7 II

AD-AO11 259

FORGES ON A SABOT IN THE GUN BORE--A

COMPUTER-AIDED DESIGN TOOL

N. Pudliener, et al

Picatinny ArsenalDover, New Jersey

March 1975

DISTRIBUTED BY:

National Technical Information ServiceU. S. DEPARTMENT OF COMMERCE

06

1'83 017

-WA

0 COPY NO. -4

TECHNICAL REPORT 4734

FORCES ON A SABOT IN THE GUN BORE-.

A COMPUTER-AIDED DESIGN TOOL

N. PUDUENERE. BARRIERES

MARCH 1975

II

II I

APPROVED FOR PUBUC RELEASE; DISTRIBUTION UNLIMITED.4

Iteptod~ced by

NATIONAL TECHNICALINFORMATION SERVICE "

U S eplttfn'fl If Cm'"Spingf eld VA 2.151 - L .

-- APICATINNY ARSENAL

DOVER. NEW JERSEY

-.-. .

IINCIASSIFIMrSECURITY CLASSIFICATION Of THIS PACE if NPAE Dae ZntoTO0

REPORT DOCMENTATION PAGE BEFORE COMPLETING FORM1. REPORT NLU'SBER 2. GOVT ACCESSION NOj 3. RECIPIENT'S CATALOG NUMBER

Technical Report 4734 |4. TITLE (Atd Subttlie) S. TYPE Or REPORT & PERIOD COVERED

FORCES ON A SABOT IN TIHE GUN BORE __

COMPUTER AIDED DFSIGN TOOL 6 PERFORMING ORG. REPORT NUMBER

7 AUTHOR(fe) . CONTRACT OR GRANT NUMBERa*)

N. Pudliener, E. Barrieres I

S. PERFORMING ORGANIIATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASK

Ammunition Development & Engineering Dir AREA A WORK UNIT NUMBERS

Picatinny ArsenalDover, New Jersey 07801 _ i

I R. COROLLING OFFICE NAME AND ADORESS I 12. REPORT DATE

ifarch 197513 NMF0 OF PACES

M4. MONITORING AGENCY NAME A ADDRESS(If different from Cntrolh Office) 'l. SEC-T CLASS. (el tIe iepo1t)

UnclassifiedIS& OECL ASSIFICATION/DOWNGRADING

SCHEDULE

16. DISTRIBUTION STATEMENT (o. f,0 Ropwe)

Approved for public release; distribution unlimited.

17. DISTRIBUTION S7 ATEMENT (of the abetract entered In Brock 20, If different Itor Report)

18. SUPPLEMENTARY NOTES

It. KEY WORDS (Contime an rto-eta. de* If necoeoy amd Identify by block rnmber)

Sabot CALCOMIP 570 Digital r" ,tter

In-bore environment NANCY Digital PrirLComputer-aided designFortran IV

20. ABSTRACT lConthrie an *ma.e efde If n.ce*Wy mad IderIty by lock besb*)

This report describes a computer program which computes the static loadsand moments .)r a sabot segment while under the in-bore environment Thephysical characteristics of the sabot segments are also computed. Addition-ally, from the input data, a tape is prepared by the CDC 6500 computer fordrawing sabot cross sections on the CALCOMP ;70 Digital Plotter, :ogetherwith a 'XANCY Digital Printer Plct. The program is intended as another toolin the Computer Ai ' ;ign - Engineer (CAD-Ei) armory.

DO 1JANj 12 1473 EDTIon or 1 mov45 IS OBSOLETE

ISECURITy CLASSIFICATIOI OF I0iS PAGE (•mS IWOI E*con)

TABLE OF CONTENTS

Page No.

Introduction I

General Instructions 1

Scope Control Cards Used in '.his Program 5

Input Data Cards 5

Equations 7

Identification of Symbols 8

Fortran Listing 11

References 20

Appendix (Sample Case) 21

Distribution List 34

Figures

I Geometry of saoot cross section 9

2 Sabot cross section 22

3 Input data car-.s format 23

4 Computer output 26

S NANCY printer plot of sabot cross section 30

6 CALCOMP digital plot of sabot cross section 31

2;

I

INTRODUCTION

The program described in this report is intended as a design aidto give the engineer a tool to establish the statit loads and momentson a sabot segment while under the in-bore environment. The physicalcharacteristics of the sabot segments are also computed. Addition-ally, from the input data, a tape is prepared by the CDC 6500 corn-puter for drawing sabot cross sections on the CALCOMP 570 digitalplotter, together with a NANCY digital printer plot.

The computation scheme is capable of ha.ndling multiple componentsof differing densities, but the forces and moments are treated asthough the entire sabot is a single rigid body. The user must des-cribe the cross section of the segment, and predetermine the mannerin which the pressure is distriouted over the surface of the sabot.Also, the weight and first moments are computed utilizing signed(4 & -) densities to describe the geometry. Tht geometry must be a

body of revolution.

GENERAL INSTRUCTIONS

"Tis sabot program, written in Fortran IV, consists of two sepa-rate sub-programs, each having its own input. The first sub-program,occurring in the program listing, computes overturning force momentson the sabot as a function of propellant pressure acting on externalsabot surfaces, such as the sabot base and loading of rear supportand obturation ring, etc. The remaining sub-program computes over-turning moments as a sole function of propellant pressure actingbetween internal sabot parting surfaces.

Instructions pertaining to each of these sub-programs are givenin succeeding paragraphs.

With regard to the first sub-program, a physical description isaccomplished by dividing the cross section of the sabot into elements,each element being originated at an inflection point in the geometry.Each component is broken down separately into these elements, whichare entered as data in x and y coordinates in an ordered sequencefollowing the contour of the components in a clockwise direction. 1The order is significant to maintain a system to ascertain the direc-tion of the pressure force vector. It is also necessary to intro-duce signed densities to distinguish a "forward surface" and a"rear surface". A zero density "end point" for components is also

!This portion of the program was written to accept a maximum of7S sets of coordinates.

used to delineate separate components. An example of a two-componentsabot divided into elements is shown in Figure 2, page 22. The data

are shown in tabular foim on page 3. Note that the concept of thenegative density is associated with a "rear surface," and that eachsurface is described in the element number which originates thatsurface.

The clockwise flow of data refers to the overall direction aroundthe component and not the direction of a point tracing an individualline; points 17 through 28 are ordered by the overall direction aroundthe sabot body, though the surface is curved, such that a point trac-ing the curve progresses in a clockwise direction. The final endpoint is entered separately, and should be the same as the first pointof the final component in order to establish a closed figure. Thisseparate entry serves the same purpose as the artificial "zero den-sity" points entered within the body of the data.

A moment center is also entered with x and y coordinates. Thispoint is chosen as the point of restraining force, usually locatedon the projectile. This moment center is the "hinge point': of asegmented ring-type sabot. Since this point will offset the resultsof the moment balance, it must be chosen with care in order to ac-curately represent the actual conditions. Also, it should be notedthat this moment center is a single point on a three-dimensionalfigure. Care must be exercised to allow for curvature in selectionof the moment center. In some geometrical construction the rotationmay occur about a shifting line of multiple points.

A radius, with the x and y coordinates of the radius center, isincluded for segments which are curved following the inflection point.These values are entered as zeros for straight line segments. !henext data item is the density, entered as positive for a forward sur-face and negative for a rear surface (a rear surface faces the X = 0coordinate). The next two entries describe the pressure field towhich the surface following the inflection point is exposed. Thefirst of these (PV) is a factor ',v which the chamber pressure (en-tered later) will be multiplied to gi' the pressure to which thesurface is exposed (usually 1.0 or O.u,. The second code (LP)chooses two options in depicting the pressure distribution on thesurface. A code of I denotes a constant pressure equal to the chamberpressure times the pressure factor. A code of 2 will distribute thepressure in a linear manner between the pressure given by this entryand the pressure given for the next point.

2

N x y R XR YR D_ a_ PV IP

1. 0.0000 .6670 0.0000 0.0000 0.0000 -. 1010 1. 1

2 0.0000 .8290 0.0000 0.0000 0.0000 -. 1010 1. 1

3 1.0070 1.0150 0.0000 0.0000 0.0000 -. 1Mo 1. 1

4 1.0070 1.4200 0.0000 0.0000 0.000 -.1010 1. 1

5 0.0000 1.688o 0.0000 0.0000 0.0000 -. 10o1 1. 1

6 0.0000 1.9700 0.0000 0.0000 0.0000 -. 1,oo 1. 1

7 .6220 2.0500 0.0000 0.0000 0.0000 -.1010 1. 1

8 .9700 2.0500 0.0000 0.0000 0.0000 .100O 1. 1

9 .9700 1.8760 0.0000 0.0000 O.,,00 0.0000 1. 1

10 1.0000 1.8760 0.0000 0.0000 0.0000 -. 0470 0. 1

1l 1.0000 2.1000 0.0030 0.0000 0.0000 -. o47o 0. 1

12 1.7350 2.1000 0.000o 0.0000 0.000o .0470 0. 1

13 1.7350 1.8760 0.0000 0.0000 0.0o00 .0470 0. 1

14 1.0000 1.876o 0.0000 0.0000 0.0000 0.0000 0. 1

15 .9700 1.8760 0.0000 0.0000 o.o0oo .1O10 1. 2

16 1.7350 1.8760 0.0000 0.0000 0.0000 -. 1010 0. 1

17 1.7350 2.0500 0.0000 0.0000 0.0000 .1010 0. 1

18 2.3780 2.0500 0.0000 0.0000 0.0000 .1010 0. 1

19 2.3780 1.9000 .3100 2.3780 1o5900 .10J0 0. 1

20 2.0680 1.5900 .3100 2.3780 1.5900 .10O 0. 1

21 2.3780 1.2800 0.0000 0.0000 0.0000 .1010 0. 1

22 5.7000 1.2800 "0000 5.7000 4.2800 -. 1010 0. 1

23 7.5740 2.0500 0.0000 0.0000 0.0000 .100o 0. 1

24 8.3240 2.0500 0.0000 0o0000 0.0000 .1o0o 0. 1

25 8.3240 1.6500 O.0o00 0.0000 0.0000 .1010 0. 1

26 7.7800 1.6500 0.0000 0.0000 0.0000 .I010 0. 1

27 6.2850 .8010 0.0000 0.0000 0.0000 .1010 0. 1

28 6.2850 .6670 OC.000 O.O000 0.0000 1010 O0. 1

There must be one card for each inflection point in this portionof the deck. The next set of two cards enters the moment centersand the end points on one card and the number of segments, the chamberpressure (psi), the spin (rev/sec), a code to determine the output,and up to 60 characters of notes or desrriptive information to beincluded in the -:rintout. An output code of "0"t will print all datapoints, "1" will print the input and pressure distribution, 1121" willprint only the forces and moments. These last two cards must appearas a set for each run to be conducted.

The following paragraph pertains to input instructions for thefinal portion of this program. A physical description of the in-ternal gas-pressurized area (defined by obturation zones) betweensabot parting surfaces is accomplished in a manner similar to thatdescribed aboie. The bounded planar area is broken down into ele-ments, each element being originated at an inflection point in thegeometry. Each element is entered as data in S and T coordinates inan ordered sequence following the boundary of the gas-pressurizedarea. 2 The final end point is the same as the first point entered tocomplete the closed figure. Therefore, no separate entry is neededfor the end point. There is no moment center entry, as the oneentered in X and Y coordinates in the first portion of this programis used.

Data organization of batch processing a job requires a data carddeck in a format similar to that shown on Figure 3, page 23. Multipleruns are possible on the same configuration. For instance, severalsets of ballistic conditions may be run, or the moment center may bevaried, or both of these may be combined. The initial card initiatesreading by giving the number of runs and the number of inflection

points in the main data. This is followed by the data cards whichdescribe the cross sectional geometry by giving the X and Y coordi-nates of each inflection point. This, in turn, is followed by datacards which describe the planar area geometry by giving the S and Tcoordinates of each inriection point. Finally, a set of two cardsis provided for each of the respective program runs. These cardsgive moment centers and descriptive text. An example of data cardsgiving four program runs is shown in Sample Case Figure 3 on page 23.

2This portion of the program was written to accept a maximum of20 sets of coordinates.

4

% !

ISCOPE CONTROL CA.ADS USED IN THIS PROGRAM

The L'oalowing control cards are used to call NANCY print plotand CALC' ' plot subroutines from permanent files stored in PicatinnyA'•,enal's CDC 6600 system (Ref 1, 2 and 31,:

Job,. ..

Request, Tape 77, NT, S. Plotape - your nameAttach k'NAN, NANCY, CY=2, SD=16, MR=l, ID=RANDERS)'-)ad (NAN)I. (Your program)

is a Fortra: deck which writes a printer plot on Tape 6 anda %-":"MP plot on Tape 77. The plot routines (Ref 1) also requirethaL UUTPUT be included on the program card. Memory required to loadis about 20,000 (octal) CfP cells.

INPUT DATA CARDS

1st Card: Header card (only fixed point entries on this card)

Column 1, number of computer runs

Columns 2 and 3, nunber of "inflection points" aboutcross section

Columns 4 and 5, number of "inflection points"about pressurized plan; area ofsabot parting planes.

2nd Group: Elements of sabot crcs section (floating point exceptfor Column 40 fixed point entry)

Columns 1-6, X coordi'ate of cross section

Columns 7-12, Y coordinate of cross section

.:olumns 13-18, length of radius of curvature

\S

N

Columns 19-?4, X coordinate of radius of curvatureorigin

Columns 25-30, Y coordinate of radius of curvature

origin

Columns 31-36, density

Columns 37 39, pressure

Column 40, pressure code

3rd Group: EI-n-ents of pr:essurized planar surface on sabotpa-pt.rti, planes (floating point entries)

Columns 1-b, S coordinate of planar surface element

Columns 7-i2, T coordinate of planar surface element

Columns 13-18, radius of curvature magnitude

Columns 19-24, S coordinate of radius of curvature ¶

origin

Columns 25-30, T coordinate of radius of curvatureorigin

4th Card: Sabot segment moment center and end points for crosssection (floating point entries)

Columns 1-6, X coordinate of moment center

Columns 7-12, Y coordinate of moment center

Columns 13-18, X coordinate of end point

Columns 19-24, Y coordinate of end point

5th Card: Sabot data input and data callout (floating pointexcept for Column 21 fixed point entry)

Columns 1-2, number of sabot segments

Columns 3-8, propellant pressure (psi)

Columns 9-12, diameter of ;aboted round (mm)

6

Columns 13-16, weight of subprojectile (lb)

Columns 17-20, spin of round (rev/sec)

Column 21, If "0" prints all data points

If "1" prints input and prozsure distribution

If '2' prints only forces and moments

Columns 22-71, Data statement such as, "sabot test formoment about front edge"

EQUATIONS

The following equations are used in this program:

The area of the trapezoidal element a, b, c, d (Fig 1) is:

AREA = - [ 2Y(n) sin (DB) + 2 Y(n+l) sin (D6)Ix [1Y(n) - Y(n+l) +

Ix (n) - X(n+l)I ]

The centroid location in the x-direction of the trapezoidalelement (Fig 1) is:XCENT = [X(n) - X(n+l) lx [2 Y(n) sin (DB) + 4Y(n+l) sin (DB)I/

3[2Y sin (DB) + 2Y sin (DB)] + X-(n) (n+J) si(DBn+ l

for case of Y Y(n) (n+l)

The weight -f the prism element formed by the "AREA" multipliedby the rectangle element e, f, g, h (Fig 1) is

i [Y~(n) " (n4l{x(XETW• = p x AREA x cos arc tan (XCENT)

p is density

7

fF

The pressure forces acting on the trapezoidal element (Fig 1),along X and Y directions, are

F = AREA x PS x cos 0

Fy = AREA x PS x sin 0

PS is pressure vector.

IDENTIFICATION OF SYMBOLS

BETAR Angle in radians between parting sabot planesN Number of inflection points about sabot cross sectionNJAY End inflection point around sabot cross section to

close loopNN Number of inflection points about pressurized zone

of sabot parting surfaceNNIJAY End inflection point around pressurized zone of

sabot planar parting surfaceNRUN Number of computer runsP(K) Pressure factorXCENhr Centroid in X-directionX(K,J) X coordinates for inflection points about sabot

cross sectionS(K,J) S coordinate for inflection points about pressurized

zone on parting planesTHETA(K,J) Angle between the horizontal and any pressure vector

T(K,J) T coordinates for inflection points about pressurizedzone on parting planes

YCENT Centroid in Y directionY(K,J) Y coordinates for inflection points about sabot

cross sectionYVAR Dummy iategration variable

8

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1 REFERENCES

.. I.E. Rucker, Instructions for Using IBM 709 Plotting Subroutines,April 1964.

2. Glen Randers-Pehrson, "NANCY" A Digital Plotting Routine,Picatinny Arsenal Technical Memorandum ESD IR 468, August 1971.

3. 1. E. Rucker, Plotting Routines, Picatinny Arsenal Information

Report NR 73-6, February 1973.

I20

20

APPENDIX

SAMPLE CASE

The following example 3hould give the user a good idea of inputformat and the usual output from this program.

This sample case is illustrated by a drawing of the cabot sec-tion (Fig 2) with points of inflection shown. This Is followed bycoding sheets (Fig 3) for its input and a listing of all its output(Fig 4). Finally, the NANICY printer plot (Fig 5) and CALCOMP digitalplot (Fig 6) are included as they would appear as part of the com-plete data printout.

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-SABOT CONFIGURATIONx Y R XR YR DENSITY

0,0000 .6670 0.,0000 0.0000 0.0000 -. 10100.0000 08290 0.0000 0.0000 0.0000 -,1010

______0__0__ * 0* 0 _ 00 -.10101.0070 1.4200 0.0000 .0000 0.o000 o.10

_ " 00oo7 t6880 0.oo0_0.oo00 0.0000 -.10100.0000 1.9700 0. 0000 0.0000 .0000 -1010

.6220 2.0500 0.0000 0.0000 0.0000 -. 1010

.9700 2.0500 0.0000 0.0000 0.0000 $1416#_97.Q1801A76.0.._9.000 0_.0000 0.0000 0.0000

1.0000 1.8760 0.0000 0.0000 0.0000 -. 0470,. o0 -,.o47-

1.7350 2.1000 0.0000 0.0000 0.0000 *04701.7350 1.8760 0.0000 0.0000 0.0000 s04701.0000 1.8760 0.0000 0.0000 0.0000 0*0000__C.9700 1A0860 0AjA0.!_0AA000 0.0000 010101.7350 1.8760 0.0000 000000 .0, -0-101.73S0 2.0500 0.0000 0.0000 000000 *10102.3780 2.0500 0.0000 040000 0.000 .1010203780 1.9000 .3100 2.3780 1.5900 .1010230680 1.5900 .3100 203780 1.5900 010102_ 3780 1 028 ..00ooo00 0.000 0.0000 .10105,7000 1.2800 3.0000 S.7000 4.2800 -. 10102-r.740 2- SOO ODJ 0.J)0000 0..a OM 1010

8.3240 2.0500 0,0000 00000 60.0000 0 10108,3240 1h6500 0.0000 0.0000 0400.' .10107.7600 106500 0.0000 00000 0.000 010106.2850 .8010 0.0000 0.0000 0.0000 .1010

6.2850 .6670 010000 0000--- 0- 0 -- TE"X NON CENT Y NON CENT X END POINT V ENr POINT

6.2850 .6610 0.0000 -6670

PRESSURE VALUES

PRESS CODE

2 60000.00 0003 60000.00 0.004 60000.00 0.00

6 6000090t 000

8 60000.00 0.009 60000.00 0.0010 0.00 0.00

-+i 1 .. . _0.000 .. 0._0_0+ .. ..

12 0000 0.0013 0.00 000014 0.00 0.00is 60000000 0000[ 16' 0.00 0o00S_~~~17_ . t0 .. .. 0*00 ... .. . ... . . . . .

18 0,00 0000-19 0.0020 0000 0.0021 0.00 06.022 0.00 000023 0.00.. 0.0024 0000 0.00-2S_ 0000 0.26 0.00 0.0027 0.00 0.0028 0*00 0.00.

Fig 4 (Continued)

30

IPA

S T_ - AMON ACUM

S1 .00000 1h6880 -000000 0.0 0.0000-1 2 0.0400 1*7162 0.0000 0.00000 0.00001 3 0.0000 1.7444 -0.00000 0,000 ""000

_I 4 0.0000 1.7726 -0.0000 0.0000 0.000015 0.0000 1.6008 -s0.0O0 .0•060 0.00001 6 0.0000 168290 -000000 000000 00000

.1 7 00000 1.82 -00000 00000 0.0000

Sa 0.0000 10854 -0.0000 0.0000 0000001 9 0.0000 1.9135 -000000 000000 0.0000

-l.i 0.0000 109418 -000000 0.0000 0.00002 1 0:0000 1.9700 -0000 - .0000 -. 00022 3 .1244 1.9860 . 0012 -. 0001 -.nU22

2 4 91866 1.9940 -. 0017 -. 0002 -. 00402 S .2458 240020 -. 0022 -. 0003 -. 0062$_______ 111 _ 200100 -. 0027 -. 0005 -. 0090

2 7 .3732 2.010 . .0032 .-. 0067 . .. 0122._______5,___3___ 2.0260 -. 0037 -. 0009 -,0159

2 9 .4976 2003 40 0002 - -00i1 0.0202210 .5598 2#0420 -. 0047 -. 0014 -002493 1 .6220 2.0500 -000000 000000 -002493 2 . ,059-0- . . -O-OPIL 0.0000 -. 02493 3 .6876 200500 -0.0000 000000 -02-"A.- 4-... .500. -000000 ....... 0o000_ -.. . 0249.3 5 .7532 200500 -000000 000000 -. 02493 6 .706002l00 -0000 0.0000 -*02493 7 .6'188 2.0500 -0 0 00000 -0249-

3 8 .8516 200500 -0,0000 0.0000 -. 02493 9 -. 6844 . . 0S00+- -0.0e00 0.0000 -. 0249'3092. 200500.. -000000 0,O0O0 -*0249

4 1 . 9.00 200S00 . 0564 . .0268 .. . 6"4 2 :Soo 1.9906 00564 .0268 008604 3 .9500 1.9312 00564 .0268 .14444 4 9500__1.8718 o0S64 .0268 0200845 .09500 1..124 .0564 - 0268 .. . 2S73

* 6 .9500 1.7530 0564 :0268 .313747 .9500 ?..6936 .0564 . 00268 . .. 3761-4 8 .9560 1.6342 .0564 e0268 .42664 9 09500 1.5746 00564 .0268 ,4830410. ,9500 lo15154 *0564 .0268 S53945 1 .9. 0- ....... 1.4S60 -. 0209 -;o0094 .. 1655 2 -. 05S0 1.4792 -*.0187 -. OOt6 .4997S ; .7600 1.5024 -. 016S - -. 00S9 - .48325 4 .6650 1.5256 -. 0143 -. 0044 .46895 5 05700 1.5408 10121 -,-"3z 04585 6 ... ..94?5k 105720 .. -.. 0099 - -. 0021 .4469s 7 .3800 1.5952 -,0017 -. 0013 04391+S 5 02850 1.6184 -*0oss -00007 ,4336S 9 .1900 1.6416 -e0033 -. 0002 .4303510 .0950 1.6648 -00011 -. 0000 04292

Fig 4 (Continued)

31

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