REPORT 1382 A COMPARATIVE ANALYSIS OF THE PERFORMANCE OF LONG-RANGE HYPERVELOCITY VEHICLES

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP71B00265R000200130002-3
• Release Decision: RIFPUB
• Original Classification: K
• Document Page Count: 22
• Document Creation Date: December 23, 2016
• Document Release Date: November 21, 2013
• Sequence Number: 2
• Publication Date: January 1, 1959
• Content Type: MISC

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REPORT 1382
A COMPARATIVE ANALYSIS OF THE PERFORMANCE
OF LONG-RANGE HYPERVELOCITY VEHICLES
By ALFRED J. EGGERS, Jr., H. JULIAN ALLEN,
and STANFORD E. NEICE
Ames Aeronautical Laboratory
Moffett Field, Calif.
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National Advisory Committee for Aeronautics
Headquarters, 1512 H Street 14., Washington 25, D. C.
Created by Act of Congress approved March 3, 1915,,for the supervision and direction of the scientific study
of the problems of flight (U. S. Code, title 50, sec. 151). Its membership was increased from 12 to 15 by act
approved March 2, 1929, and to 17 by act approved May 25, 1948. The members are appointed by the President
and serve as such without compensation.
JAMES H. DOOLITTLE, Sc. D., Vice President, Shell Oil Company. Chairman
LEONARD CARMICHAEL, Ph. 11, Secretary, Smithsonian Institution, Vice Chairman
ALLEN V. AsTIN, Ph. D., Director, National Bureau of Standards.
PRESTON R. BASSETT, D. Sc.
'DETLEV W. BRONK, Ph. D., President, Rockefeller Institute for
Medical Research.
? FREDERICK C. CRAWFORD, Sc. D., Chairman of the Board, ,
Thompson Products, Inc.
WILLIAM V. DAVIS, JR., Vice Admiral, United States Navy,
Deputy Chief of Naval Operations (Air).
PAUL D. FOOTE, Ph.])., Assistant Secretary of Defense, Re-
search and Engineering.
WELLINGTON T. HINES, Rear Admiral, United States Navy,
Assistant Chief for Procurement, Bureau of Aeronautics.
JEROME C. HUNSAKER, Sc. D., Massachusetts Institute of
Technology.
CHARLES J. MCCARTHY, S. B., Chairman of the Board, Chance
Vought Aircraft, Inc.
DONALD L. Pun. Lieutenant General, United States- Air Force,
Deputy Chief of Staff, Development.
JAMES T. PYLE, A. B., Administrator of Civil Aeronautics.
FRANCIS W. REICHELDERFER, Sc. D., Chief, United States
Weather Bureau.
EDWARD V. RICKENBACKER, Sc. D., Chairman of the Board.
Eastern Air Lines, Inc.
Louis S. Roniscuan, Ph. B., Under Secretary of Commerce for
Transportation.
THOMAS D. WHITE, General, United States Air Force, Chief of
Staff.
HUGH L. DRYDEN, PH. D., Director
JOHN F. VICTORY, LL. D., Executive Secretary
jOHN W. CROWLEY, JR., B. S., Associate Director for 7?esearch EDWARD H. CHAMBERLIN, Executive Officer
HENRY .1. E. Ritio, D. Eng., Director, Langley Aeronautical Laboratory, Langley Field, Va.
SMITH J. DEFRANCE, D. Eng., Director, Ames Aeronautical Laboratory, Moffett Field, Calif,
EDWARD It, SHARP, Sc. D., Director, Lewis Flight Propulsion Laboratory, Cleveland, Ohio
WALTER C. WILLIAMS, B. S., Chief, High-Speed Flight Station, Edwards, Calif.
II
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REPORT 1382
A COMPARATIVE ANALYSIS OF THE PERFORMANCE OF
LONG-RANGE HYPERVELOCITY VEHICLES
' By ALFRED J. EGGERS, JR., H. JULIAN ALLEN, and STANFORD E. NE10E
SUMMARY
Long-range hypervelocity vehicles are studied in terms of their
motion in powered flight, and their motion and aerodynamic
heating in unpowered flight. Powered fight is analyzed for
an idealized propulsion system which approximates 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 inatimum? 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 (NA GA Rep. 1381),
with the exception that radiant as well as conve.ctive 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 neighbor-
hood 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 above 4 it is about equal to comparable glide
vehicles. The skip vehicle experiences extremely large loads,
however, and it encounters most severe aerodynamic heating.
As a final performance consideration, it is shown that on the
basis of equal ratios of mass at take-off to mass at the end of
? powered flight, the hypervelocity vehicle compares favorably
with the supersonic airplane for ranges in the neighborhood of
and greater than one half the circumference of the earth. In the
light of this and previous findings, it is concluded that the
ballistic and glide vehicles have, in addition to the advantages
usually ascribed to great speed, the attractive possibility of pro-
viding relatively efficient long-range flight.
Design aspects of manned hypervelocity vehicles are touched
on briefly. It is indicated that if such, a vehicle is to develop
relatively high lift-drag ratios, the wing and tail surfaces should
have highly swept, rounded leading edges in order to alleviate
the local heating problem with minimum drag penalty. The
nose of the body should also be rounded somewhat to reduce
local heating rates inithis region. If a manned vehicle is de-
signed for global range flight, the large majority of lift is ob-
tained from centrifugal force, and aerodynamic lift-drag ratio
becomes of secondary importance while aerodynamic heating
becomes of primary importance. In this case a glide vehicle
which enters the atmosphere at high angles of attack, and hence
high lift, becomes especially attractive with a more or less
rounded bottom to minimize heating over the entire lower surface.
The blunt ballistic vehicle is characterized by especially low
heating, and it too may be a practical manned vehicle for ranges
in UCCA's of semiglobal if great care is taken in supporting the
occupant to withstand the order of 10 g's maximum deceleration
encountered during atmospheric entry.
INTRODUCTION
, it is generally recognized that hypervelocity vehicles are
especially suited for military application becauso of the great.
difficulty of defending against them. It is also possible
that for long-range operation, hypervelocity vehicles may
not, be overly extravagant in cost,. A satellite vehicle, for
example, can attain arbitrarily lonflange with a finite speed
and hence finite energy input. E. Sanger was among the
first to recognize this favorable connection between speed
and range (ref. I) and was, with Bredt, perhaps the first to
exploit the speed factor in designing a long-range bomber
(ref. 2). This design envisioned a rocket-boost vehicle
attaining hypervelocities at burnout and returning to earth
along a combined skip-glide trajectory. Considerable at-
tention was given to the propulsion and motion analysis;
however, little attention was given to what is now con-
sidered to be a principal problem associated with any type
of hypersonic aircraft, namely that of aerodynamic heating.
In addition, the category of expendable vehicles, perhaps
best characterized by the ballistic missile, was not treated.
Since the work of Sanger arid Bredt, there have been, of
course, many treatments of long-range hypervelocity
Supersedes NA CA Technical Note 4040 by Alfred J. Eggers, Jr., ii. Julian ARID, and Stanton' E. Melee, 1057.
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2 REPORT 1382?NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
des in which the propulsion, motion, and heating problems
have been studied in considerable detail. However, these
analyses have been devoted in the main to particular designs
and are not intended to reveal, for example, the relative ad-
vantages and disadvantages of ballistic-, skip, and glide-
type vehicles. Furthermore, it appears that the extent to
which these vehicles can compete on a simple efficiency basis
with lower speed aircraft of either the expendable or non-
expendable type has not been well established.
It has therefore been undertaken in the present report to
make a comparative analysis of the performance of hyper-
velocity vehicles having ballistic, skip, and glide trajectories.
An idealized propulsion system, whose performance approxi-
mates that of rocket motors, is assumed. The motion
analysis is simplified by treating, for the most part, only
optimum trajectories yielding the maximum range for
given initial kinetic energy per unit mass in the unpowered
portion of flight. Aerodynamic heating is treated in a man-
ner analogous to that employed by the senior authors in
studying ballistic missiles (ref. 3) with the exception that
radiant heat transfer, as well as convective heat transfer, is
considered in the treatment of glide and skip vehicles. The
efficiencies of these vehicles are compared with supersonic
aircraft with typical air-breathing power plants.
NOTATION
reference area for lift and drag evaluation, sq ft
specific heat of vehicle material, ft-lb/slug ?R
drag coefficient
lift coefficient
skin-friction coefficient
equivalent skin-friction coefficient (see eq. (40))
specific heat of air at constant pressure, ft-lb/slug
oR
specific heat of air at constant volume, ft-lb/slug
?R
drag, lb
Naperian logarithm base
performance efficiency factor (see eq. (85))
general functional designation
functions of 44,J, (see eqs. (74) and (80))
ratio of maximum deceleration to gravity
acceleration (32.2 ft/see)
acceleration due to force of gravity, ft/see
convective heat-transfer coefficient, ft-lb/ft? sec
oR
convective heat transferred per unit area (unless
otherwise designated), ft-lb/ft'
specific impulse, sec
range parameter for glide vehicle (see eq. (68))
Stefan-Boltzmann constant for black body
radiation (3.7X 10-40 ft-lb/ft, sec ?R4)
constant in stagnation point heat-transfer equa-
tion, slug in/ft (see eq. (44))
lift, lb
mass, slugs
Mach number
convective heat transferred (unless otherwise
designated), ft-lb
Vs
7
A
7/
0
A
U
distance from center of the earth, ft
radius of curvature of flight path, ft
radius of earth, ft
range, ft
distance along flight path, ft
surface area, sq ft
time, sec
temperature (ambient air temperature unless
otherwise specified), ?R
velocity, ft/sec
ratio of velocity to satellite velocity
velocity of satellite at earth's surface (taken as
25,930 ft/sec)
weight, lb
vertical distance from surface of earth, ft
angle of attack, radians unless otherwise speci-
fied
constant in density-altitude relation, (22,000 ft,-';
see eq. (15))
ratio of specific heats, Cp/C;
semivertex angle of cones, radians unless other-
wise specified
increment
lift-drag efficiency factor, (see eq. (B27))
angle of flight path to horizontal, radians unless
otherwise specified
leading edge sweep angle, deg
air density, slugs/cu ft (p0=0.0034)
nose or leading-edge radius of body or wing, ft
partial range, radians
total range, radians
remaining range (43-9), radians
Subscripts
0 conditions at zero angle of attack
1, 2, 3, .. . conditions at end of particular rocket stages
a conditions at point of maximum average heat-
transfer rate
av average values
conditions at point of maximum local beat-
transfer rate
convection
effective values
en conditions at entrance to earth's atmosphere
ex conditions at exit from earth's atmosphere
conditions at end of powered flight.
initial conditions
local conditions
ballistic phases of skip vehicles
total number of rocket stages
pressure effects
pay load
I. recovery conditions
radiation
stagnation conditions
7' total values
wall conditions
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PERFORMANCE OF LONG-RANGE HYPERVELOCITY VEHICLES
ANALYSIS
GENERAL CONSIDERATIONS
In the following analysis of long-range hypervelocity
vehicles, only flight in planes containing the great circle
arc between take-off and landing is considered. The flight
is thought of in two phases: (a) the powered phase in which
sufficient kinetic energy, as well as control, is imparted to the
vehicle to bring it to a prescribed velocity, orientation, and
position in space; and (b) the unpowered phase, in which the
vehicle travels to its destination under the influence of
gravity and aerodynamic forces.
The analyses of motion and aerodynamic heating during
unpowered flight will, of necessity, differ widely for the
several types of vehicles under consideration. On the other
hand, motion in the powered phase is conveniently treated
by a method common to all vehicles. The study of powered
flight and its relation to range is therefore taken as a starting
point in the analysis.
POWERED FLIGHT AND THE FIREGUET RANGE EQUATION
In this part of the study, the following simplifying as-
sumptions are made: (a) aerodynamic heating can be
neglected on the premise that high flight speeds are not
attained until the vehicle is in the rarefied upper. atmosphere;8
(b) sufficient stability and control is available to provide
proper orientation and positioning of the vehicle in space;
(c) the distance traveled while under power is negligible by
comparison to the overall range; and finally, (d) the thrust
is very large compared to the retarding aerodynamic and
gravity forces. In terms of present-day power plants, the
last assumption is tantamount to assuming a rocket drive
for the vehicle.
The velocity at burnout of the.first stage of a multistage
rocket (or the final velocity of a single-stage rocket) can then
be expressed as (see, e. g., ref. 4):
V
fl -=ilVs ( 72-9 (1)
/nil
where the initial velocity is taken as zero. In this expression,
nt, and in.,, represent the mass of the vehicle at the beginning
arid ending of first-stage flight, and where Vs=
VF.-=--25,930 feet per second is the satellite velocity at the
surface of the earth. The coefficient g is the acceleration due
to gravity and is, along with the specific impulse I, con-
sidered constant in this phase of the analysis. The final
velocity of the vehicle at the end of the N stages of powered
flight can be expressed as
V ,= = in Ktn (!!S (2)(2)
mfi nif2 onf
where the initial mass of any given stage differs from the
final mass of the previous stage by the amount of structure,
etc., jettisoned.
Now let us define an equivalent single-stage rocket having
the same initial and final mass as the N-stage rocket and the
$ This assumption Is In the main permissible. A possible exception occurs, however, with
the glide vehicle for which heat-transfer rates near the end of powered night can be comparable
to those experienced to unpowered gilding flight
3
same initial and final velocity. There is, then, an effective
specific impulse defined by
(
I rat.
In k?nti) (17-71)
= Mt)]
1..1
111EIM)
Mf
whereby equation (2) can be written as
?2L ln (-1"1
s
(3)
(4)
The effective specific impulse ./. is always somewhat less
than the actual specific impulse, but for an efficient design
they are not too different. Throughout the remainder of
the analysis the effective impulse It will be used.
Equation (4) might be termed the "ideal power plant"
equation for accelerated flight because, when considered in
combination with the assumptions underlying its develop-
ment, attention is naturally focused on the salient factors
leading to maximum increase in velocity for given expendi-
ture of propellant. Thus the thrust acts only in over-
coming inertia forces, and the increase in vehicle velocity
is directly proportional to the exhaust velocity (gl) of the
propellant.
Now we recognize that an essential feature of the hyper-
velocity vehicles under study here is that they use their
velocity (or kinetic energy per unit mass) to obtain range.
For this reason, equation (4) also constitutes a basic per-
formance equation for these vehicles because it provides
a connecting link between range requirements and power-
? plant. requirements.
In addition to comparing various types of hypervelocity
vehicles, our attention will also be focused upon comparison
of these vehicles with lower speed, more conventional types
of aircraft. For this purpose it is useful to develop an
alternate form of equation (4). We observe that the
kinetic energy imparted to the vehicle is
nIsTif2
This energy is equated to an effective work done, defined as
the product of the range traveled and. a constant retarding
force. (Note that the useful kinetic energy at the end of
powered flight is zero.) This force is termed the "effective
drag" D.. Thus
D el? = mfif2 (5)
where II is flight range measured along the surface of the
earth. Similarly, we may define an "effective lift" L?
equal to the final weight of the vehicle
Le=W f=mig
from which it follows that equation (5) may be written as
where (LID), is
Combining equations (4) and (6); we obtain
1?-,(1) V. ln (M)
D
R=(1)
D e 2g
(6)
termed the "effective lift-drag ratio."
(7)
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4 REPORT 1382?NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
where
(8)
and represents an "effective" flight velocity of the vehicle.
Equation (7) will prove useful in comparing hypersonic
vehicles with conventional aircraft because of its analogy
to the Breguet range equation,
R=P) IV In C.?)
nif
(9)
It will also prove useful to have equation (7) in the dimen-
sionless form obtained by dividing through with 7.0, the
radius of the earth. In this case we have
= ()D ("g1) 1 n (7 121)
ro e Vs Mf (10)
where (I, is the range in radians of arc traversed along the
surface of the earth.
MOTION IN UNPOWERED FLIGHT
Ballistic trajectory.?In studying the motion of long-range
vehicles in this trajectory, advantage is taken of the fact
that the traverse through the earth's atmosphere generally
form's only a small part .of the total trajectory. Therefore,
the deflection and deceleration encountered in the re-entry
phase (discussed in detail in ref. 3) are neglected in the
computation of the total range and rotation of the earth is
neglected in this and all other phases of the analysis. With
the added simplification that the contribution to range of
the powered phase of flight is negligible, the ballistic. tra-
jectory becomes one of Kepler's planetary ellipses, the
? major axis of which bisects the total angle of arc 43 traveled
around the earth. For the trajectories of interest here
(V,.:c 1), the far focus of the ellipse is at the mass center
of the earth. For purposes of range computation, then, the
ballistic vehicle leaves and returns to the earth's surface
at the same absolute magnitude of velocity and incidence
(see sketch).
.-Elliptical orbit
?-Earth's surface
The expression for range follows easily from the equation
of the ellipse (see, e. g., ref. 5) and can be written
R,
Lan , (r ?cos 'Ofsin f COS 0)
(Pi="a?U. ?
ro (11)
V,'
where the angle of incidence 0/. is considered positive. In
order to determine the optimum trajectory giving maximum
range for a given velocity V1, equation (11) is differentiated
with respect to Of and equated to 0, yielding
V'
V 2? =1?tan201
f Vc2
(i) ? 40 f
(12)
Equations (11) and. (12) have. been employed to determine
velocity as a function of incidence for various values of
range and the results are presented in figure 1. The "mini-
limn velocity line" of figure 1 corresponds to the optimum
trajectories (eqs. (12)).
The effective lift-drag ratios can easily be calculated for
optimum ballistic vehicles using equation (6) in combination
with the information of figure 1. The required values of
(LID), as a function of range are presented in figure 2.
Skip trajectory.?This trajectory can be thought of as a
succession of ballistic trajectories, each connected to the
next by a "skipping phase" during which the vehicle enters
the atmosphere, negotiates a turn, and is then ejected from
the atmosphere. The motion analysis for the ballistic
missile can, of course, be applied to the ballistic phases of
the skip trajectory. It remains, then, to analyze the
skipping. phases and to combine this analysis with the bal-
listic analysis to determine over-all range.
To this end, consider a vehicle in the process of executing
.a skip from the atmosphere (see Sketch).
von
vex
--- ?-Outer reach of
atmosphere
V
//Earth's surface
The parametric equations of motion in directions perpen-
dicular and parallel to the flight path s are, respectively,
?Co si dV
n o= (T.
-------
pV2 mV2
re
? 2 pV2 Amg cosCOS 0
(13)
where r, is the local radius of curvature of the flight path, 61is
the local inclination to the horizontal (positive downward),
p is the localiair..density, and (7,. and CD are the lift and drag
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PERFORMANCE OP LONG-RANGE RYPERVELOCITY 'VEHICLES
20
1.6
1.4
1.2
.4
.2
-Minimum velocity line
0 10 20 30 40 50 60
incidence angle, Of , degrees
FIGURE 1.? Variation of velocity with incidence angle for various
values of range of ballistic vehicle.
70
80
90
'coefficients, respectively, based on the reference area, A, of
the aircraft.
In the turning process, aerodynamic lift must obviously
predominate over the gravity component, mg cos O. By anal-
ogy to the- atmospheric re-entry of ballistic missiles (see ref.
3), aerodynamic drag generally predominates GVer the gravity
component, mg sin 0. Moreover, the integrated contribution
to velocity of this gravity component during descent in a skip
is largely balanced by an opposite contribution during ascent.
16
12
0
2 4 6
Range parameter,
FIGURE 2.?Variation of effective lift-drag ratio with range for optimum
ballistic vehicle.
8
16
4
Ven.18,670
ft/sec
I
14,:12,480
14.,I2,,350
ft/sec -
ft/sec
Maximum lift
:28
'
acceleration
5g
Neglecting
gravity
gravity
I
I-
I Including
0 20 . 40 60 BO
Distance along eorth'S surface, feet x10-4
FIGURE 3.?Trajectory of the first skipping phase for a skip vehicle
with a lift-diag ratio of 2 and a total range of 3440 nautical miles
(0=1).
5
IOC
For these redsOnst we will idealize the analysis by neglecting
gravity entirely. This approach is analogous to the classical
treatment of impact probleina in which all forces exclusive of
impact forces (aerodynamic forces in this ease) are neglected
as being of secondary importance. Gravity is shown to be
of secondary importance in figure 3 where the trajectory It-
Bulls obtainable from equations (13) and (14) are presented
for the first skipping phase of an LID =2, 4=1 skip missile.
With gravity terms neglected, equations (13) reduce to
CDPIrA=In
0,,p1/121. V! it,
dV (10
where &yds= ?1- to the aecuracy of this analysis.
re
Now we assume an isothermal atmosphere, in which case
P=portw (15)
where pc, and ft are constants, and y= (r ?7.0) is the altitude
from sea level (see ref. 3 for discussion of accuracy of this as-
sumption). Noting that dy/ds= ?sip 0, we combine the first
of equations (14) with equation (15) to yield
CIL" enb= sin 0d0
(14)
2m
'This expression can be integrated to give
CiroA
25wc---=cos 0?Cos oen
(16)
where D is taken as zero at the altitude corresponding to
effective "outer recta" cif the atniosphere. Equation (17)
points out an important feature of the skip path; namely,
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6 REPORT 1382?NATIONAL ADVISORY
cos 0 is a single-valued function of altitude. Since 0 proceeds
from positive to negative values, it is evident that
fienn- 17.= ?9an
(18)
where the subscripts en and ex refer to atmospheric entrance
and exit conditions, respectively, and the numbers n-1 and
n refer to successive ballistic phases of the trajectory. Now
since
dV _vdV _1 dV2
dt? ds2 cis
equations (14) may be combined to obtain
1 dV2_ V2 dO
2 ds LID (Ts
which, for constant LID, can be integrated to yield
eareast_i
'Vein
=e LID - (20)
"1/4- I
With the aid of equation (18), this expression may be
written
(19)
Vet
LID
e (21)
which relates the velocities at the beginning and end of a skip
to the lift-drag ratio and the entrance angle of the vehicle to
the earth's atmosphere. From equation (18) it follows
further that the entrance angle for each skip in the trajectory
is the same, so that
t 3 ena=0 enn_,I= ? ? ? =0,
and hence equation (21) becomes
201
Vern LD
Vass-7e
(22)
We now combine this result of the skip analysis with that
of the ballistic analysis to obtain the total flight range.
From equation (11) the range of the nth ballistic segment of
the trajectory is
sin Of COS 0,
n= 2 tan-'(23)
( Vex V 8 ?COS2 0 11
Consistent with the idealization of the skipping process as an
impact problem, we neglect the contribution to range of each
skipping phase so that the total range is simply the sum of
the ballistic contributions. From equations (22) and (23)
this range is then
R
tan-'sin 0 cos 0
(24)
4 (n-1)61
ro 111.
1 LID
e ?cos2 f
LV?
From this expression we see that for any given velocity
at the end of powered flight there is a definite skipping angle
COMMITTEE FOR AERONAUTICS
which maximizes the range of an aircraft developing a
particular lift-drag ratio. These skipping angles have been
obtained with the aid of an IBM CPC, and the corresponding
values of V., as a function of range for various LID are
presented in figure 4. Corresponding values of (LID), have
been obtained using equation (6) and the results are shown
in figure 5.
1.0
.8
2.6
.2
0
L/Dt.5
1.0
. ?
8.0
/Pr
,
Range parameter, tip
FIGURE 4.?Variation of velocity with range for various values of
lift-drag ratio for skip vehicle.
Glide trajectory,--The trajectory of the glide vehicle is
illustrated in the accompanying sketch. As in the previous
analyses, the distance covered in the powered phase will be
neglected in the determination of total range.
--Earth's surface
The parametric equations of motion normal and parallel
to the direction of flight are the relations of equations (13)
rewritten in the form
mV21
L?mg
dV
?DH-mg sin 0=
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(25)
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lii
20
16
12
4
PERFORMANCE
OF LONG-RANGE HYPERVELOCITY VEHICLES
80
S
/
6.0
.6
/ i
P/r
/ /
2, f 2.1 2
r
.3
/
/ /
/ / 4
.,
,
, / in
,
,
4.0
/ 0 ..5
/ 4.0
//
/
/
1114#
//
0 2 4 6
Range ea (meter,
' FintniE 5.?Variation of effective lift-drag ratio with range for various
values of aerodynamic lift-drag ratio of skip vehicle.
Under the assumption of small inclination angle 0 to the
horizontal (thus cos 0 Az 1 , sin 0 0) , eons,. ankgravity aecelerti
8
lion e., 1> and noting the
r?
(IV dIT
?=-
following
1 d
relations
dt
ds
2 ds
r,
(26)
ds
(10
cos?
1
ds
r
r,
equations (25) can be written in the fo tris
L=-7711,8 do -1-mg-mV2
ds
(27)
I din .
D=-2- in ?ds+ mg 0
Dividing the first of equations (27) by the second yields the
following differential equation
n 6 LL 1/2_172(1qt V2=0
\ D \2 D s dsj
(28)
But, as is demonstrated in Appendix A, the terms -go and
D
488428?MI-2
de
V' - may be neglected so that equation (28) reduces to
(1172 2 .
r0(LID) LID
V92= gr.
Since
(29)
equation (29) can be integrated for constant .25 to give the
velocity in nondimensional form as
? 2o
T72= _ _ 17,2)4b/D
This expression gives velocity as a function of range for what
Sanger (ref. 2) has termed the equilibrium trajectoi3-that
is, the trajectory for which the gravity force is essentially
balanced by the aerodynamic lift and centrifugal force, or
(30)
(31)
II follows from equation (3)) that velocity can be expressed
in the form
72_
LAVs2p
2mg
(32)
Now it is intuitively obvious that as. the maximum range is
approached, L/147-)1 and hence V' becomes small compared
to one (see eq. (31)). In this event it follows from equation
(30) that the maximum range for the glide vehicle is given by
4)._ R=1 (I, \ \
r? 2 \D) 1-17,2)
The relation between velocity and range has been deter-
mined with equation (33) for various values of LID and the
results are presented in figure 6. Corresponding values of
(LID), have been obtained using equation (6) and are
presented in figure 7. ?
These considerations complete the motion analysis and
attention is now turned to the aerodynamic heating of the
several types of vehicles under consideration.
(33)
is-
0 ?
9
/Dip
i.0
2.0
8.0
Tr
r
2 ';
4
Range parameter, 40
FIGURE G.?Variation of velocity with range for various values of
lift-drag ratio of glide vehicle.
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Declassified and Approved For Release 2013/11/21 : CIA-RDP71600265R000200130002-3
8
2
16
4
REPORT 1382?NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
IP
70.0
/
.3
plej
A
8.0 /.9
7?2.0
/2.0
Parpir
Let/#1.0
/0?,
0 2 4
Range parameter, rt)
FICURE 7.?Variation of effective lift-drag ratio with range for various
values of aerodynamic lift-drag ratio of glide vehicle.
6
8
HEATING IN UNPOWERED FLIGHT
General considerations.?Three aspects of the aerodynamic
heating of hypervelocity vehicles will be treated here; namely,
I. The total heat input
2. The maximum time rate of average heat input per unit
area
3. The maximum time rate of local heat input per unit
area
Total heat input is, of course, an important factor in deter-
mining over-all coolant weight, whether the coolant be solid
(e. g., the structure), liquid, or gas, or a combination thereof.
The maximum time rate of average heat input per unit area
can determine peak average flow rates in the case of fluid
coolants and may dictate over-all structural strength in the
event that thermal stresses predominate.
Excessive local heating is, of course, a serious problem with
hypervelocity vehicles. This problem may vary depending
upon the type of the vehicle. Thus, for the ballistic vehicle,
an important local "hot spot" is the stagnation region of the
nose, while for the skip or glide vehicle attention may also be
focused on the leading edges of planar surfaces used for de-
veloping lift and obtaining stable and controlled flight. In
this analysis attention is, for the purpose of simplicity, re-
stricted to the "hot spot" at the nose. In particular, we
consider the maximum time rate of local heat input per unit
area because of its bearing on local coolant flow rates and
local structural strength.
It is undertaken to treat Only convective heat transfer at
this stage of the study. As will be demonstrated, radiant
heat transfer from the surface should not- appreciably in-
fluence convective heat transfer to a vehicle. Therefore,
alleviating effects of radiation are reserved for attention in
tile discussion of particular vehicles later in the paper. This
analysis is further simplified by making the assumptions that
1. Effects of gaseous imperfections may be neglected
2. Shock-wave boundary-layer interaction may be neg-
lected
3. Pr and ti number is unity
4. Reynolds analogy is applicable
These assumptions are obviously not permissible for an accu-
rate quantitative study of a specific vehicle. Nevertheless
they should not invalidate this comparative analysis which is
only intended to yield information of a general nature regard-
ing the relative merits and problems of .different types of
vehicle (see ref. 3 for a more complete discussion of these
assumptions in connection with ballistic vehicles).
In calculating convective heat transfer to hypervelocity
vehicles, the theoretical approach taken in reference 3 for
ballistic vehicles is, up to a point, quite general and can be
employed here. Thus, on the basis of the foregoing assump-
tions, it follows that for large Mach numbers, the difference
between the local recovery temperature and wall temperature
can be expressed as
172 ?
T.)1=
2C,
(34)
It is clear, however, that the walls of a vehicle should be
maintained sufficiently cool to insure structural integrity.
It follows in this case that the recovery temperature at
hypervelocities will be large 11)y comparison to the wall tem-
perature and equation (34) may be simplified to read
7'?
11-2C?
(35)
To the accuracy of this analysis, then, the convective heat
transfer is independent, of wall temperature. Therefore, as
previously asserted, radiant, heat transfer should not appre-
ciably influence convective heat transfer and the one can be
studied independently of the other.
Now, according to Reynolds analogy, the local heat-
transfer coefficient kg is, for a Prand tl number of unity, given
by the expression
h1=1C.,C,,p1171 (36)
where CFI is the local skin-friction coefficient based on con-
ditions just outside the boundary layer. With the aid of
equations (35) and (36) the time rate of local heat transfer
per unit area,
can be written as
dif
dH V' (0 V
dt =40?
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(37)
(38)
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PERFORMANCE OF LONG-RANGE HYPERVELOCITY VEHICLES
9
Equation (38) can be integrated over the surface of a body For the "relatively light missile," which is of principal interest
to yield the time rate of total heat input as follows here,
dQ dH 711 pv8c," s
dt= s 48.= (39)
wherein (.1?, is set equal to C? and
C/4 L Ce, dS (40)
The parameter Cp' is termed the "equivalent skin-friction
coefficient" and will be assumed constant at a mean value
for a particular vehicle. From equation (39) we can obtain
two alternate forms which will prove useful; namely, the
altitude rate of total heat input defined by. (note that dy is
negative for dt positive)
dQ 1 dQ pine, S
dy ? V sin dt 4 sine
and the range rate of total heat input defined as
dQ 1 dQ pV2Cp'S
(l(roio) V cos 8 di? 4 cos
(41)
(42)
The total heat input may be obtained by integration of
equations (39), (41) or (42), depending upon the particular
variable used.
The time rate of average heat input per unit area may be
obtained from equation (39) as.
dna, dQ Inc ,
=-di S- di=i
(43)
Consider next the local convective heat transfer in the
region of the nose. The time rate of local heat input per
unit area was determined in reference 3 under the assump-
tions that viscosity coefficient varies as the square root of
the absolute temperature, and that flow between the bow
shock wave and the stagnation point is incompressible. In
this case it was found t hat
dH,
-re=K V'
(44)
where K=6.8X10-6. A more detailed study of stagnation
region flow, including effects of compressibility and dissoci-
ation of air molecules (ref. 6), shows that the constant, K,
should have a value more like twice the above value at the
hypervelocities of interest here.
With these relations we are now in a position to study
the heating of the several types of vehicles of interest.
, Ballistic vehicle.?The heating for this case has already
been analyzed in reference 3. Only the results will be given
here.
The ratio of the total heat input to the initial kinetic
energy was found to be
Q 1 Ca ( C0p0A
4m122 CDA \.1?e Dm sin Of (45)
CD00A
e sin f 1/2/3. For cases where 17, DIL as V2-40), and so with any significant lift-drag
ratio it is far superior to the ballistic vehicle in this respect.
In addition, the glider has the important advantage of
maneuverability during atmospheric entry. These factors
and its potential for relatively high performance efficiency
make the glider generally attractive as a man-carrying
machine.
It will be assumed that if the glider is to develop reasonably
high lift-drag ratios it should be slender in shape. But the
nose of the body and the leading edges of the wing (and tail
surfaces) should be blunt to alleviate the local heating prob-
lem. Blunting the nose of the body may not, if properly
done, increase the drag of the vehicle (see refs. 10 and 11).
Blunting the leading edge of the wing will, however, incur a
drag penalty and thereby reduce the lift-drag ratio. This
difficulty may be largely circumvented by sweeping the lead-
ing edge of the wing. The contribution to total drag of the
drag at the leading edge is, according to Newtonian theory,
reduced in this manner by the square of the cosine of the
angle of sweep for constant span. The question which arises
is how does sweep influence heat-transfer rate. The nature
of this influence (ref. 6) is shown in figure 12 and it is ob-
served that sweep decreases heat-transfer rate very substan-
tially, although not to the extent that it decreases drag.
We are led then to the conclusion that the wing on a hyper-
velocity glide vehicle which develops reasonably high lif t-
drag ratio should have highly swept leading edges. This
observation coupled with the fact that wing weight should
be minimized suggests for our consideration the low-aspect-
ratio delta wing. In addition to the wing it is anticipated
that a vertical tail will be needed to provide directional
stability and control, and so we are led to imagine as one
possibility a hypervelocity glider of the type shown in
figure 13.
The potential of the glider to have relatively high per-
formance efficiency hinges strongly on the finding that the
large majority of the heat convected to it may be radiated
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PERFORMANCE OF LONG-RANGE HYPERVELOCITY VEHICLES
1.0
",---Heat transfer
Drag
I1 i I i
0 10 20 30 40 50
Angle of sweep. A, deg
-
FIGURE 12,?'Effect of sweep on drag and heat transfer to circular
cylinders.
60 70
0
Ar2a532.
FIGURE 13.?Example high lift-drag ratio glider.
away at reasonably low surface temperatures. But it is
never possible to build a perfect radiation shield. There is
always a certain amount of heat which leaks through the
shield, to the internal structure. As 4,he duration of flight
increases this heat leakage problem may assume major pro-
portions if substantially more structure (or coolant) is re-
quired to absorb the heat. If, at the same time, the action
of aerodynamic forces has, at best, a minor influence on
range then the high lift-drag-ratio glider may cease to be an
attractive machine. For flights approaching global range
these two factors tend to come into play. That is, flight
time becomes relatively long (of the order of an hour and
a half or more) with the attendant increase in seriousness of
the heat leakage problem, while lift-drag ratio assumes a
15
FIGURE 14.?Example high lift glider.
relatively minor role in terms of performance efficiency (see
fig. 10). Accordingly, it may be attractive to launch a global
glider into a low altitude satellite orbit which itifollows over
the large majority of its range and from which it enters the
atmosphere in the terminal phase of flight to glide the short
remaining distance to its landing point. Under these cir-
cumstances, the vehicle may be designed to minimize aero-
dynamic heating during atmospheric entry and for this pur-
pose we are attracted to the use of high lift 5 as well as low
wing loading (see eqs. (76) and (77)) to reduce heating rates
and surface temperatures. Accordingly, the vehicle may
glide into the atmosphere at a high angle of attack for high
lift coefficient, maintaining this attitude until speed has been
reduced to a supersonic value where heating has become a
relatively minor problem. The angle of attack may then be
reduced to increase LID, thereby extending the glide and
increasing maneuverability to achieve the desired landing
point. For this type of application the vehicle might Wave
more of the appearance shown in figure 14, again being of
the delta-wing plan form but having a more or less rounded
bottom and sides to minimize heating rates over the leading
edge as well as the entire lower surface during re-entry.
Such a configuration bears a resemblance to a motorboat
and it may in fact be suited for landing on water as shown.
AmEs AERONAUTICAL LABORATORY
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
MOFFETT FIELD, CALIF., Dec. 10, 1954
6 High lift tends, of course, to mean Increased decelerations because of reduced LID during
atmospheric entry:however , even for LID's of the order of unity these decelerations remain
modest and they should not, therefore, constitute a serious piloting problem.
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Declassified and Approved For Release 2013/11/21 : CIA-RDP71600265R000200130002-3
APPENRIX1. A
,41M'1111.,!f: rNG, A,RNplysTIONE \ANA1lyEl?,.011. /TIRE GLIDE TRAJECTORY
.The assumption of small, Inflection angle (0