report arbrl-t'r-02300 analytical shaped code: 'basc~~ll~~el%' i-ý technical report...
TRANSCRIPT
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TECHNICAL REPORT ARBRL-T'R-02300
IMPROVED ANALYTICAL SHAPED CHARGE CODE: 'BASC
John T. Harrison
A ELECTE
JUN 161981.
MCC B
US ARMY ARMAMENT RESEARCH AND DEVELOPMENT COMMANDBALLISTIC RESEARCH LABORATORY
ABERDEEN PROVING GROUND, MARYLAND
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1. REPORT NUMBE1R ,L'GOV' ACccIION NO. 1. RECIPIENT1S CATALOG NUMBER
TECHNICAL REPORT ARBRL-TR-02300_t )A :'qz-. !i" 7,. TITLE (dad &Ah-U. ". TYPE oF REPORT & PERIOD COVERED
IMPROVED ANALYTICAL SHAPED CHARGE CODE: BASC Final
6. *ERFORMING ORG. REPORT NUMBER
7. AUTHOR(Q) - 1 . CONTRACT OR ORANT NUMBER(*)
John T. Harrison
- PERPFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASKAREA A WORK UNIT NUMBERSUS Army Ballistic Research LaboratoryATTN: DRDAR-BLTAberdeen Proving Ground, MD 21005 1LI61102AH43
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US Army Armnament Research and Development Command MARCH 1981US Army Ballistic Research Laboratory (DRDAR-BL) is. NUMBEROF PAGESAberdeen Proving Ground, MD 21005 100
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III SUPPLEMENTARY NOTES
It. KEY WORDS (Continue an rfrerse sida it neeeessry and identify by block number)
Liner acceleration and collapseShaped Charge Jet Formation TheoryShaped Charge PenetrationExplosive metal interaction
20- ABSRCT r(:C•,m,,ie -reWw ead Nnsee mid oi b,. "- y block n•ai•o ,) (ddg)
The work of many researche:-s has been combined to produce a simplified, analyti-cal, computer code to address the shaped a.harge problem. This code named BASC(BRL Analytical Shaped Charge) is programmed in the FORTRAN language.. BASCutilizes a modified version it the metal acceleration model of M. Defourneauxof France to account for both the final liner velocity and its accelerationhisiory. The BASC code accurately predicts jet-tip velocity and treats thebuildup of the massive lead pellet, for both heavy confined and unconfinedcharge geometries. Calculation of the massive lead pellet has traditionally
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been dficult and is accomplished .n BAse by Including time dep naent acceleraetion and material compressibility ip the region of the liner near the apex ofthe conical liner. The BASC code includes the jet formation theory of Pugh,Eichelberger, and Rostoker; the shaped-charge penetration theory of DePersic,Simon and Merendino for penetration-standoff curves; and the piece wise penetra-tion of Defourneaux for hole profiles. BASC enables parametric investigationsof shaped charge problems with relatively small amounts uf computer time sincethe code is basically analytic. Resvlts from the BASC code are compared toexperiments as well as to more sophicated hydrodynamic computer codes. Thereport documents BASC, including the equations utilized, necessary empiricalrelations, FORTRAN listing of the program, selected problem examples andcomparison with experiments.
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zi TABLE OF CONTENTS
Page
LIST OF ILLUSTRATIONS ....... ................... 5
LIST OF TABLES...................... 7
I. INTRODUCTION ...... ............. ......... ......... 9
II. GOVERNING EQUATIONS ......... ........ ........ 11
III. CALCULATIONAL SCHEME ...... ........... ....... . .... 30
IV. COMPARISON OF BASC CODE RESULTS ......... .......... 34
V. LIMITATIONS OF BASC ........ ................. ... 44
VI. FUTURE MODIFICATIONS TO THE CODE ..... ........... ... 44
VII. SUMMARY ....... ..... ........................ ... 46
REFERENCES ........ ..... ...................... ... 47
APPENDIX A - FLOWCHART OF COMPUTER PROGRAM .... ....... 49
APPENDIX B - FORTRAN IV COMPUTER PROGRAM LISTING,SAMPLE INPUT AND OUT .... ......... ... 59
DISTRIBUTION LIST ........ .................... 97
•,• •' •Accession For
NTI1SGAIDTIC TAB El
UnannouncedjJus;t i Icntion-
•L' Distribiition/
Avnilllbilitly CodesIAvail and/or
II
Dist ]special
i ."ý
LIST OF ILLUSTRATIONS
Figure Page
1. Projection of a Metal Plate by High Explosive ....... ... 12
2. €o and k are Functions of the Detonation Wave Angle .... 14
3. / vs V as Determined from Experiments. Data is taken
from Reference 11 ............... .................. 1s
4. Line Drawing Illustrating the Quantities Employed in theBASC Code for a Generalized Axisymmetric Collapse of aShaped-Charge .......... ............. ............... 19
5. .Illustration of the Relationship between Variables andthe Collapse Process ......... ................. ... 20
6. Illustration of the Resolved Variables in the LaboratoryCoordinate System .......... ................... .... 21
7. Illustration of the Variables Employed in the BASC Code tolimit Jet Formation. The Jet Limiting Criteria for aCohereit Jet (A and B) is M,, = Vf/c < 1.23 ..... ........ 23
8. Schematic Cross-Section of a Shaped-Charge Jet Penetratinga Target in Two States: (a) Continuous and Discontinuous,(b) Discontinuous .......... .................. .... 28
9. Comparison between Experimental and BASC Code results ofJet and Collapse Velocities from the 10S-mm, Unconfined,Shaped Charge ..... ..................... 36
10. Comparison of Calculations of Jet Mass vs Cone Massbetween BASC Code and Experimental Results from the10S-mnm, Unconfined, Shaped-Charge (Reference 13) . . . . 37
11, Comparison between BASC Code and Experimental Resultsfor Scaled, Heavily-Confined, Shaped-Charge (Reference10). Jet and Collapse Velocities vs % of the Distancefrom the Apex of the Cones are Shown. Solid Lines areBASC Code results. The Dashed Line is the Final, Com-puted, Compressed *Jet Velocity Profile. The Jet 'rip forboth Experimental and BASC Results is Shown Compressedinto a Position 48% from the Apex of the Cone.......38
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LIST OF THE ILLUSTRATIONS
Figure Page
12. Comparison of Calculations -f the Flow Field betweenBASC Code and a 2-D, Hydrodynamic Code (BRLSC)(Reference 2). These Calcula'ions are of the lOS-ram,Unconfined, Shaped-Charge Shown at the Time Approximately2511s after the initiation of the Explosive. The BRLSCCode Results are to the Left of the Axis of Symmetry andthe BASC Code Results are to the Right .......... ..... 42
13. Comparison of Calculated and Measured Jet Tip Velocitiesfrom Shaped-Charge Designs 1 tnrough 4, shown on Table
.I. ............................................ 43
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LIST OF TABLES
Table
S' 1. BASC Calculations and Measured, Experimental radio-
graphic Data of Jet Velocity, Mass, and Kinetic Energy
for the 3.2-in. (81.3-mm), BRL, Precision Shaped Charge .39
II. Summary of Results from the Small-Caliber, Shaped Charge
Study for the 3S.l-"m (1½-in.), Base Diameter Design.. . 39
III. Computational Matrix and Summary of Results . . . . . 40
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I. INTRODUCTION
The Ballistic Research Laboratory (BRL) of -the U.S, Army ArmamentResearch and Development Command (ARRADCOM) has a wide interest in theshaped-charge problems, ranging from detailed studies of the flow char-
acteristics of the collapsing liner, to designing practical devices forfuture warhead applications. For these efforts several experimentaland theoretical techniques are employed. Often, it is necessary todetermine parametric relationships in the design application. Sinceit is more feasible to utilize theoretical calcu'Lations that are eco-nomically sound' for parametric studies, the BRL has several finite-difference, hydrodynamic, computer codes that have been applied toshaped-charge problems. 1 , 2 Althou2h these codes are adaptable to vari-ous geometrical considerations, thoy require operrtor experience and aseasoned analyst to insure proper a-pplication. Further, large,high-speed compute:.s, and long calculational times are necessary.Quite often, it is desirable to have a simplified procedure foraddressing parametric design studies quickly and economically. TheBRL computer' code named BASC (BRL Analytical Shaped Charge) 3 was formu-lated from analytic expressions to provide such capability. Althoughseveral advantages occur with the original BASC approach, several areasof difficulty were experienced, particularly those relating to accuratecalculation of jet tip or lead pellet behavior and confined charges.Extensive semi-empirical functions, regaring liner acceleration andconfinement effects, have been included to provide more accurate repre-sentations. This improved, simplified procedure, hereinafter referredto as the BASC code also, together.with additional refinements are pre-sented and discussed in this report.
1J. T. Harrison and R. R. Karpp, "Terminal Ballistic Applications ofq~drodynamic Computer Code Calculations," BRLR 1.q64, April 1977.•(D#A041065)
2J. T. Harrison, "A Comparison Between the Eulerian, HydrodynamicComputer Code (BRLSC) and Experimental Collapse of a Shaped ChargeLiner," ARBRL-MR-02841, June 1978 (AD A059711)
3J. Harrison, R. DiPersio, R. Karpp and R. Jameson, "A SimplifiedVf Shaped Charge Computer Code: BASC," DEA-AF-F/G-7304 Technical
Meeting: Physics of Explosives, Vol I1, April-May 1974, Paper 13presented at the Naval Ordnance Laboratory, Silver Spring, MD.
9
.1• - -
The BASC code is an assembly of various theoretical and empiricaltechniques. Central to the procedure utilized in BASC is theDefourneaux model 4 for final plate velocity resulting from the shockof an adjacent detonating explosive. This assumption is adequate for.portions of the liner which are initially removed (remote) from thecollapse (jet formation) region or cone axis. In actuality, severalshock reverberations are required to achieve a final liner metal velo-city. Material near to the aemx of the cone can enter the collapseprocess long before the liner is accelerated fully and, hence, doesnot achieve its ultimate velocity. This leads to thi well known pheno-mena referred to as "the inverse velocity gradient" which forms themassive Jet tip. This phenomena has been observed 5 and calculatedearlier. ,2,6 The author has modified the Defourneaux model to accountfor the time-dependent acceleration of the liner resulting in a gradualbuild-up to the ultimate collapse velocity. Since liner elements nearthe apex region of a cone will not achieve this ultimate velocity, tilefirst element of the jet will move more slowly than the following dlc-ents of the jet. The faster elements collide and are compressed intothe massive lead pellet. The final jet-tip velocity will become themass-weighted average of these inverse ve.'ocity elements. This is thejet-tip velocity, which will be used in jet penetrationl theory%. BASCuses a combination of the shaped-charge penetration of DiPersio, Simonand Merendino (DSM) 7 and the piece wise penetration of Defourneaux4 .The V)SM! model is used to calculate total penetration-standoff curvesand the piecewise penetration model is used to calculate whole profiles.
In addition to the inverse velocity gradient, flow into the stagna- ftion region during the collapse process from particles near the apex ofa conical liner may be supersonic and fail to form a jet or form a so-called incoherent jet. This is the jet-no-jet criteria. The criteriaused in BASC is a modified version of the supersonic limitations ofChou, et. al.8 The final theoretical technique used in BASC is the
4 M. Defourneaux, "Hydrodynamic Theory of Shaped Charges and of JetPenetration," Memorial DeL'art Ille'rie Francasise-T, 44, 1970.
5 R. DiPersio, C. W. Whiteford, and J. Simon, "An ExperimentaL Methodof Obtaining Collapse Velocities of the Liner Walls of a LinearShaped-Charge Liner," BRL-MR-1696, 5eptember 1965.(AD #478326)
3A. Kiwan and H. Wisniewski, "Theory and Computations of Collapse andJet Velocities of Metallic Shaped Charge Liners," BRLR-1620,N,.vember 1972. (AD #907161)
7 R. DiPersio, J. Simon, and A. Ierendino, "Penetration of Shaped-
Charge Jets Into Metallic Targets," BRLR 1296, September 1965. (AD #476717)8P. Chou, J. Carleone, R. KIarpp, "Criteria for Jet Formation fromImpinging Shells and Plates," J. Appl. Phyaics, Vol. 47, No. 7,Jtuty 1976.
10'"4
Pugh, Eichelberger, and Rostoker (PER) theory of jet formation. 9
This report includes a description of analytical equations, theprocedures for their application and a FORTRAN listing of BASC. Ex-perimental results for selected shaped charge problems are presented ina comparison to the calculations. The range of useful applications isdiscussed as well as the limitations of the approach.
BASC is a "living code" which has provided insights to the jet-formation process and is a very good tool for parametric design for aselected class of problems.
A simplified flow chart and the FORTRAN code listing is presentedin Appendices A and B, respectively.
II. GOVERNING EQUATIONS
The initial equation used in the liner acceleration portion ofthe BASC code determines the angle of liner bending, ý, produced bya detonation wave traveling with a velocity, D, and inclined to theliner wall at an angle, i (the angle of incidence). This relationshipis illustrated in Figure 1. The author has modified the originalplatepush relationship of Defourneaux to be
K P
B =1+A/pc e c
where p and c are the density and thickness of the liner wall, and
e is the explosive thickness. Added are pc' and A which are,
respectively, density, thickness, and a constant, which is determinedFror the exnerinertal data 4or the confinement casing around thecharge1 0 . The constant, A, when set to %ero, represents an unconfinedexplosive charge and the Defourneaux relationship, as illustrated inFigure 1. o and K are functions of the angle of incidence, i, and
0
9 E. M. Pugh, R. J. Eichetberger and N. Rostoker, "Theory of Jet Forma-tion by Charges with Lined Conical Cavities," J. Appl. Physics, Vol.23, No. 5, May 1952.
10R. DiPersio, J. Simon, and T. Martin, "A Study of Jets From ScaledConical Shaped-Charge Liners," BRLMR-1298, August 1960. (AD #246352)
,-U
: i
¶ ---- --' , --uja
@I
i.A
0
on,,
I.-
4,J
o 0
EnM
u
Li0
oo
12
II
are determined for certain types of expiasives'.1 ripiire 2 illus-trates the functional relationship between K , K and i. K is aconstant over the range of i considered for 1ypicxl shaped-charge de-signs, i.e. a conical liner contained in a cylinder of explosive.Figure 3 illustrates the linear relationship, Equation 1, that 1/0has with the ratio of liner mass per unit volume to explosive mass perunit volume, given as
PH.E.e
where pH.E" is the den3ity of the explosive. The values of 1/0
and K used in Equation 1 are the Y-intercept and the ratio of theslope of the line to the density of explosive respectively. Equation 1along with the Taylor formula,
v = 2D sin ,0 2'
where D is the explosive detonation rate, will result in collapsevelocities, vo, obtained by Gurney. 12 Two types of explosive com-
"positions are shown in Figure 3 (data taken from reference 11) whichrepresent the linear function at a constant grazing (parallel) inci-dence, i, of the detonation from the normal to the metal surface (seeFigure 1).
From the theory of Defourneaux, as the detonation wave sweepstoward the base of a typical shaped charge, 0 decreases due to thedecrease in the explosive thickness, e, shown in Figure 3. Thisassumption that 0 decreased monotonically with a des-rease in e isjustified for most of the liner collapse since there is sufficienttime for the liner to undergo several shock reverberations andachieve a bending aigle close to its maximum before entering the f~owof jet fcrmation. However, the region near the apex of the cone
11M. DeFourieaux and L. Jacques, "Explosive Deflection of a Lineras a Diagnostic of Detonation Flows," Proceedings Fifth Symposium(Intcrnational) on Detonation, ACR-184 Office of Naval Research-Depcxtment of Navy, pp. 457-466, Pasadena, California, August 18.21,197U.
* 1 2~* W. Gurney, "The Initial Velocity of Fra'ments from Bombs, Shells,a..,nd Grenades," BRL Report No. 405, Sept. 1943. (AD #AT136218)
13
-]1
- ~. ~ . . - TLZT
40/
//
35 //
/
30 1
SI
/
¶ ~25 I
10
0I 20 40 60 s20 /
I: /, /
41
II
I
10 K
!:.'iqlANGLE OF INCLINATION i (degrees)
S", ~Figure 2. •oadKa• ucin othdenainaeanle
i 1
6
• 5
4
- 65/35 RDX/TNT
- o 65/35 H?.MX/TNT/I2
0).0 0.2 0.4 0.6 0.8 1.0
Figure 3. i/ý vs U as determined from experiments. Datais taken from Reference 11.
77 1 7
enters the flow shortly after its initial acceleration and hence doesnot achieve its ultimate bending angle. Therefore, for material closeto the liner's apex, * will increase to a maximum. This maximum willbe located near liner elements that originate frum a position approxi-mately 40% of the liner height measured from the apex of the cone.After this point, ý will decrerie according to theory. We call this"the inverse collapse process." Associated with this process is thetotal time that a liner element takes to reach the axis. The equationfor the collapse time is
T - (f sin i)/(D(sin(m+4)-sina)), (2)
where several new variables are introduced. r is the instantaneousdistance of a liner elemen from the axis before its collapse. ais the half angle of the cone of a conical liner or, in the general
* case, the instantaneous angle with the axis made by a tangent lineto the liner. T will be affected by the inverse collapse process.Material close to the liner apex enters the flow of jet formationsooner than would be predicted by the collapse of Defourneaux. 4
In order to calculate the inverse collapse process, a new equationfor the bending angle, * and an iterative scheme were added to thecode. The new equation for * is
e/_ (3)T
where b =C1
C1, is a constant determined from shape-charge collapse data. 13 Theiterative scheme, between Equations (2) and (3), continues untilthe criteria of 0N approaching * within an epsilon is satisfied."Having determined • and T, we can proceed with the collapse process.
13F.E. Allison and R. Vitali, "An Application of Jet Formation Theoryto the 105-mm Shaped-Carge," BRLR-1165, March 1962. (AD #277458)
16
______
p• ... - . . ..... .. .. . . ... -- ,-,--. • .- , .. .. •- • • w • - -- ----. ,=w--.--rr W ,r •.r.1 -- • -.... - ., :-.....- -- . ' -• - . r .. ,n
The velocity of collapse of the liner walls, Vo, toward the
charge axis to fnry the jet is given by
vo=2D(sin (*/2))/ fsin i) (4)
The apparent explosive detonation velocity, with respect to linerwall is given by
Da=D/sin i (5)
The substitution of Equation S into Equation 4 yields
v -2Da Sin(0/2) . (6)0
This is the so-called Taylor formula utilized in the code.
The angle between the collapse direction and the charge axis isgiven by
y - (t/2) - (a + (0/2)). (7)
The liner element first hits the axis at a distance, sp, from theliner apex, given by
sp = (z sin 0) / (cos u(sin (a+o) - sina)), (8)
where z is the axial component of the liner element position beforpits collapse.
While the liner is collapsing, the angle formed by a tangentto the collapsed portion on the axis and the axis itself (calledthe collapse angle) is computed from
tan Azisin (a+0) - sinai tan4 + rAO cosa (9)Az sin (a+o) - sina] - rAO cosa tan41
where Az is the axial increment chosen in the computationalscheme, and AO is the incremental change in 0 between adjacentliner elements. The cartesian coordinates of a liner element(which originates at position z,r) during collapse are given bythe pair of equations:
x (z,t) = z + vonAt sin (a + (4/2))
y (z,t) = r - vonAt cos (a + (0/2)),
17
-L•r't .•r•• ;•.:•:•`-i •'•.• • v -- 'r• > .-2 JT22LL:• • C ' ;" fl,".7',? ",'•";...''•"'
where At is the time interval taken by the detonation wave betweensuccessive liner elements and n is a positive integer. Theseequations apply in the time interval givwn by
0 < nAt < ",,
Figure 4 is an illustration of the relationship of thevariables employed in the BASC code of a generalized axisymmetriccollapse of a typical shaped charge. Shown on Figure 5 are drawingsgiving a detailed description of the collapse process. Figure SAshows the velocity vectors of an element at point, P, on the collapsing
-I liner. The element is projected toward the axis of symmetry with acollapse velocity, v 0, and a bending angle, *. When the detonationwave with velocity, D, has progressed a distance, P', (i.e. from pointP to point Q) during the time interval, t, then the element initallyat point P will collide with the cone axis, producing the geometricalrelations at the collision or stagnation point, W shown in Figure 5B.This relationship at the stagnation point is with respect to a coordi-nate system moving at the stagnation point velocity, v The velocity
of the liner wall flowing into the stagnation point is vf and the angle
between it and the cone axis is the collapse angle, 0. Figure SC showsa cross.section of the collapsing liner depicting the variables employed.Applying Bernoulli's equations at the stagnation point, we find thatthe £lo% velocity, vf, separates into two equal but directionally
opposite veiocities. One is called the jet velocity, v., and the other
is called the slug velocity, vN. This relationship is shown on Figure
6. Resolving the flow velocity, vf., at the stagnation point in the
laborator, coordinate system (Figure 6A), the following set of equationsare obtaired:
v *Vf + V pPi j " f+V.•, (11)
vN =vi - vf . (12)
In accordance with the laws of conservation of mass and momentum,when the liner material reaches the cone axis after its collapse, itproceeds either as a fast-moving jet or as the more massive but slower-moving slug (Figure 6A). The jet velocity equation that results is
V V cos(a + (0/2) - (0/2))/sin(a/2) , (13)j 0
and the equation for the slug velocity is
VN U v sin(a + (0/2) - (0/2))/cos(B/2) (14)VN = '0
The relative distribution of mass (Figure 6B) that results in jet and
I
* A ''i
zww
IZ)I
0 qtLU 5~Eb
.,.I
I "~-4 C
U) tbO 090
LLI.
I4 1k4 u
.. .... .. .
I nj
A, ~2
A. Velocity vectors of an elment of the collapsing liner,
' 0
VVV! •£. Vo
B. Geometrical rolations at the ptagnation point*
.,4 It 90 +
C N.,, - ,Cono Axia!.
C. Croua-section of collapsing linoer,
Figure S. Illustration of the relationshipbetween var 4 ables and the collanse nrocess.
20
.... .. . . . .i
-�
*1
sic
SI. I II4-i4
A0 In
I-
>'I- I� s-, I
z0 �
- I.- 4-
�I.4�-,0
0 .40
-JC,,
.1
21
-� � � Th��r�2L � .:;4LT�.. �, L*Z�P71�., � �2�P' �
slug material are calculated, respectively, by
dm$ 2-sin (f,/!J
and (is),,N . cos 2 (0/2).
Also, the relative distribution of the kinetic energy for the jet
and slug, respectively, are
dE. Cos + 2 ( /2+ -) (0/2))
Land (16)
dENEN Sin 2(a + (0/2) - (8/2))
LThe variables dm L and dL are the incremental change in the liner's
mass and kinetic energy, respectively.
The impinging flow velocity, v,, hs.• been considered by shaped-
charge researchers such as Waloh, . -11.14; Cowan, et. al. 15; andChou, et. al. 8 to be critical in the jet-formation theory. As illus-trated in Figure 7, when vf is less than the material sound speed, C, Jthe jet formed is coherent or a good jet (Figure 7A). Even when vfis slightly greater than c, this too forms a coherent jet (Figurj 7B).But, when v is sufficiently greater than c, the jet will be incoherent
or bifurcated. Wc call it a no-jet condition (Figure 7C). Fromequations 11 and 12, solving for vf yields
vf = .S(v. - vN) . (17)
We then use the following relationship as the jet limiting criteria"for a coherent jet:
MR v/d < 1. 23 (8
J.M. Walsh, R.G. ShrefflerA% and F.J. Willig, "Li~mi~ting,,Velocity Con-ditions for Jet Forriation i.n High Velocity Collisitons," Journalt ofApplied Physics, Vol. 24, No. 3, pp. 349-359, March 1957.
15G.R. Cowan and A.H. Holtzman, "Plow Configurnations in Colliding
Plates: Explosive Bonding," Journal of Applied Physics, Vol. 34,No. 4, pp. 928-939, April 1963.
S, ~22 :
A
B|
vN • - -.-_ .-,a_-
KHOOK
Vf > C
Figure 7. Illustration of the variables employed in the BASC code
to limit jet formation. The jet limiting criteria for
acoherent jet (A and B) is MR = vf/c < 1.23.
i• .
23
*;A-,
tAPý
SHC
Vf.>
Fiur 7.Ilsrto ftevrale mlydi h ACcd
so.
The threshold factor for a coherent jet, ?4-1.23, is determined bycomparing re•tographic, jet-particle data easured 16 from experi-ments 1 7 with BASC results. The threshold factor holds for severalnMaterials considered in BASC calculations.
In order to determine the jet-tip velocity and the mass of thelead pellet to be used in the shaped-charge penetration theory, theinverse velocity gradient has to be equilibrated and the jet mass inthis region to be compresser3 into a single zonal element, LP. Thiszone will then contain the so-called steady-state, lead pellet. Theequilibrated Jet-tip velocity, vJo is obtained by the followingprocess:
-. i~ii+l [dmi+1 i+l i ldm , .dvd di
'il dm1 L
dLi+l Ldm. Id m+ d -qL
for vi > vj and 1 < i < LP, where i is the i zonal element. The
equilibrated jet-tip velocity isv .LP (8
jo j
The steady-state, lead pellet mass isLPrdm~lidm
dmjo d (19)
t-1
In the theory of shaped-charge jet penetzation into a targetused in BASC, an important parameter is the time that a given linerelement, which enters into the jet, arrives at the bottom of thetarget hole when penetrat-ion is in progress. Time is usually startedfrom the moment the detonation wave reaches the apex of the liner.A time parameter, 8, is defined by
A = t +T (20)
16Private Conmnunication from J. Blische at BRL.17R. DiPersio, W.H. Jones, A.B. Merendino, and J. Simon, "Character-
istic8 of Jfets from S9naZZ Caliber Shaped Charges with Copperand Aluminum Liners," BRLMR No. 1866, September 2967. (AD #823839)
24
' Iili "
>. .1•., . ., • ,. . . . , . . .- 5 -'' - - ' - " - - r ' - - • _
where t is the time at which the detonation wave reaches the linerelement at an initial axial distance, z, from the apex and T is thetime taken by this element to collapse onto the charge axis. Thesum of standoff distance from the liner base to the initial surfaceof the target, h, and the liner height, H, defines Z:
Z = h+H. (21)
The time for the tip of the jet to reach the target surface is
T 0 /V (22)o 0 jo
It is assumed that the jet tip originates from the zonal element, LP,and contains the highest velocity of the jet, Vjo. An element fromthe line.- between LP and base results in a jet velocity, v., which isless than v. and is a function of its initial axial distýaice, z. A0Iparameter, " is defined by
P = Vjo/V (23)
The time for the portion of jet formed from a given element of theliner to reach the bottom of the target hole is
T l.+k) [T + (Afi] (24)
where (Af) i -f i-1 and denntei the ith zonal element. In
this equation, k = _Y.'V'7 where p. is the jet density (assumedequal to the liner density), and pc is the target density. f is atime parameter given by
f-= (04l) -(!V~jo)) (25)
* where ip was previously defined by Equation 8, and v. , e, and iwere defined by Equations 18, 20, and 23. The valuej8f v to beused outside the bracket in Equation 24 is that which applies tothe original elemental liner position. Af is the difference in fvalues between adjacent elemental positions, and the summationapplies to all adjacent elemental positions up to the point in
*. question on the liner.
While the jet is still continuous in nature, it stretches due
to its velocity gradient and, therefore, decreases in diameter withincrease in time. The equation for calculating the jet radius, r.,is
¶ 25
1-
e D sin'_ (/2) (26)2 A"
J TTZ -ITsini1
In this equation, r is the initial radial position of the linerelement from the charge axis, r is the liner thickness at thisposition, and B is the collapse angle that is formed when this
element reaches the charge axis. The factor,.Z• , is given byzT
•tZ-~z w(T-t ) Av . v- , + ~z-r cot(Si2))A (27)
In this equation, t is defined following Equation 20 and At isthe incremental timg interval between arrival of the detonationwave between successive liner elements (a constant). The valuecomaputed by Equation 27 is a function of time, T, which starts
at zero when the detonation wave first reaches the liner apex. Itis a negative value which increases in absolute value as T increases. ITherefore, it can be seen from Equation 26 that the jet radius, whichoriginates from material at any point on the liner, decreases with anin9rease in T. The minus sign in Equation 26 is necessary to maker a positive quantity.
When the jet cannot sustain any further stretching, it breaksup into individual axial particles. It is assumed that this occursthroughout the whole jet at the same time. The breakup time forthe jet is designated as T1 and, at present, must be obtained fromexperimental observations. At times greater than the jet breakuptime, the individual jet particles do not stretch in length ordecrease in diameter. The constant jet particle radius that oneobtains for material originating from a given element of the liner
is calculated by Equation 26 in which the factor is calculated
at the breakup time, T in Equation 27. However, radii of differentparticles are differeni due to the variability of the initial linerelement position in Equations 26 and 27.
The equations that are used for jet penetration theory aredependent upon the standoff distance between the charge and thetarget. If the target is placed close enough to the charge sothat the jet tip reaches the target before the time of jet breakup,one set of equations are used. On the other hand, if the jetparticulates before reaching the target surface, a different setof equations must be used. In the former case, even though the jet
26
U,
starts penetrating in the continuous state, it becomes discontinuousbefore the end of penetration and different equations are requiredafter time T1 . The variables and the two states of penetration areillustrated in Figure 8.
The jet penetrates the target in both the continuous and discon-tinuous state whenever the following criteria is satisfied:
Z < V T (28)*1 o jo I
The depth of penetration into the target, p, for any T, such thatT < T < T
p-= Z [( T (k/(k+l)) (29)0
where all factors have been previously defined. For times greaterthan T, the equation used is
(k+l) (k/(k+l)) (3)P = Z 0 I1 T
The total penetration depth into the target ils calculated by
(k+l)(V l k+i k+l k lm k+l-o. 1T 1 0Z T1(v.T0 (1) Z -
minlThe only hitherto undefined term in Equation 31 is thet. factor UThis is called the minimum penetration velocity. According totheory, the velocity of penetration into the target monctonicallydecreases with inrrease in penetration depth until it reaches the
value Umin. When Umin is reached, penetration stops and all'.remaining jet material just piles up at the bottom of the target
hole. Umin is an empirical constant whose value depends upon the",.target material and its hardness. It is invariant with standoffdistance. With a given charge, target, and standoff distance, thecomputer calculates the constant total penetration depth fromEquation 31. This value is used by the computer as a signal tosto' calculating p in Equation 30 and also to determine the timeat the end of the penetration process. The radius of the hole inthe target before the time of jet bri:iknp is given by
27
I 1
APEX OF CONE
- z- 0 t0j
tV (t) tiV 00
(a) )
Figure 8. Schematic cross section of a shaped-charged jet
penetrating a target in two states:
(a) Continuous and discontinuous,
(b) Discontinuous.
28
.!I
z 3+kr J T1 vo 2-- - v r .c= T(2 /+&2) kv.32)
4k F7 Z0 p JO3(2
This equatiofi contains one ]tst empirical constant of the target,ck' This is the jet kinetic energy needed to produce a unit of hole
volume in the target. Its value depends upon the target used andits hardness. The value of r. in Equation 32 is obtained by Equations26 and 27. After the breakupJtime, TI. the hole radius is obtained by
z Zo+p(c 1 ] [(k+1) .--- V rj""VjT1 kj o 30 T J' (33)
where r. is now obtained by Equations 26 and 27 with the restrictionJ AZthat the factor T-• T must be evaluated at T = T1 The hole profile,
zas computed by Equation 33, is terminated when the penetration depth,p, reaches the value PT as calculated by Equation 31.
The last set of penetration equations is used when the standoffdistance between charge and target is so large that the followingcondition is satisfied:
Zo > jo TI (34)In this case, all penetration is accomplished by the jet while itis particulated in nature. The equation for penetration depth isthen
P Jo o 1 / (T1 + (T/k)) (35)where the time factor, T,"varies between the time of first targetimpact, T0 , and the time of last jet penetration, T p. The total
penetration depth is given by
t)T [vjo T1 fUain it (Vjo T1 + (Zo/k)]k (36)
29- •
The radius of the hole produced in the target as a function of itsdepth is given by
whereth e Z V r (l-(p/k v TI)) /2 ' (37)
_.....where the jet radius, rj, is obtained by Equations 26 and 27 with
* the restriction that the factor AZ is evaluated at T = T1 .zAtz
The variation of total penetration depth with standoff distance
is computed by meaxrs of Equations 31 and 36. The factor Z is the
only variable in these equations. Equation 31 is used first until
Z 0 increases to the value vjo TV then Equation 36 is used.
III. CALCULATIONAL SCHEME
The BASC code enables one to perform parametric studies fordesigning warheads. The variables employed in the code of the
generalized, axisymmetric collapse of a shaped charge were illustrated
previously in Figure 4. The parameters which can vary include the"i' following:
a (ALPHA) The half angle of the liner (degrees)
K (CON) The empirical constant for the detonation
products. Value known for Composition Bexplosive.
(EPS) The thickness of the liner (cm)
P (RHOJ) The density of the liner (gm/cm3 )
P C (RHOC) The density of the targe (gm/cm 3 )
r (RF) Radius of the base of iarge (cm).
H (H) Height of the liner , f H is zero,S~rF
H will be calculated by H = rFnItana
S30.J
',.
D (D) Detonation velocity (cm/ps)
SO (SO) Standoff distance between base of linerand target, (cm)
CK (CK) Constant for determining hole volume
T (Tl) Jet breakup time (us)
UMIN (UMIN) Velocity cutoff for the penetration of jetinto a target (cm/ps)
L (DPOINT) Initially the total length of the charge(cm).but is converted to be the initiation
point of the explosive (i.e. DPOINT = L-H).
RDPT (RDPT) Radius above axis where explosive is- initiated (cm).
JOHN (JOHNI) If JOHNI greater than zero, _ will vary;if not, €o will be a calculated constant,
N (N) The number of zones Lito which the grid
is subdivided. If N is zero, default isseventy zones.
The code will set up the grid based upon Figuii 4 and theequation for increment in Z is
DZ H/N (38)
and from this the time increment is
DTZ = DZ/D . (39)
Therefore, at each increment in Z we have also the correspondingtime increment.
The code then marches sequentually through the governing equa-tions (1-19), calculating and storing jet formation information tobe printed and plotted at the end of the iteration. Those vari-ables include:
.th IiI zone
.a AIPHA(I) Tangent angle of liner wall to the axis(degi'ees)
z Z(I) z distance from apex to base of liner
' ~31.4 13
. I
!
-. - - - - - - - - '.4,
thtz TZ(I) Time at the i zone
y GANNA(I) Angle (degrees)
thE(I) Thickness of expinsive above if zone
* PHI(I) Angle (degrees)
BETA(I) Angle (degrees)
DPHI(I) Increment of angle
RPHI(I) Reciprocal of angle ,
V V(I) Collapse velocity (cm/ps)0
r R(I) Radius of the ith zone (cm)
STAU(I) Time to collapse ith zone (ps)
S CMI) Distance from the apex of the liner where
"ith zone will hit the axis (cm)
v. VJ(I) Velocity of the jet in (cm!us)
vN VN(I) Velocity of the slug in (cm/ps)
dm. DMJ(I) Relative m'qss of the jet, dimensionless
dmNgSDMN(I) Relative mass of the slug, dimensionless
dE. iI__ DEJ(1) Relative energy of the jet, dimensionless' ~dEL
SdEN DEN(I) Relative energy of the slug, dimensionless
dEL
vf RV(1) Relative velocity between the jet and slug
32
.4
L 5M
In the penetration portion of BASC, the constants listed belowmust be calculated:
VJO = jet tip velocity from Equation 18 (40)
ZO = H + SO (41)
TO = zo (42)T JO .o
AKAY (43)
PT = Total penetration (cm) from Equation31 or 36 (44)
The next set of outputs are for the penetration of the jetinto thc target. The code also marches through the governingEquations 20-37, calculating and storing penetration informationto be printed and plotted at the end of the iteration. The vari-ables calculated and stored are listed below:
.th1 zone
AMU(I) Relative velocity between the jet Ivelocity and jet velocity of the i zone
0 THETA(I) Time parameter in microseconds
f F(I) Time parameter in microseconds
Af DF(I) Time increment of f in microseconds.
T T(I) Time that the i th element reaches the bottomof the target hole in microseconds.
At DT(I) Time increment of T
"RSQ(I) is r 2 which is the radius of the ith
element of the jet.
A A(I) is equal to z - r cot 0/2.
AA DE' 4A(I) is the increment of A(I).
JJ'•AV. DVJ(I) is the increment of jet velocity.
;3I
, " 33
II
AzL DZODT(I) Equation 27 in governing equations
z
r RC(I) Radius of the hole in target of the ith zonec in centimeters
p'pCI) Depth of penetration in centimeters
After these parameters have been printed and plotted, the code thenreturns to start and begins- another case. This is continued untilthe end of file (i.e. next problem) is encountered causing therun to termin.;ts..
IV. COMPARISON OF BASC CODE RElSULTS
The performance of the BASC code is best illustrated by pre-senting results of a calculation and comparing these results, wherepossible, with experimental data or with results from ':her numeri-cal techniques. The first set, of comparisons will be with experi-mental results from the following:
a. 105-mm, unconfined, Jo, copper-lined shaped charge
with a Composition B explosive fill tested by Allison
and Vitali'3 .b, A study of jets from scaled, 420, copper-lined, conical
shaped charges filled with Composition B explosive (testby DiPersio, et. al. 1 0).
c. 3,-inch, BRL precision, shaped charge with a copper liner42 apex angle, and Composition B explosive fill, having itsJet characteristics measured1 6 from radiographic datarecorded at the BRL.
d. A study of jet characteristics from small-caliber shapedcharges with coppe& and a~umii)um liners and variation inapex angle from 20 to 90 . All charges were filled withComposition B explosive. The tests conducted at the BRLby DliPersio, et. al!7
The second set of comparisons will be another numerical technique.The other technique is the two-dimensional, hydrodynamic computerprogram based upon the Eulerian numerical scheme ,-alled the BRLSC(Ballistlc Research Laboratory Shaped Charge) code. 18 The BRLSC
1"M.L. Gittingq, "BRLSC: k Advanced EWerian Code for PredistingShaped Charges," VoZt. I, BRL CR 279, Prepared by System, Scienceand Software, December 1978. (AD #A023962)
34
I
S.... • • .. .. . U
code is a modified version of- the HELP (Hydrodynamic Elastic-Plastic)code 19 developed by System, Science and Software.
Figure 9 and 10 are experimental comparisons for the 105-mm,unconfined, shaped charge. Collapse velocity, v0 , and jet velocity,V. as a function of the relative distance from the apex of the coueaIe shown on Figure 9. The dashed line is the jet velocity after jetcompression and illustrates exact agreement with both the jet tip velo-city and position on the axis between BASC and experiment. This illus-trates that jet tip is compressed into one element at a position whichis approximately 40% of the distancb from the apex of the cone. Thecollapse velocity is slightly higher than that calculated by Allisonand Vitali, but the overall agreement is good. Figure 10 shows acJmparison of the predictions of jet mass versus cone mass betweenthe BASC code and Allison Lnd Vitali. Those two predictions are inslight disagreement with one another because Allison and Vitali wereunable to recover 100% of all the slug material. They used essentiallythe same theory as the BASC code to predict jet mass, and all of thematerial is required to accurately predict the true conservation laws.
Figure 11 is the second experimental comparison of the scaled,shaped charge with a heavy continement casing. This figure shows
collapse velocity, v , end jet velocity, v., as a function of therelative distance fr 8 m the apex of the ccn;. The dashed line is thecompressed jet velocity distribution. This again illustrates exact
& agreement for both jet tip velocity and its positior on the axisbetween BASC and exrdriment. The open squares at approximately the48% position fr•- the apex of the cone shows the spread in the experi-mental data from the experimental scaled rounds. The BASC code resultsare identical for the same scaled rounds (see Reference 10). Shownat the base of the cone, for values greater than 80% of the distancefrom the apex of the cone, is a change .n the slope of the jet velo-city curve. This is due to gas leakage or breaking of the confinementcasing. This phenomenon is modeled in BASC as a gradual change in theconfinement factor, A in Equation 1, until it reaches zero, i.e.unconfined. This comparison shows very good agreement with the experi-mental results.
Table I is a tabulation of a comparison between measured,radiographic experimental data and BASC code results from tht 3.2-inch, BRL, precision shaped charge. The jet tip velocity and massat jet particle number one are in agreement, but the accumulatedtotal jet mass from jet particle number one to jet particle number
I.J*.i.Hageman and J.M. Walsh, "HELP, A iulti-Material FulerianProgram For Compressible Fluid and Elastic.-Plastic Flows in TwoSpace Dimensions atc0 Time," BRL CR 39, Prepared by System, Scienceand Software, ?,zy 1971. (AD Nos. 726459 and 726460)
35
7, j
........................................... 1-
11 .0
-0.0IL-HI 39. 9000 MM
RD .0000 MM
L 9.0 E.XFERITM.NT-IL 114T P. F.
L 7.0 -- -- .""- ""'-..
6.0
.- 5.0
> 4.0I
3.0.
2-U
.02.0 7/" .1 ,, "'".•
.0 .1 .2. .3 .4 .5 .6 ,./ .e .9 1 ,11
RELRTIVE DISTRNCE FROM CONE RPFXALPHR 21.00 OEG
RF = 43.1850 MM
EPS 2.70120 MM
Figure 9. Comparison between experimental and BASC Code resultsof jet and collapse velocities from the 105-mm, uncon-fined, shaped cha-'ge.
36
1 1i
0 vi
hI 0 u)
Up .0 4 0
Iaa44
-0 WL). -
hI U
svA 0L~
37)c
IC U
.2: rL-H) 20-.537 MMS10.0 •"RD = 0,0000 MM
U . " E..•X r RIHENTI L DRTA N ,
(.3 9.0
• '" V i ,J
•-6.01
> .0
2.0
I,[
1.0
0.00.0 13.1 0.2 U1.3 0.4 0.5 0.6 0,'7 0.8, 0.9 ý.c
RELRTIVE DISTRNCE FROM CONE RPEXALPHA 21.00 OEGRF e4.0030 MMc [P 105=,59 MM
Figure 11. Comparison between BASC code and experimental resultsfor scaled, heavily-confined., shaped charges (Reference10). Jet and collapse velocities vs % of the distancefrom the apex of the cones are shown. Solid lines areBASC code results. The dashed line is the final, computed,compressed jet velocity profile. The jet tip for bothexperimental and BASC results is shown compressed intoa position 48% irom the apex of the cone.
.38
I.A
forty-three is 10 grams heavier in the BASC code results. Also, thecode results show 46% more total accumulated kinetic energy from thefirst forty-three jet particles than that obtained from experiment.Overall, this comparison is reasonable considering the material locsfrom such physical effects as erosion and possible errors in the datareduction measuremonts and calculations of the experimental results.
Table I. BASC Calcula ons and Measured, Experimental Radio-graphic Data of Jet Velocity, Mass, and KineticEnergy for the 3.2-in. (81.3-mm), BRL, Precision,Shaped Charge
Jet Velocity (km/s) Accumulated Mass (g) Kinetic Energy (kJ)
Particle No. Measured BASC Measured BASC Measured BASC
1 7.74 7.74 3.7 4.3 110. 128.
43 2.90 2.98 22.6 32.6 348. S07.
The last experimental comparison will be the characteristics ofjets from small caliber shaped charges with copper and aluminum liners.In this study, only the liner designs referred to as li-inch (38.1-mm)liner base diameter chargeg in Reference 17 will be considered. Theapex angle will include 20-, 400, 60 and 900 cones for both the cop-per and aluminum liners. These are all confined with a steel casinigaround the charge. The pertinent dimensions for the shaped-chargudesigns considered can be found in Reference 17 on pages 9 and 10. Theresults from the BASC code calculations and the experiments are sum-marized on Table II. All of the results of the BASC code are withina 5% error boundary except the liner type with a 900apex angle andaluminum cone which is 10%. The results of the calculations are slightlyhigher than the experiments for all of the aluminum liner types.
Table I. Summary of Results From the Small-Caliber, Shaped-Charge Study for the 38.1-mm (1½-in.), Base DiameterDesign
Jet Tip.4 Velocity, V. (km/s)
joLiner Type Experiment Predicted (BASC)
20° apex angle, Cu Cone 9.9 9.80
40 apex angle, Cu Cone 8.2 8.00
"60 apex angle, Cu Cone 6.7 6.64
900 apex angle, Cu Conie 5.5 5.48
39
- ~ -,
Liner Type Experiment Predicted (BASC)
200 apex angle, Al Cone 11.2 11.80
40 0 apex angle, Al Cone 9.3 9.75600 apex angle, Al Cone 8.1 8.54900 apex angle, Al Cone 6.8 7.50
The final two sets of comparisons involve the two numerical tech-niques: BASC and BRLSC. First, Figure 12, is a comparison of thecalculated flow field for the 105-mm, unconfined shaped charge reported2
for the BRLSC code and the BASC code at 25 Usec after initiation of theexplosive. The radius of the jet and slug are in excellant agreement,but the tip of the jet is slightly behind in the BASC calculation.This is due to the fact that the BASC code takes very lqrge time stepswhich will not allow the inverse velocity gradient to be equilibratedat this snap shot in time. The second set of comparisons between BASCand BRLSC codes is shown on Table III. The results shown are from animproved version of the BRLSC Code. 2 0 Table III is a tabulation ofsix calculated results from BASC and BRLSC as well as four experimentalresults, which can be used as a guide in this comparison. All of thecalculations and experiments in this study involved identical copperliners (210, 81.3-mm base diameter, 1.9-mm thickness). Calculations1 through 4 employed TNT, Comp B, Octol and P'BX, rrspectively as ex-plosive filler.
Table III. Computational Matrix and Summary of Results
CalculationNumber HE Confinement Total Jet Mass (g) Jet Kinetic Energy (kJ)
Fill BRLSC BASC BRLSC BASCI TNT Light 19.66 28.42 196. 385. J2 CoPup B Light 22.56 30.73 287. 507.3 Octol Light 27.40 32.03 349. 570.4 PBX Light 27.97 33.49 381. 614.5 Comp B Heavy 33.63 60.41 475. 1262.6 Octol Heavy 35.17 60.16 360. 1406.
2 0 R.T. Sedgwick, L.J. Walsh and M.S. ChawZa, "Effects of High ExplosiveParamebers and Degree of Confinement on Jets from Lined ShapedCharges," BRL CR 245, Prepared by System, Science and Software,July 1975. (AD #BO06987L)
40
&.hi
LC
Calculation Predicted Final MeasuredNumber Jet Tip Velocity (km/s) Jet Tip Velocity (km/s)
BRLSC BASC
1 5.95 6.79 6.8S2 7.1S 7.74 '7.7
3 7.40 8.17 8.1
4 7.80 8.44 8.3
5 7.44 8.86
6 7.78 9.36
In these four calculations, the charge was confined in analuminum casing (treated as being unconfined in the BASC code).Calculations 5 and 6 employed Cormp B and Octol as explosive fillswhich were confined in a steel casinj with a thickness of 10mm.The calculational matrix is shown in Table III with the degree ofconfinement provided by the aluminum and steel casing is referredto as light and heavy, respectively. The summary of the resultsof both codes (BASC and BRLSC) as well as the results of the jet'Lip velocities measured fxom experiments 21 are also shown in TibleIIT. The quantities summarized represent the total jet which iscomposed of jet material having a velocity greater than or equal toa velocity of 2.8 km/s. The results indicate the ratio of predictedtotal jet mass of BRLSC code to the BASC code is approximately 65-0for all calculations.
, The comparison of )et tip velocity data is illustrated onFigure 13. The theoretically predicted values for calculations 1
through 4 from both the BASC and BRLSC codes are compared with theexperimental determined jet tip velocity data. Figure 13 is aploL of calculated jet velocites versus the measured jet tip velo-cities. The open triangles are the final jet tip velocities aspredicted by the BRLSC code 2 0 and the open squares are those predictedby the BASC code. There is very good agreement between the BASC codeand the observed results for those rounds considered and the BRLSCcode's agreement is less than 10% except for TNT which is 12.5%,
In summary, we have demonstrated in these comparisons the predic-tive ability of the BASC code. In addition, several of its salientfeatures has been shown. These features include the predictive char-acteristics of BASC with respect to variations in casing confinement,variations in cone apex angle, variations in liner density and thick-ness, variations in explosive fill, and the effects of scaling. Wehave, also, demonstrated its predictive ability with respect to othersophisticated numerical schemes.
. 1J. Simon, "The Effect of ExpZosive Detonation Characteristics onShaped-Charyge Performinance," BRLMR-2414, August 1979. (AD #BOOO337L)
Vi 41
?1 ýA
"• d~, : ,M ~ tf~I ~ ~ ~ *~TrY .:~r 2'i,.~ ... ~ .L~.k
I" ]
II
Figure 12. Comparison o0 calculations of the flow field betweenBASC code and a 2-D, Hydrodynamnic Code (BRL~C1(Reference 2). These calculations are of the 105-mm,
p.' unconfined, shaped-charge shown at the time approxi-mately 2Sjis after the initiation of the explosive.The BRLSC Code results are to the left of the axisof symmuetry and the BASC code results are to theTight.
42
IIII
co
0- 04w j CD Irzs -j ) V
0 t
0..' _j#;: w >
w4J~wc
t440 i)
in i... CDI
S.
43
*4.4
L.. ol M-i
'7" =
Based upon these comp-risons, it is concluded that, for many -oni-
cal shaped-charge designs, the BASC code isa useful, predictive;model for jet characteristics. Since.it requires only fractions of aminute tc do several shaped-charge design calculations on most computingsystems (large or small), this calculational scheme is an economicalapproach for warhead design and analysis.
V. LIMITATIONS OF BASC
The current version of BASC requires several empirically deter-mined constants. The collapse model requires the determination of 0oand k; their relationship to the angle of incidence, i; the constantA for a confined casing; and finally, Cl, a constant calibrated to the105-mm, unconfined, shaped charge for the time of collapse near theapex of the cone. Penetration requires a cutoff velocity, Umin, and abreakup time, T1 .
Breakup time, as used in the theory of DiPersio, et. al. , is auquantity determined from a radiograph of the jet. It is treated as
a constant, but only approximates that value for conical liners withuniform wall thicknesses. Work by Simon 21 shows that breakup time fora given geometry remains a constant over changes in the Chapman-Jouguetpressure of 186-380 kbars. The codes, as used, requires a predeter-mined value for T1 for a given shaped-charge geometry. The value ofT, scales with cone diameter. All of these limitations stem from theempirical nature of the equations of the code.
Geometrical considerations for conical collapse may or may not be 4a limitation to the BASC code. Research will have to be conducted inorder to determine this fact. Since the initial cone half-angle variesas a function of distance along the axis, z, and since each zonal ele-ment has no interaction with other elements, all geometrical considera-tions should be solvable.
Current limitations will be corrected by future changes to thecode. These changes are explained in the next section.
VI. FUTURE MODIFICATIONS
There are several tasks intended to improve BASC. The major areas
K' of research are the following: (1) modeling the jet formation for
44
tb44
.!• 44
13
several different materials and geometrical consideration, (2) mod-Iing"the viscous effects, as suggested by Walters, 2 2 in a nature compat.1,lewith BASC, (3) modeling the~breakup of the jet with reference to •.maximum strain to break, (4) modeling the threshold for a jet-no-jetcriteria for many more materials.
"As explained earlier, elements in the apex region of a conical¶ liner reach the jet formation region before these elements are accel-
erated to their maximum attainable velocity. To account for thischaracteristic of conical, liner apex flow, which is so important indetermining exact jet-tip velocities, transient acceleration is beingmodeled by an empirical constant determined from normalized, copperliner data 1 3. This constant accounts for the number of shock rever-
-berations th•.t occur in the copper liner before it enters the flowof jet formation. Wc can improve upon this constant by obtainingexperimental collapse data for a number of different materials.
Research conducted by Simon indicates that the breakup of theshaped-charge jet may be related to a maximum strain, which is afunction of strain rate. these observations were made for copperliners with many different explosive fillers ranging from TNT (C-Jpressure 186 kbars) to a high IIMX explosive (C-J pressure 380 kbars),Nit with only one charge and liner geometry. Work is continuing byChou, el. al., 2 3,24 to define the critical condition for 1,.eakup modelsbased on these results and will be added to the code where piecewiscstrains and strain rates will be calculated. We will continue tocalculate penetration velocity, U, and will terminate penetrationaccording to a minimum value of U as demonstrated by DiPersio, el. al.;but we will explore the use of vj • as the penetration cut-off criteria.Finite-difference codes may be applied either directly or in a simpli-fied form to generate a library of parameters by computational experi-ments. This will assist in the research of some of these criticalparameters utilized in the BASC code.
As certain elements of the shaped-charge collapse problem areaccurately modelled, that section of the BASC code will be modified.The code is considered a "living" code, constantly being updated butapplied wit",in its limitations at all stages of its development.
"2•W. Walters, "Influence of Material Viscosity on the Thexooy ofShaped-Charge Penetration, " ARBRL-MR- 02.941, August 19 79. (AD #B04148.'L)
2 3p. C. Chou and J. Carleone, "Calculations of Shaped-Charge Jet
Strain, Radius and Breakup Time," BRLCR-246, July 1976. (AD #BO07240L)
24j. Carleone, P.C. Chou, and R. Ciccarelli, "Shaped-Charge JetStability and Penetration Calculations," BRLCR-351, September1977. (AD #A050117)
I4
.A
S-7
VII. SUMMARY
BASC is a simple, well-documented, shaped-charge code that maybe applied to many problems to predict trends and gross effects.Difficulties in predicting the jet-tip characteristics still existfor some materials, but future modifications should correct thisdeficiency. The code is so structured that it can Irow and becomemore widely applicable as modeling improvements are available.
ACKNOWLEDGEMENT
The author is grateful to Robert DiPersio, now retired, andRobert R. Karpp, now of Los Alamos Scientific Laboratory, for theirmany contributions in the formulation of the BASC code.
The author is grateful to Mary Scarborough of the BRL for herartistic work in the preparation of the illustrations used in thisreport.
46
I
II
... ...... . .... 4 h,........ ........ ... .. . - .
. .. .. .. .
REFERENCES
1. J.T. Harrison and R.R. Karpp, "Terminal Ballistic Applications ofHydrodynamic Computer Code Calculations," BRLR 1984, April 1977.
2. (AD #A041065)2. J.T. Harrison, "A Comparison between the Eulerian, HydrodynamicI Compucer" Code (BRLSC) and Experimental Collapse of a Shaped Charge
Liner," ARBRL-MR-02841, June 1978. (AD A059711)
3. J. Harrison, R. DiPersio, R. Karpp and R. Jameson, "A SimplifiedShaped Charge Computer Code: BASC," DEA-AF-F/G-7304 TechnicalMeeting: Physics of Explosives, Vol II, April-May 1974, Paper 13presented at the Naval Ordnance Laboratory; Silver Spring, MD.
4. M. Defourneaux, "Hydrodynamic Theory of Shaped Charges and ofJet Penetration," Memorial DeL'art Ille'rie Francasise-T, 44,1970.
5. R. DiPersio, C.W. Whiteford, and J. Simon, "An Experimental Methodof Obtaining Collapse Velocities of the Liner Walls of a LinearShaped-Charge Liner," BRL-MR-1696, September 1965. (AD #478326)
6. A. Kiwan and H. Wisniewski, "Theory and Computations of Collapseand Jet Velocities of Metallic Shaped Charge Liners," BRLH-1620,November 1972. (AD #907161)
7. R. DiPersio, J. Simon, and A. Merendino, "Penetration of Shaped-Charge Jets into Metallic Targets," BRLR 1296, September 1965.
(AD #476717)8. P. Chou, J. Carleone, R. Karpp, "Criteria for Jet Formation
from Inminging Shells and Plates," J. Appl. Physics, Vol. 47,No. 7, July 1976.
9. E.M. Pugh, R.J. Eichelberger and N. Rostoker, "Theory of JetFormation by Charges with Lined Conical Cavities," J. Appl.
Physics, Vol. 23, No. 5, May 1952.10. R. DiPersio, J. Simon, and T. Martin, "A Study of Jets From10. Scaled Conical Shaped-Charge Liners," BRLMR-1298, August 1960.
(AD #246352)
11. M. Defourneaux and L. Jacques, "Explosive Deflection of aLiner as a Diagnostic of Detonation Flows," Proceedings FifthSymposium (International) on Detonation, ACR-184 Office ofNaval Research-Department of Navy, pp.'457-466, Pasadena,California, August 18-21, 1970.
47
'1I
REFERENCES (Cont'd)12. R.W. Gurney, "The Initial Velocity of Fragments from Bombs,
Shells, and Grenades," BRL Report No. 405, Sept. 1943. (AD #AT136218)
13. F.E. Allison and R. Vitali, "An Application of Jet FormationTheory to the 105-mm Shaped Charge," BRLR-1165, March 1962.
(AD #277458)14. J.M. Walsh, R.G. Shreffler, and F.J. Willig, "Limiting Velocity
Conditions for Jet Formation in High Velocity Collisions,"Journal of Applied Physics, Vol. 24, No. 3, pp. 349-359,March 1957.
15. G.R. Cowan and A.H. Holtzman, "Flow Configurations in CollidingPlates: Explosive Bonding," Journal of Applied Physics, Vol. 34,No. 4, pp. 928-939, April 1963.
16. Private Communication from J. Blische at BRL.
17. R. DiPersio, W.I1. Jones, A.B. Merendino, and J. Simon, "Charac-teristics of Jets from Small Caliber Shaped Charges with Copperand Aluminum Liners," BRLMR No. 1866, September 1967. (AD #823839)
18. M.L. Gittings, "BRLSC: An Advanced Eulerian Code for PredictingShaped Charges," Vol. I, BRL CR 279, Prepared by System, Scienceand Software, December 1975. (AD #A023962)
19. L.J. Hlageman and J.M. Walsh, "IIELP, A Multi-Material IulerianProgram For Compressible Fluid and Elastlc-Plastic Flows in TwoSpace Dimensions and Time," BRL CR 39, Prepared by System,Science and Software, May 1971, (AD Nos. 726459 and 726460)
20. R.T. Sedgwick, L.J. Walsh and M.S. Chawla, "Effects of HighExplosive Parameters and Degree of Confinement on Jets fromLined Shaped Charges," BRL CR 245, Prepared by System, Scienceand Software, July 1975. (AD #BO06987L)
21. J. Simon, "The Effect of Explosivw Detonation Characteristic3on Shaped Charge Performance," BRLMR-2414, Septemiber 1974.(AD #B00337L)
22. W. Walters, "Influence of Material Viscosity on the Theory ofShaped-Charge Penetration," ARBRL-MR-02941, August 1979.
23. ,(AD #B041485L)"23. P.C. Chou and J. Carleone, "Calculations cf Shaped-Charge Jet
Strain, Radius and Breakup Time," BRLCR-246, July 1975.(AD #BO07240L)
24. J. Carleone, P.C. Chou, and R. Ciccarelli, "Shaped-Chargo Jet* Stability and Penetration Calculations," BRLCR-351,
September 1977, (AD #A050117)
481, 'J
SI'
APPENDIX A
FLOWCHART OF COMPUTER PROGRAM
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APPENDIX B
FORTRAN IV
COMPUTER PROGRAM LISTING, SAMPLE INPUT AND OUTPUT1
59/60
m~*1
Ps'ORAI' PASC(INPUT.OUTPUToTAPE•aINPUTTAPE6aOUTPUT)C BPL ANALYTICAL SHAPED CHARGE (RASC) COME MAIN; 3C MAlK 4C WAIN b
C PROGRAMMED BY JOhN 7. HARRISON MAIN 6c MAIN 7
C MAIN 8C BRL ANALYTICAL SHAPED CHARGE CODE MAIN 9C MAIN 10C WRITTEN IN STANDARD FORTRAN IV MAIN 11C SEMI-EMPIRICAL CODE BASED ON THF FORMULA- MAIN I1C PAIN 13C 1/PHIu1/PH10+K*RHOJeEPS/E MAIN 1IC MAIN lbC MAIN 16C UNITS FOR THIS CODE ARE CENTAMETERS9GWAMSAND MICPLSECENDS. MAIN 17C MAIN 11,C THE COnE WILL CALCULATE COLLAPSE VELOCITY OF THE LINER AND MAIN IQC VELOCITIE$,MASSES*AND ENERGIES OF BOTH THE JET AND SLUb. MPIN 20C MAIN 21C THIS CODE WILL PREDICT PENETRATION AND HOLE PROFILE AND GIVE WAIN 22C PENETkATION-STANDOFF CURVES AND TABLES. MAIN 23C NATN 24C LIST OF VARIABLES MAIN 25C 01A AIN 2?C ALkAE, c ALPHA IN RADIANS MAIN 27C CON a DETONATION PRODUCTS CONSTANT (N). MAIN 2C DZ u DELTA 7 DISTANCE ALONG THC LENGTH OF THE LINER MAIN 24C DT7 a TIME THE DETONATION WAVE ARRIVES AT EACH Z POINT MAIN 30C Al a ANGLE OF INCIDENCE PAIN 31C Z(I) a DISTANCE ALONE LINER MAIN 3?C T7(1) TIME AT EACH POINT ON LINER MAIN 33C GAMA(I)a ANGLE BETWEEN AXIS AND COLLAPSE CIkECTION. WAIN 34C BETACI)a COLLAPSE ANGLE MAIN 3tC V(I) a COLLAPSE VELOCITY MAIN 3"C TAU(I) a TIME FOR EACH ELIMENT TO kLACH THE AXIS MAIN ý7C PHI(1) a ANGLE OF LINER BENDING. MAIN 3ýC PHIV a ANGLE OF EXPLOSIVE BENDING. MAIN 39C RPHIn a I/PHIV MAIN 40C RPHI a 1/PHI MAIN 41C CMI) a POINT ON THE AXIS WHERE EACH PARTICLE WILL HIT PAIN 42C VJ(Ii w VELOCITY OF THE JET MAIN 42C VN(I) w VELOCITY OF THE SLUG MAIN 44C CO a SOUND SPEED OF LINER PATERIAL( COPPER CCm.395 CM/MSEC) MAIN 44AC wV(I) a FLOW VELOCITY (VF), DIRECTED INTO STAGNATION POINT, MAIN 46PC DFJ(I) a DELTA ENERGY IN EACH JET SEGMENT MAIN 45C DEN(I) a OELTA ENERGY IN EACH SLUG SEGMENT MAIN 46C R(I) a RADIUS OF THE CONE AT EACH DELTA 2 DISTANCE MAIN 47C DA a APARENT DETONATION RATE. MAIN 414C DwL(I) c DELTA MASS OF THE LINER MAIN 49C E(I) a AMOUNT OF EXPLOSIVE ABOVE EACH POSITION CiN THE LINER MAIN SOC OPOINT a INITIALLY IS THE TOTAL HEIGHT OF THE CHAAGEv THEN SE- MAIN 51
h C COMES THE INITIATION POINT ON THE 2 DIRECTION, MAIN 52C hNAt a RADIUS OF CURVATURE OF THE CONFINMENT. MAIN 53C IF NRADsO.-THEN THERE WILL BE A LINEAk TPICKNESS OF EXPLGkAIN 54
v c MAIN 55C INPUT PARAMETERS MAIN 56
61
• i1
II
C MAIN SbI C CARL) NUMBER I MAINc MAIN 60
C IJONN - 1, A P4AIAIET11C STUDY, 2, 4 Pilo CASEo MAIN 62C PA 11 b3C HEAD 8 A HEADING CARD. "AI 64C MAIN 66C MAIN 66C CARb NUMBER 2 MAIN 67C MAIN 6& 1C ALPHA a HALF ANGLE OF THE CONE IN DEGREES. "AIN 69C rPs u THICK•'ESS OF THE LINEk,|O IF UNKNOWN OR VARIABLE) MAIN 70C RHOJ w DENSITY OF THE.LINER MAIN Y71:lC RF a FINAL RADIUS OF THE CONE MAIN ?4
C I HEIGHT OF THE CONE. IF MC.,9 THEN H WILL BE COMPUTED. MAIN 73C COF a CONFINEMENT FACTOR(D FOP UNCONFINED, IF CONFINED a THICKNMAI 74C RHOCON u DENSITY OF THE CONFINEkENT MAIN TIC NPLT a NUMBER OF PLOTS. O-SKIP, I-ALL, P-VEL. * PENETRATIUN MAIN 76C NPOS I NUMBER OF IgRZ) POSITIONS TO BE kEAD IN. MAIN 77C IF NPOS IS 1 DO IOT READ IN (R.Z) COONIDNATIS. MAIN 78C CARD NUMBEP 3 MAIN 710C MAIN 60C RHOC a DENSITY OF THE TAkGET MAIN eiC SO a STAND OFF DISTANCE MAIN b2C IF SO Do PENA7TATION STANDOFF CURVES %ILL BE PLOTTED* MAIN 83C CK a CONSTANT FOR OLTERMINING HOLE VOLUME MAIN 84C IF (CK .O) CK WILL BE CALCULATED AND UL IN WILL THEN MAIN Bi-C 0ECOME THE SHN TO BE RFAD IN. MAIN 86C UMIN a VELOCITY MIN. USED IN THE PENETRATION THEORY MAIN 87C IFtCK w0.) UMIN WILL BE THE RHNo MAIN bbC TI a BREAKUP TIME OF THE JET MAINl. 1 'C IF( TI a 0.) TI WILL BE CALCULATED, hAIN goC OPOINT a INITALLY IS THE TOTAL HEIGHT OF THE CHARGE MAIN 91C RDPT •RADIUS ABOVE AXIS WHERE EXPLOSIVE IS INITIATLDo MAIN 92C NEXPL B EQUATION OF FTATE NUMBER FOR THE EXPLOSIVE. MAIN 93C NLAPL EXPLOSIVE DENSITY DETONATION RATE MAIN Vi.C I COMP a 1.7? ,P MAIN 95C 2 OCTOL 1.32 e65 MAIN 96C 3 LX 1oA4 .8T77 MAIN 97C N * THE NUMBER OF ZONES Z-AXIS IS Tb SUBDIVIDED. IF NPO THE MAIN 96C DEFAULT VALUE IS NE6q. MAIN 99C MAINl0C MAINIOI
DIMeNSION EXPLO(6). NHOHE(b)v OV(6) MAIN1O2DIMENSION RIF 0),IMAT(100) MA1NI03DIMENSION EPSI(lOO), DAI(1O0) MAIN104DIMENSION RP(300)#PLOT(3) MAINI05DIMENSION PSO(50)9 PPT(SO) HAINIO0DIMENSION CONF(&) MAINIO?DIMENSION UJK(200O) DMJK(200) MAIN OHDIMENSION HEAD(6) MAIN109DIMENSION D"L0IO0), RV(100), DEL(IO0) MAINI1ODIMENSION Z(100), TZ(100), TAU(100), E(hoo)t PHI(IXO)t DPHi1O(lO), MAINIll
I BETA(IO0). GAIA(IDO), U(lO0D) C(IO0), VJ(100), VN(100)9 D00.(1U0)MAINU22 o DMN(IDO), DEJ(100), DEN(1O0), RPHI(XO0) V(100) MAIN113
62
1-T.
*c COMMON P.Aki 1I5C MAI N~, II
COMMON ALP&Do EPS* RNO.I, RHOCs PF. FPH*IO, UTZ* So, LiK. OAt ht 1,it MAIN)11I PT, DEGTOR Ak1COMMON AMUCIDO), TI4ETA(1OO)9 F11O0)) DF(lonlh Td1001I ODY00O) MAINI1Q1 G(100)9 PC100)v A(000)t DELA11QO)o DV.J(100j)v OZOLT(100)v MAI.1202 PIS01000). RCIIOO)s T19 UMIN-MIN ICOMPON /LPLOT/ Zo TZs TAOv Ev PHI* OPHIo HIEAs GA$44* Ro C, Vii. VNoMAIN122I 14OaJs DM~v DEJo DEN# RPH1. V MAIN123
*c MAIN124rDAT A #4EAD(S) 11h),1 .MAINI 25t)DATA CONF(I), CoNF(2) /10MUNCONFINED, 1N),/ ,MIAANI 26riDATA COMP (3), CONF (A) /1ONCONFINE.D # 1ml-/ 0AINITDDATA PL(OT(13,FLOT(2),PLOT(3)/4HS~XP,3HALL,99MVEL * P.ENa/ -HAINI9DDATA EXPLOCI) /61COOMP A/ v EXP'LOt?) /6HOCTOL/ MAIN1280DATA EXPLO(3) /404 TNr/,EXPLOEA)/ePHP.-9AO&,,EXPL1b)/4HLX14, MaAIN13OUDATA EXPLQ(6)4HO280I MAINI 30EDATA RMOt4E.()s PHOHE(2) /1.72o 1.82/ MAIN131UDATA RHOHE(3) /1.63/, H(./bEj3~.).,E,~fAI12DATA DV(1,v DIVC2 ,DV(3,oDV14)/,7qa.&8,.eoQ0,8eSO/ MAIN133CI
DATA DS*V(/*7i.A47/PAN14.
*C READ IN HEADING ONE TIME FOR EACbw PARAMETfilC STUDY AN3C 04AIN137
I CONTINUE MAIN.138PEAD (5*37) IJOHNvHEAD HAINI39WIF(EOF(5)) WbT%*2 MAIN1 39A
2 OPITE (6v3b) IJOHNOlEAD MAINI40KC 04 IN I tC BEGIN LOOP FOR A PARAMETRIC STUDY MAINd '2
C MAINi43C MAIN145
R EAD IN INPUT ( 2 CARDS. HOTM WITH 7E10.3,21 FORMAT.) MAIN1..hc MAIN147
C REAU IN LTNý-P AND CONFINEMENT jklý,UTS AMaC L) 0~,
P5.40 (5.36) 4LPHA.EPSRtHOJRFMCOFRMOCONN4PLTNi(-S MAINISIRC MAIN15ýC READ IN TARGF.T AND EXPLOSIVE :NPUTS MAINa53
C ~U4AXN154REAP (506) RHOC. SUCKUM 1NT1,DPOINTROPTNEXPLN HAIN1SSR
SH*14 AIN15*.COC.395MAIN1564
TM J.jn m. MAIN156HJOHKI9I1 MAINIE7TECUT)'30. MAINISTATECLT?zO. MANk15TL0TECLT3sD. MAIN157CTFCUT~vO. MA1KISID
TFCU~u0*MAIN15TETMJCU Tz0. MAINIS71:TmuCI. 1:. KkINIt7G7Tr 1,2xo. MAIN157t,TMCUT3vC. MAINI S71TMC04wO imC*)IAI1N)57J
63
COUPNN*?$ MA I NI 2
Is% 14~ro 10 A IN 161If NA1407 I 6 MAIN164
~jo.O.MAIN166
1'4L~uO.M&IN1(67A
0A INI b6
MAIN171T'4'O MAIN172
~UMVJO.~ 9AIN173
IvaAssmoto MAINIT6OkMAsuo'. MAIK17Sn~ASSmo.O MAI fl ITf
00 3 .I014140 OON1f2tilsi, iAINIS1O
3 ANM 409mO MAINIbIC M41IN82
C CONVERCT ANGLE ALP"& PRO" DEORVEE TO PADIAhbo MAININa
Pla3ol4159?6SlP9793 MAIN1*'5
ALPAbuALPHAIDEGIC$N mAIN1 N7TPRV.AN4 5*A1~AO~MAINIb7A
z COMPUTE THE HFIGOT OF TOE LINEA~ IF NO GIVEK IN INPUIT. MAIN1&b9
IF(I'LE.C.I HuRF/TANCAL010) MAIN190
C MAINI91DZ'H/FLOAT (N) MAIN1 92DTYstDZ/f MAkltIl 93
C SFY UP CONSTANTS TO BE IN LATER FOUATIONS. AN4POESCONOPHOJOEPS mAIN-,Q!,SAuSIN (ALP#AD)CANCOS (ALPRAO) MAIN0 7TWuAN (ALIRAD) IAA INJlIF (PFL[C.O) RF&TAON MAIN199P 7PSeP /3 * M41000OPIP 02400PI MfzoSlGM~uRHOJI*EPS 00AINpol
c MAIN202C DETONATION POINT IS THE H4EIGHT OF THE CHARtiF H EIGHT OF THE CONE6MAINP03C MAIK-204C OPOINT*DP%.'NT-H 14AIN245
IF (DPOINT. U.. POIN782.*RF MAINZObAIF (COFoGT90,) C(JNFTKmCOF MAIN20bDELC(JFCONFYK /20. 04411207
C MAIN2Oe
64
ma mzA
C CQ - ONFNF.~NT 'ACC~F(INCOEASE IN LXPLOSIVL TFICKNESS). M~~C MAIK%210
I ,i0PCINTf2*0,53iMINIWPIIE It-92A) ALKtA9 CON* EPS9AHOJ9CONF (ICOIF) oCONFTK 9POCONvCOF s 49 r *MAIN?131bI AZODTZON MIP4bRITE (6929) FXPLOiEXPL),DI(MOHEINEXPL).oPOINTNC*T.RIUCSO. MAIN215o
t 'l'INsPL0T(NPtTI)l MAINP16wRRFvPF MAIN?17PHI (! ;3.O/OEGOQ MA!N?lb
C INITIAL TIME. OF COLLAPSE TnTAU). MA!IN219Twx,,l AIINP20
C CONIANT P04. TWE ACCELERATION ROUTINE. MAIN2FI
FTERP0a.O6OOUI MAIKieeC MAINP23C SETUP R~OUTINE MAIN??&C MAIN?25C SETUP INITIAL POSITIONS (RvZ) 4NbL MAINE27C RI- INSIDE RADIU'S OF THL CONE9 R OUTSIDE RADIUS OF THE. CONE. MAIN?2bC MAINFIQ
*1~EPCC MAIN23C TH~IS IS A SETUP ROUTINE FOR A S14APED CHAGE LINEP ýITN CONSTANT EPSMAIN232
c MAI4,?33IF (NV'OS.E.Qo0) NPOSul M4AINP34NPOSONPOS.1 MAIK.?3b
*IWRITE (6927) 14A 1 2361hIF~ (NPOS*GE*tN) 60 TO 5 MAIN?37D0 4 JUNPOSON MA1NF3A 'tZIJ)NZ(J-I) .07 MAIN23Q
Q4 t.9mZCJ)*lA MAINd.O
IF9 (I (J) .LE.0.) RI (.J)u. NIMAINi~.k
IF1AilSCRI (j)-o.0) .LE..oOD1) W(J)90, N.O624 CONTIN~UE MAIN2435 CONTINUE MA IN264
WRITTE (601fl MAIN24sw
h'.UTE (6932) IAAIK2?7?wWRITE (C-934) (jqkCI)vIulNI MAIN246w
vRITE (6.33) MA I N?9W
WPRATE. (603A) cIoPICI)9IxIN) MAIN2SOWIC SAIN251C MAIN252c E 4) OF SETUP ROUTINE M4AIN253C MAINb4
TZCI )uDPOINT/D MAIKI?SSFPSI (1)rEPS MAIN2b55A
*C MAIN?bt-C START SPAC:E 9 TIME ITERATIUN. MAIN257
c MAIN?5f.DOf 10 Iu?.I\v MA IN259
V(I~mo.MAIN260
65
C UJK(I'j1UO MAIN263
ALRADuATAN?(2 D) AN6SANSIN (ALRAD) MAIN270
CAUCOSiALRAD) MIV
COMPONENTAD MAINT72C FIA(~~gl O-9 MAIN273
CFIýALL ALA! (IZRDONTRC TJONIA! MAIN273AEPAu (I)-RuO )*A AAIN?7O
C NAINb1C OF SUBROUTOINFO CONFINEET. ACLT NLNTO NL A~ MAIN?76
C (F A)DEIS GIVEN COMPOEN. TO CELACULTE CURVE TRHIC)td./PS OFE~OlLMAIN277C MAIN276
JFiAO.I O) ()SRTASRD@2(-ZH*Z=D.D(-ZI)T MAIN280c MA IN?bl
E(I COF I FCTR FOR(1 CONF-INEMENT NCNT~7 MAWS?9C CLUAE1/H MAIN?83C MAINPA&
721321 IFA*A RA SGVNNMQ sCAUAECRE HCNS FEPOIE1AINMQ
I~I 040.67Z(I.0o() MAINW9TNQwS*IA 0AINPOPEPCLCUAT (uEXPLOSIVME9 THMNS AIN?67E(I)'E F(Ib'CO(THE)*(O-o*HCNCWY/ MAIN29C0
C CALCULATE I&EPHI 1I AINP91COCRHEC MAIN292RPHJ I)uRPHI)/DO'PEE() MAIN23OA
TWEQv.5*I-AIMA 1N029C SUBLROUTINE T ACLT HEACLRTO O H I0 MAINF96C PIIxP/CSTE0 MAIN247
CON~nPOE#ClMAIN30b
00CJ.,0 MAIN302Cc EP SUBRUTIETO ACULAT(E()THE ACEERTO OFTELIN~AIN303RPJURH (I*CAIN304
TW.R(I)/(DAO(SIN(ALRAD4I,0/RP(Jfl-SA)) MAIN310IF 60.Q.)G TO h 04AIN3114IF (Aps(RPkbJ-pp(J-1))dl.E*ETER'4) GO TO 7 MAIN312
6 CONTINUE MAIN315C MAIIN316
4,C END ITEkATIVE PPOCESS MAIN317CMAIN318
7CONTINUE MAIN320
66
Z. 7
c M4AIN321C 'T4E ENC OF THE INV'.PSE VELOCITY G3RADET1t4 SBOUT1~t. H&1N3ý2C HA I 32 3
IAU(IIRTW MAI9V32'APHI ()SRP() t4&N32b
P~ (2~1./RPH (1)MAIN32A
IFI(PIQ.Lf..0.0 G~O TO 10 MAIN3?6ASPuS1N(PVI(Ill MAIN32YTPE'AN(Pti1(1)) ~MAI1N330SAPIASIN (ALRAD#PHT (122 MAIt433
C CALCULATE TAN(WEA-ALPMA) MA1N33?c CKAIN333
1 *CA*TP) MA IN3 35C MA N 3 3bC SOLVE FOPS THE AN(6LL BETA IN iRADIANSs MAIN4337
PF¶A(IxATAN(TALPHAE2)*ALPAO MAItN33'4if (1EQ12 TA(1)mALQA0*PI4I(I) MAIN34ti
C MAAI0JC STDLVE FOP THE POINT OF COLLAPSE ON 'THE AXIS. $IA~tlA'T3ON POINT *Sk.MAp'.34?
Cl : z (I) 'SP/ (CA'(SAp-SA)) MAIQ143C SOLVE FOP COLLAPSE VELOCITY M&IN3~4
123 'OASN(PH(12052 Hlts34SGAMA(12s.5'Pl-(ALPADe.5'.PH1CI2) AN4
~J(IuV()*CS(ARAD.~'P1 ).~,~E'A(I22#SNC.'NT(12MAIN3427
1rHLII)uPIP *EPS*P(I2*DZ/CA MAItN349
DML (1w uML (32 RHOJ MAIN3*940L'MASe-mDML (12 MAIN349b
DFJtIlw.5#(l.#COS(AT2 H )C~
C COMPUTE THE PFLATIVE VELOCITY OF IHE J0' Atit SLUG. MAjt,,StC 'THiS IS 'THE FLOO, VELOCITY. (VF). HAIý.3h7
RV(122.5*(VJ(l2-VNlI)) MAIN358?F(RY(I2,CTsVMAX) 2JHW'AXNAV(I2 MAIN358A
C MAIN3S;9TMLsTML*DI'L(12 MAN3bOTMJzTM0+rlP'.j (1) *DML (1)2XNb
C IF THAE FLOw VELOCITY IS GREATEV'1 THAN 1.234COs REMOVE MASSi FiROP JfYMA1N3b1AIF~I*J (P I/OG..3 H0. 04AI N3bl 6
C ALSO PEVOYE KINETIC ENEPGY F09 JET, MAIN361C
IFl;4V(!)/CO.o'T*I.232TEJ*30. 1A1N6TMNxTMN.OMM (12 'MLII) MAIN362D)4JK (I) .DMJ (12 'CML(I) MAI N3t-:
TKEaTKE+OEL (12 MAIN36STF.JvTEJ+OEJ (I 2 'EL I MA~tN3vUJK (I)sVJ (I) MAIN3b7
VJ'l~XVJ (1)MAIN369~
67
MAZI'370
MAIN3Tb
II K CttJ ~ 1 N U M A I N 37* 4
1 0 C O N T I W U E C E j q v I A O NG I KE H E ~ i O f fA It 4 3 7
c ENI) Of T14E XNt SPAC MIN37E A
CALL ~ ~ ~ ~ ~ 4 JEPOTN 'OC~PE$ H ~T AND CxLCVLAIZ NEW JET VELOCITYMAIN?
CALL SU H UME T A1N) il
%& p483
T F J C U T OD * M A N 3 3
VAI%3b3b
I F I KMA IN30Fl(UJAWC(Ep,GE9?
5 I'tCU'U%ICU'T4~I
~P UJ~1).. J~AsTmCU'T4#CwJx(Z)OE) MAINM363E
F(UJ1t)9GED$2 WCufluCUTS*OPK ( MAILb3
if (Uj ttI).LE.UJMA) GO ¶ AIN304A
ITF UKI,CO.o¶.bZ IECUITQ. AIN8U
I tUII*'TCUTl0E. ( *E 1 1%I3 b4
I F ( u jV t 1 ) / C 0GE , 4 3 S ) j t j m E U 9 D J 1 ) * E M A I N 3 6S .
T4 TEUT41VEJO *DE 11)MAIN384E
yCTlATCU~bDE'O. tE~I MAItN3bS
Tj~j~T~a6 I N 3tti69I
yAUrluo. NAtN365DMAI N38bF
11 P~jCoo~,3 CONTINUE% MAIN31ý
Q4~ (I/o.Il#3 Ilcls MA ZN3A&b
23) tMAIN366C
23) CONTIN E INA!386
MA 1N348
C4ONI NU MAIN389A
00I Av j / a G~ M 144 N 3 764
MAItN39'2
IAIB%4rN393
IFC.E5)N25 AN9
13 CNTINt MhN368
WRITE(bo2) MAN39b14AIN~q
~W IT (;:;,.;4)7 MAIN39
* fPHI(I)mDPHI(I)*VEGTj~e MAIN401*7 (1) Z (1) /1, MAINdI0P
WRITE (6.23) 1.2(112TZ(I),EPSI( .*E(j2,PH(I).9ETA-(I).DPI4g.(12. MAINA03*
PETA(I2UBETA (II/DEGT(JR MAIN40b14 COJINUEMAIN406
GO TO 13 MAIN41015 CONTINUE MAIN411
TMJx0 .0 mAIN&IIA
ý'1:1 #4AIN4.12IF (N.GE.57) N2=5T MAIN414
16 CONTINUE MAIN*15WRITE (6923) MAIN41bW
wPITE (6*252 MAIN4 17W
CO 17 IwNI*N2 MAINAINTV.JaTMJ*DOMJK ( MAIN418AIF(RV(I2/CO.GT91.232TBmjwo. MA1AIN1RB
WW.TTL (b*23) 1.Z(I2.VJ(I) ,VNCI2,RV(I2,UOOJC22.OMN(I2 ,OEL(12,OML(I).MAINA1Vwo
c MAIN4211(12 Z (22* MN#AIN421A
17 CONTINUE MAIN'.22 :IF (N.LEoN2) GO TO 18 MAIN423NIuN?. 1 MAIN4k4NpuN MAIN42b
18CONTINUE 10AIN4.27
IF (!ERROP.EQ,12 6O TO 20 MAIN427AIF~kHMlC*EQ*O0et GO TO 20 MAIN428~
C CALL PENETRATION SUBPOUTINE CALCULATES 1JET RADIUSoEPTH OF MAIN429C IPENETRATION, HOLE RAOIUS.,ANLb ALSO PENETRATIOK, SIANDOFF CUkVES.MAIN4i3(
c ~MAIN4t31CALL PENTRAT (NZkT#M#LAI~~UKk*V)*IASMiE~POAN3lsPPl#NCO.EPSI.oAI) MAIN433
c MAIN434.C MAIN435
Do 19 I121N MAIN4364C CONVERT VELOCITIES TO (MM/MICROSEC2 FOR PLOTTING AND REPORTS, MAIN437C ALSO CONVERT DISTANCES TOl MM, MAIN43dC MLIN43Cý
8ETA (I) u8ETA (I) ODEGTO4 MAIN&d.0VJ (I) mVJ( 22 10. MAINIA41
V (IuV(1'1O.MAIN442~
C K(12C() 10.*UKl 00AIN444
S(I) aZ 212/N MAIN&44A19 CONTINUE MAIN445
IF (NPLToEQ.O) GO TO 20 MAINA446CALL PLOTS tNLI~JKDPOINTRDPTMHEOPSOPPTNC~ONPLT.2S) MAIN447
20J CONTINUE MAIN448LJ~kAX=(lJNMAX*I 0. MAINA'.9
C PF;NT SUMMARY OF RESULTS MAIN450C MAIN451
69
WRITE (6#39) 04EAD MAIN*i62%
loA!TE (6030) TM~sTMjql"*TKE#EJi*lJCUT9T~CTNJA3&tIMACHupVMAXt'CQ A~#3
WRTTF.(6941) TECUlr1,T4CU119TECUTP97MCUT29TECU13#TPCL-T3 ,ANo
ITECUT4,TMCUTA ,TECUTSTMCUTSAMMACM ANA4
WRITE (6*35) MNt2(MN)4pUJKMAK.TMASSNPOSMO
mAIN'.sSA
IF (lIJ0HNo6To1) GO TO I MAIN*56
GO TO 2 MAINAST
90765 WRITE (6,40) MAIN&S4%
WERPITE(623 I9TbIRP(J)9RPHICI)*CTobElA(I) MAIN~b0%
STPOPl MAIN"62
STO MAINaft?
C FORM"ATS 04AT N~t
C 00A1w,6b
23 FOPPAT (I4q2Xq1PI2EI0,3) .HAl ;44b6
24 FORMAT (2H11,5X9PH Zs8Xs2NTZv6X*3I4EPS#7X92M .X3P17.,HASHP~
IX*4HDPWIv6Xo4NAPNI*I6Xo4IK veb.4K H A 969.4'H lAuebt'64H C/I MXINdi6v
25 FORMAT (2HII0AX,1HZqSX93H VJqbA#2HVN%7Xv30 AV?9HO4X3HM*X4I*4
1 ,3 HDEL,7Xq3HDML.7X,~hDMJK,9Xo3HTMJ/) "l7
26 FORMAT (BE1O.4) MA IN&7?1
27 FORMAT11IHI/ INITIAL POSITIO(t'/) 14AL1472
28 FORMAT( ////%OX,'INPUT PARAMETERS#/i#SX.' ALPHA w 19F6*3,7X,'K COMAIN473
INSTANT m 1,F6.,7X,1THICKNESS OF LINER a [email protected]'' DENSITY Is MAIN'74
2F6.3//5X9A1OoSX , THICKNESS a I.Fb.397X,' DENSITY a $vF6.3e5X,'FACMAIN&75
270P a '9F6.4//SXs'LINE.R WEIGHIT a l9FIO.4*7X.'LINEP RADIUS v1.F10.AMAlN676
49//S~o' INCREMENT OF 2 MZ) x 19F1O.4*#7xvl INCREMENT of TiMI (UTZIAIN0677
5 ul*F0*4%7XvlNUM9EP OF ELEMENTS (N) l#I,49//50XIOETONATI(N //) MAIN478
29 FORVAT(SXEXPLOSIVE a ,,S7AA1O*3X~fDlETONATI0N VELOCITY(D) a :9 MAIN479
IFIA&StSWIEXPLOSIVE DENSITY so 'F601//6XPOINT OF DETONATION FROw MAIN48O
2CONE. APEX(OPOINT) a lFlo.4,7X91DEle RADIUS (RPOT) a SF1C.4//SOAvMAINAb1
31YARGET INPUTS*//SX..'TARGET DENSITY 9 ,vf79397X.,I5TANDwQFF DISTi.NCMAIN&BE
4E a lvF7,3v7Xe'CK CONSTANT(BHN) a frF1O.6//5OX40ISCs INPUTSI//SX, MAINA63
SA1O.'PLOTSI) 2 MA I%4v.
30 FOOMAT(////////l/.3099' SUMMARY OF IaESULTSI/////' LINER MASS n$MAIN66b
leFIO*',' GM 4-hX91JET PASS a 19I91 G0 *9SW,'LU6 MASS 0 ' AI~h
2FI0.',' 6M t/14 TOTAL KINETIC ENERGY it IFl.6, EMG9S1.I0El2i'//MAINAkl7
3 TOTAL JLT KINETIC ENERGY a leF1O.'' RS'.O.2'/ TOTAL ~JET KIPA1N&OP
&NETIC ENERGY AbOVE JET VELOCITY .25 CM/MSkC a 1,FIO.491 ERGS*I*OE1MAINAbBA
5?1/,Of TOTAL JET PASS AROVE JET VELOCITY .25- CM/MSfC a *.F1O.4#6 (sMMAINbaH~
31 FORMAT (//7(3k~ ItbXo2H ZvTX)) MAIN&8'4
32 FORMAT (//7T(3W 196X92H R*7X)) 0AIN4'9Q
33 FORMAT (//7(3H4 Is6X*2MPI.7X)) M4AIN441
34 FORMAT (7tIAAX9F7*A,3X)) MAIN49k
35 FOPMATt' JET TIP AT 1 £ 0,159, RELATIVE POSITION Z/H a f#FI0*8//MA1N493Is MEASURED JET TIP VELOCITY a '.P1O.t'.' Mfr/MICkOSECf//0 MEASU(4E0 MMAIN694
2ASS OF JET TIP a 99FIO.',' GM 411H1) 4AIN494A
36 FORMAT (?EIO*3*21b) ANq
37 FORMAT (119,S ) AIN49
3M FORMAT (II,30XbAIO) AAIN497
34 FOPWAT (1HI93099WAO) %AIN&9b
40 FORMAT IIERPORI) MAINA'i9
4.1 fnRMAT(/' KINETIC ENERGY ABOVE .ý' CM/MSEC a 19FI0.4, MAINSCO
If' AND JET MASS u l*F1(.4o MAIKSOl
I:2 0 KINETIC ENERGY ABOVE os CM/MSEC a IsF1O.49 MAINbOZ
30 ANV JLT MASS a * 'Flo.4.4 'KINETIC ENERGY ABOVE ." Ck/MSEC a 90F1O.A, MAIN504
t'AND ~JET MASS a F '10.4" A2N0
f. # rINETIC: ENERGY A80VE 92 CM/PSEC a fFlO.4,7' AND JET MASS a *,FI0.4/ Mzeo
p 0KINETIC ENERGY ABOVE *I CM/MSEC * #0F10.4, MAIN50d9'AND JET MASS a 0,P10.4/t MAIN509
A ' MPAXIMUN RELATIVE MACHi NUIASER '.O4/MANO
ENnlMISI
7QI
SUPROUTINE PENTPAT (NZ,~.TZDS9ETA,!AUCVJRVVJioWASS.o, * ~110 1I gHEAD9F`SO9PPTshCDoEPS!,DAI) PENTI ?
C PEN~T7 3C C13PUTE PENETkA'71ONeRAO1US OF JE79rAAOIUS OF THE HOLE* PENTT 4
C YENT! 5
F. MLAS1ON HEAU(6) PENT! 6
DI1MENSION~ kPSI(IOD)o OWI1(0O) PENT! 7DIMuENSION PPHSO0), PSO(SO)o PVJrriso) PENT! 8D, IMENSION 7000)9 TZ1100), DKMJ(100)t BETW(OO)o !AL'(100)t C(100)9 PENTT '9
1 VJC1OO)9 R(100)9 HV(100) PENTT1OC PENTT11
C C;OMM ()N PENT!T12c PENI!! 13
COMM4ON ALkAD9 EPS9 PkNOiJ RH4OC# PP. RPHI09 UTZ9 SOv CK9 DAv H'. Ut PENYT14
1 PT, OECVTOP PEN!!T15COMMDIý. AMU(10019 THETA(100)i F(100)9 DF(100)o Y(1O(0)v DT(000), PEN!TT2I G(100)9 P(100)9 A(10O)o DELA(100)o DVJ(1(00)9 7UM'!100) PENIT17
2 RsG..'0)# RC110O)s TI, UMIN PENT! iN
C PENETRATION PHASE PENT'T19
ViJovoo0 PENTT 19A
Do 11 IsiONN PENTY20
EPSWEP?.dIM PENTT21
CAsUAIM1 PEN!T22
*IF (I.LE.MN) VJ(l)mVI(mh) PENTTh'3IF (1.E~ol) RETURN PENTT24
*IF (VJ~oG!.D.0) G0 TO 'pENYT!25
VJCoVJ (MN) PENTT26
jTr1ml PENTT27AKAY&SQO! (PHO~J/PHIOC) PEN~T!~Alf)BAKAV41. PENT! 29
AX~a3.*AAY)/?.OAAY)PENY1 30
1t0K~uAV AY/AK 1 PENTT31
AhK3x (3,AKIV/C.KY PENTT31
hHNzNlko. PENT! 32~A
lF(UMIN,GT1,l.D) SHN&UMIN PENTT326
IF (CK.EQ.0.) CK:I2250.#4.2O0i8Hfv*.O- PENT133
C T1%T1l (o7b1I-.2t4)/(VJO-*28) PENTT35PENTT36
A (I~u0.PENTT37
DELA I )3. PENTT38flF (I)N. PENT13,4F (flce. PENTT40
OVJtIlsO. PENTT41
SUMMU:0 * PENTT'42K211-1PENTT42A
DW4ASSwuO~j f) PENTY42CIF (VJ(I()ý.F.0o(' V.J(K)uI..OE-02 PENT142UAMUlK)RV. ,.J(I() PENT742LTHETA(N0a'' Y,41tUW( PENTT42FF(KlmTHETAOK)/A0U(K)'It,(K/VJO PENIT42G
DP(Ol)mF(N) PENT1!2iNULO-U AFU (K) 0* 1-OKAY ) DF (K f*SUMMoU PENT7421
T (K );.hoU I K ) 00(I. +AKAY)*(Tn- I . AKAY) SUPIALI) PEN!T742%n(K).! (K )-TO PNT
G K) VJO* (T (K)/AMU 110-F(K)) PENTT42L
714
ý4.AILL
A- ..- ,.,--)OCO---FT'K)-?, PENY-2-
PENT7420
IF (SO.EGO.o) NCD*25 PENTT44DO 3 JU1.PNCD PkNTT45IF (NCD.GT.1) SOnFLOAT(J)*RF*2. fPENTT4620.1"'.SO PENTT74TOw2O/'VJOPET4
IF (J CuFI.,VO*Tl 00J3 PENYT49F*PTzAJ14uPOT )*AKIZ*AK-GYKAAKOISTIVOT PENTT6')IP OAKmPPT (#*AIO.)2 PENTT51PVJTa(J)EOV. OT)*KOlZ~6IP!Z*T)/AAOI PENTT52
C 0 ETO 2 PENTT7OI. CONTINUEPET4
P~AbAUYT(V.JO/VTJI-S) (MN*l(JOIZ/KY) ETbVITBYOAPU(AVAY*O.) RTR PENTT7b
2CNET INUETZ()TUI PENTT57PS(I)wFLOATA()i 1 ~~~CI/ PENTT7'SA
DF(1,)InF P1-C-)IENTTbyPT C1).aPP(.12*C10..AA)(OC.AA)S PENTY60PV1(!21)-VTO PENTT61
3 CNTIUE4O((~'AUI.C) PENTY63c IF POTTIN PEAR O-~ STANDOFFCURVEZ;. UE2CDTPLTHEPWPENTT645
IF.LA (12.A(I)-NCI1i3 PENTT86A
FNC#T1 nFOAJTUV.(NCD)-VJ(I- PENTTtS
IF (NC126.(T() PaPTZ(NC)DV).J()OZVJI.EAI/ PENTTbb
IF (NCI).GT.TI2 GTOPVTNCDI6 o PENTT9O
IF (ZO.GEVJO* F0TOS ENTTbc)CALCTULAEDPPN PNTAII PEN;TT70
TZ(IaTZ()-TZI) PNT72
DM-xDJI PENTT - -- -- r--------- b
-C PENTT98C CALCULATE R4ADIUS OF 7I"E 4JET fPENTT94w
C ~PENT) 00HC(UuSOSRT(RNO.J/(2.*AtKAY*CK))*ScGP?(Tl/TO)*Y.JO*(ZO/(ZO.P(I)flOOAK3 PENTIO)1 *PSCJ(I PENT 102
* GO TO 9 PENT1 035 CONTINUE PENT1 04
P(I)uVJO*(T(I)-TO)*T1/(T1.T(I)/AKAY) PENT1 O5VjPwVJO' (T1.TO/AKAY)/ (T1.T (I) AKAY) PENT106OVJPMVJP-VJPO PENT 107DZorT(l)u(T)-T(I))'DVJP-VJ)P4OELA(1) PENT1ObDIOUT C) -MZOT (I) PENT109RPO (1)32 'A (I) *PS'OA*OMASS/OZO4T (I) PENT) 10PsO (I) uSQTRTIsO (I)) PENT)))NC(I)uSOHT(kOJ/(2.eAKAYeCK)leRSg(I)*VJOOfl.-P(I)/(AIKAY*VJO.1))) PENT))?VJPORVJP PENT) 136(0 TO 10 PENT114
b CONTINUE PENT1 15IF (Pl*L.T GO TO 8 PE14TI16IF (%JCIoNf.1) GO TO 7 PENT)117.JCI&2 PENT) iN
Tpxl~l)PENT 1197 CONTINUE PENT) 20
IF (T(I).GT.TP) RETURN PENY1218 CONTINUE PENT122
DZODT CI)u(T1.TZ(!))*DVJ(I)/O)TZ-V.j(I).OELA(I)/UTZ PENT123P (I )m(AKI* (T1/TO)**AI'OKI*T(I) /(T (I).AKAYT1,i-1.O)*ZC) PENT1?4P50(1) a2.* (1) *EFS*DA.OMASS/DZUDT (I) PENT125
¶ SGCI)asOPT(A8S(kSO(Ifl) PENT12bPCCI)USOPT(RMUJ/(2.*AXAY*CKI))4(O(/AKAY)1(AK1C70O/(VJOOT1))eOA101 IPENT127I-(ZO*P(I))/(V~JC,*TI)OPRSQC1) PENT126j
9 CONTINUE PENT) 29&J~ujll PENT130
10 CONTINUE PENT13111 CONTINUE PENT132
WPITE (6.01) HFAD PENT1 33W
WRITE (6.2'?) PENT134tw
WRITE 16029) T1.TOZO.PT. VJTV.JOAKAY.UNINCK PENT13t)WNIZIPENT136~
IF (NoGEo57) NpuSS PENT130WRITE (600C) PENT2 39W
12 CONTINUE PENT140WRITE (6#23) PENT141WWRITE (6#?7) PENT142%I Iu( PENTI43D~O 13 IaNloN? PENT)1*4
*WRITE (6.23) 1,ANCJ(I).TNETA(I) .F(I),OF(I).T(I),D)T(1) ,G(I).RSQ(I). PENT145U WI A(I),OELA(I) .DVJ(I) oDZODT(l) PENT166W
13 CONTINUE PENT14.7IF (N*LEoN?) GO TO 14 PENT34&6KlZKý41 PENT) 49
PuN PENTISOI00 To 12 PENT) 51
14 CONTINUE PENT)152DO IS I=MN*N PENTIb3
A15 CnNTINUE PENT Ib4
73 '
-47
h~u1PENT I b
IF fh.GEoS0) N?ubO PENT1 57WRITE (6.31) HEAD PENTISOWSOsSO/ (2.**F) PENTI5QWOTTE (6928) SO PENf16Ch
WRITE (6:23) PENT161W
WIF E (69T25)WIT 6.i ) PENT162WI
IF (NIoGT9?5) WRITE 1791, PENT) 6DW
DO 1O 1$~*N PENTI 5
RITE (6.2k)@GT PCI),R(TOIP PENT1T2W
1 F CONTINUE eoC l lo PENT) 7'IF (N.LEN25) GO TO 20PNT6
00 TO 16 ET717CONTINUEPET7WITE) 141 )II(lpc EN12
INCONINUECII PENT173219 CONTINUE PNI7
23FOPT (N* *.#2)60 TO2E0.3 PENT175924 ORMTC3,22F1.,O*FOlOf PENT176FORMA (HI1X'(MS1X'CC.3,T(M'1,S0C)/PENT177GO MTO (16I3 ,3.P,6,R PENTITS
20 ON71NT 2H16,HUSTHTX2 F',HD7,2TBXMTPENT193
100FP')BR( PENT182A21 CONTINUTE :FO*BTOa*FO4.X'2 PENT163REPTURN).,~*VTu,1..~, J 'FO~,V~'AA PENT1842,1..C'(I .1C~5. Ka'Fo5/ PENT165
30C PA(M, PENETRATION FORMATS) PENT199
231 FORMAT (1H*X1,30x ElO//) PENT169END~*T(3*X2F05I0vl*p0) PENT2190
25FOOA (H 92X 9PCM 19$tIC(M)92XtP (MO)*IX9S IC)I)74T926 FRMA (j~s3H I#13~l~~l6XlR~) PET19
27 FRMA (2 I*XwHtt8~bHHET~bX2H Fr~tH D97X2H TbX*HDT8PET1IIX2 IX3.0$oI~SoHE~!9HV~X4UV/ E19
SUBROUTINE CALAI (I*Z9,.DPONTqRV9jqOHNI*tI) 41 7011 2
C CALAI 2
C SU~ROUTINE WILL CALCULATE INCLIN~ATION% ANGLE (AI)s DETONATION CALAT 3
C COMPONENT OF THE COLLAPSE VELOCITY (') IDWL ALCLH AA
c SURROUTINE WHICH WILL CALCULATE 1./PHIO (PHi4IO) GIVEN (Al). CALAI 5
c CALAI 6
DIMENSION Z(100)9 RUM0O CALAI 7
COMMON ALHAD9 EPSt RHOJ9 RMOC9 AF, RPPH10 DTZ9 5O. CIK. DA# He Cq. CALAI 8
1 PT, OEGTOR CALAI 9
ALPt4AuALRADODFGTOR CALA! 10
TI4FTAnATAN((Rtl)-RDPTI/(DPOINT+Z(Il)) CALAlII
THETA.TI4ETA4DEAiTOR CALA112
A 1.90.- (ALPHA-THETA) 'ALA1 13
IF (AI<@09) Au18G..s(ALP~HA-THETA) CALAI114
CALL CALPHI (AI) CALAIlS
AlwAI/DEGTOR CALA116
DAnD/SIN(AI) CALA117
RFTURN CALA!IIR
ENrl CALA119-
75
'7-Lm r-' tn
SUPPOUTINE CALPNI (Al) *720' 3C CALPI 2C GIVEN AN INCLINATION ANGLE IAI) INTERPOLATE INTO TAKLES AND FIND CALPI 3C AN ANGLE fis10. YNEN CALCULATE le/PNIO (RPNIO) AND iPETURNo CALPI 4&c CALPI 5
DIMENSION TPHI(37)o TAI (37) CAL*'I 6COMMON ALRAD* EPS. RHOJ9 RHOCv RF. RPMIOo DTZ, S09 CK. DA. No, D. CALPI 71 PT. DEGYOR CALPI 8DATA TPM! /0.0, .0b. .25. o59. 1.02. 1.43. 1.76 , ?039 2.47. 2906*CALPI 9D1 3.30. 3.70. 4.14. 4.51. 6.06. 5.6bo 5.96. 6.37, 6.70. 7.019 7*22#CALPI1OL)2 7.42, 7.58, 7.73. 7.400. .04. 8.17. 8.23. 8.26. 4.30. 8.26. Be18.CALPIIID36.08. 7.99. 7.8%. 7.75. 7.56/ CALPI112DOATA TAI /0.09 e02, .06. .159 .239 .329 94.29 .489 .609 .7?. .84. *CALP113D194,) 1.06. 1.14, 1.29. 1.'4. 1.54. 1.67, 1.79. 1.92. 2.03. 2.16. 2*CALP114D22Ao 2.41, 2.61. 2.79, 3.01o 3.14. 3.25. 3.38. 3.57# 3.729 3.8boi 4.CALPI1SD
C ~ ~ TA CL*ATO 0'E 5.01 COUNTS (SFlxb.01/100.) CALP!117c TPOI SCALE FACTOR 40 DES u A.06 COUNTS (SFPHIng.08/40.) CALPIlb
SFIn.0501 CALP119SFPHIm.20P CALPIIOXzSFI*AI CALPI22D0 1 Jul.37 CALP122
IF (TAI(J).GToX) 6O TO 2 AP21 CONTINUE CALP124.2 C(nNTINUE CAL P125
0XEXm-TAI (0-1) CALP126RflxuDxl/(TAI (J)-TAI (J-1) ) CALPI??YaRDXO (7PM!(J)-TPHI (J-1) ) TPHIl(hi-i) CALPII6IF (PIIIO*LE*#0001) P141030. CALP'129PHIOCIuYSFPHI CALP130RPHI~u1.C/PHIO CALP131APHIOuRPPNI0DEGTOR CALP132RFTURN CALP133END CALP134-
76
SUPROUTINE VELGk IIKtujo#DmJK.IS) 7S&'
D!.ENS!ON. UjiK(2'O)9 DMJK(200) VELGPk 2
EuO *VLL.GP 3
Eno.~ - VEL6P' 4
1 '(Pul VELG(ý 6
i .OMPPE.SSION OF THE JIET VEL(,f 7
Do 2 MUISq1JK VEOcDP 8
IF (U.JKOq)*GE.UJt((N41)) 60 10 2 .4.G
IF (A6IS(UJK(M)-UJK '.1))oLEol.E-C) 60 TO F2'LkITp 3x*(MJK(H*(M.)*(tICt(( ,6iV UJK(H1 *)) VELCGP1II
DOpw.O/(O*4JK0A)+DMHK(M4)) YELGk12UJK(I')2(l71T?)OLM ELRUJK~(04&1)6(T1*T?VODEIAVLHKPu 0 VELG6k1l
2 CONTINUE VELGO17IF (ýP.EQ.O) GO TO 1 VEL(AIA1RETURN VELGR IE.ND
77,
SURROUTINE PLOYS (NUJKDPOINTRDPTHEAD.PSOPPdNC.UNPLTISTAI.T) *77?* 5OnIENSION PSOIso), PPT(50)9 SCSO) PLOTS 2DIMENSION BStOOD)o HEADIA) PLOTS 3DIMErNSION UJK (200). DM.JK(200) PLOTS '.DIM4ENSION RDI419 CV(4)o Ab(4) TCca). PC(''i, DMNJ(4)o VVC(A) PLOTS bDIMENSION 7(100). TZ(100)9 rAU(IOO)s E(00019 PHI(iQO), DPHI(10(J), PLOTS A6IRETA(10019 6AMA(IO0), RIMOD), C(100)9 V.J(IOU)s VH(100)t UM~J(10O)PLOTS 7
2 s VMN(ICO), DEJ(100)t DEN(100)o RPHI(100)o V(100) PLOTS &tDIMENSION F (4) 0(4) PLOTS 9COMM4ON ALRAD9 EPS9 RHOJ, RHOC* RF9 pPPH10, C'TZ SO* CII. DAs He Do PLOTS1OIPT, DEGTOR PLOTS1ICOP-MON /LPLOT/ 2. TZ. TAU, Eq PHI* DPHI, BEYA API R0toA C. VJ% VN#PLOTSI2I PWJt OMNN DEis DEI4, QPH1, V I'LOT$13DATA DMNJ(I)9 DMNN,(?) /IONRELATIVE Ms 4HASS)./ PLDTSI$D1DATA R0(1), P0(2). AD(3) /1OHI4ELATIVE Do IOHISIANCE FP9 10HOO CONEPLOIS~bb
I AP/ PLOTS1oDDbTA ROW~ /3NEX),/ PLOT$17DDATA CVII). CV(2)9 CVC3)) /IOHCOLLAPSE Ve IOHELOCIlY IN, IO*' CM/lA1CPLO75IkD
11.05/ PLOYS19DDATA CVW4 /3HEC),/ PLOTSZODDATA A8019. AB(?)t ASW3 /1OHANGLE BETA* ION (DEGPELS), IN>/i PLOTS'RIDDATA TCt1)v TC(?)v TCW3 /IOHTIME OF CO. 1OHLLAPSE IM19 IOHCAU SLCPLOTS220
1) 3,/ PLOT$23DDATA6 PC(1)o PC(2), PCW3 /IOHPOINT OF Co lOHOLLAPSE (Me 3HM)ýP PLOT$24DDATA VVC(I). VVCC2)o VVC(3) /10k Vo V.. (00o lOh/P.ICROSEC)o IN>/ PLOTS2bLUDATA TJET /4HJET>/ PLOTS26DDITA TSLUG /SHSLUG>/ PLOTS?7DXPAGEx1A PLOTS26CALL PLTCCA (XPAGLvI.RC1).EB(SO00)) PLOT529Itak~-ISTAPT PLOTS30YMAXmI2. PLOTS31CALL PLOYS1 (3.0.3.0.1 .OYNAX,.1. .50,ADVVC,16,1Q,&) PLOTS32CALL PLTCCD (l,0,Z(ISTART)oV(lSTART)9IIl PLMT33CALL PLTCCD (1I9OZ(ISTART19VJ(ISTART)9II) PLUTS34CALL PLTCCD f4oCZ(ISTARTlvU.JKCISTAFTliII) PLOTS35
CALL PLCCSP (XSyS.LJFAC) PLOTS3bXXR.?5 PLOTS37 ~YY.V..J35)#.OA..5 PLOTS39
C PLOTS40C 00 LXPERMNI(TAL DATA POINTS FOW THE 1OSNN UNCONFINED SHAPED CH.AkiiE&PLOTS4.1
C PLOTS42
C PLOTS44
DPOINYuDPOINTOIO. PLOTS'.bENCODE (21,2.5(1 )DPOINT PLOTS460WDP~uRDPT*1 0. PLOTS 47ENCODE (17*3,5(4) )RDPT PLOTS460AL0HAwALkAD*DF GTOk PLOTS49ENCODE (20,4,5(e) ALPHA PLOTSbO*RFuPF*10. PLOTS51ENCODE (1895,S(12) )WF PLOTS52*E PS w.E P 010 0. PLOTS53ENCODE C1~e9$fS(1) )EPS PLOYS54*YYuYlAAX#.P* ys PLOTSS4A
XX..5'XMAX-s?*X5*7a PLOT$54'C
78
X~0 * 0PLOl'bS'.CALL PLTCCT(@29HEADC1)0.9.1.*X~vYY) P.lt4YVV.8S*Y#AAX PLO0554XXX f, PL.OT5sbCALL PLTCCT (.1,5(1)o.O.1..JOYY)P105Y'~u.t'O*Vp4AX PJLoTS:-CALL PLTCCT (*19S(4)sO..1.,XXYY) pjolsbtoXAx.SB.1#XS1OC. PLOTS60YAu1 * 1*Ys VLOTSblCALL PLTCCT (.lS(&i)v0.o.#.AA9YA) WLC'TS62
YAun.5. *XY'9 PROTSh36
CALL PLTCCT (.1vS(12) ,0%91.,AAvt.) iLlbY A meI.5*YS oL0OT sobCOLL PLTC'CT (olvS(lb)v0ss(a,1.AAYA) jT6
C THIS NEXT STATEMENT BYP~ASSES SOME PLOTTINHcO ROUTINES PLOTs~bhC IF (NPLT.(-T.O) 6O TO 1 P1,0756
CALL PLQTS1 (3..lb..1..160...1 ,?0.,RD.PC,16,11,4) PLOTS5T0CALL PLTCCDt (2,oZ(ISTAWTU.C(IS'rAAT.11) P40TS71CALL PLTCCP PLO'TS7 2CALL PLOTS1 (3.093.0,1 .0. 1e.0o. . , RD.DMNJ,16,10,4.) PLOT$73
x~s.35 LOT 57'YY=DNN (35) -.1 PLOT$75CALL PLTCCT (*?vTSLUGo,0. 1.XA9YY) P1,0T757VY'tVMJ (3tS,-.1 WLOTS77CALL PLICCT (.2,'JE19,t.1.%XkvYY) IJLoT7$7FCALL PLTCCD 4ls0sZ(ISAPT)9DM~.J(ISTART)!Il) PLO17s7f
CALL PLTCCD (1,0,Z(ISTART),L~mN(ISTARThI!) PI-OIS0ICALL PLOTSI (3.0,16., 1.0.180.,.] .20.,RDAb,16,10,') PLOTSblCALL PLTCCD (1,0,ZCISTART)9HETA(ISTART)#II) L7h
1 CONTINUE PLOT5h4
CA.LL PLTCCP PLOTS$AC Twis NEXT STATMENT PART OF PLOTTING BYPASS PLOrS8b
C 00 PENETRATION~ PLOTS( HOLE PROFILES)* PLOTS58b
CALL PLOTPEIy CNvSvPSnsPPFTvNCUvHEAD) Lb0kETUPN PLOT$91
C PLOrb'922 FORMAT (Qý' (L-N) at oF8eidv4t MM>) PLOT5933 FOPI.AT (51ý RD :.F.P84v4 MW LQ$44 FORMAT (9H' ALPI4A 0 oF6.2'.5I L)E0f PLOT5'~b
b FoPhiAT 46H RF tf 494 Mm>) PLOTS')bI6 FORMAT (7H4 EPS c oF8.594H MM>) $0LOT S97
F.ND PLOTS91%
79I
SUqPoUTINE PLOTSI (X AN. AR. AOMAI~~yPx,,y CANC * PLOT b
NCt) PLOTI 3
DIEKSIOIN P7X.(6)9 PTY(4) bPL011 3CNY*NNCY PLOT] 5
CNX*NNCX PLOTI 6
YSSY04AX/5 * PLOY 1 7
XSBXMAA/70 1'LOI1 b
CALL PLICCS (XAtYAq"NYI-X~S PLOTI 9mys.15PLOT 110
VI,.-. 14yS PLOYl2.1X~u.SXMAXHTOCX*XSPLOT11
CALL PLICCT (p4¶,PTX(1)vC.#.1.9.yy) 1Xxv-.OOXS LOTX I*
,,5.*YMA)X-MT*CKY*YS POI~
CALL PLTCCT (,IT.P7Y(1)*.q.0**X~YY) PLO'T11
CALL PLTCCA (D*YXIsMXtM~YXj& ILOT~lft
CALL LA!RELA C .*DY9 INXMAXYMIN9YMAX, 1.0. 1#.) PLOTI117
OIETUIkN UT1
ENO PLOT114-
*END
Li80
SUHPOUTINE PLOTPEN (NoSoPSUoPPT#NCD,*4EAD) 6 E1WQ 711IMENSIOI, TSO(&), TPT~d)sMEAD(tA) PLOTN' P0 1 0ENSIAnk SbW) # PSO ISO) PPT (50) fPLUTN 3~flIMFNSION im.CLCP) YCNUIOD)o PENI3)o PENT(3), kAPM2 I'LOIN '.
COMMON ALR~AD9 FPSv RkQJ. W01CC, WFs RPHIOs DTZo SO*i CK. "A, ,me Do PLOTN bIPT, DEGTOR PLOYN 6COMMON AMLI(100),s THETA (100) FJ100) , DF(100), 9 T100), v D(100) 9 PLVTN 71 60O0),t P (100)o A(100)o DELA(100)9 DVJ(lOOJ. D70t-T(100)o PLOYN 8
2 R$0(100)9 RC(100)9 TIv UMIN PLOYN v4
DATA )40L(1)9 I40L(2) /l0I4NOLE PROF19 3HLE),/ PLOINICODATA PEN(jC)s PEf%(2)v PENM3 /10t1RAVIUS-VS-, IONDV-1W OF P, #im~h,(MrPLOTNllD
M )I./ PL OYN121)
DATA PLNTC1)v PENriP). PENT (3 /1OI¶TIME-VS-DEs l0týPTI" OF PEN. bm-.(PLOYN13DI co I>/PLOTN14U
DATA PAD(1)o P46lfl(2) /10HPADIUS 0Nmg PH))./ PLOTN1SDDATA TSO(1). TSU(2) /10O'STANIJQFF -s SH(CD)),/ PLOTK16DDATA T5)T(1)o TPT(2) /101ýPENETRATIOq 7HN (PYP)>/ PLOIN171,
kman.PLOTKIPDO 1 !iZ.N PLOTNlyIF (P(1)oGE*PT) 6C) TCj PLOYN20P (I a-P (I PLOTN21ACN (1 -PC (I) PLOTN2?IF (¶PCC1).GT.RM) PKuRC(I) PLOIN23
1 CONTINUE PLOTK?uP (N) .-P (N) PLOTN~b
2 CONTI¶.UE PLIT N2.bPLCITNeN7
N: I(N PL()T Nk#XMAXv1O. PL DTN?'29XMINu-XMAX PLOTN3UY MI Na-PpI PLOTN31IF (PM.LT#100.) YV1Ns-100. PLOTN3?
IF (PM.LT.60e) YMINW-60. PLOTN33I
YMAX:0 * PLOTN34VS. (YMAX-YMIN)/F4. PLOT9k3b
XRAkw3. 0 PLDTK37CSALL PLCCS PLOTN3h
CALL PLTCCT (XBADMUL(1vXMO.,1.,XS*YA) PLOTN394Xf~=-. 1XS*.*1. PLDNOrN3YAw'YpVAX.!*Y$ PLOTN~4CALL PLTCCT .1.HL(~v..I,.,YA P~LOTN'6?Xhm-.1*XS*5. PLOIN43
Y~uyMIN.7~*YSPLOTN44CALL PLTCCT (.1,SA(1bC..1l.9XA9YA) PJLOTN'!5NAU-. 1*X57. PLOTN46YAzY MI N-.Y S PLOTN47
- . CALL PLTCCT (.1 .5(1)90el.,1.,AvYA) PLOTN&8
& )Aw-.iOXS*7. PLOTN4S
VAZYSMIN . PhLOTN50
CALL PLTCCT C.1.T(i)s.9..IXAYA) PLOTN~t)
Yau.ý4bYMIý&-.16YS* .501A. PLOTK-57
CALL PLTCCT (el9PEN(2)s1..O.,1A*YA) PLUl N~bA1R*..?*XS*15* POTpN51.AYAwYl01 .4 PLOYN58IiCALL PLTCC! (*2s.EAO(1)* ,qO..1XAqYA) PLOTN6bbC0131 * PLOTN59DYal. PLDTN60CALL PLTCCA (D1,DYvXPIN9XMAX9YMIhqYMA1.4) IPLOTNblDY*?.*DY PLOTN62DXu5. 0 PLOTN63XMIgNu-XPAX PLnTht,4XUA~ao. PLOTN6%CALL LAYLLA (DXDY,9'INXMA1,YMIhNYMAA,-oo-10.O,1O) PLOTNE'
DYanG. PLOThT7XMAXU-KX'IN PLOPtlbb
CALL LA9E *LA (DK.L'YXPINXMA~,YMINYMk1.10.O0.O#0 fPLOTN.70PC(9K) 3. PLOTN71
¶ P tN)wPM IDLOTK~72
CALL PLTCCD (1PR~h~)t) ~LOTIN73* RCN(N)aD. PLOTPN74
CALL PLTCCD gI9ORCNC1)*P(1)sN) PLOTN7bXAR-. lIoseloo PLOTN76YAO.POYS PLOTNYTCALL PLTCCT (.1.SCb)voav1..1AvYA) O'LOTN7bXA&-. 1*XS*9. PL0TN79YAinYS PLOTN60CALL PLTCCT (.1,5(12) ,0.*.,#XAYA) PLOT~blYAU.f*YS PLOTN82~CALL PLTCCT (.1,5(16) ,0.,1.,IAtYA) PLOTNb3
IF (NCD.GT.1) GO TO 3 PLOTtN.I4
CALL PLTCCP PLOTtNs5RE~TURN PLOTN86
3 CONTINUE PLOTNE871t4A1.PSO INCD) PLOTNbY
YMAXSO. PLOTN890O A 1n19NCD PLOTN90
IF (PPT(I)oGT.YMAX) YMAX=PPT(1) PLOTN~l4CONTINUE PLOTN92YMAXB.01*YMAX PLOYN93YbwAh3A!NT (Y4A ) * 1.0 PLOTN94YMAX=YP4AX*1 00. PLOTNgbDYw.?*YWAX PLOTN90CALL PLQTSI (3.C0,3.0.XMAX.YOAI, 1..DYTSOTPT,7,B,2) PLOTKY7
CALL PLCCSF (XS.YStUFAC) PLOT N9f.
XAm. .*XMAX- .P*X$O7. PLOTN"9AXANO. PLOTNY9EbY~wYMAAl4 ,?YS PLOTN98C
CALL PLTCCT(*2#HFAD(l) o.,1.,9XAYA) PLOTIh9bDYAR-I .V*YS PLOTNYQXAN..b*K4AI-.I*XS*IOO PLOTIUOCALL PLTCCT (.1.S(S)#0.q1.,XA9YA) PLOTl0lXAn..*XMAX-. 1eXS*9. PLOT102YAs-I .3YS PLOT103CALL PLTCCT (.1,5(12) .0*o1.,XAtYA) PLOTIOUYA&-I ,5*YS PLOT105
CALL PLTCCT (.1.5(16) .o.,1..XA9YA) PLOT10f6
V. CALL PLTCCL (l*09PSC(1),PPTC1)vNC()) P'LOT107
CALL PLTCCP PLOT 1084PETUPN P~LOT10ov
C PLOT1105 FOPd'.AT (6"t 50 a oF6.2.'i- CD>) PLOTlII
END PLOT112- '
82
SURROUTINE PLTEXP (K) *100?* b¶DIMENSION PEXY(E6O)t kEXVJ(60)o PEXvO(60)o IýXW TEXP(3)9 PLTEP~ ?
IPFXPX (4) PLTEA- 3DIMENSION IiASC(3) PLTEP 4COMMON ALk~AD9 LPS9 P0OJ9 I4HOC9 RF9 P~PHI09 0T2, SO* CK9 DA9 He U PLTEP 5QITA TEXP(1), TEXP(?)o TEXP(3) /10HEXPER!9'ENT, ICt'tI. DATA 9 ?hP,-LTEP' bDI/ PLTEIJ 7UDATA (PEXX(I)tIul99) /4.09 4.5. 5.0s 5.5, 6.0. 6.5, 7.0* 7.'.. boO/PLIEP 8tDATA (PEXVJ(1)tI:1,9) /7.01. b668. 6.35. 6.03. 5.6t'c 5.01. 4.17, 3PLTEP 9L)
DATA (PEXVOCI)9I:1,Q) /2.0509 2.069t 2.0659 290obs 2.013i, 1.9bbg 1P~LTEP'11D
DATA (PFXPX(I'tIm193) /5.btjo fh.94i. 8621/ PLTEP13i0DATA (PLXV(I)o.1.1,3) /2.,v 1.76, 1.42/ PLTE~'1*U
lorlo LTEP15
1 COUTu1COUINT.1 PLTEP1t,IF (ICDUINT.LL.1) GO TO 1 PLTEtd 7
Ms~ PLTEPIQ~
PEX~ A () S I75 LE2PEYVJ(MP4)3.13 PLTEf'21CC. TO 4 IPLTEP2i?
1 CONTINUE PLTFkV2PEXX1O0)u.P75 IPLTEP24.PEYVuJ(10)a9.13 PLTEFJ~hPEXPX (4) i.910 LEaPEXV(4,)u9.13 PLTEP27FACw.5' .7b06 PLTkuab00 2 Im1,9 P'LIEP29iFPEXX CI) PE)XX(I)+A ILt- 4PEXYCI)mPEXX(!)ý kACPLTEP31
2 CON.TINUE PLTEP3?
DO 3 1&1#3 PL TEP 33PFYI.')(I)zPE`XPX(I)#FAC PLTEP34
j PEXPXtflPF)CPEX (3)/l PLTEP3b3CONTINUE PLTLP3t,CALL PLTCCtI (2#59PEXX(1)9PEYVU(I)99) PLTE P37CALL PL7CCD (?q~qPEXPX(l)9PEXV(I)94)PLP3
'CONTINUE PLTE1139yy.9 * 'L.TEki.0
XXS. i, PLTEkm1
CALL PLTCCT (.I9TEXP(1)@0*9I1.,Z39YY) PLIEP4.2IYY~b. PLTEP4.3
C I CALL PLTCCT(.196ASC(1)90sv1@sXXsYY) PLTE P44CALL PLTCCD (?#59PEXXC1),fJEXV.J(1),tM) PLTE;046
PFTURNPLTER'bc PLTEP47
5FORPAT (15/(8~E1091)) PLTEP'.8END RLTEP'"r-
:33
SAMPLE INPUT
CANII NO$ I HEADING CARD
0 I5-'M SHAPEO CHAR(IE SAMPLE CASE
CA'D Ne 2 LINE". PAPAMETERS
ALPHA FPS HHOiJ RF H CONF TKS IHO CONF, NPLT NPOS
2 69 6 40.316S 0. 0. 0. 0 0
CApD Nn. 3 TARGET PARAMETERS
"NHOC SO CK BHN Ti UPO IT ODPI NEXP N
.8 a. O. 300. 112. 3.q3899 0. 1 100
1 . %
4,•
* 84
II' I
+~
C.,
9 w w' z QI-z
I. a0 . -,
L4 I.- i-1.- 4/ b. .,
In14 = .z 0Q
0.M 4 j 0 aCtv - 04-.
4/1 z L6
IA zA
a. 1 1a o z
m. 14 m C . I-
K 0- 0- Pc - e A .
4 ~~ ~ I r U 0 .U Q
a. LL
2. w
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N. ~ ~ ~ ~ ~ ~ ~ m Ilk %C Sp N 4 f.- 0 r) S f . . . * * * * -SS S. S S
t-
n 0, h aI
p- ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 0 4 It 0 41f n .% . i4 9 I QI
wi mW a 40 m% p 0 0 0 ý a ý 0#N a5 5 5 55 5 5 Wfs
aS %P5 14*1 21 *1 -c5 It5
SS S
- .4Om4N.Umaim -q f-amknmiinwo in n W'' WW -
.0 A n n i I Z o n & N .
.4i~o 0 -CS mop-* 1N(W7M4
0,0MP . 1% 'P-S M4 M N ,I -4 ...
6-4 g..mmgim %OF
o -u 1, -ni DP
- .ai ccp . c
ooOp a~ftN0 I~~~ to-V' t"40 ni ' 4P ,mil .a-4 M I r 0N4InOC 5 NN N
10- p- .z c 13 r- -. W~r4~ a a lW. p- ca
P. tr N 4 - -MO - 0W
4n.1 In 4. l 4. .4. 41 N. 4..4 N.4 4.4 p- In N. 4.4 f 4. 4.44 m.4 N . 4. m 44 N . 4 t. pl.4. fl. N. -J4D U. A. F- 4. # IIt*~~~~~t4)-.04-mý"Iv % ;m0 NC0NaJNa4.gN'fN 4C--k -NCO C -omto.a--Q("
CD N4- M llCC0 400a0 v-0m000000000000N- 0010, COOOOOOOOC C W 000 c0IX-M. a 0-.
0 . 00 00 C 00 C 004= 0 0C.0 0 00=C 0000 0000 0 0 0 C.000C.00 C 00 0C 0 4. 01 1 i b. . . * . .. . ... 4 *4 4 44 4.44 .. 4 4.44 4 4 4*4 4*44 4 4 4#4 4 4 4 4 .#
W w Lu Ill,44.44.4W.4Mimi4. 4...41141. UI 4..444..44Lu uJ 4. u www w W WsW J4 4 .6 w . 4 w4I4 . I 'A' .3 4 ,
ONpo - - l)Or-(10( 1 nFM0 . D9 aol m0 -t 4P . . .Mr n 1 4D "'It0-M r ,NW Q r ,t4p 0 M 4, 0 M M 0 N %0 0 0 N1 M xN AD; Ua-l ON O 40 4 N p -. rC 4 z CCC0-.V...NXM NP
r)I ¶ r - *. 4. .. *ý 444# *4 in4 . . . .-,Do
.- - - 4~ 0 C 0 00 0 00 0 OOCOOCCC00%0000000 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 00s Cc 0000000000A00 4DP pýc . .4 2 ----- -% vN zNfwI
`ý .% ."4.14.1.4 *4t~ 44. 4.4.44. . . .4iI. *4 * * ** 4 .
000 000 000 C50c 0 Q Q00CO00C30 0 0 00; Q0 00 clr,00 00c0Q0 I0Q000 Cot0CC 0 0000 ,# i +i +11 11 1 1 #I +S g+ b ., .+e e a ,. aa a ~
4 p- - 4Z N 4a4N n 40 4.4.01 MIA 04.0 4,-.a.M M M 4 .I ý4.444444 M.4M4.4.4M4N4.4IN.a.4.o.LA4M4.4.4.4.4 a )N 0NI& ) 4.
C- Cw 0 Ill 0 00 C- C. M 0 C- 000 M0 P0 0 00N 0 a 0m t C 0 D0 C . 000 m p 0 00r-P. 010 000 (v 4 p 0D0t0I C. C C- C. 004 )1 -Q CU00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
444Mll4MM 444t 44mm 4M4M4Mm 4444CI4Mm 444444Mt 4MM 44444444444 mil Me44444444444444, 0 Im
4......444444..... m44U 44 C, oc..W ..... 444444......4444444a-04.tNO~~~~~j N 0 - 0 0 - f f C 4 . 0 0 . 0 I It P O tI WI.A.W W W W
4 I 'd m, M at N b 1- & In I a N N a - ,i I-I b I I I III Ic I A, M I I 4 intm a. b ` J% la a
- 4 4 403laN0-L 4C 4 # C.4 OSf 4 44 44 0 4 NO 4 4N-O-Ig4 44 + 4 C 4~ 40
a.....................4. . . . .4 * 4 r4 P.. 444 .-I44c4W44m4...
0, - - - - - --- -o - - -- -0 P- -, -N 0-- 0 c go -7 -n -0 -, M I -S -u -W z - Q - -
00 c 1- -4 0) 0k 0 N 0m m 0L a a 0 C If00000C, 0 0 0000000
Ii ~N-.4 N- .9 4-. It-4 N4 It40 M .AAO n.CA m M m m, 4 4j .4 WC.4 4 -4 -4 .L0 -4 1 -
CL. . . . . .. . .**T 44.. . . 4 4~ +44 4 * * . *4 4 4 +4 4
It444444444 44444444*4# 4 4 + 4 4 4
000000& 000000 00L v-)( )4 l - DI ,U10MI D000 0 00 00 4 CC I .z l AI
0 0N 0 - 0N 0~tO ~ It M. X. CS .tl CY 0 1-1 NV M 4 4 it. If) MC 6r 19 14 -D I z f Lit X I 4 W 4 .r M. II IN ,.C C 01 CL a.- C X.5 4 M5.N. -1' 9
0 0 c0 00 0 00 0 0 0Zc 0 0 0 C 00l C 00 0 0 0 CD 00 00 0 0 CC CC 0 0, 0 0 Cp 0 c aCC 0 00 0c 0 0 0mc 0 0Q 4# 40 + 4 4 4 # 4 + 4 4 4 4 +4 4 4 4 4 4 4 4 +4 4 4 4 4 ++ 4 4
Nw m5. -p S r 0 a 1 0' m .a a Ir . N '4 4 C, N P. -IT C 01 W N a) ' M C.a - C 4 oit u- 0. .4 es es Ll -; N m m 0 0'LI4 U.. . .. 4 . . . 444 444 444 44. 444 444 44
C ~ ~ ~ I 0 In x c 00 0. 00 (3. 00 C0 0r M 0 -, CC00 0 0- 00 U, 0 00 00l 0N 00 00 00LAe 1111 a i all 4 a4 ra) MI at) ag a n a Ma C', (V I N ii a sea ii bl 1
4. 4.3 .4 4 .L. 4 .4 . .4 .4.4 .4 4 .4 . .4 .. .44 . .44 . .4 .4.4 .44.4 .44.4 3 . .4 . Z.4 .4
C! .cZ511v000c00 0 0 QC, ID0 C, n 0000 0000 C,0 0 C)a0 C,(D Ca C.O C0 =0 0 T T4 4 * 4 4 1444 4 4 4 + 4 +4, 4 4 4 4 4 # 4 4 44+ 4 4 4 4 4 4 4 4 4444 + 44 4 4 4 44 4 44 4
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0.00000 0.00000 v56,2f3p'9 2.0on00U
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SUMMARY OF RESULTS
INFWIm4 HS m IS8,9 11MA *11 HF ASS U 122.94%72 0' SLUG MASS ~~.I?
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IOTAL .JFT KINFT7C ENE4GY a 6*?213 ERGS*1.Or1?
TOTAL JFT K1NtUIC ENEiNUY APOVE JET VELOtIVV .2- MME FcS1O
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96
"-aW
UI. M
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12 Commander 1 DirectorDefense Technical Info Center US Army ARRADCOMATTN: DDC-DDA Benet Weapons Laboratory
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1 Commander 3 CommanderUS Army Missile Command Naval Surface Weapons Center
ATTN: Mr. W. Zecher ATTN: DG-50Redstone Arsenal, AL 35809 Mr. S. Griscavage
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"Tech Lib Code 3835, R. Sewell
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1 Director I CommanderUS Army TRADOC Systems Naval Research Laboratory
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