PROJECT RAND: PHYSICAL RECOVERY OF SATELLITE PAYLOADS - A PRELIMINARY INVESTIGATION
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June 26, 1956
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I
U. S. AIR FORCE
PROJECT RAND.
RESEARCH MEMORANDUM
PHYSICAL RECOVERY OF SATELLITE PAYLOADS --
4 PRELIMINARY INVESTIGATION
J. H. Huntzicker
H. A. Lieeke
26 June 1956
This research is' sponsored by the United States Air Force under contract No.
AF 49(638)-700 monitored by the Directorate of Development Planning, Deputy
This is. a working paper. It may be expanded, modified, or withdrawn at any
time.' The views, conclusions, and recommendations expressed herein do not
necessarily reflect the official views or policies of the United States Air Force.
.74e P~ n D e4vma~
FOR 07 F!.,ti->;fad, `aas do U' 7Z
L ~+t:s
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SUMMARY
Preliminary investigations indicate that solutions may exist for
the major problems associated with the recovery of portions of a recon-
naissance satellite. A method is described for recovering heat-sensitive
items, such as photographic film, and the weight penalties involved are
estimated. A payload of 50 lb of film, for example, could be recovered
at a total expense in weight of about 225 lb.
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TABLE OF CONTENTS
Page
SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . ii
LIST OF SYMBOLS . . . . . . . . . . . . . . . . . . . . . iv
Section
I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . 1
II. FLIGHT MECHANICS . . . . . . . . . . . . . . . . . . 2
III. PROTECTION DURING RE-ENTRY . . . . . . . . . . . . . 8
IV. PACKAGE LOCATION AFTER IMPACT . . . . . . . . . . . . 12
V. SYSTEM WEIGHTS . . . . . . . . . . . . . . . . . 13
VI. DISCUSSION OF RESULTS . . . ... . . . . . . . . . .14
A. DETERMINATION OF PROTECTIVE CASE TEMPERATURES . . . . 16
B. DETERMINATION OF SYSTEM WEIGHTS . . . . . . . . . . . 18
FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . 20
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . 31
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A area projected in the drag direction
CD coefficient of drag
c specific heat
e eccentricity of the ellipse describing the motion of
a body about the earth
g acceleration of gravity at sea level
h altitude
he conductivity
R radius (mean) of the earth
r radius from the earth's center to the vehicle and/or
recovery package
T temperature
t time
V velocity
AV incremental velocity added to the recovery package
W weight
X range measured on the earth's surface from addition
of AV to impact
a exponent of the density approximation (a = e-0h)
y angle between the velocity of a body and the horizontal
B the angle of the incremental velocity with respect to
the orbital velocity
the gravitational constant
ratio of propellant weight to gross weight for a
rocket motor
Poo
sea level air density
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a ratio of air density at altitude to that at sea level
angle between the radius vector from the earth's center
to a body moving about the earth, measured from the
radius vector 'to the apogee of the ellipse which de-
scribes the body's motion.
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I. INTRODUCTION
Development of a method for recovering certain items intact from a
reconnaissance satellite is desirable for a number of reasons. The amount
of information a satellite could gather would be substantially increased.
Materials (film, living tissue, etc.) could be examined in detail to
learn environmental effects. Also, photographic. coverage of the earth's
surface could be realized prior to the development of a dependable TV
linkage for satellite use. A less direct benefit would be knowledge
derived from working out successful recovery techniques: refinement of
such techniques may be a necessary prelude to serious consideration of
manned space flight.
Successful recovery, on command, of a satellite payload is contingent
upon three conditions:
1. The trajectory of the orbiting payload must be modified so that
it will intersect the earth's surface at a specified time and location.
2. Payload items must be protected from aerodynamic heating during
re-entry into the earth's atmosphere.
3. The payload must be located and retrieved promptly after it
impacts.
This memorandum investigates these three conditions and suggests a method
for recovering useful material from an orbiting vehicle.
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The natural decay of a satellite orbit due to atmospheric drag will
cause the body to return to the earth. The impact point could be pre-
dicted by observing the body during its re-entry into the atmosphere, but
there would be no control over the location of the impact point. However,
the position of the impact point can be selected--to some degree of
accuracy--by changing the velocity vector of the package to be recovered.
This could be done by using a rocket to apply thrust to the package after
it separates from the orbiting body either to change the magnitude, or the
direction and magnitude, of the velocity of the package relative to the
circular orbital velocity vector. The descent range and the re-entry con-
ditions of the package are a function of the initial orbital altitude and of
the direction and magnitude of the velocity increment.
The velocity for a circular orbit at any radial distance can be
expressed as
Vorb rorb
where p is the gravitational constant and is taken to be 1.41008 x 1016
ft3/sect.
In general, the magnitude of the resultant velocity of the package is
V ' /(Vb)2 + (AV)2 + 2V orb AV cos 0
where 0 is the angle of the velocity increment AV measured clockwise from
the orbital velocity vector as shown in the following sketch.
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The angle between this resultant velocity vector and the instan-
taneous horizontal is given by
tV sin 0
tan 7 orb + t cosh
jThe eccentricity of the ellipse can be written as
(2 - V2r) ?2r cos 2 . y
?/ ?
where V is the resultant velocity and r is the orbital radius.
The range angle, measured at the center of the earth, from this point
to the apogee of the ellipse is given by
1 - V2r coot 7
d _ ?
and the range angle from the apogee to the surface of the earth (r . R) is
given by
Zrcos27r
cos O2 . ? e
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Therefore, the total descent range from the point vhere the velocity
increment is added to the surface of the earth is given by
I - R (01 + d2)
for a vacuum re-entry trajectory.
For the case of a velocity increment directed rearward (0
these equations Simplify to
V- olb'AV
- 1800),
7-0
X0.-0
cos$2-
V2r
V2r r
Z-R02 .
The variation of vacuum range to impact as a function of velocity
increment is given in Fig. 1 for initial orbital altitudes of 150, 300,
land 500 statuto miles for the case of a rearward increment (0 - 180?).
It can be seen that a velocity increment of at least 2000 ft/sec is
required if the descent
rage is to be less than 3000 n sii for an initial
orbital altitude of 300 mi. The re-entry trajectory of a typical body
will intersect the earth at a point roughly 200 mi short of the vacuum
distance due to the influence of the atmospheric drag.
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The effect of varying the angle of the velocity increment 0 is shown
in Fig. 2 for an initial orbital altitude of 300 mi and a velocity
increment of 3000 ft/sec. Values of 0 of 90` deg and 180 deg give
approximately equal vacuum descent ranges, but the re-entry trajectories
are somewhat different.
An estimate of the sensitivity of descent range to errors in the
magnitude and direction of the velocity increment can be obtained from
these graphs. For a 300 mi orbit and AV - 3000 ft/sec with 0 - 180?,
the slopes are )X/ d AV - - 0.27 n mi/ft/sec and 2 X/ a 0 a - 27.1 n
mi/deg. If the velocity increment is added at an angle of about 130 deg
from the direction of motion, the slope 2 X/ 30 is seen to be near zero,
and only a velocity error would contribute to the impact point uncertainty.
The velocity and path angle of the ellipse at a given altitude above
the earth can be found from the following equations. The velocity, at an
altitude h, is
Vh2 - V2 +
2? 2?
rh rorb
and the path angle is given by
cos rh ? (V--r coo . 7')
h rh
where rh - R + h and the term (V r cos 7) is evaluated at orbital altitude
after the velocity increment has been added.
The initial conditions for re-entry into the atmosphere at a nominal
altitude of 250,000 ft are presented in Fig. 3a,b. Figure 3a shows the
variation of re-entry velocity and path angle for three initial orbital
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4
altitudes and several velocity increments for the case of 0 - 1800. For
comparison, the re-entry conditions for a 5500 n mi ICBM fired at various
ranges using its full velocity potential are indicated by the nearly
horizontal dashed line. The points on this curve cover the re-entry
conditions for the missile fired on trajectories which vary from the
3000 Ed low case through maximum range to the 5000 mi high trajectory.
Thus, we see that the terminal portions of the trajectories for the
recovery of a package from a satellite in a circular orbit around the
earth are similar to the re-entry trajectories of a 5500 n mi ICBM when
fired at shorter ranges on low non-optimum trajectories.
Figure 3b is included to show the effect of varying the angle of
the velocity increment for the case of a 300 mi orbital altitude and a
velocity increment of 3000 ft/sec. The dashed curve, representing an
orbital altitude of 300 mi with varying velocity increments added at
0 a 180?, is repeated from Fig. 3a. It is seen that the re-entry
conditions vary symmetrically around 0 - 1800 while the total vacuum
descent range as shown in Fig. 2 does not. It is interesting to note
that the re-entry velocity resulting from a 3000 ft/sec increment added
at angles of less than about 110 deg or more than about 250 deg is
greater than the local circular orbital velocity.
No re-entry trajectories have been calculated for the initial
conditions corresponding to this package recovery study, but a case
corresponding to the maximum range ICBM point has been used to compute
the temperature history shown in Fig. 4.
Reference 1 presents an approximate analytical solution of the
equations of motion during the re-entry. These equations give reasonable
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values for the various trajectory variables until the curvature of the
path becomes large.
The maximum deceleration experienced by the body is given by
tic 02 sin yo
and the velocity at which it occurs is approximately
v - 0.607 0
where Vo and y0 are the velocity and path angle respectively, at the
nominal re-entry altitude.
The altitude for maximum deceleration can be found from the equation
for the density ratio which is
g poo
where a is the constant in the exponent in the isothermal atmosphere
approximation a - e-Ch. The value of a is about k x 10-5 per foot.
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III. PROTECTION DURING RE-ENTRY
Two steps can be taken to protect the payload from excessive
temperature rises. The aerodynamic heating of the outer shell can be
reduced through control of the re-entry flight path, and the payload can
be insulated from the outer casing. First, let us consider the problem
of controlling the re-entry flight path.
For "dump ranges" (ranges on the surface of the earth from point of
impulse to impact) of a few thousand miles the descending trajectory
resembles that of an ICBM. The re-entry heating problems of ICBM war-
heads have been examined in detail by Carl Gazley, Jr. (Ref. 1). His
CD A
work demonstrates that as the ratio is increased, maxim=
deceleration occurs at successively higher altitudes and the total heating
per unit area decreases. The possibility suggests itself that a large
enough parachute would limit the total heating to such an extent that
conventional parachute fabrics would retain their strength.
This has been investigated by Gazley, in an unpublished work, for
the example of a ,re-entering warhead attached to a parachute 100 ft in
diameter with a total weight of 3500 lb. Figure 4 shove the heating
experienced by such a device. The case was assumed to be an insulated
skin of 0.05 in. stainless steel. The parachute was constructed of
fiberglas cord and cloth (designed with a factor of safety equal to 2)
and covered with an additional layer of cloth as a shield against the
high transient heating load.
This method of supplying a large drag area is a somewhat arbitrary
choice. To be suitable the device used should be able to expand its linear
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dimensions by one or two orders of magnitude and yet weigh only a
fraction of the total package weight. One might consider such devices as
balloons (the parachutes might use balloons to ensure proper opening) or
structures which telescope or fan out. However, as the design for any
such structures approaches minimum weight it begins to resemble the
design of a foil parachute. The inherent advantages of fabric (i.e.,
efficient packaging, non-continuous fra=cture and heat paths, etc.) suggest
a parachute 3f conventional construction.
The behavior of parachutes is known for reasonably dense gases and
for speeds up to low supersonic Mach numbers (Ref. 2). For estimating
performance in rarified gases at hypersonic Mach numbers a "reasonable
extra lation" was made. Obvious
po Iry, experimental investigation will be
necessary before performance can be predicted with confidence.
Peak aerodynamic heating occurs in a region of the atmosphere in
which little knowledge has been accumulated but where considerable interest
is now being directed. By conventional criterion the flow over the package
will be well within the all-lamina r regime (ignorance concerning transition
will not be critical). The mechanism of heat transfer to the parachute
cannot be well defined until the flow is better uncle]stood. The flow
and heat transfer have been assumed similar to those for a blunt body for
the temperature studies in this memorandum.
The shroud lines were treated as infinite, inclined cylinders for
the determination of heating. The covering fabric on the lines would
probably lose most of its strength at maximum temperature, but all that
is required is that it hold together for about one minute.
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Figure 4 indicates directly how the temperature of a recovery
package might be controlled. The time-temperature curves could be in-
CD
terpreted as applying to such a package if the parameter were
equal for the two cases (from Fig. 3 the angle 7 is seen to be similar
to that for an ICBM).
In the case of the re-entering warhead the parachute would be de-
tached about 30 sec after re-entry to lessen warhead vulnerability to
interception. (The effect on the warhead skin temperature of retaining
the parachute is indicated on Fig. 4 by a dashed line.) The recovery
package would retain its parachute until touchdown, not primarily because
of temperature considerations but because a longer descent time and
lover impact velocity (about 17 ft/sec) would aid in the successful
recovery of the package.
The skin temperature is a function not only of the flight path
and the skin pr
j. properties, but also of the absolute size of the
package (due to the dependence of the heat-transfer coefficient upon the
Reynold's number). This is, of course, included in the calculations
appended to this memo but it is actually a second-order effect for
these qualitative considerations.
The payload can be insulated from the heated surface with convention-
al materials and techniques. Due to the transient nature of the heating
the insulating material and the outer casing are more efficient if used in
a number of layers rather than a single layer. (This is in agreement with
the results shown in Ref. 3.)
Figure 5 illustrates the heating of an inner case as a function of
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time for an outer skin raised to a constant elevated temperature. The
distribution of metal between the outer case and successive layers
.within the fiberglas insulation is varied as follows: (a) outer and
inner cases only; (b) one intermediate layer; and (c) two intermediate
layers. This figure demonstrates the ability to increase the insulating
effectiveness to allow for increased outer-case temperatures without the
addition of appreciable weight. In essence the heat capacity of the
insulation is increased with no commensurate increase in conductivity.
In reality the temperatures of the outer case will begin to decrease
after the first half minute (i.e., dashed line in Fig. 4). The tempera-
; tures of the outer case, interlayers, and inner case are plotted as
functions of time in Fig. 6.
It is worth noting that most of the heat input to the intermediate
layers and the inner case occurs after the outer case has started to cool.
Figure 7 shows the outer-case temperature for the transient condition and
the corresponding equilibrium temperature (determined for the altitude
and velocity as functions of time during descent). It appears that a
possible aid to the protection of the package might consist of the
ejection of the front outer layer after the initial heating has concluded.
The next layer exposed would remain close to the equilibrium temperature
for the remainder of the flight path and the heating problem would be
correspondingly reduced. This technique is conceptually very simple;
C
mechanically, it implies that the . of the ejected layer is less than
that of the remaining package plus parachute (to eliminate interference
with the parachute).
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IV. PACKAGE LOCATION AFTER IMPACT
Although it appears quite possible to bring the package through the
atmosphere in an undamaged condition there remains the problem of location
and recovery after impact. This problem is lessened considerably if the
parachute is retained till touchdown. A total descent time from dump
signal to impact of from:40 to 60 minutes allows ample time for the
package to be tracked, its final position predicted, and recovery
proceedings initiated. (A small radio beacon could be included for small
cost in weight and it would facilitate tracking.)
The ease with which a package could be recovered is a direct function
of the predictability of its impact point. Figure 2 indicates the
sensitivity of range to the elevation angle of the incremental thrust.
As shown, the effects of errors in this angle are minimized if the angle
is chosen for minimum range. Angular errors of as much as +20 deg
could easily be tolerated if distance errors of as much as 100 n mi were
acceptable.
Errors in azimuth of the incremental thrust will result in
proportional errors on the ground (e.g., for h ? 150 mi and AVE:P
2000 ft/sec an angular error in azimuth of +10 deg results in a ground
error of +35 n MO.
In the unlikely event of a high wind which is invariant with altitude
these deviations could be approximately doubled. (This effect can be
estimated ahead of time.)
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V. SYSTEK WEIGHTS
An estimate has been made of the weight penalties involved If the
,equipment necessary for successful recovery were included in a satellite
'stage. The components of such a recovery system are illustrated in Fig.
8.
The prime item for which all this effort is being made is assumed
to be exposed photographic film. Total weights derived for this
assumption will be conservative for payload items of greater density and
decreased temperature sensitivity. (The film is assumed to be damaged
if its temperature exceeds 100?F.)
The component weights for a film weight of 50 lb are tabulated in
Table 1 for an orbital altitude of 150 at mi and a dump range of 2500 n mi.
,The assumptions and procedures for determining these weights are included
in Appendix B, as is the determination of total package weight as a function
of film weight, altitude, and dump range. This variation is shown in
Fig. 9.
ITEM
WEIGHT
lb)
Film
Reel
50
5
Beacon (plus power, witching,
etc.)
10
Case + Insulation
45.8
Parachute (plus positive
opening device)
25.8
Solid Rocket
91
TOTAL 227.6
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The problem of modifying the trajectory of an orbiting body so that
it will intersect the earth's surface at a specified time and location
appears to yield to simple, straightforward techniques. The method
investigated here, that of using a rocket to change the velocity vector
of the package to be recovered, is particularly suitable when the
atmosphere and/or the orbital properties are not known accurately.
Use of a rocket assumes at least a gross control of the body's attitude--
it would be sufficient to be able to point approximately downward.
The problem of protecting payload items from aerodynamic heating
during re-entry into the earth's atmosphere calls for two approaches,
both of which appear to be feasible. The payload can be insulated from
the heated surface with conventional materials and techniques; and the
aerodynamic heating of the outer shell can be reduced through control of
the re-entry flight path by means of a double-layered fiberglas parachute.
Fibers with better high-temperature characteristics than glass, such as
quartz, should be investigated. More knowledge is also needed about the
behavior of light, high-drag devices in a hypersonic, rarified gas
stream and about the reaction of parachute elements (double-layered or
otherwise) to highly transient heating loads.
When sufficient knowledge and control are available, one might con-
sider flying an orbiting body at a critically low altitude and commanding
significant increases in drag to effect a return.
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The final problem, that of locating the payload after impact,
does not appear to be of unusual difficulty. A small radio beacon and,
:possibly, flotation gear contained in the recovery package appear to
offer a reasonable solution. The long descent times might permit air-
borne units to be in the immediate vicinity When the package reaches the
surface.
In conclusion it may be said that the successful recovery of use-
ful material from orbiting vehicles appears to be an attractive possi-
bility. Because of the preliminary nature of this study no conclusive
Judgment can be made of the method outlined here for returning payloads,
but the inherent simplicity of this method suggests that it be given
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Appendix A
DETERMINATION OF PROTECTIVE CASE TEMRATURES
The efficacy of an insulating layer when protecting against highly
transient beating loads is a function of two of its properties, the
conductivity and the heat capacity. Low conductivity and high heat
capacity are desirable, but are generally incompatible in a homogeneous
material.
The heat capacity of an insulating layer can be increased by the
insertion of discrete layers of a material of high conductivity and
large heat capacity. If these layers are oriented perpendicular to the
direction of heat flow, and if the structure of the insulating material
is fine compared to the interval between layers the conductivity of the
insulating layer vill not be increased.
This effect can be demonstrated as follows--a step function is
assumed for the temperature of an outside wall, (i.e., for t < 0,
Tw 80?F and for td--O., TV T. 700?F). The effectiveness of an insulation,
composed of a total of 2 in. of Fiberglas and 0.10 in. of steel, is
investigated for the following conditions: (a) a conventional arrangement
of a 2 in. slab of fiberglas backed by a 0.10 in. skin of steel; (b) 2
slabs of fiberglas, each 1 in. thick, separated by a 0.05 in..sheet of
steel, and a 0.05 in. inner case; and (e) 3 slabs of fiberglas, each
0.667 in. thick, separated by 0.033 in. steel sheets, and an inner case
of 0.033 in. steel.
For each of these three conditions the temperature of the inner
case was determined as a function of time using the following physical
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properties--
conductivity of fiberglas, h . 0.024 BTU
c 21 Pf o.
specific heat of fiberglas, c . 0 (assumed)
conductivity of steel, h 0 ... (assumed)
specific heat of steel, c - 0.12
The results of this calculation are plotted in Fig. 5. The definite but
transient advantage of multiple layers is demonstrated.
The insulating effectiveness of category (c) has been investigated
for an outer wall exhibiting the temperature history of an insulated skin
:(of equal thickness, i.e., 0.05 in.) re-entering the atmosphere along the
;trajectory plotted in Fig. 10. This trajectory was determined for a re-
entering warhead but, as can be seen in Fig. 3, it falls veil within the
range of trajectories expected from re-entering orbiting bodies.
The following assumptions governed the determination of the outer
wall temperature. It was conservatively assumed that the surface areas
effective in convection and radiation were equal. (The expression for the
convective heat transfer coefficient is based on area projected in the
velocity direction, while that for radiation is based on total area.)
Atmospheric properties were obtained from Ref. 4.
The temperatures of the outer case and of the inner layers are
plotted as functions of time in Fig. 6. It appears possible to protect
a re-entering payload using relatively simple techniques.
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Appendix B
DETEEMINATION OF SYSTEM WEIGHTS
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The techniques and mechanisms employed in recovering film from a
satellite can be examined in terms of the orbiting weights that are implied.
Component weights have been estimated for an elementary system (see Fig. 8)
using the following assumptions:
The film and reel and the radio beacon, plus its power, switching,
etc., were assumed to have over-all specific gravities of approximately
0.5. With efficient packaging they might be enclosed within a surface
area equal to twice that for a sphere of equal volume. Of this area
three-quarters is covered by complete insulation (an outer case of 0.05
in. steel followed by three equal layers of 0.667 in. fiberglas and 0.033
in. steel) and the remaining one-quarter is covered by the inner 0.033 in.
steel only. The density of steel is taken as 485 lb/ft3 and that of
fiberglas as 7 lb/ft3.
Starting with an arbitrary film weight, increasing it by 10 per cent
to allow for the reel, and adding 10 lb for the beacon, etc., the total
weight of the insulated package can be determined. The size and weight
of the required parachute can be determined directly knowing the package
weight, the area-weight ratio of the parachute, and stipulating that the
C A
ratio, , for the package-parachute combination should equal 4.
(CD = 1.4+, Ref. 3).
Parachute weights were determined for double-layered elements through-
out and a 100 per cent margin of safety on the inner, load-carrying members.
A ratio of 0.06 lb/ft2 was used. The parachute weights determined in this
fashion were increased by 10 per cent to allow for positive opening devices.
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If the total weight of the package plus parachute is known, the size
of rocket can be determined that is needed to accomplish the specified
deceleration. The specific impulse for a solid rocket vas assumed to be
200 sec and the ratio of propellant weight to total rocket weight (v
to be 0.6.6
The aforementioned methods were used to estimate total weights as
functions of film weight, altitude and dump range. This relationship
is plotted in Fig. 9. Table I itemizes the component weights for a
system returning 50 lb from a 150 mi orbit with a dump range of 2500 n mi.
The weight estimates do not include effects on the design of the
orbiting stage. The structure of the orbiting vehicle should accommodate
the recovery system so that its components would require a minimum of
readjustment before firing.
"These assumptions introduce a considerable degree of conservatism.
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9=1800
C
a
0
0
U
E
3
V
0
orb = 500 statute miles
0 I 2 3 4 5 6 7
Velocity increment, AV, (thousands of ft/sec)
Fig. I-Ground range vs velocity increment for package drop from a satellite
RM 1811-I
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21
o a
( D0
V
O O
to 4)
o ZI%_ N
>
v U
2
4) Q1
C
w f-
o c
O
L 1 I I I I
1~ t0 K1 tr M N
(iw u jo spuosno44)`g `abuoa 4uaosap w nnoo,\
N U)
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h = 250,000 f t
AV=1000 ft/sec
9 = 180?
2000
3000
4000
ICBM Re-entry
3000 low
4000 low
M
ax range
5000 low
5000
6 00 h i g h
8000
ho-b = 500 m i
300
150
-10 -20
Path angle, y , (deg)
Fig. 3a-Re-entry initial conditions
RM I8I1-3
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Vorb
h = 250,000 ft
9 = 90?, 270?
AV=3000 ft/sec
e120?,240?
e =150?, 210?
8=1800
\horb:300mi
-10 -20
Path angle, y, (deg)
Fig. 3 b- Re-entry initial conditions
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L C
0
O U
O N
I I I I I
O O 0 0 O
tD qT N O O
ao`a.n4oAad waj
a)
E
N
C
O
10
N
-4O
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N
C
U
m
N
m
C
C
O
O
U
m
a m U
1/~ Y] ~+ ~ ? Jr K A^j
f ti ~ I 1 ~ ^~A'
0 0 0 0
O 0 OD ~O
0
.o
0
In
0
It
0
M
0
N
0 0 0 0
O 0 co 1l-
0 0
(D to
dOtain;oJadwa; uil$
c
0
4-
0
In
C
o a)
E
0.
E
I
c+
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i
2
Time from initiation of heating (thousands of seconds)
26
Fig. 6-Temperature vs time for an insulated re-entering body
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ao`a.inloiadwal uiNS
RM-1811
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27
v
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0
0
U
0
CL
0
N
C
E
N
U
.N
0
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Orbital altitude, h,
WF
3 10
E
2 3 4
Descent range, S, ( thousands of n mi )
Fig. 9-Ratio of total weight to film weight vs range
for varying altitude and film weight
RM I8II-10
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500 statute miles
300 statute miles
Film weight
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0 0
0 0 0
spuoaas `Bu140a4 ;0 u014014lul WO1 awll
o 0 0 0 0 0 0
o 0 0 O 0 0
t? N O a w
o 0 0 0 0 V0 0 0 0
0 0 0 Z5 0 0 c00 V N
0 CD t0 N
puooas .iad 4a8, `A{l30leA
RM 1811-II
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31
REFERENCES
1. Gazley, C., Jr., Heat Transfer Aspects of the Atmospheric Re-entry
of Long Range Ballistic Missiles, The RAND Corporation, Report
13, August nc assiried).
2. "United States Air Force Parachute Handbook," Headquarters, Air
Materiel Command, USAF, April 1957 (Revised December 1957)
(Confidential).
3. Fisher, W. W., and D. J. Masson, Thermal Environmental Considerations
of Measurements and Tests,Hermes XSSM-A-1 Missile, Project
Hermes Summary Report G.E. R57+AO530, September 195Ti (Confidential).
4. Kallman, H. K., Physical Properties of the Upper Atmosphere, The RAND
Corporation, Research Memorandum BM- , May 1952 Unc ssified).
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FOR OFFICIAL USE ONLY
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