DTIC ADA1031984: Survivability of Penetrators with Circumferential Shear-Control Grooves

AD A10 319 8

W-/

NWC TP 6275

Survivability of Penetrators With
Circumferential Shear-Control

Grooves

by

J. C. Schulz
and

0. E. R. Heimdahl
Research Department

April 1981

s

a-

6 .

NAVAL WEAPONS CENTER
CHINA LAKE, CALIFORNIA 93555

Approved for public release; distribution unlimited.

81 8 21 06 7

Naval Weapons Center

AN ACTIVITY OF THE NAVAL MATERIAL COMMAND

FOREWORD

The research described in this report was conducted in support of
controlled fragmentation studies for hard target penetrator warheads
under the Air Strike Warfare Weaponry Technology Block Program at the
Naval Weapons Center. The work was performed during Fiscal Year 1981,
and was funded by AIRTASK WF32395, Program Element 62332N, Work Unit
1321051.

This report was reviewed for technical accuracy by John Pearson.

Approved by
E. B. ROYCE, Head
Research Devartment
1 April 1981

Under authority of
W. B. HAFF
Capt., U.S. Navy

Released for publication by
R. M. HILLYER

Technical Director

NWC Technical Publication 6275

Published by.Technical Information Department

Collation.Cover, 15 leaves

First printing.155 unnumbered copies

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A TITLE 'and Sutorir/e)

SURVIVABILITY OF PENETRATORS WITH
CIRCUMFERENTIAL SHEAR-CONTROL GROOVES

T AuTmOP^J;

J. C. Schulz and 0. E. R. Heimdahl

9 PERFORMING ORGANIZATION NAME ANO AOOPESS

Naval Weapons Center
China Lake, CA 93555

M. CONTROLLING Office NAME ANO AOOPESS

Naval Weapons Center
China L'ake, CA 93555

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Research Report
Fiscal Year 1981

6. performing org. report number

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AIRTASK WF32395, 62332N
1321051

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April 1981

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19. KEY WOROS f Cantlnua on ravacao at da tl nacaaaary and Identity by block numbmr)

Survivabi1ity
Cylinders
Penetrators
Shear-control

Warheads

Small-scale firings

29 ABSTRACT Continua on ravaraa alda It nacaaaary and Idantlly by block numbat)

See back of form.

JAN 73 1^73 EDITION OF 1 NOV «S IS OBSOLETE
J S.'N 0102 LF 014 6601

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(U) Survivability of Penetraiors With Circumfer¬
ential Shear-Control Grooves , by J. C. Schulz and
0. E. R. Heimdahl. China Lake, Calif., Naval Weapons
Center, April 1981. 28 pp. (NWC TP 6275, publica¬

tion UNCLASSIFIED.)

(U) Small, cylindrical, steel projectiles con¬
taining circumferential grooves were fired against
simulated concrete and steel-plate targets to in¬
vestigate possible effects of shear-control grid
placement on the survivability of impacting warheads.
The projectiles fired against simulated concrete de¬
veloped a bulge near the front of the internal cavity.
The presence of a groove in this region significantly
reduced the breakup velocity, while a groove a short
distance to the rear had no effect on survivability.
Thus, a shear-control grid could be machined from
slightly behind the bulge to the rear of a warhead
case without reducing survivability while, at the
same time, maintaining a significant amount of frag¬
mentation control. Against steel-piate targets,
damage to the projectile was confined primarily to
the front end, and a groove in the internal cavity,
whether at the bulge location or behind it, had
little effect on structural survivability.

\

_ UNCLASSIFIED

SECURITY CLASSIFICATION OF THIS PAOEC***" Dm* Bn'fd)

NWC TP 6275

CONTENTS

Introduction . 3

Description of Experiments . 4

Projectiles . 4

Targets . 4

Experimental Procedure . 6

Results Against Thorite Targets . 6

Results Against Steel-Plate Targets . 12

Conclusions.17

Appendixes:

A. Procedure for Making Thorite Targets . 18

B. Photographs of Projectiles After Test . 19

Figures:

1. Cross-Sectional Views of Test Projectiles With

Details of Grooves . 5

2. Impact Behavior of Projectiles Fired Against

Thorite Targets . 10

3. Penetration Depth Versus Impact Velocity for

Test Projectiles Fired Against Thorite . 11

4. Decrease in Length Versus Impact Velocity for

Test Projectiles Fired Against Thorite . 13

5. Cavity Bulge Height Versus Impact Velocity for

Test Projectiles Fired Against Thorite . 14

6. Increase in Radius at Front End Versus Impact Velocity

for Test Projectiles Fired Against Thorite . 15

Tables:

1. Results of Projectile Firings Against Thorite Targets ... 7

2. Projectile Survival Velocities Against Thorite Targets ... 9

3. Results of Projectile Firings Against Steel-Plate Targets . 16

1

INTRODUCTION

The shear-control method of warhead fragmentation, as described by
Pearson, 1 ’ 2 has been employed in a variety of bombs and warheads to pro¬
duce fragments of pre-determined size and shape. Typically, a diamond¬
shaped grid is either machined or formed into the inside surface of a
warhead case. The grid is composed of families of left- and right-hand
spiral grooves, which act as stress raisers such that the fragmentation
process is governed by the initiation of shear fractures at the root of
the grid elements. The size and shape of the fragments produced is con¬
trolled by the design parameters of the particular grid.

For warheads required to survive penetration or perforation of
targets prior to detonation, these stress-raising grooves may have the
unwanted effect of inducing premature structural failure of tne warhead
case. It has been hypothesized that should such failure uccur, it would
be primarily due to the presence of grooves in the highly stressed region
near the front of the explosive cavity where a bulge often develops in
the warhead case at the transition location between nose and wall. Thus,
failure might be avoided by the expedient of not extending the grid
forward into this region. The effect of shear-control grids on warhead
survivability has not been extensively investigated.

This report describes the results of a series of firings of small,
cylindrical, steel projectiles containing circumferential grooves against
simulated concrete and steel-plate targets. The grooves were located
either at the point of maximum bulging near the front of the projectile
cavity or a short distance to the rear of this point. In addition, some
ungrooved projectiles were fired for comparison purposes. Similar firings
of ungrooved projectiles only have been reported by Stronge and Schulz. 3
The purpose of the current firings was to test the above hypothesis

1 John Pearson. "The Shear-Control Method of Warhead Fragmentation,"
in Proceedings of the Fourth International Symposium on Ballistics,
Monterey, California, 17-13 October 1373. Monterey, Calif., Naval Post¬
graduate School, 1978. Publication UNCLASSIFIED.

2 Naval Weapons Center. Parametric Studies for Fragmentation War¬
heads, by John Pearson. China Lake, Calif., NWC, April 1968. (NWC TM
4507, publication UNCLASSIFIED.)

3 W. J. Stronge and J. C. Schulz. "Projectile Impact Damage Analy¬
sis," in Proceedings of the Symposium on Computational Methods in linn-
linear Structural and Solid Mechanics, Arlington, Virginia, 6-3 Oct. 1360.

Published as special issue of s. Computers .5 Structures, Vol. 13, No. 1-2.
(1981), pp. 287-294.

NWC TP 6275

regarding the influence of grid placement on warhead survivability, the
grooves being intended to roughly simulate the effect of the shear-control
grid. At the same time, the results are not restricted to shear-control
grids only, but are applicable to other stress raisers in impacting pro¬
jectiles. It is anticipated that additional results obtained through
metallurgical examination of cross-sectioned projectiles will be covered
in a later report.

DESCRIPTION OF EXPERIMENTS

PROJECTILES

The projectiles were all flat-fronted, hollow cylinders, 2 inches
long and 0.5-inch in diameter. The hemispherical front of the internal
cavity was 0.25 inch from the front end of the projectile. The cavity
wall was 0.04-inch thick. The grooves were located either 0.46 or 0.71
inch from the front end, and were either 0.004- or 0.008-inch deep.

Thus, counting the ungrooved projectiles, there were altogether five
different configurations. Cross-sectional views of the projectiles with
details of the grooves are shown in Figure 1. Abbreviated designators
for the projectiles are also given (P-N, P-46S, P-46D, P-71S, and P-71D,
where N means no groove, 46 and 71 are groove distances from the front
end in hundredths of an inch, and S and D indicate the shallower and
deeper grooves, respectively). All of the projectiles were machined
from 4340 steel rods and were heat-treated to a Rockwell C hardness of
38 to 40.

TARGETS

The projectiles were fired against two different targets: simulated
concrete and steel plate.

Simulated concrete targets were made of Thorite (® Standard Dry Wall
Products), a fast-setting, high-strength (3950 psi compressive strength)
concrete patching compound consisting of sand, cement, and additives to
promote rapid curing. The largest sand grains are about 0.04 inch in
diameter. The targets were cured for 7 days prior to the firings. The
targets were wet-cured (with their surfaces covered with water) for 24
hours and allowed to dry-cure (with their surfaces exposed to air) for
the remaining 6 days. It was found that care in preparation of the tar¬
gets was required to ensure high strength and uniformity. The prepara¬
tion procedure used is described in Appendix A.

Steel-plate targets were cut from 1/16th-inch-thick sheets of a
hot-rolled, low-carbon steel with a Rockwell B hardness of 55.

4

MATERIAL: 4340 STEEL, R c 38-40

FIGURE 1. Cross-Sectional Views of Test
Projectiles With Details of Grooves.

NWC TP 6275

EXPERIMENTAL PROCEDURE

The projectiles were fired from a smooth-bore, 50-caliber powder
gun. Impact velocities were measured in the gun barrel with a photo
diode system coupled to an interval counter. The Thorite targets were
placed about 18 inches from the end of the barrel, and the steel-plate
targets about 6 inches from the end of the barrel. The projectiles
impacted the targets at normal obliquity. Projectiles that perforated
steel-plate targets were captured in a recovery trough filled with
Celotex® slabs placed immediately behind the targets. The apparatus is
described more fully by Goldsmith and Finnegan. 4

RESULTS AGAINST THORITE TARGETS

Thirty shots were fired against Thorite targets. The results are
summarized in Table 1. Photographs of all the projectiles after test
are contained in Figure B-l in Appendix B. Photographs of selected
cross-sectioned projectiles are shown in Figure B-2.

During penetration, high stresses generated near the front of the
internal cavity result in considerable plastic deformation and the de¬
velopment of a bulge near the junction between hemisphere and side wall
(Figure B-l, P-N, 2490 fps, for example). At sufficiently high impact
velocities, a circumferential fracture occurs in the bulged region,
resulting in separation of the front portion from the rear portion
(Figure B-l, P-N, 2515 fps). In some cases, the front portion, although
separate from the rear portion, was displaced backwards into the rear
portion and the two were recovered as one piece (Figure B-l, P-46S,

2480 fps). The fracturing of the rear portion into long, thin petals
reported by Stronge and Schulz for a slightly different projectile
geometry 3 did not occur.

The presence of a circumferential groove at the front of the inter¬
nal cavity (in the P-46S and P-46D projectiles) did not make a notice¬
able difference in the appearance of the primary bulge at this location
(although it did have a significant effect on the survival velocity of
the projectile, as will be discussed). The presence of a groove 0.25
inch to the rear (in the P-71S and P-71D projectiles) resulted in a sec¬
ondary bulge at this location. This secondary bulge is due to dynamic
yielding along two 45-degree trajectories emanating from the tip of the
groove which results in a wedge-shaped ring of material being displaced

4 W. Goldsmith and S. A. Finnegan. "Penetration and Perforation
Processes in Metal Targets At and Above Ballistic Velocities," Inti.
"e-Sn. S;i. , Vol. 13 (1971), pp. 843-866.

6

• **>

See footnote at end of table.

TABLE 1. (Contd.

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outwards (Figure B-l, P-71D, 2448 fps). The deformation associated with
the secondary bulge is minor compared to the primary bulge, and does not
appear to contribute to failure of the projectile.

The chart in Figure 2 shows the impact behavior of the five types
of projectiles within the velocity range studied. The solid vertical
lines denote projectiles that bulged, while the dashed vertical lines
denote projectiles that broke up. The greyed areas indicate a range of
uncertainty for the survival velocity (defined as the velocity below
which the projectiles bulge and above which they break up) for the
different projectile types.

Estimated survival velocities are given in Table 2. The uncertainty
indicated in the table is primarily due to the small number of shots
fired and not to any inherent physical randomness in the targets, pro¬
jectiles, or launch procedure. It is apparent from Table 2 that a groove
at the point of maximum bulging significantly reduces the survival veloc¬
ity and that the amount of reduction is strongly dependent on the depth
of the groove { 6 % for the P-46S projectile and 15" for the P-46D pro¬
jectile). On the other hand, a groove 0.25 inch to the rear of this
point has almost no effect on the survival velocity for either groove
depth (P-71S or P-71D).

TABLE 2. Projectile Survival Velocities
Against Thorite Targets.

Type

Survival velocity,
fps

Uncertainty,

fps

P-N

2502

±12

P-46S

2363

±43

P-46D

2135

±5

P-71 S

2467

±7

P-71 D

2469

±21

Penetration depth is plotted versus impact velocity in Figure 3.
Also shown are theoretical curves based on the penetration theory of
Bernard and Creighton 5 using Thorite property values given by Stronge
and Schulz. 3 The curve labeled ".25" radius" is the theoretical pene¬
tration curve for a non-deforming projectile. As expected, this curve

3 Defense Nuclear Agency. ?ro t ;eozile PenosMsion :n :ixt<?viai

r-zc-r;. :xnd .Jcnrutev .4r. tlusis , by R. S. Bernard and D. C. Creighton.
Washington, D.C., DNA, November 1977. (Contract Rept. S-76-13, publica¬
tion UNCLASSIFIED.)

9

>«.*

nst Thorite Targets

NWC TP 6275

lies considerably above the experimental points. During penetration the
radius of the projectile at the bulge increases significantly above its
initial value, an increase not considered by Bernard and Creighton. If
a fictitious radius of 0.291 inch (the average of the deformed cavity
radii in Table 1) is used in the penetration theory, much better agree¬
ment is obtained. For a given impact velocity, the penetration depths
of projectiles that broke up are considerably less than for those that
did not break up. This can be attributed to a greater effective radius
for the failed projectiles.

The decrease in projectile length, the height of the primary bulge
in the internal cavity (the increase in radius at this location), and
the increase in radius of the solid front end of the projectile are
plotted versus impact velocity in Figures 4, 5, and 6, respectively.

Also shown are theoretical lines obtained from finite element analysis
analogous to that of Stronge and Schulz. 3 The analysis was for an un¬
grooved projectile. Reasonable agreement between analysis and experiment
was obtained. In Figures 4 and 5 the experimental points for those pro¬
jectiles with a groove at the cavity bulge (P-46S and P-46D) lie (with
one exception) slightly above the theoretical lines, indicating that the
presence of a groove at the cavity bulge results in more bulging and a
greater decrease in length for a given impact velocity. This is consis¬
tent with the lower survival velocities found for these projectiles.

RESULTS AGAINST STEEL-PLATE TARGETS

Twenty-six shots were fired against steel-plate targets. The re¬
sults are summarized in Table 3. Photographs of the projectiles after
test are contained in Figure B-3 in Appendix B. Photographs of selected
cross-sectioned projectiles are shown in Figure B-4.

Impact at lower velocity produced cracks on the front surface of the
projectile (Figure B-3, P-N, 2480 fps, for example). The amount of
cracking increased with increasing velocity, sometimes concentrating in
a circular pattern (Figure B-3, P-N, 3230 fps). In some cases, perhaps
due to slight non-normality of the impact, fracturing and breakup of the
front end occured primarily on one side (Figure B-3, P-N, 2995 fps). At
higher velocities, the steel disk punched from the target sometimes re¬
mained attached to the front of the projectile (Figure B-3, P-46S, 3275
fps).

Damage to projectiles fired against steel-plate targets was confined
largely to the front end. Bulging occurred at the primary location at
the front of the internal cavity, but was significantly less than for
impact against Thorite. The presence of a groove at this location
resulted in increased bulging and some alteration in the shape of the

12

DECREASE IN LENGTH, IN

12

.10

.08

.06 L

.04

.02

_ Finite element
analysis

O P-N
A P-46S
V P-46D
□ P-71S
O P-71D

/ w
/

/ O o

1 o

/

0 /

/

/

/

/

/

/

0 /

/

0

1800 2000 2200 2400 2600

IMPACT VELOCITY, FPS

FIGURE 4. Decrease in Length Versus Impact Velocity
for Test Projectiles Fired Against Thorite.

CAVITY BULGE HEIGHT, IN

NWC TP 6275

.14 _

.12

_Finite element

analysis

O P-N
A P-46S
v P-46D
□ P-71S
O P-71D

.08

.06

.04

.02

bo

oy

/

0 I --- 1 - 1 -*--

1800 2000 2200 2400 2600 2800

IMPACT VELOCITY, FPS

FIGURE 5. Cavity Bulge Height (Increase in Radius) Versus
Impact Velocity for Test Projectiles Fired Against Thorite.

14

INCREASE IN RADIUS AT FRONT END, IN

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NWC TP 6275

TABLE 3. Results of Projectile Firings Against Steel-Plate Targets.

Projec.

type

Mass,

gm

Impact

velocity,

fps

Description of projectile after test

P-N

20.07

2480

Cracks on front surface, bulge at cavity front

P-N

20.02

2650

Ditto

P-N

20.04

2825

Ditto

P-N

19.82

2995

Side of front end nearly broken off

P-N

20.12

3230

Cracks on front surface form circular plug

P-N

20.05

3590

Front end disintegrated and not recovered

P-46S

20.02

2570 ,

Cracks on front surface, bulge at cavity front

P-46S

19.98

2835

Ditto

P-46S

19.72

2985

Circular pattern for cracks on front surface

P-46S

19.85

3275

Front end mashed on one side, target disk
still attached

P-46S

19.98

...

Projectile jammed in gun barrel; only front
portion struck target

P-46D

19.80

2545

Cracks on front surface; shape of cavity bulge
shows effect of groove

P-46D

19.92

'a

Ditto

P-46D

19.61

Side of front end mashed; circumferential
fracture at groove

19.92

Ditto

P-46D

19.88

.

Front end shattered on one side, target disk
still attached; fracture at groove

P-71S

19.97

2505

Cracks on front surface, slight bulge at
cavity front

P-71S

19.97

2650

Ditto

P-7 IS

20.02

2825

Ditto

P-71S

20.01

2980

Cracks on front surface form circle; bulge
at cavity front, smaller bulge at groove

P-71S

19.85

3160

Longitudinal crack in side of front end,
target disk still attached

P-71D

19.88

2495

Cracks on front surface, bulges at cavity
front and groove

P-710

19.85

2660

Ditto

P-71D

19.84

2840

Ditto

P-710

19.96

2970

Cracks on front surface form circle; distinc¬
tive shape of groove bulge apparent

P-71 D

20.05

3250

Front end shattered on one side,
target disk still attached

16

NWC TP 6275

bulge. The presence of a groove at the more rearward location produced
a secondary bulge at this point. Those projectiles containing a deep
groove at the cavity bulge location and fired at high velocities devel¬
oped partial circumferential fractures at the bulge (Figure B-3, P-46D,
2830 fps, 2950 fps, and 3230 fps). For the other types of projectiles,
however, increasing impact velocity resulted in increasing damage to the
front end with no visible damage at either the primary or secondary bulge
location. (Metallographic examination of cross-sectioned projectiles
revealed the presence of tensile cracks at the roots of the grooves in
projectiles fired against both Thorite and steel-plate targets. These
appear to have been produced during unloading. The metallurgical aspects
of projectile behavior will be discussed in a later report.)

CONCLUSIONS

The purpose of this study was to examine possible deleterious effects
of shear-control grids on the survivability of impacting warheads. The
single circumferential groove machined into the test projectiles was in¬
tended to represent the stress-raising capability of a shear-control grid
in its vicinity. To the extent that this representation is valid, the
results show that:

1. For warheads fired against concrete targets, the presence
of a shear-control grid in the vicinity of the region of maximum bulging
in the warhead case significantly weakens the warhead structurally. More¬
over, the reduction in survival velocity increases with the depth of the
groove. However, if the grid does not extend into the bulged region, no
weakening occurs. Thus, a shear-control grid can be machined from slightly
behind the bulge (half a projectile diameter in this study) to the rear

of a warhead case without reducing survivability while, at the same time,
maintaining a significant amount of fragmentation control.

2. For warheads fired against steel-plate targets, the situa¬
tion is less clear. Damage to the projectiles fired against such targets
occurred primarily at the front end, and a groove in the internal cavity,
whether at the bulge or behind it, had little effect on structural sur¬
vivability. Circumferential cracks did occur in some of the projectiles
containing a deep groove at the bulge; however, damage to the front end
was already extensive. It is likely that another projectile design with
a thinner case wall might have fractured at the bulge at a lower velocity
with little damage to the front end. In this case, the effects of groove
placement and depth on survivability might have been similar to those
found for concrete penetration.

17

I

NWC TP 6275

Appendix A

PROCEDURE FOR MAKING THORITE TARGETS

I

It is essential that the Thorite targets used in small-scale pro¬
jectile test firings be made in a consistent manner so that all targets
have the same mechanical properties. The procedure used in making these
targets so as to assure uniformity is described.

1. The targets are usually prepared in batches of 10 at one
time. This number of targets can be prepared in about 1 hour and can
be comfortably test-fired in half a day. Target preparation is usually
done out-of-doors in the early morning. On exceptionally hot or cold
days, it might be desirable to work inside to avoid temperature extremes.

2. The Thorite for each target is mixed in a circular plastic
dishpan. The water required (1250 milliliters) is poured into the dish-
pan first. Then the dry Thorite (4300 milliliters) is added. The in¬
gredients are worked with the hands (disposable vinyl gloves are worn
for protection) until thoroughly blended and lump-free.

3. The mixture is then poured into a clean, empty 1-gallon
paint can. The can is filled to just below the inner lip. The mixture
is packed slightly in the can, using the hands. After filling, the can
is held by the bail and bounced gently on a flat surface until the sur¬
face of the Thorite has smoothed out.

4. The newly filled can is placed for cooling in a tub of
water with the water level slightly below the rim of the can. After the
surface of the Thorite has set (about 5 minutes) water is poured into
the can to fill it to the rim.

5. After 2 hours, all the cans are removed from the tub and
stored indoors. The cans are kept covered with water for 24 hours after
preparation. At the end of this time the water is poured off and the
surface of the Thorite is allowed to dry out. The cans are used for
test firing 1 week after preparation.

IS

Hr***

fl

hf

FIGURE B-l. (Contd.)

Side Views of Projectiles Fired Against Thorite Targets.

FIGURE B-2. Cross-Sectional Views of Selected
Projectiles Fired Against Thorite Targets.

FIGURE B-3. Front and Side Views of Projectiles
Fired Against Steel Plate Targets.

FIGURE B-3 (Contd.). Front and Side Views of
Projectiles Fired Against Steel Plate Targets.

FIGURE B-4. Cross-Sectional Views of Selected
Projectiles Fired Against Steel Plate Targets.

NWC TP 6275

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1 Redstone Arsenal (Rocket Development Laboratory, Test and
Evaluation Branch)

1 Rock Island Arsenal
1 White Sands Missile Range (STEWS-AD-L)

1 Yuma Proving Grounds (STEYT-GTE, M&W Branch)

1 Tactical Air Command, Langley Air Force Base (TPL-RQD-M)

1 Air University Library, Maxwell Air Force Base

3 Armament Development & Test Center, Eglin Air Force Base

2 57th Fighter Weapons Wing, Nellis Air Force Base

FWW/DTE (1)

FWW/DTO (1)

1 554th Combat Support Group, Nellis Air Force Base (OT)

1 Tactical Fighter Weapons Center, Nellis Air Force Base (CC/CV)

12 Defense Technical Information Center
1 Defense Nuclear Agency (Shock Physics Directorate)

1 Weapons Systems Evaluation Group

1 Lewis Research Center

2 Allegany Ballistics Laboratory, Cumberland, MD

2 Applied Physics Laboratory, JHU, Laurel, MD (Document Library)

1 Arthur D. Little, Inc., Cambridge, MA (W. H. Varley)

2 Chemical Propulsion Information Agency, Applied Physics Laboratory,
Laurel, MD

1 IIT Research Institute, Chicago, IL (Document Librarian for
Department M)

1 Jet Propulsion Laboratory, CIT, Pasadena, CA (Technical Library)

1 Los Alamos Scientific Laboratory, Los Alamos, NM (Reports Library)

1 Princeton University, Forrestal Campus Library, Princeton, NJ
1 Stanford Research Institute, Poulter Laboratories, Menlo Park, CA
1 The Rand Corporation, Santa Monica, CA (Technical Library)

1 University of California, Lawrence Livermore Laboratory, Livermore, CA
1 University of Denver, Denver Research Institute, Denver, CO
1 University of South Florida, Tampa, FL (Dept, of Structures,

Materials, and Fluids, W. C. Carpenter)