UNCLASSIFIED

AD NUMBERAD339819

CLASSIFICATION CHANGES

TO: unclassified

FROM: secret

LIMITATION CHANGES

TO:

Approved for public release, distributionunlimited

FROM:

Distribution authorized to DoD only; Testand Evaluation; 31 JUL 1958. Otherrequests shall be referred to Army Officeof the Chief of Ordnance, Attn: DiamondOrdnance Fuze Laboratory, Washington, DC20310.

AUTHORITYhdl, d/a ltr, 20 may 1980; hdl, d/a ltr,20 may 1980

THIS PAGE IS UNCLASSIFIED

SECRET

RESTRICTED DATA

AD, 339 8 1 9

DEFENSE DOCUMENTATION CENTERFOR

SCIENTIFIC AND TECHNICAL INFORMATIONCAMERON STATION, ALEXANDRIA, VIRGINIA

RESTRICTED DATASECRET

NOTICE: When government or other drawings, speci-fications or other data are used for any purposeother than in connection with a definitely relatedgovernment procurement operation, the U. S.Government thereby incurs no responsibility, nor anyobligation whatsoever; and the fact that the Govern-ment may have fornlated, furnished, or in any waysupplied the said drawings, specifications, or otherdata is not to be regarded by implication or other-wise as in any manner licensing the holder or anyother person or cotrora'ion, or conveying any rightsor permission to manufacture, use or sell anypatented invention that may in any way be relatedthereto.

NOTICE:

THIS DOCUMENT CONTAINS INFORMATION

AFFECTING THE NATIONAL DEFENSE OF

THE UNITED STATES WITHIN THE MEAN-

ING OF THE ESPIONAGE LAWS, TITLE 18,

U.S.C., SECTIONS 793 and 794. THE

TRANSMISSION OR THE REVELATION OF

ITS CONTENTS IN ANY MANNER TO AN

UNAUTHORIZED PERSON IS PROHIBITED

BY LAW.

TM-Ol.2].-Q-l (Part II, c)

July 31, 1958SSTRICTED SECRET ('YESTRICTED)'Copy No. P, - I

/ SECRET~A'~-o C ,e -- S 2

TVENESS STUIES OF MISSIIE SYSTEMS AGAINST GROI1,f TARGET

# Part JI Spherical Damage Patterns vs. Point Targets

(c) Aoplication to Soecific Missiles Systems (U)

act

by

Don Mittleman , (,,

This document contains information affecting the Nq "ADefen! e of the United States within the meaning of theEspio..-:e Law, litle 18, U. S. C., Secton 7 3 and79.*. ts tranr wizbion or the revelataon of its contentsin any manner to an unauthorized person is prohibited

by law.'

EXCLUDED FROM AUToMATIO

REGRADING; DOD DIR 5200.10

DOES NOT APPLY,

D. 0. F. L.

DOCUMENT CONTROL

RESTRICTED DATATit doe'mjnt contain. retiri-ted data as defined

Regrading data cannot be predetermined h' the Atomic Eneuy Act of 194i. Its transmittalor the disdio,sro at its contents in, any mannerto an snaathoiimeye rson is prolibited.

DIAMOND ORDNANCE FUZE LATIlRATOR17S, DEPARTMENT OF THE ARMY, W!AqiINGTON 25, D.C.

Data and conclusions contained herein are not necessarily final. Additionalcoj.er may be obtained through the Mathematical Consultant Branch, 01.21, X7307

IitR lehED TAE c RE2 0£/- i.,, r->

TM-O.21-5h-l (Part II, c)

Copy No.

SECpFrINIHODUC ION: Ihe formuLae developes in (-art II a) of this report are

applied to the fol.lowinjy situation. A ballistic missile carrying a thermo-

nuclpar warhead is fired apainst a point target, i.e. perhaps a launching

site of an enemy ballistic missile. The t erminal ballistic characteristics

of our missile sugests that with a prfect altimeter the distribution of

burst points about the arming point is an uncorrelated bivariate normal

distribution in ranre and defection. If o and ad denote the standard

deviations of burst points about the mean in razie and deflection respectively

and aA the standard deviation about the mean value zero of an assumed

ncrmal distribution of fuze function errors for an altimeter type fuze, then

the parameters needed to effect the calculations aro obtained by means of

the formulae:

2 02 2 2+ o cot 6x r A

2 2aV 0 0

2 2z °A

a2 (cot G) 0 cot H

z A A___fX7 Y0=--x z x z 2r + cot2 e

D. 0. FL.

DOCUMENT CONTROL

FlS T I o IPTATIs dom mnt rnfains ne'fed data as deftnEdis th ,o ,ic , otvr ty Act of 194 . Its lra wn.m itit l

R egrading data cannot be p edeLe' n i]c a cr t h d j.lo vre of its contents in any mannar

to an U n uithrize. f o is pro mibitad,

,. ,S CP T

SECRET

The mean burst heirht z was chosen so that the orcbability that

the fireball touches the ground does not exceed 5; i.e.

z- b +k oz

where b, the fireball radius was calculated from the formula

b - 1180

Y is the yield in kilo-tons and k 1.65 assures the 5'* level.

In this particular application, the mean ranre was left as a parameter,

because we wished to discover if overshooting or undershooting the target

(in range) woull increase the oroballility of damage. Thus, x = 0

corresponds to shooting? so that the mean hurst point is directly over the

targ,.et, x 0 c0rresponlings to overshootingi by the amount x and

x < 0 to undershooting by the amount x.

Input Data: the following values or the parapneters were used as input data:

Y I megaton, which imolies - 1.800 feet

< r 6,(Co, ?,00 feet

od 1/3o 0r

oA 0, 500, 10(0, 1500 feet

- thOo, 3300 , 320'

x -?-00, -1000, ', +1000, +2000 feet.

t UOoo, 5000, 6000 feet

('utput Data: 'he results of the calculations are Riven in the following

table: graphs are included to illustrate the effect of certain parameters.

SECRET

SECRETTABLE I

ci 6000, a ( 2000

Sx s A 0 (A = 500 oA -1000 ()A - 1500

310 -POOO 4000 .3Lh57 .60h8 .1h 70 .07871-1000 .357P5 .P685 .IL2L4 .07295

0 .36939 .26969 .11690 .0660h+,000 •3 785 .26)439 .12803 .*05'37+2000 1 3)-157 . 22.3 . 11760 .05038

-2000 5000 .JiMO 7 .)1256P .311011 .19796-1000 .197 6 1 .143956 .31)d), .19138

0 .50346 .)41062 . 11014 .18117+1000 •.j)761 .) 43757 .30095 .16780+2000 .A"1047 .1218: . A)j 78 .1520?

-2000 6000 . <9269 .55196 .146l2 . )4651-1000 .61162 .56929 .)47370 .3150h

0 .61833 .576499 1 *74-77 .33708+1000 .,,182 .6868 .L6648 .12298+2000 .59269 .55071 .114923 .30341

3300 -2000 1O0 .310457 .26221 .1)4793 .08831

-1000 .3 T 7P'5 • 7?10 8 .11,839 .0811990 .36219 .27323 .114515 .07978

+1000 - 17,5 .26q),8 .138)45 .07305+2000 .3Y57 .25719 .I7876 .0652L

-2000 5000 .08h7 .43425 .31895 .21072-1000 .A9761- .JiA933 .325414 .20839

0 .50346 .4 5)405 .32 )36 .20131+1000 .149761 .141419 .31576 .IOO02+2000 .480h7 .043221 .30019 .1-7515

-2000 6000 .A9269 .55768 • 47912 .3659-9-1000 .6,1182 .5773 .1J9218 .692

0 .61833 .5P175 •1h91 .36h05+1000 .61182 .5753] .YjP06 .35159+2000 .59P69 .556 9 .46908 .33224

SECRET

SECRET

TAOtLE I (continued)

or = 6000, a 0 2000

oa A _ 0 QAS - 500 cA 1000 6A - 1500

1200 -2000 OO0 .311457 .26253 .l1799 .09085-1000 .35785 .27191 .50 ,A -O-9h5

0 .36239 .271.150 . .11816 .Of 7(+1000 .35785 .27009 . ? 29h opmt

+2000 .31457 .25902 .13123 .07331

-2000 5000 .404 7 .h 3638 .32071 .21177-1000 .49761. .J 52U 3 .32,°97 .?1 4l

0 . 0,i6 .1,577? .329012 .20995+1000 . 01761 .1.5215 .32199 .20068+2000 .hA8017 .)13623 .30720 . IP723

-2000 6000 .9269 .55967 .4835 .37152-1000 .611.82 57100 •)1981 .377)19

0 .613 3 .580 1.6 .502h9 .17513+1000 .61182 .57773 .49513 .36)453+2000 .59269 .55912 .477111 .3L612

SECREI

SECRETIABLE II

01 =1.20 7 W OO0

GA- o R oo1000 A = 1500

3W 0 -2000 hOOo .11732 -0.8391' .0Yq34 .02683-1000 .11.'52 .OP):57 .04508 .02621

0 .1.1893 .08.165 .04453 .0253+1O00 .1.0 52 .08415 .Oh369 .02451+2000 .1-1.732 .08309 .04258 .0237

-2000 5000 .18659 .16171 .11135 .07116-1000 .1887 .16420 .11152 .07025o .18910 .16532 .11096 .06890

O.1,847 .16511 .10969 .067114+2000 .19659 .16361 .10772 .06501

-2000 6000 .25912 .235!0 .19205 .1398F-1000 .26187 .23727 .1.9306 .13920

0 .26273 .23791 .12q5 .13767+100 ,26IP7 .?3700 .191L2 .13q30+2000 .292 .2)157 .LI",7 9 .13215

330 ° -2000 000 .11732 .091108 .0)iV66 4.02788-1000 .11852 .O01 i8 O •0)t566 .027560 . 1~.093 .o085'. .01536 .02706

-1000 .11F52 .0r)63 .04 h7! .02639+2000 .11732 .0351 .O4.96 .02556

-2000 000 .18659 .16150 .1121.7 .O?2QO-1000 .188)17 .l6h67 .11269 .. "7245

0 .18910 .1.66h9 .1.12146 AV)t3+1000 .18807 .1.6693 . ll.49 .0703t+2000 .18659 .16602 .10979 .06862

-2000 6000 .2[;932 .23582 .119396 .14256-1000 .261-87 .2307 .19532 .l)12610 26273 .23876 .19541 .IUi173+1000 .26187 .23790 .19)42h .11995+ 20C00 .25932 .235)9 .19181 .13730

5SECRET

SECRET

TABLE II (continued)

ir =-12000, od - honO

P x --0 oA = 500 A =1000 FA =1 C0

320' -2000 )4000 .11732 .08V? .0,55 7 .02,13-1000 .1-1852 .0"86 .c4582 .023000 .1 -893 .0506 .01566 .02767

+1000 .11852 .OQ1168 .0)4 519 .0271.6+2000 .11.732 .08372 . QJ4j2 .026h9

-2000 5000 .18659 .16233 .11233 .07317-1000 .IP 17 . 16f07 .l130. .07315

0 .18910 .168)9 .11100 .0726h+1000 . 1l3)17 .16953 .11221 .07166+2000 .]86 9 .16916 .11-067 .07022

-2000 6000 .p5932 .23606 .19h 51.432h-1000 .26187 .2383h .1,96C6 .11s3710 .26273 .23906 .19633 .ih3211+1000 .261"7 .23822 .1¢531 .1183*2000 .2?932 .?3583 .19301 .13952

6

SECRET1.0 --r-77

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-S 4 ,000 feet -

.2V

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Figre 1. A 0 ar -6.0. ad -2.0 0- 340', 330,320'

All distances -x oA, 0 r ,cd) in units of. 103 feet

S.ECRET

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.9

.7 j.

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Figmve2. aA -oa 12.0 ad 4.0 .e340, 330',320'

All distasces (- "A' 0 ra ad) in units of 10. feet

SECRET

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All distances (i, OA, a r , ad) in units of 103 feet

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Figure 7. aA- .5 ar =12.0 ad* 4.0 e - 3300All distances (x, -"A', 0 r , in units of 103 feet

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All distances (i,*cA, a r ad) in unit: of 10 3 feet

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SECRET

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lit; Mil .* !;t:jj !: iI it I.! iih till 1 14 itli I: q. :IJ

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Figure 16. aA 1 .5 a r 6.0 ad - 2.0 0 - 3300

All distanoss Gx, cA,' a r ad) in units of 103 feet

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Figure 17. oA 1 .5 q r 6.0 od - 2.0 8 - 3200

All distances oA, or, ad) in units of 103 feet.

SECRET

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Figure 18. oA - 1.5 Or - 121-0 ad 4.0 0 340 0

All distances (1, 6A, a r ad) in units of 103 feet

SECRET

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Figure 19. oA 1.5 Or 12.0 ad - 4.0 0 - 330'

All distances (-x, c., a r, ca) in units of 103 feet

SECRET

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9 SECRET

RESTRICTED DATA

0 3400 LI-1 I 3 0 330 1

1 7 7

6 -1 i i

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a A- igure 1. 'r- - c o 2 --- or 1 , (, 4

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