ad~-a14 6`91llcuad~-a14 6`91llcu technical report brl--tr-2892 1938 - serving the army for fifty...

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AD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS FRANZ R.T LYNN DTIC MARCH 1988 MY1 8 SH A-- APPROVED FOIL PUBLIC RELEASE; DISTRIBUTION UNLIMITED. U.S. ARMY LABORATORY COMMAND BALLISTIC RESEARCH LABORATORY ABERDEEN PROVING GROUND, MARYLAND I 8 5 09 144 S,,' .. . . . • •,:,.€ ' . '.',,',¢ .•' .:, ,t'.:,K,.•,'•'..-'•: . :.'•..:....... ,.. -•..v,. : _ ."••;': .5r-,• ': .- ;• .,,'...t.r_, ._:: ,:_.o-¢",,'.',.. &,-,.,.X,_ '' ... '• • •"•."' " " 2

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Page 1: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

AD~-A14 6`91LLCu

TECHNICAL REPORT BRL--TR-2892

1938 - Serving the Army for Fifty Years - 1983

ANALYTIC SOLUTIONS TO THE CLO'SED BOMB

FREDERICK W. ROBBINSFRANZ R.T LYNN

DTIC

MARCH 1988 MY1 8SH

A--

APPROVED FOIL PUBLIC RELEASE; DISTRIBUTION UNLIMITED.

U.S. ARMY LABORATORY COMMAND

BALLISTIC RESEARCH LABORATORY

ABERDEEN PROVING GROUND, MARYLAND I8 5 09 144

S,,' .. .. .• •,:,.€ ' . '.',,',¢ .•' .:, ,t'.:,K,.•,'•'..-'•: . :.'•..:......• . ,.. -•..v,. : _ ."••;': .5r-,• ': .- ;• .,,'...t.r_, ._:: ,:_.o-¢",,'.',.. &,-,.,.X,_ '' ... '• • •"•."' " " 2

Page 2: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

UNCLASSIFIED 111-0.419-116 91SECURITY CLASSIFICATION O-F FHIS `PAGE

REPOT DCUMNTATON AGEForm ApprovedREPOR UOICMENTTION AGE MB No. 0704 01788

1 a. REPORT SECURITY CLASSIFICATION 1b RESTRICTIVE MARKINGS

Unclassified____________________

2a. SECURITY CLASSIFICATION AUTHORITY 3 DISTRIBUTION /AVAILABILITY OF REPORT

2b. DECLASSIFICATION / DOWNGRADING SCH EDULE

4. PERFORMING ORGANIZATION REPORT NUMBER(S) S. MONITORING ORGANIZATION REPORT NUMBER(S)

BRL-TR-2 892

6&. NAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATION(if applicable)

SLCISR-lJB-A

6C. ADDRESS (City, State, and ZIP Code) 7b. ADDRESS (City, State, and ZIP Code) %

Aberdeen P1roving Ground, MD 21005-5066

8.. NAME OF FUNDING/ISPONSORING 8b. OFFICE SYMBOL 9. PROCUREMENT INSTRUMENT IDENTIFICATION NUMBERORGANIZATION j(if applicable)

8c. ADDRESS (City, State, and ZIP Code) 10l 1,01-IRCEF C fUNDING NUMBERS71ROGRAM PROJECT ITASK WORK UNITEL.MI-Nr NIo NO. NO. ACCESSION NO.

62 6 1.8A 1i1,1 62hlB8AIlB)

11. TITLE (include Security Classification)

Analytic Solutions to the Closed Boil)b

12. PERSONAL AUTHOR(S)

Frederick W. Robb ins in(, Frauxz R. L~ynn13a. TYPE OF REPORT 13b. TIME COVERED 114. DATE OF- REPORT (Year, Month, Da, PAGECON

T chni canl Repor - FROM 1 985 TO __1986 19bB Marire16. SUPPLEMENTARY NOTATION

17. ABSTRACT 1 SBJCTTEM (Continue on reverse if necessary and identify by block n.umber)

CELos GROUPl SU-G; u Lii arci ru Cc yIer osei to s tet Ir ,e Bte 1n i nea, rt bL re Lgr~ n

1i9roe Of ant, fo iI ye Lo bai li ;i tic 1~ it t (;Iwr )on ,1 :;yn Ile £I,: i z)(~~l rc li rat'

19.en ABTAT(onstcxtiu on reverse ifncssr andnienotif yelc surns i ty f leoL:1 na1a1gr hnL

prov1d 1 prdc os o oI lgtl ir isorms tof des Lengie t r:; livir burning 110'lnie of'it'

evte Od tile C~ .JANNA-so) ared routnlmy oi nc iel10d ~lt1((0Wl~ cn n;i

sotflid propel l aL- fort Ln(111 o 1(1 col~li!tr I (l rLellde; Goelwrtioinv 11(01 Vy~I)VtL tolfiI llt~lQl

srobi 0111Clos yted V ~;cioeessel firrt'gL; Ls one. (' v tldta e lb m ifew hurdn ;It( r c'ccantol Ia nLbest

ofxtenslIl~.ions Lo exitig Liioels, all.-,;s owe tWsio enoiltin ity of unci llL(1110n[1W a (11 gcol n11i top1

perfornited Ir~ui ns. SUVell :Iljebrlti c forinulai ! arc, der ivedl wh11ichi Ierill ii manIy tI~)~

C~zl -it 1;tl[ia oitl o f the p~renssure , tlep fli b rifi(d , 1111100 1)11111(0 , theit'ir re!iloe( i Ivi, dccri valI iv(,, :1101

ins~ataccneous1 -itrf actc area which i (II tielt be( Il1tsd (15 input11 to 8i hriiro I3, ralt relille ionII

201. DISTRIBUTION/IAVAILABILITY OF ABSTRACT 121 ABSTRACI SECURITY CLASSIFICATION

C] UNCLASSIFIED/UNLI-MITEI D I SAME AS RPT DIIIC USERS I Pot I ;;i I lced22a. NAME OF RESPONSIBLE INDIVIDUAL 22 ILPOL(nclude Area' ode) 22c. OFFICE SYMBOI

F-rederhck W. Robbinls (101 ))-/8-0201 511>1W- lI t-A

DD Form 1473, JUN 86 Previous editions are obsolete _____ RII CLSIFCTINOFSPG

Page 3: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

"• ~~program. The first assumes the covolume equals the reciprocal of the density; thle second "

S~~removes this restriction, , •

S.%

" A I

S ,•

'S='

-'S

.,9

.i

.A.

.. 4

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Page 4: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

ry•'y.•nY,-Vrt-sr dMA• MA. ., MA JLt ,NXNL W P. N ¶r,. p.--. .'• \.N'C• -•" S. C " • F W* -• - I -- - ,. a

TABLE OF CONTENTS

Page

1. INTRODUCTION ..................................................... 5

I . GLOSSARY OF SYMBOLS ........ ..................................... 5

III. ASSUMPTIONS ....................................................... 6

IV. ANALYSIS ......................................................... 7

V. FIRST SOLUTI('N: RESTRICTION ON THE COVOLUME ..................... .10

VI. SECOND SOLUTION: THE GENERAL COVOLUME ........................... 12

VII. VALIDATION CHECK OF THE GENERAL COVOLUME ANALYSIS .................. 14

"REFERENCES ....................................................... 15

AIAPPENDIX A FORTRAN LISTING OF BOTH ANALYSES AND A TEST

COMPUTER RUN OF GENERAL COVOLUME ANALYSIS .............. 17

APPENDIX B AN IBH1VG2 COMPUTER RUN TO COMPARE TO THE TESTCOMPUTER RUN ........................................ 53

IS) [S RIBUT ION LISTT ................................................ 85

.'" 4

)pAccession For

1NTIS GRA&IDTIC TAB ."

-Distribut ion/ _. .

Availability Codes

Avail ;iand/or?, D~~ist[ | Speoial,•

F- U CdC .. . .r . . - - - • , • • • • . • - - . - • • - - , , , . , • • . . . . - - , > • - - • , • . . , 4 - • • w • • - . - - t •f

Page 5: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

Id'VVW V.P. .~ .r.rvr .dd1~ .p1~J . . ' . . . . . . -. .....

I. INTRODUCTION

Closed vessel tests are routinely performed to determine the linearburning rates of solid propellant far inLerior ballistic studies. Thereare several established techniquesll ,34 5 for calculating burning ratesfrom the experimentally recorded pressure-time data together with relevantproperties of the test sample, igniter, and pressure vessel.

Generation of synthetic pressure traces to simulate closed vesselfirings is done to validate new burning rate reduction programs, testextensions to existing models, assess the sensitivity of computationalalgorithms to different methods of smoothing and differentiating thefundamental pressure data, and provide predictions for guiding thedecisions of test engineers. These needs became acuely evident in the

JANNAF-sponsored round robin on closed bomb methods when some easilycommunicated validation and comparison procedure would have been veryuseful.

The usual procedure1,7 is the numerical integration of a burning ratelaw to yield the depth burned into the individual propellant grains of a

charge with specified thermodynamic properties. The grain geometrydetermines burning surface area implying the mass-generation rate of

combustion gases, which is in turn integrated. Once the mass of evolvedgas is known, the energy equation and gas law yield the gas temperature andpressure at that instant. If P is required, it may either be foundanalytically from the gas law and energy equation or via numericaldifferentiation of the pressure.

Alternatively, the general problem of synthesizing closed vesselpressure data can be simplified by means of a number of assumptions whichthen allow two closed-form finita solutions for a charge of single-

perforated grains as detailed below. Seven algebraic formulas are derivedwhich permit easy computer calculation of the pressure, depth burned, massburned, their respective derivatives, and instantaneous surface area which

can then be used as input to a burning rate reduction program. The firstassumes the covolume equals the reciprocal of the density; the secondremoves this restriction.

1I. GLOSSARY OF SYMBOLS

a constant grouping

b constant grouping

c constant grouping

d initial perforation diameter of propellant grain

D initial outer diameter of propellant grain

f constant grouping

g constant grouping

11 energy loss proportionality constant

k constant grouping

5•, sorJr f. S. .r,¶J .. , ' ,nr ~-. '.M.S- .ta It ~ -. 1~I

Page 6: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

L initial length of propellant grain

ma mass of air r.

mi mass of igniter

m mass of propellant burned at time t

Soriginal mass propellant

m mass-generation rate of propellant gases at time tp- -

M molecular weight of igniter and propellant gases

P gas pressure at time t

Pact actual maximum pressure with energy loss

Ptheo theoretical maximum pressure with no energy loss

P time-rate-of-change of pressure at time t

R universal gas constant

S burning surfac, area of the charge

t elapsed time from ignition

T flame temperature of propellant, igniter gases, and air

T gas temperature

V(x) volume of each propellant grain at distancie burned x

Vb volume of empty bomb

Vfree free volume for combustion gases

x depth burned into each grain at time t

-eXL depth burned at grain extinction

Sx linear burning rate at time t

exponent in burning ratv. law

coefficient in burning rate law

SII covolume of propellant and igniter gases

density of solid propellint

lIII. ASSUMPTIONSI l

A number of simplifying assumptions are made in order to render ananalytic solution possible for a closed-form calculation. The propellantis taken to possess constant density, flame temperature, molecular weight,and covolume. The igniter material and air, if present, have the samemolecular weight, flame temperature, heat capacity, and covolume as thepropellant during combustion. Energy loss is considerod as beingproportional to the mass of propellant burned. The combustion gases are N'

completely mixed, producing a uniform prc.ssure and tpmporature throughoutthe bomb at all times related by the Nobl-Abel equation of state. Thcpropellant grains are identical single-perforated cylinders al I thesurfaces o[ which are ignited at t 0 and burn uniformly thereafter

6

Page 7: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

according to the linear burning rate law x BP with ax- 1. The igniter,

by contrast, is all burned at t = 0.

IV. ANALYSIS

For a charge of identical single-perforated propellant grains of

uniform density, the mass-fraction burned at depth x may be expressed as

__E V(O) - V(x) (4.01)m p V(0)

I147 L (D2 - d 2 ) - 1 /4 u(L - 2x)[(D - 2x) 2 - (d + 2x) 2 ]

1/4 L (D2 - d 2)

that, upon rearrangement, yields

S~8mpo8m P I4 (D - d e 2L)x -x2]

(4.02)p L(D - d)

or

m a(2b% - x 2) (4.03)

with the constant groupings

Bm

a PO (4.04)-L(D - d)

and

SD -d + 2L

8

which is valid for depths burned over the range

7

Page 8: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

0 < x < x xt X 1/2min[rL,/ 2 (D - d)]. (4.05)

We write the equation of state in the form

PV (in + in + In) -R T

Pf ree, p i a Mg

where

Vfre= Vb - in ip - In (n- I/o) - in - in n (4.06)

w th

T = (n + In. i+ n - in I) T/(rn + Il. + I,)g p p p a

The heat loss correction factor in H is derived from

(in + in. + In) () T - T = heat loss

where c ic the heat c'apacity at constant volume

or

(in + in. + in ) c T - hcat lossT - p a v8 g (m + in. + i )c

p 1 a v

Letting heat loss jH c T in

thon

(in + m. + a - i 11) TST = - p a pTg (in + . + ; ) "

p t a

Substituting T 9 into thO oquation of stato

8

Page 9: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

PV = R T(m + m. + ms - m II). (4.07)frep M a p

Since the actual maximum pressure, Pact occurs when all the

propellant is burned the numerical value of H is obtained from (4.07)

yielding

P MH= 1 act (V - (m + m. + m )n) - (m.+ ma)

RT b PO t a a P

with 0 < Pact < P theo" (4.08)

With our original assumptions, substitution of

o= a= P, (4.09)

(4.06) and (4.03) into (4.07) then produces the differential equation

[V - m /P - a(2bx - x 2 )(n - I/p) - (m. + ma) r]-- • -• [b - Po a

-- • RT

[III m+ + a(2bx - x 2 )(1 - H)] - (4.10)a I.

subject to the initial condition x=0 at time t=0.

Further, the total burning surface area (that is, the product of the number

of grains and the surface area per grain) is

@ m

S = PV(-0 {17(L - 2x)(D - 2x) + Tr(L - 2x)(d + 2x) + 2"1/41. (4.11)

[(D- 2x) 2 (d + 2x)2]}

or

9"-tN

__ _" ' '

Page 10: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

S 2a (b - x)P

with a and b given in (4.04).

V. FIRST SOLUTION: RESTRICTION ON THE COVOTIUME

We can suppose that the increase in free volume dve to the burning of

the charge is just balanced by the covolume taken up by the combustion

gases. That is, we assume

S= -(5.01)I)

In this case we can simplify and rearrange (4.10) to produce

in..,. II1

I3RT a (1 - ai) - a + 2bx - x 2 ]m[vb - in )- (il.+ m )nl a(1-l1)

p L a

or

k[ck - (x - b)2] (5.02)

for the constant groupings

kfRT a (1 - II)k -H M r V - _ p - ( m -4 -In rl lb Po i a

and

b2 + . (5.03)

a(1 - ii)

Making the substitution u = x-b implies

u kLC2 - u2]

or

du - k dL, (5.04)

c 2 _ u 2

10

Page 11: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

the left hand side of which is a standard form once we observe that

b = 1/4 I/2 (D - d) + L] >1/4 2 min[L, /2 (D - d) = Xext x (5.05)

which guarantees thaL

c > b ,b - Ix b I lul =0 (5.06)

so that

c2 > u2.

Then the solution is

I . ln1 + u] .k1*in[c _-]-j=kt + C1

2c c- 1

c -b + x C2kct (5.07)c + b - x 2 :

But the required initial condition x=0 at time t=0 forces the integrationconstant

c-= (5.08)2 c + b

which, when substituted into (5.07) produces, after some rearrangement,

2k.:t

e 2k-t I(5.09)x [ I 2kct

c b + c +b

which is valid for alL times t such that

11

Page 12: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

0 *ý t In b c b x ext]. (5.10)TkC c- ext

Once the special constant groupings have been computed, calculationsat any timo t in the above. range proceed as follows. The depth burned, x,i3 folind from (5.09), the I inear burning rate, x, from (5.02), thepressure, P, from (4.09), surface area, S, from (4.11), and the mass ofpropellant burned, nITI from (4.03). We differentiate (4.09) in conjunctionwith (5.02) to dotermineP

P - = ~(x -bx(.1

and di ffeoreiit ote (4.03) Lo determine ip

in =2;i(b - x)x. (5.12)

V1. S1LCUND SOLUTION: TII[ GE'NERAL COVOLUME

If we plaice no restrictions on the COVOlumeI We can simplify (4.10) to

x 111 1) 2L /:P T (m i 2bx + x2 ]

= ~IL+ 2b x x2 ]

or

xl + xn -1)) 2 g[c 2 -(x -b)] (6.01)

for the conlstant g~rouping;s

12

Page 13: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

Vb - in /p - (in. + in ) 11

b P i a -b

a(n - i/p)

and mg RT(l - H) (-2g - MRT IO ) (6.02)

--k As in the previous case, we make the substitution u = x- b and solve theresulting standard form thusly

f i+ u 2

c2 _ u2

f + c 2 1]du = g dt

C2 - 2

(f + C2 ) -i- [ + u] - u =gt +2c " n --u - u =g+c3

S+ c2 c b + x x + b = gt + c3 (6.03)2c c b - x 3

Imposition of the initial condition x=0 at time t=0 forces the integrationcons tant

, f + c2 c - b(6.04)c 2 ____ _ 2

so that elapsed time may be expressed as a function of depth burned

-+2 c - b + x c + b] x; t - x n• - (6.05)a' 2cg c+ b - x c b g

for any x up Lo . Because it is not possible to solve this equationfor x as a functioa of t in a finite closed form, this method cannot beused in applications where a constant time between consecutive points is a

* requirement unless we are willing to iterate (6.05) with successiveapproximations to x.

Page 14: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

Once tha constant groupings have been computed, calculations at anydepth burned x in the allowed range proceed as follows: The elapsed time,t, is found from (6.05), the linear burning rate, x, from (6.01), thepressure, P, from (4.09), surface area, S, from (4.11), the Viass ofpropellant burned, mp, from (4.03), and the mass-generation rate, m , from(5.12). We differentiate (4.09) in conjunction with (6.01) to deiermine

P

x -2g(f + c 2 ) (x - b)x ) (6.06)[+ (x -b) 2]2

VII. VALIDATION CHECK OF THE GENERAL COVOLUME ANALYSIS

In Appendix A a FORTRAN listing is provided which incorporatessolution techniques for both the restriction on the covolume and thegeneral covolume (with an iterative procedure to get constant-timeincrements). A sample problem is also provided which was run with thegeneral covolume solution technique with no heat loss. The output can becompared to the same run on IBHVG2 8 (a lumped parameter interior ballisticcomputer code) which is provided in Appendix B. As can be seen, all eightcalculated variables are the same, as they should be, within the printaccuracy of the computer codes. Similar runs and comparisons have beenperformed for the restriction on the covolume analysis with the sameexcellent agreement with IBHVG2.

VIII. REFERENCES

1. F. W. Robbins and A. W. H1orst, "Numerical Simulation of Closed BombPerformance Based on BLAKE Code Thermodynamic Data," IHMR 76-259, NavalOrdnance Station, Indian Head, MD, November 1976.

2. C. Price and A. juhasz, "A Versatile User-Oriented Closed Bomb DataReduction Program (CBRED)," BRLR 2018, Ballistic Research Laboratory,Aberdeen Proving Ground, MD, September 1977.

3 A. Pallington and M. Weinstein, "Method of Calculation of InteriorBallistic Properties of Propellants from Closed Bomb Data," TR 2005,Picatinny Arsenal, Dover, NJ, June 1954.

4. W. Wallace, "New Formulas for Rapid Calculation of Linear Burning Ratesof Solid Propellants," TR 2488, Picatinny Arsenal, Dover, NJ, April1958.

5. A. Celmins, "Solid Propellant Burning Rate Measurement in a ClosedBomb," Combustion and Flame, Vol. 23, 1974, pp. 381-397.

6. A. A. Juhasz (ed.), "Round Robin Results of the Closed Bomb and StrandBurner," CPIA Publication 361, The Johns Hopkins University, Laurel,MD, July 1982.

14

-- %

Page 15: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

7. F. Hunt and H. Hinds, "Internal Ballistics," Philosophical Library, NY,1951, pp. 53-66.

8. R. 1). Anderson and K. D. Fickie, "IBHVG2 -- A User's Guide," BRLTR-2829, Ballistic Research Laboratory, Aberdeen Proving Ground, MD, July1987.

S

15

Page 16: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

N ~a )~S~S4 t~ NVW~w J f. '..9J~1 f..' JAflAA,~flAIU LA -'U I.W XK .¶'4 I lk ipR h) wWh Lrv I,-- MMLv I% A

APPENDIX AFORTRAN LISTING OF BOTH ANALYSES

AND A TESF'T COMPUTER RUN OF GENERAL COVOLUME ANALYSIS

1

%Ip

jj

'7

~ % P ~ ' tA Xr ~ X ~ ' i i\AA i~J .. X. .Ar I~'d I iu.... UaX Ia a "

Page 17: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

CcCCcCCCCCCCCCccccccc**

CC METHOD DUE TO WORK BY F. W. ROBBINS & F. LYNN S

C DATE COMPLETED : OCTOBER 22, 1986CCccccccccccccccccCcCC**

CPROGRAM SPERF

C _CCCCCCCCCCCCCCCCCCCCC**CC A SERIES OF SUBROUTINES TO CALCULATE, FROM A CLOSED BOMBC SOLUTION, THE PRESSURE-TIME CURVE FOR A CLOSED BOMB.C ASSOCIATED VARIABLES CALCULATED ARE DISTANCE BURNT, BURNINGC RATE, DP/DT, MASS BURNT, DM/DT, AND THE SURFACE AREA. 0C THERE ARE TWO POSSIBLE SOLUTIONSCC SOLNI -- > COVOLUME = 1/DENSITY,CC SOLN2 -- > COVOLUME <> DENSITY, BUT AN ITERATIVEC PROCEDURE IS REQUIRED TO GET TIME ANDC PRESSURE AT A CONSTANT DELTA TCC ANALYSIS ASSUMES A SINGLE PERFORATED GRAIN WITH AN IGNITORC (ALL BURNT AT TIME = 0) WITH OR WITHOUT AIR OR HEAT LOSSC (AIR AND THE IGNITOR HAVE THE SAME THERMOCHEMISTRY AS THEC PROPELLANT. A BP^N BURNING RATE LAW IS ASSUMED WITH N = 1.cCCCCCCCCCCCCCCCCCCCCC**

IMPLICIT DOUBLE PRECISION (A-H,O-Z)

CCOMMON /SPECS/ BIGD,D,EL,EMI,EMPO,EMW,VB,BETA,R,TF,RHO,

+ ETAPACT,EMAIRCOMMON METHODCHARACTER HH*IDATA HH/Z'0C'/DATA NINP/7/,NOUT/8/,TOL/1.OE-04/

CcCCCCCCCCCCCCCCCCCCCCC* *

C

C THE INPUT VARIABLES ARE:C BIGD - OUTER GRAIN DIAMETERC D - PERFORATION DIAMETERC EL - GRAIN LENGTHC EMI - MASS OF THE IGNITORC EMPO - MASS OF THE PROPELLANTC EMW - MOLECULAR WEIGHTC VB - VOLUME OF THE BOMBC BETA - BURNING RATE COEFFICIENTC TF - FLAME TEMPERATUREC RHO -DENSITY OF PROPELLANTC ETA - COVOLUME (IF ETA <= 0 OR I/RHO, SOLN1 IS USED)C EMAIR - MASS OF AIR

19

Page 18: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

C PACT - ACTUAL MAXIMUM PRESSUREC (USED TO DETERMINE HEAT LOSS; IF <= 0, HEAT LOSSC NOT CONSIDERED)C R - UNIVERSAL GAS CONSTANTSC (USED TO CORRECT FOR UNITSC R = 33378.926 IN-LB F/LB MOLE DEGREE K

C DIMENSIONS OF GRAIN IN INCHES, BURNING RATEC IN INCHES/SEC, WEIGHT IN POUNDS, VOLUME INC CUBIC INCHES, FLAME TEMPERATURE IN DEGREE K,C DENSITY IN POUNDS/CUBIC INCH, COVOLUME IN

C CUBIC INCHES/POUND AND PRESSURE IN POUNDS/C SQUARE INCH).CCCCCCCCCCCCCCCCCCCCCC**C

OPEN(7,FILE='ENTER',STATUS='OLD')OPEN(8,FILE='OUTSYN',STATUS='NEW')REWIND(7)REWIND(8)

READ (NINP,*) BIGD,D,EL,EMI,EMPO,EMW,VB,BETAREAD (NINP,*) TF,RHO,ETA,EMAIR,PACT,RWRITE(NOUT,99)HH

0 WRITE (NOUT,100) BIGD,D,EL,EMI,EMPO,EMW,VB,BETA,TF,4 RHO,ETA,EMAIR,PACT,R

METHOD = 2TESTR = 1.0/RHO

C METHOD I FOR SOLN. (COVOLUME = 1/DENSITY)C METHOD = 2 FOR SOLN2 (COVOLUME <> 1/DENSITY)C

IF ( ABS( ETA - TESTR ) .LT. TOL ) METHOD 1IF (ETA .LT. TOL ) METHOD = 1CALL SBOMB

99 FORMAT(AI)100 FORMAT (IX,26HGRAIN DIAMETER= ,F20.6,/lX,

+ 26HPERFORATION DIAMETER= ,F20.6,/lX,+ 26HGRAIN LENGTH= ,F20.6,/lX,+ 26HIGNITOR MASS= ,F20.6,/lX,+ 26HPROPELLANT MASS= ,F20.6,/!X,+ 26HMOLECULAR WEIGHT= ,F20.6,/lX,+ 26HBOMB VOLUME= ,F20.6,/lX,+ 26HBURNING RATE COEFFICIENT= ,F20.6,/lX,+ 26HFLAME TEMPERATURE= ,F20.6,/lX,+ 26HDENSITY= ,F20.6,/lX,+ 26HCOVOLUME= ,F20.6,/IX,+ 26HAIR MASS= ,F20.6,/lX,+ 26HACTUAL MAXIMUM PRESSURE= ,F20.6,/lX,+ 26HUNIVERSAL GAS CONSTANT= ,F20.6//)

CLOSE(7)CLOSE(S)

ENDCC

SUBROUTINE SBOMBIMPLICIT DOUBLE PRECISION (A-H,O-Z)

20

Page 19: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

COMMON /SPECS/ BIGD, D,EL,EMI,EMPO,EMW,VB,BETA,R,TF,RHO,+ ETA,PACT,EMAIR

COMMON /CALCS/ T,TEXT,X,XEXT,XDOT,P,PDOT,EMP,EMPDOT,SCOMMON METHODCHARACTER HH*IDATA NSTEP/1200/,ERROR/I..OE-7/,NOUT/8/DATA MAXLIN /54/,HH/Z'OC'/LCOUNT = 1X= 0T 0IF (METHOD .EQ. 1) GOTO 10

CC INITIALIZE CONSTANTS

C CALL SOLN2 (0)

GOTO 20CC INITIALIZE CONSTANTSC

i0 CALL SOLNI (0)20 CONTINUE

WRITE (NOUT,98)HHWRITE (NOUT, I01)

CC GET DELTA TC

DELT = TEXT/NSTEPCC GET INITIAL GUESS FOR DISTANCE BURNT FORC USE IF METHOD = 2C

X = XEXT/NSTEPDO 30 1 = 1,NSTEPIF (METHOD 2 NE. ) GOTO 100

CC USE METHOD IC

T = I*DELTCALL SOLNI (I)GOTO 200

200 CONTINUECC USE METHOD 2 WITH NEWTON-RAPHSON ITERATIVE PROCEDURE

CALL SOLN2 (1)

IF (ABS(L.0-T/(I*DELT)) LT. ERROR) GOTO 200X = X-(T-I*DELT)*XDOTIF (X .LP. 0.0) X = (X+(T-I*DELT)*XDOT)/10. •GOTO 100

200 CONTINUEIF (LCOUNT .LE. MAXLIN) GOTO 5 •

WRITE(NOUT,98)HHWRITE (NOUT, 101)LCOUNT = 1

5 CONTINUE

21

Page 20: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

WRITE (NOUT,99) T,P,PDOT,XDOT,EMP,EMPDOT,S,XLCOUNT =LCOUNT + 1

30 CONTINUE98 FORMAT(A1)99 FORMAT (1X,8E12.5)101 FORMAT (5X,4HTIME,6X,8HPRESSURE,6X,4HPDOT,SX,

+ 4HXDOT, 2X, 16HPROPELLANT BURNT, 2X, 4HMDOT,+ REUN7X, 7HSURFACE, 2X, 14HDISTANCE BURNT//)

ENDCCCC

SUBROUTINE SOLNi (IPASS)IMPLICIT DOUBLE PRECISION (A-H,O-Z)

COMMON /SPECS/ BIGD,D,EL,EMI,EMPO,EMW,VB,BETA,R,TF,RHO,+ ETA,PACT,EMAIRCOMMON /CALCS/ T,TEXT,X,XEXT,XDOT,P,PDOT,EMP,EMPDOT,SCOMMON METHODDATA NOUT/8/

CSOLUTION METHOD 1 -- > COVOLUME 1/VDENSITY

CIF(IPASS.GT.0) GOTO 100

CCC INITIALIZE CONSTANTS, SET COVOLUME <-- 1/DENSITYC

ETA=1. 0/RHOA=8. 0*EMPO/ (EL* (BIGD-D))B= (BIGD-D+2. 0*EL) /8.0

C

C CALCULATE THEORETICAL MAXIMUM PRESSUREC (NO ENERGY LOSS)C

PTHEO= (EMPO+EMI+EMAIR) *R*TF/EW/ (VB- (EMPO+EMI+EMAIR) *ETA)WRITE (NOUT,79) PTHEO

CC DETERMINE IF HEAT LOSS IS TO BE CONSIDEREDC

IF (PACT .LE. 1.E-8) PACT = PTHEOCC CALCULATE HEAT LOSS FACTORC

H=1.0- (PACT*EMW* (VB- (EMPQ+EMI+EMAIR) *ETA) /(R*TF) -+ (EMI+EMAIR) )/EMPOXK=BETA*R*TF*A* (1.-H)/ (EMW* (VB-EMPO/RHO- (EMI+EMAIR) *ETA))C=SQRTr(B**2±(EMI±EMAIR)/(A*(l.-H)))

CC CALCULATE DEPTH BURNED AT TIME OF GRAIN EXTINCTIONC

XEXT=0.5*DMIN1(EL,0.5*(BIGD-D))CC CALCULATE TIME OF GRAIN EXTINCTION

22

Page 21: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

CTEXT=1.0/(2.0*XK*C)*DLOG( (C**2-B**2+XEXT*(C+B) )/

$ (C**2-B**2-XEXT*(C-B)))WRITE(NOUT,77) HWRITE (NOUT, 78) METHODWRITE(7,77) HWRITE(7,78) METHOD

CC CALCULATE VARIABLESCC DISTANCE BURNEDC

100 X=(EXP(2.0*XK*C*T)-~1.O)/(1.O/(C-B)+1.0/(C+B)*EXP(2.0*XK*C*T))CC BURNING RATEC

XDOT=XK* (C**2- (X-B) **2)

C PRESSUREC

P=XDOT/ BETACC RATE OF CHANGE OF PRESSUREC

PDOT=-2 .0*XK/BETA* (X-B) *XDOTCC MASS PROPELLANT BURNTC

EMP=A* (2.0*B*X-X**2)CC RATE OF CHANGE OF MASS OF PROPELLANTC

EMPDOT=2. 0*A* (B-X) *XDOTCC SURFACEC

S=2.**A* (B-X) /RHO* C

77 FORMAT (1X,2OHHEAT LOSS FACTOR -- ,F10.7)78 FORMAT (1X,1OHMETHOD -- ,Il)79 FORMAT (lX,29HTHEORETICAL MAXIMUM PRESSURE ,E20.14)

RETURNEND

Cc

SUBROUTINE SOLN2 (IPASS)IMPLICIT DOUBLE PRECISION (A-HO-Z)

COMMON /SPECS/ BIGD, D,EL,EMI ,EMPO,EMW,VB, BETA,R,TF,RHO,+ ETA,PAC'L',EMiAIRCOM4MON /CALCS/ T,TEXT, X1,XEXT, XDOT, P, PDOT, EMP,EMPDOT, SCOMMON METHODDATA NOUT/8/

CC SOLUTION METHOD 2 -- > COVOLUME <> 1/DENSITY

23

Page 22: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

CIF(IPASS.GT.0) GOTO 100

CC INITIALIZE CONSTANTSC

A=8 . *EMPO/ (EL* (BIGD-D))B= (BIGD-D+2.0*EL) /8.0

C CALCULATE THEORETICAL MAXIMUM PRESSUREC (NO ENERGY LOSS)C

PTHEO= (EMPO+EMI+EMAIR) *R*TF/EMW/ (VB- (EMPO+EMI+EMAIR) *ETA)WRITE (NOUT,79) PTHEO

CC DETERMINE IF HEAT LOSS IS TO BE CONSIDEREDC

IF (PACT .LE. l.E-8) PACT = PTHEOCC EVALUATE HEAT LOSS FACTORC

H=1.- (PACT*EMW* (yE-(EMPO+EMI-I-MAIR) *ETA)/ (R*TF) -(EMI+EMAIR) )/EMPOC=SQR.T(B**2+(EMI+EMAIR)/(A*(3..-H)))F=(VB-EMPO/RHO-(EMI+-EMAIR) *ETA)/ (A* (ETA-i. 0/RHO)) -B**2G=BETA*R*TF*(1.-H)/(EI4W*(E'TA-1.0/P.HO))

C CALCULATE DEPTH BURNED AT TIME OF GRAIN EXTINCTIONC

XEXT=0. 5*DMIN1 (EL, 0.5* (BIGD-D))CC CALCULATE TIME OF GRAIN EXTINCTIONC

TEXT=(F+C**2)/(2.0*C*G)*DLOG((C**2--B**2+XEXT*(C+B))/$ (C**2-B**2-XEXr* (C-B) ) )-XEXT/GWRITE(NOUT,77) H

* WRITE(NOUT,78) METHODCC CALCULATE VARIABLESCC TIMEC

100 T=(F+C**2)/(2.0*C*G)*DLOG((C**2-B**2+X*(C+B))/$ (C**2-B**2--X*(C-B)))-X/G

CC BURNING RATEC

XDOT=G* (C**2-(X-B) **2)/ (F+(X-B)**2)CC PRESSUREC

P=XDOT/ BETACC RATE OF CHANGE OF PRESSUREC

PDOT=-2 . Q*3*(F4C**2)* (X-B) *XDOT/ (BETA* (F+ (X-B) **2) **2)

*C

24

Page 23: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

MASS PROPELLANT BURNED

C EMP=A* (2. O*B*X-X**2)

CC RATE OF CHANGE OF MASS OF PROPELLANTC

EMPDOT=2.0 *A* (B-X) *XDOTCC SURFACEC

S=2. *A* (B-X) /RHO

77 FORMAT (1X,2OHHEAT LOSS FACTOR -- ,F1O.7)78 FORMAT (1X,1OHMETHOD -- ,Il)79 FORMAT (1X,29HTHEORETICAL MAXIMUM PRESSURE ,E20.14)

RETURN4END

25

V ~I' ~'-. ,~wf5

Page 24: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

GRAIN DIAMETER- 0.250000

PERFORATION DIAMETER- 0.050000GRAIN LENGTH= 1.000000IGNITOR MASS= 0.000200PROPELLANT MASS- 0.125000

MOLECULAR WEIGHTm 28.000000BOMB VOLUME- 12.510000BURNING RATE COEFFICIENT= 0.002000FLAME TEMPERATUREu 3400.000000

DENSITY= 0.060000

COVOLUME= 25.000000AIR KASS= 0.000000ACTUAL MAXIMUM PRESSURE= 54099.665000UNIVERSAL GAS CONSTANT= 33378.926000

THEORETICAL MAXIMUM PRESSURE 0.540996&*814499Et05HEAT LOSS FACTOR 0.0000000METHOD -- 2

I.•

it.

26

-

d.[

Page 25: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

TIME PRESSURE PDOT XDOO PROPELLANT BURNT HOOT SURFACE DISTANCE BURNT

0.25398E-05 0.78207E+02 0.16731E+06 0.15641E+00 0.10895E-05 0.43014E+00 0.45833E+02 0.396182-06

0.50796E-05 0.78633E+02 0. 16823E+06 0.15727E+00 0.21849E-05 0.43248E+00 0.45833E+02 0,'9453E-06

0.76194E-05 0.79062E+02 0.16914E+06 0.15812E+00 0.32864E-05 0.43484E+00 0.45833E+02 0.11950E-05

0.10159E-04 0.79492E+02 0.17006E+06 0.15898E+00 0.43938E-05 0.43721E+00 0.45833E+02 0.15977E-05

0.126992-04 0.79925E+02 0.17099E+06 0.15985E+00 0.55072E-05 0.43959E+00 0.45833E+02 0.20026E-05

0.152392-04 0.80361E+02 0.171922+06 0.16072E+00 0.66267E-05 0.44198E+00 0.45833E+02 0.24097E-05

0.117792-04 0.80799E402 0.17286E+06 0.161602+00 0.77523E-05 0.444392+00 0.45833E+02 0.28190E-05

0.203182-04 0.81239E+02 0.17380E+06 0.16248E+00 0.888402-05 0.44681E+00 0.45833E+02 0.32306E-05

0.22858E-04 0.81682E+02 0.17475E+06 0.16336E+00 0.10022E-04 0.44924E+00 0.45833E+02 0.36444E-05

0.253982-04 0.82127E+02 0.175702+06 0.164252+00 0.11166E-04 0.45169E+c00 0.45833E+02 0.40604E-05

0.27938E-04 0.82574E+02 0.176662+06 0.165152+00 0.123162-04 0.45415E+00 0.458332+02 0.44787E-05

0.30478E-04 0.83024E+02 0.17'762E+06 0.16605E+00 0.134'73E-04 0.45662E+00 0.458332+02 0.48993E-05

0.330182-04 0.83476E+02 0.17859E+06 0.16695E+00 0.14636E-04 0.459112+00 0.45832E+02 0.532222-050.355572-04 0.839312+02 0.17956E+06 0.167862+00 0.15805E-04 0.46161E+00 0.458322+02 0.57474E-05

0.380972-04 0.843882+02 0.180542+06 0.16878E+00 0.169812-04 0.464132+00l 0.458322+02 0.61749E-05

0.406372-04 0.84848E+02 0.181522+06 0.169702+00 0.181632-04 0.46665E+00 0.45832E+02 0.660472-05

0.431772-04 0.85311E+02 0.182512+06 0.170622+00 0.19351E-04 0.46920E+00 0.45832E+02 0.703692-050.457172-04 0.857752+02 0.183512+06 0.171552+00 0.205462-04 0.47175E+00 0.4 5832E+02 0.74714E-05

0.48256E-04 0.862432+02 0.184512+06 0.172492+00 0.21747E-04 0.474322+00 0.458322+02 0.790832-05

0.50796E-04 0.86713E+02 0,18551E+06 0.17343E+00 0.22955E-04 0.476902+00 0.45832E+02 0.834752-05

0.53336E-04 0.871852+02 0.18652E+06 0.17437E+00 0.24170E-04 0.479502+00 0.45832E+02 0.87892E-05

0.558716E-04 0.87660E+02 0.187542+06 0.17532E+00 0.253912-04 0.482112400 0.45832E+02 0.92333E-050.584162-04 0.881382+02 0.188562+06 0.17628E+00 0.26619E-04 0.48474E+00 0.45832E+02 0.967982-05

0.60955E-04 0.8U8618+02 0.189592+06 0.177242+00 0.27853E-04 0.487382+00 0.45832E+02 0.101292-040.63495E-04 0.891012+02 0.190622+06 0.178202+00 0.29095E-04 0.49003E+00 0.45832E+02 0.105802-04

0.660352-04 0.895862+02 0.19166E+06 0.17917E+00 0.30343E-04 0.49270E+00 0.458312402 0.11034E-040.68575E-04 0.90074E+02 0.19270E+06 0.180152+00 0.31597E-04 0.495392+00 0.45831E+02 0.11490E-04

0.71115E-04 0.90565E+02 0.19375E+06 0.181132+00 0.328592-04 0.49809E+00 0.458312+02 0.11949E-04

0.736542-04 0.91058E+02 0.194812+06 0.18212E+00 0.341282-04 0.500802+00O 0.45831E+02 0.12410E-04

0.761942-04 0.91555E+02 0.19587E+06 0.183112+00 0.35403E-04 0.50353E+00 0.458312+02 0.12874E-04

0.787342-04 0.920532+02 0.196942+06 0.18411E+00 0.366852-04 0.506272+00 0.45831E+02 0.133402-04

0.81274E-04 0.92555E+02 0.19801E+06 0.185112+00 0.379752-04 0.509032+00 0.458312+02 0.138092-04

0.838142-04 0.93059E+02 0.19909E+06 0.18612E+00 0.39271E-04 0.51180E+00 0.458312+02 0.14281E-04

0.86354E-04 0.93566E+02 0.200182+06 0.18713L+00 0.405742-04 0.51459E+00 0.458312+02 0.147552-04

0.888932-04 0.94076E+02 0.201272+06 0.188152+00 0.41885E-04 0.51739E+00 0.458312+02 0.15231E-04

0.914332-04 0.94589E+02 0.20236E+06 0.18918E+00 0.43202E-04 0.52021E+00 0.458312+02 0.157102-04

0.939732-04 0.951042+02 0.20347E+06 0.190212+00 0.44527E-04 0.52304E+00 0.45831E+02 0.161922-04

0.96513E-04 0.95622E+02 0.204572+06 0.191242+00 0.458592-04 0.525892+00 0.45831E+02 0.16677E-04

0.99053E-04 0.96143E+02 0.205692+06 0.19229E+00 0.47199E-04 0.52875E+00 0.45830E+02 0.17164E-04

0.10159E-03 0.966672+02 0.20681E406 0.19333E+00 0.48545E-04 0.531632+00 0.458302+02 0.17653E-04

0.104132-03 0.97194E+02 0.20794E+06 0.194392+00 0.49899E-04 0.534532+00 0.45830E+02 0.181462-04

0.10667E-03 0.97723E+02 0.209072+06 0.195452+00 0.51260E-04 0.53744E+00 0.45830E+02 0.186412-04

0.10921E-03 0.982562+02 0.21021E+06 0.19651E+00 0.52629E-04 0.540372+00 0.45830E+02 0.19139E-04

0.11175E-03 0.98791E+02 0.211352+06 0.197582+00 0.540052-04 0.54331E+00 0.45830E+02 0.196392-04

0.11429E-03 0.99329E+02 0.21251E+06 0.19866E+00 0.55389E-04 0.54627E+00 0.45830E+02 0.20142E-04

0.11683E-03 0.99871E+02 0.213662+06 0.19974E+00 0.56780E-04 0.54925E+00 0.458302+02 0.20648E-04%0.11937E-03 0.100412+03 0.214832+06 0.20083E+00 0.58179E-04 0.55224E+00 0.458302+02 0.21157E-04

0.121912-03 0.10096E+03 0.21600E+06 0.20192E+00 0.59585E-04 0.555252+00 0.45830E+02 0.21668E-04

0.12445E-03 0.101512+03 0.21718E+06 0.20302E+00 0.60999E-04 0.55827[+00 0.45830E+02 0.22183E-04

0.12699E-03 0.102062+03 0.21836E+06 0.20413E+00 0.62421E-04 0.56131E+00 0.45830E+02 0.22700E-04

0.12953E-03 0.10262E+03 0,21955E+06 0.20524E+00 0.63851E-04 0.56437E+00 0.45829E+02 0.23219E-04

0.13207E-03 0.10318E+03 0.22075E+06 0.20636E+00 0.65288E-04 0.56744E+00 0.458292+02 0.23742E-04

0.134612-03 0.103742+03 0.22195E+06 0.20748E+00 0.66733E-04 0.57053E+00 0.45829E+02 0.24268E-04

0.13715E-03 0.10431E+03 0.22316E+06 0.20862E+00 0.68186E-04 0.57364E+00 0.45829E+02 0.247962-04

27

Ar(

Page 26: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

TIME PRESSURE PDOT XDOT PROPELLANT BURNT MOOT SURFACE DISTANCE BURNT

0.13969E-03 0.104889+03 0.22437E+06 0.20975E+00 0.69647E-04 0.57676E+00 0.45829E+02 0.25327E-040.14223E-03 0.10545E+03 0.22560E+06 0.21089E+00 0.71116E-04 0.57991E+00 0.45829E+02 0.25862E-040.14477E-03 0.10602E+03 0.22683E+06 0.21204E+00 0.72593E-04 0.58306E+00 0.45829E+02 0.26399E-040.14731E-03 0.1060E+03 0.22806E+06 0.21320E+00 0.74078E-04 0.58624E+00 0.45829E+02 0.26939E-040.14985E-03 0.10718E+03 0.22930E+06 0.21436E+00 0.75571E-04 0.58943E+00 0.45829E+02 0.27482E-040.15239E-03 0.10776E+03 0.23055E+06 0.21553E400 0.77072E-04 0.59264E*00 0.45829E+02 0.28028E-040.15493E-03 0.10835E+03 0.23181E+06 0.21670E+00 0.78581E-04 0.59587E+00 0.45829E+02 0.28576E-040.15747E-03 0.10894E+03 0.23307E+06 0.21788E+00 0.80099E.04 0.59912E+00 0.45828E+02 0.29128E-040.16001E-03 0.10954E+03 0.23434E+06 0.21907E+00 0.81624E-04 0.60238E+00 0.45828E+02 0.29683E-040.16255E-03 0.11013E+03 0.23562E+06 0.22026E+00 0.83158E-04 O.60566E+00 0.45828E+02 0.30241E-040.16509E-03 0.11073E+03 0.23690E+06 0.22146E+00 0.84701E.04 0.60896E+00 0.45828E+02 0.30802E-040.16763E-03 0.11134E+03 0.23820E+06 0.22267E+O0 O.a6252E-04 0.61228EO00 0.45828E+02 0.31366E-040.17017E-03 0.11194E+03 0.23949E+06 0.22388E+00 0.87811E-04 0.61561E+00 0.45828E+02 0.31933E-040.17271E-03 0.11255E+03 0.24080E+06 0.22510E+00 0.89379E-04 0.61896E+00 0.45828E+02 0.32503E.040.17525E-03 0.11317E+03 0.24211E+06 0.22633E+00 0.90955E-04 0.62233E400 0.45828E+02 0.33077E,040.17779E-03 0.1137&E+03 0.24343E+06 0.22756E+00 0.92540E-04 0.62572E+00 0.45828E+02 0.33653E-040.18033E-03 0.11440E+03 0.24476E+06 0.22880E*00 0.94134E-04 0.62913E+00 0.45828E002 0.34233E-040.18287E-03 0.11503E+03 0.24609E÷06 0.23005E000 0.95736E-04 0.63256E000 0.45828E+02 0.34815E-040.18541E-03 0.11565L+03 0.24743E+06 0.23130E+00 0.97347E-04 0.63600E+00 0.45827E+02 0.35401E-040.18795E-03 0.11628E+03 0.24878E+06 0.23256E+00 0.98966E-04 0.63947E+00 0.45827E+02 0.35990E-040.19049E-03 0.11692E+03 0.25013E+06 0.23383E+00 0.10060E.03 0.64295E+00 0U45827E+02 0.36582E-040.19303E-03 0.11755E+03 0.25150E+06 0.23511E+00 0.10223E-03 0.64645E000 0.45827E+02 0.37178E-04 I.

0.19557E-03 0.11819E+03 0.25287E+06 0.23639E+00 0.10388E-03 0.64997E+00 0.45827E+02 0.37777E-040.19811E-03 0.11884E+03 0.25425E+06 0.23767E+00 0.10553E-03 0.65351E+00 0.45827E+02 0.38379E-040.20065E-03 0.11948E+03 0.25563E+06 0.23897E+00 0.10720E-03 0.65707E*00 0.45827E+02 0.38984E-040.20318E-03 0.12014E+03 0.25702E+06 0.24027E+00 0,10887E-03 0.66065E+00 0.45827E+02 0.39593E-040.20572E-03 0.12079E+03 0.25842E+06 0.24158E+00 0.11055E-03 0.66425E+00 0.45827E+02 0.40204E-040.20826E-03 0.12145E+03 0.25983E+06 0.24290E+00 0.11225E-03 0.66787E+00 0.45827E+02 0.40820E-040.21080E-03 0.12211E+03 0.26125E+06 0.24422E+00 0.11395E.03 0.67150E+00 0.45826E+02 0.41438E-040.21334E-03 0.12278E+03 0.26267E+06 0.24555E400 0.11566E-03 0.67516E+00 0.45826E+02 0.42060E-040.21588E-03 0.12344E493 0.26410E+06 0.24689E+00 0.11738E-03 0.67884E+00 0.45826E+02 0.42686E-040.21842E-03 0.12412E+03 0.26554E+06 0.24823E+00 0.11911E-03 0.68254E+00 0.45826E+02 0.43314E-040.22096E-03 0.12479E÷03 0.26699E+06 0.24959E÷00 0.12084E-03 0.68625E400 0.45826E+02 0.43947E-04 ¶

0.22350E-03 0.12547E+03 0.26844E+06 0.25095E+00 0.12259E-03 0.68999E+00 0,45826E+02 0.44582E-040.22604E-03 0.12616E+03 0.26991E+06 0.25231E+00 0.12435E-03 0.69375E+00 0.45826E+02 0.45221E-040.22858E-03 0.12684E+03 0.27138E+06 0.25369E+00 0.12612E-03 0.69753E+00 0.45826E+02 0.45864E-040.23112E-03 0.12754E+03 0.27286E006 0.25507E000 0.12789E-03 0.70133E+00 0.45826E+02 0.46510E-040.23366E-03 0.12823E+03 0.27434E+06 0.25646E+00 0.12968E-03 0.70515E+00 0.45825E+02 0.47160E-040.23620E-03 0.12893E+03 0.27584E+06 0.25786E+00 0.13147E-03 0.70899E+00 0.45825E+02 0.47813E-040.23874E-03 0.12963E+03 0.27734E+06 0.25926E+00 0.13328E-03 0.71285E400 0.45825E002 0.48469E-040.24128E-03 0.13034E+03 0.27885E÷06 0.26068E+00 0.13509E-03 0.71673E+00 0.45825E,02 0.49130E-040.24382E-03 0.13105E+03 0.28037E+06 0.26210E+00 0.13697E-03 0.72063E+00 0.45825E+02 0.49793E-040.24636E-03 0.13176E+03 0.28190E+06 0.26352E+00 0.13875E-03 0.72456E+00 0.45825E+02 0.50461E-040.24890E-03 0.13248E+03 0.28344E+06 0.26496E+00 0.14060E-03 0.72850E÷00 0.45825E002 0.51132E-040.25144E-03 0.13320E+03 0.28498E+06 0.26640E+00 0.14246E-03 0.73247E+00 0.45825E÷02 0.51807E-040.25398E-03 0.13393E+03 0.28653E+06 0.26785E+00 0.14432E-03 0.73646E+00 0.45825E+02 0.52485E-040.25652E-03 0.13466E+03 0.28809E+06 0.26931E+00 0.14620E-03 0.74047E+00 0.45824E+02 0.53167E-040.25906E-03 0.13539E+03 0.28966E÷06 0.27078E+00 0.14808E-03 0.74450E+00 0.45824E+02 0.53853E-040.26160E-03 0.13613E+03 0.29124E+06 0.27226E+00 0.14998E-03 0.74856E+00 0.45824E+02 0.54543E-040.26414E-03 0.13687E+03 0.29283E+06 0.27374E+00 0.15188E-03 0.75264E+00 0.45824E+02 0.55236E-040.26668E-03 0.13762E+03 0.29443E÷06 0.27523E+00 0.15380E-03 0.75673E+00 0.45824E+02 0.55933E-040.26922E-03 0.13837E+03 0.29603E+06 0.27673E+00 0.15573E-03 0.76086E+00 0.45824E+02 0.56634E-040.27176E-03 0.13912E+03 0.29764E+06 0.27824E+00 0.15767E-03 0.76500E+00 0.45824E+02 0.57339E0040.27430E-03 0.13988E÷03 0.29927E+06 0.27976E+00 0.15961E-03 0.76917E+00 0.45824E÷02 0.58048E-04

Page 27: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

TIME PRESSURE FOOT XDOT PROPELLANT BURNT MDOT SURFACE DISTANCE BURNT

0.27684E-03 0.14064E+03 O.30090E*06 0.28128E+00 0.16157E-03 0.77335E+00 0.45824E+02 0.58760E-040.27938E-03 0.14141E+03 0.30254E+06 0.28281E+00 0.16354E-03 0.77757E+00 0.45823E+02 0.59477E-04

0.28192E-03 0.14218E+03 0.30418E+06 0.28435E+00 0.16552E-03 0.78180E+00 0.45823E+02 0.60197E-04

0.28446E-03 0.14295E+03 0.30584E+06 0.28590E+00 0.16751E-03 0.78606E+00 0.458232+02 0.60921E-04

0.2C700E-03 0.14373E+03 0.30751E+06 0.28746E+-00 0.16952E-03 0.79034E+00 0.45823E+02 0.61649E-040.28954E-03 0.140~1E+03 0.30918E+06 0.28903E+00 0.17153E-03 0.79464E+00 0.458232+02 0.62381E-04

0.292082-03 0.14530E+03 0.31087Es-06 0.290602+00 0.17355E-03 0.79897E+00 0.458232+02 0.63117E-04

0.29462E-03 0.14609E+03 0.31256E+06 0.292192+00 0.17559E-03 0.80332E'-00 0.45823E+02 0.63857E-04

0.29716E-03 0.14689E+03 0.31427E+06 0.29378E+00 0.17763E-03 0.80770E+00 0.45823E+02 0.64601E-040.29970E-03 0.14769E+03 0.31598E'-06 0.295382+00 0.17969E-03 0.81210E+00 0.45822E+02 0.653502-04

0.30224E-03 0.14849E+03 0.317702+06 0.296992+00 0.18176E-03 0.81652E+00 0.45822E+02 0.66102E-04

uj.-0478E-03 0.14930E+03 0.31943E+06 0.298612.00 0.18384E-03 0.820971+00 0.45822E+02 0.66858E-040.30732E-03 0.150122+03 0.321172+06 0.300232+00 0.18593E-03 0.82544E+00 0.45822E+02 0.67619E-`

*0.30986E-03 0.15093E+03 0.32292E+06 0.30187E+00 0.18803E-03 0.82993E+00 0.45822E+02 0.68383L0.31240E-03 0.151761+03 0.324682+06 0.30351E+00 0.190142-03 0.83445E+00 0.45822E+02 0.691521-0.ý

0.31494E-03 0.15258E+03 0.326452+06 0.3051(1+00 0.19227E-03 0.83900E+00 0.45822E+02 0.69925E-04

0.317482-03 0.15341E+03 0.328232+06 0.30683E+00 0.19441E-03 0.84356E+00 0.45322E+02 0.70702E-040.320022-03 0.15425E+03 0.330022+06 0.30850E+00 0.14655E-03 0.84816E*00 0.45821E+02 0.714842-040.322562-03 0.155092+03 0.33182E+06 0.31018E+00 0.198712-03 0.852782+00 0.458211+02 0.722691-04

*0 325102-03 0.15594E+03 0.33363E+06 0.31187E+00 0.200892-03 0.85742E+00 0.45821E+02 0.73059E-040.32764E-03 0.15679E+03 0.33544E.06 0.31357E+00 0.20307E-03 0.862092+00 0.458212+02 0.73853E-04

0.330182-03 0.15764E+03 0.33727E+06 0.31528E+00 0.20527E-03 0.86679E+00 0.45821E+02 0.74652E-04

0.332722-03 0.15850E+03 0.33911E+06 0.31700E+00 0.20747E-03 0.87151E+00 0.458212+02 0.75455E-040.33525E-03 0.15936E+03 0.340962+06 0.318732+00 0.20969E-03 0.876252+00 0.45821E+02 0.76262E-04

0.33779E-03 0.16023E+03 0.342822+06 0.32046E400 0.21192E-03 0.a88102+00 0.458202+02 0.770741-040.340332-03 0.161102+03 0.344682+06 0.32221E+00 0.21417E-03 0.88582E+00 0.45820E+02 0.77890E-040.34287E-03 0.16198E+03 0.346562+06 0.323962+00 0.21642E-03 0.890652+00 0.45820E+02 0.787112-040.34541E-03 0.16286E+03 0.34645E+06 0.325731+00 0.21869E-03 0.89550E+00 0.45820E+02 0.79536E-040.34795E-03 0.16375E+03 0.350352+06 0.32750E+00 0.22097E-03 0.900372+00 0.45820E+02 0.803652-040.350492-03 0.164642+03 0.352262+06 0.329292+00 0.223271-03 0.905282+00 0.45820E+02 0.81199E-040.35303E-03 0.165542+03 0.35418E+06 0.331082+00 0.225572-03 0.910211+00 0.458202+02 0.02038E-040.355572-03 0.16644E+03 0.356112+06 0.332892+00 0.227892-03 0.91516E+00 0.45820E+02 0.82881E-040.35811E-01. 0.16735E+03 0.358052+06 0.334702+00 0.23022E-03 0.92015E+00 0.458192+02 0.837292-040.36065E-03 0.168262+03 0.36000E+06 0.336522+00 0.23256E-03 0.925161+00 0.45819E+02 0.84581E-04

0.363192-03 0.169182+03 0.361962+06 0.338362400 0.23492E-03 0.930192+00 0.458192+02 0.854382-04

0.36573E-03 0.17010E+03 0.36393E+06 0.340201+.00 0.237292-03 0.93526E+00 0.458192+02 0.86300E-04

0.36827E-03 0.17103E+03 0.365921+06 0.34205E+00 0.239672-03 0.940352+00 0.45819E+02 0.87166E-040.370812-03 0.17196E+03 0.36791E+06 0.34392E+00 0.24206E-03 0.945472+00 0.458192+02 0.88038E-040.373352-03 0.17290E+03 0.36992E+06 0.34579E+00 0.244472-03 0.950622+00 0.45819E+02 0.88913E-04

0.37589E-03 0.171384E+03 0.371932+06 0.34768E+00 0.24689E-03 0.95580E+00 0.458182+02 0.89794E-04

0.37843E-03 0.17479E+03 0.37396E+06 0.349572+00 0.249332-03 0.961002+00 0.45818E+02 0.90679E-04

0.38097E-03 0.175742+03 0.37600E+06 0.35148E+00 0.25177E-03 0.96624E+00 0.45818E+02 0.91570E-04I0.38351E-03 0.17670E+03 0.37805E+06 0.353392+00 0.254242-03 0.97150E+00 0.45818E+02 0.92465E-040.38605E-03 0.17766E+03 0.380112+06 0.35532E+00 0.25671E-03 0.97679E+00 0.458182+02 0.93365E-04

0.36859E-03 0.17863E+03 0.38218E+06 0.35725E+00 0.25920E-03 0.982111+00 0.45818E+02 0.942702-04

D.391132-03 0.17960E+03 0.384262+06 0.35920E+00 0.261702-03 0.98746E+00 0.45817E+02 0.95180E-04

0.39367E-03 0.18058E+03 0.386352+06 0.36116E+00 0.26421E-03 0.992832+00 0.458172+02 0.96094E-040.396212-03 0.18156E+03 0.38846E+06 0.36312E+00 0.26674E-03 0.99824E+00 0.458172+02 0.970142-04

0.398752-03 0.18255E+03 0.390582+06 0.36510E+00 0.269281-03 0.10037E+01 0.458172+02 0.97939E-04

0.401292-03 0.18355E+03 0.39270E+06 0.36709E+00 0.271842-03 0.100912+01 0.45817E+02 0.98869E-04

0.40383E-03 0.18455E+03 0.394842+06 0.36909E+00 0.274412-03 0.10146E+01 0.45817E+02 0.99804E-04

0.40637E-03 0.185552+03 0.39700E+06 0.37110E+00 0.27699E-03 0.10202E+01 0.458172+02 0,10074E-03

0.408912-03 0.186562+03 0.39916E+06 0.37313E+00 0.27959E-03 0.10257E+01 0.45816E+02 0.10169E-03

0.41145E-03 0.187582+03 0.40134E+06 0.375162+0 0.28220E-03 0.10313E+01 0.45816E+02 0.10264E-03

Page 28: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

AX r%^ 7U %A NKAX rAAF. rwg crcuwsw~r. W%;V a "JV UVWjM KW~r wU Wu vu r Nlu 3rJ w V Pn W. X -6 CNAW M M U XA lil A UnL MU VAW WA. N.1 vM n4 s wr~r

TIME PRESSURE POOT XDOT PROPELLANT BURNT MOOT SURFACE DISTANCE BURNT

0.41399E-03 0.1880E+03 0.40352E+06 0.37720E+00 0.28483E-03 0.10369E+01 0.45816E+02 0.10359E-030.41653E-03 0.18963E+03 0.40572E+06 0.37926E+00 0.28747E-03 0.10426E+01 0.45816E+02 0.10455E-03

0.41907E-03 0.19066E+03 0.40793E+G6 0.38132E+00 0.29013E-03 0.10482E+01 0.45816E+02 0.10552E-03

0.42161E-03 0.19170E+03 0.41016E+06 0.38340E+00 0.29280E-03 0.10539E+01 0.45816E202 0.10649E-03

0.42415E-03 0.19275E+03 0.41239E+06 0.38549E+00 0.29548E-03 0.10597E+01 0.45813E+02 0.10747E-030.42669E-03 0.19380E+03 0.41464E+06 0.38759E200 0.29818E-03 0.10655E+01 0.45815E+02 0.10845E-03.

0.42923E-03 0.19485E+03 0.41690E+06 0.38970E+00 0.30089E-03 0.10713E+01 0.45815E+02 0.10944E-03

0.43177E-03 0.19591E+03 0.41917E+06 0.39183E200 0.30362E-03 0.10771E+01 0.45815E+02 0.11043E-030.43431E-03 0.19698E+03 0.42145E+06 0.39396E+00 0.30636E-03 0.10830E+01 0.45815E+02 0.11143E-03

0.43685E-03 0.19805E+03 0.42375E+06 0.39611E200 0.30912E-03 0.10889E+01 0.45815E+02 0.11243E-03

0.43939E-013 0.19913E+03 0.42606E+06 0.39827E+00 0.31189E-03 0.10948E+01 0.45814E+02 0.11344E-030.44193E-03 0.20022E+03 0.42838E+06 0.40044E+00 0.31468E-03 0.11007E+01 0.45814E+02 0.11445E-03

0.44447E-03 0.20131E+03 0.43072E+06 0.40262E+00 0.31749E-03 0.11067E+01 0.45814E+02 0.11547E-03

0.44701E-03 0.20241E+Ot O.433n6E+06 0.40481E+00 0.32030E-03 3.11128E+01 0.45814E+02 0.11650E-030.44955E-03 0.20351E2C3 0.43542E+06 0.40702E+00 0.32314E-03 0.11188E+01 0.45814E+02 0.11753E-03

0.45209E-03 0.20462E+03 0.43780E+06 0.40924E+00 0.32599E-03 0.11249E+01 0.45814E+02 0.11857E-030.45463E-03 0.20573E+03 0.44018E+06 0.41147E+00 0.32885E-03 0.11310E+01 0.45813E+02 0.11961E-03

0.45717E-03 0.20685E+03 0.44258E+06 0.41371E+00 0.33173E-03 0.11372E+01 0.45813E+02 0.12066E-03

0.45971E-03 0.20798E+03 0.44499E+06 0.41596E+00 0.33463E-03 0.11434E+01 0.45813E+02 0.12171E-03

0.46225E-03 0.20911E+03 0.44742E+06 0.41823E+00 0.33754E-03 0.11496E+01 0.45813E+02 0.12277E-03

0.46479E-03 0.21025E+03 0.44986E+06 0.42051E+00 0.34047E-03 0.11559E+01 0.45813E+02 0.12383E-030.46733E-03 0.21140E+03 0.45231E+06 0.42280E+00 0.34341E-03 0.11622E+01 0.45813E+02 0.12491E-03

0.46986E-03 0.21255E+03 0.45477E+06 0.42510E+00 0.34637E-03 0.11685E+01 0.45812E+02 0.12598E-030.47240E203 0.21371E+03 0.45725E+06 0.42742E+00 0.34935E.03 0.11749E+01 0.45812E+02 0.12707E-03

0.47494E-03 0.21487E+03 0.45974E+06 0.42975E+00 0.35234E-03 0.11813E+01 0.45812E+02 0.12815E-03

0.47748E-03 0.21605E+03 0.46225E+06 0.43209E+00 0.35535E-03 0.11877E+01 0.45812E+02 0.12925E-03

0.48002E-03 0.21722E+03 0.46477E+06 0.43445E+00 0.35837E-03 0.11942E+01 0.45812E+02 0.13035E-03

0.48256E-03 0.21841E+03 0.46730+E06 0.43681E+00 0.36141E-03 0.12007E+01 0.45811E+02 0.13145E-030.48510E-03 0.21960E+03 0.46985E+06 0.43919E+00 0.36447E-U3 0.12072E+01 0.45811E+02 0.13257E203

0.48764E-03 0.22079+E03 0.47241E+06 0.44159E+00 0.36755E-03 0.12138E+01 0.45811E+02 0.13369E.030.49018E-03 0.22200E+03 0.47498E+06 0.44399E+00 0.37064E-03 0.12204E+01 0.45811E+02 0.13481E-03

0.49272E-03 0.22321E+03 0.47757E+06 0.44641E+00 0.37375E-03 0.12270E+01 0.45811E+02 0.13594E-03

0.49526E-03 0.22442E+03 0.48017E+06 0.44884E+00 0.37687E-03 0.12337E+01 0.45810E+02 0.13708E.03

0.49780E-03 0.22564E+03 0.48279E+06 0.45129E+00 0.38001E-03 0.12404E+01 0.45810E+02 0.13822E-03

0.50034E-03 0.22687E+03 0.48542E+06 0.45375E+00 0.38&17E-03 0.12472E+01 0.45810E+02 0.13937E-030.50288E-03 0.22811E+03 0.41807E+06 0.45622E+00 0.38635E-03 0.12540E+01 0.45810E+02 0.14053E-03

0.50542E-03 0.22935E+03 0.49073E+06 0.45871E+00 0.38954E-03 0.12608E+01 0.45810E+02 0.14169E-030.50796E-03 0.23060E+03 0.49340E+06 0.46121E+00 0.39275E-03 0.12677E+01 0.45810E+02 0.14286E-03

0.51050E-03 0.23186E+03 0.49609E+06 0.46372E+00 0.39598E-03 0.12746E+01 0.45809E+02 0.14403E-03

0.51304E-03 0.23312E+03 0.49879E+06 0.46625E+00 0.39923E-03 0.12815E+01 0.45809E+02 0.14521E-03

0.51558E-03 0.23439E+03 0.50151E+06 0.46879E+00 0.40249E-03 0.12885E+01 0.45809E+02 0.14640E-03

0.51812E-03 0.23567E+03 0.50425E+06 0.47134E+00 0.40577E-03 0.12955E+01 0.45809E+02 0.14759E-03

0.52066E-03 0.23695F+03 0.50699E+06 0.47391E+00 0.40907E-03 0.13025E+01 0.45809E+02 0.14879E-03

0.52320E-03 0.23825E+03 0.50976E+06 047649E+00 0.41239E-03 0.13096E+01 0.45808E+02 0.15000E-03

0.52574E-03 0.23954E+03 0.51254E+06 0.47909E+00 0.41572E-03 0.13168E+01 0.45808E+02 0.15121E-030.52828E-03 0.24085E+03 0.51533E+06 0.48170E+00 0.41908E-03 0.13239E+01 0.45808E+02 0.15243E-03

0.53082E-03 0.24216E+03 0.51814E+06 0.48432E+00 0.42245E-03 0.13311E+01 0.45808E+02 0.15366E-03

0.53336E-03 0.24348E+03 0.52096E+06 0.48696E+00 0.62584E-03 0.13384E+01 0.45808aE02 0.15489E-03

0.53590E-03 0.24481E+03 0.52380E+06 0.48962E+00 0.42925E-03 0.13457E+01 0.45807E+02 0.15613E-030.53844E-03 0.24614E+03 0.52666E+06 0.49228E+00 0.43267E-03 0.13530E+01 0.45807E+02 0,15738E-03

0.54098E-03 0.24748E+03 0.52953E+06 0.49497E+00 0.43612E-03 0.13604E+01 0.45807E+02 0.15863E-030.54352E-03 0.24883E+03 0.53241E+06 0.49766E+00 0.43958E-03 0.13678E201 0.45807E+02 0.15990E-03

0.54606E-03 0.25019E+03 0.53531E+06 0.50038E+00 0.44307E-03 0.13752E+01 0.45806E+02 0.16116E-03

0.54860E-03 0.25155E+03 0.53823E+06 0.50310E+00 0.44657E-03 0.13827E+01 0.45806E+02 0.16244E-03

30

% % . N :P r;roýR.f 'okI.ý.zAN

Page 29: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

TIME PRESSURE PDOT XDOT PROPELLANT BURNT MDOT SURFACE DISTANCE BURNT

0.55114E-03 0.25292E+03 0.54116E+06 0.50584E+00 045O09E-03 0.13902E+01 0.45806E+02 0.16372E-030.55368E-03 0.25430E+03 0.54411E+06 0.50860E+00 0.45363E-03 0.13978E+01 0.45806E+02 0.16501E-030.55622E-03 0.25569E+03 0.54708E+06 0.51137E+00 0.45719E-03 0.14054E+01 0.45806E+02 0.16630E-030.55876E-03 0.25708E+03 0.55006E+06 0.51416E+00 0.46077E-03 0.14131E+01 0o.4585E+02 0.16760E-030.56130E.03 O.25848E+03 0.55306E+06 0.51696E+00 0.46437E-03 0.14208E+01 0.45805E+02 0.16891E-030.56384E-03 0.25989E+03 0.55607E+06 0.51978E+00 0.46799E-03 0.14285E+01 0.45805E+02 0.17023E-030.56638E-03 0.26130E+03 0.55910E+06 0.52261E+00 0.47163E-03 0.14363E+01 0.45805E+02 0.17155E-030.56892E-03 0.26273E+03 0.56215E+06 0.52546E+00 0.47528E-03 0.14441E.01 0.45805E+02 0.17288E-030.57146E-03 0.26416E+03 0.56521E+06 0.52832E+00 0.47896E-03 0.14520E+01 0.45804E+02 0.17422E-030.57400E-03 0.26560E+03 0.56829E+06 0.53120E+00 0.48266E-03 0.14599W+01 0.45804E+02 0,17557E-030.57654E-03 0.26705E+03 0.57139E+06 0.53409E+00 0.48638E-03 0.14678E+01 0.45804E+02 0.17692E-030.57908E-03 0.26850E+03 0.57451E+06 0.53700E+00 0.49012E-03 0.14758E401 0.45804E+02 0.17825E-030.58162E-03 0.26997E+03 0.57764E+06 0.53993E+00 0.49387E-03 0.14838E+01 0.45803E+02 0.17965E-030.58416E-03 0.27144E+03 0.58079E+06 0.5428"A:+00 0.49765E-03 0.14919E+01 0.45803E+02 0.18102E-030.58670E-03 0.27292E+03 0.58395E+06 0.54583E+00 0.50145E-03 0.15000E+01 0.45803E+02 0.18241E-030.58924E-03 0.27440E+03 0.58713E+06 0.54881E+00 0.50527E-03 0.15082E+01 0.45803E+02 0.18380E-030.59178E-03 b.27590E+03 0.59033E+06 0.55180E+00 0.50911E-03 O.15164E÷01 0.45802E+02 0.18519E.030.59432E-03 0.27740E+03 0.59355E+06 0.55480E+00 0.51297E-03 0.15247E+01 0.45802E+02 0.18660E-030.59686E-03 0.27891E+03 0.59679E+06 0.55783E+00 0.51686E-03 0.15330E+01 0.45802E+02 0.18801E-030.59940E-03 0.28043E+03 0.60004E+06 0.56087E+00 0.52076E-03 0.15413E201 0.45802E+02 0.18943E-030.60194E-03 0.28196E+03 0.60331E+06 0.56392E+00 0.52469E-03 0.15497E+01 0.45802E+02 0.19086E-030.60447E-03 0.28350E+03 0.60660E+06 0.56699E+00 0.52863E-03 0.15581E+01 0.45801E+02 0.19230E-030.60701E-03 0.28504E+03 0.60990E+06 0.57005E+00 0.53260E-03 0.156-66E+01 0.45801E+02 0.19374E-030.60955E-03 0.28660E+03 0.61323E+06 0.57319E+00 0.53659E-03 0.15752E+01 0.45801+E02 0.19519E-030.61209E-03 0.28816E+03 0.61657E+06 0.57631E+00 0.54060E-03 0.15837E+01 0.45801E+02 0.19665E-030.61463E-03 0.28973E203 0.61993E+06 0.57945E+00 0.54464E-03 0.15924E201 0.45800E+02 0.19812E-030.61717E-03 0.29131E+03 0.62331E+06 0.58261E+00 0.54869E-03 0.16010E+01 0.45800E+02 0.19960E-030.61971E-03 0.29289E+03 0.62671E+06 0.58579E+00 0.55277E-03 0.16097E+01 0.45800E+02 0.20105E-030.62225E-03 0.29449E+03 0.63012E+06 0.58898E+00 0.55687E-03 0.16185E+01 0.45800E+02 0.20257E-030.62479:-03 0.29609E+03 0.63356E+06 0.59219L+00 0.56099E-03 0.16273E+01 0.45799E+02 0.20407E-030.62733E-03 0.29771E+03 0.63701E+06 0.59542E+00 0.56513E-03 0.16362E+01 0.45799E+02 0.20558E-030.62987E-03 0.29933E+03 0.64048E+06 0.59866E+00 0.56930E-03 0.16451E+01 0.45799E+02 0.20710E-030.63241E-03 0.30096E+03 0.64397E+06 0.60192E+00 0.57349E-03 0.16540E+01 0.45799E+02 0.20862E-030.63495E-03 0.30260E+03 0.64748E+06 0.60520E+00 0.5T770E-03 0.16630E+01 0.45798E+02 0.21015E-030.63749E-03 0.30425E+03 0.65101E+06 0.60850E+00 0.58194E-03 0.16721E+01 0.45798E+02 0.21170E-030.64003E-03 0.30591E+03 0.65456E+06 0.61182E+00 0.58620E-03 0.16812E+01 0.45798E+02 0.21325E-030.64257E-03 0.30758E+03 0.65813E+06 0.61515E+00 0.59048E-03 0.16903E+01 0.45798E+02 0.21480E-030.64511E-03 0.30925E+03 0.66172E+06 0.61850E+00 0.59478E-03 0.16995E+01 0.45797E+02 0.21637E-030.64765E-03 0.31094E+03 0.66532E+06 0.62187E+00 0.59911E-03 0.17088E+01 0.45797E+02 0.21795E-030.65019E-03 0.31263E+03 0.66895E+06 0.62526E+00 0.60346E-03 0.17181E+01 0.45797E+02 0.21953E-030.65273E-03 0.31433E+03 0.67259E+06 0.62867E+00 0.60784E-03 0.17275E+01 0.45796E+02 0.22112E-030.65527E-03 0.31605E+03 0.67626E+06 0.63209E+00 0.61224E-03 0.17369E+01 0.45796E+02 0.22272E-030.65781E-03 0.31777E+03 0.67995E+06 0.63554E+00 0.61666E-03 0.17463E+01 0.45796E+02 0.22433E-030.66035E-03 0.31950E+03 0,68365E+06 0.63900E+00 0.62111E-03 0.17558E+01 0.45796E+02 0.22595E-030.66289E-03 0.32124E+03 0.68738E+06 0.64248E400 0.62558E-03 0.17654E+01 0.45795E+02 0.22758E-03

V 0.66543E-03 0.32299E+03 0.69113E+06 0.64599E+00 0.63008E-03 0.17750E+01 0.45795E+02 0.22921E-030.66797E-03 0.32475E+03 0.69489E+06 0.64951E+00 0.63460E-03 0.17846E+01 0.45795E+02 0.23086E-030.67051E-03 0.32652E+03 0.69868E+06 0.65305E+00 0.63914E-03 0.17944E401 0.45795E+02 0.23251E-030.67305E-03 0.32830E+03 0.70249E+06 0.65660E+00 0.64371E-03 0.18041E401 0.45794E+02 0.23418E-030.67559E-03 U.33009E+03 0.70632E+06 0.66018E+00 0.64831E-03 0.18139E401 0.45794E+02 0.23585E-030.67813E-03 0.33189E+03 0.71017E+06 0.66378E+00 0.65293E-03 0.18238E+01 0.45794E+02 0.23753E-030.68067E-03 0.33370E+03 0.71404E+06 0.66740E+00 0.65757E-03 0.18337E+01 0.45793E+02 0.23922E-030.68321E-03 0.33552E+03 0.71793E+06 0.67103E+00 0.66224E-03 0.18437E÷01 0.45793E+02 0.24092E-030.68575E-03 0.33T35E+03 0.72184E+06 0.67469E+00 0.66694E-03 0.18538E+01 0.45793E+02 0.24263E-03

__---3.

Page 30: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

TIME PRESSURE PDOT XDOT PROPELLANT BURNT MOOT SURFACE DISTANCE BURNT

0.68829E-03 0.33918E+03 0.72578E+06 0.67837E+00 0.67166E-03 0.18639E+A 4 .0.45793E+02 0.24435E-030.69083E-03 0.34103E+03 O.7297'3E*06 0.68206E+00 0.67640E-03 0.18740E+01 0.45792E+02 0.246082-03

0.69337E-C3 0.34289E+03 0.73371E+06 0.68578E+00 0.68118E.-03 0.18842E+01 0.45792E+02 0.24781E-03

0.69591E-03 0.3447'6E+03 0.73771E+06 0.68952E+00 0.68597E-03 0.18945E+01 0.45792E+02 0.24956E-030.69845E-03 0.34664E+03 0.74173E+06 0.69328E+00 0.690801-03 0.19048E+U1 0.45791E+02 0.25131E-03

0.70099E-03 0.34853E+03 0.74578E+06 0.69705E+00 0.69565E-03 0.19151E+01 0.45791E+02 0.25308E-03

0.70353E-03 0.35043E+03 0.74984E+06 0.70085E+00 0.70053E-03 0.192561+01 0.45791E+02 0.25486E-03

0.70607E-03 0.352341+03 0.753931+06 0.70467E+00 0.70543E-03 0.19360E+01 0.45791E+02 0.25664E-03

0.70861E-03 0.35426E+03 0.75804E+06 0.70851E+00 0.71036E-03 0.19466E+01 0.45790E+02 0.25843E-03

0.71115E-03 0.35619E+03 0.762171+06 0.71237E+00 0.71532E-03 0.19572E+01 0.45790E+02 0.26024E-03

0.71369E-03 0.35813E+03 0.76632E+06 0.71625E+00 0.72030E-03 0.196782+01 0.45790E+02 0.26205E-03

0.71623E-03 0.36008E+03 0.77050E+06 0.72016E+00 0.725322-03 0.19785E+01 0.45789E+02 0.26388E-03

0.71877E-03 0.36204E+03 0.77470E+06 0.724081+00 0.730351-03 0.19893E+01 0.45789E+02 0.26571E-03

0.72131E-03 0.36401E+03 0.77892E+06 0.72803E+00 0.73542E.03 0.200011+01 0.45789E+02 0.26756E-03

0.723852-03 0,366002+03 0.78317E+06 0.73200E+00 n.740512-03 0.20110E+01 0.45788E+02 0.269412-03

0.7'.639E-03 0.367991+03 0.787441+06 0.T35981+00 0.745641-03 0.20220E+01 0.45788E+02 0.27127E-030.7.28931-03 0.37000E403 0.791713E+06 0.74000E400 0.750781-03 0.20330E-+01 0.45788E+02 0.27315E-03

0.73147E-03 0.372012+03 0.79605F+06 0.74403E+00 0.75596E-03 0.20440E+01 0..457872+02 0.27503E-03

0.73401E-03 0.37404E+03 0.80039E+06 0.74808E+00 0.76117E-03 0.20552E+01 0.45787E+02 0.27693E-030.736541-03 0.37608E+03 0.80475E+06 0.75216E+00 0.766401-.03 0.20663E+01 0.457872+02 0.278832-03

0.739082-03 0.378132+03 0.80914E+06 0.75626L+00 0.77166E-03 0.20776E+01 0.457872+02 0.28075E-030.741622-03 0.380'192+03 0.813552+06 0.76038E+00 0.77696E-03 0.20889E+01 0.457862E+02 0.28267E-03

0.74416E-03 0.38226E+03 0.817982+06 0.76452E+00 0.782281-03 0.21003E+01 0.45786E+02 0.284612-03

0.74670E-03 0.384342+03 0.822442+06 0.76869E+00 0.78762E-03 0.21117E+01 0.45786E+02 0.28656E-030.74924E-03 0.386442+03 0.826922+06 0.772881+00 0.79300E-03 0.212321+01 0.45785E+02 0.28852E-03

0.751782-03 0.38855E+03 0.831432+06 0.77709E+00 0.79841E-03 0.21347E+01 0.457852+02 0.29048E-03

0.75432E-03 0.39066E+03 0.83596E+06 0.78133E+00 0.80385E-03 0.21464E+01 0.45785E+02 0.29246E-03

0.75686E-03 0.392792+03 0.84052E+06 0.78558E+00 0.80931E-03 0.21580E+01 0.457842+i02 0.29445E-03

0.759401-03 0.394932+03 0.84510E+06 0.78986E+00 0.814812-03 0.21698E+01 0.457842+02 0.296452-03

0.76194E-03 0.397081+03 0.849712+06 0.79417E400 0.82033E-03 0.21816E+01 0.457842+02 0,29a46E-030.764482-03 0.39925E+03 0.854341+06 0.'798501+.00 0.82589E-03 0.219351+01 0.45783E+02 0.300491-030.767022-03 0.40142E+03 0.85900E+06 0.80285E+00 0.831481-03 0.22054E+01 0.457832+02 0.302522-03

0.76956E-03 0.403612+03 0.96368E+06 0.807222+00 0.83709E-03 0.2217%-+01 0.457832+02 0.30457i-03

0.77210E-03 0.405812+03 0.868391+06 0.81162E+00 0.84274E-03 0.22295E-01 0.45782E+02 0.306621-030.77464E-03 0.408021+03 0.87312E4-06 0.81605E400 0.848421-03 0.224161+01 0.45782E+02 0.308692-03

0.777182-03 0.41025E+03 0.87788E+06 0.82049E+00 0.85413E-03 0.22538E+01 0.45782E+02 0.31077E-03

0.77972E-03 0.412481+03 0.88267E+06 0.82496E+00 0.85987E-03 0.22661E+01 0.457812+02 0.31286E-030.78226E-03 0.414732+03 0.887481+06 0.82946E+00 U.865642-03 0.22784E+01 0.45781E+02 0.314962-03

0.784802-03 0.41699E+03 0.89232E+06 0.833982+00 0.871442-03 0.229081+01 0.457802+02 0.31707E-03

0.787342-03 0.419261+03 0.897181+06 0.83853E+00 0.87727E-03 0.23033E+01 0.45780E+02 0.31919E-03

0.789a85-03 0.421552+03 0.90207E+06 0.843102+00 0.88314E-03 0.23158E+01 0.45780E+02 0.32133E-03

0.792422-03 0,42385E+03 0.90699E+06 0.84769E+00 O.88904E-03 0.23284E+01 0.457792+02 0.32348E-03

0.79496E-03 0.42616E+03 0.91193E+06 0.852311400 0.894971-03 0.234111+01 0.45779E+02 0.325641-03

0.797501-03 0.42848E+03 0.91690E+06 0.85696E+00 0.90093E-03 0.235382+01 0.457792402 0.32781E-03

0.800042-03 0.43081E+03 0.92190E+06 0.86163EtOO 0.906922-03 0.23666E+01 0.45778E+02 0.329992-03

0.802581-03 0.43316E+03 0.92693E+06 0.86632E+00 0.91295E-03 0.237951+01 0.457782+02 0.332181-03

0.80512E-03 0.43552E+03 0.931982+06 0.871042+00 0.91901E-03 0.23925E+01 0.45778E+02 0.33439E-03

0.807662-03 0.43789E+03 0.93706E+06 0.87579E+00 0.925102-03 0.240552+01 0.45ý'77E+02 0.33661E-03

0.810202-03 0.440281+03 0.j4217&1+06 0.88056E+00 0.93123E-03 0.24186E+01 0.45777E+02 0.338841-03

0.81274E-03 0.44268E+03 0.94731E+06 0.885362+00 0.93739E-03 0.24317E+01 0.45776E+02 0.34108E-03

0.815281-03 0.445092+03 0.952472+06 0.89019L+00 0.943582-03 0.24450E+01 0.45776E+02 0.34335E-03

0.81782E-03 0.44752E+03 0.95766E+06 0.89504E+00 0.94981E-03 0.24583E+01 0.45776E+02 0.34560E-03

0.82036E-03 0.44996E+03 0.962852+06 0.899921+00 0.956012-03 0.24716E+01 0.45775E+02 0.34788E-03

0.82290E-03 0.452412+03 0.96813Ei 6 0.90482E+00 0.96236E-03 0.24851E+01 0.45175E+02 0.35017E-03

Page 31: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

TIME PRESSURE POOT XDOT PROPELLANT BURNT MOOT SURFACE DISrANCE BURNT

0.82544E-03 0.45488E*03 0.97341E+06 0.90975E+00 0.96869E-03 0.14986E+01 U.45775E-.02 0.352482-03

0.82798E-03 0.45735E+03 0.97872E4-06 0.91471E+00 0.97505E-03 0.25122E+01 0.45774E+0?. 0.35479E-03

0.83052E-03 0.45985E+03 0.98405E+06 0.91969E+00 0.98145E-03 0.25259E+01 0.45774a+02 0.35712E-03

0.83306E-03 0.46235E.03 0.98942E+06 0.92471E+00 0.98789E-03 0.25396E2+01 0.457732.02 0,35947E-03

0.83560E-03 0.46487E+03 0.99461E+06 0.92975E+00 0.994352-03 0.25534E+01 0.457?3t.02 0.36182E-030.83814E-03 0.467412+-03 0.10002E+07 0.934.81E+00 0.10009E-02 0.25673E.01 0.457732+02 0.36419E-03

0.840682-03 0.46995E+03 0.10057E.07 0.93991E+00 0.10074E-02 0,25813E+01 0.45772E402 0.36657E-03

0.84322E-03 0.47251E+03 0.10112E407 0.94503E+00 0.10140E-02 0.259S3E.01 0.45772E.02 0.36896E-030.84.576E-03 0.47509E+03 0.101672+07 0.95018E+00 0.10206E-02 0.26095E+0l1 0.45771E+02 0.37137E-03

0.848302-03 0.47'768E+03 0.10222E+07 0.95536E+00 0.10272E-02 0.262372+01 0.45771E+02 0.37379E-03

0.85084E-03 0.48028E+03 0.10278E+07 0.96057E+00 0.10339E-02 0.26379E+01 0.457712E+02 0.37622E-030.853382-03 0.s.8290E+03 0.103342+07 0.96580E+00 0.10406E-02 0.26523E+01 0.45770E.02 0.37867E-03

0.85592E-03 0.48553E+03 0.10390E+07 0.97106E+00 0.10474E-02 0.266672+01 0.45770E4.02 0.38113E-03

0.85846E-03 0.48818E+03 0,10447E+07 0.97636E.00 0.10542E-02 0.26812Eo.Ol 0.45769E+02 0.38360E-03

0.86i00E-03 0.49084E.03 0.10504E+07 0.98168E+00 0.106102-02 0.26958E+01 0.45769E+02 0.38609E-03

0.863542-03 0.49351E+03 0.10561E+07 0.98703E+00 0.10679E-02 0.27105E+01 0.45769E+02 0.38859E-030.86608E-03 0.496202+03 0.106192+07 0.992412+00 0.107482-02 0.27252E.01 0.45768E+02 0.39110E-03

0.86822-03 0.49891Ei-03 0.106?77+07 0.99782E+00 0.108172-02 0.27401E+01 0.1.5768E+02 0.39363E-030.87115E-03 0.50163E+03 0.10'135E.07 0.100332.01 0.10887E-02 0.27550E+01 0.45767E+02 0.39617E-03

0.87369E-03 0.50436E.03 0.10793E+07 0.100872.01 0.10957E-02 0.27700E+01 0.457672.02 0.39873E-030.87623E-03 0.507112.03 0.-10352E+07 0.10142E+01 0.11028E.02 0.278SOE401 0.45766E+02 0.40129E-03

0.87877E-03 0.509872.03 0.10911E+07 0.10197E+01 0.110982-02 0.28002E+01 0.457662+02 0.403882-03

0.8,81312-03 0.512652.05 0.10971E+07 0.10253E+01 0.11170E.02 0.28154E401 0.457662+02 0.40647E-030.83385E-03 0.515452+03 0.11031E+07 0.10309E+01 0.11241E-02 0.283072.01 0.45765E.02 0.40909E-03

0.88639E-03 0.51826E.03 0.11091E+01 0.10365E+01 0.11314E-02 0.28461E+01 0.45765E+02 0.41171E-030.88893E-03 0.52108E+03 0.11151E.07 0.10422E+01 0.11386E-02 0.28616E+01 0.45764E+02 0.41435E-030.89147E-03 0.52392E+03 0.i12l2E+07 0.10478E+01 0.11459E-02 0.28772E+01 0.45764E+02 0.417002-03

0.89401E403 0.52678E+03 0.112732.07 0.105362+01 0.11532E-02 0,289282+01 0.45*1632+02 0.41967E,03

0.89655E-03 0.52965E.03 0.11335E*07 0.10593E.01 0.11606E-02 0.29086E+01 0.45763E+02 0.42236E-030.89909E-03 0.53253E+03 0.11397E+07 0.10651E.01 0.11680E-02 0.29244E+'01 0.45762E4,02 0.42505E-03

0.90163E-03 0.535442.03 0.11459E+07 0.10709E+01 0.11754E-02 0.29403E+01 0.45762E+02 0.42777E.030.90417E-03 0.538352.03 0.11521E+07 0.10767E+01 0.11829E-02 0.29563E+01 0.45762E+02 0.43049E-03

0.90671E-03 0.54129E+03 0.11584E+07 0.10826E+01 0.11905E-02 0.29724E.01 0.45761E+02 0.4332-.E-030.90925E-03 0.54424E.03 0.11647E.07 0.10885E+01 0.119B0E-02 0.29886E+01 0.45761E+02 0.43599E-030.91179E-03 0.547202E-03 0.11711E+07 0.10944E+01 0.12056E-02 0.30U48E+01 0.45760E+02 0.43876E-03

0.91433E-03 0.55019E+03 0.11775E+07 0.11004E+01 0.12133E-02 0.302122+01 0.45760E.02 0.44155E-03

0.91687E2-03 0.55319E.03 0.118392+07 0.11064E.01 0.122102-02 0.303762+01 0.45759E+02 0.44435E-03

0.919412-03 0.55620E+03 0.119032+07 0.11124E+01 0.12287E-02 0.30541E+01 0.45759E+02 0.44717E-03

0.921952-03 0.55923E+03 0.119682+07 0.11185E+01 0.12365E-02 0.30707E4-01 0.45758E+02 0.450012-03

0.924492-03 0.56228E+03 0.12033E.07 0.11246E+01 0.12443E-02 0.308742.01 0.45758E+02 0.45285E-03

0.92703E-03 0.565342+03 0.12099E+07 0.113072401 0-12522E-02 0.31042E+01 0.45757E+02 0.45572E-030.92957E-03 0.568432.03 0.12165E+07 0.11369E.01 0.126012-02 0.312112E-01 0.45757E.02 0.458602-03

0.93211E-03 0.57152E+03 0.122312.07 0.11430E.01 0.126802-02 0.313812+01 0.457562+02 0.46149E-03

0.934652-03 0.57464E+03 0.12298E+07 0.114932+01 0.12760E-02 0.31552E+01 0.45756E+02 0.464402-03

0.93719E-03 0.57777E.03 0.123652+07 0.115552.01 0.12841E-02 0.31723E+01 0.45755E.02 0.467332-03

0.93973E-03 0.580922+03 0.124332+07 0.11613E+01 0.12921E-02 0.318962+01 0.457552+02 0.47027E-03

0.942272-03 0.58409E+03 0.125002E-07 0.11682F-+01 0. 30032-02 0.32069E.01 0.45754E.02 0.47323E-03

0.944812-03 0.587272+03 0.12568E+07 0.117452+01 0.13084E-02 0.32244E+01 0.45754E+02 0.476212-03

0.947'35E-03 0.59047E.03 0.12637E+07 0.11809E.01 0.131662-02 0.32419E+01 0.457532E-02 0.479202-03

0.94989E-03 0.593692+03 0.127062+07 0.11874E+01 0.132492-02 0.32596E+01 0.45753E+02 0.48221E-03

0.952432-03 0.59692E+03 0.12775E+07 0.11938E+01 0.133322-02 0.32773E+'01 0.45752E+02 0.485232-03

0.954972-03 0.600182.03 0.12845E+07 0.12004E.01 0.134162-02 0.32951E+01 0.45752E4-02 0.48827E-03

0.95751E-03 0.603452+03 0.129152+07 0.120692+01 0.13499E-02 0.331302+01 0.45751E.-.02 0.49133E-03

0.960052-03 0.60674E403 0.12985E+07 0.12135E+01 0.13584E-02 0.33311F.01 0.45751E+02 0.49440E-03

-3

Page 32: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

TINE PRESSURE PDOT XDOT PROPELLANT BURNT MOOT SURFACE DISTANCE BURN~T

0.96259E-03 0.61005E+03 0.130562+07 0.12201E+01 0.13669E-02 0.33492E+01 0.45750E+02 0.49749E-03

0.96513E-03 0.61337E.03 0.13127E+07 0.12267E.01 0.137'54E-02 0.33674E.Oi 0.45750E+02 0.50060E-03

0.96767E-03 0.61671E.03 0.13199E+07 0.12334E+01 0.13840E-02 0.33857E+01 0.45749E+02 0.50372E-03

0.970212-03 0.621007E.03 0.13271E.07l 0.124012.01 0.13926E-02 O.34041E+01 0,45741E+12 0,51686E-03

0.97275E-03 0.62345E+03 0.13343E+07 0.12469E+01 0.14013E-02 0.34226E+01 0.457482+02 0.51002E-03

0.97529E-03 0.62685E+03 0.13416E+07 0.12537E+01 0.14100E-02 0.34413E+01 0.45748E+02 0.51320E-03

0.97783E-03 0.630272+03 0.13489E+07 0.12605E+.01 0.14187E-02 0.34600E+01 0.457472+02 0.51639E-03

0,98037E-03 0,63370E+03 0,13563E+17 0.12674E+01 0.14276E-02 0.34788E+01 0.45741E+02 O.51960E-03

0.98291E-03 0.63716E+03 0.13637E+07 0.12743E+01 0.14364E-02 0.34977E+01 0.45746E+02 0.52283E-03

0.98545E-03 0.64063E+03 0.13711E+07 0.12813E+01 0.14453E-02 0.35167E+01 0.45746E+02 0.52607E-03

0.9879'9E--03 0.64412E+03 0.13786E+07 0.128822+01 0.145432-02 0.353592+01 0.457452+02 0.52934E-03

0.99053E-03 0.647632+03 0.138612+07 0.12953E+01 0.14633E-02 0.35551E+01 0.45745E+02 0.53262E-03

0.99307E-03 0.65116E+03 0.13937E+07 0.13023E+01 0.14723E-02 0.35744E+01 0,45744E+02 0.53592E-03

0.995612-03 0.654712+03 0.14013E+07 0.13094E+01 0.148142-02 0.35939E+01 0.45743E+02 0.53923E-03

0.9-9815E-03 0.65828c-+03 0. 14089E+07 0.13166E+01 0.14906E-02 0.36134E+01 0.45743E+02 0.54257E,-03

0.100072-02 0.6616172403 0.14166E+07 0,13237E+01 0.149982-02 0.363312+01 0.45742E+02 0.54592E-03

0.10032E-02 0.66548E+03 0.14243E+07 0.13310E+01 0.150902-02 0.365282+01 0.45742E+02 0.549292-03

0.100582-02 0.669112.03 0.14321E+07 0.13382E+01 0.151832-02 0.36727E+01 0,45741E+02 0.552682-03

0.100832-02 0.67275E+03 0.14399E+07 0.13455E+01 0.15277E-02 0.36927E+01 0.45741E+02 0.55609E-03

0.101082-02 0.67642E+03 0.14477E.07 0.13528E+01 0.15371E-02 0.37127E+01 0.45740E.02 0.55952E-03

0.10134E-02 0.68011E+03 0.14556E+07 0.13602E+01 0.15466E-02 0.37329E+01 0.45740E+02 0.56296E-03

0.101592-02 0.683812+03 0.14636E+07 0.13676E+01 0.155612-02 0.37532E+01 0.45739E+02 0.56643E-03

0.10185E-02 0.68754E+03 0.14715E+07 0.13751E+01 0.15656E-02 0.37736E+01 0.45738E.02 0.56991E-03

0.10210E-02 0.69129E+03 0.147196E+07 0.138262.01 0.15752E-02 0.37942E+01 0.457382+02 0.57341E-03

0.102352-02 0.695062+03 0.14876E+07 0.139012+01 0.15849E-02 0.381482.01 0.45737E+02 0.57693E-03

0.10261E-02 0.69884E+03 0.14958E+07 0.13977E.01 0.15946E-02 0.383552+01 0.45737E+32 0.58047E-03

0.102862-02 0.70265E+03 0.150392+07 0.14053E+01 0.16044E-02 0.385642+01 0.45736E+02 0.58403E-03

0.10312E-02 0.706481+03 0.15121E+07 0.14130E+01 0.16142E-02 0.38774E+01 0.45735E+02 0.587612-03

0.10337E-02. 0.71034E+03 0.152042+07 0.14207E+01 0.162412-02 0.38984E+01 0.45735E.02 0.59121E-03

0.10362E-02 0.71421E+03 0.15286E+07 0.14284E+01 0.16340E-02 0.391962+01 0.45734E+02 0.59483E-03

0.10388E-02 0.71810E+03 0.153702+07 0.143622.01 0.164402-02 0.394102+01 0.457342+02 0.59846E-03

0.10413E-02 0.72201E+03 0.154542+07 0.14440E+01 0.16540E-02 0.39624E+01 0.457332+02 0.60212E-03

0.10439E-02 0.725952+03 0.155382+07 0.14519E+01 0.166412-02 0.398392+01 0.457322+02 0.605802-03

0.10464L-02 0.72991E+03 0.15623E+07 0.14598E+01 0.16743E-02 0.40056E+01 0.457322+02 0.60950E-03

0.10489E-02 0.73389E+03 0.15708E+07 0.146782401 0.16845E-02 0.40274E.101 0.45731E+02 0.61321E-03

0.10515E-02 0.73789E+03 0.15794E+07 0.147582+01 0.16947E-02 0.40493E+01 0.457312+02 0.616952-03I0.10540E-02 0.74191E+03 0.158802.07 0.148382+01 0.17050E-02 0.40713E+01 0.45730E+02 0.620712-030.10566E-02 0.74595E+03 0.15966E+07 0.14919E+01 0.17154E-02 0.409342+01 0.45729E+02 0.62449E-03

0.105912-02 0.75002E+03 0.16053E+07 0.15000E+01 0.172582-02 0.41157E+01 0.457292.02 0.62829E-03

0.10616E-02 0.75411E+03 0.161412+07 0.150822+01 0.171363E-02 0.41381E+01 0.45728E+02 0.63211E-03

0.106422-02 0.75822E.03 0.16229E+07 0.15164E+01 0.17468E-02 0.416062+01 0.457272+02 0.635952-03

0.10667E-02 0.762352.03 0.16317E+07 0.152472+01 0.1'7574E-02 0.41832E+01 0.457272+02 0.63981E-03

0.10693E-02 0.76651E+03 0.16406E+07 0.15330E+01 0.176812-02 0.42059E+01 0.457262+02 0.643702-03

0.10718E-02 0.77068E+03 0.16496E+07 0.154142.01 0.17788E-02 0.42288E+01 0.45725E+02 0.647602-03

0.10743E-02 0.77489E+03 0.16586E.07 0.15498E+01 0.17896E-02 0.42518E+01 0.45725E+02 0.65153E-03

0.10769E-02 0.77911E.03 0.16676E+07 0.155822+01 0.18004E-02 0.42749E+01 0.45724E+02 0.65547E-03

0.107942-02 0.783362.03 0.16767E+07 0.15667E+01 0.18113E-02 0.42981E+01 0.457232+02 0.659442-03

0.10820E-02 0.78763E+03 0.168592+07 0.157532.01 0.18222E-02 0.43215E+01 0.45723E+02 0.66343E-03

0.108452-02 0.191922+03 0.16951E+07 0.15838E.01 0.183322-02 0.434502+U1 0.45722E+02 0.66744E-03

0.108702-02 0.79624E+03 0.17043E+07 0.15925E+01 0.18443E-02 0.43686E+01 0.45721E+02 0.671482-03

0.108962-02 0.80058E+03 0.171362+07 0.16012E+01 0.18554E-02 0.43924E+01 0.457212+02 0.67553E-03

0.10921E-02 0.80494E+03 0.17230E+07 0.16099E+01 0.18666E-02 0.44162Eý01 0.45720E+02 0.67961E-03

0.10947E-02 0.80933E403 0.17324E+07 0.16187E.01 0.18779E-02 0.44402E+01 0.45719E+02 0.68371E-03

0.10972E-02 0.81374E+03 0.17418E+07 0.16275E+01 0.18892E-02 0.44644E+01 0.45719E+02 0.687832-03

Page 33: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

TIME PRESSURE PDOT XDOT PROPELLANT BURNT MOOT SURFACE DISTANCE BURNT

0.10997E-02 0.81818E+03 0.17513E+07 0.16364E+01 0.19005E-02 0.44887E+01 0.457l8Et02 0.69198E-03

0.11023E-02 0.82264Es-03 0.17609E+07 0.16453E+01 0.19120E-02 0.45131E+01 0.45717E+02 0.69614E-03

0.110482-02 0.82712E+03 0.17705E+07 0.16542E+01 0.19235E-02 0.45376E+01 0.45717E+02 0.70033E-03

0.11074E-02 0.83163E+03 0.17801E+07 0.16633E+01 0.193502-02 0.45623E+01 0.45716E+02 0.70455E-03

0.11099E-02 0.83616E+03 0.17898Ei-O7 0.16723E+01 0.19466E-02 0.45871E+01 0.45715E.02 0.708782-03

0.11124E-02 0.840722+03 0.17996E+07 0.16814E+0)1 0.19583E-02 0.46120E+01 0.45714E+02 0.71304E-03

0.11150E-02 0.84531E+03 0.18094E+07 0.16906E+01 0.19701E-02 0.46371E+01 0.45714E+02 0.71732E-03

0.111752-02 0.84991E+03 0.10193E+07 0.16998F.01 0.19819E-02 0.46623E+01 0.45713E+02 0.72163E-03

0.11201E-02 0.85455E+03 0.18292E4-07 0.17091E4-01 0.19937E-02 0.46876E+01 0.45712F+02 0.72596E-030.11226E-02 0.85921E+03 0.18392E.07 0.17184E+01 0.20057E-02 0.47131E+01 0.45712E+02 0.73031E-03

0.11251E-02 0.86389E+03 0.18492E+07 0.17278E+01 0.20177E-02 0.47387E+01 0.45711E+02 0.73WF'-03

0.11277'E-02 0.868602.03 0.18593E+07 0.17372E+01 0.202982-02 0.476459+01 0.45710E+02 0.73909E-03

0.11302E-02 0.87333E+03 0.18694E+07 0.17467E+01 0.204.19E-02 0.47904E+01 0.45709E+02 0.74351E-030.113282-02 0.878092.03 0.18796E+07 0.17562E+01 0.20541E-02 0.48164E+01 0.45709E+02 0.74796E-03

0.11353E-02 0.88288E+03 0.18899E+07 0.17658E+01 0.20664E-02 0.48426E+01 0.45708E+02 0.75243E-03

0.11378E-02 0.887692+03 0.19002E+07 0.17754E+01 0.20787E-02 0.48689E+01 0.45707E+02 0.75693E-03

0.11404E-02 0.89253E4-03 0.19106E+07 0.17851E+01 0.20911E-02 0.48953E.01 0.45706E.02 0.76145E-03

0.11429E-02 0.89740E.03 0.19210E+07 0.17948E+01 0.21036E-02 0.49220E+01 0.45706E+02 0.766002-03

0.11455E-02 0.90229E+03 0.19315E+07 0.18046E+01 0.21161E-02 0.49487E+01 0.45705E+02 0.77057E-03

0.11480E-02 0.90721E+03 0.19420E+07 0.18144E+01 0.21287E-02 0.49756E+01 0.45704E+02 0.77516E-030.11505E-02 0.91216E.03 0.19526E+07 0.182432+01 0.21414E-02 0.50026E+01 0.45703E+02 0.77978E-03

0.11531E-02 0.91713E+03 0.19633E+07' 0.183432+01 0.215412-02 0.502989+01 0.45703E+02 0.78443E-030.11556E-02 0.92213E+03 0.19740E+07 0.18443E+U1 0.21669E-02 0.505722+01 0.45702E+02 0.78910E-03

0.11582E-02 0.92716E4-03 0.19847E+07 0.18543E+01 0.21798E-02 0.50846E+01 0.45701E+02 0.793802-03

0.11607E-0Z 0.93221E+03 0.19956E.07' 0.186442+01 0.21927E-02 0.51123E+01 0.45700E+02 0.79852E-03

0.116322-02 0.93729E+03 0.20064E+07 0.18746E+01 0.22058E-02 0.51401E+01 0.456992+02 0.80327E-030.116582-02 0.942402+03 0.20174E+07 0.188482+01 0.22189E-02 0.51680E+01 0.45699E+02 0.80804E-03

0.11683E-02 0.94754E+03 0.202842+07 0.189512+01 0.22320E-02 0.519612+01 0.456982+02 0.812842-03

0.11709E-02 0.95271E+03 0.20395E+07 0.19054E+01 0.22452E-02 0.52243E+01 0.45697E+02 0.81767E-03

0.11734E-02 0.95790E+03 0.20506E+07 0.19158E+01 0.22586E.02 0.52527E+01 0.45696E+02 0.82252E-03

0.117'592-02 0.96312E+03 0.206182+07 0.192622+01 0.22719E-02 0.52812E+01 0.45695E+02 0.82740E-03

0.117852-02 0.96837E+03 0.20730E+07 0.19367E+01 0.228542-02 0.53099E+01 0.45695E+02 0.83231E-03

0.11810E-02 0.97365E+03 0.208,43E+07 0.19473E+01 0.22989E-02 0.533a824-01 0.45694E+02 0.83724E-03

0.11836E-02 0.97896E+03 0.209572+07 U.19579E+01 0.23125E-02 0.53678E+01 0.456932+02 0.84220E-03

0.118612-02 0.98430E+03 0.2107iE+07 0.19686E+01 0.23262E-02 0.53970E+01 0.45692E+02 0.84718E-03 .0.11886E-02 0.98966E+03 0.21186E+07 0.19'1932+01 0.23399E-02 0.54263E+01 0.456912+02 0.85220E-03

0.119122-02 0.99506E+03 0.21302E+07 0.19901E+01 0.23537E-02 0.54558E+01 0.45690E+02 0.85724E-03

0.119372-02 0.100052+04 0.21418E+07 0.20010E+01 0.23676E-02 0.54854E4-01 0.456902+02 0.66231E-03

0.11963E-02 0.10059E'-04 0.21535E+07 0.20119E.01 0.23816E-02 0.55152E+01 0.45689E+02 0.86740E-03 -

0.1198BE-02 0.101142+04 0.216522+07 0.20228E+01 0.23956E-02 0.554522+01 0.45688E+02 0.87253E-03

0.120132-02 0.10169E+04 0.21771E+07 0.203392+01 0.24098E-02 0.55753E+01 0.45687E+02 0.87768E-03

0.12039E-02 0.10225E+04 0.218892+07 0.204502+01 0.24240E-02 0.56056E+01 0.45686E+02 0.88286E-03

0.120642-02 0.10281E+04 0.22009E+07 0.205612+01 0.24382E-02 0.56361E+01 0.456852+02 0.888072-03

0.12089E-02 0.103372+04 0.221292+07 0.206732.01 0.24526E-02 0.56667E+01 0.45684E+02 0.893302-03

0.12115E-02 0.10393E+04 0.22250E+07 0.20786E.-01 0.24670E-02 0.56975E+01 0.45684E+02 0.89857E-03

0.121402-02 0.10450E+04 0.22371E+07 0.20899E+01 0.24815E-02 0.57284E+01 0.45632+02 0.903862-03

0.12166E-02 0.10507E+04 0.22493E+07 0.21013E+01 0.24961E-02 0.57595E+01 0.45682E+02 0.909182-03

0.12191E-02 0.10564E+04 0.226162+07 0.21128E+01 0.25108E-02 0.5790U2+01 0.45681E+02 0.91453E-03

0.12216E-02 0.10622E+04 0.22739E+07 0.212432+01 0.252552-02 0.58223E+01 0.456,80E+02 0.91992E-03

0.12242E-02 0.10679E+04 0.228632+07 0.213592+01 0.25404E-02 0.58539E+01 0.45679E+02 0.92533E-03

0.12267E-02 0.10738E+04 0.22988E+07 0.21475E+01 0.25553E-02 0.58857E+01 0.45678E+02 0.93076E-03

0.122932-02 0.107962+04 0.23113E+07 0.215922+01 0.257032-02 0.59177E+01 0.45677E+02 0.93623E-03

0.12318E-02 0.10855E+04 0.232402E-07 0.21710E+01 0.25853E-02 0,59498E+01 0.45676E+02 0.94173E-03

0.12343E-02 0.10914E+04 0.23366E+07 0.21828E+01 0.26005E-02 0.59822E.01 0.45675E+02 0.94726E-03

Page 34: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

TINE PRESSURE PDOT XDOT PROPELLANT BURNT MDOT SURFACE DISTANCE BURNT

0.12369E-02 0.10974E+04 0.23494E+07 0.21947Ei-01 0.26157E-02 0.60146E+01 0.45675E+02 0.95282E-030.12394E-02 0.11034E+04 0.23622E+07 0.22067E+01 0.26310E-02 0.60473E+01 0.45674E+02 0.95841E..030.12420E-02 0.11094E+04 0.23751E+07 0.22187E+01 0.26464E-02 0.60802E+01 0.45673E+02 0.96403E-030.12445E-02 0.11154E+04 0.23881E+07 0.22308U+01 0.26619E-02 0.61132E+01 0.45672E+02 0.96968E-030.12470E-02 0.112152+04 0.24011E+07' 0.22430E+01 0.267752-02 0.61464E+01 0.45671E+02 0.9"1536E-030.12496E-02 0.11276E+04 0.24142E+07 0.22552E+01 0.26931E-02 0.61798E+01 0.45670E+02 0.981072-030.125212-02 0.11338E+04 0.24274E'-07 0.22675E+01 0.27089E-02 0.62133E+01 0.45669E+02 0.986822-030.12547E-02 0.11399E+04 0.24406E'07 0.22799Ee-01 0.27247E-02 0.62471E+01 0.4.5668E+02 0.99259E-030.12572E-02 0.11462E+04 0.24539E+07 0.22923E+01 0.27406E-02 0.62810E+01 0.45667E+02 0.99840E-030.12597E-02 0.115242+04 0.24673E+07 0.23048E+01 0.27566E-02 0.63151E+01 0.45666E+02 0.10042E-020.12623E-02 0.11587E4-04 0.24808E+07 0.23174E+01 0.277272-02 0.63494E+01 0.45665E+02 0.10101E-020.1264.8E-02 0.11650E+04 0.249432+07 0.23300E'-01 0.27889E-02 0.63839E+01 0.45664E+02 0.10160E-020.12674E-02 0.11714Ei-04 0.25079E+07 0.23427E+01 0.28051E-02 0.64186E+01 0.45663E+02 0.102192-020.12699E-02 0.11778E+04 0.25216E+07 0.23555E.01 0.28215E-02 0.64534E+01 0.45662E+02 0.10279E-020.12724E-02 0.11842E+04 0.25354E+07 0.23684E,01 0.28379E-02 0.64885E+01 0.456612+02 0.10339E-020.12750E-02 0.11906E4-04 0.25492E+07 0.23813E+01 0.28544E-02 0.652372+01 0.45660E+02 0.10399E-020.12775E-02 0.119710404 0.256312+07 0.23943E+01 0.287102-02 0.65591E+01 0.45659E+02 0.10460E-020.12801E-02 0.120379+04 0.257712+07 0.24073E+01 0.2a87r2E-02 0.65948E+01 0.45658E+02 0.105212-020.12826E-02 0.121022+04 0.25912E+07 0.24Z042i-01 0.29045E-02 0.66306E+01 0.45657E+02 0,10582E.020.128512-02 0.12168E+04 0.26053E+07 0.24336E.01 0.29214E-02 0.666662+01 0.45656E+02 0.10644E-020.12877E-02 0.12235E+04 0.26195E+07 0.24469E+01 0.293842-02 0.67028E+01 0.45655E+02 0.10706E-020.12902E-02 0.12301E+04 0.26338E+07 0.246022+01 0.295552-02 0.67392E+01 0,45654E+02 0.10768E.020.129282-02 0.12368E+04 0.26482E+07 0.247372+01 0.29726E-02 0.67758E+01 0.45653E+02 0.10831E-02

0.12953E-02 0.12436E'-04 0.26627E+07 0.248712401 0.29899E-02 0.681262+01 0.45652E+02 0.108942-02I

0.12978E-02 0.12504E+04 0.26772E+07 0.250072E+01 0.30072E-02 0.684962+01 0.45651E+02 0.109572-020.13004E-02 0.12572E+04 0.26918E+07 0.25143E.01 0.30247E-02 0.688672+01 0.45650E+02 0.110212-020.13029E-02 0.126402+04 0.27065E+07 0.2528124.01 0.30422E-02 0.692412+01 0.45649E+02 0.110852-020.13055E-02 0.127092+04 0.27213E+07 0.25418E+01 0.30599E-02 0.69617E+01 0.45648E+02 0.11149E-020.13080E-02 0.12779E+04 0.27361E+07 0.25557E+01 0.30776E-02 0.69995E+nl 0.45646E+02 0.11214E2-02

0.131052-02 0.128482+04 0.27510E+07 0.256962+01 0.309542-02 0.703r52+01 0.45645E+02 0.11279E-02I

0.13131E-02 0.12918E+04 0.27661E+07 0.258372+01 0.31133E-02 0.707'57E+01 0.456'4E+02 0.1 13452-020.13156-02 0.129892+04 0.27812E+07 0.259772+01 0.313142-02 0.71141E+01 0.4561#3E+02 0.11410E-020.131822-02 0.130602+04 0.27963E+07 0.261192+01 0.31495L-02 0.71528E+01 0.45642E+02 0.11477E-020.13207E-02 0.131312+04 0.281162.07 0.26261E+01 0.316772-02 0.719162+01 0.456412+02 0.115432-020.13232E-02 0.13202E+04 0.28269E+07 0.264052+01 0.31860E-02 0.72306E+01 0.456402+02 0.116102-020.13258E-02 0.13274E+04 0.2d424E+07 0.26549E+01 0.32044E-02 0.726992+01 0.45639E+02 0.116772-020.13283E-02 0.13347E+04 0.28579E+07 0.266932+01 0.32229E-02 0.73094E+01 0.45633E+02 0.11745E-020.133092-02 0.13420E+04 0.28735E+07 0.26839E+01 0.324152-02 0.73490E+01 0.45636E+02 0.11813E-020.133342-021 0.13493E+04 0.28892E+07 0.269852+01 0.32603E-02 0.73889E+01 0.45635E+02 0.11881F.-020.13359E-02 0.135662+04 0.290492+07 0.27133E+01 0.32791E-02 0.742902+01 0.45634E+02 0.119502-020.133852-02 0.13640E+04 0.292082+07 0.272812+01 0.329802-02 0.74694E+01 0.456332402 0.12019E-020.134102-02 0.13715E+04 0.29367E+07 0.27429E+01 0.331702-02, 0.75099E+01 0.45632E+02 0.12088E-02 N0.134362-02 0.137892+04 0.295282+07 0.27579E+01 0.333612-02 0.75507E+01 0.45631E+02 0.121582-020.13461E-02 0.138652.04 0.296892+07 0.277292+01 0.33554E-02 0.75916E+01 0.45630E+02 0.12229E-020.13486E-02 0.139402+04 0.29851E+07 0.27880E+01 0.337472-02 0.76328E+01 0.45628E4-02 0.12299E-020.13512E-02 0.140162+04 0.30014E+07 0.28033E+01 0.339412-02 0.767432+01 0.45627E+02 0.12370E-020.13537E-02 0. 14093E+04 0.30178E+07 0.281852+01 0.341372-02 0.77159E401 0.456262+02 0.12442E-020.13563E-02 0.141702404 0.303432+07 0.28339E+01 0.343332-02 0.775782401 0.45625E+02 0.12513E-020.13588E-02 0.14247E+04 0.30508E+07 0.28494E+01 0.345312-02 0.77999E+01 0.456242+02 0.12586E-020.13613E-02 0.143252+04 0.306752+07 0.286492+01 0.347302-02 0.78422E+01 0.45622E+02 0.126582-020.13639E-02 0.14403E+04 0.30842E+07 0.28805E+01 0.34929E-02 0.78848E+01 0.45621E+02 0.127'31E-020.136642-02 0.144812+04 0.31011E+07 0.28C -ZE.01 0.351302-02 0.792762+01 0.45620E+02 0.12804E-020.13690E-02 0.145602+04 0.31180E+07 0.29120E+01 0.35332E-02 0.79706E+01 0.45619E+02 0.128782-020.13715E-02 0.14640E+04 0.31350E+07 0.29279E+01 0.355352-02 0.80138E+01 0.45617E+02 0.12952E-02

36

Page 35: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

TIME PRESSURE PDOT XDOT PROPELLANT BURNT MOOT SURFACE DISTANCE BURNT

0.13740E-02 0.14719E.+04 0.31521E+07 0.29439E+01 0.35739E-02 0.80573E+01 0.45616E4-02 0.13027E-02

0.13766E-02 0.14800E+04 0.31693E+07 0.29599E+01 0.35944E-02 0.81010E+01 0.45615E+02 0.13102E-020.13791E-02 0.14880E.04 0.31866E.07 0.29761E.01 0.36151E-02 0.81450E.01 0.45614E+02 0.13177E-02

0.13817E-02 0.14962E+04 0.32040E+07 0.29923E+01 0.3635SE-02 0.81892E+01 0.45612E+02 0.13253E-020.13842E-02 0.15043E+04 0.32215E+07 0.30086E+01 0.%6567E-02 0.82336E+01 0.45611E+02 0.13329E-020.13867E-02 0.15125E+04 0.32391E.07 0.30250E.01 0.36776E-02 0.82783E+01 0.45610E+02 0.13406E-020.13893E-02 0.152082.04 0.32568E+07 0.30415E+01 0.36987E-02 0.832322+01 0.45609E+02 0.13483E-020.139182-02 0.15291E+04 0.32746E+07 0.30581E+01 0.37199E-02 0.836842+01 0.456072+02 0.13560E-02

0.13944E-02 0.15374E+04 0.32924E+07 0.307482.01 0.37412E-02 0.84138E+01 0.456062.02 0.13638E-020.13969E-02 0.15458E+04 0.33104E+07 0.30916E+01 0.37626E-02 0.84594E+01 0.45605E+02 0.13717E-020.13994E-02 0.15542E+04 0.33285E+07 0.31084E.01 0.37842E-02 0.850532.01 0.45603E.02 0.137952-020.14020E-02 0.15627E.04 0.334672.07 0.31254E.01 0.38058C.-02 0.85515E+01 0.45602E+02 0.13874E-020.14045E-02 0.15712E+04 0.33649E+07 0.31424E+01 0.38276E-02 0.85979E+01 0.45601E+02 0.13954E-020.14071E-02 0.15798E+04 0.33833E+07 0.31596E+01 0.38495E-02 0.86445E+01 0.45599E+02 0.14034E-02

0.14096E-02 0.15884E.04 0.34018E+07 0.317682.01 0.38715E-02 0.86914E+01 0.45598E+02 0.141'15E-020.14121E-02 0.15971E+04 0.34204E+07 0.31941E+01 0.389372-02 0.87385E+01 0.45597E402 0.141952-020.14147E-02 0.1605U2.04 0.34390E+07 0.32116E.01 0.39159E-02 0.878592+01 0.45595E+02 0.14277E-02

0.14172E-02 0.16145E+04 0.34578E+07 0.322g12.01 0.393832-02 0.88336E+01 0.45594E+02 0.14359E-020.14198E-02 0.162332+04 0.34767E+07 0.32467E.01 0.396082-02 0.888152.01 0,455932+02 0.144412-020.142232-02 0.16322E+04 0.34957E+07 0.32644E+01 0.39834E-02 0.89297E+01 0.455912+02 0.14524E-02

0.142482-02 0.16411E.04 0.351482.07 0.328222.01 0.40062E-02 0.89781E+01 0.455902+02 0.14607E-020.14274E-02 0.16501E+04 0.35340E+07 0.33001E+01 0.402902-02 0.90268E+01 0.45588E+02 0.14690E-020.142992-02 0.165912.04 0.35533E+07 0.33181E+01 0.40520E-02 0.90758E.01 0.455872+02 0.14774E-020.14325E-02 0.16681E+04 0.35727E.07 0.33362E+01 0.407512-02 0.91250E+01 0.455862.02 0.14859E-02

0.14350E-02 0.16772E+04 0.35922E407 0.335442+01 0.409842-02 0.91745E+01 0.45584E+02 0.14944E-020.143752-02 0.16863E+04 0.361182+07 0.337272+01 0.412172-02 0.92242E.01 0.45583E+02 0.15029E-020.14401E-02 0.16955E.04 0.36315E+07 0.339112.01 0.41452E-02 0.92742E+01 0.45581E+02 0.15115E-020.14426E-02 0.17048E+04 0.365132+07 0.340962+01 0.416882-02 0.93245E+01 0.45580E+02 0.15201E-02

0.14452E-02 0.171412+04 0.36713E+07 0.342822.01 0.419262-02 0.937512.01 0.45579E.02 0.152882-020.14477E-02 0.17234E+04 0.36913E+07 0.344692+01 0.421652-02 0.94259E+01 0.455772.02 0.15376E!020.14502E-02 0.17328E+04 0.371152.07 0.34657E+01 0.424052-02 0.947712.01 0.45576E+02 0.15463E-020.145282-02 0.17423E+04 0.37318E+07 0.348462.01 0.42646E-02 0.95284E+01 0.45574E.02 0.15552E2020.14553E-02 0.17'518E+04 0.37521E+07 0.35036E.01 0.42889E-02 0.95801E+01 0.45573E+02 0.15640E-020.14579E-02 0.17(614E+04 0.37726E+07 0.352272.01 0.431332-02 0.96320E.01 0.45571F+02 0.157302-02

0.146042-02 0.177102+04 0.37932E+07 0.35419E+01 0.433782-02 0.96a432.01 0.4S5702.02 0.15819E-020.14629E-02 0.17806E+04 0.38140E+07 0.35612E+01 0.43625E-02 0.97368E+01 0.45568E+02 0.15909E-020.146552-02 0.17903E.04 0.383482+07 0.35807E.01 0.43873E-02 0.97896E+01 0.45567E+02 0.160002-02

0.146802-02 0.180012+04 0.38557E+07 0.36002E+01 0.44122E-02 0.984262.01 0.45565E+02 0.16091E-020.14706E-02 0.18099E+04 0.387682+07 0.36198E.01 0.44372E-02 0.989602+01 0.45564E+02 0.161832-02

0.147312-02 0.181982+04 0.389802.07 0.363962+01 0.44625E-02 0.99496E.01 0.455622.02 0.16275E-02

0.14756E-02 0.18297E.04 0.39193E+07 0.36594E+01 0.448782-02 0.10004E.02 0.4556iE+02 0.163682-020.14782E-02 0.18397E+04 0.39407E+07 0.36794E.01 0.45133E-02 0.10058E+02 0.455592+02 0.16461E-02

0.148072-02 0.16497E+04 0.39622E+07 0.36995E+01 0.45389E-02 0.10112E+02 0.45557E+02 0.16555E-020.148322-02 0.18598E+04 0.39838E+07 0.37197E+01 0.45646E-02 0.10167E+02 0.45556E+02 0.16649E-02

0.148582-02 0.18700E+04 0.40056E+07 0.37400E+01 0.459052-02 0.10222E.02 0.455542+02 0.16'144E-02

0.148832-02 C.18802E+04 u.40275E+07 0.37604E+01 0.461662-02 0.10278E+02 0.45553E+02 0.16839E-02

0.14909E-02 0.189042+04 0.40495E+07 0.378092+01 0.46427E-02 0.103332+02 0.455512+02 0.16935E-02

0.14934E-02 0.19007E+04 0.40716E+07 0.38015E+01 0.46690E-02 0.10389E+02 0.45549E+02 0.17031E-02

0.14959E-02 0.19111E+04 0.409382+07 0.382222+01 0.469552-02 0.10446E+02 0.455482+02 0.17128E-02

0.14985E-02 0.19215E'-04 0.41162E+07 0.384312+01 0.47221E-02 0.10502E+02 0.45546E402 0.17225E-02

0.150102-02 0.19320E+04 0.41387E+07 0.38641E+01 0.47489E-02 0.10559E+02 0.45545E+02 0.17323E-02

0.15036E-02 0.19426E+04 0.416132+07 0.38851E+01 0.477572-02 0.10616E+02 0.45543E+02 0.174222-02

0.15061E-02 0,19532E+04 0.418402+07 0.39063E+01 0.480282-02 0.10674E+02 0.455412+02 0.17520E-02

0.15086E-02 0.19638E+04 0.42069E+07 0.39276E.01 0.483002-02 0.10732E+02 0.45540E.02 0.17620E-02

37

Page 36: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

TIME PRESSURE FOOT XOOT PROPELLANT BURNT MOOT SURFACE DISTANCE BURNT

0.15112E-02 0.19745E+04 0.42299E+07 0.39491E+01 0.48573E-02 0.10790E+02 0.45538E.02 0.17720E-020.15137E-02 0.19853E+04 0.42530E+07 0.39706E+01 0.48848E-02 0.1084$E+02 0.45536E+02 0.17821E-020.15163E-02 0.19961E+04 0.42762E+07 0.39923E+01 0.49124E-02 0.10907E+02 0.45535E+02 0.17922E.-020.1518SE-O2 0.20070E+04 0.42996E+07 0.40141E+01 0.49402E-02 0.10966E+02 0.45533E+02 0.18023E-020.15213E-02 0.20180E+04 0.43230E+07 0.40360E+01 0.49681E-O2 0.11026E+02 0.45531E+02 0.18126E-020.15239E-02 0.20290E+04 0.43467E.07 0.40580E+01 0.49962E-02 0.11085E+02 0.45530E+02 0.18228E-020.15264E-02 0.20401E+04 0.43704E+07 0.40801E+01 0,50244E-02 0.11146E+02 0.45528E+02 0.18332E-020.152902-02 0.20512E+04 0.43943E+07 0.410242+01 0.505282-02 0.11206E+02 0.45526E+02 0.18436E-020.15315E-02 0.20624E+04 0.44l832+07 0.412482+01 0.50813E-02 0.11267E+02 0.455242+02 0.18540E-020.153402-02 0.20736E+04 0.44424E407 0.41473E+01 0.511002-02 0.113282+02 0.45523E+02 0.186452-020.15366E-02 0.208492+104 0.44667E+07 0.41699E+01 0.51389E-02 0.11389E+02 0.45521E+02 0.18751E-020.15391E-02 0.20963E+04 0.44911E+07 0.419262.01 0.51679E-02 0.114512.02 0.45519E+02 0.18857E,,020.15417E-02 0.21078E+04 0.45157E.07 0.421552+01 0.519702-02 0.115132+02 0.45517E+02 0.189642-020.154422-02 0.21193E+04 0.45403E+07 0.42385E+01 0.52264E-02 0.11575E+02 0.45515E+02 0.1907.1E-020.15467E202 0.21308E-+04 0.45651E+07 0.426Vv-+01 0.52558E-02 0.11638E+02 0.45514E+02 0.19179E-020.154932-02 0.21424E+04 0.459012+07 0.42049E+01 0.528552-02 0.117012+02 0.45512E.02 0.192882-020;15518E-02 0.215412.04 0.46152E+07 0.43083E+01 0.53153E-02 0.117642+02 0.45510E+02 0.19397E-020.155442-02 0.21659E+04 0.46-404E+07 0.433182+01 0.53452E-02 0.11828E+02 0.45508E+02 0.19706E-020.155692-02 0.21777E+04 0.46657E.07 0.43554E+01 0.53754E-02 0.11892E+02 0.45506E+02 0.19617E-020.15594E-02 0.21896E+04 0.469122+07 0.43792E+01 0.54056E-02 0.11956E+02 0.455052+02 0.19728E-020.156202-02 0.22015E+04 0.47169E+07 0.44031E+01 0.54361E-02 0.120212+02 0.45503E+02 0.198392-020.15645E-02 0.221362.04 0.47426E+07 0.44271E+01 0.54667E-02 0.12086E+02 0.45501E+02 0.199512-020.15671E-02 0.222562.04 0.47686E+07 0.44513E+01 0.54975E-02 0.12152E+02 0.45499E+02 0.20064E-020.15696E-02 0.22378E+04 0.47946E+07 0.447552.01 0.552842-02 0.12217E+02 0.45497E+02 0.201772-020.15721E-02 0.225002+04 0.48208E+07 0.45000E+01 0.555952-02 0.12284E+02 0.45495E+02 0.20291E-020.15747E-02 0.22623E+04 0.48472E+07 0.45245E+01 0.55908E-02 0.12350E+02 0.454932+02 0.20406E-020.15772E-02 0.22746E+04 0.48737E+07 0.454922.01 0.56223E-02 0.124172+02 0.45491E+02 0.205212-020.157982-02 0.22870E+04 0.490032+07 0.45740E+01 0.56539E-02 0.1248.4E+02 0.45489E+02 0.20637E-020.158232-02 0.229952+04 0.492712+07 0.459902+01 0.568572-02 0.125522+02 0.45487E+02 0.207542-020.15848-02 0.23120E+04 0.49540E+07 0.462412+01 0.57177E-02 0.126202+02 0.45485E+02 0.208712-02

N0.15874E-02 0.23247E+04 0.498112+07 0.464932+01 0.574982-02 0.126882.02 0.45484E+02 0.209882-020.158992-02 0.23373E+04 0.500832+07 0.46747E+01 0.578212-02 0.127572+02 0.454822+02 0.211072-020.15925E-02 0.235012+04 0.50357E+07 0.470022.01 0.58146E-02 0.12826E+02 0.45480E+02 0.21226E-020.159502-02 0.236292+04 0.506322+07 0.47259E+01 0.584732-02 0.12895E+02 0.45478E+02 0.21346E-020.15975E-02 0.237582+04 0.509092+07 0.47516E+01 0.58301E-02 0.12965E.02 0.45476E+02 0.21466E-020.16001E-02 0.238832+04 0.511872+07 0.477762+01 0.59131E-02 0.13035E+02 0.45474E+02 0.215872-020.160262-02 0.24018E+04 0.51467E+07 0.48036E+01 0.5946~3E.02 0.131062+02 0.45472E+02 0.21709E-020.16052E-02 0.24149E.04 0.51748E+07 0.48299E+01 0.59797E-02 0.13177E+02 0.454692+02 0.21831E-020.160772-02 0.24281E+04 0.52031E+07 0.48562E+01 0.60133E-02 0.13248E+02 0.454,67E,02 0.219542-020.16102E-02 0,24414E+04 0.52315E+07 0.48827E+01 0.604I02-02 0..13320E+02 0.45465E+02 0.22078E-020.161282-02 0.245472+04 0.52601E+07 0.490942+01 0.60809E-02 0.13392E+02 0.45463E+02 0.22202E-020.161532-02 0.24681E+04 0.528892+07 0.49362E+01 0.61150E-02 0.13464E+02 0.454612+02 0.22327E-020.161792-02 0.24815E+04 0.53178E+07 0.49631E+01 0.61493E-02 0.13537E+02 0.454592+02 0.224532-02

0.162042-02 0.24951E+04 0.534692+07 0.49902E+01 0.618382-02 0.136102+02 0.45457E+02 0.225792-020.16229E-02 0.25087E+04 0.537612+07 0.501742+01 0.621842-02 0.13684E+02 0.45455E+02 0.22706E-020.162552-02 0.252242+04 0.540552+07 0.50448E+01 0.625332-02 0.137582+02 :.45453E+02 0.22834E-02

0.16280E-02 0.25362E+04 0.54350E+07 0.50723E+01 0.62883E-02 0.138322.02 0.45451E*02 0.22963E-02

0.163U6E-02 0.25500E+04 0.54648E+07 0.510002+01 0.632362-02 0.13907E+02 0.45448E+02 0.23092E-020.163312-02 0.25639E+04 0.549462+07 0.51279E+01 0.63590E-02 0.13983E+02 0.45446E+02 0.23222E-020.16356E-02 0.25779E+04 0.552472+07 0.51558E+01 0.63946E-02 0.14058E+02 0.45444E+02 0.233522-020.16382E-02 0.259202+04 0.55549E+07 0.51840E.01 0.64304E-02 0.14134E+'02 0.45442E+02 0.23483E-02

0.164072-02 0.26061E+04 0.55853E+07 0.52123E+01 0.64664E-02 0.14211E+02 0.45440E+02 0.236152-02

0.16,433E-02 0.262042+04 0.561582+07 0.52407E+01 0.65026E-02 0.14288E+02 0.45438E+02 0.23748E-02

0.16458E-02 0.26347E+04 0.56465E+07 0.52693E+01 0.653902-02 0.14365E.02 0.45435E+02 0.23882E-02

38

.-- ........- wri--~ x- y. V'., .Jyrv w-. rv .r.%,.rC C ~r..' r

Page 37: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

TIME PRESSURE PDOT XDOT PROPELLANT BURNT MOOT SURFACE DISTANCE BURNT

0.16483E-02 0.26490E+04 0.56774E+07 0.52981E+01 0.65755E-02 0.14443E+02 0.45433E+02 0.24016E-020.16509E-02 0.26635E+04 0.57084E+07 0.53270E+01 0.66123E-02 0.14521E+02 0.45431E+02 0.24151E-020.16534E-02 0.26780E+04 O.5'396E+07 0.53561E201 0.66493E-02 0.14599E+02 0.45429E+02 0.24286E-020.16560E-02 0.26927E+04 0.57710E+07 0.53853E+01 0.66a65E-02 0.14678E+02 0.45426E+02 0.24423E-020.16585E-02 0.27074E+04 0.58026E+07 0.54147E+01 0.67239E-02 0.14757E+02 0.45424E+02 0.24560E-020.16610E-02 0.27221E+04 0.58343E+07 0.54443E+01 0.67614E-02 0.14837E+02 0.45422E+02 0.24698E-020.16636E-02 0.27370E+04 0.58662E+07 0.54740E+01 0.67992E-02 0.14917E+02 0.45419E+02 0.24837E-020.16661E-02 0.27519E+04 0.58983E+07 0.55039E+01 0.68372E-02 0.14998E+02 0.45417c-+02 0.24976E-020.16687E-02 0.27670E+04 0.59305E+07 0.55339E+01 0.68754E-02 0.15079E+02 0.45415E+02 0.25116E-020.16712E-02 0.27821E+04 0.59630E+07 0.55641E+01 0.69138E-02 0.15161E+02 0.45412E+02 0.25257E-020.16737E-02 0.27972E+04 0.59956E+07 0.55945E+01 0.69524E-02 0.15243E+02 0.45410E+02 0.25399E-020.16763E-02 0.28125E+04 0.60284E+07 0.56250E+O1 0.69912E-02 0.15325E+02 0.45408E+02 0.25541E-020.16788E-02 0.28279E+04 0.60613E+07 0.56557E+01 0.70303E-02 0.15408E+02 0.45405E+02 0.25685E-020.16814E-02 0.28433E+04 0.60945E+07 0.56866E+01 0.70695E-02 0.15491E+02 0.45403E+02 0.25829E-020.16839E-02 0.28588E+04 0.61278E+07 0.57176E+01 0.71090E-02 0.15575E+02 0.45400E+02 0.25973E-020.16864E-02 0.28744E+04 0.61613E+07 0.57489E+01 0.71486E-02 0.15659E+02 0.45398E+02 0.26119E-020.16890E-02 0.289(JLE+04 0.61950E+07 0.57802E+01 0.71885E-02 0.15744E+02 0.45396E+02 0.26265E.020.16915E-02 0 29059E+04 0.62289E+07 0.58118E+01 0.72286E-02 0.15829E+02 0.45393E+02 0.26413E-020.16941E-02 0.29218E+04 0.62630E+07 0.58435E+01 0.72689E-02 0.15914E÷02 0.45391E+02 0.26561E-020.16966E-02 0.29377E+04 0.62972E+07 0.58754E+01 0.73094E-02 0.16000E+02 0.45388E+02 0.26709E-020.16991E-02 0.29537E+04 0.63317E+07 0.59075E+01 0.73502E-02 J.16087E+02 0.45386E+02 0.26859E-020.17017E-02 0.29699E+04 0.63663E+07 0.59397E+01 0.73911E-02 0.16174E+02 0.45383E+02 0.27010E-020.17042E-02 0.29861E+04 0.64011E÷07 0.59722E+01 0.74323E-02 0.16261E+02 0.45381E+02 0.27161E-020.17068E-02 0.30024E+04 0.64362E+07 0.60048E+01 0.74737E-02 0.16349E+02 0.45378t+02 0.27313E-020.17093E-02 0.30188E+04 0.64714E+07 0.60376E+01 0.75154E-02 0.16437E+02 0.45376E+02 0.27466E-020.17118E-02 0.30353E+04 0.65063E+07 0.60705E+01 0.75572E-02 0.16526E+02 0.45373E*02 0.27620E-020.17144E-02 0.30518E+04 0.65424E+07 0.61037E+01 0.75993E-02 0.16616E+02 0.45370E402 0.27774E-020.17169E-02 0.30685E+04 0.65781E+07 0.61370E+01 0.76416E-02 0.16705E+02 0.45368E+02 0.27930E-020.17195E-02 0.30852E+04 0.66141E+07 0.61705E+01 0.76842E-02 0.16796E+02 0.45365E+02 0.28086E.020.17220E-02 0.31021E+04 0.66503E+07 0.62042E+01 0.77270E-02 0.16886E+02 0.45363E+02 0.28243E-020.17245E-02 0.31190E+04 0.66a67E+07 0.62381E+01 0.77700E-02 0.16977E+02 0.45360E+02 0.28401E-020.17271E-02 0.31361E+04 0.67233E407 0.62721E+01 0.78132E-02 0.17069E+02 0.45357E+02 0.28560E-020.17296E-02 0.31532E+04 0.67601E+07 0.63064E+01 0.78567E-02 0.17161E+02 0.45355E+02 0.28720E-020.17322E-02 0.31704E+04 0.67971E+07 0.63408E%101 0.79004E-02 0.17254E+02 0.45352E+02 0.2880E-020.17347E-02 0.31877E+04 0.68342E+07 0.63754E+01 0.79443E-02 0.17347E+02 0.45349E202 0.29042E-020.17372E-02 0.32051E+04 0.68716E+07 0.64102E+01 0.79885E-02 0.17441E+02 0.45347E+02 0.29204E-020.17398E-02 0.32226E+04 0.69092E+07 0.64452E+01 0.80329E-02 0.17535E+02 0.45344E+02 0.29367E-020.17423E-02 0.32402E+04 0.694702E07 0.64804E+01 0.80776E-02 0.17630E+02 0.45341E+02 0.29532E-020.17448E-02 0.32579E+04 0.69851E+07 0.65158E+01 0.81225E-02 0.17725E+02 0.45338E+02 0.29697E-020.17474E-02 0.32757E+04 0.70233E+07 0.65514E+01 0.81676E-02 0.17821E+02 0.45336E+02 0.29863E-020.17499E-02 0.32936E+04 0.70617E+07 0.65872E+01 0.82130E-02 0.17917E+02 0.45333E+02 0.30029E-020.17525E-02 0.33116E+04 0.71004E+07 0.66231E+01 0.82586E-02 0.18014E+02 0.45330E+02 0.30197E-020.17550E-02 0.33296E+04 0.71392E+07 0.66593E+01 0.83045E-02 0.18111E+02 0.45327E+02 0.30366E-020.17575E-02 0.33478E+04 0.71783E+07 0.66956E+01 0.83506E-02 0.18209E+02 0.45324E+02 0.30535E-020.17601E-02 0.33661E'04 0.72176E+07 0.67322E+01 0.83970E-02 0.18307E+02 0.45322E+02 0.30706E-020.17626E-02 0.33845E+04 0.72571E+07 0.67690E+01 0.84436E-02 0.18406E+02 0.45319E+02 0.30877E-020.17652E-02 0.34030E+04 0.72968E+07 0.68059E+01 0.84905E-02 0.18505E+02 0.45316E+02 0.31050E-020.17677E-02 0.34216E+04 0.73367E+07 0.6&31E+01 0.85376E-02 0.18605E+02 0.45313E+02 0.31223E-020.17702E-02 0.34402E+04 0.73769E+07 0.68805E+01 0.85850E-02 0.18705E402 0.45310E+02 0.31397E-020.1T728E-02 0.34590E+04 0.74173E+07 0.69180E+01 0.86326E.02 0.18806E+02 0.45307E+02 0.31573E-020.17753E-02 0.34779E+04 0.74579E+07 0.69558E+01 0.86805E-02 0.18908E+02 0.45304E+02 0.31749E-020.17779E-02 0.34969E+04 0.74987E+07 0.69938E+01 0.87287E-02 0.19010E+02 0.45301E+02 0.31926E-020.17804E-02 0.35160E+04 0.75397E+07 0.7U320E+01 0.87771E-02 0.19112E+02 0.45298E+02 0.32104E-020.17829E-02 0.35352E+04 0.75810E+07 0.70704E+01 0.88257E-02 0.19215E+02 0.45295E+02 0.32283E-02

S-"

Page 38: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

TIME PRESSURE PDOT XDOT PROPELLANT BURNT MOOT SURFACE DISTANCE BURNT

0.17855E-02 0.35545E+04 0.76225E+07 0.71090E+'01 0.88747E-02 0.19319E+02 0.45292E+02 0.32463E-02

0.17880E-02 0.35739E+04 0.76642E+07 0.71479E+01 0.89239E-02 0.19423E+02 0.45289E+02 0.32644E-02

0.17906E-02 0.35934E+04 0.77062E+07 0.718695.01 0.897335- 02 0.195-285.02 0.45286E+02 0.32826E- 020.17931E-02 0.36131E+04 0.77484E+07 0.72261E+01 0.90231E-02 0.19633E+02 0.45283E+02 0.33009E-020.17956E-02 0.36326E+04 0.719085+07 0.72656E+01 0.90731E-02 0.19739E402 0.45280E+02 0.33193E-020.1 9825-02 0.36526E.04 0.78334E.07 0.73053E+01 0.91233E-02 0.19846E+02 0.452775+02 0.33378E-020.180075-02 0.367265.04 0.78763E+07 0.73452E+01 0.91739E-02 0.19953E+02 0.45274E+02 0.33564E-020.18033E-02 0.369275.04 0.79194E+07 O.73853E+01 0.92247E-02 0.20060E+02 0.45271E+02 0.33751E-020.180581-02 0.371285.04 0.79628E+07 0.742565.01 0.92758E-02 0.20169E4-02 0.45268E+02 0.33940E-020.18083E-02 0.373315.04 0.80064E+07 0.74662E+01 0.932715-02 0.20277E+02 0.452655+02 0.34129E-02

0.18109E-02 0.37535E+04 0.80502E+07 0.75070E+01 0.93788E-02 0.20387E+02 0.45261E+02 0.34319E-020.181345-02 0.37740E+04 0.80943E+07 0.75480E.01 0.94307E-02 0.20496E.02 0.45258E+02 0.34510E-02

0.18160E-02 0.37946E+04 0.81386E+07 0.758925+01 0.948295-02 0.206075+02 0.45255E+02 0.34702E-02

0.181855-02 0.381535+04 0.81832E+07 0.76307ss-01 0.95354E-02 0.207185.02 0.45252E+02 0.34895E-02

0.18210E-02 0.383625.04 0.822805+07 0.76724E+01 0.95881E-02 0.208305+02 0.45249E+02 0.35090E-02

0.182365-02 0.38571E+04 0.827,315+07 0.7'7143E.01 0.964125-02 0.20942E+02 0.45245E+02 0.35285E-02

-0.18261E-02 0.387825.04 0.83184E+07 0.77564E.01 0.969455-02 0.210555+02 0.452425.02 0.35482E-02

0.18287E-02 0.38994E.04 0.836395+07 0.779885.01 0.97481E-02 0.21168E.02 0.45239E+02 0.356795-02

0.18312E-02 0.39207E+04 0.840975+07 0.78414E+01 0.980205-02 0.21282E+02 0.452355+02 0.35878E-02

0.18337E-02 0.39421E+04 0.845585.07 0.788425.01 0.98562E-02 0.21397E+02 0.452325+02 0.360785-02

0.18363E-02 0.39636E+04 0.85021E+07 0.79273E.01 0.99107E-02 0.215125.02 0.45229E+02 0.36278E-02

0.183885-02 0.398535+04 0.85487E+07 0.79706E+01 0.996555-02 0.216285+02 0.45225E+02 0.36480E-02

0.15414E-02 0.40071E+04 0.859555.07 0.80141E+01 0.10021E-01 0.21745E+02 0.45222E+02 0.36683E-02

0.184395-02 0.40290E.04 0.86426E.07 0.80579E+01 0.10076E-01 0.21862E.02 0.45219E+02 0.36887E-02

0.184645-02 0.40510E+04 0.86899E+07 0.81019E.01 0.10132E-01 0.21980E+02 0.45215E+02 0.37093E-02

0.184905-02 0.4073,E+04 0.87375E+07 0.81462E+01 0.101885-01 0.22098E+02 0.452125+02 0.37299E-02

0.18515E-02 0.40953E.04 0.878545+07 0.81907E.01 0.10244E-01 0.22217E+02 0.45208E+02 0.37506E-02

0.18541E-02 0.411'77E+04 0.883355+07 0.823545+01 0.10300E-U1 0.22337E+02 0.45205E+02 0.37715E-02

0.18566E-02 0.414025+04 0.88819E+07 0.828045+01 0.10357E-01 0.224575.02 0.452015.02 0.37925E-02

0.185915-02 0.416285+04 0.89305E.07 0.83257E.01 0.104155-01 0.22578E+02 0.45198E+02 0.38136E-02

0.18617E-02 0.41856E+04 0.89794E.07 0.83712E+01 0.10472E-01 0.22700E+02 0.45194E+02 0.38348E-02

0.186425-02 0.42085E+04 0.902a6E+07 0.84169E+01 0.10530E-01 0.22822E.02 0.45191E+02 0.38561E-02

0.18668-02 0.42314E+04 0.90781E+07 0.84629E+01 0.105885-01 0.229455.02 0.45187E+02 0.387755-02

0.186935-02 0.42546E+04 0.912785+07 0.85091E+01 0.106465-01 0.230685+02 0.45183E+02 0.38991E-02

0.187105-02 0.42778E+04 0.91778E+07 0.85556E.01 0.10705E-01 0.23193E+02 0.45180E+02 0.39207E-02

0.18744E-02 0.430125.04 0.92281E+07 0.86U245.01 0.10764E-01 0.233175+02 0.45176E+02 0.39425E-02

0.18769E-02 0.43247E+04 0.92787E.07 0.86494E+01 0.10824E-01 0.23443E+02 0.45173E+02 0.39644E-02

0.18795E-02 0.434835+04 0.932955+07 0.86966E+01 0.108835-01 0.235695+02 0.45169E+02 0.39865E-02

0.188205-02 0.43721E+04 0.93806E.07 0.87442E.01 0.109435-01 0.236965+02 0.45165E+02 0.400865-02

0.18845E-02 0.43960E.04 0.94321E+07 0.87919E+01 0.110045-01 0.23823E+02 0.451625+02 0.403095-02

0.18871E-02 0.442005+04 0.94837E+07 0.8.8400E+01 0.11064E-01 0.239525+02 0.45158E+02 0.40533E-02

0.18896E-02 0.44441E+04 0.95357E,,07 0.88835+01 0.11125E-01 0.24081E+02 0.45154E+02 0.407585-02

0.189225-02 0.44684E.04 0.95880E+07 0.893695+01 0.11187E-01 0.24210E+02 0.45150E+02 0.40984E-02

0.18947E-02 0.44928E+04 0.96405E+07 0.89857E+01 0.112485-01 0.243405+02 0.45146E+02 0.41212E-02

0.18972E-02 0.451745+04 0.96933E+07 0.903485+-01 0.11310E-01 0.24471E+02 0.45143E+02 0.41441E-02

0.18998E-02 0.45421E+04 0.974655+07 0.908425.01 0.113735-01 0.24603E+02 0.45139E+02 0.416715-02

0.190235-02 0.45669E+04 0.97999E+07 0.91338E+01 0.11435E-01 0.247355+02 0.45135E+02 0.41902E-02

0.19049E-02 0.45919E+04 0.985365+07 0.91837E+01 0.11498E-01 0.24868E.02 0.45131E+02 0.42135E-02

0.19074E-02 0.46170E+04 0.99076E+07 0.92339E+01 0.11562E-01 0.25002E+02 0.45127E+02 0.42369E-02

0.19099E-02 0.464225+04 0.99619E.1-07 0.928445+01 0.116255-01 0.25137E+02 0.45123E+02 0.42604E-02

0.191255-02 0.46676E+04 0.10017E+08 0.93351E+01 0.11689E-01 0.25272E+02 0.45119E4-02 0.42840E-02

0.19150E-02 0.469315+04 0.10071E+08 0.93861E+01 0.11754E-01 0.25408E+02 0.45115E+02 0.43078E-02

0.19176E-02 0.47187E+04 0.10127E+08 0.94374E+01 0.11818E-01 0.25544E+02 0.45111E+02 0.43317E-02

0.19201E-02 0.47445E+04 0.10182E+08 0.94890E+01 0.11883E-01 0.25681E+02 0.45107E+02 0.43557E-02

LaV . 1 L ll ~J L. N- A. LaVaVt.VAI Vb.LAI V~d a0

Page 39: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

TIME PRESSURE PDOT XDOT PROPELLANT BURNT MOOT SURFACE DISTANCE BURNT

0.19226E-02 0.47704E+04 0.10238E+08 0.95409E+01 0.11949E-01 0.25820E+02 0.45103E+02 0.43799E-020.19252E-02 0.47965E+04 0.10294E+08 0.95930E4-01 0.12015E-01 0.25958E+02 0.45099E+02 0.44042E-020.192772-02 0.48227E+04 0.10351E+08 M.6455E+01 O.12081E-01 0.26098E+02 0.45095E+02 0.44286E-020.19303E-02 0.48491E.04 0.10407E+08 0.969822+01 0.12147E-01 0.26238E+02 0.45091E.02 0.44532E-02

0.19328E-02 0.48756E+04 0.104641408 0.97512E+01 0.12214E-01 0.26379E+02 0.45087E+02 0.44779E-020.19353E-02 0.49022E+04 0.10522E+08 0.98045E+01 0.122812-01 0.26521E+02 0.45083E+02 0.45027E-020.19379E-02 0,49290E.04 0.10579E+08 0.98581E+01 0.12349E-01 0.266632.02 0.450*19E.02 0.45277E-020.19404E-02 0.49560E+04 0.106372408 0.99120E+01 0.12417E-01 0.268072+02 0.45075E+02 0.455281-020.19430E-02 0.49831E.04 0.10696E+08 0.99662E+01 0.12485E-01 0.269512.02 0.450702.02 0.457802-020.194552-02 0.501032+04 0.10754E+08 0.100212.02 0.125532-01 0.27095E+02 0.45066E+02 0.46034E-020.19480E-02 0.50377E+04 0.108132+08 0.10075E.02 0.12622E-01 0.27241E+02 0.45062E+02 0.46289E-020.19506E-U2 0.50652E+04 0.10873E408 0.10130E.02 0.12692E-01 0.27387E.02 0.45058E+02 0.465462-020.19531E-02 0.50929E.04 0.10932E+08 0.10186E.02 0.12762E-01 0.27534E+02 0.45053E+02 0.46804E-020.19557E-02 0.51208E+04 0.10992E.08 0.10242E+02 0.12832E-01 0.27682E+02 0.45049E+02 0.47063E-020.19582E-02 0.51488E+-04 0.11053E+08 0.102988+02 0.129022-01 0.27831E.02 0.45045E+02 0.47324E-020.19607E-02 0.517692.04 0.11113E+08 0.10354E+02 0.129732-01 0.27980E+02 0.450402+02 0.475866E-02.0.19633E-02 0.52052E+04 0.11174E+08 0.10410E+02 0.13044E-01 0.28131E.02 0.45036E+02 0.47850E-020.19658E-02 0.52337E.04 0.11235E.+08 0.10467E.02 0.13116E-01 0.28282E+02 0.45031E.02 0.481152-020.19684E-02 0.52623E+04 0.11297E+08 0.10525E+02 0.131888-01 0.284332.02 0.45027E+02 0.48382E-020.19709E-02 0.52911E+04 0.11359E+08 0.10582E+02 0.13260E-01 0.28586E.02 0.45023E+02 0.48650E-020.19734E-02 0.532002+04 0.11421E408 0.10640E.02 0.13333E-01 0.28739E.02 0.450188.02 0.489192-020.19760E-02 0.53491E+04 0.11484E+08 0.106982.02 0.134062-01 0.28894E.02 0.450132.02 0.491902-020.197852-02 0.53783E.04 0.11547E.08 0.10757E+02 0.13480E-01 0.29049E.02 0.45009E+02 0.49463E-020.19811E-02 0.54077E.04 0.116102+08 0.108152.02 0.135541-01 0.292052+02 0.450042+02 0.49737E-020.19836E-02 0.54373E+04 0.11674E+08 0.10875E.02 0.136282-01 0.29361E+02 0.450002+02 0.500122-020.19861E-02 0.54670E+04 0.11738E+08 0.109341+02 0.13703E-01 0.29519E+02 0.449952+02 0.50289E-020.198872-02 0.54969E+04 0.118022+08 0.10994E.02 0.13778E-01 0.29677E+02 0.4499112.02 0.505682-020.17912E-02 0.552702.04 0.11867E+08 0.110542+02 0.138542-01 0.29836E+02 0.44936E.02 0.508482-020.199382-02 0.55572E+04 0.11932E+08 0.111142+02 0.13930E-01 0.29996E.02 0.44981E.02 0.51129E-020.19963E-02 0.55876E+04 0.119982+08 0.11175E+02 0.14006E-01 0.30157C.+02 0.44976E.02 0.51412E-020.19988E-02 0.561822+04 0.12064E.08 0.112362.02 0.14083E-01 0.30319E+02 0.449722+02 0.51697E-020.20014E-02 0.56489E.04 0.121302.08 0.11298E+02 0.141602-01 0.304822+02 0.44967E.02 0.519832-020.20039E-02 0.567982.04 0.12196E+08 0.11360E+02 0.14238E-01 0.30645E+02 0.44962E+02 0.52271E-020.20065E-02 0.57108E+04 0.12263E.03 0.11422E+02 0.14316E-01 0.308092+02 0.44957E+02 0.52560E-020.20090E-02 0.57421E+04 0.123312+-08 0.11484E+02 0.14394E-01 0.309741+02 0.44952E+02 0.528512-020.201152-02 0.577352+04 0.12398E.08 0.115472+02 0.14473E-01 0.311402+02 0.44948E+02 0.53,143E-020.201e.1E-02 0.58050E+04 0.12466E+08 0.11610E.02 0.14553E-01 0.31307E.02 0.44943E+02 0.53437E-020.201662-02 0.58368E+04 0.125352+08 0.11674E+02 0.146322-01 0.31475E.02 0.44938E+02 0.53733E-020.20191E-02 0.58687E.04 0.126042+08'0.117371+02 0.14712E-01 0.316442+02 0.44933E+02 0.54030E-020.202172-02 0.59008E+04 0.12673E+08 0.118021+02 0.14793E-01 0.318132+02 0.44928E+02 0.54329E-020.20242E-02 0.59331E+04 0.12742E+08 0.11866E+02 0.14874E-01 0.31984E.02 0.449232+02 0.54630E-020.202682-02 0.59655E+04 0.128122+08 0.11931E+02 0.14955E-01 0.32155E+02 0.449182+02 0.54932E-020.20293E-02 0.59982E+04 0.128832.08 0.11996E+02 0.150372-01 0.32327E.02 0.449132+02 0.55236E-020.20318E-02 0.60310E+04 0.129532+08 0.12062E+02 0.151202-01 0.325002+02 0.44908E+02 0.555411-02

0.203442-02 0.606402+04 0.130242+08 0.121282+02 0.152022-01 0.32674E+02 0.44903E+02 0.55849E-020.20369E-02 0.609712+04 0.130962.08 0.12194E+02 0.152862-01 0.32849E+02 0.44897E.02 0.561581-020.20395E-02 0.61305E+04 0.13168E+08 0.12261E.02 0.15369E-01 0.33025E2ý02 0.44892E+02 0.56468E-02

0.20420E-02 0.61640E+04 0.132402408 0.12328E+02 0.15453E-01 0.33202E+02 0.44887E+02 0.567801-020.20445E-02 0.61977E+04 0.13313E+08 0.123951+02 0.15538E-01 0.333802+02 0.448822.02 0.570942-02

0.20471E-02 0.62316E+04 0.13386E+08 0.12463E.02 0.15623E-01 0.33559E+02 0.44877E.02 0.574101-020.204962-02 0.62657E.04 0.13459E+08 0.12531E+02 0.15708E-01 0.337381+02 0.44871E+02 0.57727E-020.205222-02 0.63000E.04 0.13533E+08 0.12600E+02 0.15794E-01 0.33919E+02 0.44866E+02 0.58047E-020.20547E-02 0.63345E+04 0.13608E+08 0.12669E+02 0.158811-01 0.34100E+02 0.448611+02 0.58367E-020.20572E-02 0.63691E+04 0.136821+08 0.12738E.02 0.15968E-01 0.34283E+02 0.448551+02 0.58690E-02

41

---- -----

Page 40: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

TIKE PRESSURE PDOT XDOT PROPELLANT BURNT MOOT SURFACE DISTANCE BURNT

0.205988-02 0.64040E+04 0.137588+08 0.128082+02 0.16055E-01 0.34466E+02 0.44850E+02 0.59014E-020.20623E-02 0.64390E+04 0.13833E+08 0.12878E+02 0.16143E-01 0.34650E402 0.44844E+02 0.59341E-02

0.20649E-02 0.64743E4-04 0.13909E+08 0.12949E+02 0.16231E-01 0.34836E.02 0.44839E+02 0.59669E-020.20674E-02 0.65097E+04 0.13985E+08 0.13019E+02 0.16320E-01 0.35022E+02 0.44833E+02 0.599988-02

0.20699E-02 0.65453E+04 0.14062E+08 0.13091E+02 0.16409E-01 0.35209E+02 0.448288+02 0.60330E-020.20725E-02 0.65811E+04 0.14140E+08 0.131622.02 0.164988-01 0.353988.02 0.44822E+02 0.60663E-020.20750E-02 0.66171E+04 0.14217E+08 0.13234E+02 0.16589E-01 0.35527E+02 0.44817E+02 0.60999E-020.20776E-02 0.66533E+04 0.14295Ee-08 0.13307E+02 0.16679E-01 0.35777E+02 0.44811E+02 0.61336E-020.20801E-02 0.66897E+04 0.14374E+08 0.13379E+02 0.16770E-01 0.359688402 0.44805E.02 0.61674E-020.20826E-02 0.67263E+04 0.14453E+08 0.13453E+02 0.16862E-01 0.36161E+02 0.44800E+02 0.620151-020.20852E-02 0.6'1631E+04 0.14532E+08 0.13526E+02 0.16954E-01 0.36354Et02 0.44794E+02 0.6235BE-020.20877E-02 0.68002E+04 0.14612E.08 0.136001+02 0.170471-01 0.36548E+02 0.447882+02 0.627021-02

0.209031-02 0.68374E+04 0.14692E+08 0.13675E+02 0.17140E-01 0.36743E+02 0.44783E+02 0.63049E-020.20929E-02 0.68748E+04 0.14773E.08 0.13750E+02 0.17233F-01 0.36940E+02 0.44777E+02 0.63397E-020.20953E-02 0.69124E+04 0.14854E+08 0.13825E+02 0.17'327E-01 0.37137E+02 O.4471E+02 0.63747E,020.20979E-02 0.69502E+04 0.14936E+08 0.13900E+02 0.174221-01 0.37335E+02 0.44765E+02 0.64099E-020.21004E-02 0.698831+04 0.150181.08 0.139771.02 0.175171-01 0.37535E+02 0.44759E+02 0.64453E-020.21030E-02 0.702652.04 0.15100E+08 0.14053E+02 0.17613E-01 0.37735E.02 0.44753E+02 0.64809E-020.210551-02 0.70650E+04 0.15183E+08 0.146130E+02 0.177092-01 0.379372.02 0.44747E+02 0.65167E-020.210801-02 0.71037E.04 0.15267E+08 0.14207E+02 0.17805E-01 0.38139E+02 0.447'41E+02 0.65527E-02

0.21106E-02 0.71425E+04 0.153511.08 0.14285E+02 0.17902E-01 0.383431+02 0.44735E+02 0.65889E-020.21131E-02 0.71816E.04 0.154352408 0.14363E+02 0.18000E-01 0.38547E+02 0.44729E+02 0.66253E-020.21l57E-02 0.72209E+04 0.15520E+08 0.14442E+02 0.180981-Cl 0.387531.02 0.44723E+02 0.66618E-02

0.21182E-02 0.72605E+04 0.15605E+08 0.14521E+02 0.18197E-01 0.38960E+02 0.447178+02 0.66986E-020.21207E-02 0.73002E.04 0.15691E+08 0.14600E+02 0.13296E-01 0.39168E+02 0.44711E+02 0.67356E-020.212332-02 0.73402E.04 0.157778.+08 0.14680E+02 0.183968-01 0.39377E+02 0.447051+02 0.67728E-020.2125aE-02 0.73804E+04 0.15864E+08 0.14761E+02 0.184968-01 0.395871+02 0.44698E+02 0.68102E-020.21284E-02 0.74208E.04 0.159511.08 0.14842E+02 0.18597E-01 0.39798E+02 0.446922.02 0.68478E-020.21309E-02 0.74614E.04 0.16039E.08 0.14923M.02 0.18698-01 0.400101+02 0.44661E+02 0.68856E-020.21334E-02 0.75022E.04 0.16127E.08 0.15004E+02 0.188002-01 0.40223E+02 0.44679E.02 0.69236E,020.21360E-02 0.75433E.04 0.16216E.08 0.150877+02 0.18903E-01 0.404381.02 0.44673E+02 0.696181-020.21385E-02 0.758461.04 0.16305E+08 0.151691.02 0.190068-01 0.40653E.02 0.44667E+02 0.70002E-020.21411E-02 0.76261E+04 0.16595E+08 0.15252E.02 0.19109E-01 0.40870E+02 0.44660E+02 0.70388E-020.21436E-02 0.76679E.04 0.164851.08 0.15336E+02 0.19213E-01 0.41088E+02 0.44654E+02 0.70777-02P.21461E-02 0.77099E+04 0.16576E+08 0.154202.02 0.19318F-01 0.41307E.+02 0.44647E+02 0.71167E-u20.21487E-02 0.775211.04 0.166671.08 0.15504E+02 0.194232-01 0.415278.02 0.44641E.02 0.71560E-020.215121-02 0.77945E.04 0.16758E+08 0.15589E+02 0.195291-01 0.417458E+02 0.44634E.02 0.71955E-020.215381-02 0.783721+04 0.16851E.08 0.15674E.02 0.19635E-01 0.419712+02 0.44627E+02 0.72352E-02

0.21563E-02 0.78801E.04 0.169431+08 0.15760E+02 0.19742E-01 0.42194E+02 0.44621E+02 0.727S12-020.2'15a88-02 0.792332+04 0.17037E+08 0.15847E+02 0.198491-01 0.42419E+02 0.446141+02 0.73152E-020.21614E-02 0.79667E.04 0.17130E.08 0.15933E+02 0.19957E-01 0.426458+02 0.446071402 0.73556E-020.21639E-02 0.80103E.04 0.17224E+08 0.16021E.02 0.20066E-01 0.42872E+02 0.446011+02 0.73962E-020.21665E-02 0.805421+04 0.17319E.08 0.161081+02 0.20175E-01 0.43100E+02 0.44594E+02 0.74370E-020.216901-02 0.809831+04 0.17415E.08 0.16197E+02 0.202852-01 0.433291+02 0.445871+02 0.747801-020.21715E-02 0.81426E.04 0.17510E+08 0.16285E+02 0.20395E-01 0.43560E+02 0.445802+02 0.751932-020.21741E-02 0.81872E+04 0.17607E+08 0.16374E+02 0.20506E-01 0.43792E+02 0.44573E+02 0.75607E-020.21766E-02 0.82321E+04 0.17704E+08 0.164642+02 0.206181-01 0.440251+02 0.445661.02 0.76024E-02

0.21792E-02 0.82771E+04 0.178012.08 0.16554E+02 0.20730E-01 0.44259E.02 0.44559E+02 0.76444E-02

0.21817E-02 0.832252+04 0.178991+08 0166.451+02 0.20a43E-01 0.44494E.02 0.44552E+02 0.76865E-020.21842E-02 0.83681E+04 0.17997E+08 0.16736Eý02 0.20956E-01 0.44731E+02 0.44545E+02 0.717289E-020.218681-02 0.841391.04 0.18096E+08 0.16828E+02 0.21070E-01 0.449691.02 0.44538E.02 0.77715E-020.21893E-02 0.84600E.04 0.18196E+08 0.16920E+02 0.211841-01 0.45208E+02 0.44531E.02 0.78144E-020.21919E-02 0.85063E.04 0.18296E.08 0.17013E+02 0.21299E-01 0.45448E+02 0.44524E+02 0.78575E-02

0.21944E-02 0.85529E+04 0.18397E+08 0. 17106E+02 0.21415L-01 0.45690E+02 0.44517E+02 0.79008E-02

42

Page 41: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

TINE PRESSURE POOT XDOr PROPELLANT BURNT MOOT SURFACE DISTANCE BURNT

0.21969E-02 0.85998E+04 0.18498E+08 0.17200E+02 0.21531E-01 0.45932E+02 0.44509E+02 0.79444E-02

0.2199SE-02 0.86469E+04 0.18600E+08 0.17294E+02 0.21648E-01 0.46176E+02 0.44502E+02 0.79a82E-02

0.220Z0E-02 0.86943E+04 0.18702E+08 0.17389E+02 0.21766E-01 0.46422E+02 0.44495E+02 0.80322E-02

0.22046E-02 0.87419E+04 O.1b8V7+O8 0.17484E+02 0.21884E-01 0.4.6668E+02 0.44487E+02 0.80765E-02

0.22071E-02 0.87898E*04 0.18909E.08 0.17580E+02 0.22003E-01 0.46916E+02 0.444801+02 0.812101-02

0.22096E-02 0.883*191+04 0.19013E+08 0.17676E+02 0.22123E-01 0.471651+02 0.44472E+02 0.816581-02

0.22122E-02 0.88864E+04 0.19118E+08 0.177731+02 0.222431-01 0.47416E+02 0.44465E+02 0.821081-02

0.22147E-02 0.89351E+04 0.19223E+08 0.17870E+02 0.22363E-01 0.47667E+02 0.444571+02 0.82561E-02

0.22173E-02 0.898401+04 C.19329E+08 0.17968E4-02 0.22485E-01 0.47920E+02 0.444501+02 0.83016E-02

O.22198E-02 0.90332E+04 0.19435E+08 0.18066+02 0.22607E-01 0.48175E+02 0.44442E+02 0.834731-02

0.22223E-02 0.90927E+04 0.19542E+08 0.18165E+02 0.22729E-01 0.48430E+02 0.44434E+02 0.83934E-02

0.22249E-02 0.91325E+04 0.19650E+08 0.18265E+02 0.22853E-01 0.486871+02 0.44427E+02 0.84396E-02 1

0.22274E-02 0.91825E+04 0.197581+08 0.18365Ei-02 0.229771-01 0.48946E+02 0.44419E+02 0.84861E-02

0.22300E-02 0.92329E+04 0.198671+08 0.18466Ei'02 0.23101E-01 0.49205E+02 0.44411E+02 0.85329E-02

0.22325E-02 0.928351+04 0.19976E+08 0.185671+02 0.23227E-01 0.49466E+02 0.44403E+02 0.85799E-02

0.22350E-02 0.93343E+04 0.20086E+08 0.18669E+02 0.23353E-01 0.497281+02 0.44395E+02 0.86272E-012

0L22376E-02 0.93855E+04 0.20197E+08 0.18771E+02 0.234791-01 0.49992E+02 0.44388E+02 0.86748E-02

0.224011-02 0.94369E+04 0.20308E+08 0.18874E+02 0.2360?1-01 0.50257E+02 0.443801+02 0.87226E-02

0.22427E-02 0.94887E+04 0.20420E+08 0.18977E+02 0.237351-01 0.50523E+02 0.443721+02 0.87706E-020.22452F.-02 0.95407E+04 0.20533E+08 0.19081E+02 0.23863E-01 0.50791E+02 0.44364E+02 0.88190E-02

0.22477E-02 0.95930E+04 0.20646E+08 0.19186E+02 0.23993E-01 0.510601+02 0.44355E+02 0.88676E-02

0.22503E-02 0.96455E+04 0.207601+08 0.19291E+02 0.241231-01 0.51330E+02 0.443471+02 0.89164E-02

0.225281-02 0.96984E+04 0.20874E+08 0.19397E+02 0.24253E-01 0.51602E+02 0.44339E+02 0.89656E-02

0.22554E-02 0.97516E+04 0.20989E+08 0.195031+02 0.2438SE-01 0.51875E+02 0.443311+02 0.901501-02

0.225'9E-02 0.98050E+04 0.21105E+08 0.19610E+02 0.245171-01 0.521501+02 0.44323E+02 0.90646E-02

0.226041-02 0.985881+04 0.21221E+08 0.19718E+02 0.24650E-01 0.52426E+02 0.44314E+02 0.911461-02

0.22630E-02 0.991281+04 0.21338E+08 0.198261+02 0.24783E-01 0.527041+02 0.44306E+02 0.916481-02

0.226551-02 0.99672E+04 0.21455E+08 0.19934E+02 0.24917E-01 0.52982E+02 0.442971+02 0.92153E-02

0.22681E-02 0.10022E+05 0.21574E+08 0.20044E+02 0.25052E-01 0.53263E+02 0.44289E+02 0.92660E-02

0.22706E-02 o.1ooaE.os 0.21693E+08 0.20153E+02 0.25188E-01 0.53544E402 0.44280E+02 0.93171E-02

0.227311-02 0.10132E+05 0.21812E+06 0.20264ý+02 0.25324E-01 0.53828E+02 0.44272E+02 0.936841-02

0.227571-02 0.10188E+05 0.21932E+08 0.20375E+02 0.254611-01 0.541121+02 0.442631+02 0.942001-02

0.22782E-02 3.10243F+05 0.22053E+08 0.20467E+02 0.25599E-01 0.54398E+02 0.44255E+02 0.94719E-02

0.22807E-02 0.10300E+05 0.221751+08 0.20599E+02 0.257381-01 0.54686E+02 0.44246E+02 0.95241E-02

n.22833E-02 0.10356E+05 0.22297E+08 0.20712E+02 0.25877E-01 0.54975E+02 0.44237E+02 0.95166E-02

0.22858E-02 0.104131+05 0.22420E+08 0.20826E+02 0.26017E-01 0.552651+02 0.44228E+02 0.96293E-02

0.22884E-02 0.104701+05 0.22544E+08 0.20940E+02 0.26158E-01 0.55557F+02 0.442201+02 0.96823E-02I0.229091-02 0.10527E+05 0.22668E+08 0,21055E+02 0.262991-01 0.558511+02 0.442i11E+0ý 0.97357E1020.22934E-02 0.10585E+05 0.22793E+03 0.21170E+02 0.26441E-01 0.561451+02 0.44202E+02 0.978931-02

0.22960E-02 0.10643E+05 C.22919E+08 0.21286E+02 0.26584E-01 0.56442E+02 0.44193E+02 0.98432E-02

0.229851-02 0.10701E+05 0.230451+08 0.21403E+02 0.267281-01 0.567401+02 0.44184E+02 0.98974E-02

0.23011E-02 0.10760E+05 0.231721+08 0.21520E+02 0.26873E-01 0.57039E+02 0.44175E+02 0.99519E-02I0.23036E-02 0.10819E+05 0.23300E+08 0.21638E+02 0.270181-01 0.57340E+02 0.44166E+02 0.100071-01

0.230611-02 0.10879E+05 0.23429E+08 0.217ý7E.02 0.27164E-01 0.57643E+02 0.44156E+02 0.100621-01

0.23087E-02 0.10938E+05 0.23558E+08 0.21876E+02 0.27311E-01 0.579471402 0,44147E+02 0.10117E-01

0.23112E-02 0.10998E+05 0.23688E+08 0.21996E+02 0.274581-01 0.58252E+02 0.441381+02 0.101731-01

0.231381-02 0.11059E+05 0.23818E+08 0.22117E+02 0.27607E-01 0.58560E+02 0.44129E+02 0.10229E-01

0.231631-02 0.11119E+05 0.239501+08 0.22238E+02 0.27756E-01 0.588681+02 0.44119E+02 0.10285E-01I0.231881-02 0.11180E+05 0.24082E+08 0.22360E+02 0.27906E-01 0.591791+02 0.44110E+02 0.10342E-010.23214E-02 0.11242E+05 0.24215E+08 0.22483E+02 0.28056E-01 0.59490E+02 0.44100E+02 0.103991-01

0.23239E-02 0.11303E+05 0.24348E+08 0.22606E+02 0.28208E-01 0.59804E+02 0.44091E+02 0.10456E-01

0.23265E-02 0.11365E+05 0.244831+08 0.22730E+02 0.283601-01 0.60119E+02 0.44081E+02 0.10514E-01

0.23290E-02 0.11428E+05 0.24618E+08 0.22855E+02 0.28513E-01 0.60435E+02 0.44071E+02 0.105721-01

0.23315E-02 0.11490E+05 0.24754E+08 0.229811+02 0.28667E-01 0.60754E+02 0.44062E+02 0.10630E-01

43)

Page 42: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

TIME PRESSURE POOT XOOT PROPELLANT BURNT MDOT SURFACE DISTANCE BURNT

0.23341E-02 0.11553E+05 0.24890E+08 0.23107E+02 0.28822E-01 0.61073E+02 0.44052E+02 0.10688E-01

0.23366E-02 0.11617E+05 0.25028E+08 0.23233E+02 0.28977E-01 0.61395E+02 0.44042E+02 0.10747E-01

0.23392E-02 0.11680E+05 0.25166E+08 0.23361E+02 0.29134E-01 0.61718E+02 0.44032E+02 0.10806E-01

0.23417E-02 0.11745V>05 0.25305E+08 0.23489E+02 0.29291E-01 0.62043E+02 0.44022E+02 0.1086.6E-01

0.23442E-02 0.11809E+05 0.25444E+08 0.23618E+02 0.29449E-01 0.62369E+02 0.44012E+02 0.10926E-01

0.2346B8-02 U.11874E+05 0.25585E+08 0.23748E+02 0.29608E-01 0.62697E+02 0.44002E+02 0.10986E-01

0.d3493E-02 0.11939E+05 0.25726E+08 0.23878E+02 0.29767E-01 0.63026E502 0.43992E+02 0.11046E-01

0.23519E-02 0.12004E+05 0.25868E+08 0.24009E+02 0.29928E-01 0.63358E+02 0.43982E+02 0.11107E-01

0.23544E-02 0.12070E+05 0.26011E+08 0.24141E+02 0.30089E-01 0.63691E+02 0.43972E+02 0.11168E-010.23569E-02 0.12137E+05 0.26154E+08 0.24273E+02 0.30251E-01 0.64025E+02 0.43962E+02 0.11250E-01

0.23595E-02 0.12203E+05 0.26299E+08 0.24406E+02 0.30414E-01 0.64362E+02 0.43951E+02 0.11292E-01

0.23620E-02 0.12270E+05 0.26444E+08 0.24540E+02 0.30578E-01 0.64700E+02 0.43941E+02 0.11354E-010.23646E-02 0.12338E+05 0.26590E+08 0.24675E+02 0.30743E-01 0.65039E+02 0.43931E+02 0.11416E-01

0.23671E-02 0.1240SE+05 0.26737E+08 0.24810E+02 0.30909E-01 0.6S381E÷02 0.43920E+02 0.11479E-010.23696E-02 0.12473E+05 0.26885E+08 0.24947E+02 0.31075E-01 0.65724E+02 0.43910E+02 0.11542E-01

0.23722E-02 0.12542E+05 0.27033E+08 0.25084E+02 0.31242E-01 0.66069E+02 0.43899E+02 0.11606E-01.0.23747E-02 0.12611E+05 0.27182E208 0.25221E+02 0.31411E-01 0.66415E+02 0.43888E+02 0.11670E-01

0.23773E-02 0.12680E505 0.27333E+08 0.25360E+02 0.31580E-01 0.66764E+02 0.43878E+02 0.11734E-010.23798E-02 0.12749E;-05 0.2748a4E+08 0.25499E+02 0.31750E-01 0.67114E+02 0.43867E+02 0.11798E-01

0.23823E-02 0.12819E+05 0.27635E+08 0.25639E+02 0.31921E-01 0.67465E+02 0.43856E+02 0.11863E-01

0.23849E-02 0.12890E+05 0.27788E+9O 0.25780E+02 0.32093E-01 0.67819E+02 0.43845E+02 0.11929E-010.23874E-02 0.12961E+05 0.27942E+08 0.25921E+02 0.32265E-01 0.68174E+02 0.43834E+02 0.11994E-01

0.23900E-02 0.13032E+05 0.28096E+08 0.26064E+02 0.32439E-01 0.68531E+02 0.43823E+02 0.12060E-010.23925E-02 0.13103E+05 0.28251E+08 0.26207E+02 0.32613E-01 0.6890E+02 0.43812E+02 0.12127E-01

0.23950E-G2 0.13175E505 0.28407E+08 0.26351E+02 0.32789E-01 0.692512E02 0.43801E+02 0.12194E-01

0.23976E-02 0.13248E+05 0.285645E08 0.26495E+02 0.32965E-01 0.69614E+02 0.4370E+02 0.12261E-01

0.24001E-02 0.13320E+05 0.28722E508 0.26641E+02 0.33142E-01 0.69978E+02 0.43779E+02 0.12328E-01

0.24027E-02 0.13394E+05 0.28881E+08 0.26787E+02 0.33321E-01 0.70344E+02 0.43767E+02 0.12396E-01

0.24052E-02 0.13467E+05 0.29040E+08 0.26934E402 0.33500E-01 0.70712E+02 0.43756E+02 0.12464E-010.240771-02 0.13541E+05 0.29201E+08 0.27082E+02 0.33680E-01 0.71082E+02 0.43745E+02 0.12533E-01

0.24103E-020.13615E+05 0.29362E+08 0.27231E+02 0.33861E-01 0.71453E+02 0.43733E+02 0.12602E-01

0.24128E-02 0.13690E+05 0.29525E+08 0.27380E+02 0.34043E-01 0.71827E+02 0.43721E+02 0.12671E-01

0.24154E-02 0.13765E+05 0.29688E+08 0.27531E+02 0.34226E-01 0.72202E+02 0.43710E+02 0.12741E-010.24179E-02 0.13841E205 0.29852E+08 0.27682E+02 0.34409E-01 0.72579E+02 0.43698E+02 0.12811E-01

0.24204E-02 0.13917E+05 0.30017E+08 0.27834E+02 0.34594E-01 0.72958E+02 0.43686E+02 0.12881E-01

0.24230E-02 0.13993E+05 0.30183E+08 0.27987E+02 0.34780E-01 0.73339E*02 0.43675E+02 0.12952E-01

0.24255E-02 0.14070E+05 0.30350E+08 0.28141E+02 0.34967E-01 0.73722E+02 0.43663E+02 0.13024E501

0.24281E-02 0.14148E+05 0.30518E+08 0.28295E+02 0.35155E-01 0.74107E+02 0.43651E+02 0.13095E-01

0.24306E-02 0.14225E+05 0.30686E+08 0.28451E+02 0.35343E-01 0.74493E+02 0.43639E+02 0.13167E-01

0.24331E-02 0.14304E505 0.30856E+08 0.28607E+02 0.35533E-01 0.74882E+02 0.43627E+02 0.13240E-01

0.24357E-02 0.14382E+05 0.31027E+08 0.28764E+02 0.35724E-01 0.75272E+02 0.43615E+02 0.13313E-010.24382E-02 0.14461E+05 0.31198E+08 0.28922E+02 0.35915E-01 0.75,6655+02 0.43602E+02 0.13386E-01

0.24408E-02 0.14541E+05 0.31371E÷08 0.29081E+02 0.36108E-01 0.76059E+02 0.43590E+02 0.13460E-01

0.24433E-02 0.14620E+05 0.31544E+08 U.29241E+02 0.36302E-01 0.76455E+02 0.43578E+02 0.13534E-01

0.24458E-02 0.14701E+05 0.31719E+08 0.29402E+02 0.36496E-01 0.76854E+02 0.43565E+02 0.13608E-01

0.24484E-02 0.14782E+05 0.31894E+08 0.29563E+02 0.36692E-01 0.77254E+02 0.43553E+02 0.13683E-01

0,24509E-02 0.14863E+05 0.32071E+08 0.29726E+02 0.36889E-01 0.77656E402 0.43540E202 0.13758E-010.24535E-02 0.14945E+05 0.32248E+08 0.29889E+02 0.37057E-01 0.78060E+02 0.43528E+02 0.13834E-01

0.24560E-02 0.15027E+05 0.32426E+06 0.30053E+02 0.37285E-01 0.78466E+02 0.43515E+02 0.13910E-01

0.24585E-02 0.15109E205 0.32606E+08 0.30218E+02 0.37485E-01 0.78874E+02 0.43502E+02 0.13987E-01

0.24611E-02 0.15192E+05 0.32786E+08 0.30385E+02 0.37686E-01 0.79284E+02 0.43489E+02 0.14064E-01

0.24636E-02 0.15276E+05 0.32967E+08 0.30552E+02 0.37888E-01 0.79696E+02 0.43477E+02 0.14141E-01

0.24662E-02 0.15360E+05 0.33150E+08 0.30719E+02 0.38091E-01 0.80111E02 0.43464E+02 0.14219E-01

0.24687E-02 0.15444E+05 0.33333E+08 0.30888E502 0.38295E-01 0.80527E+02 0.43450E+02 0.14297E-01

•4I

Page 43: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

TIME PRESSURE POOT XDOT PROPELLANT BURNT NDOT SURFACE DISTANCE BURNT

0.24712E-02 0.15529E+05 0.33518E+08 0.31058E.02 0.38500E-01 0.80945E+02 0.43437E+02 0.14376E-01

0.24738E-02 0.15614E+05 0.337032.08 0.312291*02 0.38706E-01 O.81365E.02 0.43424E+02 0.14455E-010.24763E-02 0.15700E+05 0.338901.08 0.31401E+02 0.38913E-01 0.81786E+02 0.43411E+02 0.14534E-010.24789E-02 0.157871+05 0.34077E+08 0.31573E.02 0.39121E-01 0.82212E.02 0.43398E+02 0.14614E-010.24814E-02 0.15873E+05 0.34266E+08 0.31747E+02 0.39331E-01 0.82636E+02 0.43364E+02 0.14695E-010.24839E-02 0.15961E+05 0.34456E+08 0.31921E+02 0.39541E-01 0.83067E.02 0.43371E+02 0.14776E-010.24865E-02 0.160481.05 0.34646E+08 0.32097E+02 0.39753E-01 0.83497E.02 0.43357E+02 0.14857E-010.24890E-02 0.16137E+05 0.34838E+08 0.32273E+02 0.39965E-01 0.83930E+02 0.43344E.02 0.14939E-010.24916E-02 0.16225E+05 0.3503iE.08 0.32451E+02 0.40179E-01 0.84365E+02 0.43330E.02 0.15021E-010.249412-02 0.16315E+05 0.35225E+08 0.32629E.02 0.40394E-01 0.84802E.02 0.43316E.02 0.15103E-010.24966E-.02 0.16404E+05 0.35420E.08 0.32809E.02 0.40610E-01 0.85241E.02 0.43302E.02 0.15187E2-010.24992E-02 0.16494E+05 0.35616E.08 0.32989E+02 0.40827E-01 0.85682E+02 0.43288E+02 0.15270E-010,25017E-02 0.165851.05 0.35813E+08 0.33170E+02 0.410452-01 0.86126E+02 0.43274E+02 0.15354E-010.25043E-02 0.16676E+05 0.360111+08 0.33353E.02 0.41264E-01 0.86571E.02 0.43260E.02 0.15439E-010,250682-02 0.16768E+05 0.36211E.08 0.33536E+02 0.414855-01 0.87019E+02 0.432462.02 0.155242-010.25093E-02 0.16860E+05 0.36411E.08 0.33721E+02 0.41706E-01 0.874682.02 0.432322.02 0.15609E-01

0O.25119E-02 0.16953E.05 0.36613E+08 0.33906E.02 0.41929E-01 0.87920E+02 0.43218E+02 0.156951-010.25144E-02 0.17046E+05 0.36816E+08 0.34093E+02 0.421532-01 0.883752+02 0.432032.02 0.15781E-010.25170E-02 0.17140E.05 0.370202.08 0.342802.02 0.42378E-01 0.88312.02 0.43189E.02 0.15868E-010.25195E-02 0.17234E.05 0.372251.08 0.34469E.02 0.4260-42-01 0.89289E.02 0.43174E+02 0.1595SE-010.25220E-02 0.17329E405 0.37431E.08 0.34658E402 0.421132E-01 0.89750E.02 0.43159E.02 0.16043E-010.25246E-02 0.174242+05 0.37638E+08 0.34349E.02 0.430602-01 0.902C -E+02 0.43145E.02 0.16131E-010.25271E-02 0.17520E.05 0.37847E.08 0.353411.02 0.43290E-01 0.9067a82J12 0.43130E.02 0.16220E-010.25297E-02 0.176172.05 0.38056E+08 0.35233E+02 0.43521E-01 0.91146E,02 C.431152.02 0.16309E-010.25322E-02 0.l77i4E.05 0.382671.08B 0.35427E.02 0.437532-01 0.91615E+02 0.43100E.02 0.16399E-010.25347E-02 0.17811E2.05 0.38479E+.08 0.35622E.02 0.43986E-01 0.92087E.02 i0.430852.02 0.16489E-010.25373E-02 0.17909E+05 0.38692E+08 0.35618E+02 0.44221E-01 0.92562E+02 0.43070E+02 0.16580E-010.253982-02 0.18008E.05 0.38907E+08 0.36015E.02 0.444562-0l 0.93038E.02 0.43055E+02 0.16671E-010.25423E-02 0.18107E.05 0.39122E.08 0.36214E.02 0.446932-01 0.93517E+02 0.43040E.02 0.16763E-010.25449E-02 0.18206E+05 0.39339E+08 0.36413E+02 0.44931E-01 0.93998E.02 0.43024E+02 0.16855E-010.2547412-02 0.18307E.05 0.39557E.08 0.366132.02 0.45171-01 0.94481E.02 0.43009E+02 0.16948E-010.255002-02 0.18407E+05 0.39776E.08 0.36815E+02 0.45411E-01 0.949671.02 0.42993E+02 0.17041E-010.25525E-02 0.185092.05 0.39997E+08 0.37017E.02 0.45653E-01 0.954552+02 0.429782.02 0.17135E-010.25550E-02 0.18611E.05 0.40218E.08 0.372212.02 0.45896E-01 0.95945E+02 0.42962E+02 0.17229E-010.25576E-02 0.18713E.05 0.40441E.08 0.37426E.02 0.46140E-01 0.964372.02 0.42946E.02 0.17324E-01

0.25601E-02 0.18816E+05 0.40665E.08 0.37632E+02 0.463862-01 0.96932E+02 0.42930E+02 0.17419E-01I0.25627E-02 0.189202.05 0.40891E+08 0.37839E.02 0.46633E-01 0.974302.02 0.42914E.02 0.17515E-010.25652E-02 0.19024E405 0.411171.081 0.380471.+02 0.468812-01 0.97929E.02 0.42898E+02 0.17612E-01

0.25677E-02 0.19128E.05 0.413452.08 0.38257E.02 0.47130E-01 0.98431E.02 0.42882E+02 0.177082-010.257032-02 0.19234E.05 0.41574E+08 0.38467E+02 0.47381E-01 0.98936E.02 0.42866E.02 0.17806E-010.25728E-02 0.193402.05 0.41805E.08 0.38679E.02 0.476332-01 0.99442E.02 0.42849E+02 0.17904E-010.25754E-02 0.19446E.05 0.42037E.08 0.38892E.02 0.47886E-01 0.99952E+02 0,42833E.02 0.15002E-010.25779E-02 0.19553E.05 0.42270E.08 0.39106E+02 0.48140E-01 0.10046E.03 0.42816E.02 0.1810112-010.25804E-02 0.196612.05 0.42504E.08 0.39121E.02 0.483961-01 0.10098E.03 0.42800E+02 0.18201E-01

0.258302-02 0.19769E+05 0.42740E.08 0.39538E.02 0.48653E-01 0.10149E.03 0.427832.02 0.183012-01

0.25855E-02 0.19878E.05 0.429771.08 0.39756E.02 0.48912E-01 0.10201E+03 0.42766E+02 0.18402E-01

0.258812-02 0.19987E.05 0.432152.08 0.39975E.02 0.49172E-01 0.10253E.03 0.42749E+02 0.18503E-01

0.25906E-02 0.20097E.05 0.43454E.08 0.40195E.02 0.494332-01 0.10306E403 0.427331.02 0.18605E-010.25931E-02 0.20208E+05 0.436952.08 0.40416E.02 0.49695E-01 0.10358E+03 0.42715E.02 0.18707E-010.25957E-02 0.20319E.05 0.43938E.08 0.40639E.02 0.49959E-01 0.104112+03 0.42698E+02 0.18810E-01

0.259822-02 0.20431E+05 0.441812.08 0.40862E+02 0.50224E-01 0.10464E.03 0.426812.02 0.18914E-01

0.26008E-02 0.20544E.05 0.444262.08 0.41087E.02 0.50490E-01 0.105182+03 0.42664E+02 0.190182-01

0.26033E-02 0.20657E+05 0.446732.08 0.41314E+02 0.50758E-01 0.10571E.03 0.426-46E+02 0.19122E-01

0.260582-02 0.20771E+05 0.44920E.02 0.41541E.02 0.51027E-01 0.10625E+-03 0.42629E.02 0.19228E-01

45K

Page 44: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

TIME PRESSURE POOT XDOT PROPELLANT BURNT MOOT SURFACE DISTANCE BURNT

0.26084E-02 0.20985E+05 0.45169E+08 0.41770E+02 0.5129aE-01 0.10679E+03 0.42611E+02 0.19333E-01

0.26109E-02 0.21000E+05 0.45420E+08 0.42000E+02 0.51570E-01 0.10734E+03 0.42593E+02 0.19440E-01

0.26135E-02 0.21116E+05 0.45672E+08 0.42232E+02 0.51843E-01 0.107882+03 0.42576E+02 0.19547E-01

0.26160E-02 0.21232E+05 0.45925E+08 0.42464E+02 0.521188-01 0.10843E+03 0.42558E+02 0.19654E-01

0.26185E-02 0.21349E+05 0.46180E+08 0.426982+02 0.52394E-01 0.10898E+03 0.425402+02 0.19762E-01

0.26211E-02 0.214672+05 0.46436E+08 0.42933E+02 0.52671E-01 0.10954E+03 0.425212+02 0.19871E-01

0.26236E-02 0.21585E+05 0.46694E+08 0.43170E+02 0.52950E-01 0.11009E+03 0.42503E+02 0.19981E-01

0.26262E-02 0.217042+05 0.46953E+08 0.4340aE+02 0.53231E-01 0.11065E+03 0.42485E+02 0.20090E-01

0.26287E-02 0.21823E+05 0.4.7213E+08 0.43647E+02 0.53512E-01 0.1l12iE+03 0.42466E+02 0.20201E-01

0.26312E-02 0.21944E+05 0.47475E+08 0.43867C+02 0.537962-01 0.11178E+03 0.424482+02 0.20312E-01

0.26338E-02 0.22065E+05 0.47738E+68 0.44129E+02 0.54080E-01 0.11234E+03 0.42429E+02 0.204242-01

0.26363E-02 0.22186E+05 D.48003E+08 0.44372E+02 0.54366E-01 0.11291E+03 0.42411E+02 0.20536E-01

0.26389E-02 0.22308E+05 0.48269E+08 0.44617E402 0.54654E-01 0.11348E+03 0.42392E+02 0.20649E-01

0.26414E-02 0.22431E+05 0.48537E+08 0.44863E+02 0.549432-01 0.11406E+03 0.42373E+02 0.20763E-01

0.264392-02 0.225552+05 0.4a8806+08 0.45110E+02 0.55233E-01 0.11463E+03 0.42354E+02 0.20877E-01

0.26465E-02 0.22679E+05 0.49077E+08 0.453592+02 0.555252-01 0.115212+03 0.42335E+02 0.209922-01

0,2649011-02 0.22804E+05 0.49349E+08 0.45609E+02 0.55818E-01 0.115802+03 0.42315E+02 0.21108E-01

0.26516E-02 0.229302+05 0.49623E+08 0.45860E+02 0.56113E-01 0.1163aE+03 0.42296E+02 0.212242-01

0.26541E-0Z 0.23056E+05 0.49898E+08 0.46113E+02 0.564102-01 0.11697E+03 0.422772+02 0.21341E-01

0.265662-OZ 0.23183E+05 0.50175E+08 0.46367E+02 0.56707E-01 0.117562+03 0.42257E+02 0.214582-01

0.26592E-02 0.233112+05 0.504542+08 0.46622E+02 0.57007E-01 0.11815E+03 0.422376+02 0.215762-01

0.26617E-02 0.23440E+05 0.50734E.-08 0.46879E+02 0.573082-01 0.11875E+03 0.42218E+02 0.21695E-01

0.26643E-02 0.235692405 0,510152+08 0.471382+02 0.57610E-01 0.119352+03 0.42198E+02 0.218142-01

0.266682-02 0.23699E405 0.51298E+08 0.47398E+02 0.579142-01 0.119952+03 0.421782+02 0.21934E-01U0,.26693E-02 0.238302+05 0.515832+08 0.476592+02 0.58219E-01 0.12055E+03 0.42157E+02 0.220552-010.26719E-02 0.23961E+05 0.51869E+08 0.47922E+02 0.58526E2-01 0.121162+03 0.421379+02 0.22176E-01

0.267442-02 0.24.093E+05 0.52157E+08 0.481862+02 0.588352-01 0.121772+03 0.42117E+02 0.222982-01

0.26770E-02 0.242262+05 0.52446E+08 0.48452E+02 0.591452-01 0.122382+03 0.420962+02 0.22421E-01

0.26795E-02 0.243592405 0.52737E+08 0.487192+02 0.59456E-01 0.12299E+03 0.42076E+02 0.225452-01

0.26820E-02 0.24494E+05 0.53030E+08 0.48987E+02 0.59769E-01 0.123612403 0.420552+02 0.226692-01I0.26846E-02 0.246292+05 0.53324E+08 0.49258E+02 0.60084E.01 0.124232+03 0.42034E+02 0.227932-010.268712-02 0.24765E+05 0.53620E2P08 0.495292+02 0.604002-01 0.12485E+03 0.42014E+02 0.22919E-01

0.26897E-02 0.249012+05 0.53917E+08 0.49802E+02 0.607182-01 0.1251.82+03 0.41993E+02 0.230452-01

0.26922E-02 0.25038E+05 0.54216E+08 0.500772+02 0.610382-01 0.126112+03 0.41971E+02 0.23172E-010.26947E-02 0.251rt2+05 0.545172+08 0.503532+02 0.61359E-01 0.126742+03 0.41950E+02 0.23299E-01

0.26973E-02 0.25315E+05 0.54820L+08 0.50312+02 0.61682E-01 0.12737E+03 0.41929E+02 0.23428E-01

0.26998E-02 0.25455E+05 0.55124E+08 0.50910E+02 0.62006E-01 0.12801E+03 0.41907E+02 0.23557E-01

0.27024E-02 0.25595F+05 0.55430E+08 0.51191E+02 0.623322-01 0.12865E4.03 0.41886E+02 0.23686E-01

0,27049E-02 0.25737E+05 0.557372+08 0.514732+02 0.626592-01 0.12929E+03 0.418642+02 0.23817E-01

0.270742-02 0.258792405 0.560462+08 0.51757E+02 0.62989E-01 0.12994E+03 0.41842E+02 0.239482-01

0.271002-02 0.260212+05 0.563572+08 0.520422+02 0.63319E-01 0.13059E+03 0.41820E+02 0.24079E-01

0.27125E-02 0.26165E+05 0.56670E+08 0.52330E+02 0.63652E-01 0.13124E+03 0.41798E+02 0.24212E-01

0.271512-02 0.26309E+05 0.56984E+08 0.52618E+02 0.63986E-01 0.13189E+03 0.41776E+02 0.243452-01

0.271762-02 0.26454E+05 0.57300E+08 0.52908E+02 0.64322E-01 0.13255E+03 0.41753E+02 0.24479E-01

0.27201E-02 0.26600E+05 0.57618E+08 0.53200E+02 0.646592-01 0.13321E+03 0.41731E+02 0.24614E-01

0.272272-02 0.26747E+05 0.579382+08 0.53494E+02 0.64999E-01 0.133872+03 0.41708E+02 0.247502-01

0.272522-02 0.26894E+05 0.582592+08 0.537892+02 0.65339E-01 0.134532+03 0.41686E+02 0.248862-01

0.272*782-02 0.270432+05 0.58583E+08 0.540862+02 0.65682E-01 0.13520E+03 0.416632+02 0.25023E-01

0.273032-02 0.271922+05 0.58908E+08 0.54384E+02 0.66026E-01 0.135872+03 0.41640E+02 0.25161E-01

0.273282-02 0.27342E+05 0.59234E+08 0.54684E+02 0,66372E-01 0.13655F+03 0.41617E+02 0.252992-01

0.27354E-02 0.27493E+05 0.59563E+08 0.54986E,02 0.66720E-01 0.13722E+03 0.41594E+02 0.25438E-01

0.27379E-02 0.27645E+05 0.59893E+08 0.55209E+02 0.67069E-01 0,13790E+03 0.41570E+02 0.255782-01

0.27405E-02 0.27797E+05 0.60226E+08 0.55594E+02 0.67420E-01 0.13859E+03 0.41547E+02 0.25719E-01

0.27430E-02 0.27951E+05 0.60560E+08 0.559012+02 0.677732-01 0.139272+03 0.41523E+02 0.25861E-01

46)

-- Ahj'm A

Page 45: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

TIME PRESSURE POOT XDOT PROPELLANT BURNT MOOT SURFACE DISTANCE BURNT

0.27455E-02 0.281058+05 0.60895E.08 0.56210E+02 0.681288-01 0.13996E+03 0.41499E+02 0.26003E-010.27481E-02 0.28260-.+05 0.61233E+08 0.56520E.02 0.68484E-01 0.11.065E+03 0.414768+02 0.26146E-01

0.275068-02 0.28416E.05 0.61573E+08 0.56832E.02 0.68842-01 0.14135E+03 0.41452E+02 0.26290E-01

0.27532E-02 0.28573E+05 0.61914E+08 0.57145E.02 0.69202E-01 0.14204E+03 0.41428E+02 0.26435E-010.27557'E-02 0.28730E.05 0.62258E.08 0.57461E+02 0.69564E-01 0.112748+03 0.41403E+02 O.265S0E-010.27582E-02 0.28889E.05 0 .62603E*08 0.577M8+02 0.69927E-01 0.14345E.03 0.413798.02 0.267278-01

0.27608E-02 0.29048E+05 0.62950E+03 0.58097E+02 0.702928-01 0.14415E+03 0.41354E+02 0.26874E-010.27633E-02 0.29209E.05 0.63299E.08 0.58417E+02 0.70659E-01 0.14466E+03 0.413308402 0.27022E-01

0.2,7659E-02 0.29370E+05 0.636508.08 0.58740E.02 0.710288-01 0.14557E.03 0.41305E.02 0.27171E-01

0.27684E-02 0.29532E+05 0.64003E408 0.59064E+02 0.71399E-01 0.14629E+03 0.41280E+02 0.27320E-010.27709E-02 0.29695E.05 0.643588.08 0.59390E.02 0.717718-01 0.147018+03 0.4125$E+02 0.274718-010.277358-02 0.298598.05 0.647158.08 0.59718E.02 0.721468-01 0.14773803 0.41230E+02 0.27622E-010.27760E-02 0.30024E8,05 0.65073E+08 0.600478+02 0.72522E-01 0.14345E+03 0.41204E+02 0.27774E-010.27786E-02 0.30189E.05 0.65434E+08 0.603798.02 0.729008-01 0.1491U8+03 0.411798+02 0.27927E-010.278118-02 0.303568+05 0.657978.08 0.60712t+02 0.73280E-01 0.14991E.03 0.41153E+02 0.280818-01

0.27836E-02 0.305248+05 0.66161E+08 0.61047E.02 0.73661E-01 0.150648+03 0.411278+02 0.28235E-010.27862E-02 0.30692E.05 0.665281+08 0.61381.9.02 0.7404S8-01 0.151388+0)3 0.41102E+02 0.28391E-010.27887E-02 0.30862E+05 0.668978+08 0.61723E.02 0.74430E-01 0.15212E+03 0.41075E+02 0.28547E-010.27913E-02 0.31032E.05 0.672678.08 0.62064E.02 0.74817E-01 0.15286E+03 0.41049E+02 0.28704E-010.279358-02 0.31203E+05 0.676401.08 0.624078.02 0.75207E-01 0.15361E+03 0.41023E+02 0.288628-01

0.27963E-02 0.31376E.05 0.68015E.08 0.62751E+02 0.73598E-01 0.15435E.03 0.40996E+02 0.290218-010.27939E-02 0.31549E+05 0.68392E.08 0.630988+02 0.759911-01 0.15511E+03 0.40970E+02 0.291818-010.28014E-02 0.317238+05 0.68771E+08 0.63446E+02 0.76386E-01 0.155868+03 0.409438.02 0.293428-01

0.28040E-02 0.31898E.05 0.69152E.08 0.63796E+02 0.767828-01 0.15662E+03 0.40916E+02 0.295048-010.280658-02 0.32074E+05 0.69535E+08 0.64149E+02 0.771818-01 0.15738E+03 0.40889E+02 0.296668-010.28090E-02 0.322518+05 0.69920E+08 0.64503E+02 0.77582E-01 0.15814E+03 0.40862E.02 0.29829E-010.28116E-02 0.32429E.05 0.70307E+08 0.64859E+02 0.77984E-01 0.158918+03 0.40834E+02 0.299948-010.28141E-02 0.326088+05 0.7069U8+08 0.65217E+02 0.783839E-01 0.15968E.03 0.40807E+02 0.30159E-010.28166E-02 0.32789E.05 0.710888+08 0.65577E.02 0.787968-01 0.160458+03 0.407798.02 0.30325E-010.28192E-02 0.32970E.05 0.71481E+08 0.65939E+02 0.79204E-01 0.16123E+03 0.407518.02 0.304928-010.282178-02 0.33152E405 0.71877E+08 0.66303E402 0.796158-01 0.162018.03 0.40723E.02 0.306608-010.28243E-02 0.33335E+05 0.72275E+08 0.66669E+02 0.800278-01 0.16279E.03 0.40695E+02 0.30829E-010.28268E-02 0.33519E+05 0.72675E.08 0.670388.02 0.80441E-01 0.163578.03 0.40667E.02 0.30999E-010.28293E-02 0.33704E+05 0.730778+08 0.674088+02 0.80858E-01 0.16436E.03 0.406388+02 0.31169E-010.28319E-02 0.33890E+05 0.734818.08 0.67780802 0.81276E-01 0.165158+03 0.406108+02 0.31341E-010.28344E-02 0.340778+05 0.738W+808 0.68154E+02 0.816978-01 0.16595E+03 0.405818+02 0.31514E-01

0.28370E-02 0.34265E+05 0.74297E403 0.65531E+02 0.821198-01 0.16674E+03 0.405528+02 0.31687E-01

0.283958-02 0.34455E+05 0.747088408 0.68909E+02 0.82544E-01 0.16754E+03 0.40523E+02 0.318628-010.284208-02 0.34645E.05 0.751218.08 0.69290E.02 0.82970E-01 0.16835E.03 0.40494E+02 0.3203IFE-01

0.284468-02 0.34836E+05 0.75536E+08 0.69672E+02 0.83399E-01 0.16915E+03 0.40464E+02 0.32214E-01

0.284718-02 0.35028E+05 0.759548+08 0.700578+02 0.83830E-01 0.16996E+03 0.40435E+02 0.32391E-010.28497E-02 0.35222E+05 0.76374E+08 0.70444E+02 0.84262E-01 0.17078E.03 0.404058+02 0.32570E-010.285228-02 0.354168.05 0.76796E+08 0.708338+02 0.846978-01 0.17159E+03 0.40375E.02 0.32749E-01

0.28547E--02 0.35612E+05 0.77220E.08 0.71224E+02 0.851348-01 0.17241E+03 0.40345E+02 0.32929E-010.28573E-02 0.35809E.05 0.776478+03 0.71617E+02 0.85573E-01 0.17323E+03 0.40315E+02 0.331118-01

0.285988-02 0.36006E+05 0.78076E+08 0.72013E+02 0.56014E-01 0.17406E+03 0.40284E.02 0.33293E-01

0.28624E-02 0.36205E+05 0.78507E+08 0.724118+02 0.86457E-01 0.17489E+03 0.40254E+02 0.33477E-01

0.28649E-02 0.36405E+05 0.78941E+08 0.72810E+02 0.86902E-01 0.17572E+03 0.402238+02 0.336618-01

0.28674E-02 0.36606E.05 0.793778+08 0.732138+02 0.87350E-01 0.17655E+03 0.40192E+02 0.33846E-01

0.287008-02 0.36808E+05 0.79815E+08 0.73617E+02 0.87799E-01 0.17739E+03 0.40161E+02 0.34033E-01

0.28725E-02 0.37012E.05 0.80256E+08 0.74023E.02 0.88251E-01 0.17823E+03 0.40130E+02 0.342208-01

0.287518-02 0.37216E+05 0.806998+08 0.74432E+02 0.88704E-01 0.17908803 0.40099E+02 0.34409E-010.28776E-02 0.37422E.05 0.81145E+08 0.74843E+02 0.891608-01 0.17992E+03 0.40067E+02 0.345988-01

0.28801E-02 0.37628E+05 0.91592E+03 0.75257E+02 0.89618E-01 0.13077E+03 0.40035E+02 0.34789E-01

Page 46: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

TIME PRESSURE PD07 MOOT PROPELLANT BURNT P4007 SURFACE DISTANCE BURNT

0.28827E-02 0.37836E+05 0.82042E+08 0.75672E+02 0.90079E-01 0.18163E+03 0.40003E+02 0.34981E-01

0.28852E-02 0.38045E+05 0.82495E+08 0.76090E+02 0.90541E-0l 0.18248E+03 0.39971E+02 0.35173E-01

0.288785-02 0.38255E+05 0.82950E+08 0.76510E+02 0.91006E-01 0.18334E+03 0.39939E+02 0.35367E-01

0.28903E-02 0.38466E+05 0.83407E+08 0.76933Ei-02 0.91472E-01 0.1842iE+03 0.39906E+02 0.35562E-01

0.28928E-02 0.38679E+05 0.83867E+08 0.77358E+02 0.91941i:-O1 0.18507E+03 0..39874E+02 0.35758E-01

0.28954E-02 0.38892E+05 0.84329E+08 0.77785E+02 0.92412E-01 0.18594E+03 0.39841E+02 0.35955E-01

0.28979E-02 0.39107E+05 0.84794E+08 0.78214E+02 0.928861-01 0.18681E403 0.39808E+02 0.36153E-01

0.290055-02 0.39323E+05 0.85261E+08 0.78646E+02 0.93361E-01 0.18769E4-03 0.39775E+02 0.36352E-01

0.29030E-02 0.39540E405 0.85731E+08 0.790815+02 0.93839E-01 0.18857E+03 0.39741E+02 0.36553E-01

0.29055E-02 0.39759E+05 0.86203E+08 0.795175+02 0.94319E-01 0.18945E+03 0.397085+02 0.36754E-01

0.29081E-02 0.39978E+05 0.86678E+08 0.79956E+02 0,94801E-01 0.19033E+03 0.39674E+02 0.36957E-01

0.29106E-02 0.40199E+05 0.871555+08 0.80398E+02 0.95286E-01 0.191225+03 0.39640E+02 0.371605-01

0.29132E-02 0.40421E+05 0.876345+08 0.80842E+02 0.95773E-01 0.192115+03 0.39606E+02 0.37365E-01

0.291575-02 0.40644E+05 0.88117E+08 0.812885+02 0.96262E-01 0.19300E+03 0.395725+02 0.37571E-01

0.29182E-02 0.40868E+05 0.88601E+08 0.81737E+02 0.96753E-01 0.193190E+03 0.395375+02 0.37778E-01

U.292085-02 0.41094E+05 0.890885+08 0.82188E+02 0.97247E-01 0.19480E+03 0.39502E+02 0.379865-01

0.29233E-02 0.41321E+05 0.895785+08 0.82642E+02 0.97743E-01 0.19570E+03 0.39467E+02 0.381955-01

0.29259E-02 0.415495+05 0.90071E+08 0.830985+02 0.98241E-01 0.196615+03 0.39432E+02 0.38406E-01

0.292845-02 0.41779+05 0.90565E+08 0.83557E+02 0.98741E-01 0.19751E+03 0.39397E+02 0.38617E-01

0.29309E-02 0.42009E+05 0.91063E+08 0.84018E+02 0.99244E-01 0.19843E+03 0.39362E+02 0.38830E-01

0.293355-02 0.42241E+05 0.915635+08 0.84482E+02 0.997495-01 0.19934E+03 0.39326E+02 0.39044E-01

0.29360E-02 0.42474E+05 0.92066E+08 0.84949E+02 0.100265+00 0.2002654+03 0.392905+02 0.39259E-01

0.29386E-02 0.42709E+05 0.925715.08 0.85418E+02 0.10077E+00 0.201185+03 0.39254E+02 0.39476E-01

0.29411E-02 0.42945E5105 0.93079E+08 0.85889E+02 0.10128E+00 0.202105+03 0.39218E+02 0.39693E-01

0.29436E-02 0.43182E+05 0.93590E+08 0.86363E+02 0.101795+00 0.20303E+03 0.391815+02 0.39912E-01

0.29462E-02 0.434205+05 0.94103E+08 0.86840E+02 0.10231E+00 0.20396E+03 0.39145E+02 0.40132E-01

0.294875-02 0.43660E+05 0.94619E+08 0.87319E+02 0.10283E+00 0.204895+03 0.39108E+r. ý 403535-01

0.295135-02 0.43901E+05 0.95137E+08 0.87801E+02 0.103355+00 0.20583E+03 0.3907' 1.40575E-01 r

0.29538F.-02 0.44143E+05 0.95658E+08 0.68286E+02 0.10387E+00 0.20677E+03 0.39033. 40799E-01

0.295635-02 0.443865+05 0.961825+08 0.88773+02 0.104405+00 0.20771E+03 0.389965+02 0.41024E-01

0.29589E-02 0.44631E+05 0.96709E+08 0.89263E+02 0.).493E+00 0.20865E+03 0.389585+02 0.41250E-01

0.29614E-02 0.44878E+05 0.97238E+08 0.897555+02 0.10546E+00 0.20960E+03 0.38920E+02 0.41477E-01

0.29640E-02 0.45125E+05 0.97770E+08 0.902515+02 0.10599E+00 0.21055E+03 0.388825+02 0.41706E-01

0.29665E-02 0.45374E+05 0.98304E+08 0.90'749E+02 0.10653E+00 0.211505+03 0.38844E+02 0.419365-01

0.296905-02 0.45625E+05 0M8842E+08 0.91249E+02 0.10707E+00 0.21246E+03 0.38806E+02 0.42167E-01

0.29716E-02 0.45876E+05 0.993825+08 0.91753E+02 0.10761E+00 0.213425+03 0.38767E+02 0.42399E-01

0.29741E-02 0.46130E+05 0.99,925E+08 0.92259E+02 0.108155+00 0.214'38E+03 0.387285+02 0.42633E-01

0.29767E-02 0.46384E+05 0.10047E+09 0.92768E+02 0.10870E+00 0.21534E+03 0.386895+02 0.42868E-01

0.29792E-02 0.466-405+05 0.10102E+09 0.93280E+02 0.10925E+00 0.21631E+03 0.38649E+02 0.43104E-01w

0.29817E-02 0.46897E+05 0.10157E+09 0.93794E+02 0.109805+00 0.21728E+03 0.38610E+02 0.43342E-01

0.298435-02 0.471565+05 0.102125+09 0.94312E+02 0.11035E+00 0.218265+03 0.38570E+02 0.43581E-01

0.29868E-02 0.47416E+05 0.102685+09 0.94832E+02 0.11091E+00 0.219235+03 0.38530E+02 0.43821E-01

0.29894E-02 0.476775+05 0.103245+09 0.95355E+02 0.11146E+00 0.220215+03 0.38490E+02 0.440625-01

0.29919E-02 0.47940E+05 0.10380E+09 0.958815+02 0.11202E+00 0.221195+03 0.384495+02 0.443055-01

0.29944E-02 0.48205E+05 0.10437E+09 0.96409E+02 0.112595+00 0.22218E+03 0.38408E+02 0.44549E-01

0.29970E-02 0.48470E+05 0.10494E+09 0.96941E+02 0.113155+00 0.223165+03 0.38368E+02 0.44795E-01

0.29995E-02 0.48738E+05 0.10551E+09 0.97475E+02 0.11372E+00 0.224155+03 0.38326E+02 0.45042E-01

0.30021E-02 0.49006E+05 0.10608E+09 0.980135+02 0.11429E+00 0.22515E+03 0.38285E402 0.45290E-01

0.30046E-02 0.49277E+05 0.10666E+09 0.985535+02 0.11486E+00 0.22614E+03 0.38243E+02 0.45540E-01

0.30071E-02 0.49548E+05 0.107245+09 0.99096E+02 0.11544E+00 0.227145+03 0.38202E+02 0.45791E-01

0.300975-02 0.498215+05 0.10782E+09 0.996435+o02 0.11602E+00 0.22814E+03 0.38159E+02 0.46043E-01

0.301225-02 0.50096E+05 0.10840E+09 0.10019E+03 0.11660E+00 0.22914E403 0.38117E+02 0.46297E-01

0.30148E-02 0.50372E+05 0.10899E+09 0.10074E+03 0.11718E+00 0.23015E+03 0.38075E+02 0.46552E-01

0.301735-02 0.50649E+05 0.10958E+09 0.101305+03 0.11777E+00 0.23116E403 0.38032E+02 0.46809E-01

48F

Page 47: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

TINE PRESSURE PDOT XDOT PROPELLANT BURNT HOOT1 SURFACE DISTANCE BURNT

0.30198E-02 0.50929E+05 0.11017E+09 0.10186E+03 0.11836E+00 0.23217E÷03 0.37989E+02 0.47067E-010.30224E-02 0.51209E+05 0.11077E+09 0.10242E+03 0.11895E+00 0.23318E+03 0.37946E+02 0.47326E-010.30249E-02 0.51491E+05 0.11137E+09 0.10298E+03 0.11954E+00 0.23420E+03 0.37902E+02 0.4'5878-010.3027SE-02 0.51775E+05 0.11197[+09 0,10355E+03 0.12014E+00 0.23521E+03 0.37858E+02 0.47849E-010.30300E-02 0.52060E+05 0.11258E+09 0.10412E+03 0.12074E+00 0.23623E+03 0.37815E+02 0.48113E-010.30325E-02 0.523478*05 0.i1319i.09 0.10469E1s603 0.12134E+00 0,23726E+03 0.37770E+02 0.48378E-01

0.30351E-02 0.52635E+05 0.11380E+09 0.10527E÷03 0.12194E+00 0.23828E+03 0.37726E+02 0.48645E-010.30376E-02 0.52925E+05 0.11441E+09 010585E+03 0.12255E+00 0.23931E+03 0.37681E+02 0.48913E-010.30402E-02 0.53216E+05 0.11503E+09 0.10643E+03 0.12316t+00 0.24034E+03 0.37636E+02 0.49182E-010.30427E-02 0.53509E+05 0.11565E+09 0.10702E+03 0.12377E+00 0.24138E+03 0.37591E+02 0.49453E-010.30452E-02 0.53804E+05 0.11627E+09 0.10761E+03 0.12438E+00 0.24241E+03 0.37546E+02 0.49726E-01

0.30478E-02 0.54100E+05 0.11690E.09 0.10820E+03 0.12500E+00 0.24345E+03 0.37500E+02 0.50000E-01

4.9

U'i

Page 48: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

ID

APPENDIX BAN IBHVG2 COMPUTER RUN TO

COMPARE TO THE TEST COMPUTER RUN

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Page 49: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

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Page 51: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

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Page 52: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

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Page 53: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

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Page 54: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

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Page 65: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

40

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Page 66: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

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Page 74: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

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Page 75: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

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Page 77: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

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Page 78: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

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No. of No. ofCopies Organization Copes Organization

12 Administrator 5 Project ManagerDefense Technical Info Center Cannon Artillery WeaponsATTN: DTIC-FDAC System, ARDC, AMCCOMCameron Station, Bide 5 ATTN: AMCPM-CW,Alexandria, VA 22304-6145 AMCPM-CWW

AMCPM-CWSCommander M. FisetteUSA Concepts Analysis Agency AMCPM-CWAATTN: D. Hardison H. Hassmann8120 Woodmont Avenue AMCPM-CWA-SBethesda, MD 20014-2797 R. DeKleine

Dover, NJ 07801-50011 HQDA/DAMA-ZA

Washington, DC 20310-2500 2 Project ManagerMunitions Production Base.

I HQDA, DAMA-CSM, Modernization and ExpansionWashington, DC 20310-2500 ATTN: AMCPM-PBM, A. Siklosi

AMCPM..PBM-E, L. LaibsonI HQDA/SARDA Dover, NJ 07801-5001

Washington, DC 20310-25003 Project Manager

I C.I.A. Tank Main Armament SystemOIR/DB/Standard ATTN: AMCPM-TMA, K. RussellGE47 HQ AMCPM-TMA-105Washington, D.C. 20505 AMCPM-TMA- 120

Dover, NJ 07801-5001CommanderUS Army War College I CommanderATTN: Library-FF229 US Army Watervliet ArsenalCarlisle Barracks, PA 17013 ATTN: SARWV-RD, R. Thierry

Watervliet, NY 12189-5001US Army Ballistic Missile

Defense Systems Command I CommanderAdvanced Technology Center U.S. Army ARDECP. O. Box 1500 ATTN: SMCAR-MSIHuntsville, AL 35807-3801 Dover, NJ 07801-5001

Chairman 1 CommanderDOD Explosives Safety Board U.S. Army ARDECRoom 856-C ATTN: SMCAR-TDCHoffman Bldg. 1 Dover, NJ 07801-50012461 Eisenhower AvenueAlexandria, VA 22331-9999 4 Commander

US Army Armament MunitionsSCommander and Chemical Command

US Army Materiel Command ATTN: AMSMC-IMP-LATTN: AMCPM-GCM-WF Rock Island, IL 61299-73005001 Eisenhower AvenueAlexandria, VA 22333-5001 1 HQDAS~DAMA-ART-M

I Commander Washington, DC 20310-2500US Army Materiel CommandATTN: AMCDRA-ST I Commander5001 Eisenhower Avenue US Army AMCCOM ARDEC CCACAlexandria, VA 22333-5001 ATTN: SMCAR-CCB-TL

Benet Weapons LaboratoryI Commander Watervlict, NY 12189-4050

US Army Materiel CommandATTN: AMCDE-DW5001 Eisenhower AvenueAlexandria, VA 22333-5001

81

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3 Commander 1 CommanderUS Army ARDEC US Army Communications -ATTN: SMCAR-MSI Electronics Command

SMCAR-TDC ATTN: AMSEL-EDSMCAR-LC Fort Monmouth, NJ 07703-5301

LTC N. BarronDover, NJ 07801-5001 1 Commander

CECOM R&D Technical Library7 Commander ATTN: AMSEL-M-L (Report Section)

US Army ARDEC B.2700ATTN: SMCAR-LCA Fort Monmouth, NJ 07703-5000

A. BeardellD. Downs I CommanderS. Einstein US Army Harry Diamond Lab.S. Westley ATTN: DELHD-TA-LS. Bernstein 2800 Powder Mill RoadC. Roller Adelphi, MD 20783-1145J. Rutkowski

Dover, NJ 07801-5001 CommanderUS Army Missile Command

3 Commander ATTN: AMSMI-RX- US Army ARDEC M.W. Thauer

ATTN: SMCAR-LCB-I Redstone Arsenal, ALD. Sprin 35898-5249SMCAR-LCE

SMCAR-LCM-E I CommanderS. Kaplowitz US Army Missile and Space

Dover, NJ 07801-5001 Intelligence CcnterATTN: AIAMS-YDL

4 Commander Redstone Arsenal, ALUS Army ARDEC 35898-5500ATTN: SMCAR-LCS

SMCAR-LCU-CT I CommanderE. Barrieres US Army Missile CommandR. Davitt Research, Development, and

SMCAR-LCU-CV Engineering CenterC. Mandala ATTN: AMSMI-RD

Dover, NJ 07801-5001 Redstone Arsenal, AL35898-5245

3 CommanderUS Army ARDEC I CommandantATTN: SMCAR-LCW-A US Army Aviation School

M. Salsbury ATTN: Aviation AgencySMCAR-SCA Fort Rucker, AL 36360

L. StiefelB. Brodman I Commander

Dover, NJ 07801-5001 US Army Tank AutomotiveCommand

Commander ATTN: AMSTA-TSLUS Army Aviation Systems Warren, MI 48397-5000

CommandATTN: AMSAV-ES I Commander4300 Goodfellow Blvd. US Army Tank AutomotiveSt. Louis, MO 63120-1798 Command

ATTN: AMSTA-CGDirector Warren, MI 48397-5000US Army Aviation Research

and Technology ActivityAmes Research CenterMoffett Field, CA 94035-1099

82

V I M d z y - -- - - - - -- - - - - -----.". r t " • ' ... ' : " " " ". '

Page 80: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

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I Project Manager I CommanderImproved TOW Vehicle US Army Logistics Mgmt CtrATTN: AMCPM-ITV Defense Logistics StudiesUS Army Tank Automotive Fort Lee, VA 23801

"CommandWarren, MI 48397-5000 1 Commandant

US Army Infantry School2 Program Manager ATTN: ATSH-CD-CS-OR

M1 Abrams Tank System Fort Benning, GA 31905-5400ATTN: AMCPM-GMC-SA,

T. Dean 1 CommandantWarren, MI 48092-2498 US Army Command and

General Staff CollegeProject Manaper Fort Leavenworth, KS 66027

:• Fighting Vehicle SystemsATTN: AMCPM-FVS I CommandantWarren, MI 48092-2498 US Army Special Warfare

SchoolPresident ATTN: Rev & Tng Lit DivUS Army Armor & Engineer Fort Bragg NC 28307

BoardATTN: ATZK-AD-S 3 CommanderFort Knox, KY 40121-5200 Radford Army Ammunition Plant

ATTN: SMCRA-QA/HI LIBProject Manager Radford, VA 24141-0298M-60 Tank DevelopmentATTN: AMCPM-M60TD I CommanderWarren, MI 48092-2498 US Army Foreign Science &

Technology CenterSDirector ATTN: AMXST-MC-3

US Army TRADOC Systems 220 Seventh Street, NEAnalysis Activity Charlottesville, V A

ATTN: ATOR-TSL 22901-5396White Sands Missile Range,NM 88002 Commandant

US Army Field ArtilleryCommander Center & SchoolUS Army Training & Doctrine ATTN: ATSF-CO-MW B. Willis

Command Ft. Sill, OK 73503-5606ATTN: ATCD-MA/ MAJ WilliamsFort Monroe, VA 23651 1 Commander

US Army Development and"2 Commander Employment Agency

US Army Materials and ATTN: MODE-OROMechanics Research Center Fort Lewis, WA 98433-5099

ATTN: AMXMR-ATLTech Library I Office of Naval ResearchWatertown, MA 02172 ATTN: Code 473, R. S. Miller

800 N. Quincy Street1 Commander Arlington, VA 22217-9999

US Army Research OfficeATTN: Tech Library 3 CommandantP.O. Box 12211 US Army Armor SchoolResearch Triangle Park, NC ATTN: ATZK-CD-MS27709-2211 Mi. Falkovitch

Armor AgencyCommander Fort Knox, KY 40121-5215US Army Belvoir Research

and Development CenterATTN: STRBE-WCFort Belvoir, VA 22060-5606

83

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2 Commander 2 SuperintendentNaval Sea Systems Command Naval Postgraduate SchoolATTN: SEA 62R Dept. of Mech. Engineering

SEA 64 Monterey, CA 93943-5100Washington, DC 20362-5101

Program ManagerCommander AFOSRNaval Air Systems Command Directorate of AerospaceATTN: AIR-954-Tech Lib SciencesWashington, DC 20360 ATTN: L. H. Caveny

Boiling AFB, DC 20332-0001I Assistant Secretary of theNavy (R, E, and S) 5 Commander

ATTN: R. Reichenbach Naval Ordnance StationRoom 5E787 ATTN: P. L. StangPentagon Bldg. L TorreysonWashington, DC 20350 T. C. Smith

D. BrooksNaval Research Lab Tech LibraryTech Library Indian Head, MD 20640-5000Washington, DC 20375 I AFSC/SDOA

5 Commander Andrews AFB, MD 20334Naval Surface Weapons CenterATTN: Code G33 J. L. East 3 AFRPL/DY, Stop 24

W. Burrell ATTN: J. Levine/DYCRJ. Johndrow R. Corley/DYC

Code G23, D. McClure D. Williams/DYCCCode DX-21 Tech Lib Edwards AFB, CA 93523-5000

Dahlgren, VA 22448-50001 AFRPL/TSTL (Tech Library)

Comander Stop 24US Naval Surface Weapons Edwards AFB, CA 93523-5000Center

ATTN: J. P. Consaga 1 AFATL/DLYVC. Gotzmer Eglin AFB, FL, 32542-5000Indian Hlead, MD 20640-5000

1 AFATL/DLXP4 Commander Eglin AFB, FL 32542-5000Naval Surface Weapons Center

ATTN: S. Jacobs/Code 240 1 AFATL/DLJECode 730 Eglin AFB, FL 32542-5000

K. Kim/Code R- 13R. Bernecker I AFATL/DOIL

Silver Spring, MD 20903-5000 ATTN: (Tech Info Center)

2 Commanding Officer Eglin AFB, FL 32542-5438Naval Underwater Systems 1 NASA/Lyndon B. Johnson Space

Center CenterEnergy Conversion Dept. ATTN: NHS-22, LibraryATTN: CODE 5B331, R. S. Lazar SectionTech Lib Houston, TX 77054Newport, RI 02840 1 AFELM, The Rand Corporation

4 Commander ATTN: Library DNaval Weapons Center 1700 Main StreetATTN: Code 388, R. L. Derr Santa Monica CA

C. F. Price 90401-3297T. Boggs

Info. Sci. Div.China Lake, CA 93555-6001

84

: •,•% _

Page 82: AD~-A14 6`91LLCuAD~-A14 6`91LLCu TECHNICAL REPORT BRL--TR-2892 1938 - Serving the Army for Fifty Years - 1983 ANALYTIC SOLUTIONS TO THE CLO'SED BOMB FREDERICK W. ROBBINS

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General Applied Sciences Lab Hercules, Inc.ATTN: J. Erdos Radford Army Ammunition PlantMerrick & Stewart Avenues ATTN: J. PierceWestbury Long Isid, NY 11590 Radford, VA 24141-0299

2 AAI Corporation Honeywell, Inc. - MN64 2200ATTN. J. Hebert Defense Systems Division

J. Frankle ATTN: C. HargreavesD. Cleveland 6110 Blue Circle Drive

P. 0. Box 6767 Minnetonka MN 55436Baltimore, MD 21204 Lawrence Livermore National

Aerojet Ordnance Company LaboratoryAlIN: D. Thatcher ATTN: L-355,2521 Michelle Drive A. BuckinghamTustin, CA 92680-7014 M. Finger

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ATTN: M. K. king P. 0. Box 8085390 Cheorokee Avenue Livermore, CA 94550-0622Alexandria, VA 22312-2302 Olin CorporationAVCO Everett Rsch Lab Badl r Armp Ammunition Plant

ATTN: D. Stickler ATTN: R. J. Thiede2385 Revere Beach Parkway Baraboo, WI 53913Everett, MA 02149-5936 Olin Corporation

2 Calspan Corporation Smokeless Powder OperationsATTN: C. Morphy ATTN: D. C. MannP. 0. Box 400 P.O. Box 222Buffalo, NY 14225-0400 St. Marks, FL 32355-0222

General Electric Company Paul Gough Associates, Inc.Armament Systems Dept. ATTN P . CoughATTN: M. J. Bulman, P. 0. Box 1614,Room 1311 1048 South St.128 Lakeside Avenue Portsmouth, NH 03801-1614Burlington, VT 05401-4985 Physics International Company

I ITRI ATTN: LibraryATTN: NM J. Klein H. Wayne Wampler10 W. 35th Street 2700 Merced StreetChicago, IL 60616-3799 San Leandro, CA 94577-5602

Hercules Inc. Princeton Combustion ResearchAllegheny Ballistics Lab., Inc.

Laboratory ATTN: Mi SummerfieldATTN: R. B. Miller 475 US Highway OneP. 0. Box 210 Monmouth Junction, NJCumberland, MD 21501-0210 08852-9650

Hercules, Inc. 2 Rockwell InternationalBacchus Works Rocketdyne DivisionATTN: K. P. McCarty ATTN: 1A08 8. E. FlanaganP. 0. Box 98 J. GrayMagna, UT 84044-0098 6633 Canoga Avenue

Canoga Park, CA 91303-2703

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Science Applications, Inc. 1 University of IllinoisATTN: R. B. Edelman Dept of Mech/Indust Engr23145 Cumorah Crest Drive ATTN: H. KrierWoodland Hills, CA 91364-3710 144 MEB; 1206 N. Green St.

Urbana, IL 61801-29783 Thiokol Corporation

Huntsville Division I University of MassachusettsATTN: D. Flanigan Dept. of Mech. Engineering

R. Glick ATTN: K. JakusTech Library Amherst, MA 01002-0014HuntsvtilleAL- 35807

University of Minnesota2 Thiokol Corpt-:ition Dept. of Mech. Engineering

Elkton Division ATTN: E. FletcherATTN: R. Biddle Minneapolis, MN 55414-3368Tech Lib.P. 0. Box 241 1 Case Western ReserveElkton, MD 21921-0241 University

Division of Aerospace2 United Technologies Sciences

Chemical Systems Division ATTN: J. TionAT-TN: R. Brown Cleveland, OH 44135Tech LibraryP. 0. Box 358 3 Georgia Institute of TechSunnyvale, CA 94086-9998 School of Aerospace Eng.

ATTN: B.T. ZinnVeritay Technology, Inc. E. PriceATTN: E. Fisher W. C. Strahle4845 Millersport Hwy. Atlanta, GA 30332P. 0. Box 305East Amherst, NY 14051-0305 1 Institute of Gas Technology

ATTN: D. GidaspowUniversal Propuls'on Company 3424 S. State StreetATTN: H. J. McSpadden Chicago, IL 60616-3896Black Canyon Stage IBox 1140 1 Johns Hopkins UniversityPhoenix, AZ 85029 Applied Physics Laboratory

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brighctin Young University I Massachusetts Institute ofDcpx. of Chemict I Engineering Technology-ATI N: M. Beckstcad Dept of Mechauical EnginceringProvo. UT 84601 ATTIN: T. Toong

77 Massachetts AvenueCajifornia Institute of Tech Cambridge, MA 02139-4307204 Karman LabMain S:op 301-46 1 G. M. FacthATTN: F. E. C. Culick Pennsylvania State University1201 L. California Street Applied Research LaboratoryPasadena, CA 91109 University Park, PA

16802-750California Institute of Tcf.hJet Propulsion Laboratory I Pennsylvania State UniversityATTN: L. D. Strand Dept. of Mech. Engineering4800 Oak Grove Drive ATTN: K. KuoPasadena, CA 91109-8099 Universit Park, PA16802-7501 •_

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I• Purdue University Cdr, USATECOMSchool of Mechanical ATTN: AMSTE-SI-FEngineAring AMSTE-CM-F, L. Nealley

ATTN: J. R sbornTSPC Chaffce Hall Cdr, CSTAWest Lafayette, IN 47907-1199 ATTN: STECS-AS-H, R. Hendricksen

SRI International Cdr, CRDC, AMCCOMPropulsion Sciences Division ATTN: SMCCR-RSP-AATTN: Tech Library SMCCR-MU333 Ravenswood Avenue SMCCR-SPS-ILMenlo Park, CA 94025-3493

Rensselaer Polytechnic Inst.Department of MathematicsTroy, NY 12181

2 DirectorLos Alamos Scientific LabATTN: T3, D. Butler

M. Division, B. CraigP. 0, Box 1663Los Alamos, NM 87544

Stevens Institute ofTechnology

Davidson LaboratoryATTN. R. McAlevy, IIICastle Point StationHoboken, NJ 07030-5907

Rutgers UniversityDept. of Mechanical and

Aerospace EnginccringATTN; S. TemkinUniversity Heights CampusNew Brunswick, NJ 08903

I 'University of SouthernCalifornia

Mechanical Engineering Dept.ATTN: 0HE200. N. GersteinLos Angeles, CA 90089-5199

2 University of UtahDept. of Chemical EngineeringATTN: A. BaerG. FlandroSalt Lake City, UT 84112-1194

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Abcrdecn Proving Ground

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