M MEMORANDUM REPORT NO. 2796

S(Supersedes IMR No. 233)

MISSILE WARHEAD MODELING: COMPUTATIONS

AND EXPERIMENTS

William W. Predebon I-l, ,Walter G. SmothersCharles E. Anderson r

October 1977

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., USA ARMAMENT RESEARCH AND DEVELOPMENT COMMANDM- USA BALLISTIC RESEARCH LABORATORY

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Sulwi? Isreds In terim In emoz-an dum Reoer t No, 233 dated ,Junoc 197d.

I9. KEY WORDS (Continue on roer**. side it neceusary anid IdentIty, by block number)

H emp C omputat.ionis Wa rhead Modeling Rad iographice t oehn iquesVelocity voctor predictions Eixplosive testingSAM-I1) Liner effectsAnti -alirerm ft watrhcads Geometri cal variat ionsPreformed fragments Froaumnt recovery' test ing

20. ABSTRACT (CoiIInuo on roverer side It nec*eewy aid identify by block number) (k I b)A comiputat ionail warhead modeling capability has boon developed wh ich models thoeffcets of warhead length to diameter ratio, end confinement variation, cxplosivcmaterial and initiation posture, and internal cavity shape and material. Theseeffocts ore modeled with a. time-dependent, two-dimensional, Lagrangian finite -difference computer code, integrally modified to include fragment separation (orfragmentation for continuous warheads) and subsequent explosive ga' leakagebetween fragments. - .. /

DO D I'jMA" 1473 EDITION OF I NOY 65 It O@%OLtTE JC.SS1tL

576 17 - SECURITY CLASSIFICATION OF THIS PAGE (Who"Voe E*. ntered)

UINCLASS I F I I11IICURITY CLASIIiCCATION OF THIS PAOG(Wh DWe.O ,nW

20. E Bxperimental results of a variety of modeled missile warheads

(discrete-fragment warheads) are presented and compared with the computationalresults. In the experiments the fragment speed and angle distributions with

respect to their original position on the warhead are determined through time-

sequential, orthogonal flash radiograph, of the warhead fragment spray inflight, and soft recovery of the fragments after launch.,

iI

UNCLASSIFIEDuRcUmgTY CLASSIFICATION OF THIS pAor(WIhon Dom. Rlered)

TABLiF, 01' ,ON'I'I.NTS

,IST1 1 OF IIJUJSTRAT IONS . . . . . . . . . . . . . . . . . . . 5

1I. INTROI)UCTION . . . . . . . . . . . . . . . . . . . . . . . 9

TI . FX11iRIMEN'rAI, 11ROGRAM ............ ................... ... 11

III. COMPUTATIONAL MODELING ...... .......... . 27

A. Modeling of Discrete Fragments ...... .......... ... 29

B. Fragment Separation and Explosive Gas Leakage ..... 31

C. Criterion for Fragment Separation .... ........... ... 31

IV. COMPARISON BETWEEIN COMPUTATIONAL AND EXPERIMENTAL RESULTS . 32

V. CONCLUSIONS AND RECOMMENDATIONS ....... ............ ... O50

ACKNOWLEDGIWMENTS . ..................................... 51

LIST OF SYMBOLS ............... ...................... ... 52

DISTRIBUTION LIST ................ .................. ... 53

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1IST OF ILLUSTRATIONS

F:i gure Pa ge

1. Typical Test Configuration . . . . . . . . . . . . . . . . 12

2. Test Warhead of L/11 = 2.0, with Azimuthal Fragment-Bear-ing Sector Angle of 22.50 ....... ................ ... 13

3. Typical Radiographic Results for L/ID 1,0 Warhead . . .. 15

4. Tyypical Radiographic Results for L/ID 2.0 Warhead . 16

5. Identification of Fragments in Figure 3 ... ......... ... 18

6. Identification of Fragments in Figure 4 ... ......... .. 19

7. Radiographic View of Fragment Focusing, L/) = 2.0: DualEnd Axial Initiation ........... ................... 20

8. Identification of Fragments in Figure 7 ... ......... .. 21

9. Comparison of Round to Round Variation of Warhead Tests . 22

10. Variation of "Warhead Performance" with Azimuthal Fragment-Bearing Sector Angle, L/D = 1.0 .............. ..... 23

11. Variation of "Warhead Performance" with Azimuthal Fragment-Bearing Sector Angle, L/D w 2.0 .... ............. .. 24

1.2. Double-Layered Discrete-Fragment Warheads: Fragment SpeedVersus Projection Angle ....... ................. .. 26

13. Preformed-Fragment Warhead with Al Liner and Al Endplates,L/D ) 2.0: Fragment Speed and Projection Angle Distri-bution ........... .......................... ... 28

14. Comparison of Gurney Velocity and Taylor Angle with HEMP(Fluid Model) Computations and Experimental Data, L/D -1.0 Cylindrical Preformed-Fragment Warhead ..... ....... 30

15. Comparison of Fluid Model Computations and Discrete-Fragment Model Computations with Experimental Data, L/D1.0 Cylindrical Preformed-Fragment Warhead .... ..... ... 33

-MDI tAIX -S- AWI ... '' 'I'

I. 1S' OF ILLUSTRATIONS (Cont.)

Figure Page

16. Comparison of Fluid Model Computations and Discrete-Frag-ment Model Computations with Experimental Data, I/1 = 2.0Cylindrical Preformed-Fragment Warhead .......... 34

17. Comparison of Discrete-Fragment Model Computations withExperimental Data for L/D - 2.0 Cylindrical Preformed-Fragment Warhead with Dual End Axial Initiation , . , 35

18. Initiation Postures ........... .... . 37

19. Calculations of Fragment Speed and Projection Angle Dis-tributions for L/D - 2.0 Cylindrical Preformed-FragmentWarheads with Dual Axial Point Initiation at 0,10 L ., . 38

20. Calculations of Fragment Speed and Projection Angle Dis-tributions for L/D 2.0 Cylindrical Preformed-FragmentWarheads with Dual Axial Point Initiation at 0.25 L . . . 39

21. Calculations of Fragment Speed and Projection Angle Dis-tributions for L/I) = 2.0 Cylindrical Preformed-FragmentWarheads with Axial Point Initiation at 0.50 L . . . . . 40

22. Calculations of Fragment Speed and Projection Angle Din-tributions for L/D = 2.0 Cylindrical Preformed-FragmentWarheads with Dual End Plane Initiation at 1.00 D . . . . 41

23, Calculations of Fragment Speed and Projection Angle Dis-tributions for I,/D = 2.0 Cylindrical Preformed-FragmentWarheads with Dual End Plane Initiation at 0.50 D . . . . 42

24. Calculations of Fragment Speed and Projection Angle Dis-tributions for L/D = 2,0 Cylindrical Preformed-FragmentWarheads with Dual End Peripheral Initiation ......... ... 43

25. Calculations of Fragment Speed and Projection Angle Dis-tributions for L/D - 2.0 Cylindrical Preformed-FragmentWarheads with Dual End Ring Initiation at 0.50 D ..... 44

26. Calculations of Fragment Speed and Projection Angle Dis-tributions for L/D - 2.0 Cylindrical Preformed-FragmentWaiheads with Axial Line Initiation .... ........... ... 45

3I

: : " " " I I l 'I I.I I .. ' ,- -

I1sT' O1 I IIIS'IrlA'IIONS (Cont.)

Fi gure PageI

27. Ca•iculaitions of Ft'ragment Speed aid Projection AngloIDistributions for an L/) -- 2.0 Cylindrical Preformed-Firagment Warhead with Internail Aluminum Cavity Linerand Dual Ind Axial Initiation . . . . . .. . . . .. . 40

28. Calculations of Fragment Speed and Projection AngleDistributions for an L/u ) 2.0 Cylindrical Preformed-Fragment Warhead with Internal Tungsten Alloy CavityLiner and Dual l nd Axial Initiation ... ......... .... 47

29. Calculations uf Pragment Speed and Projection AngleDistributions for an LID = 2.0 Cylindrical Preformed-Fragment Warhead with an Internal Cavity Modeled as aVacuum and Dual tind Axial Initiation ........... 48

3o, Calculations of Fragment Speed and Projection AngleDistributions for an L/I = 2.0 Cylindrical Preformed-Fragment Warhead with an Internal Cavity Modeled as Rigidand Dual End Axial Initiation .............. 49

7I

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-11.. I

I. INTIOIUIICTION

Mltssilý warheads are generally quite different in design andconstruct ion than warheads used in other military applications, such asartillery shells. Thi,; difference mainly is a consequence of the lowlatunch loads experienced by missile warheads. Warhead design inapplications where high launch loads are experienced (artillery shel Is)are usually of the natural fragmentation or controlled fragmentation "type. By way of background, natural fragmentation warheads are continuousmetal casing warheads with no preselected control sites of failure.Controlled fragmentation warheads, on the other hand, are continuouswarheads with preselected control sites or lines of failure. Thesefailure sites are usually arrived at mechanically, metallurgically orexplosively. However, missile warheads are generally discrete-fragmentwarheads and not continuous metal-casing systems. Discrete-fragmentwarheads are preformed-fragment warheads in which the fragments of thedesired shape and mass are placed on a liner (metal or plastic) whichencases the high explosive. The warhead is then placed inside a missilecasing (skin). These preformed-fragments are attached to the liner andneighboring fragments by an epoxy filler. Due to the very low launchload environment of a missile, this evidently is sufficient for structuralintegrity.

In the past the main analytical method for predicting fragmentationwarhead performance*, i.e., fragment speed and direction, has been the

Gurney and Taylor2 formulae. These formulae are one-dimensional byassumption and the Gurney formula requires an empirically determinedconstant. This constant, called the Gurney constant, is obtainedexperimentally via warhead tests for each different situation. Due tothe one-dimensional nature of these formulae, their utility for predictingwarhead performance near the ends is questionable. It has been

shown' that for cases when the flow is essentially one-dimensional, such

"•Warhead performance as used in this report will mean fragment velocitydietribution, which, it can be shown, yields fragment mass distribution.

iGurney, R. W., "The Initial Velocitiezi of Fragments from Bombs, Shellsand Grenades", BRL Report 405, September 1943, AD#36218.

22B-irkhoff, G., MacDougall, P., Pugh, E. M. and Taylor, G. i., Sir.,"Fx)losives with Lined Cavities", J. Appl. Phys., Vol. 19, p. 563,June 1948.

3Karpp, R. R. and Predebon, W. W., "Calculations of Fragment Velocitiesfrom Naturally Fragmenting Munitions", BRL Memorandum Report No. 2509,July 1,975. (AD #BO07377L)

9"

•s long artillery projectiles (L/D > 2), these formulae are adequatefor predicting fragment velocity. However, for cases where the flow istwo-dimensional, such as near the warhead ends for any size projectile,and for axisymmetrLc warheads with length to diameter ratios less thanor equal to two, these formulae are inadequate 3 . Lastly, these formulaewere initially derived for continuous warheads (i.e., natural fragmenta-tion warheads) and for one specific initiation posture. Consequently,for discrete-fragment warheads, these formulae are not applicable with-out significant modification and experimental recalibration.

In an effort to find a method to predict warhead performance notonly over its midsection but over its entire length Including the ends,a time-dependent, two-dimensional, Lagrangian computer code has beennpplied to naturally fragmenting warheads. In Reference 3, finite-difference calculations of warheads with varying explosive fills andcasing materials were compared with experimental results; good agreementwas demonstrated. However, the computer code used to obtain the cal-culations in Reference 3 assumes a continuum. Warheads eventuallyfragment, and after fragmentation the continuum assumption needs to bemodified. A method to model the effects of fragmentation and subsequentexplosive gas leakage was presented in Reference 3 as an integral partof the computational scheme.

In this report the earlier work by Karpp and Predebon 3 on naturalfragmenting warhead is extended to missile warheads, i.e., discrete-fragment warheads. The objective of the work reported here was todevelop a warhead modeling capability to predict the performance ofmissile warheads in general, as well as warhead designs pertinent to the"Focused-Blast-Fragment" advanced development program,* Computational

modeling was emphasized with limited experimental verification as needed.

In the next section the experimental program is discussed in detail.In Section III the computational modeling is explained. Comparisonsbetween the computational and experimental results are discussed inSection IV. The conclusions and recommendations follow in Section V.

*Ti' work was supported by the BRL, Picatinny Areenal and AMC, HQ.

I 0

I I. EX PERIMMENTAIL PROGRAM

Fitgure 1 is a schematic drawing of part of a typical test set-uptised in the warhead test firings for this program. Shown .hs the warhead

on an angled* wood stand which rests on metal plates on the floor of the

second level of the test facility. The two metal plates form a preset

aperture through which passes the column of fragments to be radiographed.

The lower level of the test facility contains two orthogonal banks (each

bank has four flash x-ray tubes) which provide time-sequential, ortho-gonal radiography.

Due to the funding and time constraints on part of this program, itbecame obvious at the very beginning that cubical fragments** could not

be placed completely around each test warhead and still complete the

minimum number of warhead tests planned. Also, from a long term point

of view, It is desirable to have a morc economical method for tc.stingpreformed-fragment warheads. The method used determined the minimumanzimuthal-sector angle containing preformed- fragments which adequately

represented the situation where the entire cylindrical warhead contained

preformed-fragments. All the warheads tested had an overall cylindrical

shape. Figure 2 illustrates a test warhead with an azimuthal fragment-

bearing sector angle of 22.50 for a typical length to diameter (1,/D)

ratio of 2.0. In all tests where an azimuthal sector of the warhead

contained the preformed-fragments, the remainder of the warhead con-taimed strips (rods) of the same material. The width of the strips was

equal to the width of the fragments (for proper radial explosive gas

leakage), and the strip lengths were equal to the explosive charge

length.

Table I contains all the characteristics of the test warheads by

their respective round number. As indicated in Table I, the warhead

length to diameter ratio was varied from 1.0 to 2.0. The explosive

charge in all cases was Octol (25% TNT, 7s• i.mX). Trhe fragments were

steel (AISI 1018 or 1020) cubes and, in all but one test, were placed

directly on the bare explosive charge. This type of configuration was

adopted in order to determine with greater accuracy the effect which

explosive gas leakage between fragments has on the fragment velocity

distribution, particularly for the computational modeling portion of the

program.

Figures 3 and 4 illustrate typical radiographic results from 1,/)

1.0 and I/I) = 2.0 warheads, respectively. Both test warheads were initi-

ated on the axis at the loft end. Figures 3 and 4 show the longitudinal

and orthogonal views of the fragment distributions in their actual spacial

positions at two different times, In each of the test cases the fragments

in the radiographed column were premarked for identification and wererecovered in Celotex. The spacial location of the recovered premarked

'*1' a angle wod stand is used to rotate the main fragment distribution

into the available radiographic view.**rn all the warhead tests the fragment shape was cubical.

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fragments, in conjunct ion with the t lIme-sequent I I , orthogonal radiographyof the fragments, permitted development of the results shown In Figures 5and 0 for the two tests i Ilustrated In Figures 3 and 4. In Figures 5 andb, each of the fragments in flight are labeled according to their originalposition on the warhead (shown at the top of the figures). Two differenttimes are shown for both longitudinal and orthogonal views.

To illustrate radiographically the fragment focusing that can be,achieved, Figure 7 shows (for two different times) the longitudinal andorthogonal views of an ,/) = 2.0 warhead which was initiated simultan-

eously at both ends on the axis of symmetry. The fragments of Figure 7are labeled in Figure 8 according to their original position on thewarhead. Again two different times are shown for the longitudinal andorthogonal viewi.

To determine the accuracy of the experimental procedure, a simpleerror analysis of the measurements was conducted and the round to roundvariation was quantified. Using a conservative approach to erroranalysis wherein only maximum differences are considered, for two time-sequential observations of fragments the measurement uncertainty in thefragment speed Is less than j- 1% and is less than ± 0.004 for the tangentof the fragment projection angle, The round to round variation in thewarhead tests is shown in Figure 9. Plotted in Figure 9 is the fragmentspeed and projection angle distributions versus fragment number orrelative initial axial position from two tests of nominally identical(See Table I) L/) = 2.0 cylindrical warheads. The round to roundvariation in fragment speed Is ± 3% for two time-sequential observationsof the fragments and ± 13% for single time observations of fragments(which occurs for a few fragments at both ends). The overall round toround variation In the tangent of the fragment projection angle is± 0.02. Therefore, it appears that the variations from one round toanother (nominally the same) are larger than the measurement uncertainty.Consequently, it was inadvisable to attempt to improve the accuracy ofthe measurement procedure.

As previously mentioned, the cubical fragments were placed on thewarhead in varying azimuthal sector angles, with strips in the rema.ningazimuthal angle, to determine the minimum azimuthal fragment-bearingsector angle required to approximate the situation in which fragmentscovered the entire round. Plotted in Figures 10 and 11 are the fragmentspeed and projection angle distributions for varying azimuthal fragment-bearing sector angles a for L/I) = 1.0 and 2.0 warheads, respectively.Since the percent difference between the a = 45' and a = 90* cases inFigure 10 is within round to round variation shown in Figure 9, it isfelt that a 45' azimuthal fragment-bearing sector angle is adequate forthe L/D = 1,0 case. For the L/D = 2.0 case, Figure 11 indicates a largedifference between a = 22.50 and a = 450, 900 and 1350. However thedifferences are much smaller between the a = 45°, 90* and 135' cases,although the fragment speeds for a = 450 tend to be greater than or

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24

equal to a = 90* or ki = 135 0 , especially in areas remote from end vare-factions. Mindful of the latter point and the round to round variationshown in Figure 9, the variation In fragment speed between the a = 900and 1.35° is within the round to round variation; whereas the same varia-tion between the a =45' and 900 is generally not. In view of the aboveit is felt that a = 900 is desirable for the !./fl = 2.0 caise.

Returning to the a = 22.S* case in Figure 1., due to the unexpectedlarge differences between it and a - 450, 900 and 135*, particularlynear the ends where one would expect the fragment speeds to converge toa common value for most practical a's, it Is questionable whether theselarge diffoiences are due to increased confinement for a - 22.50 orperhaps some uncovered error in the data. An additional test at a22.50 will be required to clarify these questions; however, it wasjudged that the results of such a test would not significantly changethe main thrust and purpose of this study and therefore was not com-pleted at this time.

The experimental results of cases in which computaticnal resultswere obtained are discussed in Section IV. There arc a few test casesfor which the computations were not performed during this program andthese experimental resulLs will be presented at this time.

Trho modeling of multi-fragment layering is immensely complicatedduo to the many combinations of layer patterns that can be placed on thewarhead. In order to bracket the effects of the simplest multi-fragmentlayering case, i.e., two layers of fragments, two double-layered discrete-fragment warheads were fired. 'The fragment layers were aligned withrespect to each other for the first warhead; the other warhead had thefragments bricked (that is, the fragments on the top layer were displacedby a distance equal to half of a cube side relative to the fragments onthe bottom layer). In Figure 12 are plotted the results of the alignedand bricked double-layered warheads. In order to compare these resultsto the single layered test, the charge mass to metal mass (C/M), thetype of explosive, explosive initiation and explosive dimensions werekept the same as the single layered L/P - 2.0 case (shown in Figure 16).Further, the fragment shape and fragment material were kept the same.Those constraints thus imposed that the double-layered fragment massesbe 1/8 the single layered masses. Due to the resulting lower cubemasses (0.486 gin), and therefore much smaller dimensions, the previouslyused cube numbering system was not effective in identifying the cubeswith respect to their original position on the warhead. When the cubeswere recovered they had generally collided with each other during flightand the punched numbers on each fragment were unidentifiable. Consequentlythe fragment speed is plotted with respect to Its projection angle inFigure 12 rather than its initial position on the warhead.

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•~.ISIS

III Figure 12 it is quite evident that there exists a significantvariation of the magnitude of the velocity at any projection angle; thisobservation applies both to the aligned and bricked warheads, By compari-son, if the data from the single fragment layer case of Figure 16 wereplotted versus projection angle, as in Figure 12, only one fragment wouldappear at any particular projection anylc. It is important to note, forreasons previously discussed, It was very difficult to identify the samefragment in two time-sequential, radiographic views for many of the frag-ments in the double-layered cases, Consequently, the only fragments thatare plotted are those in which this identification was confidently made.Therefore, although the single fragment layer case cannot be comparedwith the double-layered case over the entire projection angle distribution,meaningful comparisons cari be made over the projection angle range forwhich data were obtained. In the two examples depicted in Figure 12, thespread in the speeds ranges from 0.15 to 0.40 mm/isec over the projectionangle distribution. The most probable contributing cause of this spreadin speed at a given projection angle is slippage between the layer frag-wients. Thus, instead of fragments leaving the warhead at a given anglehaving one particular velocity, collective effects result in a number offragments with varying velocities at the specified angle.

It is lastly noted that the plotted speeds in Figure 12 have notbeen corrected for drug, which from the data was estimated to be causinga 4%-7% decrease in fragment speeds. This dccrease was oTbtained bycomparing single and double flash calculations of identical cubes. Thiscalculation was also completed in the singlu layered cases; however, inthese cases the drag was always negligible. Because of the lower cubemasses (0.486 gm) in the double-layered warheads, drag is no longernegligible.

Shown in Figure 13 are the experimental results for single-layeredfragments on an aluminum liner with aluminum endplates, L/D = 2.0 cylin-drical warhead. As shown, initiation was on the axis on the left side ofthe warhead. All the necessary data are given in Table I. This is theonly test case reported with a liner and endplates. These results willbe discussed in some detail in Section IV along w'"h a similar test casewithout a liner and endplates.

III. COMPUTATIONAL MODELING

The computer code that is being used for the computation modeling isa modified version of the HEMP4 computer code. The HEMP code, which wasoriginally developed at the Lawrence Livermore Laboratories, California,is a time-dependent, two-dimensional, Lagrangian finite-difference code.

"•WiZkins, M. L., "Calculations of Eiastic-Plastic Flow," Methods of

Computational Phyvics, Vol. 3, edited by Alder, B., Fernback, S. andRotenburg, M., Academic Press, NY, 1964.

27

2.0-• ••O O• • 0 00

"~ 1.5 *:L

6 RD No. 9457

+0

" 1.STEEL FRAGMENTS0 1.o-0

> Al 4-AI0 LINER ENDPLATES

,L, 0.5-o BOOSTER

z0 I I I . . ....

0 .2 .4 .6 .e 1.0RELATIVE INITIAL AXIAL POSITION

i I . .j1 8 16 24 32

FRAGMENT NUMBER

In

wu 20-

- 10egO• OS *• **0 00 @6O 0o0

.. 0 'I ,. _jJ, . .o *0z

u -20LU

BCL

Figure 13. Preforned-Fragment Warhead with Al Liner and AlEindplates, L/t) = 2.0: Fragment Spced and ProjectionAngle Distribution

28

If the standard form of the HEMP code is used to predict the performanceof discrote-fragment warheads without including the effects of fragmentseparation and subsequent explosive gas leakage between fragments, thedashed line results shown in Figure 14 are obtained. Shown in Figure 14is a comparison between these [HEMP calculations and experimental data offragment speed and projection angle distributions for an L/D = 1.0 cylin-drical warhead. In the HEMP calculations the fragments are modeled as afluid, i.e., the fragments cannot accommodate a tensile force but theycan be recompressed. This would be a logical approach with a continuumcode since the fragments are not a continuum but discrete particles whichwill separate with the application of a small tensile force. It isobvious that this modeling is superior in predictive ability than theprediction of velocity and angle by Gurney and Taylor, also shown inFigure 14. However, the agreement between the HEMP computations andexperiment is not as good as desired. Because of this and other objec-tions 5 , modeling of the effects of fragment separation and explosive gasleakage between fragments was initiated to improve the overall predictivecapability of the computations.

The discrete-fragment warhead (missile warhead) model presentedinvolves the following three essential features: A) modeling of thediscrete-fragments, B) modeling of fragment separation and subsequentexplosive gas leakage and, C) criteria for fragment separation andmethod to determine this criteria.

A. Modeling of Discrete-Fragments

When discrete-fragments are placed on a cylindrical body, whether itbe the bare explosive or a liner containing the explosive, (assumingconventional fragment shapes) air gaps will occur between the fragmentsin the circumferential direction. Consequently, the discrete-fragmentcasing forms a composite of metal and air. In reality, this is a three-dimensional system. However, the approach that was adopted with the two-dimensional modeling is similar to the methods used in the modeling ofcomposite materials. The discrete metal-air composite casing (metalpreformed-fragments) is modeled as a homogeneous continuous material ofthe same metal material as the experimental fragments, but with therequirement that the total mass of the new continuous metal casing equalthe total niss of all the fragments on the experimental warhead. Forexample, in the case of cubical fragments, the resulting continuous metalcasing wall thickness in the model will be less than one of the sides of

5Karpp, R. R. and Predebon, W. W., "CaZcutations of Fragment Velocitiesfrom Fragmentation Munitions," First International Symposium on Balzlis-tics, Orlando, Florida, .13-15 November 1974, Section IV, pp. 146-176,Proceedings Published by American Defense Preparedness Association, UnionTrust Building, Washington, DC.

29

2.5

- ... .. LGURNEY VELOCITY

2.0

1.5 - * RD No, 93 10 I\El rl RD No. 9264

P 0 -- - FLUID MODEL0.

1.0

uJ cc8

u.0.5 ,0,93MzD|, ,G I .. ..V

0.5__

0 .2 .4 .6 .8 1.0RELATIVE INITIAL AXIAL POSITION

I -I --I1 4 812 16

FRAGMENT NUMBER

w 201

10- TAYLOR ANGLE

0 ir I I

10--

a1-20 ldU.,

II

12.

Figur"e 14. Comparison of Gurnoy Velocity and Taylor Angle withHEPMP (Fluid Model) Computations and ExperimentalData, LID v 1.0 Cylindrical Preformed,,ragment

Warhead

30

Iii actunl cubical |fragment. For a cylindrical warhead, the modeledcasing outside diameter for a given explosive diameter is obtained from

MT = •.• I = f {T lw (M - III: }

where NIT is the li mc" surtd total fragment mass (pl us litner mass if thevarihoad has a liner), Ili are the micasured individual fragment masses, P1:

is the fragment density, 1,w Is the total length of the fragments on the

warhead, 1IIIH Is the measured diamoter of the explosive und I)M Is the

Outside diameter of the continuous metal casing to be computed. If oneignores the air gap between the fragments and uses the fragment cubedimension as the continuous eusing wall thickness, then for the casesreported in Sections 11 and IV, the modeled total mass will be as muchas (1, greater than the actual total mass.

B. Fragment Separati.on and Eixplosive Gas Leakage

The general ideas of the model for fragment separation and explosivegas leakage will he presented heroe however, the specific details andequations have been presented in an earlier reports.

The IIIHEMP code models continuum behavior in general. However, inreality, when fragment separation occurs a continuous casing circumfer-ence ceases to increase. But the standard form of the code causes thecasing to remaLn continuous. This treatment tends to yield a higherradial acceleration and thus a higher final fragment velocity. This canbe corrected by computing the true force acting on an element of thecasing. The true force Is computed in the code by reducing the pressureacting on the interface of the casing by the factor Rb/R, where Rb is

the radius at fragment separation and R is the current radius. Atpresent, R1) must be determined by experiment. After fragment separation,

i.e., R > R1, a void appears bctween fragments and gas leakage occurs.

This effect is modeled in the code by calculating the rate of uffluxfrom an ideal nozzle passing its maximum rate of flow. The rate ofefflux is computed in the code for every cycle, and the mass leaked fora single cycle is the product of the mass rate and the cycle timeincrement. In this manner, the model accounts for gas leakage betweenfrngmonts after casing breakup. (,as leakage reduces the pressure accord-ingly. Lastly, to simulate a loss in circumferential stress upon casingbreakup, the yield strength of the fragment material is set equal tozero when R > Rb.

C. Criterion for Fragment Separation

Currently, the criterion for fragment separation, Rb, is an emnpiri-

cally determined quantity. As discussed in Section 1I the fragments

are all premarked and recovered in a soft recovery medium (Celotex)after firing. The recovered fragments are weighed and measured fortheir dimensions, Obtained from these measurements is the fragmentplastic deformation due to the explosive loading (or final dimensions).Since its original dimensions are known a straight forward calculationdetermines the corresponding radius of the warhead at which the fragmentsseparated. (The elastic displacements are neglected in this analysis).For the case of cubical fragments on bare explosive for L/D - 1.0 and2.0 cases, the expansion ratio at fragment separation, i.e., Rb/Ro where

R is the inside radius of the casing, was found to be 1.2. The recovered

fragment measurements and expansion ratios are tabulated in Table I.This criterion for fragment separation is empirical; the criterion willnot be applicable in general, Thus, the next refinement in this analysisis to relate this criterion to a fundamental material property.

IV. COMPARISON BETWEEN COMPUTATIONAL AND EXPERIMENTAL RESULTS

In Figures 15-17 are shown comparisons between the calculationswith the discrete-fragment model (labeled Elastic-Plastic with GasLeakage Model) and experimental results. In Figure 15 and 16 the calcu-lated fragment speed and projection angle distributions are comparedwith the experimental data for L/D - 1.0 and 2.0 cylindrical warheads,respectively. Data from two test firings are plotted in each figure.In both cases the agreement between computation and experiment is extremelygood. Also shown in Figures 15 and 16 are the calculations without thediscrete-fragment model, namely, a fluid model, and the Gurney velocityand Taylor angle predictions. Shown in Figure 17 is a comparison betweenthe computations and experimental data for the same case as shown inFigure 16 except with dual-end axial initiation. Again the agreementbetween computation and experiment is very good. Note that the computa-tions model the region where the two detonation waves collide (higherpressure region) at 0.5 relative initial axial position.

Returning to the test results shown in Figure 13, note that thewarhead configuration in Figure 13 is similar to the configuration inFigure 16. Both are L/D = 2.0 cylindrical warheads with the same explo-sive material, fragment material and size, and with essentially the sameexplosive diameter. However, the test warhead in Figure 13 has a linerbetween the explosive and fragments, and endplates. The reasons givenfor placing the liner between the fragments and the explosive are oftenvaried. It was the intent of this initial experiment, in conjunctionwith computational modeling (yet to be performed), to help explain theeffect of a liner on warhead performance. Due to the additional widthof the Al liner, the inside fragment radius increased, which resulted inmore fragments on the warhead, and thus a larger total metal weight, andlower C/M. These data are given in Table 1 by Rd. No. 9457. Consequently,the results of Figures 13 and 16 cannot be directly compared. However,it is the authors'judgment at this time, based on these data and other

32

2.5

GURNEY VELOCITY

2.0

I-

11. RD No.9393

O0~ ~ RD. No. 92,64• _

Uj FLUID MODELRELASTIC -PLASTIC

44 1.0-WITH GAS LEAKAGE MODEL1.0z

0,. 0.93

0.26 . 1.0.2RELATIVI! INITIAL AXIAL POSITION

1 4 8 12 16FRAGMENT NUMBER

U,

10- ..,eTAYLOR ANGLE

-,J C ;

z -10-0U -t

u -20-

IL

Figure 15, Comparison of Fluid Model Computations and I)is-croto-'ragmont Model Computations with ExperimentalData, L/D = 1.0 Cylindrical Proformod-FragmentWarhead

33.

2.5 2.5.•_ GURNEY VELOCITY

13 RD No. 9302

M RD No. 9283

---- FLUID MODEL- ELASTIC-PLASTIC

WITH GAS LEAKAGE MODELW

S1.0z

o I -0.934 M

0.5 L 4t2.0

p.. . , I I _ I

0 0.2 0.4 0.6 0.8 1,0RELATIVE INITIAL AXIAL POSITION

, I ... I , I ... I ...

I 8 16 24 32FRAGMENT NUMBER

tw 20 -

TAYLOR ANGLE"" 10 . _.

w* 0 -- .

O_

zz - 1 0 -0

"u -20-a.

Figure 16. Comparison of Fluid Model Computations and U)is-crete-Fragment Model Computations with ExperimentalData, L/D 2.0 Cylindrical Proformed-FragmentWarhead

34

2.5

2.0-.

> 0 RD. No. 9323PRESENT CALCULATIONS

i.1.5-

0 +-J 1

LU>

U- 0 - - - . 3L/D • 2.0

C/M u 0.93

Z 0.5

0 I I I0 0.2 0.4 0.6 0.8 1.0

RELATIVE INITIAL AXIAL POSITIONII I I I i

I 8 16 24 32FRAGMENT NUMBER

20

10

z.g -10LUI • -20 -

Figure 17. Comparison of Discrete-Fragment Modol Computationswith Experimental I)ata for L/Di 2.0 CylindricalPreformed-Fragment Warhead with Dual End AxialInitiation

't4 1..

calculations, that the effect of a liner is to contain the explosivegases for a longer period of time. This in turn causes leakage of explo-sive gases between fragments to occur at a larger expansion ratio, result-ing In a higher final fragment speed, as compared to the case without aliner (assuming all other quantities being equal). This can be .llus-trated from a plot 6 of calculated fragment speed versus time (from detona-tion) for these cases. From a plot of this type one observes that frag-ment separation and leakage occurs during the initial, approximatelyexponential, acceleration rise. By placing a liner between the fragmentsand explosive, one can prolong fragment separation and subsequent leakageuntil the fragment speed versus time profile flattens, which then resultsin a higher final fragment velocity. From these and other computations,it Is estimated that up to ,pproximately a 10% increase in final fragmentvelocity can be obtained with a liner between the fragments and explo-sive versus the case without a liner.

Having demonstrated extremely good agreement between the presentcalculations and experimental data for both L/D u 1,0 and 2.0 cylindricalwarheads with single-end and dual-end axial initiation, the computationswere then confidently utilized, without experimontnl verification, tostudy the effect of initiation posture on warhead performance. Shownin Figure 18 are the nine initiation postures that were computed. Thecylindrical warheads that are drawn in Figure 18 are all with a length(L) to diameter (D) ratio of two and initiated as shown. The first caseof dual end axial booster initiation, i.e., initiation with two 19.05 mmdiameter explosive boosters, is shown in Figure 17, The computationalresults of the remaining eight cases are shown respectively in Figures19-26. Shown in Figure 07 and Figures 19-26 is the effect of a largevariety of initiation postures on warhead performance. The general ideaof this set of computations is, un the one hand, to demonstrate theversatility and generality of this computational tool, and on the otherhand to aid in the understanding of the effect of initiation posture onwarhead performance. Furthermore, should the initiation posture ofinterest lie somewhere between these cases, a simple interpolation ofthe already computed cases is all that is required for a first approxima-tion of the warhead performance. Similarly, since the computationalresults are general, i.e., scalable, then if the geometry of interest isnot precisely the same as the cases calculated, these results can bescaled up or down assuming proper scaling procedures are followed.Lastly, it is worth while to note that axial line initiation, Figure 26,Is the one case of the initiation variations studied in which the frag-ment projection angle and speed dist'ibution are significantly differentfrom the dual end axial initiation case, Figare 17.

Shown in Figures 27 through 30 are the computational results fortwo different internal cavity sizes and materials for the same generalL/D - 2.0 cylindrical geometry. Shown in Figure 27 are the results for

6KXrpp, R. R. and Predebon, W. W., "Ca'lcouations of Fragment Velocitivsfrom Fragmentation Munitiona," p. I'V-164.

.o

Luz

-o i zo-JL

I-

z L

z Lz...j 000

00ugoo

I 3

2.5

2.0-

EE

>,

S 1.0 .. .. .. .. .. .. .. .. .. ..

S0.5...... ., ..... , ,.

INITIATION: DUAL AXIAL POINT AT 0.10L15 2.0 •=0.93

OO- 0.2 0.4 0.6 08 1,.0RELATIVE INITIAL AXIAL POSITIONSI I i . . . I

1 8 16 24 32FRAGMENT NUMBER

,A 30

-20-

-10uJ

z 0-. .

0 1-I

0

Figure t1. Calculations of Pragmont Spled and Projection AngloDistributions for L/D 2.0 Cylindrical Preformed-F'ragment Warhoads with Dual Axial Point Initiationat 0. 10 1,

S5j

2.5

2,0

E

0.I

w

0

Lu:>

U.I- 0° :

S0 5 ,. . .• , . . o. . .•

INITIATION: DUAL AXIAL POINT AT 0.251cz12.0 0-'.93D

0It. .. l .,i I .I

0 0.2 0.4 0.6 0.8 1.0RE ATIVE INITIAL AXIAL POSITION

1 8 16 24 32FRAGMENT NUMBER

30-.• 20-

- 10'

i I

- 20

z 0

-30 LF:igure 20. C:alcullatkons of" Fragnment Speod and Projoction AngleI

1)stribut ions for L/I) - 2,0 Cylindrical P-roformod-F~ragmenlt Walrhuds with• Dual Axial Point Initialtion

ut 0.2s 1,

2.5-J

" 2.0

EE

tI,. 1.,.

0LLI

z

INITIATION AXIAL POINT AT 0.50 L

2.0 6 .093M

0 0!2 0.4 0.6 0.8 1.0RELATIVE INITIAL AXIAL POSITION

1 8 16 24 32FRAGMENT NUMBER

30

20Co

lo- S0

- 10

U.'

;5-20

-09-301

Vigur•c 21. Calculations of Fragmont Speed and Projection AngleDistributions for 1,/D 2,0 Cylindrical Preformed-Fragment Warheads with Axial Point Initiation at(1.50 1,

4 (1

2.5

•2,0 I2.0

EE

>_

LUS/-

0.5. -------- '-.--..-. I

INITIATION: DUAL END PLANE AT 1.00D-- 2.0 -"0,93

02D

00 0.2 0.4 0.6 0.8 1.0RELATIVE INITIAL AXIAL POSITION

1 8 16 24 32FRAGMENT NUMBER

. 30

." 20

-10-

z• 0

z0 -10

LU"" -200

"-30LFigure 22. Calculations of Fragment Speed and Projection Angle

l)istrihutions for I/D = 2.0 Cylindrical Preformed-Fragment Warheads with Dual End Plane Initiationat 1.00 1)

I I

2.5-

S2.0-

EE>

+8 V

z

RAVINITIATION: DUAL END PLANE AT 0.50DL -D2.0 M"nO.93

RELATIVE INITIAL AXIAL POSITION

1 8 16 24 32FRAGMENT NUMBER

"A 30-

20-

z 0

0 t'--10, _,-,

-20

-30

Figure 23, Calculations of F~ragment Speed and Projection Angle, Distributions for L/D = 2.0 Cylindrical Preformed-i! Fragment Warheads with Dual End Plane Initiation

at 0.50 D

1242;-3

2.5-

S2.0-

EE

u 1.5-

0

u-

zS 0 .5 ... .. .. .. .. ... .... .. ..

S~INITIATION !DUAL END PERIPHERALL_ =2.0 -ý= 0,9 3

DM00.6 0.8 1,0,

0 ~R2ELATIVE (F41TIAL AXIAL POSITION

1816 24 32FRAGMENT NUMBER

30 -

o I

w -I

uA

O.a-30 -

30 - Cragment speed and Projection Angle

D)Istributions for L,/1 = 2.0 Cylindrical Preformod-Fragment Warheads with Dual IEnd Peripheral Initiation

R EIIA PI

2.5

" 2.0.

EE

)11.5.

I-U

200

LU

~0,5INITIATION: DUAL END RING AT 0.50D

2.0 0.93

0.2 0!4 0.6 0.8 1,0

RELATIVE INITIAL AXIAL POSITION

8 16 24 32FRAGMENT NUMBER

i 30

~20-

10LU

-J 0

zo0-10-

20[a.-30 Figure 25. Calculations of Fragment Speed and Projection Angle

Distributions for L/D 2,0 Cylindrical Preformed-Fragment Warheads with Dual End Ring Initiationat 0.50 D

44

.1

-l. M!

2.5

U

v, 2.0

E

>

U

>w

0-

z00.5.

INITIATION: AXIAL LINEL 2 0 C• 093

0 0.2 0.4 0.6 0.8 1.0RELATIVE INITIAL AXIAL POSITION

1 .. I III

1 8 16 24 32FRAGMENT NUMBER

• .20 -

-- 10

~0

z-- 10

U

"20Cr.

Figure 26. Calculations of rragmont Speed and Projoction Angle

Distributions for L/D = 2.0 cylindrical Proformed-Fragment Warheads with Axial Line Initiation

45

................... , • ._ .fl. ...

2.5-

EE

H 0.056 ::.528 D H 07

L 0.799 LINITIATION: DUAL END AXIAL BOOSTER.L t2.0, CAVITY LINER MATERIAL iALUMINUMD

0 . .4060.8 1.0RELATIVE INITIAL AXIAL POSITION

I8 16 24 32FRAGMENT NUMBER

30

20

~-10

Uj

00z -

-30-Figure 27. Calculations of Fragment Speed and Projection

Angle Distributions for an L/D w 2,0 CylindricalPreformed-Fragment Warhead with Internal AluminumCavity Liner and Dual E~nd Axial Initiation

41(,

2.5

S2.0-

EE

+8 V

O .0 .0.05 2 8 D0 , 0 , -0 .. . .. .. ... .

TZ VACUUM t= 0.70 D

L22~INITIATION : DUAL END AXIAL BOOSTER

-- 2,0, CAVITY LINER MATERIAL i TUNGSTEN ALLOY00 . . 2 I I .

0.2 0.4 0.6 0.8 1.0RELATIVE INITIAL AXIAL POSITION1 I I .I ...

1 8 16 24 32

FRAGMENT NUMBER

30 -0

20 -o2Q.

-0 -

- 0

zQ-10-

LU

S-20

CL -3 0 LFI gure 28. Calculations of Fragment Speed and Projection

Angle Distributions for an L/D - 2.0 Cylindrical

Preformed-Fragment Warhead with Internal Tungsten

Alloy Cavity Liner and Dual End Axial Initiation

47

Ii

2.5

2.0

0,0

UJ

> 1.000U.=

Lu VA:CUU:M O.J060D

z __________

INITIATION: DUAL EN XIAL BOOSTER

0 0.2 0.4- Ob OA 1.0RELATIVE INITIAL AXIAL POSITION

1 8 16 24 32FRAGMENT NUMBER

30

• 20

lvj

z -10-

U

•-_30'1

Figure 29. Calculations of Fragment Speed and ProjectionAngle Distributions for an L/D - 2.0 CylindricalPreformed-Fragment Warhead with an InternalCavity Modeled as a Vucuum and Dual End AxialInitiation

2,5

EE

1,5

Sj~.60 D+8 V

INITIATION : DUAL END AXIAL BOOSTER

V.~ ~ ~ 1. 2..0zczczzc

0

0 0,2 0.4 0.6 0.8 1.0

RELATIVE INITIAL AXIAL POSITION, ... I . .. I, I . . .. I

1 8 16 24 32FRAGMENT NUMBER530

.20

S10

Z 0 0. 0. . . ,

-1 0 -

20a.

- 30 -Figure 30. Calculations of Fragment Speed and Projection

Angle Distributions for an LID * 2.0 CylindricalPreformed-Fragment Warhead with an lnternaiCavity Modeled as Rigid and Dual End Axial Initiation

UJ]

the case with an aluminum cavity liner material with the dimensions asindicated. Comparing the results shown in Figure 27 with those inFigure 17 it can be soon that although the projection angle distributionis only slightly altered, the fragment speed is significantly reduced.

3The computational results with a tungsten alloy (p = 16890 KG/M )cavity liner material for the same cylindrical geometry and cavity shapegiven in Figure 27 are shown in Figure 28. As expected, due to thehigher density cavity liner material the fragment speed distribution issomewhat higher than with aluminum; however, the fragment projectionangle distribution is not noticeably altered. It is important to notethat these results are for one cavity shape and therefore are not neces-sarily true for all cavity shapes and sizes, In Figures 29 and 30 areshown the computational results for a slightly different cavity sizewhere the cavity is modeled either as a vacuum (Figure 29) or as acavity whose boundaries are rigid (Figure 30) for all time. The purposeof these two computations is to provide a qualitative lower (Figure 29)and upper (Figure 30) bound on fragment speed and projection angledistributions that can be expected for the cylindrical geometry andcavity shape shown.

V. CONCLUSIONS AND RECOMMENIOATIONS

A dig-rt~r-fragment warhead (missile warhead) computational modelingcapability has been developed which is capable of modeling with a satis-factory degree of confidence the performance of a large variety of axi-symmetric warhead configurations. The computational warhead modelincludes the ability to model the effects of varying L/D, fragmentmaterial and size, explosive material, initiation posture, and internalcavity material and shape. It is felt that the modeling capability canbe extended to include two layers of fragments on the warhead, a linerbetween the fragments and the explosive, and end confinement. Theexperiments were completed for these cases and are discussed in SectionII.

Future efforts should include additional experiments and computa-tional modeling with different liner materials, shapes and sizes, andend confinement to understand fully the influence of these variables onwarhead performance. Also, future work should include generalization ofthe empirical criterion for fragment separation to a more fundamentalcriterion. For example, material properties, such as the total plasticstrain to failure, might be used to predict fragment separation.

It is also believed that the modeling capability can successfullybe applied to certain aspects of eccentric warheads (a three dimensionalproblem). However, while some degree of success may be had, in order tomodel eccentric warheads properly, a three dimensional computer code isneeded.

s0

AC KNOW LEDG L•MUNTS

'rhe authors wish to thank Dr. Robert R. Karplp for the many helpfultechnical discussions during the course of the work. Also the authorsare grateful to Mr. G. Gentle and Mr. Carroll West for their assistancewith the experimental program.

51

. . .

LIST OF SYMBOLS

Nominal charge (explosive) mass to metal mass (fragment +liner) ratio

D Explosive diameter

DM Calculated outside diameter of continuous metal casing model,

from K4., -a Pf (w/4 LW (DM2 - DHE)

L c Side of a cubical fragment

L HE Explosive Length

LW Length of fragments on warhead (equal to LHE in all cases)

Mc Mass of a cubical fragment (also equivalent to mi)

MHE Mass of the explosive charge

MR Mass of a rod

mi Individual fragment mass

M RC Mass of a recovered cubical fragment

'IT Total mass of fragments and liner on warhead

Ncc Number of cubical fragments per column (along warhead length)

N Number of columns of cubical fragmentsC

NR Number of rods per warhead

R Current warhead radius in computations

Rb Radius of warhead at fragment separation in computationsi

R Expansion ratio at fragment separation or breakage ratio;S0 equivalent to WRc/Lc

o 0Initial inside radius of casing (metal fragments)

WRC Recovered cube dimension in the circumferential (hoop) direction.

Uf Azimuthal fragment-bearing sector angle

Pf Fragment mass density

52

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DRSEL-HL-CT, S. CrossmanFort Monmouth, NJ 07703

53

i)ISTRIBUTION LIST

No. of No. ofop s.. Organiza tion Cpies OrJ.tn i zat ion

3 Commander 1 IIQDA (I)AMA-MS)US Amy Armament Research Washington, DC 20310

and Development CommandAT'TN: DRDAR-LCP,, Dr. R.Walkur 1 Commander

DRDAR-TS-S US Army Research OfficeDRDAR-LC, Mr. R. Nixon ATTN: Dr. H., Saibel

Dover, NJ 07801 P. 0. Box 12211Research Triangle Park

Commander NC 27709US Army Hev.?- Diamond LabsATTN: DRXDO-Tl I Commander2800 Powder Mill Road US Naval Air Systems CommandAdolphi, MD 20786, AT'rN: AIR-604

Washington, DC 203602 Commander

US Army Materials and I CommanderMechanics Research Center US Naval Ordnance Systems Cmd

ATTN: J, Mescall ATTN: ORD-9132D. Roylance Washington, DC 20360

Watertown, MA 021721 Chief of Naval Research

Commander ATrTN: Code ONR 439, N.PerroneUS Army Natick Research Washington, DC' 20360

and Development CommendATTN: DRXRE, Dr. D, Sioling 1 CommanderNatick, MA 01762 US Naval Air Development Ctr

Johnsvil leI Director Warminster, PA 18974

US Army TRADOC SystemsAnalysis Actidity 1 Commander

ATTN: ATAA-SL (Tech Lib) US Naval Missile CenterWhite Saands Missile Range Point Mugu, CA 93041NM 88002

2 CommanderI Deputy Assistant Secretary David W. Taylor Naval Ship

of the Army (R41D) Research & Development CenterDepartment of the Army A'rTN: D. R. GarrisonWashington, DC 20310 A. Wilner

Bethesda, MD 200341 HQDA (DAMA-CSM)

Washington, DC 20310 3 CommanderUS Naval Surface Weapons Center

I1 1QDA (DAMIA-ARP) ATTN: Code TED , D.W.ColbertsonWashington, DC 20310 Mr. L. Hock

Code TX, Dr. W.G. SoperDahlgron, VA 22448

54

DISrRIBUTION LIST

No. of No. of"organ i zat ion (?9 organszation

2 Commander 2 AFMLuS Naval Surface Weapons Center Wright-I'atterson APB, OH 45433

ATTN: WR-13Tech Library 1 AFFDL (I•DT)

Silver Spring, MD 20910 Wright-Patterson AFB, OH 45433

6 Commander 3 ASD (YII/EX, John Rievley;US Naval Weapons Center XRIHD, Gerald Bennett;A'rN: J. Pearson, Code 383 EINYS, Matt Kolleck)

J.S. Rinehart, Code 383 Wright-Patterson APB, OH 45433M. Backman, Code 3831C.F. Austin, Code 3833 1 lleadquartersR.G.,S. Sewell, Code 3835 National Aeronautics andJ. Weeks, Code 3266 Space Administration

China Lake, CA 93555 Washington, DC 20546

2 Commander 2 DirectorUS Naval Research Laboratory National Aeronautics and

ATTN: Tech Lib Space AdministrationJ. Baker John F. Kennedy Space Center

Washington, DC 20375 AT"N: KN-ES-3KN-ES-34

1. Superintendent Kennedy Space Center, FL 32899

US Naval Postgraduate SchoolATTN: Dir of Lib 2 DirectorMonterey, CA 93940 National Aeronautics and

Space AdministrationI AFATL (Mr. Leonard T. Wilson) Langley Research Center

Eglin AFB, FL 32542 ATTN: R. .1. HaydukTech Lib

3 AFATL (DLRD, K. McArdlet Hampton, VA 23665DLRV, G. Crews; DLYD)

Eglin AFB, FL 32542 1 US Energy Research andDevelopment Administration

I ADTC/DIJW (CPT D, Matuska) Los Alamos Scientific Lab

Eglin AFB, FL 32542 ATTN: Mr. R. Craig, MS-960Dr. L. Hantel, WX-2

I AFATL (DLDL, MAJ J.E. Morgan) Dr. Robert Karpp!Eglin AFB, Fl, 32542 Los Alamos, NM 87544

2 AFWL (WLL)Kirtland AFB, NM 87117

1 ASD (ASBRS)Wright-Patterson AFB, OH1 45433

~ s.