.
for most of the experiments, airflow stagnation temperatures ranged from
ratios of about 0.15 . the range of test conditions at this stagnation
temperature encompassed the limiting cases of dominant bluntness and
dominant viscous-interaction effects . heat-transfer distributions were
also measured on a sharp plate for air stagnation temperatures ranging
from 2,000degreek up to 4,000degreek .
the experimental data are quite well correlated in terms of the
foregoing theoretical similitude variables characterizing combined effects
of boundary-layer displacement and bluntness . the correlations obtained
suggest that for the present experimental conditions, at least, the
hypersonic viscous similitude is valid even with leading-edge bluntness
in the paper, is generally fair .
.I 573
.T
viscous hypersonic similitude .
.A
hayer,w.d. and probstein,r.f.
.B
j. ae. scs. 26, 1959, 815.
.W
viscous hypersonic similitude .
an extension of classical hypersonic similitude is developed
which takes into account the interaction effect of the
displacement thickness of the boundary layer . a basic result of this
viscous similitude is that the total drag including frictional drag
obeys the classical similarity law for the pressure drag .
additional similarity conditions governing viscous effects must be
imposed in this similitude .
underlying the similitude is a new hypersonic boundary-layer
independence principle . according to this principle, the
principal part of a hypersonic boundary layer with given pressure
and wall temperature distributions and free-stream total
enthalpy is independent of the (high) external mach number
distribution outside the boundary layer .
various features of viscous hypersonic similitudes are
discussed . it is found, for example, that it applies to three-
dimensional boundary-layer interaction effects on flat bodies, provided
the concepts of strip theory may be applied, and provided the
aspect ratio is an invariant .
.I 574
.T
inviscid flow with nonequilibrium molecular dissociation for pressure
distributions encountered in hypersonic flight .
.A
bloom, m.g. and steiger, m.h.
.B
j. aero. sc. v. 27, pp 821-835, 1960 .
.W
inviscid flow with nonequilibrium molecular dissociation for pressure
distributions encountered in hypersonic flight .
one-dimensional inviscid nonequilibrium flows of a two-component model
gas are studied for prescribed pressure variations and an average
reaction rate based on recent data for oxygen recombination . these flows
are interpreted in relation to the flow along streamlines around blunt
hypersonic bodies . assuming equilibrium conditions in the subsonic
region, it is estimated that the flow in the initial supersonic
expansion region, which is approximately of prandtl-meyer character, will be
chemically frozen with respect to the molecular dissociation of the
primary components under the hypersonic, high-altitude flight conditions
considered . the flight conditions consist of flight velocities between
furthermore, on bodies of small surface inclination beyond the nose, the
flow will continue to be effectively frozen for at least 20 ft
down-stream of the nose . these conclusions may lead to the simplification of
procedures for theoretical calculation and testing .
the problem of distinguishing a dimensionless length-reaction rate
parameter, which characterizes the extent of departures from equilibrium or
from frozen behavior in the flow fields of interest here, is discussed
.I 575
.T
atomic recombination in a hypersonic wind tunnel nozzle .
.A
bray, k.n.c.
.B
j. fluid mech. v.6 part 1, 1-32. july, 1959 .
.W
atomic recombination in a hypersonic wind tunnel nozzle .
the flow of an ideal dissociating gas through a nearly conical nozzle is
considered . the equations of one-dimensional motion are solved
numerically assuming a simple rate equation together with a number of
different values for the rate constant . these calculations suggest that
deviations from chemical equilibrium will occur in the nozzle if the
rate constant lies within a very wide range of values, and that, once
such a deviation has begun, the gas will very rapidly 'freeze' . the
dissociation fraction will then remain almost constant if the flow is
expanded further, or even if it passes through a constant area section .
an approximate method of solution, making use of this property of
sudden 'freezing' of the flow, has been developed and applied to the
problem of estimating the deviations from equilibrium under a wide range of
conditions . if all the assumptions made in this paper are accepted,
then lack of chemical equilibrium may be expected in the working
sections of hypersonic wind tunnels and shock tubes . the shape of an
optimum nozzle is derived in order to minimize this departure from
equilibrium .
it is shown that, while the test section conditions are greatly affected
by 'freezing', the flow behind a normal shock wave is only changed
slightly . the heat transfer rate and drag of a blunt body are estimated
to be reduced by only about 25 per cent even if complete freezing
occurs . however, the shock wave shape is shown to be rather more
sensitive to departures from equilibrium .
.I 576
.T
viscous and inviscid stagnation flow in a dissociated hypervelocity free
stream .
.A
inger, g.r.
.B
proc. 1962. heat transfer and fluid mech. inst .
.W
viscous and inviscid stagnation flow in a dissociated hypervelocity free
stream .
high reynolds number hypersonic stagnation flow over a blunt-nosed body
in a nonequilibrium dissociated free stream is analyzed and compared to
a similar flow in an initially undissociated ambient gas . free stream
dissociation effects on various equilibrium stagnation flow properties
in air are presented as a function of the ambient atom mass fraction and
dissociation energy for velocities ranging from 15,000 to 25,000 fps .
significant changes in the bow shock geometry, stagnation gas state, and
boundary layer behavior are found when the free stream dissociation
involves more than 10( of the total energy . it is observed that for
large amounts of both atomic oxygen and nitrogen ahead of the body, the
equilibrium shock layer properties converge toward those pertaining to
chemically and vibrationally-frozen flow across the bow shock .
moreover, under certain conditions, the ionization level can be increased by
an order of magnitude and the usual reduction in frozen boundary layer
heat transfer due to a highly-cooled noncatalytic surface can increase
from stall of adjacent stages .
the effects of compromises of stage matching to favor part-speed
operation were also considered . this phase of the study indicated that
such compromises would severely reduce the complete-compressor-stall
margin . furthermore, the low-speed stage stall problem is transferred
from the inlet stages to the middle stages, which are more susceptible
to abrupt-stall characteristics .
the analysis indicates that inlet stages having continuous performance
characteristics at their stall points are desirable with respect to
part-speed compressor performance . these characteristics must, however,
be obtained when the stages are operating in the flow environment of
the multistage compressor . alleviation of part-speed operational
problems may also be obtained by improvement in either stage flow range or
stage loading margin .
the results of this analysis are only qualitative . the trends obtained,
however, are in agreement with those obtained from experimental studies
of high-pressure-ratio multistage axial-flow compressors, and the
results are valuable in developing an understanding of the off-design
problem . in addition to these stage-matching studies, a general
discussion of variable-geometry features such as air bleed and adjustable
gas model . numerical solutions of non-equilibrium airflows with fully
coupled chemistry provide a preliminary verification of such scaling for
benser, w.a.
.W
limit characteristics . the analysis indicated that all these problems
could be attributed to discontinuities in the performance
characteristics of the front stages . such discontinuities can be due to the type
of stage stall or to a deterioration of stage performance resulting
blades is included .
.I 577
.T
on hypersonic similitude .
.A
hayes,w.d.
.B
q. app. math. 5, 1947, 105.
.W
on hypersonic similitude .
tsien in a recent paper (j. math. phys. mass. inst. tech.
sonic flows around slender bodies and has pointed out that
the product of mach number and fineness ratio is a basic
similarity parameter . the author enlarges on this notion,
indicating that the problem of hypersonic flow about a
slender body in three dimensions is the same as that of a
certain two-dimensional nonsteady flow (with time replacing
the lengthwise spatial coordinate) characterized by
essentially the same similarity parameter .
.I 578
.T
dissociation scaling for nonequilibrium blunt nose flows .
.A
gibson, w.e.
.B
ars journal. vol. 32pp. 285-287. 1962 .
.W
dissociation scaling for nonequilibrium blunt nose flows .
stage-stacking study . the principal problems considered were poor
low-speed efficiency, multiple-valued performance characteristics at
intermediate speeds, and poor intermediate-speed compressor surge or
stall-naca rm e56b03b, 1956 . chapter xiii
.W
compressor operation with one or more blade rows stalled .
an analysis of the part-speed operating problems of high-pressure-ratio
air .
.I 579
.T
further developments of new methods in heat flow analysis .
.A
biot,m.a.
.B
j.ae.scs.26, 1959.
.W
further developments of new methods in heat flow analysis .
lagrangian methods in heat-flow problems and transport
phenomena were introduced by the writer in some previous work .
the present paper develops further one particular aspect of the
method,--i.e., the elimination of /ignorable coordinates ./ this
is accomplished by a special choice of generalized coordinates,
each of which is constituted by an arbitrary temperature
distribution and an /associated flow field ./ the latter is a vector
field which is derived from the corresponding scalar field by a
variational method . the procedure is valid for a certain class of
nonlinear problems, provided we replace the temperature by the heat
content as the unknown . it is shown that for normal coordinates
derivation of the associated flow field is immediate . the use
of normal coordinates and their associated flow fields is
illustrated by an example . introduction of dirac functions and
associated flow fields yields a procedure which constitutes a
generalization of the classical formulation by green's functions
and integral equations . this is illustrated by application to
one-dimensional problems of heating of a homogeneous or composite
slab and directly verified by classical methods in the appendix .
.I 580
.T
new thermo-mechanical reciprocity relations with application
to thermal stress analysis .
.A
biot,m.a.
.B
j. ae. scs. 26, 1959.
.W
new thermo-mechanical reciprocity relations with application
to thermal stress analysis .
based on the variational formulation of linear
thermodynamics as developed previously by the writer, thermomechanical
reciprocity relations are discussed which lead to new methods of
analysis of thermal stresses . these reciprocity relations are quite
different from the usual ones derived from the analogy of thermal
loading with a combination of surface and body-force distribution .
the results are applicable to stationary and transient
temperatures in elastic and viscoelastic structures . the methods are
entirely variational and do not require the evaluation of the
temperature field . the stresses at one point are expressed
directly in terms of any arbitrary distribution temperatures applied
externally, including the effect of surface heat-transfer layer .
the concepts and procedures are illustrated on a simple
example . the relation is pointed out between the reciprocity
property and the generalization of castigliano's principle to
thermomechanics .
.I 581
.T
approximate formulas for thermal-stress analysis .
.A
d. j. johns
.B
lecturer, the college of aeronautics, cranfield, england
.W
approximate formulas for thermal-stress analysis .
the basis of any thermal-stress analysis is the determination of the
temperature distributions in the structure . for arbitrary flight
histories, the determination of such distributions is rather tedious
and not completely general . this latter fact handicaps optimization
studies in the project design stage when it is desirable to be able to
express the thermal-stress distributions in a general manner .
in this note, general expressions are derived for the thermal-stress
distributions in a typical i-section using similar assumptions to
those of biot .
.I 582
.T
the melting of finite slabs .
.A
goodman,t.r. and shea,j.j.
.B
j. app. mech. 27, 1960, 16.
.W
the melting of finite slabs .
an approximate method, known as the
heat-balance integral, is used to determine the
melting rate of a finite slab which is initially
at a uniform temperature below the melting
point . the slab is acted upon by a
constant heat input at one face and has its other
face either insulated or kept at its initial
temperature . the first three terms of series
solutions in an intrinsically small parameter
are obtained for the time histories of
melting and the temperature distribution in the slab .
.I 583
.T
influence coefficients for real gases .
.A
mario william cardullo
.B
u.s. naval air rocket test station, lake denmark, dover, n.j.
.W
influence coefficients for real gases .
in the analysis of one-dimensional fluid-flow problems, it is often
assumed that the behavior of the medium is that of a perfect gas .
this assumption is justified, provided the pressure and temperature
range of interest is small and near atmospheric . at higher pressures
and temperatures various deviations are introduced thereby causing
deviations from the results obtained by using the ideal fluid-flow
equations .
in this note, influence coefficients, similar to those developed by
shapiro, are presented for the case of real gases . this analysis is
based upon the use of various functions of the compressibility factor
emmons . some of the assumptions made were as follows.. (1) the flow
is one-dimensional and steady, (2) changes in the stream properties
are continuous, and (3) the flow is comprised of imperfect gases
.I 584
.T
conduction of heat in a solid with a power law of heat
transfer at its surface .
.A
jaeger,j.c.
.B
proc. cam.phil. s. 46, 1950, 634.
.W
conduction of heat in a solid with a power law of heat
transfer at its surface .
the nonlinear boundary value problem, where
and m are constants, is solved formally by first
introducing power series in t for the unknown temperature
and flux at the surface and then determining the coefficients
in those series . in this manner the temperature function is
determined as a series of repeated integrals of error
functions . the convergence is rapid only for small values of t .
the special cases and generalizations of
the condition at the surface for which the same method
applies, are noted . surface temperatures are also found by
methods of difference equations, where t is not limited to
small values . graphs of these temperatures corresponding
to various laws of heat transfer at the surface are shown .
.I 585
.T
nonlinear heat transfer problem .
.A
chambre,p.l.
.B
j. app. phys. 30, 1959, 1683.
.W
nonlinear heat transfer problem .
a study has been made of the time-dependent heat
conduction in a semi-infinite medium subject to a
boundary condition which can involve the temperature
in a nonlinear manner . a formulation for the
determination of the surface temperature, which is often
of greatest physical interest, leads to a nonlinear
volterra integral equation . a simple iterative solution
method, with an accuracy suitable for many practical
purposes is presented . as an example, the problem
of the time-dependent surface temperature of a body
receiving heat according to the stefan-boltzmann law
is treated . the analysis is also applicable to physical
adsorption or chemisorption processes which occur at
the boundary .
.I 586
.T
an approximate treatment of unsteady heat conduction
in semi-infinite solids with variable thermal properties .
.A
yang,k.t. and szewczyk,a.
.B
j. heat trans. asme trans. 81, 1959, 251.
.W
an approximate treatment of unsteady heat conduction
in semi-infinite solids with variable thermal properties .
this very short paper presents an approximate procedure for the
calculation of unsteady heat conduction in semi-infinite solids
with variable thermal properties . it is claimed to be an
improvement over previous efforts in this area since it yields physically
sensible results for cases where thermal properties have a large
dependence on temperature . instead of using polynomials to
represent an unsteady temperature profile an exponential form is used .
good agreement is shown for several cases where the method of
the paper is compared with exact solutions .
.I 587
.T
variational analysis of ablation .
.A
m. a. biot and h. daughaday
.B
consultant and principal research engineer, respectively, cornell
aeronautical laboratory, inc., buffalo 21, n.y.
.W
variational analysis of ablation .
the variational and lagrangian thermodynamics developed in earlier
publications are directly applicable to problems of heat conduction
with melting boundaries . these techniques are used here in treating
the problem of a half-space subjected to a constant rate of heat input
at the melting surface (fig. 1) .
the applicability of the lagrangian equations to this case follows
from the fact that the basic variational principle is valid whether the
boundaries are fixed or move as arbitrary functions of time . this
can be seen if we remember that the equations govern only the
instantaneous configuration of the flow rates for a given geometry and
temperature field .
.I 588
.T
compressor operation with one or more blade rows stalled .
.A
.B
naca rm e56b03b, 1956 . chapter xiii
.W
compressor operation with one or more blade rows stalled .
an analysis of the part-speed operating problems of high-pressure-ratio
ratio multistage axial-flow compressors was made by means of a
simplified stage-stacking study . the principal problems considered
were poor low-speed efficiency, multiple-valued performance
characteristics at intermediate speeds, and poor intermediate-speed compressor
surge or stall-limit characteristics . the analysis indicated that all
these problems could be attributed to discontinuities in the performance
characteristics of the front stages . such discontinuities can be due
to the type of stage stall or to a deterioration of stage performance
resulting from stall of adjacent stages .
the effects of compromises of stage matching to favor part-speed
operation were also considered . this phase of the study indicated that such
compromises would severly reduce the complete-compressor-stall margin .
furthermore, the low-speed stage stall problem is transferred from the
inlet stages to the middle stages, which are more susceptible to
abrupt-stall characteristics .
the analysis indicates that inlet stages having continuous performance
characteristics at their stall points are desirable with respect to
part-speed compressor performance . these characteristics must, however,
be obtained when the stages are operating in the flow environment of the
multistage compressor . alleviation of part-speed operation problems may
also be obtained by improvement in either stage flow range or stage-
loading margin .
the results of this analysis are only qualitative . the trends
obtained, however, are in agreement with those obtained from experimental
studies of high-pressure-ratio multistage axial-flow compressors, and
the results are valuable in developing an understanding of the
off-design problem . in addition to these stage-matching studies, a general
discussion of variable-geometry features such as air bleed and
adjustable blades is included .
.I 589
.T
some stall and surge phenomena in axial flow compressors .
.A
.B
.W
some stall and surge phenomena in axial flow compressors .
observations of rotating stall have shown that a wide variety
of stall patterns is possible .
hot-wire anemometer data on a multistage compressor have
shown a progressive-type stall at low speeds . the amplitude
of the flow fluctuations increases in magnitude through the first
few stages and then diminishes rapidly to a small value in the
latter stages . a stage-stacking analysis has shown that rotating
stall will exist over a large portion of the compressor map at low
speeds but will be instigated almost simultaneously with
compressor surge at high speeds .
blades failures attributable to resonant vibrations excited by
rotating stall have been experienced in single and multistage
compressors .
in the stage-stacking analysis no deterioration of stage
performance due to unsteady flow resulting from stall of adjacent stages
was considered . in general, the pressure drop at the stall point
is believed to be much larger than indicated by an analytical
formulation of compressor performance . compressor surge is
attributed to a limit cycle operation about the compressor stall
point, and, as indicated in a few compressor tests and in
jet-engine tests, a small compressor discharge receiver volume may
result simply in stall of the compressor without the cyclic
characteristics of compressor surge . in this event, engine operation
will be limited because of the large drop in performance which
accompanies compressor stall .
.I 590
.T
effects of stage characteristics and matching on axial flow compressor
performance .
.A
stone, a.
.B
trans. asme, v. 80, p. 1273, 1958 .
.W
effects of stage characteristics and matching on axial flow compressor
performance .
the use of stage characteristics obtained from test data in the
performance analysis and development of an axial-flow compressor is described
relative stage matching as shown by an idealized example and also by
test experience . factors governing major performance parameters are
discussed and certain development problems and possible solutions are
reviewed .
.I 591
.T
an approximate equation for the /choke line/ of a compressor .
.A
csanady, g.t.
.B
j. aero. sc. p. 637, august 1960 .
.W
an approximate equation for the /choke line/ of a compressor .
discussion of a similarity between the pressure-ratio versus
inlet-mass-flow-coefficient characteristic of a stream or gas turbine and the
analogous characteristic of an expansion /laval/ nozzle . this idea is
extended to a compressor and a compression nozzle, and an approximate
expression for the /choke line/ of the compressor is developed .
.I 592
.T
design of axial compressors .
.A
howell, a.r.
.B
proc. i mech. e. v. 153, 1945 .
.W
design of axial compressors .
the main types of axial compressors are described, and the use of
generalized design curves to make performance estimates is advocated . the
different variables are weight, power, pressure ratio, temperature rise,
mass flow, rotational speed, stage efficiency, blade bending stresses
due to aerodynamic loading, and methods and materials of construction .
air outlets, flow coefficients and different blade forms are also
considered .
.I 593
.T
theoretical considerations of flutter at high mach
number .
.A
morgan,h.g., runyam,h.l. and huckell,v.
.B
j. ae. scs. 25, 1958.
.W
theoretical considerations of flutter at high mach
number .
some of the theories for two-dimensional oscillatory air forces
which may be applied in flutter calculations at high mach
numbers are discussed . these include linear theory, van dyke's
second-order theory, piston theory, landahl's method,
tangent-wedge and tangent-cone approximations, newtonian theory, and
a new nonlinear-pressure method . a comparison of the theories
is made by showing the results of flutter calculations for mach
numbers up to 10, and the possibility of flutter at these higher
mach numbers is pointed out .
results of flutter calculations are shown to illustrate the
various effects arising from a nonlinear thickness theory . the
possibility of large flutter speed thickness effects which depend on
frequency ratio is shown . the influence of airfoil shape is discussed
and flutter speed trends with center of gravity and elastic axis
locations are presented . some possible refinements of piston
theory are discussed for use at very high mach numbers . these
include the use of local flow conditions and the use of newtonian
theory over the leading edge of a blunt-nosed airfoil .
.I 594
.T
wind tunnel techniques for the measurements of oscillatory
derivatives .
.A
bratt, j.b.
.B
arc 22, 146, 1960
.W
wind tunnel techniques for the measurements of oscillatory
derivatives .
this paper discusses the basic principles employed in techniques for the
measurement of oscillatory derivatives in wind tunnels, and gives some
account of the associated instrumentation . the suitability of the
various techniques for different test conditions is also discussed and
brief reference is made to wind tunnel effects on the measurements .
.I 595
.T
the equilibrium piston technique for gun tunnel operation .
.A
east,r.a. and pennelegion,l.
.B
arc 22, 852, 1961.
.W
the equilibrium piston technique for gun tunnel operation .
a modified technique for the operation of a gun tunnel is
suggested based on experimental results . if the piston mass and the
initial barrel pressure are chosen correctly, then the peak pressures
associated with the gun tunnel may be eliminated . under these
conditions the piston is brought to rest with no overswing . some
measurements of the piston motion using a microwave technique are
reported which confirm this idea .
the wave diagram associated with this mode of operation is
shown, and some calculations of the stagnation pressure are given which
show that during the suggested running time, the stagnation pressure
may be considerably greater than the driving pressure if the driving
chamber cross-sectional area is large compared with that of the driven
section . for a uniform shock tube the stagnation pressure will always
be less than the driving pressure . the use of air, helium and
hydrogen as driving gases has been considered .
experiments in a gun tunnel are reported which show that the
equilibrium piston technique enables steady stagnation pressures to be
achieved over a time of approximately 15 ms using air as the driving
gas . the expansion caused by the piston acceleration is shown to
interact with the stationary piston, but this is found to produce only a
small drop in stagnation pressure .
.I 596
.T
the properties of crossed flexure pivots, and the influence of the
point at which the strips cross .
.A
wittrick, w.h.
.B
aero. quart. v. 2, 1950-1 .
.W
the properties of crossed flexure pivots, and the influence of the
point at which the strips cross .
it is shown that the rotational stiffness of a crossed flexure pivot
varies considerably when subjected to an applied force . the type of
variation can be radically changed simply by moving the point at which
the strips cross . the relation between torque and rotation for a given
applied force is not exactly linear and the extent of the non-linearity
is determined by taking into account the small movements of the centre
of rotation of the pivot . finally, for design purposes, an analysis of
the maximum stresses in the strips is given .
.I 597
.T
measurements of pitching moment derivatives for blunt-nose aerofoils
oscillating in two-dimensional supersonic flow .
.A
pugh, p.g. and woodgate, l.
.B
arc. 23, 012, 1961 .
.W
measurements of pitching moment derivatives for blunt-nose aerofoils
oscillating in two-dimensional supersonic flow .
direct pitching moment derivatives have been measured using the method
of scruton, woodgate et al for two single wedge blunt-nosed aerofoils .
these measurements were made at mach numbers of 1.75 and 2.47 and
frequency parameters less than 0.02 . in general, nose blunting was found
to have little effect on the derivatives although changes were observed
for the thinner wedge at a mach number of 1.75 .
.I 598
.T
new test techniques for a hypervelocity wind tunnel .
.A
stalmach, c.j. and cooksey, j.m.
.B
aerospace engineering. vol. 21. march 1962 .
.W
new test techniques for a hypervelocity wind tunnel .
the measurement of rocket exhaust effects on vehicle stability and the
measurement of aerodynamic damping were made in an arc-discharge type of
hypervelocity wind tunnel . sample data are given to indicate the
quality of data obtainable in this tunnel, and samples of self-luminous
and shadowgraph photographs are also presented .
.I 599
.T
aerodynamic forces, moments and stability derivatives
for slender bodies of general cross section .
.A
sacks,a.h.
.B
naca tn.3283, 1954.
.W
aerodynamic forces, moments and stability derivatives
for slender bodies of general cross section .
the problem of determining the total
forces, moments, and stability
derivatives for a slender body performing
slow maneuvers in a compressible
fluid is treated within the assumptions
of slender-body theory . general
expressions for the total forces (except
drag) and moments are developed
in terms of the geometry and motions of
the airplane, and formulas for
the stability derivatives are derived in
terms of the mapping functions
of the cross sections .
all components of the motion are
treated simultaneously and second
derivatives as well as first are obtained,
with respect to both the
motion components and their time rates of
change . coupling of the
longitudinal and lateral motions is thus
automatically included . a number of
general relationships among the various
stability derivatives are found
which are independent of the configuration,
so that, at most, only 35
of a total of 325 first and second
derivatives need be calculated
directly . calculations of stability
derivatives are carried out for two
triangular wings with camber and thickness,
one with a blunt trailing
edge, and for two wing-body combinations, one having a plane wing and
vertical fin .
the influence on the stability
derivatives of the squared terms in
the pressure relation is demonstrated,
and the apparent mass concept as
applied to slender-body theory is discussed
at some length in the light
of the present analysis . it is shown that
the stability derivatives can
be calculated by apparent mass although the
general expressions for the
total forces and moments involve additional terms .
.I 600
.T
the calculation of lateral stability derivatives of
slender wings at incidence including fin effectiveness,
and correlation with experiment .
.A
ross,a.j.
.B
rae r.aero.2647, 1961.
.W
the calculation of lateral stability derivatives of
slender wings at incidence including fin effectiveness,
and correlation with experiment .
comparisons are made between
low-speed experimental results and
estimates based on attached-flow
theory for the lateral stability
derivatives of slender wings at
incidence, and it is found that the flow
separation has little effect on
the sideslip derivatives . the reduction
in due to part-span anhedral
is evaluated, and a semi-empirical formula
is derived to account for important
second-order terms . for the rotary
derivatives, an attempt is made
to estimate the effect of the leading edge
vortices, but no satisfactory
conclusions have been reached .
the fin contributions to
the derivatives are evaluated on the basis
of treating the wing surface as
a total reflection plate . good agreement
with experiment is reached for
the sideslip derivatives, and for the
damping-in-yaw at moderate incidences .
sidewash is found to have a large
effect on the rolling derivatives,
and further information on the strength
and position of the leading edge
vortices in non-symmetric flow is required
before a complete calculation of
the sidewash can be given .
.I 601
.T
calculation of the flow past slender delta wings with
leading edge separation .
.A
mangler,k.w. and smith,j.
.B
rae r. aero.2593, 1957.
.W
calculation of the flow past slender delta wings with
leading edge separation .
the flow past a slender delta
wing with a sharp leading edge, at
incidence, usually separates along
this edge, i.e. a vortex layer extends
from the edge and rolls up to form
a /core/ (a region of high vorticity) .
a potential flow model of this is
constructed in which the layer is
replaced by a vortex sheet which
is rolled up into a spiral in the region
of the /core/ . this problem
is reduced to a two-dimensional one by
assuming a conical field and using
slender wing theory . the shape and strength
of the sheet are determined by
the two conditions that it is a stream
surface and sustains no pressure
difference . use is made of results
previously obtained for the core
region and the remaining finite part of
the sheet is dealt with by choosing
certain functions for its shape and
strength . the parameters in these
functions are found by satisfying the
two conditions stated above at
isolated points . results are obtained for
the pressure distribution, chord
loading and norman force coefficient as
functions of the ratio of the
incidence to the apex angle . the lift for a
given incidence is about 15
below that found by brown and michael . flow
patterns are indicated in two
typical cases . the effect of separation on
the drag due to lift of a wing
with small thickness is discussed .
.I 602
.T
the 7 x 7 in . hypersonic wind tunnel at rae farnborough,
part 1, design, instrumentation and flow visualization
techniques .
.A
crabtree,l.f. and crane,j.
.B
rae tn.aero.2716.
.W
the 7 x 7 in . hypersonic wind tunnel at rae farnborough,
part 1, design, instrumentation and flow visualization
techniques .
this is the first of three parts of
the calibration report on the r.a.e.
some details of the design and lay-out
of the plant are given, together
with the calculated performance figures,
and the major components of the
facility are briefly described .
the instrumentation provided for
the wind-tunnel is described in some
detail, including the optical and other
methods of flow visualization used
in the tunnel .
later parts will describe the
calibration of the flow in the
working-section, including temperature measurements .
a discussion of the heater
performance will also be included as
well as the results of tests to determine
starting and running pressure ratios,
blockage effects, model starting loads,
and humidity of the air flow .
.I 603
.T
the 7 in. x 7 in. hypersonic wind tunnel at r.a.e. farnborough
part ii. heater performance .
.A
j. f. w. crane
.B
.W
the 7 in. x 7 in. hypersonic wind tunnel at r.a.e. farnborough
part ii. heater performance .
tests on the storage heater, which is cylindrical in form and mounted
horizontally, show that its performance is adequate for operation
at m=6.8 and probably adequate for flows at m=8.2 with the existing
nozzles . in its present state, the maximum design temperature of 680
degrees centigrade for operation at m=9 cannot be realised in the tunnel
because of heat loss to the outlet attachments of the heater and
quick-acting valve which form, in effect, a large heat sink . because of this
heat loss there is rather poor response of stagnation temperature
in the working section at the start of a run . it is hoped to cure this
by preheating the heater outlet cone and the quick-acting valve .
at pressures greater than about 100 p.s.i.g. free convection through the
fibrous thermal insulation surrounding the heated core causes the top
of the heater shell to become somewhat hotter than the bottom, which
results in /hogging/ distortion of the shell . this free convection
cools the heater core and a vertical temperature gradient is set up
across it after only a few minutes at high pressure .
modifications to be incorporated in the heater to improve its
performance are described .
.I 604
.T
the 7 in. x 7 in. hypersonic wind tunnel at r.a.e., farnborough
part iii - calibration of the flow in the working section .
.A
j. f. w. crane
.B
.W
the 7 in. x 7 in. hypersonic wind tunnel at r.a.e., farnborough
part iii - calibration of the flow in the working section .
the fused silica nozzle to give m=7 in the 7 in. x 7 in. hypersonic
wind tunnel produces a flow field with an average mach number of 6.85
along the centreline of the working section . the mach number gradually
decreases towards the boundary layer, and over a core of approximately
mach number .
the nozzle heats up during a run but this has little effect on the
mach number distribution . at one station the mach number was one-third
per cent greater for a run of 1 minute than for a run of 10 seconds .
the temperature field in the inviscid flow has an average variation of
in temperature with time throughout a run .
.I 605
.T
pressure measurements on a cone-cylinder-flare configuration at small
incidences for m 6.8 .
.A
woodley, j.g.
.B
r.a.e. tn. aero. 2739 .
.W
pressure measurements on a cone-cylinder-flare configuration at small
incidences for m 6.8 .
pressure measurements were made on a slender cone-cylinder-flare
configuration, slightly blunted at the nose, for 0, 3 and 6 degrees
incidence at a free-stream mach number of 6.8 .
it was found that the surface pressures obtained on the cone agreed with
extrapolations to m equals 6.8 of theoretical values given in m.i.t.
tables /kopal/for yawed cones, and that impact theory gave a good
indication of the pressure level to be expected on all parts of the body
where surface incidence was sufficiently large to merit its use .
the semi-angles of the conical and flared parts of the model were both
the pressure level on the flare rose in all cases to approximately that
developed upstream on the cone surface .
no evidence of a marked over-expansion to pressures below the
free-stream value was noticed at the junction between cone and cylinder .
.I 606
.T
formulae and approximations for aerodynamic heating rates in high speed
flight .
.A
monaghan, r.j.
.B
rae. tn. aero. 2407 .
.W
formulae and approximations for aerodynamic heating rates in high speed
flight .
this note gives formulae and approximations suitable for making
preliminary estimates of aerodynamic heating rates in high speed flight .
the formulae are based on the /intermediate enthalpy/ approximation
which has given good agreement with theoretical and experimental
evidence . in the general flight case they could be used in conjunction with
an analogue computer or a step-by-step method of integration to
predict the variations of heat flow and skin temperature with time .
in the restricted case of flight at constant altitude and mach number,
simple analytical methods and results are given which include the
effects of radiation and can be applied to /thick/ as well as /thin/ skins
where h is the aerodynamic heat transfer factor, and g, d and k are the
heat capacity, thickness and thermal conductivity of the skin . if 0.1
the skin is approximately /thin/, i.e. temperature gradients across its
thickness may be neglected .
.I 607
.T
duct flow in magnetohydrodynamics .
.A
chang,c.c. and lundgen,t.s.
.B
z.angew. math.phys., 12 100-114, 1961.
.W
duct flow in magnetohydrodynamics .
this paper is an extension of the work of hartmann (2) and shercliff
transverse magnetic fields -- the simplest class of magnetohydrodynamic
problems . we are concerned here mainly with the boundary value
problems associated with flow in ducts with conducting walls .
.I 608
.T
aerodynamic noise in supersonic wind tunnels .
.A
laufer, j.
.B
j. aero. sc. v. 28, sept. 1961 .
.W
aerodynamic noise in supersonic wind tunnels .
hot-wire measurements in the free stream of a supersonic wind tunnel
were made in the mach number range of 1.6 to 5.0 . it is shown that the
mass-flow fluctuations increase very rapidly with increasing mach
number . if the fluctuation field is assumed to consist of sound waves-dash
an assumption that is consistent with the measurements-dashthe sound
intensity is approximately proportional to m, within the range of the
experiments . furthermore, the orientation of the field is found to be
different from the mach line direction,. it corresponds to a
sound-source velocity of approximately one-half the free-stream velocity for
the higher mach numbers . it is shown that the turbulent boundary layer
along the nozzle and the tunnel walls is responsible for this sound
field .
.I 609
.T
on three dimensional bodies of delta planform which
can support plane attached shock waves .
.A
peckman,d.h.
.B
rae tn. aero.2812.
.W
on three dimensional bodies of delta planform which
can support plane attached shock waves .
this note collects together in one report available theoretical work
on bodies which can support attached plane shock waves, discusses some
of the possible merits of such shapes, and includes some calculations
illustrating their properties . also, some preliminary results from
wind tunnel tests are given, together with details of proposed future
tests .
.I 610
.T
corner interference effects .
.A
gersten,k.
.B
agard r.299, 1959.
.W
corner interference effects .
the three-dimensional incompressible flow of fluid along the corner of
two semi-infinite plates intersecting at right angles, especially the
interference of the boundary layers of the two plates, is discussed .
mainly, the more important case of turbulent boundary layer is treated
by means of experimental studies carried out at the technical university
of braunschweig . some theoretical results for laminar flow are also
taken into account .
in order to describe the interference effects in the boundary layer,
an interference displacement thickness and an interference skin friction
have been introduced . it is shown from experiments and also from
theoretical considerations how these two quantities depend on reynolds
number . furthermore, the influence of interference on the transition
from laminar to turbulent flow is investigated . in addition, some
preliminary results are given about the effect of the pressure gradient
on the interference effects .
.I 611
.T
an approximate solution of the compressible laminar
boundary layer on a flat plate .
.A
monaghan,r.j.
.B
rae tn. aero.2025.
.W
an approximate solution of the compressible laminar
boundary layer on a flat plate .
following a major assumption that enthalpy and velocity are dependent
only on local conditions, an enthalpy-velocity relation
is obtained for the laminar boundary layer on a flat plate where
subscripts p refer to the plate, 1 to the free stream and e to the
equilibrium temperature condition at the plate . when compared with
general results, this relation (exact for prandtl number o = 1)
gives a close approximation to crocco's numerical results for o = 0.725
and 1.25, up to .
using the above relation in conjunction with the approximate
viscosity-temperature relation suggested by chapman and rubesin, and
with young's suggested first approximation for shearing stress it is
shown that close approximations to displacement thickness and velocity
distribution are given by and where and which serves to define c .
these have the advantage of being algebraic in form whereas previous
results have involved complex numerical integrations for individual
cases .
.I 612
.T
pressure distributions and flow patterns at m=4 . on
some delta wings of inverted 'v' cross section .
.A
squire,l.c.
.B
rae tn.aero.2838, 1962.
.W
pressure distributions and flow patterns at m=4 . on
some delta wings of inverted 'v' cross section .
wind tunnel tests have been made
to measure pressure distributions
and to study flow patterns on a series
of delta wings of inverted 'v'
cross-section . each of these wings
was designed to have a plane shock
wave in the plane of the leading edges
at a chosen mach number and incidence .
it was found that for a wide
incidence range about the design point
the shock wave remained virtually
attached to the leading edges and at
each incidence the pressure was
approximately constant over the lower
surface .
.I 613
.T
the contraction of satellite orbits under the influence of air drag
part i . with spherically symmetrical atmosphere .
.A
king-hele, d.g., cook, g.e. and walker, d.m.c.
.B
r.a.e. tn. gw. 533. 1959 .
.W
the contraction of satellite orbits under the influence of air drag
part i . with spherically symmetrical atmosphere .
the effect of air drag on satellite orbits of small eccentricity e/0.2/
is studied analytically by a perturbation method, on the assumption that
the atmosphere is spherically symmetrical . equations are derived which
show/1/how orbital period and perigee distance vary with eccentricity
as the orbit contracts, and/2/how each of these quantities varies with
time . the equations of type/1/are nearly independent of the oblateness
of the atmosphere . in all the equations, terms of order e and higher
are usually neglected . the results are also presented graphically, in a
manner designed for practical use .
the theory is to be extended to an oblate atmosphere in part ii, and
will later be compared with observation .
.I 614
.T
the contraction of satellite orbits under the influence of air drag .
.A
part ii . with oblate atmosphere .
.B
king-hele, d.g., cook, g.e. and walker, d.m.c.
r.a.e. tn. gw. 565. 1960 .
.W
the contraction of satellite orbits under the influence of air drag .
part ii . with oblate atmosphere .
the effect of air drag on satellite orbits of small eccentricity e/0.2/
was studied in part i/technical note no.g.w.533/on the assumption that
the atmosphere was spherically symmetrical . here the theory is extended
to an atmosphere in which the surfaces of constant density are
spheroids of arbitrary small ellipticity . equations are derived which
show how perigee distance and orbital period vary with eccentricity, and
how eccentricity is related to time . expressions are also obtained
which give lifetime and air density at perigee in terms of the rate of
change of period . in most of the equations, terms of order e and higher
are neglected . the results take different forms according as the
eccentricity is greater or less than about 0.025, while circular orbits
are dealt with in a separate section . the results are also presented
graphically in a manner designed for practical application, and examples
of the theory in use are given .
the influence of atmospheric oblateness is difficult to summarize fairly
simultaneously assume their'worst'values, some of the
spherical-atmosphere results can be altered by up to 30( as a result of oblateness
and 5-10( would be a more representative figure .
.I 615
.T
the contraction of satellite orbits under the influence of air drag .
part iii . high eccentricity orbits . /0.2 e 1/ .
.A
king-hele, d.g.
.B
r.a.e. tn. space 1, 1962 .
.W
the contraction of satellite orbits under the influence of air drag .
part iii . high eccentricity orbits . /0.2 e 1/ .
the effect of air drag on satellite orbits of eccentricity e less than
between 0.2 and 1 is presented . equations are derived which show how
perigee distance and orbital period vary with eccentricity during the
satellite's life, and how eccentricity is related to time,.and formulae
are obtained for the lifetime and the air density at perigee, in terms
of the rate of change of period . the results are also presented
graphically and their implications and limitations are discussed .
.I 616
.T
determination of upper-atmosphere air density and scale height from
satellite observations .
.A
groves, g.v.
.B
proc. roy. soc. a. 252, 16-27, 1959 .
.W
determination of upper-atmosphere air density and scale height from
satellite observations .
a solution is obtained for the rate of change of semi-major axis and
perigee distance of a satellite orbit with time due to the resistance of
the atmosphere . the logarithm of air density is assumed to vary
quadratically with height, and the oblateness of the atmosphere is taken
into account .
the calculation of perigee air density in terms of the rate of change
of satellite period is dealt with,. and the method is applied to data
at present available on six different satellites . the variation of air
density with height is obtained as
in p-28.59/0.15/-h-200//46/5/0.028/0.013//h-200///46/
for h in the range of approximately 170 to 700 km, where p is in grams/c
m, h is in kilometres and standard deviations are given in brackets .
.I 617
.T
determination of upper-atmosphere air density profile from satellite
observations .
.A
groves, g.v.
.B
proc. roy. soc. a. 252, 28-34, 1959 .
.W
determination of upper-atmosphere air density profile from satellite
observations .
the theory previously developed for the changes in the perigee distance
and semi-major axis of a satellite orbit due to air drag is extended to
enable the air-density profile/i.e.its relative variation with height/to
be derived from the motion of the orbit's perigee . the solution is
first obtained in terms of the change in perigee distance and then in
terms of the change in the radius of the earth at the sub-perigee point
the scale height in the 180 and 220 km altitude regions .
.I 618
.T
orbit decay and prediction of the motion of artificial satellites .
.A
michielsen, h.f.
.B
advances in astronautical science, vol 4 plenum press 1959 . pp 255-310
.W
orbit decay and prediction of the motion of artificial satellites .
the rate of decay of elliptic satellite orbits, due to atmospheric drag,
is investigated through variation of parameters and through use of an
atmospheric model involving a power function between density and
altitude . this model is shown to fit actual conditions better than an
exponential function .
the effects of the equatorial belt and the rotation of the earth are
investigated . the conclusion is reached that through these anomalies
atmospheric drag substantially affects the orbit elements, especially
those defining the orbit plane .
an alternate approach of variation of parameters is presented, by which
a direct relation between period decay and instantaneous density
conditions is established . this approach, by itself specifically adequate
for prediction work, also opens an avenue for systematic and unified
evaluation of observed decay .
.I 619
.T
density of the upper atmosphere from analysis of satellite orbits ..
further results .
.A
king-hele, d.g.
.B
nature, v184, 1267-1270, 1959 . r.a.e. rep. gw. 25. appendix y .
.W
density of the upper atmosphere from analysis of satellite orbits ..
further results .
the method previously described has been refined by taking into account
atmospheric rotation . further results are given from satellites of
latitude and season and day-to-night changes are reported .
.I 620
.T
earth satellite observations and the upper atmosphere .
.A
priester, w., martin, h.a. and kramp, k.
.B
nature, 188, pp 200-204. 1960 .
.W
earth satellite observations and the upper atmosphere .
atmospheric densities have been derived from artificial satellites in
altitudes 200-700 km. and from rockets up to about 200 km. to
consolidate the two sets of data, h.k. kallmann suggested a model with a
exact form of this curve has now been derived . corrections for the
is excellent .
very close correlation between atmospheric density variations/h180 km./
and the solar 20-cm. radiation implies that the origin of the'solar
effect'may lie in the absorption of solar ultra-violet radiation .
the atmospheric density curve between 180 and 200 km. shows a
temperature inversion in the fl-layer . it is not yet possible to decide
whether solar ultra-violet radiation as well as the solar he line and
solar x-ray radiation contribute to the heating of the fl-layer .
diurnal and seasonal density variations at altitudes 210, 562 and 660
km. have been derived from variations in acceleration of three
satellites/sputnik 3, vanguard 1 and 2/ . group averages of diurnal
variations are taken from different dates within the period
may 15, 1958-october 1, 1959 . physcal conditions in the upper
atmosphere are briefly summarized ..the'solar effect'originates in the
fl-layer as a result of heating by the solar he line at 304 a. diurnal
density variation at 210 km. is only a few per cent . absorption of
solar electromagnetic radiation in the f2-layer, and large heat
conductivity cause intense diurnal density and temperature variations above
.I 621
.T
latitude and diurnal variations of air densities from 190 to 280 km.
as derived from the orbits of discoverer satellites .
.A
groves, g.v.
.B
proc. roy. soc. a. 263. 212-216. 1961 .
.W
latitude and diurnal variations of air densities from 190 to 280 km.
as derived from the orbits of discoverer satellites .
variations in air density between day and night in the region 190 to 280
km are found to be small/less than about 25(/ . the presence of a
possible region of local heating at about 220 km which disappears at
night . the night-time density profile conforms with a constant scale
height of 35/2/km.no definite variation of air density with latitude is
evident apart from a possible increase of about 60(, which is indicated
by rather limited polar-region data . for other latitudes and seasons a
variation of less than about 20( is indicated .
.I 622
.T
scale height in the upper atmosphere, derived from changes in satellite
orbits .
.A
king-hele, d.g. and hughes, k.m.
.B
r.a.e. tn space 4, 1962 .
.W
scale height in the upper atmosphere, derived from changes in satellite
orbits .
the'density scale height'h in the upper atmosphere is a measure of the
rate at which air density p varies with height y, being given by
h-p//dp/dy/ . the value of h, although important because/with the
molecular weight of the air/it determines the air temperature, has not
as yet been well determined at heights above 200 km .
this note develops methods for finding h from the decrease in a
satellite's perigee height and from the decrease in the orbital period
of a satellite in a small-eccentricity orbit . these methods are then
applied to all the 14 satellites found suitable for the purpose . the 44
values of h obtained, for heights of 200-450 km, represent an average
over day and night and probably have errors/s.d./of 5-10( . it is found
that, as solar activity declined between 1957 and 1961, h decreased
greatly ..e.g.at height 275 km, h decreased from 60 km in early 1958 to
height becomes much less rapid above 350 km, and are consistent with the
supposition that h had low values, near 35 km, at heights near 250 km,
for 1959-61 . the results could be greatly extended in scope and
improved in accuracy if more accurate orbits were available for
short-lifetime satellites .
.I 623
.T
on the coupling between heat and mass transfer .
.A
tewfik,o.e.
.B
j. ae. scs. 28, 1962, 1009.
.W
on the coupling between heat and mass transfer .
in mixtures of two different gases or liquids, one constituent
will migrate spontaneously toward the warmer parts, and
the other toward the colder parts . this phenomenon, known
as the soret effect, and its converse the dufour effect, were
discovered as early as 1856 and 1873 respectively . the two
effects can also be considered as a simultaneous transport of
mass and heat, or as a coupling between heat and mass transfer .
the effects of this coupling have been neglected in all
investigations of heat transfer in multicomponent flow systems so far,
on the a priori assumption that they are small . in a recent
publication however, it was shown that they can be large in
laminar-boundary-layer-type flows with helium injection .
turbulent-boundary-layer measurements and an analysis conducted
at the heat transfer laboratory clearly showed significant
effects of the coupling on heat transfer and adiabatic wall
temperature . from additional measurements, the results of which
are presented below, it is possible to separate the heat flux at the
model wall into one part depending on the temperature gradient
and a second part caused by the coupling . it is shown that
the latter exceeds the former, and hence the coupling may not
be neglected a priori without careful consideration .
.I 624
.T
cruise performance of channel-flow ground effect machines .
.A
strand,t.
.B
j. ae. scs. 29, 1962, 702.
.W
cruise performance of channel-flow ground effect machines .
the performance theory for high-speed air-cushion vehicles
operating in close proximity to the ground is developed . the
analysis is restricted to cruise flight of vehicles of rectangular
planform employing an air pressure seal between the ground and
the vehicle along the two streamwise sides . the variation of
the optimum rearward deflection angle of the side jet pressure
seal with speed for minimum overall power expenditure and
maximum range is found . it is concluded that a mixed
propulsion system (jet deflection plus propeller(s)) is required .
volume flow and the corresponding fan pressure rise needed are
also calculated . the maximum lift drag ratio is determined .
the maximum thickness ratios of the vehicles are considered
to be large compared with the ground-height vehicle-length
ratio . two-dimensional airfoil theory is employed to show that
close to stagnation conditions exist below the vehicles . the
lower-surface lift, pitching moment, and aerodynamic-center
location are determined .
the flow over the upper surface is identified with flow over
mounds . upper-surface lift coefficients are determined for
typical mound shapes .
it is shown that high total lift coefficients are theoretically
obtainable with almost zero induced drag . the conventional
induced-drag power penalty is replaced by a sealing-air power
expenditure, which is shown not to be excessive .
.I 625
.T
viscous and inviscid nonequilibrium gas flows .
.A
whalen,r.j.
.B
j. ae. scs. 29, 1962, 1222.
.W
viscous and inviscid nonequilibrium gas flows .
the condition of immediate freezing of the mass fraction of
dissociated species of air at the equilibrium value behind the
shock envelope prevails over a major portion of the flight
spectrum associated with lifting re-entry vehicles . this is observed
by means of order-of-magnitude considerations within the limits
of the present knowledge of chemical reaction rates for the
constituents of air . accordingly, investigations of the viscous and
inviscid hypersonic flow about blunt and sharp leading edge
slender bodies are made . the investigations are generalized to
consider an arbitrary degree of dissociation in the ambient free
stream . this condition is included in order to allow comparison
with the flow field about a model in the test section of a
hypersonic facility with dissociated air species present in the free
stream .
inviscid frozen flow investigations are made for blunt and
sharp leading edge slender body power-law geometries . the
results indicate that the influence of a finite leading edge, in
inducing a pressure field far downstream (/blast-wave/ analogy),
is considerably diminished for this model . this conclusion is
verified numerically by a characteristics solution for the
hypersonic flow about a /sonic-wedge/ slab .
the viscous investigations consider the boundary-layer
interaction problem with a frozen degree of dissociation . in
this case, as in the inviscid analysis, the governing parameter is
observed to be the ratio of the
dissociation energy to the free-stream kinetic energy . the
influence of this parameter on the boundary-layer interaction
mechanism for a highly cooled, noncatalytic wall is presented .
the influence of a frozen flow field on skin friction and heat
transfer is also discussed .
finally, since higher mach number gas flows may be generated
in wind tunnel nozzles where dissociation nonequilibrium effects
are present, the possibility of employing expansions with a
controlled degree of dissociation as a technique for aerodynamic
simulation is presented .
.I 626
.T
some features of supersonic and hypersonic flow about
blunted cones .
.A
traugott,s.c.
.B
j. ae. scs. 29, 1962, 389.
.W
some features of supersonic and hypersonic flow about
blunted cones .
for a family of cones of various semiapex angles blunted by
spherical caps, shock shapes and surface pressure distributions
have been obtained from both the belotserkovskii method and
experiment . these results are used to study convergence to
conical flow . conditions leading to both overexpansion and
underexpansion on the surface with respect to the asymptotic
conical pressures are described as well as conditions leading to
bow shock inflection points . conditions also exist for which a
second shock may occur, or for which the sonic line cannot touch
the body surface . the implications of these conditions for
various blunt-body methods are discussed . for cones blunted
in such a manner as to keep the flow entirely supersonic, the flow
field is found to exhibit certain similarities with that for genuine
blunting . this is related to the fact that the surface entropy
layer for blunt bodies can be most influential, in determining
surface pressure, in the interior of the flow field rather than near
the surface .
.I 627
.T
flutter analysis of circular panels .
.A
rattayya,j.v.
.B
j. ae. scs. 20, 1962, 534.
.W
flutter analysis of circular panels .
the flutter problem of flat circular panels with edges elastically
restrained against rotation has been formulated in terms of
small-deflection plate theory . the panel is subjected to uniform
all-round tension or compression in its middle plane, in addition to
the supersonic compressible flow passing over its upper surface
with still air below . linear piston theory is employed to predict
the aerodynamic load on the vibrating panel .
the problem is investigated by a rayleigh-type analysis
involving chosen modes of the panel as degrees of freedom .
in order to investigate the convergence of the solution, the
flutter-mode shape of the clamped-edge panel has been expressed
in a series form in powers of r cos o . the results of three-, four-,
and five-term approximations have displayed oscillatory
behavior with apparently rapid convergence of the solution .
.I 628
.T
thermal effects on a transpiration cooled hemisphere .
.A
gollnick,a.f.
.B
j. ae. scs. 29, 1962, 583.
.W
thermal effects on a transpiration cooled hemisphere .
an approximate method is used to obtain the
injection distribution which would exist on an isothermal,
transpiration-cooled hemisphere in a supersonic stream .
this distribution is the same for both air and helium
injection, and is independent of the blowing level . a
model having this distribution was tested in the naval
supersonic laboratory wind tunnel at a mach number
of 3.53 . it is concluded that the design technique is
reasonably accurate . data taken near the nose are
compared with the theories for air and helium
injection . the agreement in the case of the reduction in
heat-transfer coefficient is good . the values of
insulated wall temperature obtained near the nose with
helium injection are 8 percent above the local
stagnation temperature, and largely independent of injection
rate . it is believed that this phenomenon may be
attributed to the thermal diffusion of the helium within
the boundary layer . air injection causes a slight
reduction in the insulated wall temperature . it is shown
that injection of either air or helium at the hemisphere
nose considerably reduces the heat flux at the surface .
the additional reduction in heat flux resulting from
helium injection as opposed to air injection, and
predicted by existing theory, is largely absent .
.I 629
.T
second-order effects in laminar boundary layers .
.A
maslen,s.h.
.B
a.i.a.a. j. 1963, 33.
.W
second-order effects in laminar boundary layers .
second-order boundary layer disturbances are
due to the displacement of the main flow by
the boundary layer, surface curvature, freestream
vorticity, and slip . a procedure for finding
these is given for compressible flow of a perfect gas
having a classically similar boundary layer .
solutions are given for the flat plate and circular
cylinder and for the hypersonic axisymmetric
stagnation point . for the latter flow, the dominant
effect is that of vorticity, which increases
both shear and heat flux . for the plate or cylinder,
the same conclusion tends to hold for high
speed flow . the vorticity effect is governed by the
entire outer flow--not just the wall vorticity .
.I 630
.T
stagnation region in rarefied high mach number flow .
.A
cheng,h.k. and chang,a.l.
.B
a.i.a.a. j. 1963, 231.
.W
stagnation region in rarefied high mach number flow .
paper describes results of numerical solution of the viscous
shock-layer equations for axisymmetric stagnation region, using
the viscosity-temperature law with w=0.65, pr=0.71 and
y=1.25 . purpose is to establish applicability of the simple
approximation of w=1 (obtained earlier) to air at low reynolds
numbers and low ratios of wall temperature to stagnation
temperature . using a reference temperature (closely equal to
eckert's) to interpret the linear results, excellent agreement is found,
in the limit of, over a wide range of reynolds numbers,
covering fully merged shock layers as well as boundary layers
with and without vorticity interaction . agreement with recent
experiments of ferri et al is as good as to be expected from
shock-layer approximation . paper provides valuable extension of the
applicability of the reference temperature concept .
.I 631
.T
low speed wind tunnel tests on a two dimensional aerofoil
with split flap near the ground .
.A
bagley,j.a.
.B
arc cp.568, 1961.
.W
low speed wind tunnel tests on a two dimensional aerofoil
with split flap near the ground .
pressure distributions have been
measured on a 10 thick two-dimensional
aerofoil of r.a.e.101 section fitted with
split flaps deflected at 15 and 55 .
measurements were made at two distances
above a ground plate, and also without
the ground plate . the results have been
integrated to give the sectional
lift, drag and pitching-moment coefficients .
.I 632
.T
calculated lift distributions in incompressible flow
on some sweptback wings .
.A
bagley,j.a. and joyce,g.m.
.B
rae tn. aero.2836, 1962.
.W
calculated lift distributions in incompressible flow
on some sweptback wings .
in the course of a larger survey of some aerodynamic characteristics
of a family of sweptback wings, the low-speed lift distributions were
calculated . the 35 planforms considered cover a range of leading-edge
sweep angles from 55 to 70, and aspect ratios from 2 to 3.9 . the
results are given here, together with a comparison with other
calculations and with experimental results on one particular wing .
.I 633
.T
an extension of the method of generalised conical flows
for lifting wings in supersonic flow .
.A
portnoy,h.
.B
rae tn. aero.2849, 1962.
.W
an extension of the method of generalised conical flows
for lifting wings in supersonic flow .
the method of generalised conical
flows has previously been developed
subject to the condition that the
upwash divided by the streamwise
co-ordinate to the power k, where
k is the order of the conical flow, must
have vanishing (k+1)th derivative
with respect to the conical co-ordinate .
in the present note this restriction is removed .
the results are also used to
discuss the effect of the application of
the leading edge attachment condition
on the wing pressure and geometry .
.I 634
.T
effects of leading edge bluntness on flutter characteristics
of some square- planform double-wedge airfoils at a
mach number of 15 .4.
.A
goetz,r.c.
.B
nasa tn.d1487, 1962.
.W
effects of leading edge bluntness on flutter characteristics
of some square- planform double-wedge airfoils at a
mach number of 15 .4.
results are presented from a wind-tunnel
investigation in helium flow at a
mach number of 15.4 . the models were
square-planform, double-wedge, shaft-mounted
airfoils with leading- and trailing-edge
radii of 0, 1, 3, and 6 percent chord .
in general, the tests indicate that bluntness
effects on the model flutter
characteristics are stabilizing as the leading-edge
radius is increased from 0 to
destabilizing with further increase in
bluntness .
results of flutter calculations made
by using newtonian theory aerodynamics
and a combination of newtonian theory and
piston theory aerodynamics in
conjunction with an uncoupled two-mode analysis
are compared with experimental results .
the piston-theory results accurately
predicted flutter speeds for the models with
.I 635
.T
heat transfer and pressure distributions on a hemisphere-cylinder and a
bluff-afterbody model
in methane-air combustion products and in air .
.A
irving weinstein
.B
national aeronautics and space administration .
technical note d-1503
.W
heat transfer and pressure distributions on a hemisphere-cylinder and a
bluff-afterbody model
in methane-air combustion products and in air .
an experimental investigation has been made to indicate the validity of
using methane-air combustion products as the test medium for aerodynamic
heating and loading tests . tests were conducted on a
hemisphere-cylinder and on a bluff-afterbody model, both in methane-air combustion
products and in air alone, and covered a range of mach numbers from 6 to
the data showed that the nondimensional heating-rate distribution
along a hemisphere-cylinder as obtained in combustion products was in
good agreement with that obtained in air, and the results were in
reasonable agreement with theory . the stagnation-point heating rates
in air and in combustion products over the hemisphere-cylinder agreed
within 10 percent of the theoretical values . the pressure
distributions around a hemisphere-cylinder obtained from tests in combution
products were in good agreement with those obtained in air and could
be predicted by newtonian flow theory . the tests in combustion
products of a bluff-afterbody model produced nondimensional
heat-transfer coefficients which were in fair agreement with results
obtained in air .
.I 636
.T
pressure distribution induced on a flat plate at a free-stream
mach number of 1.39 by rockets exhausting upstream and downstream .
.A
abraham leiss
.B
national aeronautics and space administration
technical note d-1507
.W
pressure distribution induced on a flat plate at a free-stream
mach number of 1.39 by rockets exhausting upstream and downstream .
an experimental investigation was made of the pressures induced on
a flat plate at a free-stream mach number of 1.39 by a supersonic
rocket jet exhausting upstream and downstream . measurements of the
pressure distribution on a flat plate were made at zero angle of
attack for 11 different locations of the jet exhaust nozzle beneath
the wing . measurements were made at ratios of rocket-exit total
pressure to free-stream static pressure from 6 to 60 and at a reynolds
number per foot of approximately 10 times 10 to the power of 6 . the
rocket when exhausted upstream produced a strong shock that moved
further upstream with increasing rocket-exit total-pressure ratio .
positive incremental normal-force coefficients were obtained at all test
positions . data at 11 test positions are tabulated for rocket-on
and rocket-off pressure coefficients as well as for incremental pressure
coefficients for the 48 orifices of the flat plate for the range of
ratio of rocket-exit total pressure to free-stream static pressure
of the investigation . changing the location of the model with
respect to the plate had a negligible effect when the rocket was
varied in the chordwise direction, but the pressure coefficients
were reduced as the rocket was lowered away from the flat-plate wing .
.I 637
.T
an integral equation relating the general time-dependent lift and
downwash distributions on finite wings in subsonic flow .
.A
joseph a. drischler
.B
national aeronautics and space administration
technical note d-1521
.W
an integral equation relating the general time-dependent lift and
downwash distributions on finite wings in subsonic flow .
an integral equation for obtaining the unsteady air forces on finite
wings in subsonic compressible flow is presented . this equation
is applicable for any arbitrary time-dependent motion and can be
utilized for flexible as well as rigid wings . the approach involves
the derivation of an integral equation relating the unknown pressure
the form of the equation is such that it should lend itself readily to
modern high-speed computers for obtaining pressure distributions .
special cases of the integral equation are treated for two-dimensional
incompressible flow and are presented in an appendix .
.I 638
.T
longitudinal aerodynamic characteristics at low subsonic
speeds of a highly swept wing utilizing nose deflection
for control .
.A
spencer,b.
.B
nasa tn.d1482, 1962.
.W
longitudinal aerodynamic characteristics at low subsonic
speeds of a highly swept wing utilizing nose deflection
for control .
an investigation has been conducted
in the langley 7- by 10-foot transonic
tunnel at low subsonic speeds to determine
the longitudinal aerodynamic
characteristics associated with deflection of the
nose section of a highly swept delta
wing having an aspect ratio of 1.33 . in order
to illustrate the effectiveness of
this forward control, the longitudinal control
characteristics are also presented
for the wing with upper-and lower-surface
split flaps located at the trailing
edge .
comparison between the longitudinal
aerodynamic characteristics of the wing
utilizing the nose control and those of
the wing utilizing the upper-surface
split flap located at the trailing edge
indicated similar control effectiveness
for high control deflections (15) and
similar values of trimmed lift-drag ratio
with increasing lift coefficient . use
of the nose control, however, indicated a
lower value of trimmed angle of attack
for a given value of trimmed lift
coefficient than that realized from use of
the upper-surface split flap . further
reductions in trimmed angle of attack
for a given value of trimmed lift
coefficient may be realized from deflection
of the lower-surface split flap at the
wing trailing edge in combination with
the nose control and would be accompanied
by large reductions in lift-drag ratio .
.I 639
.T
analytical study of the tumbling motions of vehicles
entering planetary atmospheres .
.A
tobak,m.
.B
nasa tn.d1549, 1962.
.W
analytical study of the tumbling motions of vehicles
entering planetary atmospheres .
the tumbling motion of vehicles
entering planetary atmospheres is
analyzed . a differential equation
governing the tumbling motion, its
arrest, and the subsequent oscillatory
motion is obtained and identified
as the equation for the fifth painleve
transcendant . an approximate
analytical solution for the transcendant
is derived . comparisons with
results obtained from numerical
integration of the exact equations of
motion indicate that the solution for the
angle-of-attack history is
sufficiently accurate to be of practical use .
.I 640
.T
the design of structures to resist jet noise fatigue .
.A
b. l. clarkson
.B
j. royal aero. soc. 66, oct. 1962
.W
the design of structures to resist jet noise fatigue .
the design of structures to resist jet noise fatigue demands a
knowledge of a wide range of subjects from pure acoustics at one
hand to metal physics at the other . at the present time the various
aspects of the problem are not sufficiently well know
quantitatively for a purely theoretical design study to be made . never-
the-less a knowledge of the behaviour of typical forms of
construction in noise environments can be used with a limited
amount of theoretical work to indicate tne most efficient types of
structure . this approach to the problem is adopted in this
lecture as it seems to be the most promising one available at the
moment . it must be emphasized, however, that although some
progress has been made in dicsovering the behaviour of a
structure subjected to noise it is not possible to estimate the life
of any component at the drawing board stage . some prototype
strain measurements and proof testing are therefore essential if
one is to prove the integrity of the design .
within the structural limits of single skin construction set in
this lecture the main conclusion to be reached is that no
reasonable estimate of fatigue life can yet be made in the drawing
board stage of a structure . nevertheless, a study of the form of
behaviour of typical structures has led to a theoretical
simplification of the problem of skin vibration . from this it has been
possible to suggest an optimum deisgn for a skin stiffened by
stringers . a suggestion for an optimum design of skin and rib
for control surfaces to minimise stresses at the rib-skin
intersection is put forward but no experience can check this yet .
the most resonable basis for the future estimation of
fatigue life of a component appears to be the /random/ s-n
curve and consierable effort should be made to obtain the
necessary test data .
the life expectation of a new design will be uncertain and
some proof testing is essential if the integrity of structure in high
noise levels (150 db) is to be guaranteed .
.I 641
.T
reduction of the clamped plate to two membrane problems
with an application to uniformly loaded sectors .
.A
morley,l.s.d.
.B
rae r.struct.277, 1962.
.W
reduction of the clamped plate to two membrane problems
with an application to uniformly loaded sectors .
the clamped plate problem in
the classical theory for the small
deflection bending of flat plates
is reduced to the solution by variational
methods of two successive membrane
problems . the first requires the least
square minimisation of the average
curvature of the deflected surface while
the second problem concerns the
integral of the gaussian curvature . there
is a similar reduction for extensional
problems where the boundary tractions
are specified .
the method is demonstrated by
giving three distinct solutions to the
problem of the clamped sector under
a uniformly distributed load . one
solution is of special interest because
it is derived from a single membrane
problem . numerical data are given .
.I 642
.T
the buckling strength of a uniform circular cylinder
loaded in axial compression .
.A
sobey,a.j.
.B
rae r. struct,279, 1962.
.W
the buckling strength of a uniform circular cylinder
loaded in axial compression .
the theoretical estimation of the buckling strength of a cylinder
loaded in axial compression is improved by the use of a more
representative deflected form for the buckled cylinder than has
previously been used . kempner's buckling strength for dead weight
loading is reduced by 18 . the presentation of the magnitude and
distribution of the constraint system required to maintain the mode is
novel and instructive .
.I 643
.T
an investigation of wing-aileron flutter using ground
launched rocket models .
.A
gaukroger,d.r. and curran,j.k.
.B
rae tn. struct.308, 1962.
.W
an investigation of wing-aileron flutter using ground
launched rocket models .
control surface flutter of the
wing torsion-control rotation type has
been investigated for an unswept wing
with an under-massbalanced, half span,
outboard aileron . thirteen pairs of
wings were tested, using ground launched
rocket driven vehicles, and a range of
values of aileron natural frequency
was covered . the test results showed
considerable scatter, but enabled
upper and lower limits of a flutter
boundary to be determined approximately .
it was established that aileron flutter
could be eliminated on the models
tested provided the aileron frequency
exceeded the wing torsional frequency
by 20 per cent or more . in this
condition the models were also free from
single degree of freedom flutter
.I 644
.T
a study of the cantilever square plate subjected to
a uniform loading .
.A
leissa,a.w. and niedenfuhr,f.w.
.B
j. aero. sc. 29, 1962.
.W
a study of the cantilever square plate subjected to
a uniform loading .
plate problems involving free edges have been historically
difficult to solve, particularly when two free edges are adjacent,
resulting in a free corner . the cantilevered square plate
subjected to a transverse loading is one such problem for which an
exact solution has not been achieved .
in the present paper results obtained by various approximate
methods are presented for this problem for the case of a uniform
loading . solutions obtained by the authors using the technique
of point matching and the rayleigh-ritz method are compared
with previously published finite-difference and experimental
results and with bernoulli-euler beam and plane-strain approaches .
numerical results for deflections, slope components, bending and
twisting moments, and transverse distributed shears are presented
for a relatively fine gridwork of points on the plate boundary
and within the interior . the antielastic curvature is exhibited by
all methods except beam theory . all methods present the
interesting conclusion that the free edge deflection is greater when
the plate is treated as a plate rather than a beam .
.I 645
.T
thermodynamic coupling in boundary layers .
.A
baron,j.r.
.B
ars space flight rep. to the nation, 2206-61, 1961.
.W
thermodynamic coupling in boundary layers .
experimental results gathered in recent years for binary
mixture mass transfer models are shown to yield consistent
evidence of discrepancies with analytic considerations . specifically,
measured recovery temperatures are appreciably higher than those
predicted ,. while heat transfer coefficients are satisfactorily
reproduced . it is shown on the basis of both approximate and exact
solutions for plates and stagnation points that the discrepancies in
previous results are related to thermal diffusion effects, a major
influence being apparent in application of the surface boundary
condition for an adiabatic wall . as a result, some reexamination is
necessary of past criteria for mass addition effects as they pertain to
specific injected media . a prime example is the /equivalence/ of
helium and air as coolants despite the heretofore suggested preference
for low density injectants on a perfect gas basis . ref. 16 .
.I 646
.T
thermal diffusion effects on energy transfer in a turbulent
boundary layer with helium injection .
.A
tewfik,o.e., eckert,e.r.g. and shirtliffe,c.j.
.B
to be presented at the 1962 heat transfer and fluid mech.inst. seattle,
.W
thermal diffusion effects on energy transfer in a turbulent
boundary layer with helium injection .
a circular cylinder with two-inch
diameter and with a porous wall
fabricated out of woven wire material was
aligned with its axis parallel to an air
stream with approximately 100 ft sec
velocity . helium gas was injected into
the turbulent boundary layer through
the cylinder walls at a uniform rate in
the range 1.55 x 10 to 1.08 x 10
of the free stream mass velocity . the
local energy transfer along the cylinder
was measured at various values of
the wall temperature level for the
situation that the energy flows from the
cylinder to the boundary layer and
vice versa . the results showed clearly
that the wall temperature for zero
energy transfer - the adiabatic wall
temperature - was larger than the free
stream temperature by up to about 40 f,
although viscous dissipation effects
are negligible . this temperature excess
increases with increasing injection
rate and is independent of reynolds
number .
an analysis in which the laminar
sublayer is treated as couette flow
with helium injection and which includes
thermal diffusion in this layer is
formulated . the results show appreciable
thermal diffusion effects on
adiabatic wall temperature, increasing it
over its value for zero injection
by amounts of the same order of magnitude
as found by measurements . thermal
diffusion however has negligible effects
on the heat transfer coefficient .
its effects on the concentration and
temperature distribution are discussed
and are shown to produce appreciable
modifications in the latter .
.I 647
.T
bending of a uniformly loaded rectangular plate with
two adjacent edges and the others either simply supported
or free .
.A
huang,m.k. and conway,d.
.B
j.app.mech. 1952, 451.
.W
bending of a uniformly loaded rectangular plate with
two adjacent edges and the others either simply supported
or free .
the distribution of deflection and bending moment in a
uniformly loaded rectangular plate having two adjacent
edges clamped and the others either simply supported or
free, are obtained by a method of superposition .
numerical values are given for square plates and, in one case, the
results are compared with those obtained by another
method .
.I 648
.T
the approximate analysis of certain boundary value
problems .
.A
conway,h.d.
.B
j. app. mech. 1960, 275.
.W
the approximate analysis of certain boundary value
problems .
a simple method is given which is suitable
for the approximate analysis of certain
boundary-value problems, including, for
example, the small deflections of clamped
plates and the torsion of prismatic bars .
the analysis is particularly simple and lends
itself well to the use of the digital computer .
the method is applied here to four
problems, the uniformly loaded, clamped square,
and equilateral-triangle plates, and the
torsion of bars of square and hexagonal cross
section . the results agree well with
the exact solutions, where these are known .
.I 649
.T
the hovercraft - a new concept in maritime transport .
.A
crewe,p.r. and eggington,w.j.
.B
trans. roy. inst. naval arch. 1960.
.W
the hovercraft - a new concept in maritime transport .
the hovercraft is the first operational british
project in the ground-effect machine field .
although there has, for a number of years, been
a tentative searching after the principles
underlying such machines, it is only now that their
possibilities as commercial transport and
service craft are beginning to be developed .
since the hovercraft is a new vehicle, the appearance
of the saunders-roe sr-n1, a manned
experimental craft, excited considerable public attention
and there have been a number of
descriptive articles in the press . papers of a more
technical type, on ground-effect machines,
are now beginning to appear and it is to be expected
that these will rapidly increase in number,
especially since american interest in both the commercial
and defence fields is expanding fast .
the authors of the present paper have, therefore,
concentrated attention upon features
about which they had something personal to say, and
which they consider to be of particular
significance for assessing the possibility of the
hovercraft becoming important in maritime
transport . these features
are ..- the hovercraft as a fundamentally new
principle in the transport field .
the powering requirements and resistance
characteristics .
the likely operating costs of hovercraft
in comparison with other forms of maritime transport .
in addition, relatively brief descriptions of
the history and the current work being undertaken
on the ground-effect machine and of the design,
construction, and testing of the saunders-roe
sr-n1 are provided . the final section discusses
outstanding problems and some future
possibilities .
.I 650
.T
some design problems of hovercraft .
.A
stanton-jones,r.
.B
inst. aero. sc. paper 61-45, 1961.
.W
some design problems of hovercraft .
analysis of the influence various aerodynamic parameters have on
the performance of a simple peripheral jet system . power weight
ratio, lift drag ratio, and effect of jet angles and thickness are
each considered . structural requirements, optimum cushion
pressure, and dynamic stability over waves are examined and then
related to the economics of ground-effect machine operation .
.I 651
.T
heat transfer to separated and reattached subsonic
turbulen flows obtained downstream of a surface step .
.A
seban,r.a., emery,a. and levy,a.
.B
j. ae. scs. 1959, 809.
.W
heat transfer to separated and reattached subsonic
turbulen flows obtained downstream of a surface step .
local heat-transfer coefficients and recovery factors are
presented for separated and reattached turbulent flows as obtained
by a downward step in an otherwise flat surface in a two-
dimensional, subsonic, air flow . the region downstream of the step,
the focus of this investigation, contained a region of separated
flow with reattachment at about five step heights downstream,
followed by a section of reattached flow . the salient feature of
the results is the maximum in the local heat-transfer coefficient
at the reattachment point, with values thereof diminishing in the
separated region and also in the reattached region, where they
tend toward values characteristic of turbulent boundary-layer
flow . it is found that for most of the region the heat-transfer
coefficient depends on the velocity to about the 0.8 power, though
a decreased dependence may exist in the separated region .
recovery factors have the characteristically low values associated
with separated flows, and do not attain values typical of
turbulent boundary-layer flows within the downstream lengths
available .
.I 652
.T
pressure distribution on two dimensional wings near
the ground .
.A
bagley,j.a.
.B
rae r. aero.2625, 1960.
.W
pressure distribution on two dimensional wings near
the ground .
a simple method of calculating
the pressure distribution in
incompressible flow on two-dimensional aerofoils
of arbitrary section at moderate
distances from the ground is developed .
comparisons with an /exact/ potential
flow solution, and with measurements
on a 10 thick aerofoil of rae.101
section, provide a satisfactory
verification of the adequacy of the method ,.
but it is shown that it is necessary
to take account of the boundary layer
on the aerofoil in the calculations .
.I 653
.T
transient magnetohydrodynamic duct flow .
.A
lundgen,t.s., atabeck,b.h. and chang,c.c.
.B
phys. fluids 4, 1961, 1006.
.W
transient magnetohydrodynamic duct flow .
parallel flow of an electrically conducting viscous
incompressible fluid in a rectangular duct with
transverse magnetic field is considered . the walls
of the duct which are parallel and perpendicular
to the imposed magnetic field are taken to be
nonconducting and perfectly conducting, respectively .
assuming the fluid to be at rest at the initial
moment, exact solutions for the velocity and magnetic
field components are obtained in the form of
convolution integrals taking the longitudinal pressure
gradient as an arbitrary given function of time .
later, taking a step function for the pressure gradient,
these expressions are integrated . for this case,
the effect of the strength of the imposed magnetic
field on the development behavior of the flow is
studied . it is found that except for very large magnetic
fields, the flows are over damped .
.I 654
.T
on the propagation and structure of the blast wave .
part 1.
.A
sakuri,a.
.B
j. phys. soc. japan, 9, 1954.
.W
on the propagation and structure of the blast wave .
part 1.
as a continuation of part 1 (j. phys. soc. japan 8 (1953) 662), the
second approximation for the propagation and structure of a blast
wave is now discussed . the solution for r=1.4 is obtained by a
numerical method, using the results of the first approximation obtained
in part 1 . by use of this solution, u-r curves, distance-time curves
and the changing feature of distributions of velocity, pressure and
density behind the shock front are discussed .
further, the approximate solution of the equation is discussed by
a refinement of the wkb method due to imai .
.I 655
.T
effects of boundary layer displacement and leading edge bluntness on
pressure distribution, skin friction, and heat transfer of bodies at
hypersonic speeds .
.A
bertram, m.h. and henderson, a.
.B
naca tn 4301, july 1958 .
.W
effects of boundary layer displacement and leading edge bluntness on
pressure distribution, skin friction, and heat transfer of bodies at
hypersonic speeds .
results are presented of an investigation to determine the effect of
boundary-layer displacement and leading-edge bluntness on surfaces in
hypersonic flow . the presence of the boundary layer and the blunt
leading edge induce pressure gradients which in turn affect the skin
friction and heat transfer to the surface . methods for predicting these
phenomena on two-dimensional surfaces are given and a brief review of
recent three-dimensional results is presented .
.I 656
.T
departure from dissociation equilibrium in a hypersonic nozzle .
.A
bray, k.n.c.
.B
a.r.c. 19, 983, march 1958 .
.W
departure from dissociation equilibrium in a hypersonic nozzle .
the equations of motion for the flow of an ideal dissociating gas
through a nearly conical nozzle have been solved numerically, assuming
a simple equation for the rate of dissociation, and a number of
different values of the rate constant . the results of these
calculations suggest that deviations from dissociation equilibrium will
occur in the nozzle if the rate constant lies within a very wide range
of values . they also suggest that once such a deviation has begun the
gas will very rapidly/freeze/, so that the dissociation fraction will
remain almost constant if the flow is expanded further, or even if it
passes through a constant area test section . an approximate method
of solution, making use of this property of sudden/freezing/of the flow,
has been developed and applied to the problem of estimating the
deviations from equilibrium under a wide range of conditions . if all
the assumptions made in this report are accepted, then lack of
dissociation equilibrium may be expected in the working sections of
hypersonic wind tunnels and hypersonic shock tubes .
it is shown, however, that the flow behind a normal shock wave in such a
wind tunnel will not be greatly affected by any freezing that may take
place in the nozzle upstream of the shock wave . even so, the stand-off
distance of a shock wave in front of a blunt model may be quite
sensitive to deviations from equilibrium .
.I 657
.T
interferometric studies of supersonic flows about truncated
cones .
.A
giese,j.h. and bergdolt,v.e.
.B
j.app.phys. 24, 1953, 1389.
.W
interferometric studies of supersonic flows about truncated
cones .
fringe shifts on interferograms of flows at m=2.45
about variously truncated 15 (half-angle) cone
cylinders in free flight in a pressurized range have been
examined for similarity of the flow fields, occurrence of
scale effects, and convergence to conical flow . it was
found that flows over similar objects with equal tip
reynolds numbers were similar and that convergence
to conical flow occurred before the disturbance at the
tip had been reflected the second time along
characteristics to the body . density distributions have been
determined, and a number of comparisons have
been made with theoretical predictions .
.I 658
.T
review of panel flutter and effects of aerodynamic noise
part i.. panel flutter .
.A
l. e. goodman and j. v. rattayya
.B
university of minnesota, minneapolis, minnesota
.W
review of panel flutter and effects of aerodynamic noise
part i.. panel flutter .
with the development of high-speed aircraft and missiles, vibration
of panels has become a problem of practical significance . many
of the failures of the early german rockets after attaining supersonic
speed have been attributed to the development of such panel
oscillations . it appears this
phenomenon is not of much concern in the subsonic
speed range., however, in the supersonic speed range panels may develop
oscillations which cause instability of the structure . this effect has
been exhibited experimentally under controlled laboratory conditions
motion is limited and buckling may not be a serious design problem .
in these cases panel flutter is still of importance because of its
effect on the fatigue life and the allowable stresses for design of
the panel material .
the oscillations of panels may be due either to aerodynamic force
induced by the motion of the panel, or to aerodynamic noise, or
buffeting (irregular motion induced by turbulence in the flow) .
the interaction between aerodynamic forces and panel motions, usually
referred to as /panel flutter,/ has been investigated by several workers
in recent years . since the problem is too complex to be dealt with
in its entirety, simplifying assumptions have been made in these
investigations . the literature is marked by a certain degree of
controversy over the validity of these assumptions and the applicability of
the results obtained . a brief review of the literature with reference
to several of the approximations made and the results obtained follows .
.I 659
.T
nonuniform shear flow past cylinders .
.A
murray,j.d.
.B
q. j. mech. app. math. 10, 1957, 406.
.W
nonuniform shear flow past cylinders .
a general method is described whereby
an approximation of any desired degree
of accuracy to the stream functions for
two types of variable shear flows past
finite cylinders can be obtained . the two
shear distributions in the free stream can
be approximated to the linear shear
distribution and the shear present in an
unretarded incompressible boundary layer
respectively . in every case the stagnation
streamline is displaced from the position
opposite the line of symmetry of the
cylinder, and general expressions are
obtained for this displacement . the line of
symmetry may be in the direction of
or perpendicular to the direction of flow .
the two particular examples cited are
those of a general elliptic cylinder and
cylinders of the form where and being the polar
coordinates, and 2p the maximum width
of the cylinder .
.I 660
.T
the fundamental solution for small steady three dimensional
disturbances to a two dimensional parallel shear flow .
.A
lighthill,m.j.
.B
j. fluid mech. 3, 1957, 113.
.W
the fundamental solution for small steady three dimensional
disturbances to a two dimensional parallel shear flow .
after a brief review of methods of calculating the flow
fields produced by disturbances in rotational basic flows,
the author points out a fundamental difficulty in the
treated as a perturbation of the disturbance field that
would occur if the basic flow were uniform) .. slow
attenuation of the secondary-flow disturbance with distance
from the obstacle . the author conjectured (same j. 1
the trouble was caused by nonuniform validity of the
approximation sequence in the region far from the
obstacle . the analogy with /stokes' and whitehead's
paradoxes/ is mentioned, and a solution analogous to
oseen's is suggested, one in which disturbances, but not
the shear, are assumed to be small . in this paper, such a
solution is found, and is shown to overlap with the
small-shear, secondary-flow solution . the basic flow is a parallel,
steady, inviscid, two-dimensional shear flow . the /
fundamental solution/ due to a weak source is sought .
the method of fourier transforms is used . simple
solutions are found for a uniformly sheared basic flow (where
the result coincides with the secondary-flow solution) and
for an exponential basic-flow profile . in the general case
it is assumed that the parallel basic flow becomes uniform
at, where the x-axis lies in the flow direction .
the character of the solution is determined by studying
its hankel transform, especially for the class of flows
where the total variation of the basic stream speed v(y)
is small . an interpretation in terms of images, due to
m. b. glauert, is given, and finally the relationship of the
present work to theories of the displacement of the
stagnation streamline (displacement effect of pitot
tubes) is discussed .
.I 661
.T
summary of laminar boundary layer solutions for
wedge-type flow over convection and transpiration cooled
surfaces .
.A
livingood,j.n.b. and donoughe,p.
.B
naca tn.3588, 1955.
.W
summary of laminar boundary layer solutions for
wedge-type flow over convection and transpiration cooled
surfaces .
a summary of exact solutions of the
laminar-boundary-layer equations
for wedge-type flow, useful in estimating
heat transfer to such
arbitrarily shaped bodies as turbine blades,
is presented . the solutions are
determined for small mach numbers and
a prandtl number at the wall of 0.7 ,.
ranges of mainstream pressure gradients
and rates of coolant flow through
a porous wall are considered for the
following cases .. (1) small
temperature changes in the boundary layer
along a constant- and along a
variable-temperature wall, and (2) large
temperature changes in the boundary layer
along a constant-temperature wall .
dimensionless forms of heat-transfer
and friction parameters and
boundary-layer thicknesses are tabulated .
the results indicate that
coolant emission and increased stream-to-wall
temperature ratios diminished
the friction and heat transfer for a
constant wall temperature . for a
variable wall temperature with small
temperature differences in the
boundary layer, the friction was unaffected,
but the heat transfer was greatly
increased for increased wall-temperature
gradient . heat-transfer results
in the literature reveal that transpiration
cooling is much more effective
for prandtl numbers of the order of 5.0 than for 0.7 .
.I 662
.T
theoretical and experimental investigation of
aerodynamic-heating and isothermal heat transfer parameters on
a hemisphere nose with laminar boundary layer at supersonic
mach numbers .
.A
stine,h.a. and wanlass,k.
.B
naca tn.3344, 1954.
.W
theoretical and experimental investigation of
aerodynamic-heating and isothermal heat transfer parameters on
a hemisphere nose with laminar boundary layer at supersonic
mach numbers .
the effect of a strong, negative
pressure gradient upon the local
rate of heat transfer through a laminar
boundary layer on the isothermal
surface of an electrically heated,
cylindrical body of revolution with a
hemispherical nose was determined from
wind-tunnel tests at a mach number
of 1.97 . the investigation indicated
that the local heat-transfer
parameter, based on flow conditions
just outside the boundary layer,
decreased from a value of 0.65 0.10 at
the stagnation point of the
hemisphere to a value of 0.43 0.05 at the
junction with the cylindrical
afterbody . because measurements of the
static pressure distribution over
the hemisphere indicated that the local
flow pattern tended to become
stationary as the free-stream mach number
was increased to 3.8, this
distribution of heat-transfer parameter is
believed representative of all
mach numbers greater than 1.97 and of
temperatures less than that of
dissociation . the local heat-transfer
parameter was independent of reynolds
number based on body diameter in the
range from 0.6x10 to 2.3x10 .
the measured distribution of
heat-transfer parameter agreed within
theoretical distribution calculated with
foreknowledge only of the pressure
distribution about the body . this
method, applicable to any body of
revolution with an isothermal surface,
combines the mangler transformation,
stewartson transformation, and thermal
solutions to the falkner-skan wedge-flow
problem, and thus evaluates the
heat-transfer rate in axisymmetric
compressible flow in terms of the known
heat-transfer rate in an approximately
equivalent two-dimensional
incompressible flow .
measurements of recovery-temperature
distributions at mach numbers
of 1.97 and 3.04 yielded local recovery
factors having an average value
of 0.823 0.012 on the hemisphere which
increased abruptly at the shoulder
to an average value of 0.840 0.012 on
the cylindrical afterbody . this
result suggests that the usual representation
of the laminar recovery
factor as the square root of the prandtl
number is conservative in the
presence of a strong, accelerating pressure gradient .
.I 663
.T
viscous flow along a flat plate moving at high speeds .
.A
kuo,y.h.
.B
j.ae.scs. 23, 1956, 125.
.W
viscous flow along a flat plate moving at high speeds .
by the distortion of coordinates, it is shown that, in the case
of supersonic viscous flow past a flat plate, the boundary-layer
and simple wave theories can be combined to give a complete
representation of the velocity and pressure fields . consistent
first-order solutions are considered . an expression for the
induced pressure on the plate, correct to the second order, is
obtained . at high mach numbers the important parameter
satisfies the hypersonic similarity law ,. and for arbitrary mach and
reynolds numbers and for different gases, the theoretical curve
correlates closely the experimental data . asymptotic shock
curve and skin-friction coefficient are also deduced, but the
experimental verifications are yet to be made .
.I 664
.T
the boundary layer on a flat plate in a stream with
uniform shear .
.A
murray,j.d.
.B
j. fluid mech. 11, 1961, 309.
.W
the boundary layer on a flat plate in a stream with
uniform shear .
the incompressible laminar boundary layer
on a semi-infinite flat plate is
considered, when the main stream has uniform
shear . a solution is obtained for
the first two terms of an asymptotic solution
for small viscosity . it is shown that
one of the principal effects of free-stream
vorticity is to introduce a modified
pressure field outside the boundary-layer region .
.I 665
.T
on the theory of hypersonic gas flow with a power law
shock wave .
.A
sychev,v.v.
.B
j. app. math. mech. 24, 1960, 756.
.W
on the theory of hypersonic gas flow with a power law
shock wave .
plane and axisymmetric hypersonic gas flows are considered with shock
waves of very great intensity that have a power-law form . on the basis
of an investigation of the portions of the flow with high entropy
adjoining the surface of the body (not necessarily for a shock wave of the
given form) it is shown that the use in the flow problem of the exact
solution for the corresponding unsteady self-similar gas motion requires
a supplementary refinement of the thickness of the high entropy layer .
a method is shown for introducing such a correction and constructing the
shape of the body contour, on which is to be applied the pressure
distribution obtained on the basis of the theory of small disturbances .
.I 666
.T
blunt body heat transfer at hypersonic speed and low reynolds numbers .
.A
ferri, a. zakkay, v. and ting, l.
.B
j. aero. sc. v. 28. p. 862. 1961 .
.W
blunt body heat transfer at hypersonic speed and low reynolds numbers .
an analytical method for the determination of effect of shock curvature
on heat transfer in the region of the nose has been developed . it is
shown that for practical body shape the viscous terms in the
navier-stokes equations are not important in the region of the flow far from
the wall, and the displacement thickness can be neglected . then the
flow can be approximately represented by an inviscid-flow solution
having as boundary conditions the body shape, which is not affected by
the reynolds number, and by a boundary-layer type of flow near the
wall, having appropriate boundary conditions . this approach permits us
to determine the heat transfer in the region of the nose even at very
low reynolds numbers .
experimental results are presented . the experimental results agree
with the values given by the analysis .
.I 667
.T
hypersonic shock layer theory of the stagnation region at low reynolds
number .
.A
cheng, h.k.
.B
proc. 1961, heat transfer and fluid mech. inst. stanford. univ. press.
1961 . p.161
.W
hypersonic shock layer theory of the stagnation region at low reynolds
number .
cheng, h.k.
hypersonic flow at low reynolds number is studied utilizing the
shock-layer concept . the present formulation takes into account the salient
features of the transport processes within the shock layer in a manner
consistent with the shock-layer approximation . the rankine-hugoniot
shock relations are modified to include contributions due to heat
conduction and viscous effects immediately behind the shock .
the specific problem of an axisymmetric stagnation region is treated .
the flow regimes for this problem can be classified according to whether
or not the transport effects are important immediately behind the
shock . in one regime where the ordinary rankine-hugoniot relations hold
across the shock, the vorticity-interaction theory based on the
boundary-layer approximation is shown to be sufficient . in the other
regime where the rankine-hugoniot relations have to be modified but the
continuum-flow model applies, an approximate, an analytical solution is
obtained . this solution reveals a substantial reduction of the
temperature behind the shock and of the shock stand-off distance in the
presence of strong surface cooling .
the present study is intended to provide a knowledge to bridge the gap
between the free-molecule flow regime and that of the boundary layer via
the continuum theory . in this respect, the solution obtained appears
to be satisfactory in that it yields the correct free-molecule limits
for the skin friction and surface-heat transfer rate .
.I 668
.T
measurements of stagnation point heat transfer at low
reynolds number .
.A
ferri,a. and zakkay,v.
.B
j. ae. scs. 28, 1962, 847.
.W
measurements of stagnation point heat transfer at low
reynolds number .
measurements of stagnation point heat transfer are presented
in the reynolds number range between the free molecular flow
and the range where modified boundary layer theory still applies .
the measurements are compared with the analytical methods
set forth by ferri, zakkay, and ting . the results show smooth
transition between the two regions and indicate that the
predicted reynolds number for which the modified boundary layer
theory can be used is in agreement with experiments . in the
lower range of reynolds number the ratio of
decreases and reaches a value of 1 at a reynolds number of 40 .
.I 669
.T
subsonic potential flow past a sphere inside a cylindrical duct .
.A
william l. haberman
.B
david taylor model basin, carderock, md.
.W
subsonic potential flow past a sphere inside a cylindrical duct .
the subsonic potential flow of a compressible fluid past a sphere
in an infinite medium was first determined by rayleigh . subsequently,
caplan and tamada extended the solution to include the fourth power
of the mach number . to the author's knowledge, no solution for
subsonic flow past a sphere in a finite medium has been published . it
is the purpose of this note to present a solution for subsonic
potential flow past a sphere inside a circular cylindrical duct .
.I 670
.T
on blunt-body heat transfer at hypersonic speed and low reynolds
number .
.A
ferri, a. zakkay, v. and ting, l.
.B
j. aero. sc. v. 29. p. 882, 1962 .
.W
on blunt-body heat transfer at hypersonic speed and low reynolds
number .
a discussion of differences arising between experimental and analytical
results, in particular those due to inconsistencies introduced in the
presentation of data and the way the comparison is made .
.I 671
.T
pressure and boundary-layer measurements on a two dimensional wing at
low speed .
.A
brebner, g.g. and bagley, j.a.
.B
a.r.c. r + m 2886, july, 1962 .
.W
pressure and boundary-layer measurements on a two dimensional wing at
low speed .
results are given of pressure measurements and boundary-layer traverses
on a two-dimensional wing with 10 per cent rae 101 section at reynolds
numbers of 1.6x10 and 3.2x10 . these results which have been integrated
to give lift, drag and aerodynamic-centre characteristics, are used to
check some calculation methods for the growth of the turbulent boundary
layer and for the effect of a known boundary layer on the pressure
distribution .
it is concluded that the calculation of the boundary layer still needs a
little refinement before it is accurate enough to predict viscosity
effects on pressure distribution, lift, drag and aerodynamic center,.but
that these effects can be calculated if the actual boundary-layer
characteristics are known .
.I 672
.T
tunnel interference effects .
.A
pankhurst, r.c. and holder, d. w.
.B
wind tunnel techniques, chapter 8 pitman. 1952 .
.W
tunnel interference effects .
the problems of solid blockage, wake blockage, lift effect, and the
influence of boundary constraint at high mach number are considered in
detail . corrections are given for various open and closed tunnels,
rectangular, circular and octagonal, and different speeds, two and
three dimensional flows, with several aerofoils and wings . other
interferences include the wall boundary layer, gradient of static
pressure and problems with the working fluid used .
.I 673
.T
investigation of full scale split trailing edge wing
flaps with various chords and hinge locations .
.A
wallace,r.
.B
naca r.539, 1935.
.W
investigation of full scale split trailing edge wing
flaps with various chords and hinge locations .
an investigation was conducted in the n. a. c. a.
full-scale wind tunnel on a small parasol monoplane
equipped with three different split trailing-edge wing
flaps . the object of the investigation was to determine
and correlate data on the characteristics of the airplane
and flaps as affected by variation in flap chord, flap
deflection, and flap location along the wing chord . the
chords of the flaps were 10, 20, and 30 percent of the
wing chord and each flap was tested at deflections from 0
to 75 when located successively at 68, 80, and 88.8
percent of the wing chord aft of the leading edge . the
investigation included force tests, pressure-distribution
tests, and downwash surveys . the results give the lift,
the drag, and the pitching-moment characteristics of the
airplane, the flap forces and moments, the pressure
distribution over the flaps and wing at one section,
and the downwash characteristics of the flap and wing
combinations .
an increase in flap chord or distance of the flap from
the leading edge of the wing increased the lift of the
airplane but had an adverse effect on the wing pitching
moment . the ld ratio of the airplane decreased with
increase in flap deflection or flap chord . flap
normal-force coefficients were primarily a function of flap
deflection and were relatively independent of flap chord,
hinge-axis location, and airplane attitude . the location of
the flap center of pressure in percentage of flap chord aft of
the hinge axis remained practically constant
irrespective of airplane attitude and of flap deflection, chord, or
location . flap hinge-moment coefficients varied with a
power of flap chord greater than the square so that with
regard to hinge moments narrow flaps were the most
efficient in producing a given increase in lift .
split trailing-edge flaps materially affected the
magnitude and distribution of pressures over the entire wing
profile . at low angles of attack the predominant effect
of the flaps was to increase positively the lower-surface
pressures ,. at high angles of attack, to increase negatively
the upper-surface pressures . downwash surveys
indicated that horizontal tail planes located above the wing
chord line would be more effective than those below the
chord in counteracting the increased diving moment of
the airplane with flaps deflected .
.I 674
.T
the shapes and lift-dependent drags on some sweptback
wings designed for m= 1. 2.
.A
bagley,j.a. and beasley,j.a.
.B
rae r. aero.2620, 1959.
.W
the shapes and lift-dependent drags on some sweptback
wings designed for m= 1. 2.
the camber and twist distributions
needed to produce a constant
span-wise -distribution and certain linear
chordwise load distributions have
been calculated by linearised supersonic
theory at for a set of 34
thin sweptback wings . the wing planforms
cover a range of aspect ratios
from 2.0 to 3.5 and leading-edge sweep
angles from 55 to 70 . both leading
and trailing edges are subsonic at the
design mach number, and the
slenderness parameter is between 0.19 and 0.40 .
the lift-dependent vortex and wave
drags associated with these loadings
have also been calculated, and appear not
to be excessive in almost all the
cases considered .
.I 675
.T
pressure distribution and surface flow on 5( and 9( thick wings with
curved tip and 60degree sweepback .
.A
garner, h.c. and walshe, d.e.
.B
a.r.c. 20,982, r + m 3244. may 1959 .
.W
pressure distribution and surface flow on 5( and 9( thick wings with
curved tip and 60degree sweepback .
extensive tables are given of pressure coefficients measured at reynolds
numbers from 1.3x10 to 3.9x10 on two half-models of identical planform
with 5( rae 101 and 9( rae 101 streamwise sections . the planform of
aspect ratio 3.899 has a straight trailing edge with 60degree of
sweepback, constant chord over most of the span and a parabolic outer portion
of the leading edge curving to a pointed tip . the overall wing
characteristics are obtained from integrated normal pressures and are
compared with lifting-surface theory .
the low-speed experimental pressure distributions and surface oil-flow
patterns are analysed and discussed in relation to the onset of
separation and the distinct vortex flows that develop at high
incidence . series of contrasting upper-surface isobars illustrate some
features of the different stalling processes of the two wings . the
direct influence of the main vortex on local surface pressures is
assessed in general terms . a fuller appraisal of secondary surface flow
is obtained from the oil patterns, observations in water and
measurements of high suction near the trailing edge .
studies of the extent of leading-edge stall and location of part-span
vortices, in particular two simultaneous leading-edge vortices on the
thinner wing, follow from further analysis of local surface pressures .
after a detailed discussion of the effect of reynolds number and the
distinct types of separated flow, a few results with leading-edge
roughness are considered in relation to scale effect on separation and
the extensive influence of part-span roughness .
.I 676
.T
a simple method for calculating the span and chordwise loading on
straight and swept wings of any aspect ratio at subsonic speeds .
.A
kuchemann, d.
.B
r + m 2935, r.a.e. rep. aero. 2476, a.r.c. 15,633. august 1962 .
.W
a simple method for calculating the span and chordwise loading on
straight and swept wings of any aspect ratio at subsonic speeds .
the methods of the classical aerofoil theory are used to derive a
general theory for wings of any given planform . the load over the
whole surface of a given wing can be calculated at a given subcritical
mach number, and the procedure is as simple and rapid as that of the
classical aerofoil theory . the calculated results are confirmed by
experiments .
.I 677
.T
methods for calculating the lift distribution of wings /subsonic
lifting surface theory/ .
.A
.B
r + m 2884, r.a.e. rep. aero. 2353. a.r.c. 13,439. january 1950 .
.W
methods for calculating the lift distribution of wings /subsonic
lifting surface theory/ .
this report contains some fairly simple and economic methods for
calculating the load distribution on wings of any plan form based on
the conceptions of lifting surface theory . the computer work required
is only a small fraction of that of existing methods with comparable
accuracy . this is achieved by a very careful choice of the positions
of pivotal points, by plotting once for all those parts of the downwash
integral which occur frequently and by a consequent application of
approximate integration methods similar to those devised by the author
for lifting line problems .
the basis of the method is to calculate the local lift and pitching
moment at a number of chordwise sections from a set of linear equations
satisfying the downwash conditions at two pivotal points in each
section . interpolation functions of trigonometrical form are used for
spanwise integration both in setting up the downwash equations and in
getting the resultant forces on the wing from the local forces . the
preliminary chordwise integrations for the downwash are predigested in
a series of charts/figs.1-6/,.it is these which make the method a
practical computing proposition .
the theory is outlined in sections 2-5,.section 6 deals with the
solution of the linear equation and section 7 with the resultant forces
on the wing . some examples are worked out in section 8 to compare with
other methods,. one solution is given in full detail in tables 8-30 as a
guide for computers . appendices i-vi discuss more carefully some
salient points of the mathematical theory, and appendix vii is intended
to instruct the computer how to carry out the steps of the calculation .
.I 678
.T
the effect of end plates on swept wings .
.A
kuchemann,d. and kettle,d.j.
.B
rae r.aero.2429, 1952.
.W
the effect of end plates on swept wings .
existing methods of calculating
the effect of endplates on straight
wings are modified so as to apply to
swept wings . the changes in overall
lift and drag, and also the spanwise
distribution of the additional load,
can be calculated .
the theoretical results are
compared with experimental results
obtained on swept wings, including
new measurements of lift, drag and
pitching moment, made on an untapered
the method of calculation is also
extended to cover the effect of
the tip vortex which is formed on wings
without endplates .
.I 679
.T
low speed tests on 45 sweptback wings .
.A
weber,j., brebner,g.g. and kuchemann,d.
.B
rae r. aero.2374, 1958.
.W
low speed tests on 45 sweptback wings .
this report contains the results
of pressure measurements on three
and aspect ratio 5, over an
incidence range up to 10 . chordwise
and spanwise lift distributions
are given, mostly near the centre
where, on two of the wings,
modifications had been made to the section
shape . it was found that altering
the thickness distribution in the
centre did not affect the loading but
that approximately straight isobars
could be obtained at values of
below about 0.1 . by the incorporation
of twist and camber in the central
part the distortion of the lift
distribution in the centre could be
avoided at one particular incidence,
and thus the same chordwise
distribution obtained over most of the span .
twist and camber alone do not improve
the isobar pattern and
therefore a thickness modification would be
needed to give the desired
lift distribution and isobar pattern at one
particular incidence .
the results of experimental investigations
of the boundary layer
and of the effect of aspect ratio will be given
in a later report .
.I 680
.T
generalized conical flow fields in supersonic wing theory .
.A
lomax, h. and heaslett, m.a.
.B
naca tn 2497, september 1951 .
.W
generalized conical flow fields in supersonic wing theory .
linearized, compressible-flow analysis is applied to the study of
quasi-conical supersonic wing theory . single-integral equations are
derived which relate either the loading to the shape of a lifting
surface or the thickness of a symmetrical wing to the pressure
distribution for triangular wings with subsonic leading edges . the forms of
these equations and their inversions are simplified through the
introduction of the finite part and the generalized principal part of an
integral .
applications of the theory, in the lifting case, include previously
known results . in the nonlifting case, it is shown that for a specified
pressure distribution the theory does not always predict a unique
thickness distribution . this is demonstrated for a triangular plan form
having a constant pressure gradient in the stream direction .
.I 681
.T
integrals and integral equations in linearized wing theory .
.A
lomax, h. haslet, m.a. and fuller, f.b.
.B
naca rep. 1054, 1951 .
.W
integrals and integral equations in linearized wing theory .
the formulas of subsonic and supersonic wing theory for source, doublet,
and vortex distributions are reviewed, and a systematic presentation is
provided which relates these distributions to the pressure and to the
vertical induced velocity in the plane of the wing . it is shown that
care must be used in treating the singularities involved in the analysis
and that the order of integration is not always reversible . concepts
suggested by the irreversibility of order of integration are shown to be
useful in the inversion of singular integral equations when operational
techniques are used . a number of examples are given to illustrate the
methods presented, attention being directed to supersonic flight
speeds .
.I 682
.T
the lift of twisted and cambered wings in supersonic flow .
.A
lance, g.n.
.B
aero. quart. v. 6/2/, may, 1955 .
.W
the lift of twisted and cambered wings in supersonic flow .
a generalised conical flow theory is used to deduce an integral equation
relating the velocity potential on a delta wing/with subsonic leading
edges/to the given downwash distribution over the wing . the complete
solution of this integral equation is derived . this complete solution
is composed of two parts, one being symmetric and the other
antisymmetric with respect to the spanwise co-ordinate,. each part
represents a velocity potential . for example, if y is the spanwise
co-ordinate and x is measured in the free stream direction, then a
downwash of the form w-a ux/y/is symmetric and will give rise to a
symmetric potential, whereas w-a ux/y/sgn y is anti-symmetric and gives
rise to an anti-symmetric potential . the velocity potentials of such
flows are given in the form of tables for all downwashes up to and
including homogenous cubics in the spanwise and streamwise
co-ordinates . table iii gives similar formulae in the limiting case
were used over a cycle of the tumbling motion . the analytical
expression was in good agreement with numerical solutions of the complete
non-linear equations of motion .
.I 683
.T
the use of conical camber to produce flow attachment at the leading
edge of a delta wing and to minimize the lift-dependent drag at sonic
and supersonic speeds .
.A
smith,j.h.b. and mangler, k.w.
.B
r.a.e. rep. aero. 2584. arc 19,961, september 1957 .
.W
the use of conical camber to produce flow attachment at the leading
edge of a delta wing and to minimize the lift-dependent drag at sonic
and supersonic speeds .
in an attempt to avoid flow separation at the leading edge of a thin
delta wing with subsonic leading edges, an attachment line is prescribed
there . this is done by requiring the load, as predicted by attached
flow theory, to vanish along the leading edge at the design lift
coefficient . for sonic speed, a complete account of this flow is given
in terms of slender wing theory and the load distributions corresponding
to arbitrary conical camber are calculated . for supersonic speeds
load distributions arising in the slender wing theory are considered and
the corresponding conical camber distributions are found by linearized
theory . the lift-dependent drag for a given lift is then minimized with
respect to the coefficients of a linear combination of these load
distributions . it is found that the lift-dependent drag factor for these
conically cambered wings approaches the value it takes for the attached
flow/in which leading edge suction occurs/past the uncambered wing at
the same mach number, as more terms are included in the linear
combination . however, when the leading edge is almost sonic an appreciable
reduction is predicted . the corresponding load distributions and wing
shapes are calculated and drawn . the optimum shapes for a fixed number
of terms resemble flat plates drooped downwards near their edges, so
that the localised leading edge suction is replaced by a distributed
force on a forward-facing surface, producing an effect of similar
magnitude .
.I 684
.T
tables of complete elliptic integrals .
.A
heuman,c.
.B
j. maths. and phys. v. 20, 1941, pp 127-206 .
.W
tables of complete elliptic integrals .
the present paper contains a set of tables of complete elliptic
integrals computed and collected especially for applications to certain
dynamical problems .
the tabulated functions are four in number and are denoted by
f/a/, g/a/, e/a/, and/a,b/respectively . the definitions of these
functions and their connections with the functions of legendre will be
discussed in the following .
.I 685
.T
aerodynamic effects of some configuration variables
on the aeroelastic characteristics of lifting surfaces
at mach numbers from 0. 7 to 6. 86 .
.A
hanson,p.w.
.B
nasa tn.d984, 1961.
.W
aerodynamic effects of some configuration variables
on the aeroelastic characteristics of lifting surfaces
at mach numbers from 0. 7 to 6. 86 .
results of flutter tests on
some simple all-movable-control-type
models are given . one set of models,
which had a square planform with
double-wedge airfoils with four
different values of leading- and
trailing-edge radii from 0 to 6 percent chord
and airfoil thicknesses of 9, 11,
at mach numbers from 0.7 to 6.86 .
the bending-to-torsion frequency
ratio was about 0.33 . the other set of
models, which had a tapered planform
with single-wedge and double-wedge
airfoils with thicknesses of 3, 6, 9,
and 12 percent chord, was tested
at mach numbers from 0.7 to 3.98 and
a frequency ratio of about 0.42 .
the tests indicate that, in general,
increasing thickness has a
destabilizing effect at the higher mach
numbers but is stabilizing at
subsonic and transonic mach numbers .
double-wedge airfoils are more
prone to flutter than single-wedge
airfoils at comparable stiffness
levels . increasing airfoil bluntness
has a stabilizing effect on the
flutter boundary at supersonic speeds
but has a negligible effect at
subsonic speeds . however, increasing
bluntness may also lead to
divergence at supersonic speeds .
results of calculations using
second-order piston-theory aerodynamics
in conjunction with a coupled-mode
analysis and an uncoupled-mode analysis
are compared with the experimental
results for the sharp-edge airfoils at
supersonic speeds . the uncoupled-mode
analysis more accurately predicted
the flutter characteristics of the
tapered-planform models, whereas the
coupled-mode analysis was somewhat
better for the square-planform models .
for both the uncoupled- and coupled-mode
analyses, agreement with the
experimental results improved with
increasing mach number . in general,
both methods of analysis gave unconservative
results with respect to the
experimental flutter boundaries .
.I 686
.T
flutter tests of some simple models at a mach number
of 7. 2 in helium flow .
.A
morgan,h.g. and miller,r.w.
.B
nasa memo 4-8-59l, 1959.
.W
flutter tests of some simple models at a mach number
of 7. 2 in helium flow .
results of hypersonic flutter
tests on some simple models are
presented . the models had rectangular
plan forms of panel aspect ratio 1.0,
no sweepback, and bending-to-torsion
frequency ratios of about . two
airfoil sections were included in the
tests ,. double wedges of 5-, 10-,
and 15-percent thickness and flat plates
with straight, parallel sides
and beveled leading and trailing edges .
the models were supported by a
cantilevered shaft .
the double-wedge wings were tested
in helium at a mach number of 7.2 .
an effect of airfoil thickness on flutter
speed was found, thicker wings
requiring more stiffness to avoid flutter .
a few tests in air at a mach
number of 6.9 showed the same thickness
effect and also indicated that
tests in helium would predict conservative
flutter boundaries in air .
the data in air and helium seemed to be
correlated by piston-theory
calculations . piston-theory calculations
agreed well with experiment for
the thinner models but began to deviate
as the thickness parameter
approached and exceeded 1.0 .
a few tests on flat-plate models
with various elastic-axis locations
were made . piston-theory calculations
would not satisfactorily predict
the flutter of these models, probably
because of their blunt leading
edges .
.I 687
.T
oscillating airfoils at high mach number .
.A
lighthill, m.j.
.B
j. aero. sc. v. 20. june 1953. pp 402-406 .
.W
oscillating airfoils at high mach number .
a simple formula is given for the pressure distribution on an
oscillating airfoil in two-dimensional flow at high mach number . the
formula is expected to be reasonably accurate if the pressure on the
surface remains within the range 0.2 to 3.5 times the mainstream
pressure . to illustrate the application of the formula, some results
for symmetrical airfoils performing pitching oscillations are obtained
and compared with results obtained from existing theories in the case of
high mach number .
.I 688
.T
tables of aerodynamic coefficients obtained from developed newtonian
expressions for complete and partial conic and spheric bodies at
combined angles of attack and sideslip with some comparisons with
hypersonic experimental data .
.A
wells, w.r. and armstrong, w.o.
.B
nasa tr r -dash 127, 1962 .
.W
tables of aerodynamic coefficients obtained from developed newtonian
expressions for complete and partial conic and spheric bodies at
combined angles of attack and sideslip with some comparisons with
hypersonic experimental data .
closed-form expressions and tables composed from these expressions are
presented for complete and partial conic and spheric bodies at combined
angles of attack and sideslip in newtonian flow . aerodynamic
coefficients of these bodies are tabulated for various body segments
over a range of angles of attack from 1degree to 85degree and angles of
sideslip from 0degree to 15degree .
some comparisons between newtonian predictions and hypersonic
experimental aerodynamic characteristics were made for conic bodies
having various surface slopes, nose bluntnesses, and body cross sections
to indicate the range of validity of the theory . in general, the
theory is shown to agree quite well with experimental results for
sharp-nose complete cones and for configurations having large blunted
noses and steep surface slopes . however, agreement between theory and
experiment generally is poor for the more slender, slightly blunted
complete or half conic bodies and also for sharp-nose half conic bodies
where real-flow phenomena such as forebody interference, viscous forces,
leeward surface contributions, or leading-edge pressure reductions may
have significant effect . the agreement between theory and experiment
for the bodies considered can be improved by using the stagnation
pressure coefficient behind a normal shock rather than 2 as the newtonian
coefficient, although for the sharp-nose half conic bodies there is no
theoretical justification for this modification .
.I 689
.T
investigation of the laminar aerodynamics heat transfer
characteristics of a hemisphere cylinder in the langley
11-inch hypersonic tunnel at a mach number of 6. 8.
.A
crawford,d.h. and mccauley,w.d.
.B
naca r.1323, 1957.
.W
investigation of the laminar aerodynamics heat transfer
characteristics of a hemisphere cylinder in the langley
11-inch hypersonic tunnel at a mach number of 6. 8.
a program to investigate the aerodynamic heat transfer of a
nonisothermal hemisphere-cylinder has been conducted in the
langley 11-inch hypersonic tunnel at a mach number of 6.8
and a reynolds number from approximately 0.14x10 to
experimental heat-transfer coefficients were slightly less over the
whole body than those predicted by the theory of stine and
wanlass (naca technical note 3344) for an isothermal
surface . for stations within 45 of the stagnation point the
heat-transfer coefficients could be correlated by a single relation
between local stanton number and local reynolds number .
pitot pressure profiles taken at a mach number of 6.8 on a
hemisphere-cylinder have verified that the local mach number or
velocity outside the boundary layer required in the theories may
be computed from the surface pressures by using isentropic flow
relations and conditions immediately behind a normal shock .
the experimental pressure distribution at a mach number of
velocity gradients calculated at the stagnation point by using
the modified newtonian theory vary with mach number and
are in good agreement with those obtained from measured
pressures for mach numbers from 1.2 to 6.8 .
at the stagnation point the theory of sibulkin, in which the
diameter and conditions behind the normal shock were used,
was in good agreement with the experiment when the velocity
gradient at the stagnation point appropriate to the free-stream
mach number was used .
.I 690
.T
investigaion of the flow over a spiked-nose hemisphere
cylinder at a mach number of 6. 8.
.A
crawford,d.h.
.B
nasa tn.d118, 1959.
.W
investigaion of the flow over a spiked-nose hemisphere
cylinder at a mach number of 6. 8.
the shape and nature of the
flow over a spiked-nose
hemisphere-cylinder was studied in detail
at a nominal mach number of 6.8 and in a
reynolds number range (based on
diameter and stream conditions ahead of
the model) of 0.12 x 10 to 1.5 x 10 .
schlieren photographs showed
the effect of varying the spike length
and reynolds number upon the shape
of the separated boundary and upon the
location of transition . the heat
transfer and pressure distribution over
the body were then correlated
with the location of the start of
separation, the location of
reattachment, and the location of the start of
transition .
.I 691
.T
calculation procedure for thermodynamic transport, and flow properties
of the combustion products of a hydrocarbon fuel mixture burned in air
with results for ethylene-air and methane-air mixtures .
.A
.B
nasa tn d-914, 1962 .
.W
calculation procedure for thermodynamic transport, and flow properties
of the combustion products of a hydrocarbon fuel mixture burned in air
with results for ethylene-air and methane-air mixtures .
a procedure is presented whereby the composition, thermodynamic
properties, and transport properties of the dissociated combustion
products of a fuel consisting of a mixed hydrocarbon compound burned in
air may be calculated . equations and procedures for determining
supersonic nozzle ordinates and flow properties for the dissociated
combustion products are presented in an appendix . results are presented
for the respective hydrocarbon fuels, methane and ethylene, at the
equivalence ratios of 1.0, 0.9, 0.8, and 0.7 for pressures varying
between 10 and 8 x 10 atmospheres and temperatures from 200degree k to
.I 692
.T
investigation of the jet effects on a flat surface downstream of the
exit of a simulated turbojet nacelle at a free-stream mach number of
2.02 .
.A
bressette, w.e.
.B
naca rm l54e05a, 1954 .
.W
investigation of the jet effects on a flat surface downstream of the
exit of a simulated turbojet nacelle at a free-stream mach number of
2.02 .
an investigation at a free-stream mach number of 2.02 was made to
determine the effects of a propulsive jet on a wing surface located in
the vicinity of a choked convergent nozzle . static-pressure surveys
were made on a flat surface that was located in the vicinity of the
propulsive jet . the nozzle was operated over a range of exit pressure
ratios at different fixed vertical distances from the flat surface .
within the scope of this investigation, it was found that shock waves,
formed in the external flow because of the presence of the propulsive
jet, impinged on the flat surface and greatly altered the pressure
distribution . an integration of this pressure distribution, with the
location of the propulsive jet exit varied from 1.450 propulsive-jet
exit diameters to 3.392 propulsive-jet exit diameters below the wing,
resulted in an incremental lift for all jet locations that was equal to
the gross thrust at an exit pressure ratio of 2.86 .
this incremental lift increased with increase in exit pressure ratio,
but not so rapidly as the thrust increased, and was approximately
constant at any given exit pressure ratio .
.I 693
.T
investigation of jet effects on a flat surface downstream of the exit of
a simulated turbojet nacelle at a free-stream mach number of 1.39 .
.A
bressette, w.e. and leiss, a.
.B
.W
investigation of jet effects on a flat surface downstream of the exit of
a simulated turbojet nacelle at a free-stream mach number of 1.39 .
an investigation at a free-stream mach number of 1.39 utilizing a
blowdown-type tunnel was made to determine the effects of a propulsive
jet on a zero angle-of-attack wing surface located in the vicinity of
both a choked convergent nozzle and a convergent-divergent nozzle .
staticpressure surveys were made on a flat surface that was located in
the vicinity of the propulsive jet . the nozzles were operated over a
varied range of both exit static- and total-pressure ratios at different
within the scope of this investigation, it was found that shock waves,
formed in the external flow because of the presence of the jet exhaust,
impinged on the flat surface and greatly altered the pressure
distribution . an integration of this pressure distribution for the choked
convergent nozzle, with the location of the propulsive-jet exit varied
from 1.747 jet-exit diameters to 4.981 jet-exit diameters below the wing
surface, resulted in a positive incremental normal force on the wing at
all positions .
.I 694
.T
pressure distribution induced on a flat plate by a supersonic and sonic
jet exhaust at a free-stream mach number of 1.80 .
.A
leiss, a. and bressette, w.e.
.B
naca rm l56106, 1957 .
.W
pressure distribution induced on a flat plate by a supersonic and sonic
jet exhaust at a free-stream mach number of 1.80 .
as a continuation of previous research at mach numbers of 2.02 and 1.39,
an experimental investigation was made of the pressures induced on a
flat plate by a propulsive jet exhausting from sonic and supersonic
nozzles at a free-stream mach number of 1.80 . measurements of the
pressure distribution on a flat-plate wing were made at zero angle of
attack for four different locations of the jet exhaust nozzle beneath
the wing . both a choked convergent nozzle and a convergent-divergent
nozzle on the nacelle were used . the nozzles were operated at
nacelle-exit total-pressure ratios from 2 to 16 and the reynolds number per foot
was approximately 13 x 10 .
two distinct shock waves impinged on the wing surface and greatly
altered the pressure distribution at all nozzle positions . positive
incremental normal force resulted on the wing at all positions .
comparisons are presented for two free-stream mach numbers .
.I 695
.T
some experiments relating to the problem of simulation of hot jet
engines in studies of jet effects on adjacent surfaces at a free-stream
mach number of 1.80 .
.A
bressette, w.e.
.B
naca rm l56e07. 1956 .
.W
some experiments relating to the problem of simulation of hot jet
engines in studies of jet effects on adjacent surfaces at a free-stream
mach number of 1.80 .
an investigation at a free-stream mach number of 1.80 in a blowdown type
tunnel was made to study the effect on the pressure distribution of a
zero angle of attack wing surface when certain exhaust parameters of a
hot turbojet engine are varied . static-pressure surveys were made on a
wing surface that was located in the vicinity of a small-scale
propulsive jet . this propulsive jet was operated with four types of jet
exhausts . these jet exhausts were a hot jet /hydrogen burned in air/, a
cold air jet, a cold helium jet, and a jet composed of a mixture of two
cold gases /hydrogen and carbon dioxide/ . the hot jet, because of its
high exhaust temperature /3,300degreer/ and because combustion was
performed in air, was believed reasonably able to simulate the exhaust
parameters of an actual afterburning turbojet engine . the cold jets
used were selected in order that the effects of a variation in the
exhaust parameters of jet-exit static-pressure ratio, ratio of specific
heats, density, and velocity, could be obtained by comparing each cold
jet with the hot jet or with another cold jet . the tests were made over
a range of jet-exit staticpressure ratios from 1 to 9 with values of
the ratio of specific heats of 1.27, 1.40, and 1.66 and at variations in
density and velocity of the order of approximately 8 and 3 times,
respectively .
within the scope of this investigation, it was found that jet-exit
static-pressure ratio and the ratio of specific heats affected the
pressure distribution on the wing associated with jet interference while
a variation in exit velocity and density did not . the jet-exit
staticpressure ratio affected the wing pressure distribution in a major
way while the ratio of specific heats had only a minor effect . the
addition of temperature in the propulsive jet exhaust at a jet-exit
staticpressure ratio of 4 had little or no effect on the pressure
distribution associated with jet interference on the wing .
.I 696
.T
pressure loads produced on a flat-plate wing by rocket jets exhausting
in a spanwise direction below the wing and perpendicular to a
free-stream flow of mach number 2.0 .
.A
falangan, r.a. and janos, j. j.
.B
nasa tn d-893, 1961 .
.W
pressure loads produced on a flat-plate wing by rocket jets exhausting
in a spanwise direction below the wing and perpendicular to a
free-stream flow of mach number 2.0 .
an investigation at a reynolds number per foot of 14.4 x 10 was made to
determine the pressure loads produced on a flat-plate wing by rocket
jets exhausting in a spanwise direction beneath the wing and
perpendicular to a free-stream flow of mach number 2.0 . the ranges of the
variables involved were /1/ nozzle types - one sonic /jet mach number of
two-dimensional supersonic /jet mach number of 1.71/,. /2/ vertical
nozzle positions beneath the wing of 4, 8, and 12 nozzle-throat
diameters,. and /3/ ratios of rocket-chamber total pressure to
free-stream static pressure from 0 to 130 .
the incremental normal force due to jet interference on the wing varied
from one to two times the rocket thrust and generally decreased as the
pressure ratio increased . the chordwise coordinate of the
incremental-normal-force center of pressure remained upstream of the nozzle center
line for the nozzle positions and pressure ratios of the investigation .
the chordwise coordinate approached zero as the jet vertical distance
beneath the wing increased . in the spanwise direction there was little
change due to varying rocket-jet position and pressure ratio . some
boundary-layer flow separation on the wing was observed for the rocket
jets close to the wing and at the higher pressure ratios . the magnitude
of the chordwise and spanwise pressure distributions due to jet
interference was greatest for rocket jets close to the wing and decreased as
the jet was displaced farther from the wing .
the design procedure for the rockets used is given in the appendix .
.I 697
.T
effects on adjacent surfaces from the firing of rocket jets .
.A
bressette, w.e. and leiss, a.
.B
naca rm l 57d19a, 1957 .
.W
effects on adjacent surfaces from the firing of rocket jets .
this paper is a preliminary and brief account of some research currently
being conducted to determine the jet effects on adjacent surfaces from
the firing of rocket jets . measurements of jet-effect pressures on a
flat plate as well as shadowgraphs are presented that were obtained when
a rocket jet at a mach number of 3 was exhausted downstream and
upstream into free-stream flow at a mach number of 2 located from 2 to 4.7
rocket-jet-exit diameters from the plate . the jet effects on the flat
plate with the rocket jet exhausting downstream are of the same order of
magnitude as those previously obtained from sonic exits with a total
pressure 10 times lower . a maximum pressure coefficient on the plate of
rocket-jet-exit diameters below the plate, and an integration of the
measured jet-effect pressures at this position resulted in a normal
force on the plate equal to 2.3 times the thrust output of the rocket
jet .
.I 698
.T
the unsteady lift of a wing of finite aspect ratio .
.A
jones, r.t.
.B
1940, naca rep. 681 .
.W
the unsteady lift of a wing of finite aspect ratio .
unsteady-lift functions for wings of finite aspect ratio have been
calculated by correcting the aerodynamic inertia and the angle of attack of
the infinite wing . the calculations are based on the operational
method .
the starting lift of the finite wing is found to be only slightly less
than that of the infinite wing,. whereas the final lift may be
considerably less . the theory indicates that the initial distribution of
lift is similar to the final distribution .
curves showing the variation of lift after a sudden unit change in angle
of attack, during penetration of a sharpedge gust, and during a
continuous oscillation are given . operational equivalents of these
functions have been devised to facilitate the calculation of lift under
various conditions of motion . as an application of these formulas, the
vertical acceleration of a loaded wing caused by penetrating a gust has
been calculated .
.I 699
.T
approximate indical lift functions for several wings of finite span in
incompressible flow as obtained from oscillatory lift coefficients .
.A
drischler j.a.
.B
naca tn 3639, 1956 .
.W
approximate indical lift functions for several wings of finite span in
incompressible flow as obtained from oscillatory lift coefficients .
the unsteady-lift functions for a wing undergoing a sudden change in
sinking speed have been presented for delta wings having aspect ratios
of 0, 2, and 4 and for rectangular and elliptical wings having aspect
ratios of 0, 3, and 6 . for the elliptical and rectangular wings the
spanwise lift distributions were also presented . these functions were
calculated from the lift coefficients associated with a wing oscillating
harmonically in pure translational motion, as obtained from several
sources .
the results of these calculations indicate that the normalized
unsteady-lift functions are substantially independent of the shape of
the plan form for elliptical, rectangular, or moderately tapered wings,.
however, for delta wings the increase of lift toward the steady-state
value is much more rapid than that for the aforementioned wings of the
same aspect ratio . these results also corroborate the results of other
investigations in that the rate of growth of lift tends to increase with
a decrease in aspect ratio . the shape of the spanwise distributions of
the indicial lift seems to be, for all practical purposes, independent
of time for rectangular and elliptical wings .
.I 700
.T
two and three-dimensional unsteady lift problems in high speed flight .
.A
lomax et al.
.B
naca rep. 1077, 1952 .
.W
two and three-dimensional unsteady lift problems in high speed flight .
the problem of transient lift on two- and three-dimensional wings flying
at high speeds is discussed as a boundary-value problem for the
classical wave equation . kirchhoffs formula is applied so that the
analysis is reduced, just as in the steady state, to an investigation of
sources and doublets . the applications include the evaluation of
indicial lift and pitchingmoment curves for two-dimensional sinking and
pitching wings flying at mach numbers equal to 0, 0.8, 1.0, 1.2, and
triangular wings in both forward and reversed flow are presented and
compared with the two-dimensional values .
.I 701
.T
numerical determination of indical lift of a two-dimensional sinking
airfoil at subsonic mach numbers from oscillatory lift coefficients with
calculations for mach number 0.7 .
.A
mazelsky, b.
.B
naca tn 2562, 1951 .
.W
numerical determination of indical lift of a two-dimensional sinking
airfoil at subsonic mach numbers from oscillatory lift coefficients with
calculations for mach number 0.7 .
the reciprocal equations for relating the incompressible circulatory
indicial lift to the lift due to harmonic oscillations have been
modified to include the noncirculatory lift associated with
apparent-mass effects . although the apparent-mass effects are impulsive in
nature in incompressible flow, the lift due to apparent-mass effects in
compressible flow is a time-dependent function . the corresponding
reciprocal equations for the total compressible lift are given . by use
of the reciprocal equations for compressible flow, the indicial lift and
moment functions due to an airfoil's experiencing a sudden acquisition
of vertical velocity are determined numerically for mach number 0.7 .
lack of sufficient flutter coefficients prevents the calculation of
these functions at other mach numbers .
although the indicial lift and moment functions due to penetration of a
sharp-edge gust may be obtained from the oscillatory tab or aileron
coefficients by a similar analysis, sufficient coefficients are not
available at the present . however, an approximate method is shown for
determining a portion of this unsteady-lift function .
when a comparison is made of the indicial lift functions at mach numbers
appears to be less rapid for the compressible case than for the
incompressible case . consequently, the calculation of the gust load factor
at high subsonic mach numbers utilizing the two-dimensional
incompressible indicial lift functions and an over-all correction for
compressibility such as the prandtl-glauert factor might be conservative .
.I 702
.T
numerical determination of indical lift and moment functions for a two
dimensional sinking and pitching airfoil at mach numbers 0.5 and 0.6 .
.A
mazelsky, b. and drischler, j.a.
.B
naca tn 2739, 1952 .
.W
numerical determination of indical lift and moment functions for a two
dimensional sinking and pitching airfoil at mach numbers 0.5 and 0.6 .
the indicial lift and moment functions are determined approximately for
sinking and pitching motion at mach numbers m of 0.5 and 0.6 . these
functions are determined from a knowledge of the existing oscillatory
coefficients at the low reduced frequencies and from approximate
expressions of these coefficients at the high reduced frequencies .
the beginning portion of the indicial lift function associated with an
airfoil penetrating a sharp-edge gust in subsonic flow is evaluated by
use of an exact method . by use of an approximate method for determining
the remaining portion, the complete indicial gust function is
determined for m 0.5, m 0.6, and m 0.7 .
all the indicial lift and moment functions are approximated by an
exponential series,. the coefficients which appear in the exponential
approximations for each indicial function are tabulated for m 0.5,
m 0.6, and m 0.7 .
.I 703
.T
general airfoil theory .
.A
kussner, h.g.
.B
naca tm 979, 1941 .
.W
general airfoil theory .
on the assumption of infinitely small disturbances the author develops
a generalized integral equation of airfoil theory which is applicable
to any motion and compressible fluid . successive specializations yield
various simpler integral equations, such as possio's, birnbaum's, and
prandtl's integral equations, as well as new ones for the wing of
infinite span with periodic downwash distribution and for the oscillating
wing with high aspect ratio . lastly, several solutions and methods for
solving these integral equations are given .
.I 704
.T
a systematic kernel function procedure for determining aerodynamic
forces on oscillating or steady finite wings at subsonic speeds .
.A
watkins, c.e., woolston, d.s. and cunningham, h.j.a.
.B
nasa tr r-48, 1959 .
.W
a systematic kernel function procedure for determining aerodynamic
forces on oscillating or steady finite wings at subsonic speeds .
a detailed description is given of a method of approximating solutions
to the integral equation that relates oscillatory or steady lift and
downwash distributions on finite wings in subsonic flow . the method of
solution is applicable to general plan forms with either curved or
straight leading and trailing edges . moreover, it is directly
applicable to control surfaces such as all-movable tails but modifications
are needed to apply it to controls in general . applications of the
method involve evaluations of numerous integrals that must be handled by
numerical procedures but systematic schemes of evaluations have been
adopted that are well suited to the routines of automatic digital
computing machines . these schemes of evaluation have been incorporated in
a program for an ibm 704 electronic data processing machine . with this
machine, a pressure distribution together with such quantities as
section or total lift and moment coefficients or generalized forces can be
determined for a given value of frequency and mach number and for
several /four or five/ modes of oscillation in about 4 minutes of
machine time . in the case of steady downwash conditions corresponding
quantities can be obtained in about 2 minutes of machine time .
in order to illustrate applications of the method, results of several
calculations are presented . in these illustrations total forces and
moments are compared /1/ with results of analytic procedures for a
circular plan form with steady downwash conditions, /2/ with results of
other theories and with experiment for a rectangular plan form of aspect
ratio 1 at a uniform angle of attack, and /3/ with some experimental
results for a rectangular plan form of aspect ratio 2 undergoing
pitching and flapping oscillations . also included in the illustrations are
results of flutter calculations compared with experimental results for
an allmovable control surface of aspect ratio 3.50 and for a
cantilevered rectangular plan form of aspect ratio 5.04 .
.I 705
.T
on the kernel function of the integral equation relating the lift and
downwash distributions of oscillating finite wings in subsonic flow .
.A
watkins, c.e. and runyal, h.l. and woolston, d.s.
.B
naca rep. 1234, 1955 .
.W
on the kernel function of the integral equation relating the lift and
downwash distributions of oscillating finite wings in subsonic flow .
this report treats the kernel function of an integral equation that
relates a known or prescribed downwash distribution to an unknown lift
distribution for a harmonically oscillating finite wing in compressible
subsonic flow . the kernel function is reduced to a form that can be
accurately evaluated by separating the kernel function into two parts ..
a part in which the singularities are isolated and analytically
expressed and a nonsingular part which may be tabulated . the form of the
kernel function for the sonic case /mach number of 1/ is treated
separately . in addition, results for the special cases of mach number
of o /incompressible case/ and frequency of o /steady case/ are given .
the derivation of the integral equation which involves this kernel
function, originally performed elsewhere /see, for example, naca
technical memorandum 979/, is reproduced as an appendix . another appendix
gives the reduction of the form of the kernel function obtained herein
for the three-dimensional case to a known result of possio for
two-dimensional flow . a third appendix contains some remarks on the
evaluation of the kernel function, and a fourth appendix presents an
alternate form of expression for the kernel function .
.I 706
.T
on som reciprocal relations in the theory of nonstationary flows .
.A
garrick, i.e.
.B
naca rep. 629. 1938 .
.W
on som reciprocal relations in the theory of nonstationary flows .
in the theory of nonstationary flows about airfoils, the /indicial lift/
function k /s/ of wagner and the /alternating lift/ function c /k/ of
theodorsen have fundamental significance . this paper reports on some
interesting relations of the nature of fourier transforms that exist
between these functions . general problems in transient flows about
airfoils may be given a unified broad treatment when these functions are
employed . certain approximate results also are reported which are of
notable simplicity, and an analogy with transient electrical flows is
drawn .
.I 707
.T
thermal analysis of stagnation regions with emphasis on heat-sustaining
nose shapes at hypersonic speeds .
.A
hanawalt, a.j., blessing, a.h. and schmidt, c.m.
.B
j.aero. sc. may 1959. p. 257-263 .
.W
thermal analysis of stagnation regions with emphasis on heat-sustaining
nose shapes at hypersonic speeds .
the leading edges and noses of hypersonic vehicles are subjected to
severe aerodynamic heating and must be cooled in some manner-dash e.g.,
internal convection, transpiration, or radiation . it is this latter
mode of handling the problem that is discussed in this paper .
neglecting conduction in the leading-edge region, the maximum temperature for
long-range hypersonic gliders is of the same order as the melting point
of refractory materials, with a corresponding large temperature gradient
away from the leading edge . inclusion of conduction in the aft
direction reduces the maximum temperature and distributes the heat to a
location that will radiate it out from the surface . for either
steady-state or transient conditions, the temperature at the leading edge is
reduced by conduction, while the temperature aft of the leading-edge
shoulder is increased, thus setting up a heat transmission balance
between the convective influx of heat, the redistribution of heat by
conduction, and the radiation of heat from the surface . the feasibility of
such a mechanism can be enhanced by suitably choosing leading-edge
shapes and materials . the philosophy behind the choice of leading-edge
shapes is discussed and the effects of varying parameters, such as
shape, diameter, emissivity, conductivity, thickness, etc., are shown .
.I 708
.T
aerodynamic characteristics of two winged reentry vehicles at supersonic
and hypersonic speeds .
.A
ladson, c.l. and johnston, p.j.
.B
nasa tm x 346, 1961 .
.W
aerodynamic characteristics of two winged reentry vehicles at supersonic
and hypersonic speeds .
tests were conducted at the langley research center on two winged
lifting hypersonic reentry glider configurations . performance, stability,
and control data are presented at mach numbers of 1.62 and 2.91 for
angles of attack up to 15degree and at mach numbers of 6.8 and 9.6 for
angles of attack up to 25degree .
.I 709
.T
static longitudinal aerodynamic characteristics at transonic speeds and
angles of attack up to 99degree of a reentry glider having folding
wingtip panels .
.A
olstad, w.b.
.B
nasa tm x-610, 1961 .
.W
static longitudinal aerodynamic characteristics at transonic speeds and
angles of attack up to 99degree of a reentry glider having folding
wingtip panels .
data are presented which were obtained from a transonic wind-tunnel
investigation of a reentry glider having folding wing-tip panels . the
tests were conducted at angles of attack from -4degrees to 99degrees .
the reynolds number based on the mean geometric chord of the fixed
planform varied from 2.35 x 10 to 2.99 x 10 .
the maximum lift-drag ratio for the model with the folding wing-tip
panels fully extended decreased from a maximum value of 7.8 at a mach
number of 0.60 to about 3.4 at mach numbers from 1.03 to 1.20 . the
model with the folding wing panels fully extended was stable for values
of the lift coefficient from 0 up to at least 0.8 . above this lift
coefficient pitch-up tendencies were observed, followed by an unstable or
neutrally stable region which extended up to values of angle of attack
of 50degrees or 60degrees . deflecting the folding wing panels between
ducing a significant change in the trim angle of attack or in any of the
force or moment coefficients in the angle-of-attack range from 49degree
to 99degree .
.I 710
.T
the smallest height of roughness capable of affecting boundary-layer
transition .
.A
smith, a.m.o. and clutter, d.w.
.B
j. aero. sc. april, 1959. p.229-245, 256 .
.W
the smallest height of roughness capable of affecting boundary-layer
transition .
an investigation was made to determine the smallest size of isolated
roughness that will affect transition in a laminar-boundary layer .
critical heights for three types of roughness were found in a low-speed
wind tunnel . the types were /1/ two-dimensional spanwise wires, /2/
three-dimensional discs, and /3/ a sandpaper type . in addition to type
of roughness, test variables included the location of roughness,
pressure distribution, degree of tunnel turbulence, and length of natural
laminar flow .
the most satisfactory correlation parameter was found to be the
roughness reynolds number, based on the height of roughness and flow
properties at this height . the value of this critical reynolds number was
found to be substantially independent of all test variables except the
shape of roughness . this parameter also correlates well other published
data on critical roughness in low-speed flow . the value of the
roughness reynolds number necessary to move transition forward to the
roughness itself was also determined for the three types of roughness and was
found to be approximately constant for a given type of roughness .
an investigation of the limited amount of available data on critical
roughness in supersonic flow indicates that the effects of roughness may
still be correlated by the roughness reynolds number . the value of
this reynolds number depends primarily on the mach number at the top of
the roughness . when this mach number is greater than 1.0, the roughness
reynolds number based on conditions behind a shock is probably the
characteristic parameter .
.I 711
.T
an investigation at subsonic speeds of aerodynamic characteristics at
angles of attack from -dash 4degrees to 100degrees of a delta-wing
reentry configuration having folding wingtip panels .
.A
spencer, b.
.B
nasa tm x-288, 1960 .
.W
an investigation at subsonic speeds of aerodynamic characteristics at
angles of attack from -dash 4degrees to 100degrees of a delta-wing
reentry configuration having folding wingtip panels .
an investigation was made at subsonic speeds in the langley highspeed
lifting reentry configuration having folding wingtip panels . the
configuration is of the type used in a high angle-of-attack /near 90degree/
reentry to minimize aerodynamic heating . by unfolding the wingtip
panels into the airstream, a moderate angle-of-attack glide is used for
a controlled landing . the basic configuration tested utilized a
whose area was 25 percent of the total wing area . the effects of
varying the plan form and size of the wingtip panels was studied as well
as the effects of unfolding the wingtip panels in a high angle-
of-attack attitude . tests were made at mach numbers of 0.40, 0.60, and
.I 712
.T
low-speed longitudinal aerodynamic characteristics associated with a
series of low-aspect ratio wings having variations in leading-edge
contour .
.A
spencer, b. and hammond, a.d.
.B
nasa tn d-1374, 1962 .
.W
low-speed longitudinal aerodynamic characteristics associated with a
series of low-aspect ratio wings having variations in leading-edge
contour .
an investigation has been conducted at various reynolds numbers and low
subsonic speeds to determine the longitudinal aerodynamic
characteristics associated with a series of low-aspect-ratio wings having
variations in leading-edge contours . the planforms included a highly swept
triangular wing, a rectangular wing, and intermediate wings including
planforms having elliptic and parabolic leading-edge contours, all
having an aspect ratio of 1.33 . the effects of changing aspect ratio for a
given leading-edge contour were investigated for two of the wings
presented,. also included are the longitudinal characteristics associated
with various fuselage sizes . an effort has been made to estimate the
lift variation with angle of attack for the wing planforms of the
present investigation .
improvements in the lifting capabilities at low subsonic speeds
associated with a basic triangular planform of low aspect ratio are possible
by slight alterations in leading-edge design, which should still conform
to possible design requirements at hypersonic speeds . these changes in
planform resulted in increases in lift-curve slope, lift at high angles
of attack, and in the maximum untrimmed lift-drag ratio, provided the
fuselage was sufficiently small . the longitudinal stability
characteristics of the majority of planforms indicate more desirable stability
characteristics at high lifts than either a triangular wing or
rectangular wing of the same aspect ratio . the effects of increasing
reynolds number for each of the planforms investigated generally resulted
in slight reductions in the lift at high angles of attack . a method is
presented for estimating the subsonic-lift variation with angle of
attack for the low-aspect-ratio wings of the present investigation and
indicated good agreement with experimental data throughout the
angle-of-attack range of this investigation .
.I 713
.T
static longitudinal stability characteristics of a blunted glider
re-entry configuration having 79.5degree sweepback and 45degree dihedral at
a mach number of 6.2 and angles of attack up to 20degree .
.A
mayo, e.e.
.B
nasa tm x-222. 1959 .
.W
static longitudinal stability characteristics of a blunted glider
re-entry configuration having 79.5degree sweepback and 45degree dihedral at
a mach number of 6.2 and angles of attack up to 20degree .
an experimental investigation was conducted at a mach number of 6.2 to
determine the static longitudinal stability characteristics of a model
of a blunted glider reentry configuration having 79.5degree sweepback
and 45degree dihedral . the free-stream reynolds number for the
investigation was 3.0 x 10 based on the basic model length of 7.5 inches .
tests were made through an angle-of-attack range from 0degrees to
investigation showed that incorporating 10degree nose incidence in the
basic model resulted in a lower lift-curve slope, a lower lift-drag
ratio, a higher value of trim lift coefficient, and a decrease in static
longitudinal stability . in comparison, the effect of extending the
configuration length and incorporating 10degrees and 20degrees boattail
angles resulted in smaller changes in the longitudinal stability
characteristics of the model .
.I 714
.T
blockage corrections for three-dimensional flow closed
throat wind tunnels, with considerations of the effect
of compressibility .
.A
herriot,j.g.
.B
naca r.995, 1950.
.W
blockage corrections for three-dimensional flow closed
throat wind tunnels, with considerations of the effect
of compressibility .
theoretical blockage corrections are presented for a body of
revolution and for a three-dimensional unswept wing in a
circular or rectangular wind tunnel . the theory takes account of
the effects of the wake and of the compressibility of the fluid,
and is based on the assumption that the dimensions of the model
are small in comparison with those of the tunnel throat .
formulas are given for correcting a number of the quantities, such
as dynamic pressure and mach number, measured in
wind-tunnel tests . the report presents a summary and unification
of the existing literature on the subject .
.I 715
.T
motion of a ballistic missile angularly misaligned
with the flight path upon entering the atmosphere and
its effect upon aerodynamic heating, aerodynamic loads
and miss distance .
.A
allen,h.j.
.B
naca tn.4048, 1957.
.W
motion of a ballistic missile angularly misaligned
with the flight path upon entering the atmosphere and
its effect upon aerodynamic heating, aerodynamic loads
and miss distance .
an analysis is given of the
oscillating motion of a ballistic missile
which upon entering the atmosphere
is angularly misaligned with respect
to the flight path . the history of
the motion for some example missiles
is discussed from the point of view
of the effect of the motion on the
aerodynamic heating and loading .
the miss distance at the target due to
misalignment and to small accidental
trim angles is treated . the
stability problem is also discussed for
the case where the missile is
tumbling prior to atmospheric entry .
.I 716
.T
study of the oscillatory motion of manned vehicles
entering the earth's atmosphere .
.A
sommer,s.c. and tobak,m.
.B
nasa memo 3-2-59a, 1959.
.W
study of the oscillatory motion of manned vehicles
entering the earth's atmosphere .
an analysis is made of the oscillatory
motion of vehicles which
traverse arbitrarily prescribed trajectories
through the atmosphere .
expressions for the oscillatory motion
are derived as continuous functions
of the properties of the trajectory .
results are applied to a study of
the oscillatory behavior of re-entry
vehicles which have decelerations that
remain within limits of human
tolerance . it is found that a deficiency of
aerodynamic damping for such
vehicles may have more serious consequences
than it does for comparable
ballistic missiles .
.I 717
.T
motions of a short 10degree blunted cone entering a martian atmosphere
at arbitrary angles of attack and arbitrary pitching rates .
.A
peterson, v.l.
.B
nasa tn-d 1326 .
.W
motions of a short 10degree blunted cone entering a martian atmosphere
at arbitrary angles of attack and arbitrary pitching rates .
the dynamic behavior of two probe vehicles entering a martian atmosphere
in a passive manner with arbitrary initial angles of attack and
pitching rates to 12degree per second has been determined . results for an
entry velocity of 21,700 feet per second and an entry angle of -40degree
were obtained from machine calculated solutions of the six-degree-
of-freedom rigid-body equations of motion using experimental aerodynamic
characteristics for the vehicles . one of the vehicles had a flat base
and was statically stable in two attitudes /nose forward and base
forward/ . the other vehicle, derived from the first by adding a conical
afterbody, was statically stable in only one attitude /nose forward/ .
a 10-rpm vehicle spin rate, believed ample for the purpose of
distributing solar and aerodynamic heating over the vehicle surface, and
model atmospheres encompassing the probable extremes for the planet
were also considered .
it was found that while the motion of the flat-based vehicle could be
oscillatory about either the nose-forward or base-forward stable trim
attitudes when aerodynamic heating rates were high, the range of initial
angles of attack resulting in base-forward orientation was reduced by
more than a factor of 3. when initial pitch rates were increased from
body having only nose-forward stability showed that oscillatory angles
of attack at maximum heating-rate conditions probably would not exceed
about 25degrees although angles of attack when heating rates were 50
percent of maximum could be as high as 40degree . values of these upper
bound angles of attack were essentially independent of initial pitch
rates for the range considered . furthermore, the envelope of maximum
probable angles of attack was increased only slightly when the vehicle
was given a 10-rpm spin rate . the relationship between maximum
amplitudes of oscillation and heating rates through high heating portions of
the trajectories was preserved when model atmospheres believed to
encompass the extreme possibilities for mars were used in the calculations
.I 718
.T
means and examples of aeronautical research in france at onera .
.A
maurice roy
.B
the twenty-second wright brothers lecture
office national d'etudes et de recherches aeronautiques
.W
means and examples of aeronautical research in france at onera .
cosmonautics is currently very much to the forefront in the news .
it embraces and extends aeronautics, and i would like to propose
including both, at least on certain occasions, under a general
denomination of /aerocosmonautics/ .
in your country, the sciences and technology of space are subjects which
have been backed by initial advances and abundantly treated .
since france has not yet launched any artificial satellite or built
any circumlunar space vehicle, i propose to confine myself here to the
field of aeronautics, where there is still so much progress of manifest
utility to accomplish .
i shall accordingly content myself with presenting some examples of
aeronautical research and experiments undertaken in my country by
onera, a body whose mission is akin to that of the illustrious naca,
now nasa, but bearing in mind the considerable difference between the
scales of the respective resources .
.I 719
.T
tumbling bodies entering the atmosphere .
.A
remmler, k.l.
.B
ars jnl. v. 32, january 1962. pp 92-95 .
.W
tumbling bodies entering the atmosphere .
the equations of motion of a tumbling flat plate entering an exponential
atmosphere were linearized and solved analytically to obtain a simple
expression for the altitude at which tumbling would cease and libration
would commence . the plate had only three degrees of freedom, and
aerodynamic forces were derived from newtonian impact theory . in the
linear analysis, mean values of the drag and pitch damping coefficients
so that flutter occurs in the range of a low-speed wind tunnel .
a particular type of construction for supersonic flutter models is
described in detail . methods of vibration testing, static testing, and
flutter testing are discussed . particular emphasis is placed on the
technique of varying flow parameters rather than model parameters to
precipitate flutter . the tool for varying flow parameters is the
variable mach number supersonic test section of the massachusetts
institute of technology blowdown wind tunnel . the aerodynamic features of
the supersonic test section are presented .
.I 720
.T
a note on the use of sandwich structures in severe acoustic
environments .
.A
d. j. mead, d. c. ae.
.B
d. j. mead, d.c.ae.
.W
a note on the use of sandwich structures in severe acoustic
environments .
this paper reviews some of the experience to date of using sandwich type
structures in severe acoustic pressure environments . the methods
used for testing sandwich structures for acoustic fatigue are described
and their limitations considered . experimental and theoretical work
relating to the damping and mode-frequency relationships of certain
sandwich configurations is also reviewed .
special attention is given to the estimation of the stress in the bond
of a honeycomb sandwich panel subjected to sudden pressure
fluctuations . a /uni-modal/ theory is presented, relating the
mean-square bond-stress to the random exciting pressure and panel dynamic
characteristics . this theory indicates that tensile bond stresses
may be encountered of up to six times the local r.m.s. exciting
pressure . these must be combined with bending and shear stresses
to obtain the principal stresses which precipitate bond fatigue
failures .
finally, an outline is given of some of the lines of future research
which should lead to the achieving of the maximum possible fatigue
resistance from sandwich configurations .
.I 721
.T
near noise field of a jet engine exhaust .
.A
callaghan,e.e., howes,w.l. coles,w.d. and mull,r.h.
.B
naca r.1338.
.W
near noise field of a jet engine exhaust .
aircraft structures located in the near noise field of a jet
engine are subjected to extremely high fluctuating pressures that
may cause structural fatigue . studies of such structures have
been limited by lack of knowledge of the loadings involved .
the acoustic near field produced by the exhaust of a stationary
turbojet engine having a high pressure ratio was measured for
a single operating condition without afterburning . the
maximum over-all sound pressure without afterburning was found
to be about 42 pounds per square foot along the jet boundary in
the region immediately downstream of the jet-nozzle exit .
with afterburning the maximum sound pressure was increased
by 50 percent . the largest sound pressures without
afterburning were obtained on a constant percentage band width basis in
the frequency range from 350 to 700 cps .
additional tests were made at a few points to find the effect
of jet velocity on near-field sound pressures and to determine
the difference in value between sound-pressure levels at rigid
surfaces and corresponding free-field values . near the jet
nozzle, over-all sound pressures were found to vary as a low
power (approx. unity) of the jet velocity . over-all sound-pressure
levels considerably greater than the corresponding free-field
levels were recorded at the surface of a rigid plate placed along
the jet boundary .
the downstream locations of the maximum sound pressure
at any given frequency along the jet-engine-exhaust boundary
and the longitudinal turbulent-velocity maximum of the same
frequency along a small cold-air jet at 1 nozzle-exit radius from
the jet axis were found to be nearly the same when compared on
a dimensionless basis . also, the strouhal number of the
corresponding spectra maximums was found to be nearly equal at
similar distances downstream .
in addition to the magnitude and frequency distribution of
the acoustic pressures, it is necessary to know the cross
correlation of the pressure over the surface area . cross-correlation
measurements with microphones were made for a range of jet
velocities at locations along the jet and at a distance from the
jet . free-field correlations of the over-all sound pressure and
of the sound pressure in frequency bands from 100 to 1000 cps
were obtained both longitudinally and laterally . in addition,
correlations were obtained with microphones mounted at the
surface of a rigid plate that was large compared with the
distance over which a positive correlation existed .
the region of positive correlation was generally found to
increase with distance downstream of the engine to 6.5
nozzle-exit diameters, but remained nearly constant thereafter . in
general, little change in the correlation curves was found as a
function of jet velocity or frequency-band width . the distance
from unity correlation to the first zero correlation was greater for
lateral than for longitudinal correlations for the same
conditions and locations . the correlation curves obtained in free
space and on the surface of the plate were generally similar .
the results are interpreted in terms of pressure loads on
surfaces .
.I 722
.T
random excitation of a tailplane section by jet noise .
.A
clarkson,b.l. and ford,r.d.
.B
univ. southampton r. a.a.s.u.171.
.W
random excitation of a tailplane section by jet noise .
the response of a section of tailplane structure to both discrete
and random noise pressures has been studied in detail . initially the
specimen was mounted behind a jet engine and the induced strains were
analysed with the object of determining both the resonant frequencies
and the corresponding modes of vibration . during these tests a survey
was made of the spectrum and correlation pattern of the jet noise on
the surface of the model . secondly the specimen was mounted in front
of a loudspeaker in an acoustics laboratory and the structural
resonances were excited by means of discrete frequency sound . the mode
shapes were studied in detail with the aid of a stroboscope .
it is concluded that the tailplane skin on this particular piece
of structure only responds to any significant degree in one structural
mode . although reasonable comparison has been obtained between the
random and discrete tests, it was not possible to calculate the induced
stresses using the observed mode shapes and measured pressure
excitation .
.I 723
.T
on the fatigue failure of structures due to vibrations excited
by random pressure fields .
.A
alan powell
.B
the university, southampton
.W
on the fatigue failure of structures due to vibrations excited
by random pressure fields .
on the assumption that the forced modes of vibration of a structure,
subjected to pressure fluctuations random in time and space, can be
approximated by the composition of the motions of the uncoupled
natural modes, a general analysis is made using the ideas of vibration
theory and spectrum analysis . the power spectrum, and hence the
rms value, of any quantity depending linearly upon structural
distortions is derived and it involves a quantity (called the /joint
acceptance/) concerning the spacewise structure of the pressure
field and of the geometry of the modes of vibration . it is shown how
this result may be used (on assuming /normal/ randomness) to estimate
the fatigue life on the hypothesis of cumulative damage .
.I 724
.T
structural acoustic proof testing .
.A
schjeldrup,h.c.
.B
air eng. 1959.
.W
structural acoustic proof testing .
with the introduction of high-powered
propulsion systems, and paralleling their
continued development, an
accompanying increase in acoustical problems has arisen .
of these acoustical problems, that of
acoustical fatigue failures has become paramount
in the eyes of the structural engineer . aircraft
designed to normal strength requirements have
been known literally to fall apart under acoustical
loading . this problem has required much
endeavour to produce a solution, and considerable
structural research, based upon results of siren or
other testing, have proved inadequate . this
failure to find a satisfactory solution has resulted
in the conviction that the final proof of a design
can be found only in proof testing . proof testing,
in the acoustic fatigue sense, is the testing of a
design structure in a simulated acoustical
environment for a period of time long enough to assure
equality with design life .
.I 725
.T
the response of a typical aircraft structure to jet
noise .
.A
clarkson,b.l. and ford,r.d.
.B
j. roy. aero. soc. 1962.
.W
the response of a typical aircraft structure to jet
noise .
an analysis is made of experimentally determined mode shapes
excited on the rear structure of a modern airliner by jet noise from
a pod-mounted turbojet engine . power spectra of stresses
determined from strain-gage measurements are obtained and cross
correlated . extensive measurements were made on skin panels of the
fuselage and elevator and limited ones were made on fuselage
stringers and frames . the skin-panel results are compared with
theoretical predictions . reviewer believes that this paper is of
considerable value for those concerned with response of
aircraft-type structures to jet-induced noise .
.I 726
.T
on structural fatigue under random loading .
.A
miles,j.w.
.B
j. ae. scs. 21, 1954, 753.
.W
on structural fatigue under random loading .
experience has shown that the fluctuating loads induced by a
jet may cause fatigue failure of aircraft structural components .
in order to throw some light on this and similar problems, the
stress spectrum and the /equivalent fatigue stress/ of an elastic
structure subjected to random loading are studied . the analysis
is simplified by assuming the structure to have only a single
degree of freedom and by using the concept of cumulative damage,
the results being expressed in terms of quantities that can be
directly measured . as an example, a similarity expression for
the probable value of the equivalent fatigue stress of a panel
subjected to jet buffeting is derived .
.I 727
.T
a study of the acoustic fatigue characteristics of
some flat and curved aluminium panels exposed to random
and discrete noise .
.A
hess,r.w., herr,r.w. and mayes,w.h.
.B
nasa tn.d1.
.W
a study of the acoustic fatigue characteristics of
some flat and curved aluminium panels exposed to random
and discrete noise .
a study was made of the fatigue
life of simple 2024-t3
aluminum-alloy panels measuring 11 by 13
inches and exposed to both
discrete-frequency noise from a siren and
random noise from an air jet . noise
levels varied from approximately
panel variables included thickness,
edge conditions, curvature, and
static-pressure differential .
no significant differences were noted
in the nature of failures
experienced for the two types of loadings .
at a given root-mean-square
stress level, the failure times were
generally shorter for the random
loading than for the discrete-frequency
loading . these differences in
failure times were noted to be a function
of stress level, the larger
differences occurring at the lower stress levels .
increases in time to failure were
obtained as a result of increased
panel thickness, increased panel curvature,
and particularly for increased
static-pressure differential across curved panels .
for the discrete-type loading,
the location of weak points in these
simplified structural designs can be
satisfactorily accomplished but
quantitative predictions of fatigue
life are much more difficult .
.I 728
.T
free vibrations of continuous skin stringer panels .
.A
lin, y.k.
.B
j. appl. mech. december 1960 .
.W
free vibrations of continuous skin stringer panels .
the determination of the natural frequencies and normal modes of
vibration for continuous panels, representing more or less typical fuselage
skin-panel construction for modern airplanes, is discussed in this paper
are considered . a numerical example is presented, and analytical
results for a particular structural configuration agree favorably with
available experimental measurements .
.I 729
.T
stresses in continuous skin stiffener panels under random loading .
.A
lin, y.k.
.B
j. aero. sc. january 1962 .
.W
stresses in continuous skin stiffener panels under random loading .
theoretical aspects involved in the prediction of stress levels for
continuous skin-stiffener panels subjected to a random pressure field
are considered in the light of powell's general theory for statistical
superposition of modal response . the choice of structural model is
dictated by the prevalence of skin-stiffener construction in modern
flight vehicle design . the present study clearly demonstrates that any
truly adequate prediction of stress levels in actual aircraft structures
requires a much better representation of structural characteristics
than can be provided by single panel idealizations . in an example
considering fuselage panels exposed to jet engine noise, essential
agreement is shown with experimental data, although better correlation is
shown for rms stress than for power spectrum . it is shown that
reduction of stress level by increasing damping is effective only in the
higher frequency range .
.I 730
.T
on the bending of a clamped plate .
.A
weinstein,a., rock,d.h.
.B
q. app. math. 2, 1944, 262.
.W
on the bending of a clamped plate .
the present paper contains an application
of a recently developed variational
method to the boundary value problem of the
bending of a clamped plate of
arbitrary shape . it will be shown that this problem
can be linked to the simpler problem
of the equilibrium of a membrane by a chain
of intermediate problems, which can be
solved explicitly and in finite form in terms
of the membrane problem . in the
intermediate problems, the deflection converges
uniformly in the domain of the plate
of the clamped plate, and the derivatives
of all orders of the deflection converge
uniformly in every domain completely interior
to the plate . (in the ritz method, not even
the convergence of the slopes can be
guaranteed .) the method yields numerical
results for plates of all shapes for which
the membrane problem (which we shall call
the base problem) admits an explicit
solution . as an example we shall consider a
clamped square plate under a uniform load .
this problem has been the object of
numerous investigations, some of which are
theoretical, while others are purely numerical,
use infinite simple and double series,
and operate with an infinite number of
linear equations and an infinite number of
unknowns . an inspection of the general
formulae derived in the present paper,
formulae which become simple in numerical
applications, would show how some of the
numerical methods might be rendered
rigorous . the convergence of higher
derivatives is of great practical interest for
the approximate computation of the stresses .
.I 731
.T
upper and lower bounds for the solution of the first
biharmonic boundary value problem .
.A
diaz,g.b., and greenberg,h.g.
.B
j. math. phys. 27, 1948, 193.
.W
upper and lower bounds for the solution of the first
biharmonic boundary value problem .
let w(x,y) be a solution of the boundary value problem
where r is a plane
domain with the boundary c . the authors obtain upper and
lower bounds for, the value of w at a point in r,
by a method which is applicable to many other problems .
if u is a function satisfying the boundary conditions
and v is a function satisfying the partial differential
equation, then the authors obtain by applying green's
classical identity and schwarz's inequality a pair of inequalities
of the form where .
together with the function w the authors consider a
function the solution of the boundary value problem
on c, and in
analogy with the functions u and v associated with the
function w a pair of functions and associated with the
function . in the expression for derived from green's
classical identity appears an unknown line integral
containing the values of w and on c . but the same line
integral appears also in the expressions for
to which the above inequalities are
applicable .
in this way the authors obtain two inequalities of the form
where b and b', respectively, are approximate
values of . in order to improve these bounds
one may add to u a linear set of functions and to v a
linear set of functions and then minimize h(u-v) in order
to determine the coefficients of the best linear combinations .
if the sequences and are complete in a certain sense
defined by the authors the approximations will converge to
the value .
.I 732
.T
on the analogues relating flexure and extension of
flat plates .
.A
southwell,r.v.
.B
q. j. mech. app. math. 3, 1950, 257.
.W
on the analogues relating flexure and extension of
flat plates .
the displacement of a flat plate bent
by transverse loading, and the extensional
or in 'plane stress', are governed by equations
of identical form ,. and the boundary
conditions have identical form when
edge-displacements are specified in the flexural,
edge-tractions in the extensional problem,
so mathematically, in these circumstances,
only a single problem is presented . this,
the 'first analogue' relating flexure and
extension, is well known .
a 'second analogue', relating the flexural
problem when edge-tractions with the
extensional problem when edge-displacements
are specified, is believed to have been
first propounded in 1941 . by introducing
two quantities u and v, analogous with
the components u and v of extensional
displacement, it permits a treatment of the
flexural problem by any method--e.g.
which yields extensional solutions of this
second type .
in this paper both analogues are combined
in an inclusive statement covering the
perforated (multiply connected) plates which
were discussed in 1948 . reasons are
stated for believing that 'two-diagram technique'
is preferable in problems governed
by 'mixed' boundary conditions .
.I 733
.T
the bending of a sectorial plate .
.A
carrier,g.f.
.B
j. app. mech. 11, 1944, 134.
.W
the bending of a sectorial plate .
the problem of evaluating the bending moments,
existing in a uniformly loaded clamped plate having the form
of a sector of a ring, is one which arises in connection with
the stress analysis of reinforced piston heads and in other
design problems . in this paper, expressions are derived
for the bending moments along the edges of such a plate .
similar problems, i.e., those of the clamped rectangular
plate under uniform pressure, under a central
concentrated load, and that of the simply supported sector of a
disk under uniform pressure, have been discussed by
previous authors . the general approach used in the
foregoing problems is adopted in the present case ,. a
considerable reduction in the computational work is achieved,
however, by the use of an integral-equation method of
solving the boundary-condition equations . numerical
results are obtained for plates of various dimensions, and
the edge moment distributions are plotted for these cases .
curves are also plotted which indicate the relationship
existing between the maximum bending moments derived
for sectorial plates and those previously obtained for
clamped rectangular plates of similar size .
.I 734
.T
the bending of uniformly loaded clamped plate in the
form of a circular sector .
.A
hasse,h.r.
.B
q. j. mech. app. math. 3, 1950, 271.
.W
the bending of uniformly loaded clamped plate in the
form of a circular sector .
the deflexion of a uniformly loaded
plate in the form of a semicircle clamped
along its boundary is obtained by a
method due to weinstein . this problem
requires the solution of the biharmonic
equation where z is given,
subject to the conditions that w = 0 and
on the boundary, n being the
direction of the outward normal . the solution
is expressed in the form
where, writing is found
by solving (in succession) two harmonic
equations of the forms where z may
be zero, and where f and
have to satisfy certain boundary conditions .
the constants are then determined
to satisfy the boundary condition .
numerical calculations show that five or six
terms of the series give a
good approximation to the accurate value as
judged by the closeness with which
the approximate solution satisfies the boundary
condition . the
procedure to be adopted in the case of the general
circular sector and for non-uniform
loading is indicated briefly .
the connexion between the deflexion problem
and that of plane strain in which
the stress function satisfies the equation,
where and have given
values on the boundary, is discussed as a preliminary
to the further consideration
of the latter problem by a method of the same type .
.I 735
.T
the bending of uniformly loaded sectorial plates with
clamped edges .
.A
conway,h.d. and huang,m.k.
.B
j. app. mech. 19, 1962, 5.
.W
the bending of uniformly loaded sectorial plates with
clamped edges .
this paper analyzes the bending of a sectorial plate,
clamped on all edges and subjected to uniformly
distributed load, by using two different methods of superposition
on the elementary solution for a uniformly loaded circular
plate with a clamped edge .
.I 736
.T
the bending of a wedge shaped plate .
.A
woinowsky-krieger,s.
.B
j. app. mech. 20, 1953, 77.
.W
the bending of a wedge shaped plate .
a general method of solution is given in this paper for
the problem of bending of a wedge-shaped thin elastic
plate with arbitrary boundary conditions on the radial edges
in the case of a single load . the solution is carried out for
a plate with clamped edges and a single load on the bisector
radius of the plate . stress distribution along the edges
is shown and the behavior of the solution near the corner
point is discussed for several opening angles of the plate .
.I 737
.T
on the analysis of elastic plates of variable thickness .
.A
mansfield,e.h.
.B
q. j. mech. app. math. 15, 1962, 167.
.W
on the analysis of elastic plates of variable thickness .
the extensional and flexural equations
governing the elastic behaviour of a plate
of variable thickness are expressed in
terms of the laplacian operator .
temperature variations in the plane of the
plate and across the thickness of the plate
are taken into account .
general solutions are given for a rectangular
plate whose thickness varies
exponentially along the length, and for a circular,
or annular, plate whose thickness varies
as a power of the radius .
the large-deflexion equations, including
effects of initial irregularities, are also
discussed .
.I 738
.T
finding zero's of arbitrary functions .
.A
frank,w.l.
.B
j. assoc. comput. mach. 5, 1958, 154.
.W
finding zero's of arbitrary functions .
a method for finding real and complex
roots of polynomial equations, due to
d. muller, is applied to finding roots of
general equations of the form f(z) = 0,
where f(z) is analytic in the neighborhood
of the roots . the procedure does not
depend on any prior knowledge of the
location of the roots nor on any special
starting process . all that is required is
the ability to evaluate f(z) for any
desired value of z . multiple roots can also be
obtained . a general purpose program,
prepared for the univac scientific 1103
and 1103a, is described and numerical
results are presented for the following
applications .. finding eigenvalues of
differential operators ,. finding eigenvalues of
arbitrary matrices ,. finding zeros of the
generalized eigenvalue problem ,. finding
roots of a number of transcendental
equations .
.I 739
.T
the buckling of thin cylindrical shells under axial
compression .
.A
von karman,t. and tsien,h.s.
.B
j. ae. scs. 8, 1941, 303.
.W
the buckling of thin cylindrical shells under axial
compression .
in two previous papers the authors have discussed
in detail the inadequacy of the classical theory of
thin shells in explaining the buckling phenomenon of
cylindrical and spherical shells . it was shown that
not only the calculated buckling load is 3 to 5 times
higher than that found by experiments, but the
observed wave pattern of the buckled shell is also different
from that predicted . furthermore, it was pointed
out that the different explanations for this discrepancy
advanced by l. h. donnell and w. flugge are
untenable when certain conclusions drawn from these
explanations are compared with the experimental facts .
by a theoretical investigation on spherical shells the
authors were led to the belief that in general the
buckling phenomenon of curved shells can only be
explained by means of a non-linear large deflection theory .
this point of view was substantiated by model
experiments on slender columns with non-linear elastic
support . the non-linear characteristics of such structures
cause the load necessary to keep the shell in
equilibrium to drop very rapidly with increase in wave
amplitude once the structure started to buckle . thus, first
of all, a part of the elastic energy stored in the shell is
released once the buckling has started,. this explains
the observed rapidity of the buckling process .
furthermore, as it was shown in one of the previous papers
the buckling load itself can be materially reduced by
slight imperfections in the test specimen and vibrations
during the testing process .
in this paper, the same ideas are applied to the case
of a thin uniform cylindrical shell under axial
compression . first it is shown by an approximate
calculation that again the load sustained by the shell drops
with increasing deflection . then the results of this
calculation are used for a more detailed discussion of
the buckling process as observed in an actual testing
machine .
.I 740
.T
the behaviour of a cylindrical shell under axial compression
when the buckling load has been exceeded .
.A
leggett,d.m.a. and jones,r.p.n.
.B
arc r + m.2190, 1942.
.W
the behaviour of a cylindrical shell under axial compression
when the buckling load has been exceeded .
the value of the compressive stress at which
a thin circular cylindrical shell becomes unstable has been
worked out theoretically by southwell (1914) . subsequent
experimental results, however, have indicated that this
value is appreciably too high and that the form of distortion
which occurs in practice differs from that assumed in theory .
in recent years much work has been done on this problem
in america . lundquist (1933) and donnell (1934)
have concluded that the buckling of a cylindrical shell is greatly
influenced by initial irregularities,. von karman and
tsien (1941) have indicated that a thin cylindrical shell can be
maintained in a buckled state by a compressive load
considerably smaller than that previously predicted by theory .
the present paper is an extension of the work of von karman
and tsien . it shows that the smallest load which will
keep a thin cylindrical shell in a buckled condition is about one-third
of that given by southwell, a result in very fair
agreement with experiment, and that once the cylinder has buckled,
and so long as the stresses remain within the elastic
range of the material, the cylinder has only about one-quarter of its
original stiffness .
.I 741
.T
the behaviour of thin cylindrical shells after buckling
under axial compression .
.A
michielsen,h.f.
.B
j. ae. scs. 15, 1948, 738.
.W
the behaviour of thin cylindrical shells after buckling
under axial compression .
the fundamental investigations of von karman and tsien
on the buckling of cylindrical shells under axial compression
are continued . the energy expression is simplified and
minimized with respect to the axial and circumferential wave-length
parameters . solution of the equations obtained yields curves
of the reduced average stress and of the wave dimensions plotted
against the reduced average strain . they illustrate the behavior
of the cylinder during the buckling process . the minimum
buckling stress is found to be 0.195e(tr) .
.I 742
.T
post-buckling behaviour of axially compressed circular
cylinder shells .
.A
kempner,j.
.B
j. ae. scs. 21, 1954, 329.
.W
post-buckling behaviour of axially compressed circular
cylinder shells .
the postbuckling characteristics of an axially compressed
thin-walled circular cylindrical shell loaded either by dead weights
or by a rigid testing machine are determined . it is shown that
for either loading condition the minimum applied stress in the
postbuckling region is 0.182(er) and that the region of stable
equilibrium corresponding to loading by the rigid testing machine
includes and extends beyond that obtained with dead weight
loading . the work here described is a continuation of work done
earlier by von karman and tsien, by michielsen, and by leggett
and jones .
.I 743
.T
new developments in the nonlinear theories of the buckling of thin
cylindrical shells .
.A
w. f. thielemann
.B
deutsche versuchsanstalt fur luftfahrt mulheim (ruhr), germany
.W
new developments in the nonlinear theories of the buckling of thin
cylindrical shells .
in the present paper a short survey will be given first of the buckling
and postbuckling behavior of isotropic cylindrical shells subjected
to different loading conditions as obtained by the nonlinear theory
of finite deflections of shells during the last twenty years .
next a report will be given on new investigations carried out in the
structures department of the dvl concerning the elastic stability of
isotropic and orthotropic cylindrical shells loaded in axial compression
and internal pressure . these studies are based on the nonlinear theory
of finite deformations . the theoretical rsults will be compared with
new experimental results obtained with a series of axially loaded
pressurized isotropic and orthotropic cylindrical shells .
.I 744
.T
lower buckling load in the non-linear buckling theory
of thin shells .
.A
tsien,h.s.
.B
q. app. math. 5, 1947, 236.
.W
lower buckling load in the non-linear buckling theory
of thin shells .
for thin shells the relation between
the load p and the deflection beyond the
classical buckling load is very often
non-linear . for instance, when a uniform thin
circular cylinder is loaded in the axial
direction, the load p when plotted against the
end-shortening has the characteristic
shown in fig. 1 . if the strain energy s and the
total potential are calculated,
their behavior can be represented by the
curves shown in figs. 2 and 3 . it can be
demonstrated that the branches oc and ab
corresponds to stable equilibrium configurations
and the branch bc to unstable
equilibrium configurations . the point b is then
the point of transition from stable to
unstable equilibrium configurations .
.I 745
.T
an automatic method for finding the greatest or least
value function .
.A
rosenbrock,h.h.
.B
computer jnl. 1960.
.W
an automatic method for finding the greatest or least
value function .
the greatest or least value of a function of several
variables is to be found when the variables
are restricted to a given region . a method is
developed for dealing with this problem and is
compared with possible alternatives . the method
can be used on a digital computer, and is
incorporated in a program for mercury .
.I 746
.T
aeroelastic problems in connection with high speed
flight .
.A
broadbent,e.g.
.B
j. roy. aero. soc. 1956.
.W
aeroelastic problems in connection with high speed
flight .
a review is given of developments
in the field of aeroelasticity during the
past ten years . the effect of steadily increasing
mach number has been two-fold .. on
the one hand the aerodynamic derivatives have
changed, and in some cases brought new
problems, and on the other hand the design for
higher mach numbers has led to thinner
aerofoils and more slender fuselages for which
the required stiffness is more difficult to
provide . both these aspects are discussed,
and various methods of attack on the
problems are considered . the relative merits
of stiffness, damping and massbalance
for the prevention of control surface flutter are
discussed . a brief mention is made of
the recent problems of damage from jet efflux
and of the possible aeroelastic effects
of kinetic heating .
.I 747
.T
bodt freedom flutter of ground launched rocket models
at supersonic and high subsonic speeds .
.A
gaukroger,d.r.
.B
rae r. struct.237, 1957.
.W
bodt freedom flutter of ground launched rocket models
at supersonic and high subsonic speeds .
a theoretical investigation of symmetric
body freedom flutter of a rocket model is described . the results
confirm that structural failures of models were caused
by this type of flutter, and an extension of the investigation
indicates the parameters that are of importance . a high
ratio of body to wing mass and a well forward position of the
overall centre of gravity are conditions under which flutter
may occur . increase of body pitching radius of gyration
and tailplane volume are beneficial .
it is concluded that this type of flutter may be significant
in some aircraft designs, and that the canard has no
advantage in this respect over the conventional lay-out of wing
and tailplane .
.I 748
.T
subsonic aerodynamic flutter derivatives for wings and control surfaces,
/compressible and incompressible flow/ .
.A
minhinnick, i. t.
.B
r.a.e. rep. structs. 87. july 1950 .
.W
subsonic aerodynamic flutter derivatives for wings and control surfaces,
/compressible and incompressible flow/ .
this report gives tables of the two-dimensional subsonic flutter
derivatives,. where possible the values given are based on the published
work of various authors, but some have been specially calculated for
this report . wing derivatives are given for mach numbers 0, 0.5, 0.6
and 0.7 for the frequency parameter range 0 /0.04/ 0.2 /0.2/ 1.6 and
mach numbers 0 and 0.7 for frequency parameter 5.0 . control surface
derivatives are given for mach numbers 0 and 0.7 for control surface/
wing chord ratios 0.02 /0.02/ 0.10 /0.05/ 0.50 and frequency parameters
are also given for mach numbers 0, 0.5, 0.6 and 0.7 for frequency
parameter 0 /0.04/ 0.2 /0.2/ 1.4 . control surface-tab derivatives are
given for some particular values of the variables and methods of
obtaining approximate values of these derivatives for other values of
the variables are suggested . control surface and tab derivatives are in
all cases for no aerodynamic balance .
.I 749
.T
the aerodynamic effects of aspect ratio and sweepback
on wing flutter .
.A
molyneux,w.g. and hall,h.
.B
arc r + m.3011.
.W
the aerodynamic effects of aspect ratio and sweepback
on wing flutter .
the report describes tests to obtain direct
measurements of the aerodynamic effects of aspect ratio and
sweepback on wing flutter . the tests were made on rigid
wings with root flexibilities .
it is shown that measured effects of aspect ratio and
sweepback on the flutter of these wings can be represented
quite closely in flutter calculations based on two-dimensional
flow theory by multiplying the two-dimensional
aerodynamic coefficients by appropriate factors . the effect of
sweepback is represented by multiplying all aerodynamic
coefficients by cos, where is the wing leading-edge
sweepback, and the effect of aspect ratio is represented by
multiplying the aerodynamic damping coefficients by 1f(a) and,
the stiffness coefficients by 1(f(a)) where a is the
aspect ratio .
for the wings tested an average value for
f(a) is f(a) = (1 + (0.8a)) .
.I 750
.T
transonic flow in two dimensional and axially symmetrical
nozzles .
.A
hall,i.m.
.B
arc 23,347, 1961.
.W
transonic flow in two dimensional and axially symmetrical
nozzles .
by means of suitable expansions
in inverse powers of r, the
radius of curvature of the nozzle profile
at the throat measured in throat
half-heights, the velocity components
in the throat region of a
convergent-divergent nozzle can be
calculated . the first three terms of
the series solution have been obtained
both for two-dimensional and for
axially-symmetric nozzles . the
numerical accuracy of the solution is
confirmed by comparison with the
known exact solution along the branchline .
.I 751
.T
a note on the use of end plates to prevent three dimensional
flow at the ends of bluff cylinders .
.A
cowdrey,c.f.
.B
npl aero. r.1025, 1962.
.W
a note on the use of end plates to prevent three dimensional
flow at the ends of bluff cylinders .
the results are given of
some observations of the effects of
end plates on the three-dimensional
separated flow at the ends of
cylindrical models . while these are
by no means exhaustive, it is felt
that they are of sufficient interest
to merit putting on record .
.I 752
.T
slender not-so-thin wing theory .
.A
cooke,j.c.
.B
rae r.aero.2660, 1962.
.W
slender not-so-thin wing theory .
a method for making an approximate thickness correction to slender
thin-wing theory is presented . the method is tested by applying it to
cones with rhombic cross-sections and the agreement is found to be good
if the cones are not too thick . it is then suggested that the
thickness correction to slender thin-wing theory may be applied
unchanged to linear thin-wing theory . this suggestion is compared with
some experiments on delta wings and it is found that there is
considerable improvement over thin-wing theory near the centre line, but that
this improvement is not maintained as the wing tips are approached .
.I 753
.T
development of a quasi-steady approach to flutter and
correlation with kernel-function results .
.A
gravitz,s.i., laidlaw,w.r., bryce,w.w. and cooper,r.e.
.B
j.ae.scs. 29, 1962, 445.
.W
development of a quasi-steady approach to flutter and
correlation with kernel-function results .
the quasi-steady approach to flutter utilizes experimental or
theoretical steady-state aerodynamic data to arrive at increased
understanding of the flutter mechanism, and also, in many cases,
acceptably accurate quantitative flutter predictions .
circulation lag effects are neglected, but aerodynamic damping is
included in the evaluation of the air forces . situations requiring
the inclusion of rate aerodynamics for accurate flutter estimation
are specified .
a quasi-unsteady approach is also discussed, in which the
approximate magnitude of the circulation lag function at flutter
is included in simple modifications of quasi-steady parameters .
closed-form solutions are derived for the flutter characteristics
of a typical section with and without rate aerodynamics .
application is then made to the rational flutter analysis of
three-dimensional multi-degree-of-freedom lifting surfaces .
a specific planform is evaluated in the mach-number range
from zero to two . quasi-steady, quasi-unsteady, and
kernel-function results are compared subsonically . quasi-steady
results are utilized supersonically .
primary applications of the quasi-steady approach are in the
areas of preliminary design and parameter-variation studies,
modification of more sophisticated flutter theories to force
compatibility with available steady-state data, and flutter evaluation
of complex configurations which can be rationally analyzed by
steady-state aerodynamic theories, but for which no complete
unsteady aerodynamic theories are presently available .
.I 754
.T
heat transfer through laminar boundary layers on
semi-infinite cylinders of arbitrary cross section .
.A
bourne,d.e. and wardle,s.
.B
j. ae. scs. 29, 1962, 460.
.W
heat transfer through laminar boundary layers on
semi-infinite cylinders of arbitrary cross section .
this paper shows how to calculate the rate of heat transfer
through a laminar boundary layer on a semi-infinite cylinder of
arbitrary cross section . the cylinder is placed in a stream of
incompressible fluid, the flow at infinity being parallel to the
generators, and is maintained at a uniform temperature . a
series solution for small downstream distances and an asymptotic
formula for large downstream distances are given . to cover
the intermediate range an approximate pohlhausen solution is
obtained,. a correction of the error involved in the pohlhausen
solution is suggested which, it is believed, will lead to final errors
of at most 2 percent . the calculations are applied to elliptic
cylinders, and illustrate the effect on the local rate of heat transfer
of varying the ratio of the major and minor axes of cross section,
the length of perimeter being held fixed .
.I 755
.T
oscillatory derivative measurements on sting-mounted
wind tunnel models method of test and results for pitch
and yaw on a cambered ogee wing at mach numbers up
to 2. 6.
.A
thompson,j.s.
.B
rae r.aero.2668, 1962.
.W
oscillatory derivative measurements on sting-mounted
wind tunnel models method of test and results for pitch
and yaw on a cambered ogee wing at mach numbers up
to 2. 6.
this report describes a method which has been developed for measuring
oscillatory derivatives on sting-mounted models in the 8 ft by 8 ft
supersonic tunnel at r.a.e. bedford . direct and cross derivatives with
respect to angular displacements and velocities in pitch and yaw have
been measured satisfactorily, and results are given of tests on a
cambered ogee wing at six mach numbers from 0.2 to 2.6 . some tests
were made on this model in the course of the preliminary development
work in the 13 ft by 9 ft low speed wind tunnel, and results of these
are included .
.I 756
.T
further comments on the inversion of large structural matrices .
.A
charles h. samson, jr.
.B
professor, departments of aeronautical and civil engineering,
a. and m. college of texas
.W
further comments on the inversion of large structural matrices .
in a recent note, klein referred to a paper co-authored by the writer,
and to ref. 3 . regarding the subject of inversion of large-order
matrices, klein stated that he would show 'that the situation is not as
hopeless as the anove-mentioned authors intimate' .
the purpose of this note is not to take exception to klein/s
conclusions, but rather to disagree with his implication that the
authors of ref. 2 were pessimistic with respect to large-matrix
inversions . two general methods of analysis were treated.. the
method of consistent distortion and the method of transfer matrices .
the first method leads directly to a relatively large matrix of
structural coefficients of both internal forces and displacements .
this matrix must be inverted to solve the problem . the second method
ultimately produces a relatively small matrix requiring inversion.,
however, to arrive at this point one must perform a number of matrix
multiplications .
.I 757
.T
an investigation of the flow about a plane half-wing
of cropped delta planform and 6( symmetrical section
at stream mach numbers between 0. 8 and 1. 41 .
.A
rogers,e.w.e., hall,i.m. and berry,c.j.
.B
arc r + m.3286, 1960.
.W
an investigation of the flow about a plane half-wing
of cropped delta planform and 6( symmetrical section
at stream mach numbers between 0. 8 and 1. 41 .
a study has been made of the flow development
over the wing as the incidence and stream
mach number vary and this is illustrated by surface pressure
distributions and oil-flow patterns . the growth
and movement of the two main surface shocks (the rear and
forward shocks) is discussed, and conditions for
flow separation through these shocks are considered . for
the rear shock, which has little sweep, these
conditions are similar to those for shock-induced separation
on two-dimensional aerofoils . the forward
shock is comparatively highly swept and separation seems
to correspond to two rather different but
simultaneously-attained conditions, one related to the
component mach number normal to the shock front
and the other to the position of the reattachment line .
the flow in the region between the leading edge and
the forward shock is shown to have certain characteristics
analogous to those found upstream of the shock on
two-dimensional aerofoils . to the rear of the forward
shock, but ahead of the rear shock, the flow at low
supersonic speeds resembles in some respects that about
a simple cone .
the general flow development is related in the
text to the wing lift and pitching moment, and the drag .
the first two are most affected by the aft movement
of the rear shock, which also stimulates the transonic
drag rise . the lift-dependent drag is shown to be
influenced by the appearance of leading-edge separation
and possibly also by some stage in the development
of the forward shock .
the flow over the cropped-delta planform is
noteworthy for the absence of the strong outboard shock
and this is attributed partly to the cropped tip and
partly to the unswept trailing edge . a comparison is made
with results obtained during preliminary tests in
which the wing planform closely resembled that of a true
delta .
.I 758
.T
the lower bound of attainable sonic-boom over-pressure
and design methods of approaching this limit .
.A
carlson,h.w.
.B
nasa tn.d1494, 1962.
.W
the lower bound of attainable sonic-boom over-pressure
and design methods of approaching this limit .
from a study of existing sonic-boom
theory it has been possible to establish
an approximate lower bound of attainable
sonic-boom overpressure, which depends
only on the airplane length, weight, and
volume and on the flight conditions .
this lower bound may be approached over
a narrow range of flight conditions
through the application of appropriate
design considerations . in general, for
intermediate values of lift coefficient
the major portion of the lift generating
surfaces must be located aft of the
maximum cross-sectional area, whereas for
higher values of lift coefficient
the maximum area must be well forward and or
the lift-producing surfaces must extend well toward the airplane nose .
.I 759
.T
stability investigation of a blunted cone and a blunted
ogive with a flared cylinder afterbody at mach numbers
from 0. 30 to 2. 85 .
.A
coltrane,l.c.
.B
nasa tn.d1506, 1962.
.W
stability investigation of a blunted cone and a blunted
ogive with a flared cylinder afterbody at mach numbers
from 0. 30 to 2. 85 .
a cone with a blunt nose tip and a
blunt nose tip and a 20 flared cylinder
afterbody have been tested in free
flight over a mach number range from 0.30
to 2.85 and a reynolds number range
from 1 x 10 to 23 x 10 . time histories,
cross plots of force and moment
coefficients, and plots of the longitudinal-force
coefficient, rolling velocity,
aerodynamic center, normal-force-curve slope,
and dynamic stability are presented .
with the center-of-gravity location at about
models were both statically and dynamically
stable throughout the mach number
range . for the cone, the average aerodynamic
center moved slightly forward with
decreasing speeds and the normal-force-curve
slope was fairly constant throughout
the speed range . for the ogive, the average
aerodynamic center remained
practically constant and the normal-force-curve
slope remained practically constant to
a mach number of approximately 1.6 where
a rising trend was noted . maximum drag
coefficient for the cone, with reference
to the base area, was approximately 0.6,
and for the ogive, with reference to the
area of the cylindrical portion, was
approximately 2.1 .
.I 760
.T
inelastic buckling of initially imperfect cylindrical
shells subject to axial compression .
.A
lee,l.h.n.
.B
j. ae. scs. 29, 1962, 87.
.W
inelastic buckling of initially imperfect cylindrical
shells subject to axial compression .
an analytical and experimental study is made for inelastic
instability of initially imperfect cylindrical shells subject to
axial compression . donnell's equations and the principle of
virtual work are adapted to determine the effects of initial
imperfections on the buckling modes and the critical buckling
stresses . the deformation theory and the incremental theory
of plastic stress-strain relationships are both considered . the
experimental results of ten tests on specimens made of aluminum
alloy 3003-0 are presented . comparison of experimental with
theoretical results indicates that the application of the
deformation theory provides a fairly accurate prediction of buckling
strength, but fails in this case to yield a correct description of
post-buckling behavior . on the other hand, the application of
the incremental theory, which is mathematically and physically
more rigorous, leads to an overestimation of buckling strength,
even though initial imperfections are considered . this paradox
has existed for years, and remains to be resolved .
.I 761
.T
buckling of sandwich under normal pressure .
.A
yao,j.c.
.B
j. ae. scs. 29, 1962, 264.
.W
buckling of sandwich under normal pressure .
a theoretical study is made of the buckling of a sandwich sphere
comprised of a core layer of low-modulus material and two thin
facing layers of higher modulus material . the solution for the
buckling resistance of the sphere under normal external pressure
is obtained by linearized theory, and is reducible to the classical
solution for monocoque spherical shells . critical buckling
pressures are calculated for various radius-thickness ratios and sphere
materials .
.I 762
.T
allowable axial loads and bending moments for inelastic structures
under nonuniform temperature distribution .
.A
b. e. gatewood and r. w. gehring
.B
the ohio state university and north american aviation, inc.
.W
allowable axial loads and bending moments for inelastic structures
under nonuniform temperature distribution .
a strain-analysis method is derived and demonstrated for the
calculation of design allowable load-strain curves for the cross section
of a structure supporting axial loads and bending moments . the
temperature effects of thermal stresses and changed material properties
and all inelastic effects are included in the calculations so that
the final curve is a design curve for the applied stresses as calculated
by room-temperature elastic procedures . the method allows for sequence
application and removal of load and temperature, as well as cycling
of load and/or temperature . applications are shown for a rectangular
bar under temperature cycling with axial loads and/or bending moments
and for a box beam with one bending-moment temperature cycle .
interaction curves beyween axial load and bending moment with inelastic
effects included are given, the calculations being done on a digital
computer . a procedure is given for using the method to construct
design curves .
.I 763
.T
effects of internal pressure on the buckling of circular-cylindrical
shells under bending.
.A
weingarten,v.i.
.B
.W
effects of internal pressure on the buckling of circular-cylindrical
shells under bending.
the effect of internal pressure on the small-deflection buckling
of thin-walled cylinders under bending is investigated by means
of a modified donnell equation . the results indicate that the
maximum critical stress due to bending increases with internal
pressure, unlike the case of pressurized cylinders under
compression . these results represent the moment at which
significant deformations appear in the cylinder, rather than the
maximum moment able to be carried, but may be a good
approximation to the latter for metal cylinders .
.I 764
.T
breathing vibrations of a circular shell with an internal
liquid .
.A
lindholm,u.s., kana,d.d. and abramson,h.n.
.B
j. ae. scs. 29, 1962, 1052.
.W
breathing vibrations of a circular shell with an internal
liquid .
resonant breathing frequencies and mode shapes are
determined experimentally for a thin-walled, circular cylindrical shell
containing a nonviscous incompressible liquid . the resonant
frequencies determined for the full shell are in good agreement
with those predicted by reissner's shallow-shell vibration theory
with the inclusion of an apparent-mass term for the liquid . the
effect of the internal liquid on the shell mode shapes is significant
only for the partially full shell . in this case the circumferential
node lines tend to shift toward the bottom or filled portion of the
shell .
excitation of low-frequency liquid-sloshing motion by
high-frequency forced oscillation of a partially filled shell occurred in
many cases . this low-frequency liquid response is tentatively
explained as being excited by a beat frequency in the forced
oscillation . a similar type of response has been reported by
yarymovych in axially excited rigid tanks .
.I 765
.T
clamped short oval cylindrical shells under hydrostatic
pressure .
.A
vafakos,w.p.
.B
j. ae.scs. 29, 1962, 1347.
.W
clamped short oval cylindrical shells under hydrostatic
pressure .
the principle of the minimum of the total potential is
employed to obtain stresses and displacements for clamped, short,
oval cylindrical shells under hydrostatic pressure . classical
shell theory, in which buckling effects are not considered, was
used . a fourier series is assumed for the deflections in the
closed circumferential direction so that the partial differential
equations of equilibrium are replaced by a set of ordinary
differential equations . the energy solution is compared with a
simplified approximation which can be considered an equivalent circular
cylinder solution . graphs of the significant stresses and
displacements are presented for oval cylinders having major to minor
axis ratios of 1.10, 1.30, and 1.50 . it is shown that the maximum
stresses and displacements increase significantly as the major to
minor axis ratio is increased .
.I 766
.T
experimental investigation at mach number of 3. 0 of
effects of thermal stress and buckling on flutter characteristics
of flat single-bay panels of length-width ratio 0. 96 .
.A
dixon,s.c.
.B
nasa tn.d1485, 1962.
.W
experimental investigation at mach number of 3. 0 of
effects of thermal stress and buckling on flutter characteristics
of flat single-bay panels of length-width ratio 0. 96 .
flat, single-bay, skin stiffener
panels with length-width ratios of 0.96
were tested at a mach number of 3.0,
at dynamic pressures ranging from 1,500 to
stagnation temperatures from 300 f to
effects of thermal stress and buckling on the
flutter of such panels . the panel
supporting structure allowed partial thermal
expansion of the skins in both the
longitudinal and lateral directions . panel
skin material and skin thickness were varied .
a boundary faired through the
experimental flutter points consisted of a
flat-panel portion, a buckled-panel
portion, and a transition point, at the
intersection of the two boundaries,
where a panel is most susceptible to flutter .
the flutter region consisted of two
fairly distinct sections, a large-amplitude
flutter region and a small-amplitude
flutter region . the results show that an
increase in panel skin temperature
flutter . the flutter trend for buckled
panels is reversed . use of a modified
temperature parameter, which approximately
accounts for the effects of differential
pressure and variations in panel skin
material and skin thickness, reduced the
scatter in the data which resulted when
these effects were neglected . the results
are compared with an exact theory for
clamped panels for the condition of zero
midplane stress . in addition, a
two-mode /transtability/ solution for clamped
panels is compared with the
experimentally determined transition point .
.I 767
.T
mathematical techniques applying to the thermal fatigue behaviour
of high temperature alloys .
.A
.B
.W
mathematical techniques applying to the thermal fatigue behaviour
of high temperature alloys .
during thermal fatigue testing
of a specimen with a thin edge, or
during rapid temperature changes in the gas
flow past turbine blades, the thin
edges are deformed plastically in compression
during heating and subsequently
creep in tension as the bulk of the specimen
or blade heats up . the plastic
deformation is determined from temperature
distributions, which are calculated
by biot's variational method . the creep
deformation is determined as a function
of time by a differential equation, which
expresses the balance between increasing
elastic stress and reduction of stress due
to creep relaxation, and which is solved
to a riccati equation soluble in
terms of bessel functions, or (iii) by transformation
to a second-order differential
equation with a periodic coefficient .
using the thermal stresses obtained from
the solution of the differential equation, the theoretical thermal
fatigue endurance
is determined from cyclic (mechanical) stress
endurance data . agreement between
theoretical and experimental thermal fatigue
endurances is obtained, over ranges
of temperature, strain, and strain rate, or equivalently, over ranges
of temperature-edge radius and heat transfer coefficient .
this agreement supports the use of
the theoretical methods in wider contexts .
the accuracy of the temperature
distributions is better than the accuracy of
other factors entering into the correlation
between theoretical and experimental endurances .
improvement in the
interpretation of experimental results requires
consideration of the alteration
of the stress cycles during the course of thermal
fatigue testing . this requirement
is catered for partially by the various solutions of the differential
equation for thermal stress .
.I 768
.T
formulae for use with the fatigue load meter in the
assessment of wing fatigue life .
.A
phillips,j.
.B
rae tn. struct.279, 1960.
.W
formulae for use with the fatigue load meter in the
assessment of wing fatigue life .
this note gives a method for the derivation of suitable constants
which, when multiplied by the readings recorded at each appropriate
acceleration level on a fatigue load meter and then added together, give
directly the proportion of fatigue life used up in the wing . it is
suggested that when the estimated proportion is of order 80, then a more
detailed assessment of fatigue life should be made .
.I 769
.T
local circumferential buckling of thin circular cylindrical
shells .
.A
johns,d.j.
.B
nasa tn.d1510, 1962, 267.
.W
local circumferential buckling of thin circular cylindrical
shells .
the problem of circumferential
buckling of a thin circular
cylindrical shell due to compressive
hoop stresses which vary in the axial
direction is examined . for
extremely localised compressive hoop stress
distributions resulting from
thermal discontinuity effects, or from a
uniform, radial line loading,
the buckle pattern should also be
localised . simplified analyses
into these two types of problem are
considered which show that only
a limited number of buckle deflection
modes needs to be assumed .
.I 770
.T
the flow of a compressible fluid past a sphere .
.A
caplan,c.
.B
naca tn.762, 1940.
.W
the flow of a compressible fluid past a sphere .
the flow of a compressible fluid past a sphere fixed
in a uniform stream is calculated to the third order of
approximation by means of the janzen-rayleigh method .
the velocity and the pressure distributions over the
surface of the sphere are computed and the terms involving
the fourth power of the mach number, neglected in rayleigh's
calculation, are shown to be of considerable importance as
the local velocity of sound is approached on the sphere .
the critical mach number, that is, the value of the mach
number at which the maximum velocity of the fluid past the
sphere is just equal to the local velocity of sound, is
calculated for both the second and the third
approximations and is found to be, respectively, and .
.I 771
.T
on the flow of a compressible fluid past a sphere .
.A
tamada,k.
.B
proc. physico-math. soc japan, 21, 1939, 743.
.W
on the flow of a compressible fluid past a sphere .
it was shown by raleigh (philos. mag. 32, 1 (1916))
that the velocity potential for the subsonic flow of a
compressible fluid past a sphere can be expressed as a power
series in terms of mach's number m (which is the ratio of
the undisturbed velocity u, divided by the velocity of sound
for the undisturbed flow) . the equation in question is
and boundary conditions are prescribed for
raleigh himself computed the first two terms of this series,.
the author finds the third term . he gives some graphs
showing numerical differences between raleigh's and his
approximation .
.I 772
.T
an experimental study of jet-flap compressor blades .
.A
clark, e.l. /jnr./ and ordway, d.e.
.B
j. aero. sc. november 1959. p. 698-702, 738 .
.W
an experimental study of jet-flap compressor blades .
the results of a preliminary experimental investigation to determine the
feasibility of using the jet flap to improve the section
characteristics of an axial-flow compressor blade are presented and discussed
trailing edge . internal design of the blade is described and details
of the resulting jet flow are given . also included are wind-tunnel
design and test procedures for the two-dimensional cascade used in the
test .
test results are presented in the form of the measured turning angle,
pressure rise, and lift coefficient . they are examined with particular
reference to the prevention of rotating stall .
.I 773
.T
q . app . math . 7, 1950, 381 . experiments on porous-wall
cooling and flow separation control in a supersonic
nozzle .
.A
green,l. and nall,k.l.
.B
j. ae. scs. 1959, 689.
.W
q . app . math . 7, 1950, 381 . experiments on porous-wall
cooling and flow separation control in a supersonic
nozzle .
control of flow separation by fluid injection at one diverging
boundary of a two-dimensional, transparent-walled de laval
nozzle was investigated by spark schlieren photography of dry
nitrogen flows expanded from two stagnation temperatures
injection conditions at the permeable boundary were varied by
the use of three grades of porous stainless steel with nominal pore
diameters of 10, 20, and 30 microns, through which nitrogen was
forced by coolant reservoir pressures of 25, 50, and 100 psig, in
addition to the case of no forced injection . pressure
distribution measurements were made along the nonpermeable diverging
boundary . it was found that flow separation at expansion ratios
approaching the optimum value for maximum thrust coefficient
could be induced at the porous wall by a local injection mass
velocity of the order of a few per cent of the local main-stream
mass velocity . separation at the solid boundary was not
noticeably influenced by injection at the opposite wall, and the
asymmetrical separation thus effected jet deflections of up to 10
degrees at the lower stagnation-pressure levels . variation of the
wall heat-transfer condition by changing the stagnation
temperature did not significantly influence separation behavior .
temperature measurements at the reservoir face of the porous
section, together with use of published correlations and of the
rube-sin analysis for estimation of stream-side stanton numbers under
noninjection and injection conditions, respectively, permitted
heat-transfer calculations which indicated that the effectiveness
of the transpiration technique in controlling nozzle wall
temperatures derives primarily from intimate fluid-solid contact in a
porous material of high specific surface .
.I 774
.T
general characteristics of the flow through nozzles
at near critical speeds .
.A
sauer,r.
.B
naca tm.1147, 1944.
.W
general characteristics of the flow through nozzles
at near critical speeds .
the characteristics of the position and form of
the transition surface through the critical velocity
are computed for flow through flat and round nozzles
from subsonic to supersonic velocity . corresponding
considerations were carried out for the flow about profiles
in the vicinity of sonic velocity .
.I 775
.T
studies on two dimensional flows of compressible fluid.
.A
.B
.W
studies on two dimensional flows of compressible fluid.
it is well-known that when the flow is everywhere subsonic in a field
of flow, the nature of the two-dimensional isentropic flow of a
compressible perfect fluid differs only slightly from that of the
corresponding flow of an incompressible perfect fluid . thus, in such a
case, we can calculate the field of flow by any of the well-known
methods of approximation . on the other hand, if the flow is supersonic
throughout the field, we can determine the flow pattern by the method of
characteristics .
.I 776
.T
force measurements on square and dodecagonal sectional
cylinders at high reynolds numbers .
.A
cowdrey,c.f. and lawes,j.a.
.B
npl. aero.351.
.W
force measurements on square and dodecagonal sectional
cylinders at high reynolds numbers .
results are given of measurements in the compressed air tunnel
of the forces on two cylinders, one of square cross-section and the
other dodecagonal . the tests were carried out at various reynolds
numbers ranging from approximately 0.1 x 10 to 5.5 x 10, based on
the distance between parallel faces .
.I 777
.T
a technique for rendering approximate solutions to
physical problems uniformly valid .
.A
lighthill,m.j.
.B
phil. mag. 40, 1949, 1179.
.W
a technique for rendering approximate solutions to
physical problems uniformly valid .
a method is described for treating
some of the characteristically
non-linear problems of physics, in
particular those involving a non-linear
partial differential equation for
which an approximate linearization is
permissible everywhere except in a
limited region, such as the
neighbourhood of (5) a singular characteristic
of the approximate solution, or of
approximation is valueless . the
method involves a transformation of
an independent variable, which is
determined progressively with successive
approximations to the solution ..
only one step being necessary if a
first approximation valid uniformly
be obtained . the method is most
easily understood in its application
to simple first order ordinary
differential equations, which are
studied in detail in 2 and 3 as a
preparation for the extension to
more complicated problems in 4, 5
and 6 . physically, the longest
section, 6, concerns the /spread/ of
a progressive wave at infinity,
an important and essentially non-linear
process .
.I 778
.T
an integral related to the radiation integrals .
.A
powell,e.o.
.B
phil. mag. 34, 1943, 600.
.W
an integral related to the radiation integrals .
the author points out the relation of the integral
to problems in astrophysics and quantum mechanics, and
because of its importance supplies a table of values . the
table gives rl(x) to seven places of decimals from x=0 to
x=6.00 at intervals of 0.01 . second order central differences
are tabulated to assist in interpolation .
.I 779
.T
calculation and compilation of the unsteady lift functions for a rigid
wing subjected to sinusoidal gusts and to sinusoidal sinking
oscillations .
.A
drischler, j.a.
.B
naca tn 3748, october 1956
.W
calculation and compilation of the unsteady lift functions for a rigid
wing subjected to sinusoidal gusts and to sinusoidal sinking
oscillations .
the total lift responses of wings to sinusoidal gusts and to sinusoidal
vertical oscillations are calculated from the response to gust
penetration and to a sudden change in sinking velocity through use of the
well-established reciprocal relations for unsteady flow . the cases
considered are two-dimensional wings in incompressible, subsonic
compressible, sonic, and supersonic flow,. elliptical and rectangular wings
in incompressible flow,. wide rectangular and delta wings in supersonic
flow,. and delta wings of vanishingly low aspect ratio in
incompressible and compressible flow . for most of the cases considered,
closed-form expressions are given and the final results are presented in
the form of plots of the square of the modulus of the lift coefficient
for wings in a sinusoidally oscillating gust and in the form of the real
and imaginary parts of the lift component for wings undergoing
sinusoidal sinking oscillations . a summary table is presented as a guide to
the scope and results of this paper,. this table contains the figure
and equation numbers for the types of flow and plan forms considered .
.I 780
.T
the transonic characteristics of 38 cambered rectangular
wings of varying aspect ratio and thickness as determined
by transonic-bump technique .
.A
nelson,w.h. and krumm,w.j.
.B
naca tn.3502, 1955.
.W
the transonic characteristics of 38 cambered rectangular
wings of varying aspect ratio and thickness as determined
by transonic-bump technique .
an investigation to determine
the effects of camber on the
aerodynamic characteristics of a series
of rectangular wings having various
aspect ratios and thickness-to-chord
ratios was conducted in the ames
the transonic-bump method .
the mach number range of the
investigation was from 0.6 to 1.12, with
a corresponding reynolds number
range of 1.7 to 2.2 million . the lift,
drag, and pitching-moment data
are presented for wings having aspect
ratios of 4, 3, 2, 1.5, and 1,
and naca 63a2xx and 63a4xx sections with
thickness-to-chord ratios of
.I 781
.T
use of subsonic kernel function in an influence-coefficient method of
aeroelastic analysis and some comparisons with experiment .
.A
john l. sewall, robert w. herr, and charles e. watkins
.B
technical note d-515
.W
use of subsonic kernel function in an influence-coefficient method of
aeroelastic analysis and some comparisons with experiment .
this paper illustrates the development and application of an
influence-coefficient method of analysis for calculating the response
of a flexible wing in an airstream to an oscillating disturbing force
and for treating such aeroelastic instabilities as flutter and
divergence . aerodynamic coefficients are derived on the basis of
lifting-surface theory for subsonic compressible flow by use of the method
presented in nasa technical report r-48 .
application of the analysis is made to a uniform cantilever
wing-tip tank configuration for which responses to a sinusoidal disturbing
force and flutter speeds were measured over a range of subsonic mach
numbers and densities . calculated responses and flutter speeds based
on flexibility influence coefficients measured at nine stations are in
good agreement with experiment, provided the aerodynamic load is
distributed over the wing so that local centers of pressure very nearly
coincide with these nine influence stations . the use of experimental
values of bending and torsional structural damping coefficients in the
analysis generally improved the agreement between calculated and
experimental responses . some calculations were made to study the
effects of density on responses near the flutter conditions, and linear
response trends were obtained over a wide range of densities .
.I 782
.T
calculated subsonic span loads and resulting stability derivatives of
unswept and 45degree sweptback tail surfaces in sideslip and steady roll .
.A
queiijo, m.j. and riley, d.r.
.B
naca, tn 3245, 1954 .
.W
calculated subsonic span loads and resulting stability derivatives of
unswept and 45degree sweptback tail surfaces in sideslip and steady roll .
subsonic span loads and the resulting stability derivatives have been
calculated for a systematic series of vertical- and horizontal-tail
combinations in sideslip and in steady roll in order to provide
information embracing a wide range of probable tail configurations . all
calculations were made by application of the discrete-horseshoe-vortex
method to the problem of estimating loads on intersecting surfaces . the
investigation covered variations in vertical-tail aspect ratio, the
ratio of horizontal-tail aspect ratio to vertical-tail aspect ratio, the
effects of horizontal-tail dihedral angle /for the sideslip case/, and
the effects of vertical position of the horizontal tail for surfaces
having their quarter-chord lines swept back 0degrees and 45degrees . the
results of the investigation are presented in charts from which the
span loads for the various conditions can be obtained . the resulting
stability derivatives are presented as vertical- and horizontal-tail
contributions as well as total-tail-assembly derivatives .
the results of this investigation, which was made for a wider range of
geometric variables than previous studies, showed trends which were in
general agreement with the results of previous investigations . also
presented in this paper and used in the computations is an extensive
table of values of sidewash due to a rectangular vortex .
.I 783
.T
a method for calculating the subsonic steady-state loading on an
airplane with a wing of arbitrary planform and stiffness .
.A
gray, w.l.
.B
naca tn 3030, 1953 .
.W
a method for calculating the subsonic steady-state loading on an
airplane with a wing of arbitrary planform and stiffness .
a method for computing the steady-state span load distribution on an
elastic airplane wing for specified airplane weights and load factors is
given . the method is based on a modification of the weissinger
l-method and applies at subcritical mach numbers . it includes the effects
of external stores and fuselage on the spanwise loading .
modifications are outlined for treating tail-boom and tailless airplane
configurations and for calculating the divergence dynamic pressure of a
swept wing with a large external store . a method is also outlined for
reducing wind-tunnel data to obtain effective aerodynamic coefficients
which are free of model flexibility effects . the effects of mach number
can readily be evaluated from the aerodynamic coefficients thus
obtained .
.I 784
.T
heat transfer through the laminar boundary layer on
a circular cylinder in axial incompressible flow .
.A
bourne,d.e. and davies,d.r.
.B
q. j. mech. app. math. 11, 1958, 52.
.W
heat transfer through the laminar boundary layer on
a circular cylinder in axial incompressible flow .
this paper presents a method of calculating
the distribution of rate of heat transfer
into a laminar incompressible boundary layer
from the exterior surface of a long thin
circular cylinder, when the surface of the
cylinder is maintained at a constant
temperature and the flow is parallel to the
cylinder axis,. the temperature difference
between the surface and the main stream
is taken to be small enough to neglect
buoyancy effects . a series solution, valid
for small downstream distances from the
nose, has been obtained already by seban,
bond, and kelly . this is now extended
by deriving an asymptotic series solution,
valid at large downstream distances, and
bridging the gap between these two series
solutions by an approximate solution,
based on the method used recently by davies
and bourne to calculate heat transfer
from a flat plate . the calculation is used to
demonstrate the effect of curvature
and of prandtl number on the local rate of heat
transfer at various downstream
distances by comparing with the corresponding flat plate results .
.I 785
.T
the flow of fluid along cylinders .
.A
cooke, j.c.
.B
quart. j. mech. app. math, vol.x /3/, 1957, p. 312-321 .
.W
the flow of fluid along cylinders .
the boundary layer equations for uniform flow parallel to the generators
of any cylinder without corners are put into the form of a series of
linear third-order differential equations . the first three of these are
the same as those obtained by seban and bond /1/ for a circular
cylinder and solved by kelly /2/ . the rest have additional terms
depending on the radius of curvature of the cylinder and its derivatives . the
problem is also attacked by a pohlhausen method as far as four terms of
the series . for large distances from the front, rayleigh's method, as
given by hasimoto /3/, gives the first two terms of an asymptotic
expansion for the drag . explicit calculations are made of the drag of
an elliptic cylinder of eccentricity 1/2 3 . there is evidence that the
drag is everywhere less than that of a circular cylinder of the same
perimeter .
.I 786
.T
the skin friction on infinite cylinders moving parallell to their length .
.A
batchelor, g.k.
.B
quart. j. mech. app. math. vol. vii, /2/, 1954, p. 179-192 .
.W
the skin friction on infinite cylinders moving parallell to their length .
the frictional force on a cylinder moving steadily parallel to its
length through a viscous liquid which is initially at rest is determined
with reasonable accuracy over the whole range of values of the duration
of the motion and for a wide variety of shapes of the cylinder
cross-section . when the time t is small, the first approximation gives a
force per unit area which is the same as that for a flat plate of
infinite width . the second approximation takes the shape of the cylinder
into account and the force on unit length of cylinder is determined in
terms of the number of corners, and their angles, in the cylinder cross
linder is the same, to this approximation, as that on a circular
cylinder of the same perimeter . for large values of t the determination of
the frictional force is reducible to that of a potential problem, the
solution of which is known for a number of different shapes . the
approximations for small and large values of t for any one cylinder do
not overlap but can be joined without much ambiguity . for no value of t
do the forces on cylinders of different shape /excluding those whose
curvature is not everywhere inwards/ differ by more than about 25 per
cent .
.I 787
.T
rayleigh's problem for a cylinder of arbitrary shape .
.A
hasimoto, h.
.B
j. physical soc. of japan, vol. 9 /4/, 1954, p. 611-619 .
.W
rayleigh's problem for a cylinder of arbitrary shape .
the motion of an incompressible viscous fluid generated by a cylinder of
arbitrary cross-sectional form which is started to move suddenly from
rest with uniform velocity in the direction of its length is considered
formulae in powers of are derived for the velocity distribution /valid
in the vicinity of the cylinder/ and for the frictional drag on the
cylinder, correct to the order of a, where a is the characteristic length
of the cross section, v is the kinematic viscosity, and t is the time .
these formulae are given in terms of only the analytic function which
maps conformally the region outside the cross section of the cylinder
onto the region outside the unit circle, and of certain integrals e
which are common to any arbitrary cylinder . in particular, when a is
sufficiently small, the total frictional drag on the cylinder per unit
length is expressed as, irrespective of the cross-sectional form, where
b 2 and y 0.5772.../euler's constant/ .
.I 788
.T
an approximate boundary layer theory for semi-infinite cylinders of
arbitrary cross-section .
.A
varley, e.
.B
j. fluid mech. vol. 3. 1958, p. 601-614 .
.W
an approximate boundary layer theory for semi-infinite cylinders of
arbitrary cross-section .
an estimate is given of the distribution of skin frictional force per
unit length, and of displacement area, on the outside of a semi-infinite
cylinder, of arbitrary cross-section, moving steadily in a direction
parallel to its generators . a pohlhausen method is employed with a
velocity distribution chosen to yield zero viscous retarding force on
the boundary layer approximations . /the smallness of the fluid
acceleration far from the leading edge has been pointed out by batchelor
reasonable results atlarge distances from the leading edge . however,
for a large class of cross-sections, which includes all convex
cross-sections and locally concave cross-sections with re-entrant angles
greater than 1/2, the method yields the expected square root growth of
the boundary layer at the leading-edge, with a fairly close
approximation to the coefficient, and it is supposed that the skin-frictional
force and displacement area are given with reasonable accuracy along the
whole length of the cylinder .
results for the elliptic cylinder and the finite flat plate are given in
closed form, valid for the whole length of the cylinder, and are
expected to be in error by at most 20 per cent . in addition, some
estimate is given of the effect of corners on skin frictional force and
displacement area .
.I 789
.T
a further note on the calculation of heat transfer
through the axisymmetrical laminar boundary layer on
a circular cylinder .
.A
bourne,d.e., davies,d.r. and wardle,s..
.B
q. j. mech. app. math. 12, 1959, 257.
.W
a further note on the calculation of heat transfer
through the axisymmetrical laminar boundary layer on
a circular cylinder .
by using a karman-pohlhausen method
the distribution of local rate of heat
transfer is ovaluated for the case of air flow
in an axisymmetrical laminar boundary
layer on a heated circular cylinder, the temperature
of the cylinder being independent
of downstream distance . this calculation
serves to link the numerical values
obtained by seban, bond, and kelly
for small downstream distances to those
obtained by bourne and davies for large
downstream distances .
.I 790
.T
a wind-tunnel test technique for measuring the dynamic rotary
stability derivatives at subsonic and supersonic speeds .
.A
report 1258
.B
benjamin h. beam
.W
a wind-tunnel test technique for measuring the dynamic rotary
stability derivatives at subsonic and supersonic speeds .
a method is described for measuring the dynamic stability derivatives
of a model airplane in a wind tunnel . the characteristic features
of this system are that single-degree-of-freedom oscillations were
used to obtain combinations of rolling, yawing and pitching motions.,
that the oscillations were excited and controlled by velocity feedback
which permitted operation under conditions unfavorable for more
conventional types of oscillatory testing., and that data processing was
greatly simplified by using analog computer elements in the strain-gage
circuitry .
the system described is primarily for measurement of the damping
derivatives damping
in roll damping in pitch, damping in yaw, and the cross derivatives
rolling moment due to yawing and yawing moment due to rolling . the
method of testing also permits measurement under oscillatory conditions
of the static derivatives rolling moment due to sideslip, yawing moment
due to sideslip, and pitching moment due to angle of attack . all these
derivatives are of particular importance in estimating the short-period
oscillatory motions of a rigid airplane .
a small number of experimental data are included to illustrate the
general scope of results obtainable with this system .
.I 791
.T
measurements at mach numbers up to 2. 8 of the longitudinal
characteristics of one plane and three cambered slender
'ogee' wings .
.A
taylor,c.r.
.B
rae r. aero.2658, 1961.
.W
measurements at mach numbers up to 2. 8 of the longitudinal
characteristics of one plane and three cambered slender
'ogee' wings .
measurements have been made of
the longitudinal characteristics of one
plane and three cambered slender ogee
wings (p = 0.45,) at two
subsonic and eight supersonic mach
numbers up to 2.8 . the tests also included
measurements of the zero-lift pressure
drag and support interference of the
plane wing . the results have been analysed
to give data for estimating the
performance of supersonic transport aircraft .
.I 792
.T
some low speed problems of high speed aircraft .
.A
spence, a. and clean, d.
.B
j. royal aero. soc. v. 66, april 1962, pp 211-225 .
.W
some low speed problems of high speed aircraft .
the first part of the paper deals with the low speed aerodynamics of
aircraft shapes suggested by kuchemann, at the second international
congress in aeronautical sciences at zurich in 1960, as suitable for
achieving a required range at supersonic speeds, namely wingbody
arrangements with sweepback angles of 55degrees or 60degrees and
streamwise thickness-chord ratio of about 5 per cent suitable for low
supersonic speed, and slender near-triangular wings with sharp leading
edges suitable for mach numbers of about 2 or more .
no attention is given to /slewed/ wings, powered lift or variable
geometry .
in dealing briefly with swept wings, the need for avoiding separation of
flow from the leading edge is demonstrated, with the conclusion that it
is desirable to use leading edge flaps with blowing or suction at the
knee together with blown trailing edge flaps . wind tunnel tests are
described on a simplified model with these boundary layer control
methods applied . mention is made of the possibility of adverse ground
effect on maximum lift .
more attention is given to the case of slender wings because their use
involves a new type of flow with separation from all edges . this flow
and its steadiness are therefore discussed from the point of view of
the possibility of buffeting,. the effect of plan form on static
longitudinal stability and pitch-up is analysed,. and a short summary of
available results on damping in pitch is given . large rolling moments
due to sideslip are shown to give rise to serious problems of control,
and the present state of knowledge of static lateral and directional
stability and rolling and yawing rotary derivatives is discussed .
finally the effects of proximity to the ground are summarised .
the second part of the paper is concerned with work aimed at clarifying
some of the requirements for handling qualities of future aircraft . it
is not so much concerned with forecasts of the dynamic behaviour of
these future aircraft as with determining what the pilot wants .
two aspects of control in the vertical plane are discussed in some
detail namely speed control and glide path holding . flight tests on an
avro 707a aircraft, with artificially worsened characteristics, are
described, and it is shown that substantially constant performance in the
piloting task can be achieved at the expense of increased pilot effort .
some tentative conclusions on desirable levels of speed stability and
phugoid damping are, nevertheless, drawn .
a brief review of the present status of lateral/directional handling
requirements, using mainly american data, is also included .
.I 793
.T
the flow pattern on a tapered sweptback wing at mach numbers between 0.6
and 1.6 .
.A
hall, i.m. and rogers, e.w.e.
.B
a.r.c. r + m 3271, part 1, july 1960 .
.W
the flow pattern on a tapered sweptback wing at mach numbers between 0.6
and 1.6 .
the development of the flow pattern on a swept wing with incidence and
stream mach number is described . the wing, of aspect ratio 2 828,
taper ratio 0 333 and leading-edge sweep 53 5 deg, was tested at mach
numbers between 0 6 and 1 6 at incidences up to about 12 deg . the test
reynolds number varied with mach number, being typically 2 3 x 10 at m
leading edge .
it is shown that the flow pattern at moderate incidences develops
smoothly from a subsonic type involving leading-edge separation to a
supersonic type where the flow is attached near the leading edge and
with shock-induced separation further aft . the formation and movement
of the shock-wave system and the vortices near the wing surface are
briefly discussed .
.I 794
.T
experiments with a tapered swept-back wing of warren 12 planform at mach
numbers between 0.6 and 1.6 .
.A
hall, i.m. and rogers, e.w.e.
.B
a.r.c. r + m 3271, part ii, july 1960 .
.W
experiments with a tapered swept-back wing of warren 12 planform at mach
numbers between 0.6 and 1.6 .
the development of the flow pattern on a wing of aspect ratio 2 828,
taper ratio 0 333, leading-edge sweepback 53 5 deg and 6 per cent
thickness/chord ratio in the streamwise direction has been described in
part 1, which discussed oil-flow patterns obtained on the surface of the
wing . the complete programme of tests also included pressure plotting
at four spanwise stations and force measurements . these are discussed
in relation to the flow development in this part of the report .
the wing was tested at mach numbers between 0 6 and 1 6 for incidences
up to about 14 deg . the tunnel stagnation pressure was held constant at
a value near atmospheric pressure during the tests, so that the reynolds
number varied with mach number .. at m 1 0 it was 2 3 x 10 based on the
mean aerodynamic chord . boundary-layer transition was fixed by a
roughness band at the leading edge .
a detailed analysis has been made of the pressure distributions on the
surface of the wing and the chordwise distributions integrated to
determine the spanwise loading . the overall lift and pitching moment of
the wing were also obtained from these data, as well as from direct
measurements using a strain-gauge balance, by means of which the wing
drag was also determined . these results are considered in some detail
to illustrate the effects of mach number and incidence on the flow about
the model . a preliminary analysis is also made of the conditions for
boundary-layer separation due to shock waves on the wing surface . the
principal factor appears to be the component of mach number normal to
the shock front .
.I 795
.T
the operation of the npl 18in x 14in. wind tunnel in the transonic speed
range .
.A
hall, i.m.
.B
a.r.c. c.p. 338, january 1957 .
.W
the operation of the npl 18in x 14in. wind tunnel in the transonic speed
range .
a brief description of the slotted liners used is given together with
the power requirements and some flow surveys .
some observations are made on wall interference on a half-model of a
swept wing tested in the wind tunnel .
.I 796
.T
an investigation at transonic speeds of the performance of various
distributed roughness bands used to cause boundary layer transition
near the leading edge of a cropped delta half-wing .
.A
rogers, e.w.e. and hall, i.m.
.B
a.r.c., c.p. 481, may 1959 .
.W
an investigation at transonic speeds of the performance of various
distributed roughness bands used to cause boundary layer transition
near the leading edge of a cropped delta half-wing .
distributed roughness bands of no.320 and no.500 carborundum were found
to be effective in causing boundary-layer transition if they extended
over the first 5( and 10( respectively of the local chord . use of
larger grain sizes, or increases in the band width for a given grain
size resulted in a drag penalty . with very large particle sizes /about
between the particles . the drag penalty was constant over the test mach
number range /0.80 to 1.15/ and decreased slowly with incidence . the
wing lift and pitching moment were only slightly modified by the
presence of any of the roughness bands tested, but this result would not
of course necessarily apply to wings of other planforms or section
shapes . the test reynolds number was about 2.7 million .
in the appendix, the structure of the roughness bands is discussed, as
well as the details of the materials used and the techniques used to
apply the band .
.I 797
.T
a study of the effect of leading-edge modifications on the flow over
a 50degree sweptback wing at transonic speeds .
.A
rogers, e.w e., townsend, j.e.g. and berry, c.j.
.B
a.r.c., r + m 3270, may 1960 .
.W
a study of the effect of leading-edge modifications on the flow over
a 50degree sweptback wing at transonic speeds .
summary . an investigation has been made in the n.p.l. 18 in. x 14 in .
tunnel of the effects of leading-edge modifications on the flow and
forces on an untapered wing of 50 deg leading-edge sweep, at stream mach
numbers between 0 60 and 1 20 . seven leading-edge profiles were
tested, ranging from a drooped extension of 18 per cent of the chord of
the basic sharp-nosed section to a round-nosed section with a
leading-edge radius of 1 0 per cent of the basic chord .
leading-edge droop was found to increase the wing drag near zero lift
but to reduce appreciably the lift-dependent drag component, except at
the highest test mach numbers . droop also increased the lift
coefficient at which leading-edge separation occurred on the upper surface
at moderate subsonic speeds, but in addition reduced the mach number for
transonic flow attachment . the appearance of the forward shock /but
not the rear shock/ is considerably delayed when the leading edge is
drooped .
with the undrooped sections an increase in leading-edge radius was
accompanied by successively earlier appearances of the forward shock,
and hence the outboard shock with its attendant separation . the
conditions at which the rear shock first appeared changed only slowly as the
section was changed .
the variations in wing flow pattern as the leading edge is modified are
discussed and related to measured changes in the wing lift and drag .
an attempt is also made to estimate the local mach numbers on some parts
of the wing from the oil-flow patterns,. this material is used to
assess the flow conditions appropriate to shock-induced separation .
the main section of the report concludes with a tentative discussion of
the significance of the present results to the design of swept wings .
in an appendix results obtained with the wing in a sweptforward
configuration are briefly considered .
.I 798
.T
interaction between shock waves and boundary layers, with a note on the
effects of the interaction of the performance of supersonic intakes .
.A
holder, d.w., pearcey, h.h. and gadd, g.e.
.B
a.r.c., c.p. 180, february 1954 .
.W
interaction between shock waves and boundary layers, with a note on the
effects of the interaction of the performance of supersonic intakes .
the interaction between shock waves and boundary layers has important
effects in many problems of high-speed flow . this paper has been
written as a guide to the literature on the subject, and as a critical
review of the present state of knowledge concerning both the underlying
physical processes and the practical applications . it will be clear to
the reader that, although substantial progress has been made, our
knowledge is still far from complete and that more work both of a
fundamental nature and on specific applications is needed before the problem
is understood sufficiently well for design purposes .
part i of the paper describes experiments on comparatively simple types
of flow designed to provide fundamental information and to assist in the
development of the theory . these experiments show that the interaction
depends mainly on the mach and reynolds numbers and on the strength of
the shock wave . in particular, the interaction of a shock wave with a
laminar boundary layer is shown to produce much larger effects than if
the boundary layer is turbulent . for most cases where the effects of
the interaction are large enough to have serious practical consequences
it is found that the boundary layer separates from the surface, and the
difference between the interaction with laminar and turbulent layers
arises mainly because the laminar layer separates much more readily in
an adverse pressure gradient . the details of the interaction downstream
of the separation point thus depend critically on the behaviour of the
separated layer, and on the conditions under which it reattaches to the
surface .
many of the features found in the fundamental experiments appear also in
practical applications and these are considered in parts ii and iii of
the paper . although the emphasis hero is on the performance of
aerfoils and wings moving at high subsonic speeds, the importance of the
interaction in other examples such as at supersonic trailing edges and
in supersonic intakes is also discussed briefly . the differences
between the interaction with laminar and turbulent boundary layers are
often a source of serious discrepancy between model experiments and
full-scale conditions . for small-scale models it is, therefore,
frequently essential to make the boundary layer turbulent by artificial
means . some of the difficulties involved in doing this, and certain of
the more promising methods are briefly discussed . it is shown that
experiments on models with transition fixed can be used to explain a
number of aerodynamic effects encountered in transonic flight, and
connected with the occurrence of shock-induced separation of the
turbulent boundary layers . for both two-dimensional aerofoils and straight
and sweptback wings, turbulent separation occurs for shocks above a
certain strength which applies for both model and full-scale conditions
full-scale conditions,. differences in magnitude would be expected if
the pressure recovery along the separated layer between the shock and
the trailing edge is affected by reynolds number, but little information
is at present available on this point .
most of the repercussions of turbulent separation on the steady-motion
characteristics of aerofoils and wings can be traced to the associated
reduction in the pressure recovery over the roar of the surface . this
is because the pressure at the trailing edge controls the inter-relation
between the two surfaces /so long as the flow at the trailing edge
remains subsonic/, and in particular the relative movements of the shock
waves and the extents of the local regions of supersonic flow . certain
unsteady-flow characteristics such as buffeting and control surface
separation .
some evidence is presented on the influence of section shape on the
occurrence and effects of separation, but in this, as in many other
respects, information relevant to turbulent boundary layers is scarce .
some notes on the further work which is required are given in part iv of
the paper .
.I 799
.T
some effects of wind-tunnel interference observed in tests on
two-dimensional aerofoils at high subsonic and transonic speeds .
.A
pearcey, h.h., sinnott, c.s. and osborne, j.
.B
n.p.l. aero. 373. february 1959 .
.W
some effects of wind-tunnel interference observed in tests on
two-dimensional aerofoils at high subsonic and transonic speeds .
in the high-speed research on two-dimensional aerofoils at the national
physical laboratory the need to keep model size above a certain minimum,
in order to reproduce correctly the boundary layer separation effects
experienced at full scale, has been considered paramount even at the
risk of incurring significant tunnel interference effects .
this report discusses the interference effects for the slotted working
sections now in use . the magnitudes of the blockage and lift effect
corrections are deduced for the ratio of model chord to tunnel height
normally used . it is shown that a simple adaptation to reduce the open
area of the walls would reduce both corrections to insignificant
proportions simultaneously, but would give a reduced choking mach number
separated flows . the observed trends in the variation of the blockage
effects for other ratios of model chord to tunnel height differ from
those predicted theoretically, and so the results cannot be applied more
generally until these trends have been checked by further
investigations .
it is suggested that wake interference effects can significantly
influence the manner in which separated flows develop with increasing
incidence or mach number, particularly for walls of small open area .
examples are also given of effects of distortions in the local
supersonic flow, which are most noticeable for walls with relatively large
open areas .
.I 800
.T
wall interference at transonic speeds on a hemisphere cylinder model .
.A
rogers, e.w.e. and hall, i.m.
.B
a.r.c., c.p. 510, september 1959 .
.W
wall interference at transonic speeds on a hemisphere cylinder model .
tests have been made in three n.p.l. wind tunnels on a pressure-plotting
model consisting of a long cylinder with a hemispherical nose . the
surface pressure distributions were measured for stream mach numbers
between 0.7 and 1.1 at zero model incidence, and schlieren photographs
were taken . the blockage ratios were 0.211(, 0.117( and 0.120( .
the principal feature of the flow is the effect of working section size
on the rate at which the terminal shock wave moves back along the model
with increasing stream mach number . this is thought to depend mainly
on the distance from the model to the slotted walls of the tunnel,
and not necessarily on the blockage ratio . the distance of the solid
sidewall is important in influencing the local mach number ahead of the
terminal shock, by reflecting the expansion-wave system originating near
the model nose .
.I 801
.T
experimental study of the equivalence of transonic
flow about slender cone-cylinders of circular and elliptic
cross section .
.A
page,w.a.
.B
naca tn.4233, 1958.
.W
experimental study of the equivalence of transonic
flow about slender cone-cylinders of circular and elliptic
cross section .
this report describes an experimental investigation of the equivalence
relationship and the related theory for lifting forces proposed by
transonic slender-body theory . the models chosen for this study are a
flat, winglike, elliptic cone-cylinder and its equivalent body of
revolution, a circular cone-cylinder . it is determined that the flows
about the two models are closely related in the manner predicted by the
theory, the relationship persisting over a mach number range of 0.92 to
cone-cylinder vary linearly only over the small angle-of-attack range of
approximately 1 and that the aerodynamic loading at sonic speed compares
favorably with jones' slender-wing theory .
the results of the investigation suggest that at transonic speeds and
at small angles of attack the calculation of all aerodynamic
characteristics of slender, three-dimensional shapes can be made by use
of transonic slender-body theory when the pressures on the equivalent
body of revolution are known, either by experiment, or by an adequate
nonlinear theory . from transonic slender-body theory it is deduced
that the slenderness required for this application is the same as that
required for the successful application of the transonic area rule .
.I 802
.T
the behaviour of supersonic flow past a body of revolution
far from the axis .
.A
whitham,g.b.
.B
proc. roy. soc. a, 201, 1950, 89.
.W
the behaviour of supersonic flow past a body of revolution
far from the axis .
a theory is developed of the supersonic flow past a body of revolution
at large distances from the axis, where a linearized approximation is
valueless owing to the divergence of the characteristics at infinity .
it is used to find the asymptotic forms of the equations of the shocks
which are formed from the neighbourhoods of the nose and tail . in the
special case of a slender pointed body, the general theory at large
distances is used to modify the linearized approximation to give a
theory which is uniformly valid at all distances from the axis . the
results which are of physical importance are summarized in the
conclusion (9) and compared with the results of experimental
observations .
.I 803
.T
the shock pattern of a wing-body combination far from
the flight path .
.A
walkden,f.
.B
aero. quart. 9, 1958, 164.
.W
the shock pattern of a wing-body combination far from
the flight path .
the position and strength of the front shock wave at large
distances from a wing-body combination, are deduced from the linear
theory for the combination, using a method developed by whitham . the
combination consists of a body of revolution and a wing which has
thickness and is lifting . the effects of interference between the flow
over the body and the flow over the wing are included . in any
direction the flow far from the wing-body combination is equivalent to
the flow past a body of revolution determined from the configuration of
the combination . the modified formulae for unsteady flow are given and
some results are evaluated for the combination of a body of revolution
and a delta wing with subsonic leading edges .
.I 804
.T
a flight test investigation of the sonic boom .
.A
mullens,m.e.
.B
afftc-tn-56-20, air res. and dev. command, u.s.a.f., 1956.
.W
a flight test investigation of the sonic boom .
the /sonic boom/ as it is now popularly called, has become the
center of considerable interest during the past few years because of
widespread public disturbance and possible damage that can result
from it . in the hopes of minimizing this disturbance and to extend
the general knowledge of the shock waves which produce the booming
noise, the aeronautical research laboratory, wright air development
center, has initiated an extensive research program to study the sonic
boom phenomenon .
this report presents the results of flight tests undertaken as one
phase of this program . the tests had as their objective the
determination and measurement of the shock wave pressure pattern surrounding
an f-100 aircraft in level supersonic flight .
the flight tests were conducted at the air force flight test
center, edwards air force base, california, under the authority of air
research and development command test directive no. 5524-f1 .
.I 805
.T
ground measurements of the shock wave noise from airplanes
in level flight at mach numbers to 1. 4 and at altitudes
to 45,000 feet .
.A
maglieri,d.j., hubbard,h.h. and lansing,d.l.
.B
nasa tn.d48, 1959.
.W
ground measurements of the shock wave noise from airplanes
in level flight at mach numbers to 1. 4 and at altitudes
to 45,000 feet .
time histories of noise pressures near ground level were measured
during flight tests of fighter-type airplanes over fairly flat, partly
wooded terrain in the mach number range between 1.13 and 1.4 and at
altitudes from 25,000 to 45,000 feet . atmospheric soundings and
radar-tracking studies were made for correlation with the measured noise
data .
the measured and calculated values of the pressure rise across the
shock wave were generally in good agreement . there is a tendency for
the theory to overestimate the pressure at locations remote from the
track and to underestimate the pressures for conditions of high tailwind
at altitude . the measured values of ground-reflection factor averaged
about 1.8 for the surfaces tested as compared to a theoretical value
of 2.0 . two booms were measured in all cases . the observers also
generally reported two booms,. although, in some cases, only one boom
was reported . the shock-wave noise associated with some of the flight
tests was judged to be objectionable by ground observers, and in one
case the cracking of a plate-glass store window was correlated in time
with the passage of the airplane at an altitude of 25,000 feet .
.I 806
.T
ground measurements of airplane shock wave noise at
mach numbers to 2, and at altitudes of 60,000 feet .
.A
lina,l.j. and maglieri,d.j.
.B
nasa tn.d235, 1960.
.W
ground measurements of airplane shock wave noise at
mach numbers to 2, and at altitudes of 60,000 feet .
the intensity of shock-wave noise at the ground resulting from
flights at mach numbers to 2.0 and altitudes to 60,000 feet was
measured . measurements near the ground track for flights of a
supersonic fighter and one flight of a supersonic bomber are
presented .
level cruising flight at an altitude of 60,000 feet and a mach
number of 2.0 produced sonic booms which were considered to be
tolerable, and it is reasonable to expect that cruising flight at higher
altitudes will produce booms of tolerable intensity for airplanes of the
size and weight of the test airplanes . the measured variation of
sonic-boom intensity with altitude was in good agreement with the
variation calculated by an equation given in nasa technical note d-48 .
the effect of mach number on the ground overpressure is small between
mach numbers of 1.4 and 2.0, a result in agreement with the theory . no
amplification of the shock-wave overpressures due to refraction effects
was apparent near the cutoff mach number .
a method for estimating the effect of flight-path angle on cutoff
mach number is shown . experimental results indicate agreement with the
method, since a climb maneuver produced booms of a much decreased
intensity as compared with the intensity of those measured in level flight at
about the same altitude and mach number .
comparison of sound pressure levels for the fighter and bomber
airplanes indicated little effect of either airplane size or weight at an
altitude of 40,000 feet .
.I 807
.T
ground measurements of the shock wave noise from
supersonic bomber airplanes in the altitude range from 30,000
to 50,000 feet .
.A
maglieri,d.j. and hubbard,h.h.
.B
nasa tn.d880, 1961.
.W
ground measurements of the shock wave noise from
supersonic bomber airplanes in the altitude range from 30,000
to 50,000 feet .
shock-wave ground-pressure measurements
have been made for
supersonic bomber airplanes in the mach number
range from 1.24 to 1.52, for
altitudes from about 30,000 to 50,000 feet,
and for a gross-weight range
from about 83,000 to 120,000 pounds . the
measured overpressures were
generally higher than would be predicted
by the theory which accounts
only for volume effects . there is thus
a suggestion that lift effects
on sonic-boom intensity may be significant
for this type of airplane
for the altitude range of the present tests .
.I 808
.T
an investigation of some aspects of the sonic boom
by means of wind tunnel measurements of pressures about
several bodies at a mach number of 2. 01 .
.A
carlson,h.w.
.B
nasa tn.d161, 1959.
.W
an investigation of some aspects of the sonic boom
by means of wind tunnel measurements of pressures about
several bodies at a mach number of 2. 01 .
an investigation of some aspects
of the sonic boom has been made
with the aid of wind-tunnel measurements
of the pressure distributions
about bodies of various shapes . the
tests were made in the langley
at a mach number of 2.01 and
at a reynolds number per foot of 2.5 x 10 .
measurements of the pressure
field were made at orifices in the surface
of a boundary-layer bypass
plate . the models which represented both
fuselage and wing types of
thickness distributions were small enough
to allow measurements as far
away as 8 body lengths or 64 chords . the
results are compared with
estimates made using existing theory .
to the first order, the boom-producing
pressure rise across the bow
shock is dependent on the longitudinal
development of body area and not
on local details . nonaxisymmetrical shapes
may be replaced by
equivalent bodies of revolution to obtain satisfactory
theoretical estimates
of the far-field pressures .
.I 809
.T
an investigation of the influence of lift on sonic-boom
intensity by means of wind tunnel measurements of the
pressure fields of several wing-body combinations at
a mach number of 2. 01 .
.A
carlson,h.w.
.B
nasa tn.d881, 1961.
.W
an investigation of the influence of lift on sonic-boom
intensity by means of wind tunnel measurements of the
pressure fields of several wing-body combinations at
a mach number of 2. 01 .
an investigation of the effect
of lift on sonic-boom intensity has
been performed by means of wind-tunnel
measurements of the pressure fields
surrounding small wing-body combinations .
the tests were conducted in
the langley 4- by 4-foot supersonic
pressure tunnel at a mach number of
per foot . effects of lift were
found to be real and significant .
measured bow-shock intensities agreed
fairly well with, but were consistently
less than, shock intensities
estimated by theoretical methods .
available flight data were examined
for correlation with wind-tunnel test
results .
.I 810
.T
the shock wave noise problem of supersonic aircraft
in steady flight .
.A
maglieri,d.j. and carlson,h.w.
.B
nasa memo 3-4-59l, 1959.
.W
the shock wave noise problem of supersonic aircraft
in steady flight .
data are presented which provide
an insight into the nature of the
shock-wave noise problem, the significant
variables involved, and the
manner in which airplane operation
may be affected . flight-test data
are also given, and a comparison with
the available theory is made . an
attempt is also made to correlate the
subjective reactions of observers
and some associated physical phenomena
with the pressure amplitudes
during full-scale flight .
it is indicated that for the proposed
supersonic transport airplanes
of the future, booms on the ground will
most probably be experienced
during the major portion of the flight
plan . the boom pressures will be
most severe during the climb and descent
phases of the flight plan .
during the cruise phase of the flight,
the boom pressures are of much
lesser intensity but are spread laterally
for many miles . the manner
in which the airplane is operated appears
to be significant,. for example,
the boom pressures during the climb,
cruise, and descent phases can be
minimized by operating the airplane at
its maximum altitude consistent
with its performance capabilities .
.I 811
.T
an investigation of lifting effects on the intensity
of sonic booms .
.A
morris,j.
.B
j. roy. aero. soc. 64, 1960, 610.
.W
an investigation of lifting effects on the intensity
of sonic booms .
this paper is a brief summary of
an investigation made to check the effect of lift
on the shock noise of aircraft flying at supersonic
speeds . the method of hayes has been
combined with the theory of whitham to
predict the asymptotic shock strength of wings
carrying lift and of combinations of bodies
and lifting wings . (a similar, but not quite as
general, method was derived by walkden in
ref. 6 .) whitham's formula, including only the
volume term, has been used extensively to predict
the boom intensity of aeroplane type bodies
and the agreement with experiment has, so far,
been quite reasonable . the test data obtained
to date extends only up to about 40,000 ft.
altitude and the calculations of this paper show
that under those conditions the shock noise of
the aircraft tested so far will, in most cases,
be dominated by the volume term . it is shown
that at higher altitudes lifting effects will
dominate for even the small fighter and they will
dominate over most of the altitude range
for large bomber and supersonic transport
aircraft . the boom intensity due to lift decreases
with altitude as which compares to
in the volume case (=pressure at
altitude h) . it is insensitive to mach number,
wing loading, wing plan shape and
lift distribution . a simple rule for calculating
the shock noise due to combined volume and
lifting effects is proposed which is applicable to
configurations with wings located towards the
rear of the fuselage . the rule states that the shock
noise of an aircraft carrying lift is equal
to the shock noise due to volume (neglecting lift)
or the shock noise due to lift (neglecting
volume), whichever is the greater . a chart is
presented from which rapid estimates can be
made of the shock noise of lifting
wing-body combinations .
.I 812
.T
investigation of two bluff shapes in axial free flight
over a mach number range from 0. 35 to 2. 15 .
.A
coltrane,l.c.
.B
naca rm l58a16, 1958.
.W
investigation of two bluff shapes in axial free flight
over a mach number range from 0. 35 to 2. 15 .
a fineness-ratio-2.71 right circular cylinder and a fineness-
ratio-been tested in free flight over a mach number range of 0.35 to 2.15 and
a reynolds number range of 1 x 10 to 12 x 10 . time histories, cross
plots of force coefficients, rolling velocity, and longitudinal-force
coefficient are presented for both cylinders . in addition, cross plots
of moment coefficients and plots of the normal-force curve slope and
the aerodynamic center are presented for the fineness-ratio-2.71
cylinder . the average aerodynamic center of the right circular
cylinder moved rearward with decreasing speeds until at the subsonic
mach numbers it remained approximately constant and comparisons of the
drag data of this test with wind tunnel and other free-flight data show
good agreement . an appreciable decrease in drag was observed when the
data of the present test of the rounded nose cylinder were compared with
data of a right circular cylinder of a similar configuration .
.I 813
.T
the motion of rolling symmetrical missiles referred
to a body-axis system .
.A
nelson,r.l.
.B
naca tn.3737, 1956.
.W
the motion of rolling symmetrical missiles referred
to a body-axis system .
the linearized equations of motion have been derived for a rolling
missile having slight aerodynamic asymmetries . time histories of
rolling-missile motions referred to a body-axis system have been
prepared to show the types of missile motions that can be encountered .
the motions resulting from a trim change and a pulse-rocket disturbance
are shown to be determined mainly by the ratio of rolling velocity to
pitching frequency .
finally, the derived equations are used in establishing a technique
for the reduction of rolling-missile oscillation data . it is shown
that the aerodynamic derivatives can be obtained from flight data if
four accelerations are measured . the method is applied to the results
obtained from a flight test of a missile configuration .
.I 814
.T
stability derivatives of cones at supersonic speeds .
.A
tobak,m. and wehrend,w.r.
.B
naca tn.3788, 1956.
.W
stability derivatives of cones at supersonic speeds .
the aerodynamic stability derivatives due to pitching velocity and
vertical acceleration are calculated by use of potential theory for
circular cones traveling at supersonic speeds . the analysis is based on
two theoretical techniques used successfully previously in application
to the case of uniform axial and inclined flow . in the first,
potential solutions for axial flow and crossflow are derived from the
first-order wave equation but in application to calculations for the
forces no approximations are made either to the tangency condition or
to the isentropic pressure relation . the second method consists in
combining the first-order crossflow potential with an axial-flow
potential correct to second order . closed-form solutions by both
methods are found for a cone, and numerical results for the stability
derivatives are presented as a function of mach number for cones having
semivertex angles of 10 and 20 .
in addition, expressions for the forces, moments, and stability
derivatives of arbitrary bodies of revolution are obtained using
newtonian impact theory . numerical results for cones compare well
with those obtained from the combined first- and second-order potential
theory at the highest mach number for which the latter theory is
applicable .
.I 815
.T
investigation of several blunt bodies to determine
trans- onic aerodynamic characteristics including effects
of spinning and of extendible afterbody flaps and some
measurements of unsteady base pressures .
.A
fisher,l.r. and dicamillo,j.r.
.B
nasa memo 1-21-59l, 1959.
.W
investigation of several blunt bodies to determine
trans- onic aerodynamic characteristics including effects
of spinning and of extendible afterbody flaps and some
measurements of unsteady base pressures .
several blunt bodies having shapes that may be suitable for
atmospheric reentry vehicles were tested to determine the aerodynamic
characteristics of such shapes for angles of attack up to 34 . the tests
were conducted through the transonic mach number range and at reynolds
numbers from 1.74 x 10 to 2.78 x 10, based on body diameter .
a full-skirted rather than a short-skirted type of shape developed
the greatest amount of static stability and the largest lift-curve
slopes . the angle of attack for maximum lift for such bodies appears
to be subject to mach number effects . spinning a full-skirted body
about its longitudinal axis generally increased the lift and reduced the
pitching moment at angles of attack and reduced the aerodynamic static
stability parameter through the transonic mach number range . the
extension of segmented clamshell-shaped flaps from the afterbody of a
short-skirted model served to increase the lift and static stability
only if the flaps extended into the airstream .
some evidence was found of oscillatory base pressures on two
dissimilar shapes at certain high angles of attack and the highest mach
number in these tests . there is doubt, however, that these pressures
can induce any significant oscillatory motion for a reentry vehicle
because of their small amplitude and phasing .
.I 816
.T
experimental investigation at a mach number of 3. 11
of the lift, drag and pitching moment characteristics
of a number of blunt low-fineness-ratio bodies .
.A
letko,w.
.B
nasa memo 1-18-159l, 1959.
.W
experimental investigation at a mach number of 3. 11
of the lift, drag and pitching moment characteristics
of a number of blunt low-fineness-ratio bodies .
a number of blunt bodies having shapes that may be suitable for
atmospheric reentry were tested to determine the lift, drag, and
pitching-moment characteristics at a mach number of 3.11 and a reynolds
number of 6 x 10 based on maximum body diameter of 2 inches .
the results of the tests showed that all the bodies were statically
stable about a point located one-third of the body length from the
nose . the results also showed that high-drag bodies which have a large
portion of their afterbodies negatively sloped (decrease in
cross-sectional area from nose to base) may have a negative lift-curve slope .
this negative slope results from the large negative lift component of
the axial force obtained with those bodies and the fact that with
negatively sloped afterbodies only small normal forces are developed .
.I 817
.T
loading paths and the incremental stress law .
.A
hankelman,g.h. and warner,w.h.
.B
j. math. and phys. 33, 1954, 157.
.W
loading paths and the incremental stress law .
this paper will be concerned with some properties of the
stress-strain law for work hardening materials introduced by w. prager
incremental strain or plastic flow law by which it is meant that the
differentials of strain are expressed as functions of the stresses,
strains, and differentials of the stress . we shall also have occasion
to refer to total strain or plastic deformation laws, in which the
strains are given directly as functions of the stress .
.I 818
.T
a quantitative comparison of flow and deformation theories
of plasticity .
.A
hodge,p.g. and white,g.n.
.B
j. app. mech. 17, 1950.
.W
a quantitative comparison of flow and deformation theories
of plasticity .
the stresses and displacements in a partly plastic,
infinitely long, hollow cylinder are obtained according to the
flow type of stress-strain law of prandtl-reuss and to the
deformation law of hencky . in both cases the mises yield
condition is used and the compressibility of the material is
taken into account . it is shown that under these
assumptions the two theories yield substantially the same
results for this particular problem, but that one theory or
the other may be preferable for computing purposes in
certain cases . the results are compared with those of
other investigations in which different combinations of
stress-strain law, yield condition, compressibility, and end
loading were assumed .
.I 819
.T
stresses in the plastic range around a normally loaded
circular hole in an infinite sheet .
.A
magasarian,o.l.
.B
j. app. mech. 27, 1960, 65.
.W
stresses in the plastic range around a normally loaded
circular hole in an infinite sheet .
the stresses in the plastic range around a normally loaded circular hole
in an infinite sheet are found numerically on the basis of both
deformation and incremental theories . the results of deformation
theory are quantitatively assessed in the light of a criterion, recently
developed by budiansky, for the acceptability of deformation theories .
the criterion is completely satisfied . moreover, the results obtained
by using these two different theories of plasticity do not differ
greatly despite the fact that the stress paths are far from being
radial .
.I 820
.T
theories of plastic buckling .
.A
batdorf,s.b.
.B
j. ae. scs. 16, 1949, 405.
.W
theories of plastic buckling .
the theory for the plastic buckling of columns which appears
finally to have achieved a satisfactory form, rests upon the
well-established uniaxial stress-strain relation . the development of
a correspondingly satisfactory theory for the plastic buckling of
plates has been hampered by the nonexistence of an established
polyaxial stress-strain relation in the plastic range .
present theories for the polyaxial stress-strain relation beyond
the elastic range can be divided into two types, often called flow
and deformation theories . theories of plastic buckling based on
deformation theories are in better agreement with experiment
than those based on flow theories . on the other hand, tests in
which a material is compressed into the plastic range and then
subjected to shear at constant compressive stress are in better
agreement with flow than with deformation theories . legitimate
doubt therefore has existed as to the validity of any theory for
the plastic buckling of plates .
as a result of studying these apparent contradictions, a new
theory of plasticity has been developed which is of neither the
flow nor the deformation type . it is based upon the concept of
slip, and its formulation was guided more by physical, and less
by mathematical, considerations than previous theories .
experimental evidence of limited scope but of crucial character is in
better agreement with the new theory than with either flow or
deformation theories . the new theory accounts for the apparent
contradictions previously alluded to and justifies the use of
deformation theory in the analysis of the plastic buckling of plates .
.I 821
.T
inelastic column theory .
.A
shanley,f.r.
.B
j. ae. scs. 14, 1949, 261.
.W
inelastic column theory .
the action of a column in the plastic range is analyzed on the
basis that bending may proceed simultaneously with increasing
axial load . this leads to a new column formula that includes
both the tangent-modulus (engesser) and the reduced-modulus
the tangent-modulus load and that the column load increases
with increasing lateral deflection, approaching the
reduced-modulus load as a limit if the tangent modulus is assumed to
remain constant .
.I 822
.T
effects of imperfections on buckling of thin cylinders
and columns under axial compression .
.A
donnell,l.h. and wan,c.c.
.B
j. app. mech. 1950.
.W
effects of imperfections on buckling of thin cylinders
and columns under axial compression .
von karman and tsien have shown that under elastic
conditions the resistance of perfect thin cylinders
subjected to axial compression drops precipitously after
buckling . it is considered that this indicates that this type of
buckling is very sensitive to imperfections or disturbances .
in this paper the effects of certain imperfections of shape
turbances combined) are studied by the large-deflection
shell theory developed in a previous paper (2) .
it is found that two types of buckling failure may occur .
one is of a purely elastic type which occurs when the peak
of the average stress versus average strain curve is reached,
while the other type is precipitated by yielding, which for
thicker cylinders or lower-yield material may occur before
such a peak is reached . curves are derived giving the
dependence of each type of failure upon the dimensions and
elastic and yield properties of the specimen and also upon
an /unevenness factor/ u which determines the
magnitude of the initial imperfections and is assumed to depend
on the method of fabrication . the relations derived are in
line with test results, and similar studies of the buckling
of struts indicate that the magnitude of the initial
imperfections which have to be assumed to explain test strengths
are reasonable .
.I 823
.T
plastic torsional buckling strength of cylinders including
the effects of imperfections .
.A
lee,l.h.n. and ades,c.s.
.B
j. ae. scs. 24, 1957, 241.
.W
plastic torsional buckling strength of cylinders including
the effects of imperfections .
the torsional buckling strength of a cylinder in the plastic
range has been determined . an energy solution and a more exact
solution, both based on a plastic stress-strain relationship given
by the simple deformation theory, are presented . close
agreement between the two solutions is found . the effects of large
deflections and imperfections on buckling strength are analyzed .
for two groups of experimental results used for comparison, the
effects of geometrical imperfections in the plastic range are
negligible . the theoretical results are found to be in good
agreement with the experimental results .
.I 824
.T
on the concept of stability of inelastic systems .
.A
drucker,d.c. and onat,e.t.
.B
j.ae.scs., 21, 1954, 543.
.W
on the concept of stability of inelastic systems .
simple models are employed to bring out the large and
important differences between buckling in the plastic range and
classical elastic instability . static and kinetic criteria are
compared and their interrelation discussed . nonlinear behavior in
particular is often found to be the key to the physically valid
solution . the nonconservative nature of plastic deformation in
itself or in combination with the nonlinearity requires concepts
not found in classical approaches . conversely, the classical
linearized condition of neutral equilibrium is really not relevant
in inelastic buckling . plastic buckling loads are not uniquely
defined but cover a range of values and are often more properly
thought of as maximum loads for some reasonable initial
imperfection in geometry or dynamic disturbance .
the models indicate that basically the same information is
obtained from essentially static systems by assuming initial
imperfection in geometric forms as by assuming dynamic
disturbances . one approach complements the other and both are
helpful in obtaining an understanding of the physical phenomena .
.I 825
.T
inelastic instability and incremental theories of plasticity .
.A
onat,e.t. and drucker,d.c.
.B
j. ae. scs. 20, 1953, 181.
.W
inelastic instability and incremental theories of plasticity .
a most troublesome paradox has existed for a number of years
with respect to buckling in the plastic range . theoretical
considerations and all direct experimental evidence show
conclusively that an incremental or flow type of mathematical theory
of plasticity is valid . however, the results of plastic buckling
tests are well correlated by a simple total or deformation theory
and bear no resemblance to published predictions of incremental
theory .
the suggestion was made that initial imperfections of shape
or loading might well explain this most peculiar result .
however, subsequent investigations by several authors seem to have
given the impression that excessively large imperfections would
be needed and that the answer would be overly sensitive to the
magnitude of such imperfections .
it is the purpose of this paper to demonstrate that extremely
small, and therefore unavoidable, imperfections of shape do
account for the paradox in a simple manner . the buckling load is
shown to be extremely insensitive to the amount of imperfection .
the example chosen is a simplified version of the long rectangular
plate hinged along one edge and free on the other under
uniform compressive stress at the ends . this is the equivalent of
the case of the cruciform column, which has been so disturbing
in the past because incremental theory applied to a perfect
cruciform column did lead to an entirely incorrect result .
.I 826
.T
small bending and stretching of sandwich type shells .
.A
reissner,e.
.B
naca tn.1832, 1949.
.W
small bending and stretching of sandwich type shells .
a theory has been developed for small bending and stretching of
sandwich-type shells . this theory is an extension of the known theory
of homogeneous thin elastic shells . it was found that two effects are
important in the present problem, which have not been considered
previously in the theory of curved shells .. (1) the effect of
transverse shear deformation and (2) the effect of transverse normal stress
deformation . the first of these two effects has been known to be of
importance in the theory of plates and beams . the second effect was
found to occur in a manner which is typical for shells and has no
counterpart in flat-plate theory .
the general results of this report have been applied to the
solution of problems concerning flat plates, circular rings, circular
cylindrical shells, and spherical shells . in each case numerical
examples have been given, illustrating the magnitude of the effects
of transverse shear and normal stress deformation .
the results of this investigation indicate the necessity of
taking account of transverse shear and normal stress in sandwich-type
shells, as soon as there is an order-of-magnitude difference between
the elastic constants of the core layer and of the face layers of the
composite shell . it was found that the changes due to transverse
shear and normal stress deformation in the core may be so large as to
be no mere corrections to the results of the theory without transverse
core flexibility .
the actual magnitude of the changes is greatly dependent on the
geometry and loading condition of the structure under consideration
so that no general rules may be given which indicate for which elastic
modulus ratio the changes begin to be significant .
solutions of problems in the present theory may in general be
obtained by mathematical methods which are similar to those employed
in the theory of plates and shells without the effect of transverse
shear and normal stress deformation included . the present work does
not include consideration of buckling and finite deflection effects .
.I 827
.T
a nonlinear theory of bending and buckling of thin
elastic shallow spherical shells .
.A
kaplan,a. and fung,y.c.
.B
naca tn.3212, 1954.
.W
a nonlinear theory of bending and buckling of thin
elastic shallow spherical shells .
a shallow spherical dome subjected to lateral pressure is a structure
for which the deformation departs appreciably from the linear theory at
relatively small values of the deflection amplitude . it is also one
for which the buckling process is characterized by a rapid decrease in
the equilibrium load once the buckling load has been surpassed . for
structures having this type of buckling characteristics the question
arises as to whether the proper buckling criterion to apply is the
classical criterion, which considers equilibrium with respect to
infinitesimal displacements, or the finite-displacement /energy
criterion/ proposed by tsien .
in this paper the problem of the finite displacement and buckling
of a shallow spherical dome is investigated both theoretically and
experimentally . in the theoretical approach the nonlinear equations
are converted into a sequence of linear equations by expanding all of
the variables in powers of the center deflection and then equating the
coefficients of equal powers . the basic parameter for the shallow dome
is proportional to the ratio of the central height of the dome h to its
thickness t . for small values of this ratio the expansions converge
rapidly and enough terms are computed to determine the buckling load
according to the classical criterion . for higher values of h t,
convergence deteriorates rapidly and it was not possible to determine the
buckling load with the number of terms which were computed . however
even for these higher values of h t the deflection shapes are determined
for deflection amplitudes below the amplitude at which buckling occurs .
these deflection shapes are characterized by their rapid change as h t
increases and by the fact that, over most of the range of h t studied,
the maximum deflection does not occur at the center of the dome .
experimental results seem to indicate that the classical criterion
of buckling is applicable to very shallow spherical domes for which the
theoretical calculation was made . a transition to energy criterion for
higher domes is also indicated .
.I 828
.T
stresses and small displacements of shallow spherical
shells .
.A
reissner,e.
.B
j. math. phys. 25, 1946, 80.
.W
stresses and small displacements of shallow spherical
shells .
the purpose of the present paper is to derive a system of
equations which can be used for the analysis of shallow segments of
thin, elastic, spherical shells . a segment will be called shallow if
the ratio of its height to base diameter is less than, say . the
results obtained on the basis of this assumption will often also be
applicable to shells which are not shallow, namely then, when the loads
are such that the stresses are effectively restricted to shallow zones .
the problem of the spherical elastic shell has been the subject of
numerous researches . for the rotationally symmetric case the
fundamental results were obtained in 1912 (1) and have been the starting
point of many applications . while it is possible to deduce from these
results approximate equations equivalent to part of what follows, it is
believed that the present approach to the problem of the shallow shell
may be of some interest even for rotationally symmetric cases .
a number of investigations have been concerned with the shell loaded
in a non-rotationally symmetric manner (2,3,4) . in its general form
this problem is quite difficult and the results so far obtained are not
easy to apply . restricting attention to the shallow shell in the
manner of the present paper brings with it a very considerable
simplification of the analysis .
.I 829
.T
stability of thin-walled tubes under torsion .
.A
donnel,l.h.
.B
naca r.479, 1933, 12.
.W
stability of thin-walled tubes under torsion .
in this paper a theoretical solution is developed for the
torsion on a round thin-walled tube for which the walls
become unstable . the results of this theory are given by
a few simple formulas and curves which cover all cases .
the differential equations of equilibrium are derived in a
simpler form than previously found, it being shown that
many items can be neglected . the solution obtained is
length ratio is zero and infinite, and is a good
approximation for intermediate cases . the theory is compared
with all available experiments, including about 50 tests
made by the author . the experimental-failure torque is
always smaller than the theoretical-buckling torque,
averaging about 75 percent of it, with a minimum of 60
percent . as the form of the deflection checks closely with
that predicted by theory and the experiments cover a great
range of shapes and materials, this discrepancy can
reasonably be ascribed largely to initial eccentricities in
actual tubes .
.I 830
.T
nonlinear deflections of shallow spherical shells .
.A
reiss,e.l., greenberg,h.j. and keller,h.b.
.B
j. ae. scs. 24, 1957, 533.
.W
nonlinear deflections of shallow spherical shells .
the equations obtained by chien for the nonlinear deflection
of shallow spherical shells under uniform external pressure are
solved by means of power series expansions, following procedures
introduced by friedrichs and stoker in their treatment of
buckling of circular plates . these equations depend upon two
parameters . one of these parameters is related to the external
pressure, while the other depends upon the dimensions of the shell .
the equations are solved for several ranges of the parameters
under boundary conditions corresponding to a fixed edge .
the solution, carried out numerically on the aec univac
at new york university, yields a complete description of the
stresses and deflections as functions of the polar angle over a
wide range of values of the loading parameter and the
dimensional parameter . prediction of the upper buckling load is then
made by means of a numerical criterion based on the load vs.
deflection curve . for some cases, the postbuckling behavior
is investigated . the results agree well with existing
experimental and theoretical studies and cover a wide range of cases
not previously treated .
.I 831
.T
buckling of shallow shells under external pressure .
.A
reiss,e.l.
.B
j. app. mech. 25, 1958,556.
.W
buckling of shallow shells under external pressure .
a formula for the initial buckling loads for clamped, shallow spherical
shells under uniform external pressure is obtained by combining the
solutions of two linearized versions of the original nonlinear problem .
one of these versions is a linear eigenvalue problem while the other is
the bending problem for a shallow cap in the linear theory of
elasticity . the formula, which is obtained in a simple manner, yields
buckling loads that are in better agreement with experiments than
previous approximate solutions to the nonlinear problem .
.I 832
.T
accelerating convergence of iteration processes .
.A
wegstein,j.h.
.B
comm. of assoc. for computing mach. 1958.
.W
accelerating convergence of iteration processes .
a technique is discussed which, when applied to an iterative procedure
for the solution of an equation, accelerates the rate of convergence if
the iteration converges and induces convergence if the iteration
diverges . an illustrative example is given .
.I 833
.T
a simple method of matric structural analysis, part
iv, non-linear problems .
.A
klein,b.
.B
j. ae. scs. 26, 1959.
.W
a simple method of matric structural analysis, part
iv, non-linear problems .
the method presented in the previous parts is employed to
solve various kinds of nonlinear problems, such as problems
concerning large deflections or buckling, or thermal creep, or
inelastic stress redistribution involving thermal gradients, or
design . the procedure used in each case is one of direct
iteration--i. e., after one assumes a starting point all subsequent cycles are
self-generating . simple numerical examples are worked out .
.I 834
.T
limit design for economical missile structures .
.A
l. a. riedinger
.B
assistant manager-rand d structures dept., missile systems div.,
lockheed aircraft corp.
.W
limit design for economical missile structures .
a special safety factor alone won't do the trick in the design of
lightweight, high temperature missile structures . if you really want
to end up with the most efficient structure you can get, an entirely
new design approach is needed .
.I 835
.T
the problem of strain accumulation under thermal cycling .
.A
b. e. gatewood
.B
research coordinator, air force institute of technology,
wright-patterson air force base, ohio
.W
the problem of strain accumulation under thermal cycling .
parkes and sprague and huang have shown that it is possible for strain
growth to occur in a beam structure under temperature-load cycling .
the various aspects of this problem as to criteria for convergence and
divergence of the strain accumulation can be simply demonstrated by
thermal cycling one element of a two-element structure .
.I 836
.T
analytical and experimental investigation of stress distributions in
long flat plates subjected to lingitudinal loads and transverse
temperature gradients .
.A
sprague, g.h. and huang, p.c.
.B
wadc tr 55-350, 1955 .
.W
analytical and experimental investigation of stress distributions in
long flat plates subjected to lingitudinal loads and transverse
temperature gradients .
stress and strain distributions were studied in long flat plates in
order to develop practical analytical procedures for the design
analysis of aircraft structures at elevated temperatures .
various load-temperature conditions are presented . these include ..
methods of analysis for calculation of stress distributions under
and plastic range,.
ture .
experimental verification of the analytical procedures is shown with
comparisons between the use of constant room temperature or temperature
dependent values of modulus of elasticity and coefficient of thermal
expansion .
the test specimen, equipment, instrumentation, and experimental program
are discussed in detail . experimental data obtained from the specimen
and associated material control coupon tests are presented .
.I 837
.T
inelastic behaviour of structures subjected to cyclic
thermal and mechanical stressing conditions .
.A
padlog,j., huff,r.d. and holloway,g.f.
.B
wadc tr 60-271, 1960.
.W
inelastic behaviour of structures subjected to cyclic
thermal and mechanical stressing conditions .
a general analytical procedure is outlined for structures subjected to
varying thermal and mechanical stressing conditions . consideration is
given to the accumulation of time-independent plastic strains and creep
strains . stress-strain-temperature-time relations for uniaxial and
multiaxial stresses are defined, based on various material behavior
assumptions . several of the assumptions are compared with a limited
number of time-varying temperature and uniaxial stress tests .
the procedure is illustrated by its application to uniaxial stress
problems in which /planes originally plane remain plane/ and to plane
stress plate problems . a solution, based on the influence coefficient
approach to the plane stress plate problem, is obtained which is
applicable to all plate plan forms, edge boundary conditions, and
inplane thermal and mechanical loading conditions .
from the predicted inelastic behavior of a three-bar structure
subjected to cyclic thermal and mechanical loading conditions, it is
shown that eventual failure could result from large permanent
deformation accumulations, tensile rupture, or thermal-stress-fatigue .
a sample plate with a centrally located hole was analyzed for two
cycles of a time-varying temperature and edge stress condition . both
plastic strain reversals and plastic strain growths were predicted at
the hole . however, a test-theory comparison indicated failure by
creep-rupture .
.I 838
.T
bending and compression tests of pressurised ring-stiffened
cylinders .
.A
dow,m.b. and peterson,j.p.
.B
nasa tn.d360, 1960.
.W
bending and compression tests of pressurised ring-stiffened
cylinders .
the results of tests on pressurized ring-stiffened cylinders
subjected to compression and bending are presented and discussed . the
results obtained at high values of internal pressure differ from those
obtained by previous investigators in that the theoretical
small-deflection compressive buckling coefficient of 0.6 was nearly achieved
in each test . small amounts of internal pressure had a greater
stabilizing effect in the bending tests than in the compression tests .
.I 839
.T
the bending stability of thin-- walled unstiffened
circular cylinders including the effects of internal
pressure .
.A
suer,h.s., harris,l.a., skene,w.t. and benjamin,r.j.
.B
j. ae. scs. 25, 1958.
.W
the bending stability of thin-- walled unstiffened
circular cylinders including the effects of internal
pressure .
in a recent paper, the authors presented a statistical,
semiempirical design procedure for the determination of the buckling
strength of unpressurized and pressurized cylinders under axial
compression . this procedure has been extended in the present
paper to the bending of unpressurized and pressurized cylindrical
shells and allows the calculation of the critical bending stress with
a knowledge of the cylinder geometry and the internal pressure
only .
because no published data could be found, an extensive series
of bending tests of pressurized cylinders has been performed .
these new data for pressurized cylinders are treated
semiempirically together with all of the other known test data for
unpressurized cylinders . best-fit curves are presented using applicable
theoretical parameters . design curves for determining the
critical buckling stress for unpressurized and pressurized cylinders
in bending are then developed as 90 per cent probability curves
from the test data .
.I 840
.T
analysis of partly wrinkled membrane .
.A
stein,m. and hedgepeth,j.m.
.B
nasa tn.d813, 1961.
.W
analysis of partly wrinkled membrane .
a theory is derived to predict the stresses and deformations of
stretched-membrane structural components for loads under which part of
the membrane wrinkles . rather than studying in detail the deformations
in the wrinkled region, the present theory studies average displacements
of the wrinkled material . specific solutions of problems in flat and
curved membranes are presented . the results of these solutions show
that membrane structures retain much of their stiffness at loads
substantially above the load at which wrinkling first occurs .
.I 841
.T
on the bending of circular cylindrical shells under
pure bending .
.A
seide,p. and weingarten,v.i.
.B
j. app. mech. 28, 1961.
.W
on the bending of circular cylindrical shells under
pure bending .
the stability of circular cylindrical shells under pure bending is
investigated by means of batdorf's modified donnell's equation and the
galerkin method . the results of this investigation have shown that,
contrary to the commonly accepted value, the maximum critical bending
stress is for all practical purposes equal to the critical compressive
stress .
.I 842
.T
an improvement on donnell's approximation for thin-walled
circular cylinders .
.A
morley,l.s.d.
.B
q. j. mech. app. math. 12, 1959.
.W
an improvement on donnell's approximation for thin-walled
circular cylinders .
donnell's equation for thin-walled circular cylinders is replaced by
where w is a non-dimensional form of the radial displacement and q is
the distributed radial loading . this equation retains the essential
simplicity of the original but, unlike donnell's equation, the accuracy
does not decrease as the wavelength of circumferential distortion
increases .
.I 843
.T
a simplified method of elastic stability analysis for
thin cylindrical shells .
.A
batdorf,s.b.
.B
i. donnell's equation. naca tn.1341, 1947.
.W
a simplified method of elastic stability analysis for
thin cylindrical shells .
the equation for the equilibrium of cylindrical
shells introduced by donnell in naca report no. 479 to
find the critical stresses of cylinders in torsion is
applied to find critical stresses for cylinders with
simply supported edges under other loading conditions .
it is shown that by this method solutions may be obtained
very easily and the results in each case may be expressed
in terms of two nondimensional parameters, one dependent
on the critical stress and the other essentially
determined by the geometry of the cylinder . the influence of
boundary conditions related to edge displacements in the
shell median surface is discussed . the accuracy of the
solutions found is established by comparing them with
previous theoretical solutions and with test results .
the solutions to a number of problems concerned with
buckling of cylinders with simply supported edges on the
basis of a unified viewpoint are presented in a convenient
form for practical use .
.I 844
.T
flexural vibrations of the walls of thin cylindrical
shells having freely supported ends .
.A
arnold,r.n. and warburton,g.b.
.B
proc. roy. soc. a, 197, 1949, 238.
.W
flexural vibrations of the walls of thin cylindrical
shells having freely supported ends .
the paper deals with the general equations for the vibration of thin
cylinders and a theoretical and experimental investigation is made of
the type of vibration usually associated with bells . the cylinders are
supported in such a manner that the ends remain circular without
directional restraint being imposed . it is found that the complexity
of the mode of vibration bears little relation to the natural
frequency,. for example, cylinders of very small thickness-diameter
ratio, with length about equal to or less than the diameter, may have
many of their higher frequencies associated with the simpler modes of
vibration . the frequency equation which is derived by the energy
method is based on strain relations given by timoshenko . in this
approach, displacement equations are evolved which are comparable to
those of love and flugge, though differences are evident due to the
strain expressions used by each author . results are given for
cylinders of various lengths, each with the same thickness-diameter
ratio, and also for a very thin cylinder in which the simpler modes of
vibration occur in the higher frequency range . it is shown that there
are three possible natural frequencies for a particular nodal pattern,
two of these normally occurring beyond the aural range .
.I 845
.T
the flexural vibrations of thin cylinders .
.A
arnold,r.n. and warburton,g.b.
.B
j. proc. i. mech. e. 167, 1953, 62.
.W
the flexural vibrations of thin cylinders .
the flexural vibrations of the walls of thin cylinders are considered .
in this type of vibration many forms of nodal pattern may exist owing to
the combination of circumferential and axial nodes . theoretical
expressions are developed for the natural frequencies of cylinders with
freely-supported and fixed ends and a comparison is made with the
frequencies obtained experimentally .
in practice, the ends of cylinders are subjected to a certain degree
of fixing by end-plates, flanges, etc., and the natural frequencies thus
lie between the corresponding values for freely-supported and fixed
ends . to make possible the estimation of such frequencies, a method is
devised in which an equivalent wavelength factor is used . this factor
represents the wavelength of the freely-supported cylinder that would
have the same frequency as the cylinder under consideration when
vibrating in the same mode . the results of experimental investigations
with various end thicknesses and flange dimensions are recorded, and
from these the equivalent factors are derived .
sets of curves calculated for cylinders with freely-supported ends and
covering a range of cylinder thicknesses are given . from these it is
possible to obtain close approximation to the frequencies of cylinders
under other end conditions by the use of an appropriate factor . an
example is given of frequency calculations for a large air-receiver for
which two frequencies were identified by experiment .
.I 846
.T
on the vibration of thin cylindrical shells under internal
pressure .
.A
fung,y.c., sechler,e.e. and kaplan,a.
.B
j. ae. scs. 27, 1957, 650.
.W
on the vibration of thin cylindrical shells under internal
pressure .
the frequency spectra and vibration modes of thin-walled
circular cylinders subjected to internal pressure are considered .
it is shown that for very thin cylinders the internal pressure
has a significant effect on the natural vibration characteristics .
for these cylinders, particularly those having smaller length to
diameter ratios, the mode associated with the lowest frequency
is in general not the simplest mode . the exact number of
circumferential nodes, n, which occur in the mode associated
with the lowest frequency, depends on the internal pressure p .
if this number n is large, it decreases rapidly with increasing p
when p is small, and the /fundamental/ frequency--the lowest
frequency at each p--increases rapidly with increasing internal
pressure . at higher values of internal pressure the frequency
spectrum tends to be arranged in the regular manner, the
frequency increases with the increasing number of circumferential
nodes, and the lowest frequency rises slowly with the internal
pressure .
experimental results on the frequency spectra, vibration
modes, and structural damping of a series of thin-walled cylinders
subjected to internal pressure are briefly described . these
results show agreement with the features predicted by reissner's
the effect of slight deviation of the cylinder from perfect
circular symmetry is discussed .
.I 847
.T
experimental study of the vibrations of a circular
cylindrical shell .
.A
gottenberg,w.g.
.B
j. acoust. soc. america, 32, 1960, 1002.
.W
experimental study of the vibrations of a circular
cylindrical shell .
an apparatus is described which permits the mode
shape of a vibrating circular cylindrical shell to be
obtained quite easily . these measurements are made
without contacting the cylinder and can be converted
to actual lineal values . a representative number of
results obtained with such a system are shown to
illustrate the relationship between the nodal pattern and
frequency in a cylinder as well as the effect of internal
pressure on these frequencies . finally, comparisons
are made between these results and timoshenko theory
and an appropriate shell theory .
.I 848
.T
the effect of an internal compressible fluid column
on the breathing vibrations of a thin pressurised cylindrical
shell .
.A
berry,j.g. and reissner,e.
.B
j. ae. scs. 25, 1958,288.
.W
the effect of an internal compressible fluid column
on the breathing vibrations of a thin pressurised cylindrical
shell .
the free oscillations of a thin pressurized cylindrical shell
containing a compressible fluid are studied here . the use of an
approximate set of shell equations (shallow shell theory) leads to
a relatively simple formula for the natural frequencies of the
coupled fluid-cylinder system . the results of some
computations are presented .
.I 849
.T
a theory of imperfection for the vibrations of elastic bodies of
revolution .
.A
s. a. tobias, ph.d.
.B
.W
a theory of imperfection for the vibrations of elastic bodies of
revolution .
various observations and preliminary experiments
have shown that the effect of imperfections upon the
vibrations of bodies of revolution cannot be neglected .
owing to the possibility of applying the lagrange
equation, the influence of the imperfections could be
traced through the kinetic energy, the potential energy
and the dissipation function . although the fundamental
difficulty of the uncertainty of certain variables
was not eliminated, this procedure permitted at least
the making of general qualitative statements as to the
behaviour of the system if imperfections are present .
.I 850
.T
remarks on donnell's equations .
.A
kempner,j.
.B
j. app. mech. 22, 1955.
.W
remarks on donnell's equations .
flugge's set of differential equations of equilibrium for
circular cylindrical shells is expressed in a form analogous
to the donnell equations . the results of solutions of the
two sets of equations for a simply supported cylinder under
a centrally applied, uniformly distributed radial line load
over a generator segment, as well as under sinusoidally
applied line loads, are in very good agreement for the
particular geometry investigated .
.I 851
.T
energy expressions and differential equations for stress
and displacement analysis of arbitrary cylindrical
shells .
.A
kempner,j.
.B
j. ship res. 1958, 8.
.W
energy expressions and differential equations for stress
and displacement analysis of arbitrary cylindrical
shells .
energy expressions and the related equilibrium equations and natural
boundary conditions for the determination of the stresses in and
displacements of uniform, thin-walled cylinders of arbitrary cross section
loaded in an arbitrary manner by surface and edge forces and moments are
presented . the derivations are based upon the kirchhoff-love
assumptions of the classical theory of shells and are performed to
within a degree of accuracy employed by flugge in his derivation of the
equilibrium equations applicable to circular cylindrical shells,. hence,
in terms of stress resultants, the exact, small-deflection equilibrium
equations are obtained . methods of simplification of the relations
derived and of solution of the differential equations presented are
indicated .
.I 852
.T
stress and displacement analysis of simply supported
non- circular cylindrical shell under lateral pressure .
.A
romano,f. and kempner,j.
.B
pibal r.415, 1958.
.W
stress and displacement analysis of simply supported
non- circular cylindrical shell under lateral pressure .
this paper presents an analysis of the deflections of and stresses in a
short noncircular cylindrical shell of uniform wall thickness whose
median-surface cross section is described analytically by a simple
expression corresponding to a family of doubly symmetric ovals . the
cylinder is under a uniform lateral load and is simply supported at its
edges . the small deflection analysis considered is based upon a series
solution of appropriate differential equations of shell theory which
leads ultimately to infinite sets of algebraic equations, truncated
forms of which are considered . numerical values of the significant
stresses and displacements for points of the oval cylinder, which are 5
percent of the axial length and 2.5 percent of the circumferential
length apart, have been calculated for an oval cross section with a
major-minor axis ratio of 1.10 .
.I 853
.T
the accuracy of donnell's equations .
.A
hoff,n.j.
.B
j. app. mech. 22, 1955.
.W
the accuracy of donnell's equations .
solutions of donnell's equations of the small
deformations of the perfectly elastic thin-walled circular
cylindrical shell are compared with those obtainable from flugge's
equations . the range of the basic parameters is found
within which the two solutions are approximately equal .
.I 854
.T
boundary-value problems of the thin-walled circular
cylinder .
.A
hoff,n.j.
.B
j. app. mech. 21, 1954.
.W
boundary-value problems of the thin-walled circular
cylinder .
the homogeneous differential equations of donnell's
theory of thin cylindrical shells are integrated .
expressions are obtained in closed form for the displacements,
membrane stresses, moments, and shear forces .
.I 855
.T
simplified formulas for boundary value problems of
the thin-- walled circular cylinder .
.A
pohle,f.v. and nardo,s.w.
.B
j. app. mech. 22, 1955.
.W
simplified formulas for boundary value problems of
the thin-- walled circular cylinder .
n. j. hoff has presented formulas which can be used in
the solution of boundary-value problems of circular
cylinders . the purpose of this note is to express these
results in exact simplified form,. a more detailed
investigation appears elsewhere . the notation will be that of
hoff unless otherwise stated .
.I 856
.T
some experimental studies of panel flutter at mach
1 .3.
.A
sylvester,m.a. and baker,j.e.
.B
naca tn.3914, 1957.
.W
some experimental studies of panel flutter at mach
1 .3.
experimental studies of panel flutter were conducted at a mach
number of 1.3 to verify the existence of this phenomenon and to study the
effects of some structural parameters on the flutter characteristics .
thin rectangular metal plates were used in these studies and were
mounted as a section of the tunnel wall . most of the data were obtained by
using aluminum-alloy panels, although a few steel, magnesium, and brass
panels were also used . different materials with various thicknesses
and lengths were used to determine the effect of these parameters on
panel flutter . the experimental program consisted of three phases ..
panels clamped front and rear, and (3) buckled panels clamped on all
four edges .
panel flutter was obtained under controlled laboratory conditions
and it was found that, at the flow conditions of these tests, increasing
tensile forces were effective in eliminating flutter, as were
shortening the panels or increasing the bending stiffness . no apparent
systematic trends in the flutter modes or frequencies could be observed,
and it is significant that the panel flutter sometimes involved higher
modes and frequencies . the presence of a pressure differential