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TECHNICAL REPORT BRL-TR-3080

AD-A219 374BRL -'0

E3FII

LARGE-SCALE SIMULATIONS OF MONOLITHICAND SEGMENTED PROJECTILES

IMPACTING SPACED ARMOR

DANIEL R. SCHEFFLERTHOMAS M. SHERRUCK DTICS~DTIC

ELECTEFEBRUARY 1990 MAR 16 1990 D

AM3OVW M~ M"R RMZIAS% DISTMMTIN UNLU~N=.

U.S. ARMY LABORATORY COMMAND

BALLISTIC RESEARCH LABORATORYABERDEEN PROVING GROUND, MARYLAND

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4. TB Final. June 88 to SntUETITLarge-Scale Simulations of Monolithic and Segmented Projectiles Impacting Spaced

Armor

SLAUTHCRS) " ""

Scheffler, Daniel R., and Sherrick, Thomas M.

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11. ABSTRACT (M• Mu ' 200 =..W.

Numerical simulations are presented describing the performance of segmented and monolithic kinetic energy penetralorsagainst oblique-spaced-rolled homogewous armor (RHA) plates. The three-dimensional simulations depict the effectsof striking velocity; target plate thickness-to-feneMor dicameter ratio (T/D); segment spuing-to-penetrator diameterrailo (S/D); and the number of segments, o.. penetrator performance.

14. SU(AC TIM" It NUMBER OF PAGES

kinetic energy penetrator, rolled homogeneous armor, RHA, segmented penetrator, 66spaced armor, inipac computer simulations, penetraion, perforation, kineu it. PIKE cooleanrrv. armor ,(/.,::( ..

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TABLE OF CONTENTS

Page

TABLE OF CONTENTS .................... iii

LIST OF FIGURES .................. ..................... v

Paragraph 1 INTRODUCTION ............. ....................... 1

2 SIMULATION MATRIX ............................ .. I

3 RESULTS AND DISCUSSION .. . .............. 3

4 CONCLUSIONS ................ ....................... .. 23

LIST OF REFERENCES ........... .................... ... 24

APPENDIX A - Keel Input Data ....... ............... ... 25

APPENDIX B - Material Properties ....... ............. 35

APPENDIX C - Plots Used For Residual Mass Calculations . . 37

DISTRIBUTION LIST .............. ...................... 55

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IVV

LIST OF FIGURES

Figure Page

i. Segmented penetrator, N-5, V-1.5 km/s into 60' RHA (T/D-2) at 60microseconds . .......................................... 5

2. Segmented penetrator, N-5, V-1.5 km/s into 60' RHA (T/D-2) at 120microseconds.................. . . . . . . ..... ........... 6

3. Segmented penetrator, N-5, V-1.5 km/s into 60' MA (T/D-2) at 140microseconds . . . . . . . . . . . . . . . . ............ 7

4. Segmented penetrator, N-5, V-1.5 km/s into 60' RHA (T/D-2) at 160microseconds ...................... ................ ....... . . 8

5. Segmented penetrator, N-S, V-1.5 km/s into 600 RHA (T1'D-2) at 180iaicroseconds . . ........................... 9

6. Seqmented penetrator, N-5, V-2.0 km/s into 60' RHA (T/D-2) at 60microseconds ......... ......... ........ . . 10

7. Segmented penetrator, N-5, V-2.0 km/s into 60' RHA (T/D-2) at 80mioroseconds . . . . . . . . . . . . . . .......... . . .. 11

8. Segmented penetrator, N-5, V-2.0 km/s into 600 RHA (T/D-2) at 100microseconds ...................... ................ ...... . .12

9. Segmented penetrator, N-5, V-4.0 km/s into 60' RHA (T/D-2) at 40microseconds ...................... ....................... ... 13

10. Segmented penetrator, N-5, V-4.0 km/s into 60' RHA (T/D-2) at 60microseconds . . . . . . . . . . ......... . . . . . . . . . 14

11. Segmented penetrator, N-5, V-2.0 km/s into 60' RHA (T/D-4) at 120microseconds . . . . . . . . . . . ......... . ........ 15

12. Segmented penetrator, N-5, V-2.0 km/s into 60* RHA (T/D-4) at 160microseconds ...................... ..................... ... .. 16

13. Segmented penetrator, N-5, V-3.0 km/s into 60' RPA (T/D-4) at 4)microseconds ................ ............................ 17

14. Segmented penetrator, N-5, V-3.0 km/s into 600 RHA (T/D-4) at 80microseconds .......................... ........................ 18

15. Segmented penetrator, NH-5 V-3.0 km/s into 60' RHA (T/D-4) at 240microseconds .............................................. 19

16. Segmented penetrator, N-5, V-4.0 km/s into 60' RHA (T/D-4) at 120microseconds .................... .......................... .. 20

17. Segmented penetrator, N-20, V-4.0 km/s into 600 RHA (T/D-4) at 170microseconds .................... .......................... .. 21

18. Monolithic penetrator, N-1, V-4.0 km/s into 60' RHA (T/D-4) at 160microseconds .................... .......................... .. 22

'p

II~mmoNALLY LE~ BLAN4K,

ACKNOWLEDGEMENTS

The authors wish to thank the reviewers, Dr. Ennis F. Quigley andMr. Kent D. Kimsey, for their helpful conents and suggestions in preparing thisreport. Special thanks go to Mrs. Brenda L. Tucker and Miss Melissa A. Boonewho prepared the manuscript.

vii

IMMMONALLY LE"T BLANK.

viii

I. INTRODUCTION

Within the last several years there has been a lot of interest in theperformance of segmented kinetic energy penetrators at velocities greater than2 km/s. Both experimental and analytical investigations of the penetrationmechanisms have been conducted. For example, in 1981 V. Kucher', conducted 2-Dsimulations of a segmented projectile that showed improved performance forsegmented projectiles and improved performance with increased segment spacing.Since then, several computer studies have been conducted, among them W. de Rossetand K. D. Kimsey', D. R. Scheffler', and R. T. Sedgwick and co-workers 4, allshowed improved penetrator performance for the segmented rod over an equivalentmass and diameter monolithic rnd. In addition to computer simulations,experiments conducted by A. Charter*'$', and Bell' also suggest that segmentedpenetrators exhibit improved performance.

Numerical simulations are well suited for the study of segmented kineticenergy penetrators. Numerical studies permit the examination of segmentedpenetrators without the typical problems encountered in ballistic tests such as;alignment of the individual segments, constraints of pre-extended projectilelengths, projectile yaw, structural integrity of the launch package, andsynergistic effects of carrier tubes or carrier rods on overall penetration.Thus, simulations can increase our understarning of the penetration phenomenonas well as supplement the limited ballistic test data.

Most of the data in the literature concentrates on the performance of high-velocity segmented kinetic energy penetrators against semi-infinite steel armor.Some ballistic tests of segmented projectiles impacting spaced plate arrayshave been conducted; however, the data is sparse. For example, A. Charters""'''..conducted a limited number of ballistic tests ahowing that each segment "punchesthrough" a target plate in an array allowing the remaining segments to passthrough undisturbed, each defeating one plate. Since computations are wellsuited for modeling segmented projectile impacts, a series of three-dimensionalsimulations have been conducted to characterize the penetration/perforationphenomenon against spaced armor. The projectile impacts were modeled usingversion 121 of the HULL finite-difference code.

HULL","' is an Fulerian wave propagation code that uses a second orderaccurate finite-difference scheme. The material advection scheme is first order.The code solves the partial differential equations of continuum mechanicsignoring heat conduction and viscosity terms. The Mie-Gruneisen equation ofstate is used to model solids. After vaporization occurs, the Gamma Law equationis used to model the gas. Explosives can be modeled using the Jones-Wilkins-Leeequation of state. Material failure models include: maximum principle stress,maximum principle strain, and the Hancock-Mackenzie triaxial failure model"2 .When material failure occurs, a numerically significant void (i.e. air), isintroduced in the cell which permits relaxation of the tensile forces.Recompression is permitted.

2. SIMULATION MATRIX

A series of three-dimensional simulations have been conducted to determinethe performance of segmented projectiles striking spaced armor. The performanceof the segmented projectile is measured relative to an equivalent massmonolithic penetrator. The length-to-diameter ratio, L/D, of the monolithictungsten alloy (90W-7Ni-3Fe) penetrator is 20, with a total mass of 274 grams.The segmented projectile geometry separates the monolithic rod into N individualsegments with the same diameter as the monolithic projectile.

A number of impact conditiono have been modeled to characterize the effectsof: striking velocity (1.5-4.0 km/a); target thickness-to-penetrator diameterratio, T/D, (2 and 4); segment spacing-to-penetrator diameter ratio, S/D, (0 to8); and the number of individual segmenti, N, (5 and 20) on penetration/perforation performance. The computational matrix is summarized in the Table1. For the cases modeled, the target was comprised of two rolled homogeneousarmor (RHA) plates with the same T/D ratio and a normal spacing of 50.8 mm atan obliquity of 60 degrees.

Table 1. Computational Matrix (Nominal Projectile Mass 274 grams).

Problem No. Velocity N* S/D* T/DS.... {(10 /s) ,, ..

5.0004 1.5 5 1 25.0000 1.5 1 0 25.0005 2.0 5 1 25.0001 2.0 1 0 25.0006 3.0 5 1 25.0002 3.0 1 0 25.0007 4.0 5 1 25.0003 4.0 1 0 2

518.8800 2.0 5 1 46.0002 2.0 1 0 4

518.8833 3.0 5 1 46.0003 3.0 1 0 4

518.8844 4.0 5 1 46.0004 4.0 1 0 47.0001 4.0 5 4 47.0002 4.0 58 48.0000 4.0 20 1 4

*NOTR N - I Lmlieu a mAlItbLe pltIo394Il

IOM loi eeftanI projetlea #lainI.t

In an effort to preserve material interfaces and minimize material diffusiontypically encountered in Eulerian codes, a constant subgrid was chosen for thex-y plane covering a region two diameters away from the penetrator. The constantsubgrid provides six cells across the diameter of the penetrator. Beyond theconstant subgrid in the x-y plane, an expansion factor of 1.1 was used to keepproblem size and runtime within practical limits. In the z-direction, or axialdirection. a constant cell spacing was used, which was 1.5 times the spacing ofthe constant subgrid in the x-y plane. The number of cells used to model aparticular problem depended on the size of the target plates and overall lengthof the penetrator; however, the cell sizes in the constant sub-grid remainedthe same for all simulations. Appendix A contains a listing of KEEL input datafor all of the problems modeled. If the only difference in a particular problemwas the striking velocity, inpuxt data is listed for only one velocity.

The hydrodynamic behavior of the metals were modeled using the Mie-Gruneisenequation of state. The coefficients for the equation of state data were obtainedfrom Kohn".

An incremental elastic-plastic fozmulation following the description givenby Wilkins" is used to describe the deviatoric response of the metals. Anelasetic-perfectly plastic model has been used for the tungsten alloy and RHA with

2

20 kb" and 15 kb" yield strengths, respectively. A complete listing of the

material properties and equation of state data are provided in Appendix B.

3. RESULTS AND DISCUSSION

Residual penetrator mass and residual kinetic energy have been used tomeasure performance. The greater the residual penetrator mass at a givenvelocity, the greater its performance. Residual mass was determined using thesame technique ballisticians use to determine residual mass from radiographs.The complete set of density contour plots from which residual mass was determinedcan be found in Appendix C. Residual kinetic energy was determined using theresidual mas= from density contour plots and the velocity from velocityhistograms. For the segmented penetrators residual energy is the summation ofthe individual segment residuals.

Results for the simulations against the RMA spaced plates for T/D of 2 aresummarized in Table 2. Table 2 shows a significantly greater (31 percent)residual mass for the monolithic penetrator at a velocity of 1.5 km/s. Theresidual kinetic energy of both monolithic and segmented penetrators are aboutthe same. At higher striking velocities the segmented penetrator showsessentially the same if not greater performance than the monolithic penetrator.Figures 1 to 5 show velocity histograms and density contour plots 'or thesegmented penetrator at a velocity of 1.5 km/s at various times. The figuresshow a sequence of events in which individual segments collide and eventuallybecome misaligned, i.e. not colinear. At 2 km/s collisions between individualsegments still occur. Figures 6 to 8 show the lead segment losing velocity afterperforating the first target allowing the next segment the catch up. However,misalignment of individual segments is not observed. The collisions tend tomake the segmented rod appear much like a monolithic rod since the lead segmentis not entirely eroded before being impacted by a subsequent segment. At 4 km/s,see Figures 9 and 10, most of the lead segment is eroded in perforating thefirst target plate. Though the lead segment is impacted by the second segment,only minimal loss of kinetic energy takes place in the second segment. Trailingsegments uninvolved in collision retain their initial velocities and suffer noloss in kinetic unergy. Due to the decrease in the time interval between targetplates, no further collisions occur until lead segments impact the next plate.

TABLE 2. Residual Mass of Monolithic and Segmented Rods (N-5, S/D-l)against T/D-2 Spaced Plates

Striking Striking Segmented Segmented Monolithic MonolithicVelocity Energy Residual Residual Residual Residual(km/3) (MJ) Mas ( ars) Energy (MIJ) Mass (0s) -Eneriv (MJ)

1.5 0.308 47.9 0.016 63.0 0.0182.0 0.548 107.0 0.166 108.0 0.1473.0 1.233 149.0 0.637 143.0 0.5894.0 2.192 152.0 1.183 150.0 1.141

Results for the simulations against the RHA spaced plates for T/D of 4 aresummarized in Table 3. Simulations at a velocity of 1.5 km/s were conducted,however, both the monolithic and segmented penetrators failed to perforate thesecond target plate and are therefore not included. Table 3 shows higherresidual mass for the segmented penetrator at all striking velocities. The datapresented in Table 3 shows the greater the striking velocity, the greater theincrease in residual mass. Figures 11 and 12 show velocity histograms andcontour plots for the segmented penetrator at a velocity of 2.0 km/s. As withthe simulation for the T/D of 2 case at a velocity of 1.5 km/a, individual

3

segment interactions occur which lead to the misalignment of segments. At 3km/s, move of the lead segment is eroded before any interaction occurs, seeFigure 13. In Figure 13, what appears to be a single seqment is a fraction ofthe preceding segment and the subsequent segment. The alignment of the segmentsis less severely affected, see Figure 14. Segment interactions are also observedwell after perforation of the second target plate, leading to severe misalignmentof the segments, see Figure 15. At 4 km/s the lead segment is almost entirelyeroded before interactions occur, see Figure 16. In Figure 16, what appears tobe a single lead segment is the almost entirely eroded second segment beingimpacted by the third segment.

TABLE 3. Residual Mass of Monolithic and Segmented Rod*(N-5, S/D-1) against T/D-4 Spaced Plates

Striking Striking Segmented Segmented Monolithic MonolithicVelocity Energy Residual Residual Residual Residual(km/s) (MJ) Mas Mass tame) Enorav (MJ)

2.0 0.548 18.4 0.0018 14.6 0.00033.0 1.233 68.6 0.250 58.1 0.1864.0 2.192 99.9 0.725 62.0 0.413

The interactions between segments for both T/D of 2 and 4, suggest a spacingof I D is not optimum. The effect of segment spacing on performance for theT/D of 4 target has been studied numerically for segment spacing-to- penetratordiameter ratios, S/D, of 4 and 8. No segment interactions occurred inperforating the spaced plate array. However, the two lead segments for the S/Dof 4 case collided well after (t-100 micro-seconds) perforating the second plate.Thýs occurs because the lead segment did not completely erode during perforationof the second spaced plate. Thus the lead segment loses velocity allowingremaining segments to catch up. Table 4 shows the affect of segment spacing onpenetrator performance. Note that as S/D increases the residual ponetrator mr.ssincreases.

TABLE 4. Residual Mass vs Segment Spacing forVs - 4.0 km/u, N - 5, and T/D - 4 Plates

Spacing Residual ResidualDiameter Mass (rma) Enerav (MJ)

none 62.0 0.4131 99.0 0.7254 108.0 0.8648 126.0 0.9851* 129.0 1.183

* 20 Segment Rod

Table 4 also presents the results for a 20 segment projectile with a S/Dof 1. These results suggest that trailing segments, unaffected by impact withthe spaced plates and/or individual segment interactions, retain more kineticenergy than an equivalent monolithic rod. Figures 17 and 18 show velocityhistograms and density contour plots of the 20 segment pinetrator and theequivalent monolithic penetrator. The monolithic penetrator's velocity is

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reduced while perforating the spaced plate array, while trailing segmentsunaffected by interactions retain their initial striking velocity. Table 4 showsa 108 percent improvement in residual mass over the equivalent monolithic rod.The improvement in residual mass of the 5 segment penetrator with an S/D of 8over the equivalent monolithic rod is 103 percent.

4. CONCLUSIONS

A number of 3-D simulations have been conducted to determine the performanceof segmented rods impacting spaced plate arrays. The performance of segmentedrods is characterized based on residual mass and kinetic energy. In general,segmented rods outperform their monolithic counterparts for the spaced platearrays studied at velocities above 2 km/s. The increase in performance isenhanced for thick target plates. Furthermore, the simulations show thatincreasing the spacing between segments increases performance. It is desirable,though not always practical, for spacing to be such that every segment acts asan independent penetrator. Finally, it should be noted that increasing thenumber of segments increases the residual mass and kinetic energy. The increasein performance derived from a greater number of segments is greater than theincrease derived from increased segment spacing.

23

LIST OF REFERENCES

1. Kucher, V. "Multiple impacts on Monolithic Steel", Ballistic ResearchLaboratory Technical Report ARBRL-TR-02406, April 1982.

2. do Rosset, W. S. and Kimsey, K. D., "Calculation of Multiple Copper RodImpacts on Steel Targets", Proc. Ninth International Symposium on Ballistics,Shrivenham, U. K., April 29-30, May 1, 1986.

3. Scheffler, D. R.,"2-D Computer Simulations of Segmented Penetrators",Ballistic Research Laboratory Technical Report, BRL-TR-3013, July 1989.

4. Sedgwick, R. T., Waddell, J. L., and Wilkinson, 0. M., "High Velocity LongRod Impact: Theory and Zxperx..ment", Proc. Tenth International Symposium onBallistics, San Diego, October 1987.

5. Charters, A. C., "The Penetration of Rolled Homogenous Armor by Continuousand Segmented Rods at High Velocity: Theory and Experiments", General ResearchCorporation Technical Report CR-86-1031, April 1986.

6. Charters, A. C., "The Penetration of Rolled Homogenous Armor by Continuousand Segmented Rods at High Velocity: Theory and Experiments", General ResearchCorporation Technical Report CR-87-1008, December 1986.

7. Charters, A. C., and Manna, T. L., "Armor/Anti-armor Program: AdvancedPonetrator Concepts Evaluation Program", General Research Corporatimn briefingpackage presented at the DARPA Armor/Anti-Armor Executive Steering Committee,Arlington, Virginia, August 25, 1987.

8. Charters, A. C., and Manna, T. L., "Armor/Anti-armor Program: SecondQuarterly Review", General Research Corporation briefing package presented atthe DARPA Impact Physics Team Second Quarterly Review, Lawrence LivermoreNational Laboratories, October 14-15, 1987.

9. Bell, L. P., "Evaluation of Segmented and Solid Projectiles DuringHypervelocity Flight and Impact", Arnold Engineering Development Center TechnicalReport AEDC-TRS-87-V6, March 1987.

10. Matuska, D. A. and Osborn, J. J.,"HULL Technical Manual", vol I, OrlandoTechnology Incorporated, 1986.

11. Matuska, D. A. and Osborn, J. J.,"HULL Users Manual", vol 11, OrlandoTechnology Incorporated, 1986.

12. Hancock, J. W., and Mackenzie, A. C., J. Mech. Phys. Solids, 24, 147.

13. Kohn, B. J., "Compilation of Hugoniot Equations of State", Air Force WeaponsLaboratory Technical Report AFWL-TR-69-38, April 1969.

14. Wilkins, M. L., in B. Adler et al. (Eds.), Methods in Computational Physics,Academic Press, New York, 1964.

15. Nicholas, T., "Dynamic Tensile Testing of Structural Materials Using a SplitHopkinson Bar Apparatus", Air Force Wright Aeronautical Laboratories TechnicalReport AFWAL-TR-80-4053, October 1980.

24

APPENDIX A - KEEL Input Data

25

KEEL Input For Monolithic Penetrators, Into T/D-2 Spaced Plates

KEEL PROBLEM 5.0000*NM-3 AIR-i WALLOY-2 RHA-3

DIMEN-3 VISC-1 FLUXER-3 STRESS-iIMAX-51 JMAX-31 KMAX-241 IQ-50 JQ-30 KQ-240FAIL-i STRAIN-i REZONE-0NSTN-2 NOP-2000AREF-.TRUE. BREF-.FALSE. FREF-.FALSE.LREF-.FALSE. RREF-.FALSE. TREF-.FALSE.HEADERL/)) - 20 VS - 1.5 KM/SEC T/D - 2

MESHCONSTANT SUBORID NX-30 XO-2.5 XMAX-2.5 RXNEG-i.i RXPOS-i.1

XOLJM-.O.42045 XMLIM-4.g8g57NY-i5 YO-O.0 YMAX-2.6 RYPOS-1.1YOLIM-0. YMLIM-9,0g078NZ-241 Z0--21.0 ZMAX-39.25 RZNEG-1.O

RZPOS-1.0ZOLIM--2i.0 ZMLIM-39.25

GENERATEPACKAGE WALLOY W-1.GE5

CYLINDER XC-0.0 YC-0.0 ZB--20. ZT--..0. RADIUS-.6PACKAGE AIR W-1.5ES

CYLINDER XC-O.0 YC-0.0 ZB--1.0E20 ZT--20. RADIUS-.5PACKAGE RHA

BOX XI-m.8.0 X2-8.0 Y1-0.0 Y2-8.0 Z1-O.0 Z2-2.0XCO-0.0 YCC-0.0 ZCC-0.88803ANGLB-60

* PACKAGE RHABOX XIina..0 X2'.8.0 Y1.a0.0 Y2-8.0 Z1-0.0 Z2-2.0XCC-0.O YCC-0.0 ZCC-15.02803ANGLB-60

PACKAGE AIR W-1.0E4 BOX FILLSTATION XS-0. YS-0. ZL-0.

XS-0. YS-0. ZL--20.END

26

KEEL Input For Segmented Penetrator, Into T/D -2 Spaced Plates

KEEL PROBLEM 5.0004NM-3 AIR-i WALLOY-2 RHA-3DIMEN-3 VISC-1 FLUXER-3 STRESS-iIMAX-61 JMAX-31 KMAX-273 IQ-50 JQ-30 KQ-272FAIL-i STRAIN-1 REZONE-0NSTN-2 NOP-2000AREF-.TRUE. BREF-.FALSE. FREF-.FALSE.LREF-.FALSE. RREF-.FALSE. TREF-.FALSE.HEADERL/D -20 VS-I1.5 KM/S T/D -2

MESHCONSTANT SUBORID NXm30 XO-2.S XMAXm2.5 RXNEGml.l'RXPOSmi.1

XOLIM--8.42045 XMLIM-4.98g67NY-~iS YO-0 .0 YMAX-2 .5 RYPOS-1 .1YOLIM -0. YMLIM -9.09078NZ-273 Z0--29.0 ZMAX-39.25 RZNEG -1.0

RZPOS-1 .0ZOLIM--29.0 ZMLIM-39.25

GENERATE-PACKAGE WALLOY W-I.5E5

CYLINDER XC-O.0 YC-0.0 ZBm-4. ZT-0.0 RADIUSm.6PACKAGE AIR W-1.2E6

CYLINDER XC-0.0 YCm0.0 Z13-8. ZTm-4. RADIUS-.5PACKAGE WALLOY W-1.5ES

CYLINDER XC-0.0 YC-0.0 ZB--10. ZT-0. RADIUSUM.6PACKAGE AIR W-1.6E5

CYLINDER XC-0.0 YC-0O.0 ZB--12. ZT--10. RADIUS-.6PACKAGE WALLOY W-1.6E5

CYLINDER XC-0.0 YC-0.0 ZB--18. ZT--12. RADIUS-.5PACKAGE AIR W-1.5ES

CYLINDER XC-0.0 YC-0.0 ZB-.18. ZT--18. RADIUS-.5PACKAGE WALLOY W-1.6E5

CYLINDER XC-0.0 YC-0.0 Z13-22. ZT--18. RADIUS-.5PACKAGE AIR W-1.SES

CYLINDER XCm-0.0 YO.-0.0 ZB-*-24, ZT--22. RADIUS-.5PACKAGE WALLOY W-1.5E5

CYLINDER XC-0.0 YC-0.0 ZB-.28. ZT--24. RADIUS-.5.PACKAGE AIR W-1.5E5

CYLINDER XC-0.0 YC-0.0 ZI3--1.0E20 ZT--28. -RADIUS-.5PACKAGE RHA

BOX X1-8.0 X2-8.0 Y1-0.0 Y2-8.0 Z1-0.0 Z2-2.0XCC-0.0 YCC-OA) ZCC-0.88803ANGLB-80

PACKAGE RHABOX X1-8.0 X2-8.0 YI-0.O Y2'-8-0 Z1-0.O Z2-2.0XCCrO.0 YCCu'0.0 ZCCa.16.02003ANGLBm6O

PACKAGE AIR W-1.0E4 BOX FILLSTATION XS-'0. YS=O. ZL-0.

XS-0. YS-0. ZL--28.END

27

* ~KEEL Input For Monolithic Penetrators Into T/Du-4 Spaced Plates

KEEL PROBLEM 8.0001NMý3 AIR-i WALLOY-2 RHA-3DIMEN-3 VISCami FLUXER-"3 STRESS-IIMAX-58 JMAX-33 KMAX-284 IQ-65 JQ-32 KQ-283FAIL-., STRAIN-i REZONE-0NSTN-2 NOP-2000AREF-.TRUE. BREF-.FALSE. FREF-.FALSE.LREF-.FALSE. RREF-.FALSE. TREF-.FALSE.HEADERL /D - 20 VS - 1.5 KM /SEC T/D - 4

MESHCONSTANT SUBORID NX-30 XO-2.5 XMAX-2.5 RXNEG-1.1 RXPOS-1.i

XOL[Mm--.99583 XMLIM-6.g9683NY-iS YO-0.0 YMAX-2.8 RYPOS-1.1YOLIMm0. YMLIM-i0.85g85

* ~NZ-2g8 Z0--21.0 ZMAX-47.26 RZNEO-1.0RZPOS- 1.0

ZOLIM--21.0 ZMLIM-50.GENERATE

PACKAGE WALLOY W-1.05ECYLINDER XC-0.0 YC-0.0 ZB--20. ZT--0.0 RADIUS-.5

PACKAGE AIR Wm1.5E5CYLINDER XC-O.0 YC-0.0 ZB--i.0E20 ZT--20. RADIUS-.6

PACKAGE RHABOX X1-10.0 X2-10.0 Y1-0.0 Y2-10.0 Z1-0.0 Z2-4.0XCC-i.7321 YCC-0.0 ZCC-3.88803ANGLB-80

PACKAGE RHABOX X1-10.0 X2-10.0 Y1-0.0 Y2-10.0 ZI-0.0 Z2-4.0XCCmi.7321 YCC-0.0 ZCC-22.02603ANGLB-80

PACKAGE AIR W-1.0E4 BOX FILLSTATION XS-0. YS-0. ZL-0.

XS-O. \'S-O. ZL--20.END

28

KEEL Input For Segmented Penetrators Into T/D -4 Spaced Plates

KEEL PROBLEM 518.88NM-3 AIR-i WALLOY-2 RHA-3DIMEN-3 VISC-I FLUXER-3 STRESS-iIMAX-68 JMAXa-33 KMAX-316 IQ-53 JQ-32 KQ-315PAIL-I STRAIN-i REZONE-ONSTN-2 NOP-2000AREF-.TRUE. BREF-.FALSE. FREF-.FALSE.LREF-.FALSE. RREF-.FALSE. TREF-.FALSE.HEADERSEGMENTED ROD L/D - 20 VS - 2.0 KM/SEC T/D - 4

MESHCONSTANT SUBGRID NX-30 XO-.2.5 XMAX-2.5 RXNEG-i.1 RXPOS-1.1

XOLIM-..6.99583 XMLIM-8.gg583NY-iS YO-0.0 YMAX-2.5 RYPOS-1.1YOLIM-.0. YMLIM-i0.85g85NZ-316 ZO--2g.0 ZMAX-50. RZNEG-1.O

RZPOS-i.OZOLIMý-29.0 ZMLIM-50.

GENERATEPACKAGE WALLOY W-2.0E5

CYLINDER XC-O.0 YC-0.0 ZB--4. ZT-O.O RADIUSWU,5PACKAGE AIR W-2.0E5

CYLINDER XC-0.O YC-O.O ZB--8. ZT-.4. RADIUS-.5PACKAGE WALLOY W-2.0E5

CYLINDER XO-O.O YC-O.O ZB--10. ZTm-6. RADIUSm.6PACKAGE AIR W-2.05S

CYLINDER XC-O.O YC-OO ZB.--I2. ZT-m-iO. RADIUS-.5PACKAGE WALLOY W-2.0E5

CYLINDER XC-0.0 YC-O.O ZB--18. ZT-.12. RADIUS-.5PACKAGE AIR W-2.OE5

CYLINDER XC-O.0 YC-0.O ZB--18. Z'r--is. RADIUS-.6PACKAGE WALLOY W-2.0E5

CYLINDER XC-OO0 YC-O.O ZB--22. ZTý-.18. RADIUS-.6PACKAGE AIR W-w2.OES

CYLINDER XC-O.O YC-0.O ZB--24. ZT--22. RADIUS-.5PACKAGE WALLOY W-2.0E5

CYLINDER XC-OO0 YC-O.O ZB--28. ZT--24. RAD[US-.5PACKAGE AIR W-2.0E5

CYLINDER XC-D.O YC-O.O ZB--i.0E20 ZT-..28. RADIUS-.5PACKAGE RHA

BOX X--.1O.O X2-10.0 Y1-0.0 Y2-10.0 Z1-0.0 Z2-4.0XCC-1.7321 YCC-O.O ZCC-3.88603ANGLB-80

PACKAGE RI4ABOX X1-101.0 X2-."10.0 Y1-0.0. Y2-"10.0 ZIv-0.O Z2-4.0XCC-1.7321 YCC-O.O ZCiCm22.02603ANGLB-e0

PACKAGE AIR W-1.0E4 BOX FILLSTATION XS-O. YS-O. ZL-O.

XS-O. YS-O. ZL--28.END -

29

KEEL Input For S/D-4 Segmented Penetrator Into T/D-4 Spaced Plates

KEEL PROBLEM 7.0001NM-3 AIR-I WALLOY-2 RHA-3DIMEN-3 VISC-1 FLUXER-3 STRESS-iIMAX-68 JMAX-33 KMAX-348 IQ-55 JQ-32 KQ-347FAIL-i STRAIN-i REZONE-0NSTN-2 NOP-2000AREF-.TRUE. BREF-.FALSE. FREF-.FALSE.LREF-,FALSE. RREF-.FALSE. TREF-.FALSE.HEADERSEGMENTED ROD L/D - 20 VS - 4.0 KM/SEC T/D - 4

MESHCONSTANT SUBORID NX-30 XO-2.5 XMAX-2.5 RXNEG-i.1 RXPOS-1.i

XOLIM--8.9g583 XMLIM-6.9g583NY-15 YO-"0.0 YMAX-2.5 RYPOS-il1YOLIM-0. YMLIM-10.85985NZ-348 ZO--37.O ZMAX-50. RZNEG-1.0

RZPOS-i .0ZOLIMm-37.0 ZMLIM-50.

GENERATEPACKAGE WALLOY W-4.OES

CYLINDER XC-0.O YC-O.0 ZB--4. ZT-0.0 RADIUS-.5PACKAGE AIR W-4.0E5

CYLINDER XC-0.0 YC0.0. ZB--8. ZT-4. RADIUS,5PACKAGE WALLOY W-4.OE6

CYLINDER XC-0.0 YC-0.O ZB-.12. ZT--8. RADIUS-.5PACKAGE AIR W-4.OES

CYLINDER XC-0.0 YC-0.0 ZB--16. ZT--12. RADIUS-.SPACKAGE WALLOY W-4.0ES

CYLINDER XC-0.0 YC-O.0 ZB--20. ZT--16. RADIUS-'.6PACKAGE AIR Wý4.OE5

CYLINDER XC-0.0 YC-0.0 ZB--24. ZT--20. RADIUS-.6PACKAGE WALLOY W-4.0E5

CYLINDER XC-0.O YC-0.0 ZB--28. ZT--24. RADIUS-u.SPACKAGE AIR W-4.0E5

CYLINDER XC-0.O YC-O.0 ZB--32. ZT--28. RADIUS-.5PACKAGE WALLOY W-4.0E5

CYLINDER XC-O.O YC-0.O ZB--38. ZT--32. RADIUS-.5PACKAGE AIR W-4.OES

CYLINDER XC-0.O YC-0.O ZB-.i.0E20 ZT--38. RADIUS-.5PACKAGE RHA

BOX XI--10.0 X2-10.0 Yi-0.0 Y2-10.0 Z1-0.0 Z2-4.0XCC-1.7321 YCC-0.0 ZCC-3.86603ANGLB-60

PACKAGE RHABOX X1-10.0 X2-10.0 Yi-0.0 Y2-10.0 ZJ-0.fl Z2-4.0XCC-1.732i YCC-0.0 ZCC-22.02603ANGLB-60

PACKAGE AIR W-l.0E4 BOX FILLSTATION XS&aO. YSO0. ZLO0.

XS-O. YS-0. ZL--52.END

30

KEEL Input For S/D-8 Segmented Penetrator Into T/D=4 Spaced Plates

NM-3 AIR-I WALLOY-2 RHA-3DIMEN-3 VISC-i FLUXER-3 STRESS-IIMAX-58 JMAX=33 KMAX-412 IQ-55 JQ-32 KQ-411.FAIL-i STRAIN-i REZONE-0NSTN-2 NOP-2000AREF-.TRUE. BREF-.FALSE. FREF-.FALSE.LREF-.FALSE. RREF-.FALSE. TREF-.FALSE.

* HEADERSEGMENTED ROD L/D - 20 VS - 4.0 KM/SEC T/D - 4

MESHCONSTANT SUBGRID NX-30 XO-2.5 XMAX-2.5 RXNEG-i.i RXPOS-1.i

XOLIM--8.99583" XMLIM-8.9g583NY-15 YO-O.0 YMAX-2.5 RYPOS-i.iYOLIM -0. YMLIM -iO.8508SNZ-412 Z0--53.0 ZMAX-50. RZNEG -1.0

RZPOS-i .0ZOLIM--53.0 ZMLIM-60.

GENERATEPACKAGE WALLOY W-4.0E5

CYLINDER XC-0.0 YC-0.0 ZB--4. ZT-0.0 RADIUS-.6PACKAGE AIR W-4.OE5

CYLINDER XC-O.O YC-0.0 ZB--12. ZT--4. RADIUS-.5PACKAGE WALLOY W-4.OES

CYLINDER XC-0.0 YC-O.0 ZB--18. ZT--12. RADIUS-.5PACKAGE AIR W-4.0ES

CYLINDER XC-0.O YC-0.0 ZB--24. ZT--18. RADIUS-.6PACKAGE WALLOY W-4.0E5

CYLINDER XC-O.0 YC-0 0 ZB--28. ZT--24. RADIUS-.5PACKAGE AIR W-4.0E5

CYLINDER XC-0.0 YC-O.0 ZB--38. ZT--28. RADIUS-.5PACKAGE WALLOY W-4.0E5

CYLINDER XC-0.O YC-0.0 ZB--40. ZT--38. RADIUS-.5PACKAGE AIR W-4.0E5

CYLINDER XC-0.O YC-0.O ZB--48. ZT--40. RADIUS-.5PACKAGE WALLOY W-4.OES

CYLINDER XC-0.O YC-0.0 ZB--52. ZT--48. RADIUS-.5PACKAGE AIR W-4.OES

CYLINDER XC-0.O YCiv0.0 ZBý--.0E20 ZT--52. RADIUS-.5PACKAQE RHA

BOX X1-10.0 X2-10.0 Y1-0.0 Y2-10.0 ZI-0.0 Z2-4.0XCC-1.7321 YCC-0.0 ZCC-3.86003ANGLB-60

.PACKAGE RHABOX X1-10.0 X2'-10.0 Y1-0.0 Y2-10-0 ZI-0.0 Z2-4.0XCC-1.7321 YCC-0.O ZCC-22.02803ANGLB-60

PACKAGE AIR NW-i.0E4 BOX FILLSTATION XS-0. YS-O. ZL-0.

XS-O. YS-0. ZL--52.END

3 1

KEEL Input For 20 Segment S/D -1 Penet~rtor Intoo T/D -4 Spaced Plates

KEEL PROBLEM 8.0000NM-3 AIR-I WALLOY-2 RHA-3DIMEN-3 VISC-1 FLUXER-3 STRESS-IIMAX-68 JMAX-33 KMAX-380 IQ-56 JQ-32 KQ-359FAIL-i STRAIN-i REZONE-0NSTN-2 NOPm2000AREF-.TRUE. BREF-.FA LSE. FREF-.FALSE.LREF-.FALSE. RREF-.FALSE. TREF-.FALSE.HEADERSEGMENTED ROD L/D - 20 VS m 4.0 KM/SEC T/D - 4

MESHCONSTANT SUBGRID NX-30 XO-2.S XMAX-2.6 RXNEG-1.1 RXPOS-1.1

XOLIM-..6.g9583 XMLIM-8.g9583NY-15 YO-0.0 YMAX-2.5 RYPOS-1.1YGLIM-0. YMLIM-10.85g85NZ-380 ZO--40.0 ZMAX-50. RZNEG -1.0

RZPOSm1.0ZOLIM--40.0 ZMLIM-50.

GENERATEPACKAGE WALLOY W-4.0E5

CYLINDER XC-0.0 YC-0.0 ZB--1. ZT-0.0 RADIUS-.6PACKAGE AIR W-4.0E5

CYLINDER XC-O.0 YC-0.0 ZB--2. ZT--i. RADIUS-.6PACKAGE WALLOY Wm4.0E5

CYLINDER XC-0.0 YC-0.0 ZP--3. ZT-2. RADItJS-.6PACKAGE AIR W-4.0E5

CYLINDER XC-0.0 YC-0.0 ZB--4. ZT-.3. RADIUS-.6PACKAGE WALLOY W-m4.OES

CYLINDER XC-0.0 YC-0.O ZB~-S. ZTa-4. RADIUSm.5PACKAGE AIR W.-4.0E5

CYLINDER XC-0.0 YC-0.0 ZBwu.6. ZT-5. RADIUS-.5PACKAGE WALLOY W-4.0E5

CYLINDER XC-0.0 YC-0.0 ZB.--7. ZT--8. RADIUS-.5PACKAGE AIR W-4.0E5

CYLINDER XC-0.0 YC-0.0 ZB--8. Z'r-7. RADIUS-.SPACKAGE WALLOY W-4.OE5

CYLINDER. XC-0.0 YC-0.O ZB--9. ZT-8. RADIUS-.5PACKAGE AIR W-4.0E5

CYLINDER XC-0.0 YC-0.0 ZBu-i10. ZT--Q.. RADIUS-.5PACKAGE WALLOY W-4.0EF5

COYLINDER XC'.-0.0 YC-0.0 ZBm-11. ZTm-10. RADIUS-S'PACKAGE AIR W-4.0E5

CYLINDER XC-0.0 YC-0.0 ZB--i2. ZT--il. RADIUS-.5PACKAGE WALLOY W-4.0E5

CYLINDER XC-0.0 YC-0.0 ZBi-i13. ZT--12. RADIUS-S5PACKAGE AIR W-4.0E5

CYLINDER XO-0.0 YCwuO.O ZB-i14. ZT--13. RADIUS-.5PACKAGE WAALLOY W-4.0E5

'YLINDER XC-0.0 YC-0.0 ZB--i5. ZT-.14. RADIUS-u.5PACKAGE AIR W-4.0ES

CYLINDER XC-O.0 YC-0.0 ZB--16. ZT--15. RADIIUS-.5PACKAGE WALLOY W-4.OE5

32

CYLINDER XC-O.O YC-O.O ZB--17. ZT--lb. RADIUS-.5PACKAGE AIR W-4.OES

CYLINDER XC-O.O YC-O.O ZB--18. ZT--17. RADIUS-.5PACKAGE WALLOY W-4.0E6

CYLINDER XC-O.O YC-O.O ZBon-19. ZTm-18. RADIUS-.6PACKAGE AIR W-4.0ES

CYLINDER XC-O.O YC-O.O ZB--20. ZTý--I. RADIUS-.5PACKAGE WALLOY W-4.0ES

CYLINDER XC-O.O YC-O.O ZB--21. ZT--20. RADIUS-.5PACKAGE AIR W-4.OE6

CYLINDER XC-O.O YC-O.O ZB--22. ZT--21. RADIUS-.6* PACKAGE WALLOY W-4.0E5

CYLINDER XC-O.O YC-O.O ZB--23. ZT--22. RADIUS-.5PACKAGE AIR W-4.0ES

CYLINDER XC-O.O YC-O.O ZBý-24. ZT--23. RADIUS-.5PACKAGE WALLOY W-4.OES

CYLINDER XC-O.O YC-O.O ZB-.25. ZT--24. RADIUS-.6PACKAGE AIR W-4.OE6

CYLINDER XC-O.O YC-O.O ZB--26. ZTmm-2J5. RADIUS-.5PACKAGE WALLOY W-4.0E5

CYLINDER XC-O.O YC-O.O ZB--27. ZT--28. RADIUS-.6PACKAGE AIR W-4.OES

CYLINDER XC-O.O YC-O.O ZB--28. ZT--27. RADIUS-.6PACKAGE WALLOY W-4.OE5

CYLINDER XC-O.O YC-0.O ZB--29. ZT-.'28. RADIUS-.5PACKAGE AIR W-4.OES

CYLINDER XC-O.O YC-O.O ZB--30. ZT-..29. RADIUS-.5PACKAGE WALLOY W-4.OES

CYLINDER XC-O.O YC-O.O ZB--31. ZT--30. RADIUS-.5PACKAGE AIR W-4.0E5

CYLINDER XC=O.O YC-O.O ZB--32. ZTm--31. RADIUS-.5PACKAGE WALLOY W-4.0E5

CYLINDER XC-O.O YC-O.O ZB--33. ZT-32. RA DIU S-.6PACKAGE AIR W-4.0ES

CYLINDER XC-O.O YC-O.O ZB--34. ZT--33. RADIUS-.5PACKAGE WALLOY W-4.0E5

CYLINDER XC-.O. YCOO. ZB--36. ZT--34. RADIUS-.6PACKAGE AIR W-4.OE5

CYLINDER XC-O.O YC-O.O ZB--36. ZT--36. RA DIU S-.6PACKAGE WALLOY W-4.OES

CYLINDER XC-O.O YC-O.Q ZB--37. ZT--30. RADIUS-,5PACKAGE AIR W-4.OES

CYLINDER XC-O.O YC-O.O ZB--38. ZT--37. RADIUS-.5PACKA GE WA LL OY W-4.OE6

* CYLINDER XC-O.O YC-0.O ZB--39. ZT--38. RADIUS-.6PACKAGE AIR W-4.0E5

CYLINDER XC-O.O YC-O.O ZB-lI.0E20 ZT--39. RADIUS-.5PACKAGE RHA

* ~BOX X1-10.0~ X2-10.0 Y1-O.O Y2-10.0 ZI-O.O Z2-4.0XCC-1.7321 YCC-O.O ZCC-3.86603ANGLB-60

PACKAGE RHABOX X1-10.0 X2-10.0 Yl-0.O Y2-10.0 Z1-O.O Z2-4.0XCC-1 .732 1 YCC-O.O ZCC-22.02803

33

ANGLB-80PACKAGE AIR W-1.0E4 BOX FILL

STATION XS-0. YS-0. ZL-0.XS--0. YS-0. ZL--40.

END

34

APPENDIX B - Material Properties

35

APPENDIX B

Material Propertieb and Equation of State Dat&

Ambient deusity (g/cc) 7.83 6T,3

Ambient sound speed (cm/i) 4.61ob 4,0e6

Shock velocity/put•cle velocity slope 1.73 1.268

Initial Grnseieen ratio 1.67 1.43

Minimum Premiere (dynem/cmeO2) *.,0020 .10.09

Poion'4 rtio 0.26 0.3

Atomic weight 58,86 184.

D*Bye'e temperature (K) 385 270

Vapor coefcient 0.26 0.2

Ambient eneru per unit mum (erp/g) 0.0 0,0

Ambient melt energy per unit mum (erp/g) 7.040 4,7700

Fusion energ7 per Unit mam (Grp/g) 2.74.0 1.34o0

Sublimation energy per unit mum (oerl/g) 74.209 46,5

Ambient vaporisation energy per unit mum (elrgm/g) 22.4,09 13.09

Ambient energy per unit mass at end of vaporisation 96.3i0 68.400(eOrv/g)

Initial yield strength (dyaei/cmee2) 16.e0 20.e09

Saturalaon yield strength (dynem/cm,•2) S1e0 20.e@

rIustic strain ai saturation yield trengith 0,3 0.3

Yield strength ratio for irst point on thermal 0.9 0.9softennlg curve

Energy ratio for first point on thermal soft4mnitg 0.6 0.6curve

Yield strength ritio for second point on thernial 0.9 0.9softening curve

Energy ratio for second point on thermal moftuing 0.6 0.8Scurve

Second coefficient in Hugoniot proesmre curve 4.21968.12 4.6987.12(dynes/cm'e2)

Third coelcient in Hugoniot pressure curve 6.12016.12 3.345e12

(dynem/cm-e2)

Ultimate failure stres (dynes/cmeos) 42.eg 1.ebO

Ultimate failure strain 1.78 0.14

36

APPENDIX C - Plots Used For Residual Mass Calculations

37

Den~itym~I.A'.i.4xl0" a ,(J - ! )an. '0 " - " •' - CM' Q

"40A 0102030 W 273RKA WAUJOY

3 5 .0 /6floolu e

Won 250LOO4.00 240

30.0 1.00 ,.o 231.OoxlO,.20xt'o

140 22025.0 1.so mlO 21 .AX ,a S.3xtO"

2in . 000 200

15.0 1 so

N 170

16O

101305.0o 150

1200.0 11

100

-* 1. 00go.

.ZV-. 0.0 4. £R 2Xn I KYV 8

Tie Q30 Cycle 22~01 Problem .004

SEGMENTED ROO A* -LD 20 VS- 1.5 KM/SEC -2

38

Densityn .t Y -. IA4W10- on (J - I)

4010 ¶ 102030 M . 241

Conto•u njUJMfrV" •/•2202.004.0 210

0.100 6.006.00 2001.20M0 190

I.IONO 180

2010 Mai a L730~

150150N 140

130

0 0 50. 120S1`10

---- 5.o 100

390

o~o 80

70d 60

- 2ic , -1d.0 -4.0o -ic.o -11.0 o'a . 0 Io ' oo Is. 5ý oId0o

Y an a MWO a

VO -2C v M .5 KMXSEC T/O - 2

39

Densityan PW t•= ,4, lp 6..0 n(J = I)

1 102030 W SAWAA 273

35.0 ConUr vopuaso

Ao/ 2502!.004.00 240

30.0 1,00 4.00I.Ooxoo 230120x10

25.0 t.14xO220

20.0 Ma a 1.74viO190

15.0 13N I 170

10.0 160

1505.0 14 .0

130

0.0 120

11A0

-5.0 100

"-2i.0 -20.0 -i1.o - od.0 -4.o do i.o0 Io. 15s.o' 2d.0 2..oS x 1. 19 NOV 88

Time 280.000 Cycle, Problem AS)00,5SEGMENTED ROD L/D- 20 ., 2.0 KM/SEC C- 2

40

Density

on Soa1Y.w. 1.4x 10' on(J I)

1 102030 W 241,M4A WA.LOYW.

35.0 clw Pro('o / 2202.004.00 210

30.0 o.006.00 200

4 qfll LOWx 101.20xlO 190

25.0 1 40x1O, t.Sox 1 0 lao

200•0.0 00

15.0 150N 10

13010.0 -120

1105.0 - 100

900.0 .8 o~o 80

70-5.0

6C

-10.0~ --- -I '.0' , , ,,' 1.0.. , , - =-. 0 -20.0 -15.0 -10.0 -5.0 0. 6.0 0.0 15.0 20.0 25.0

X am 86NOYrime 2400800 j~&s Cycle 1654 Problem 510001

L/0. 20 VS - 2.0 KM/SEC T/0 - 2

41

Density

40,0 "- Y- m .41:1 4 " "(J I "1 102030 W 273

Nta WALJ.OY

31.0 Catetw 1 ajiso 6

2.004.00 24030.0 -e 6,00

1.0o910 2301.20N10

25.0i 220j50 1.60MIO 21

A ,- 5.2310"NI4 Eh w- 0.0 20020.0 1 1.74X10

190

S 11.O 180

170

10`0 160

130

5.2110

I -•LO

-10.0S,0 -o.-o -id.o -101.0 51.0 doo i.0 lio 1.0o 2.0 -25.0

X am 9 NOV BeTime 1 60.000 A.s Cycle 928 Problem 5.0D0

SEGMENTED ROD L/D -20 VS 3.0 KM/SEC T/D - 2

42

Density

an ft at Y ,w .4xl0 4 amn( - 1J )40.0 ." .

1 102030 W 241RNA WAL.LOYw€contour Ve.luQ.P3

35.0 flV/am ,0,0 ,v222.004.00 210

30.0 5.00,100 200

1.00K 101.20O)1 19g

25.0 1.40x10l.eOXlO 180

20o.0 M = 1.741# 0

15.015N 140

10.0

100.0 10

-0.0 soI

- -2d.0 -13.0 -10.0 4 1 .0S-oo -5.0 0.0 5'.0 10.0 '. 20.0 25'.0

Xcm 8 NOV88Time 140 000/a3 C 10 824. C Problem 5.0002

L/D -. 20,3.0 K20 C TD 82

43

Density

40.0 On PWII 1 _Y. .4xl0" om (J - I)

1 102030 'M 273RHA WMALL0

U.0 ~C~ntOW !QaJUG12

Val 250

0, 6100 240',:o 1 230

1.20M10254 1.4o0Xi0 220SI1010 21

20.0 wing \ a 0.0 200

15.0 180170

100, 16K, • 150

5.0 10130

.0 ' o120110

-5.0 10090

- .0 -2o.o -14- -Id- 4 - dO o'. o , I', d .0 7 '20'.0 25.0rime 1:20.000 /ps 141c~e P + :roblem '5.0007NVl

SI'GMENTD ROD L/O 0 VS-2 4.0 0M/SEC T/D - 2

44

Density

40.0 !.WM Y. (J1 102030 W 241

WA WALW.Y

35.0 Contou Voju6;3

..0/• 2202.004.00 21030.0 6 I.00

i.00 20025.0 1: 410 X 1,0 s1.2oXIO 1g0

*A , 1,20M 125.0 ,14W 120

M3.0 u .

20.0

0 1.0 1

13010o,0 120

115.010

-10.0 -i'--0

00

-5..0 .0-25.0 -20.0 -17.0 -10.0 4S.0 0.0 i.0 I0.0 15.0 20.0 25.0

X cma 8NOV 88"Time 100 000 g0 Qyc/le 631 Problem 5.0003

LD - 20 VV 4.0 KM/SEC, T/D -2

45

I.

Density

.0o' P= .t Ya L4x10" m(J- I)1 10203040 56 ,1

45.0 2goLaO

40.01.Ooxlo 2701.20xI035g.4mox 260

250X ,- 7Sx10"

30.0~I ,,Mn 0.0 240u0 a -1.71x10

23025.0 220

210

20.0 200

19015.0 180

So~o10 -ri

10

0. U-'-O. -20.0 -15.0 -10.0 -5.0 60. 5.o 1.o 0" 20.0 25.0X CM 5 ,W , 09

Time 360.194 pa Cycle 1977 Problem 518.8800SEGMENTED ROD L/D -. 20 VS - 2.0 KM/SEC T/D - 4

46

Density

df#St V SAW10- I CmJu )40.0 .. ,

I1 020-V40 561 1OO3O4 56 RPA WAUOY •40!

0. .0/mlo 2.30

400 2J0,0 6.003.00 210] .004 l 0t.2�20 20

S.•.0 r 1.40410i.eIo 190

Ax . 5.75kgo20.Min a 0.0

20.0 " .- 1.7149>1

IS

tO 140

5o.0 130

-0.090

- -5.o 70

60

"-2d.0 -20.0 -1,.0 -10.0 -4.0 0.0 .C o'1.0 1 0.0 20.0X aINOVYa

Time 360,000 AS Cyck. 2463 Problem 6.0002iD - 20 VS- 2.0 KM/SEC T/O - 4

47

Density

ati Ma ~Y - 0.4-a 1 mn(J- I

5s I It103O4O 56 W*U.LOY RMu~Owttfw m~us.3o

rO/" 290*LOD

4 2. 040.0* 27

3.01.0 M •ie. -' 1.?4,N10

8220NM 270

25.2Il010

1.4xi 2600

Min0 a--.24

19015.00

1803S= • 170

| , ~160 .i0.0

S150

0. , -2..0 I4. 15.0 20'.0 45.0xl•• 4 JAN av

rimeNT 00s Cycle 1S77 Problem 5188833SEGMENTED ROD LI- 20 VS 3.0 KIA/SEC TD

48

Density

0.0 oOn fiM @t Y , ,A,1,0', (M J- ()1 10203040 56

wrALLDY 28445.0 Conhup !ojuu

4.0 270

40.0 4.0 2608.00 250•

/% .1 .00xtl01,20*10 2 0

35,0 1.64010

AI ,x 5.75,9 ,U0, •m 0.0

30. M= 1.73xjjq

,,25.0 200

180

20.0 70

160

15.0 150

10.0 130,. • 120

1.0 11

0.01-2i.o -26.0 -lio -70.0 -5'A 00. 5.o I0.0 15.0 0 O.0 25.0

Xcm 9 WW PTime 200,00 0•.s Cycle 1458 Problem 6.0003

L/D-2 VS w 3.0 KM/SEC T/1r 4

49

Density10.0a ipigMat Y -lxI.4x60 4 an (J I

1 10203040 56 310

WA.LOY WA

45.0 -oltd Vujuui

of 290

4.00 28040.0 - Is6:O 6.00tox2o 2701.20KI0

I3 %• q 14Ol 260

, o we 5 . 7 , 1 0

3~~Mn*0.0 2 an .4* 230

123.0 - 220210

20.0 20190

15.0 18I

170

10.0 10

5.014

0.0 Tm 1 , ,q , , ,.oi.'0- -20.o -. -i0o 0 -o o ' i.0 20.0 25.o

Time 160000Cycle 975 7roblem 518.0844SEGMENTED ROD LD/0 - 20 VS- 4.0 KM/SEC T/D - 4

50

Domn~ityon a t ,,.Y 9.,,,? ,.on (J. I

.0 .1 10203O4 56

V"• 2704000.o * 00 250

40.0 6.00

61l00 2501.40x10

10. IA : 2.7s 0I

20.00

1-20X17020

35.0 1M 10

m0.0 0 .

20 2000

L 200.0KM/SEC T/1 - 4

51

Denuity

anoP! iseY - AA.X10' am (J.)1 10203040 56

2.0o 320.

40.0 .:00 310.& 3 ,00II1.00i1 3O•0',3010

i .20MI0a ',40%10 290

1.Io0'10

SAx -X 5.75*3#,,to~ • I ,.,.Uln a 0,0

L~260250

240

20.0 230220

15.0 o 210', 20D

10.0 1901 180

5.0 170160.

0.0 -d 4 o4s0o¶ oi7,I~- .0 -,&d.0 ,-Ii.0d.o -d.o d .0,o Io',o lio 20.0 21.0

Time 180.000 pa ýCylo 1351 .Problem 7P001SEGMdENTED ROD L/D -20 VS -4.0 KM/SEC T/D .4.

52

S3 1 11 . .. . . . . . .. .

Densityp.Wm at Y€ .- .4A X o"• - a m QJ - I );

£0.0 - P0A WM.Y 400)

I ~~ccitoiw Yeju"45.0 390

'0"Z'OU 3804,.0U

1.0ow 10

35.0 Leon10 350

Ax *5.75X3~Mlin 0.0

30.0 Ma *1.74M3

32J

20.0 31

25

15.0 27

260

10.0 25240

5.0 230

220,

-2.0 -06. 0l0-0. 22.0.0o -6.0 -4 -;. - -16.' 1o"0Xm' 9 NOV so

Time 290.000 & C ycle 1492 Problem 7.0002SEGMENATD ROD L/D -VS 4.0 K0./EC T/D 4

53

Dlensity

aniet Ym -. 410 IVCM (J I)10.0 . ,,, . 0 , 5

. ite1 0 ,04 5" R

2.00 304.00

40.0 ,o 320', "K 1,00 0iMoo•0,10¶.201110

35.0 I.BoxiO 300

AX 5.75x 2 #Min 0.0

2702_.o 260

25020.0 240

230

15.0 220

o0.0 200

5.0 180170

SEG.0 1~ RO46.1¶. ~0 00 2.-25.0 -2.0 -. o.o i.0 1. 5.0 20.0 2m.0X off 0V Nov u-

Time 170.000 *s C Ycle 1287 Problem 8.000SEGMENTED ROD L/0 20 VS 4.0 KM/SEC T 0 -

54

No of No of

c:,wi,..... .eawA.i)12 Administrator CommanUdudmi.., 1-1,,d) 2 Defense TechnWcu1 Info Center US Army Missil CommendIcmA.d) 2 ATTN: DTIC.DDA ATrN: AMSMI-RD-CS-R (DOC)

Cameron Station Redstone Arsenal, AL 35898-5010Alwkdiria, VA 22304-6145

1 CommanderHQDA ,(SARD.TR) US Army Tonk Automotive CommandWASH DC 20310,0001 ATIN: AMSTA.TSL (lToclcal LIbruy)

Warn, AI 48397.50=0CommanderUS Army Material Command 1 DirectorATIN: AMCDRA-ST US Army TRADOC Andysis Commend5001 isenhower MAvan ATT ATAASLAexandria, VA 2233-3X001 Whift Suads Milib RIMa, NM 86002-5502

Commander P=. w 1 CommandantUS Army Laboratory Command US Army Inbfury SchoolATMN: AMSLC.DL ATTN: ATSH.CD (Security •'4M.)Adephi, MD 20783.1145 P SnBonin& GA 3190S-566

2 CommanderMe"o,., MW• 1 ConmmndantArmament RD&, Cenwe US Army Indeomy SchoolUS Army AMCCOM ATMN: ATSH-CDCS0ORAW'N: SMCAR-MSI Fort BeDnn. GA 31905-5660Plcutiy ArsoaMl, 0I 07806-50WI (C-'i. ')1 Tin Rand COIPOIMIC

2 Commander P.O. Box 2138Armamet RD&] Cen. San Monicka CA 90401-2138US Army AMCCOMAMlN: SMCAR-TDC .1 Air Pace Amament iLabm r yPicatinny Arenl, Wi 07806.5000 ATTN: A. ATLDLODL

El& AF, IL 32542-5000I Directo

knot Weapons LaboratoryAnument RIME Cen D, USAMSAA-US Army AMCCOM ATrrN AMXSY-DATTN: SMCAR-LCB-TL AMXSY-MP, H. CohenWatervliet, NY 12189-4050 Cdr, USATECOM

ATFN: AMSTE-TO-FCommanMde Cdr, CRDEC, AMCCOMUS Army Amamment, Munitions ATrN: SMCCR-RI.P.A

and Chemical Comnamnd SMCCR-MU`ATIN: SMCAR-.EP-L SMCCR-MS1Rock Wand, IL 61299-5000 Dir, VLAMO

ATrN: AMSLC-VL-DCommanderUS Army Avl•im Symns CommandATTN: AMSAV-DACL4300 Ooodfedbow Blvd.St. Louis, MO 63120.1798

DirectorUS Army Aviation Rasearh

and Technology ActivityAme Rese• h CenterMoffen Field, CA 94035-1099

55

14o. ofC~ft QesmizalIoi No. of

4 CommanderNaval Surface Warfare Center 1 Systems, Science and SoftwareATIN: Paula Walter ATIN: Dr. R. Sedgwlck

Kenneth Kiddy La Jolla, CA 92038F. J. ZerllaLisa Maud I Orlando Technology Inc.

10901 New Hampahke Avenue ATIN: Mr. N. PiburnSilver Spring, MD 20903-5000 2340 Alamo SE, Suite 101

Albuquerque, NM 871062 APATJ.DLJW

ATTN: Dr. W. CookM. Nixon

ElgUn AFB, FL 32542

4 Lot Alamos National LaborinyATrN: Dr. E. Cort

Dr. L. FitaDr. L. Kp (MS P940)Dr. M. Burkett

P.O. Box 1663Los Alamos, NM 87545

3 Sandia Naional LaboratoryATIN: M. KIpp

W. Herrmann (On1. 150)Albuquerque, NM 87115

2 Orlando Technology Inc.ATMN: Mr. D. Matuska

Mr. 1. OsborneP.O. Box 85560 Secod StreetShalimar, FL 32579

General Research CoporationATMN: Dr. A. ChartersP.O. Box 67705383 Hollister AvenueSanta Barbara, CA 93160-6770

General DynamicsATI'N: J. H. CumdroP.O. Box 2507Pomona, CA 91745

2 Honeywell Inc.ATrN: Dr. 0. Johnson

R. Stryk7225 Northland DriveBrooklyn Park, MN 55428

56

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