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CRATERING FROM HIGWN EXPLOSIVE F-'HARGGS,

'ANALYSIS OF CRAT-ER`:DATA-".

TECHNICAL RE-PORT NO. 2-547,

Report 2

Jun* 1961

U. S. Army E-ngineer Waterways Experiment StationdbRPS OF FN GINEERS

Vidcksurg, Mits issippiARMY-MAC7 VICKVBUPGQ, Minis.

PREFACE

-Thl~ ~report is the"!%econd and fina, report on the general spUbject-)cratering from high explosive charges. Presented herein is an ~empirical..nalysis of all the HE cratering data-c ompi led in the firs3t repbrt,

Compendium of.Crater Data.The study was conducted for the Office, Chief of Engineers, Depart-

ment of the Army, as'a part of Research 'and Develop ,ment Project 8S12-95-002,"*"Nuclear Weapons Effects on Structure s, ,Terrain, and.Waterways (U),:" it'was accohmplished-during the perio4-July 1959 through.Junie 196O.',by.p~rsonnel

of the-Special .Investigations Section, Hydraulics Division, U.S.' Army En-

gineer Idatezfways Experiment Station, under the general superlision of

Me~ssrs.':E. P.Fortson, Jr., and F. R. Brown. This report was prepared byMlr.-J. N..StranLgIe SP-4 C. W. Denzel, and sp-h T.' I. McLane, III, under thedirect.: supervision of Mr. G. L.' Arbuthnot, Jr.

Col. Edmund..H. Lang, CE, was Director of the Waterways Experiment KStatio In during the reparation of this report, and Mr. J. B. Tif -fany was*the Technical Director..

%P

CONTENTSl Page,

PRE-FACE . i.. ...

NOTATIONS. ............................ .. .................. vii,Slhv!MARY. .............. ............................... ix

* 4 PART I: INTRODUCTION...........................PART-' II: EXPERIENCE FROM EARLIER INVESTIGATIONS............3

British Investigations.................... 3* Uh~T~n.t~ed !Dtates. Investigations....................

PART III: VARIABLES TKAT 'AFFECT CRATERING PHENOME~NA. ................. 5.Propertieb of..Explosive Charge. ..................... ............. 6Properties of the Medium Cratered . .'. .. .. .. .. ... 7Position of Charge.........................7

PART IV: DISCUSSION OF SCALING CONSIDERATIONS...............9PART V., ANALYSIS OF CRATERING DATA. ............................ :2

Available Data. .. .......... ................................... 12Methods of Analysis. .............. ...........................13Hesiults of Analysis.......... .............................. 14

PART VI: 'CONCLUSIONS AND RECOMMENDATIONS....... ............... 0

Recommendations.................... ........... 20

REFEREN4CES....... ............ .. .. ................ 2

TABLES 1-2

PLATES 1-71

. ', . 'V

NOTATIONiS

C s harge.,shape factor) dimensi onlessdS et fcaef

d Depth of aprn cra~ter, ft

a

d Depth of true crater, ft

DhThiqzPt.Pr of' cawi' -t (honrivonta1 'dire~etion)', ft

D Diameter of camouflet (vertical direction), f't

E- Elastic properties of medium &i~tere'd, lb/ft's

h, Crater lip height, ft

K Constant, dimensionless

n Exponent of the charge weight, dimensionless

r Radius of crater, ft

*ra. Radius of apparent crater': ft

r Radius of explosive charge,-ft

r adius of true crater, ft

~S SJoil resistance function dependent upon soil type, dimensionless'3

V Volume of crater, ft 3

V d Petonatiofi velocity of explosive, ft/sec

WWeight of charge -(TXT equivalent), lb

' Position of charge'above ()qp' below ()air,,-ground interface, ft

* vii1j

jA

2\ VI

7' Specific weight of ex- losive, lb/f't6 Ener'Ay.. density ntl ex-p lo s ive .(Tt -l tlb/ft3 ), 2

1/3 1/3X Reduce~d.charge pobition (/ ),ft/lb _

~iPoi~on'L)W ratio of' the q~edium cratezred, diznensi~niess

Moisture-content of med~uim cratlered, per cent by weight, dimensionlessv. Void, ratio of wedluin ~ratered, dim~ensionless

PC Lasting or p .acking de~nsity of' the charge, lb-sec2/ft4

P Density of medium cratered, I b-sec 2 /rt4m

Cl Jrnghpoperties, of' mcdium cratered. (compression, shear, andtcnjilo*), lb/ft 2

viii

ff.

ItI

I If. b)

eledi Iapoe n'qu rpeitnCrtratier.-rnesurenialngtr~s ffor aproimtes fir00 onorindeore than 20nd-withahrge weightsagn. frm les-aess thanedre th lbato of30,0 b ~analzed o: () gan & ette 'understnined aofnhgo~~* ivlvdi

the liinngb-0 the ri shm~l and iz af w~aesfre yith explosivs;,, (b.esmtaz,~ therb orer ofvalriatgemiorictatl theractrizes crwtatern relate;n

* c)ae dezelo nd charoved and/or> more weerll-kned tchiube-otscln lor peitincratenir ienlyos 4ccept alin toreoalnps. dormshosfired on oruner ahepgreuntl-this were dearmined wroh lts tp'of'mduben craterraiu and deph e fuchtiono

leimh~n oit io, theebystbliin aempiricallyd theasi~ sncalicing las ht eati

s3ize 'and, shape for charges up to 1,9000,000 lb of TNT. Also, the influenceof various soil tyes on-crater sLe is shown graphically.

hA

ix

'fit,

J'I d",XI

C15TEIN FRM*,"O V CAG9

ANPlS OF RRTE .' I .A

"PR ' .NTOUCI'

i., Fo ayyas lweeVdnit xlsvshaebe sdAcostucio o""tin toacIlls ag xvto ~jcsb osn

in rfamnizigte arh' rs. Eqully ipranisterxt -

til~ Fori malnyn yperarsiows. Oneyre-enitlyhv explosives hv been" sdi

*very large 'amotnts to both loosen and remove unwanted or,,waste materials.* Te ue o hu~ed ofthusands and even millions ,of pounds of exp'losives* to excavate arevoumeso materials is' daily becoming more commonplace.

Hlowever, c~mrilbla~sting operations usually employ special techniquesof delayed iritiation and programmed firing of a number of carefully lo-'

*cated charges pre-positioned at prebcribed d~epths~, ,.Because "of, the special,,.methbds employed, cor~mercial blasting operation's' normally prbvide very lit-

* tle information that is-usable in predicting the size of crater that agiven quantity of hl.h explosive (HE) will produce, and-certainly,' it isthe cii.er formed by the deionation of single charges* that ,is 'of major

* milita\-S interest.2~The imp~ortance of-cratering was greatly 'increased when,,' through

*~e use of nuclear weapons,, it became possible tob release enormous amountsof, energy from essentially, a point source. With the coming o.~tenuclearwea~poni came also the requirement that' prospective 4sers.,understand fullyits potential and' its limitations'. Niiturally),"the most certain* way torealize a complete understanding of each weapon's effects is from repeated',tests at full scale, in which suffi2~ient measurements are made to define

.each 'effect. Although this method is'-preferable from the poito iwo

"'accurately establishibgw,eapon efet, 'it is-economically (and perhapsbiolbgia'ly, _becla~se of the radioactive fallout).Infeaasible; therefore,efforts have beeW-made to establish and define many of the full-scale.

P ~effects by use o! ml-cl HE ch~rges., Crate&ring Is- oni-of the effects.of nuclear we~poIns that has been studied using HE charges.

*.3'.Over a jipriod of the last twenty d~ oyaa many HE ciateri~nge~eriments have been ..conducted, in. an effort to determine the ,cratering

* .-. a' '1 **' ' 9

a ~ . 0"

capab~ility of v~ar16us 'explosives Pr'imarily ti ~ crtrpg phenomena have

been considered -.to be afunction, of_(a..) the depth of u al ofi),,chd~rge,

(b):'t'he propertiesp of the. medium in which the charge Is placed, (c) thetype o xlsv,"ni()tewih ftecag ot ramnsothe subject of cratering h; ve made use of data lb~tained in a specific testseries. As a-'4esult, few 'ollations among Various test "series were at-

teimpted.-' When comparisons were at-tempted andi found tollbe widely diverge~nt,

justifications were soul\ i~o why 'ne test series sh ould be used. inpreference~to another. iSu 1 practices in some. instances greatly reduced.

scatterr and/or served to b as .tile conclusions reached.4~. It .seemed approp*]fiate thdiref ore thaat- a study should bel'initiated

in 'i~hich (a) all, 1knwn era le'ring da'tae woikd be tabulated along with perti-nent soil properties,- expljtlve types', and charge weights and dep~ths ofburial; &nUd (b) the. data s8 coirpileI d would be analyzed as thoroughly asprac-ticable. The s'tudy undertaken was divided into two ,phases, vizk,com~pilation 6f7 crater data, and analysis of crater data. 'The report on.

the 'f irst-phase entitled Compendiumn ofCrater Data, was published as

Report 1 of this series in May 196'o.7 Thie major objectives of this, thesecond phase of the"'Istudy,-were to (a) obtain a better understanding of thecraterinly process,"(b assess the order of variation. (scatter) that charAc-terizes craterinC phenomena in~ specific and widely divergent materials, and(c) devclop, if practicn.ble, improved-'and/or more -generalized methods ofpredicting the sizp and shape of explosively gene~r-ted crater s for a

variety of soil. conditions'4

5. Since the mtbasurem~ents of explosively generated craters were veryoften reported merely as by-products. of test serie8 plapined for other pur-

poses, riost,,of the data tabulateld in the compendium are grossly inadequatefor a-truly 6cientific approach to a general solution'-of the cratering 7'

problem,, C onsequenltlk, it was not possible to realize an "analysis that*fulfilled all'of the objectives ;t~ated above.' 'Attempts to refine the anal-'

ysi-s to include the. effe~ts of additional paramneters were. unsuccessful.Results are presented in asG.;reat deta~il as the, input" data Ywarrant.

4* Haised.:numbers, ref'er to sitiaynmee tnrs in %h is fref er-- .- , encs -'at end -of' text. , a .

A II A

PART II: EXPERIENCE FROM EARLIER INVESTIGATIONS

British Investigations

6. In 1940 the, British conducted a series .of -tests to determine,'empirically, equatibns that would provide meahs or predicting the sizei'and

shape of craters' resulting from the detonation of HE charges (bpmbs) above,on, or beneath the aityground interface. These tests were conducted within

sil and rock masses slo chosen as to be generally representative of the

land mass .of England From these teLts, a set of cratering capabilitycurves* was produced for predicting crater dimensions in a variety ofearth media.

7. By the erid fi41 the British had aoo lat d s ffioient datafrom actual bombings %0 formulate a second Set of cmpirical equations.

These differed somewd t from the first, mainly becauseiof a difference in ithe methods of, emplacing the charge. In the experimental tests much larger

cavities were formed than. in the actual bombings. In the experimentaltests the backfilling materials used in the bomb emplacement were carefullytamped and controlled, whereas in the actual bombings the bomb itself was"open to the atmosphere through the penetration burrow. Obviously the en-ergy released by the detonations was partitioned differently between theT edia and the air.1 8. Within the range of charge weJgh1s involved, the data, both from'actual bombings and from the experimental work, conformed satisfactorilyto Hopkinson's law. This law states that .if charges of the same explosive,

differing in weight but not in shape, are detonated,, the explosivre effectsare proportional to the linear dimensions of the two charges. Thus, a

sphere of-TNT that has a diameter t4ice that of a second sphere will, upon-detonatior, produce twice .s, big a crater and twice as much damage (i.e...

-the explosive effects will be twice as 9evere)..

%%" '":7I "3

*,Any plot, of a reducd crater dimension versus: the reduced charge ,posi-"1/3 13tion; e.g., d/W versus X d vw0.3 versus x 1/3 erus

"X ; etc.

JI'

United States Investigationg

9o.se Some experimnents were conducted by the United ~States in19.41to asessthedamage that structures might, re'ceiv Ofrom bombs bursting

nearby. -The tests showed that, even in the case If burie bombs, it-waspossible to cause considerable damage to bidnisituated near the explo-

so.From the results it was dete'rmined tha t 11a br Io:.ad ,experi Imental programwould be requir-ed to assess the'roles of the various best' parameters" incausing damage. The tests also revealed that underg,'ound installationscould best be attacked by actual i~rate"ring of the soti-structure mas,4;ther-efore, the relative Influence of the various test"pd~rameters on thecratering pr 12ess became important. A

10.1 These sLudles were among the first which led-to a series of pro-longed studies of the cratering problem ana..the various factors whichinfluence crater formation.

nI

0/.

PART III: VARIABLES THAT AFFECTICRATERING PHlC*ENKA6

siz an shap of ant explosively geeatdcater Aedepndent uo.te

quatit an tye f' xplsiv'usdthe medi'imin which the crateringtksplace, and the method'of..emplacement of the charge and its positionreatveto the medium-Air interfacge. Ths nde'pendent varia-"~ are vr

I'comple'x 'and cannot be de'fined complete, or' dqaey enough to pemta* study of the cratering problem in minnu1ie\detail.. Ever~y attempt at analysis,

.:is complicated "by other variables,,that ar'~ less obvious and by an inter-relation of the variables namned ab~pve. IA view of these- difficulties, itis..very likely that, crater-prediction mthdswlf'or some time at least,

contain provig~ional technique's for assessin certain factors 'wh'~h exert

considerable influence on the cratering process.12. The following tabulation lists the more obvious variables that

are believqd to hav&"signific'Ant 'influence upon the cratering' problem.

The extent to) which other variables' might' conceivably influence the problemis indeterminable. Because of the quality of the data available, the ef-

fects of several of the' more obvious variables on crater formation could

not be determined in .this study.

Properties of Medium BeingProp ert ie s of.harge ____ Cratered Charge Position

Weight Density "...Above-ground regime

Shape Moisture content, Air-ground ,interface.

Packing or casting Dynamic load-deformation Below-ground regimedensity ' charActe'ristic.s:, modulus

of elasticity, ultimateEnergy density,' strength (compression,

*~ .tension, and shear).,Detonatioqill velocity, Poiczsori's ratio, etc.

/ * Void ratio

9ther soil properties whichmay' produce third- or higher-;a ~rder effects

I.' '4, I

Poetjpof Exp~losive Char&6J

13'. Properties of the" explosive' re of major importance in dete'rmin- Jing the size cratpr that A given chargwilpoue The weight of ex hi0

sive, in 'conjunctio'n with the shape and .5ieo h, large, determinesl.packring 'eity. Idalfrpurposps other~ hn'vlaii sh~aped-ch'6rgeeffects, spherical charges are best suited',to"E~xperiment~al' tes~ts wherein itis desirable to eliminate the, charer, shape, as, ,.a factor in thc cratcrling

process and 'to mdre nearly simulate a point -source of energy,. Experiencehas shown, however, that ch4fr.ges which do not-deviate greatly from'a cubi-cal shape" produce little or' no charge-shape effect, on' the size or shape o f

th rter formed. Tests have been'condvuctd 2 ,3 ta eedsge pcf

ically toL evaluate -the effect of charge shape on crater shape an~d size.However, these testy were for a particular pth-pose .and are not consideredper'tinent to the g~eneral solution of the cratering,,problem when spherical',,ch~irges are used.

14.. Since craterizig involves deformation, displacement, an~d throwoutof the.. soil mass that ha~s received, loads sufficient to exceed the elasticlimit of the medium, it 4-~ obvi~ous -that such effects w:ill increase in mag-nitude as the charge weight is increased. Experience has shown that forthe smaller charges. (vi < 1060 lb), the explosion effects are fairlyr well,predicted by-Hopkinson's law (see paragraph 8). Although all exp] ',osioneffects .do not adhere. to thi law in the absolute sens~e, it may bJL used todescribe the behavior" of the ex Iplosion effects in.. an appro'ximate hmanner.

15. From certain test results where comparison is pogs'iblk,, it hasbeen qualitatively determined'that explosioh effectiveness in prod`cing acrater is "a function of the detonation veplodity. ,,A -"'rule of thumb"' summa-tion~ of test results shows that.the more effectiv,,e crater-producinik explo-3' sves are those hiaving the slower. detonat'ion velocities. For exam~ple, 6o%armmoniumn dynamite '(detonation velocity approximately 9700 ft/sec') 'is about30 to. 50% more, effective than ,C-4'(detonation velocity' abgut 24,000 ft/see')in producing'a crwter when equal amounts of energy a~re rel~eiised,.1., Further-more, explosives having detonation velocities slower thhn thatofmonu"

J;:'dynamite are- ev~en more ef'fective f rom *the standpoint o. producing -crat~ers.Since the enrg density of, explosive,-, is directlyieae to 7

detonation velocity, low en-ergy-dens~ity explosives dre more, efficient

cratering charges.

Properties of the Medium Cratered

16. Several properties of the medium being ctatered influence to apronounced'' cdegree tfre size of c iater which-the detonation of a given amount.

of explosive can produce. Generally, the earth's crust may be described- ab

being a nor.~iniform, nonlinebir, randomly constituted mass that m~ak~es up theexposed and sh Ia 'low laer otheart' sur ace. One auth oiOdescribeo itJ) as being "rionlin ar, .pla2ptic, absorptive, disjbersive,,aiorpc and non-

JI homogeneous." "Wi`th the"'wide variation of mat~iial propertiesifrom one lo-~calle to another. even when the materials are similarly classified, it is riotsurprising that crater results exhibi t considerable scatter.'Ih eut

of a. set of' carefully controlled cratering -expe:imcnts conducted-at WE9inmaterials that were probably as homogeneous as navire provid'es'exhibited.

..devi at ions in the range of -l,"which 'is believed to be what might be-regarded as minimal scatter. Most experiments are characterized by scat-ter in the range of +30 to 40,1.

17. The extent to which the various properties of the medium affect-the-cratering process is somcwil')hat uncertain. Tests havc never been con-ducte-d in sufficient number or in. sufficient detail to establish tkke rela-tive influence of -each major'soil parameter orV the total process. However,it would seem from an intuiitive point of view that thei-greatest influence

should be attributed to the moi;ture content and strength properties.Actually, these two variabiles are so closely relate-d that they cannot be

isolated. The strength properties referred to here are those perta~ining toconditions of dynamic 'loading. The other properties q~f the medium,, such asdensity, void ratio, etc., are believed to produce second- orthird-order,effects.'and arc thcrefore "of little czuxsequerpce,, in develop1~ng an. empiricalsolution of the crrxterin g problem.

Positipn of Charge

1.The pooit*qfi of~ the charge,, relative 'to the air-ground interface,-i~ also a Pr'ime factor, in' doeterinini~nig the crater' size and shape., since the,11diOe ito relative .to" the interfa P fixes 'the amoun fe~g

F.q'

.paritinedbeteenthetwomedia,, Most-of the energy released by charges~plac~ed-above the interface goes directly into the air;coeqntychargcs in this posiLioriare ineffective as crater-producing explosions.'Charges placed on or ,belo~w t.he air-ground interface are much m~ore effectivesince there is direct coupling 'of the-.energy to, the earth medium. Hence,7these charge positions are- of principal interest 8fld are considered ingreater detail-in this study. The-results of above-surface -detonationsare Ireported simply as a matteoi of ac ade mic' inter'est.

19. The gam of charge -pucsiltons ob-- ~~>2: . . served ha~s been -di-Vi~e ~&tje eea

groupsJ, "nam Iely, 'the. lbove-ground regime, theS ~ ..*....~air-ground interface, a~d the below-mgr-ound_

regime (see t~bulati~on in. paragraph 12).'Charges placed in thee belqw-ground regimeMay be further grouped as to crater shaapie(,fig. 1).; Prom experimental evidence,"ithas been established that in most in-situmaterials, conventional craters are formed

-when the value of the reduced charge posi-tion X lies between +0.5 and--2.0(fig. l!'). Partial cwnouflets (fig. lb)are forpned when X~ lies between approxi-

ad cmatelyll,-2.0 and~ and in materials ex-

C IV , ~hibiting appreciable cohesive strength,full caxnoufiets are formed when X < !-3.-5

Fig, 1. Typical cratershapes and the range (i.l)of charge positions ,with which they are.

associated

* A' . . . 4

. #

S 'A

20 The pupseoftevrou xIimnag~~~ar%~~~ tauaednteCmedu a en ofruae clpglwfr

sos.-othef purposp othe ars u be pen drientt clscn-ffeRp

of' iiclear weapon? by using high explosi'ves 4z a sf~4saen@ergy source.-_Since this renort)4.doe3s rtht eonsIder craier.Q Lrevf- t1n Frm 1 'h de.opt

of a ula ~zE., the sc&lih~g effects that are discussjed herein 22 yonl toHEdetons o 42,4o ,000, 000 lb of ~'T. The following severalparagraphs discusis the sgaling aspects bf. the- c'ratering problem in general

and point out redsonq for the failure of the scaling laws to predict re-sults over wide ranged of explosive yields and types of media.

21. Any dimension of 'a crater, such as radius, depth., volume,. etc.,

in a general sense is a runction of the: weight of the charge (W l b);shape of the charge (C, i, dimenbion~less); casting or packing density of the

explsiv ~ lb.se~/f 4);. ener6, density of the ex losive (F.ft -lb/ft 3.); detonat~ioni velocity of' the ex'plosive. (Vd ft/sec"); density ofthe medium cratered (Pm . lb--sec /ftl "' _Jture 'con-ten-t of. the medium inper' cen/:'LV_'egh (I k. Y dimensionless); eaas~tic'"properties of the medium(E, lb/ ftc) strength propertieu of the 'medium/1 i.'e. compression, shear,and tension (a ' lb/ft2) void ratio of' the, medium (v, dimensionless);Pidiss on "s ratio of the medium dimensionltssj;, and position of thecharge relative to the air-groirnd interface (Z. ,ft).

Expressed mathemat~ically,

r, dV, etc. = (WC , P E Vd, P E,

ni m

*Although this expression may represent iixnost the absolute solution of the

cratering problem, it-is recognized thtto acq'uire sufficient experimL'ental

*data wherein each. of, thc 1-nd~ep(nden't.,.-voriables -are fully dsibdbdes

.:,cie border

10

on the, ridieulols.. In the first place, there'aire n6 method., at th~e presenttime for e,(aluuting the varii~uo propcrtico'of .thc soil in situ when thesoil i s eX ooecd t o t rload Ij hence:,, the problem, fox, practical andeconomic reaoon.,, rnu;;t bN. he rit's11lY ~limplified.

?2", For the `iurpo.se( 4j' unaiys.ing, the dlata preocented in the Compen-diluml the' foirLowing e cn reasonable:

7 d. !!V .'etc (2)

Wh Crer, I.; thle C rat~ 0 iadiviA *d the crater depth, V the crater volume,W thle..chnrt~e wei.,tU (lb.1 ofI TN'P), the charg~e poscition relative to the

aii'-riedliutm interi"tce, "III, -,oil ruAs;tance function described by, soiltype Only.. 'to~ .1 L;)proach.., 'prcscnts wha1t might, be cOnlside d a f irst-Qrder solutiun o!' the eruturirwg problern and, in-view of' th6 d ata avdilablePorP' analy 3i:, is;,the onily praictilcdble type of solution.

2.Ifi~,e problem were as si';mple ti ontlined above, a curve 11re-latingt thc dimlenLsions of -the crate:', the char~ge, weight, and. the charge p0o-.zition relative to the interlk'tiie couOd be developed, for each,, soil typeb

'!"using dimensnionless .,roupingo lof these variables, as developed frowi-,,dimen-.uionai anaiy',; i. For example, ii, the Cube rool. of''the ehchrge weight iseuonsidert~d .a linear dimension' (this is-an entirely proper assumption since

y~ 4/3 itr3fW/ aplto /1313v~r~ s 1/Wl/ , from which r c N , a p o 01 d W / or r/Wl/ ./w3for various SOil types, Provides a graphic so'lution oX' the

pi'oblenm. However, the problemn i.' 'not tilat simple, and there exist devia-;tirins fromn the scaling procedurei ple bth clsicue-root lawI1(Hopkinson's-iaw) The most important de-viation from the implied pri,,ci-

p~cc01'~inilarit'o'ccurs,-notiAn~thevery early history' of the expl~~n

b ut af~tex-riso f h hc ae andater the termination of ess~enLially hydr'odynamnic behavior,, -'The later stages of crate3P fonrmation arehighily Aependb on "gravitational f'orcees -C[or -xnle, the eff ect of grav-ity_ cauipes' the shear. resisztance of the soil'to increase wth an increase inthe s;cale of the e)ploL400io. '3irice gravity is niot readily ,calable, thl,,phenompenon will. de) i,ite fr om the l1awsL of sirnilarit associjated-,iyth cube-root "ItA.,aii,; iscaling arc to be expect-edweiitoralzdth~at parameters -uibh a-, the de iyo~th~eim ts-par'ticre, size, y~d

it tent properties ,cannot be scal ed in proportion to the rati f h"cute rootsl Pbthe. saled charge~ and prototype charge..

241, -Experimenital results. -show that cube-root scaling is "'approxi-

miatelyif valid when ch~arg'e weights 5ane from about,;1 to .1000'lb. A hrange.,of charge weiglhts is enlarge'd to include charges up tio-,several tens,.of thuas opund, te deViation i~ncube- ro caigbecornes'm.ore

discernible. ,Even at this scale,. -the deviations are not-ob~ectionablylarGe because the physical. siye 'of the charge is ealable and its .sizeten~ds to hold the deviations to a minimum. As the' energy'density of the

explosive i; increazed to greater and greater amounits, the deviations con-

-tinue to, increase,, such that for nuclear weapons, scaling from TNT sourceson the basis-of the cube-root law yields completely misleading results.

25. Tn .ounary, the cube-root law is invalid over a wide ranige ofyicids;. particulodrly i* this true when,,h explosives involved ha~ve wi ~lyvarying energy dendities and detonation velocities. ~Afirst-orde~r approxi-ination 'of the. cratering problem may botandhruhheue o, cube-root scaling when TNT, or a nearly.,equivalent type of explosive, is theon ly en Iergy source used. In this report, the data contained in the Compen-

diuln are analyzed to, reflect any. scale effect due tp a wide'variation incharge weight by plotting crater dimensions, as, a function' of charge weight.He~pcQ, a best-fit scaling procedure (based on the least-squares method).isused to minimize scatter eind-to. increase' the accuracy of predictionmnethods.

12

PART V:" ANALYSIS OF CRATERING DATA .

Ava~Aable Data

6 Cratermeasurements suitable for use in analysis are availablefrom approximately 1000 shots involving the use of TNT or some other ex-

plosive for which conversion factors are available to make possible thereduction P. of its yield to an equivalent TM yicld. The charges were det-onated iy:more than, 20 different media and 24 tyes of explosives were em-

.7?ployed, as summarized in table 1. In order .to establish prediction curves-for frozen ground and ice, it was necessary to use the weight of'chargerecorded, sinceeconversion factors were not available for the types of- ex.plosives used in these test programs. The propriety of doing this may bequestionable, but in the absence of proper conversion factors,. no other

procedure seemed realistic.

27. The ranges of variables (charge weight, depth of burial of'charge, and reduced depth of.;burial of charge),are presented:in tabJT 2. -From this table, it would appear that sufficient data are available fromwhich a rigorous empirical solution of the cratering problem might be made.

'dHowcver, the fact:-is that the data are not well distributed over the range-of variables stipulated. In some cases, there is an overabundance of data

for certain values whereas for other cases there is a definite scarcity-ofuseful data. These areas of "famine or feast" result from a lack of-coordination in past research efforts and the fact that a considerable

portion ,of the dtta as a whole was derived from research projects whereincrater measurements were by-products onlyoand were inadequately reported.

28. Certainly, any future expIlosion-effects research resulting incrater formation should report such measurements in order to. supplementdata likjted in the Compendium.. Any further research that may be directed

.,toward a1irancing the state of the art of piedicting the size of explosivelygenerated craiters should be carefully plannedto ensure as broad a coverageSof the ranges of primary interest as pos~sible. To date, no work of anyreal significance has been done to. ascertain the effectis of energy density

7 and detonation velocity.on thecratering efficienicy 6f,-.various types ofexplosives.' This should be done to assist in developing a m.re'wor1able

-' -' -'

theory of the cratering problem in general. It'is further believed that'work in. this area may weil lead to a more realistic means of scaling HE reisults into the nuc lar range with confidence.

Methods-of Analys..

29." To determine the scaling trends that would best fit thedata

tabulated in the Compendium, 7 plots of crater depth and radius as a func-tion of charge weigh~t for thc various types ol boll and for the. selected

ranges'of charge position were made (see plates l-51).*4' Plates-1-6 and30 and 31 present, for various types of soil, crater dimensions plotted asa function of charge weight for broad ranges of charge position. Theseranges were made large in an attempt to group together as many individualcrater measurements as possible without assuming similar behavior to existover an" absurdly broad yang(. This procedure permits the plotting q(-hun-dreds of points over a(Cwide range of, charge weights. Of course, it 'alsopresupposes that there exists a balance in the number of charges positionedover the range of charge positions and weights involved. Otherwise, ifmore low-yield shot results from deeply buried charges were available com-pared to high-yield shot results, most of which were obtained from shal-lowly placed charges, the line of best fit would have a biased and flatterslope than a balanced set of results would exhibit. Plots of crater di-mensions versus charge weight 'for' more specific charge positions (having arelatively narrow range)and for various types of soil are presented inplates 7-12 and 32-37. The .remaining plates (plates 13-29 and 38-51) showthe crater radius or depth as a function of the charge weight for a spe-cific soil type and for a -specific charge position.'

'30. Limit lines are shown in' plates 1-51 (except 40 and 41) 'whichdescribe an interval within which 95%'of the experiment'&l data fall. Thelimit lines, also provide an indication of the levels of scatter associpatedwith the phenomenon. Particularly is thi, true where an. appreciable number

of bbservatiqnsare involved,. The limits also illustrate that'there is

"* The reference' numbers. that appear in all plates of this report refer tosimilarly number&. iteuts in the Bibliography contained in the.CompendiumT"

if _ _- 11~ . * ' I

_ _ _ _ _ _ - - - - -- "-- --- --. ' -~ .- . I

14,.

less scatter associated with the measurement of crater radius than, withcrater depth.

31. The line of best fit and its equAtion>,,as determined by themethod o~f least squares,' is sonalso -in Plates 1-51. -,The f orm of eachof these equations is: I

wherein the value of n% stablishes the scaling trend of the plotted data.In arriving at general scaling trnsfor all of the plots (plates 1-51),It was. necessary to'consider-each value of n .in which the number.,of ob-jervations, the distributioin of the plotted points, and the~scatter were.all Tactors,. Since the true crater data are-the more reproducible, these.data were worte prowilln-nly considered than portions of' the apparent crater,'data. Above-ground shots were -not ~considered in establishing the,,scaling,trends.

32. The values of the exponent n were tabulated and cross-tabulated with various parameters. Th'e end result of the analysis of the"tabulations a-nd data plo~tf3 presented in plates 1-51 was the decision that

0.3crater depth is more ne ox 1y described.by W scaling and cr-ater radius

-by W1/3 !;caling. Since the crater depth scaless differently thani theradius, the shape of the crater will, depend on the yield of the explosion

(scale of the'experiment).

Results of Analysis

Prediction curves

33. To establish cr'ater prediction curves based on the scaling lawsdecidfed upon, it was nacensary .r-rnrdce 9,11 the radits, and depth mca~ure-ment6 by W~/ and W0 , respectively. No effort was made to analyzecrater volume or the crater lip height, primarily because. of the lack ofsufficient dbata. (Normally, the crater vo~umoe may -be-.,sat',i'sfid't .orily de-Iterm-4necd by computations made from the crd~te prof ile shpaped to,!'conformto the known. radips 'and depth.) The reducedcrate3Z d, Ih and radii (d/W03 .

/3,and, r/W" irespectively) 'w'ere then plotted as a fun tion 6k tile redu.d-

15

carge position. (Z/w' for those types of media for whicN),,suf fieclent datawere available. The crater prediction curves are presented in pilates 52-711Tn e~tr'h plate, nouiographs are provided to assist in making estimates, of' crka..

ter dimensions for a variety of charge weights and~depths of burial. Appar-ent crater prediction curves are shown in plates 52-63 for wet clay, moistclay, dry &lay, wet, sand, 'dry-to-mQist, saild,- loess, silt, frozen ground,basalt, sbale, P;e a nd,,, nOW;L respectively.. T rue crater curve s are shownin plates 64-117 for moist clay, dry clay, basalt, chalk, granite, maristone,sandstt~nc, and shnlc,. respectively..,Variation of 'data

34. .A study',,of.,the scatter exhibited by the-exp'erinmefltal data showsthat in soils crater radius ,measurements vary approximately 20% and 'crater

dept mesurem~ 'prxmately 30% regardless,:of the pos tion of the

charge. Although a marked tendency exists which implies 1ss scatter inthe measurement of true craters, the paucity of"'the data precludes a spe-cific conclusion to this effect. A simbilar study of scatter associatedwith measurements in rock indicates a scatter of approximately 40 to 50%for crater depth, and about 30 tn 40% fonr c'rater radius'.The maximum crater

35. The crater prediction curvres (Plates 52-71,) provide a graphicVicture of Lhe influence of' the charge position on crater size. Fromjitheplotp, it can b6 seen that the msaximumn apparent crater results from a,

charge positioned Such that

:Similarly, the true crater is maximum when the rbduced charge position is

approximately equal to -2.0.

Comparison of ap ar-en-t and 'true craters

36.. tWherp direct comparisons of app~rernt and true crater dimensionsare possible '('compare yjiate 53 with 64' 54 with 65, `60 with 66, and, 61 with71), -the following relations appear applicable. First, the true crater ra.-dius is, roughly 10 to 20% larger than the apparent-crater ra9dius. 3eqon&J',this- dif f irehce in 'crater .Adii seems "true .re~gardless,of the chare \"

Itt

It: ~ - .*

16

,\Position and type of medium. Onthe other hand, the ratto of the.,

-- ____true crater depth to the apparentSA c~r~tter depth is highly sensitive to

charge position as can be seen in.0 1 5 fig. 2. Thus,,estimates of the t~rue

crater radjus and depth may..be madeFig. 2. Ratio of -true crater depth fo~ 1~ a-n rtrrdu nto apparent. craLer depth ror, vari-

ous charge positions depth by ,using these factdrs.'

Generalizations of' the'&vatering capability curves

37'. If the craterin data shoiin'in plates 52-7 are consi-d red to-gether ana summarized, the res~lting single plot of each crater dimensioncan be used to ptesent an approximate -arid somewhat generalized solution ofthe crater prediction problem" Figs.' 3 and, 4 present plotslof' this 'typefor the ap~arent crater radius and depth.- A stu~dy of allthe crater lipinformation contained in the Compendium 7shows that teratio of h/idvari'es as X ;this vazriati-on is shown in fig. 5 (page 19). The samestudy showos also that .the width of the crater lip normally vari,,es from

abu.0.7 to 1 .0 crater radi-os for chai'gu positioned between 0 > X > -'1. 0and is about one-half the crater radius for 'charges between -1.0 > X

> -20. With these three ptlots (figs;. 3-)and the "'rule of thumb"' asnses-merit of crater lip width, the profile of any crater can be developed aslong as the charge is HE an d its weight doesqnot sCLignif icantly.;ecd1,000,000 lb. "Ohrrestrictions, which:oannot be ass~essed at present,should be impoqsed for situations wherein the medium cratered is s.tratified,'or is highly sdturated or heteragenous in nature,-

Formation of campuflets38. Gconrally, cvaxouiflets, are, for~aed when explosive charges are acdt-

onated aL depths of burial equal to or greater than approxipiately3.5'W X -35). The stability of the caniou Iflets dependstoap-

nounced degree on the strength properties of the material, particularly, thecohesiv~e properties, for they, to,,a large,~degree, detersrRie the arching,.characteristics of. the_ soil.' !Tus ,k_the maximum size 'cavity that can bcf'orned ia gien tral',by the" use of explosives cunnot be determined by

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charLge positions

extrapolation of experimpntr~1 rat~a withonut detailed considerationts Iof thematerial r; proportics. Fxpoi-tmentnl evidence currentlW 4vailable indi-'

cates thait for cohesl.ve 8oilD suoh as less Lind clay (each having moderatewater contents) the camouficut diameter will be close~ly approximated by:

D or D =(2.3 + o.4)wl/ '(4)

W~hcrc D and D~ arc, the dianieters, of the, C-amouf let in" thc ve~tic al and

horizontail direction~s., resproctively. The same experiments showed that forall practical. purposes the ,two-- diameters were equal-. The possibility thatcainoufiets can be formed in granular materials is questionable; however,

* .since' granular rnaterials do develop some shear strength (friction) withdqpth,"it is conceivable that such cavities could be6 formed. if charges

were buried suf fic iently deep.

- .3. For the purpo.se of' predi tang the ~iecamouflet' that' will beAforiefed by an explosive "charge propeprly PosItIned in a. cohesive ooil mass,

*it i~l' re~commrended that equation 4~ be used to stimate the carnouflet',sdiarnctea. The soil properties should then bf, carefully considered to de..termine the ability. of the s~oil to arch over such a cavity withoultap-preciat4,e failu-re of t~he highly compy'essed shell. ~

01.

20

PART oVI: CONCLUSIONS AND RECOMMENIATIONS

Conclusiod's

ho. FrOn the analysis reported herein, based upon available HEcratering data, 7 the following conclusions were formed:-

a. The crater radius Is best described by cube-root scaling,;f whereas the crater depth iz best described when scaled as

b. Cratering in soils is characterized by a +20% scatter forcrater radius and a +30% scatter for crater depth. Thesescatter limits increase to +30 to 40% for width and +|40to 50% for depth when the material being cratered isrock.

c. The maximruni upparent.. crater is formed when -1.0 > Xc > -1.5;the' maximum true crater is formed when the reduced chargeposition equals approximately -2.0.

d. Cainouflets are formed in cohesive soils when the charge ispositioned so that X 1

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2 3s

Iaa2.1

33

13J9. to,

7~~~ 7 7 i0j05 0 -05 -1 -S -2 5 0

-100 -90 80 -0 -so- -50 -40; -30 -20 -IC0 0 toZ - DPT0N Of BURIAL Or CHAprC: f r

0 - APAREN f CRATLA RADIUS NOMOGRAPH FOR CRATERA- A~AR~r CA1~ Of illDPTH AND RADIUS

* ~~~~~NOTE DATii, PLOT *ED ABOVE WERE.APfE T RTRI OS0676BIED FROM RELfERENCES APP~ uCATRI OS20.39,

'V1 "*' r.' 1 71.i I * I . TE 57 -A- I

-, 4

.3

3

60' t 3l

A1 IQ'

6%0 0462/6 3

3 3-.'K.. i. 0

""I W 2 0

I0' 7~ 3 0'

a 2IA' 7

-100 -90 -80 -70 -60 .50 -40 -10 -20 -10 0 10Z- DEPTH OF BURIAL Of CHARGE. I'T

0 IAPPAAENT CAATER 'ADIUS NM GAHFOR CRATERa -APPARENT CRATER DEPTH4- DEPTH -AND RADIUS .NOTE' DATA PI70TTCd3 ABOVWE WEL- APRN CAE NSL

OBTAINED FROM REFERENCES APR1TCAE NSL

* ' PLATE 58--

-- t- --

33~~ 333 -33.3~4

... 3.

3 -I750 S0 '2'0 A. 2 0

33i 20% 06 04 71a

3 3

fl 0 0% .4 167 g

1. %_ to a

I- 4 4 ,

4 22 -

-tIs .i 0_ sstI S4* 2 5 3

4 a -4IS a I to

it 33. 41 2

4- 1 2t1 4

33 2 3 . .3

233 33: J

K4 3~

3 331

to.3

us 0 AP0REN CRATE RADIU NO OR-2 O CAE

7~~~~~~ -DPT Of .UILO . APRETCAUADPT EPH ANrRDIS

A BA3E -RMRtRNE APPARENT CRATER.N FROENGRUN

II. 3 43 . 3 3 . . 3,PLATE 59333 .43

1~~~~'Z_7z 4 -7

7* 172s1

3 31 L

00.

410 '00 510

0 0 1~ 4Ot

00-- e.,Q 10"

4 4* 1

2 A 1 K2~~ . .2 i

10~a 10 I2065 4

10" 080 1 -S -0

9 9,

If~~ 7 '

T- . --100 -90 -60 -70 -60 -. 60. -40 -30 -20 -I0 0 10 m

z -OZptp 0r sIAIAL 011 CHAROC, FT

C, -APPARENT ICRAT .ER RADIUS NM RAHFOR CRATER IA-APPARENT '.t.RATER. DEPTH . ,DEPTH AND. RADIUS

NOTE DAT^,PLOTTCD ASKII WrCM RArt06TAINCO IFROM REfEREW.E 46 APPARENT C~tkI AAT

PLATE 60

~ - -.-- .- - -. .... .

U~~~ -1r - 1-

4 .3

.4

aa

5 1041 a

3- 3

a to -to'

15 3

2- -21 10

3 .50 Ile' a

'5J -- '

- 6 -70 ri -20 P3z-oETH o,"iA or t&%C or

,7~0

NOMORAPH'FORCR Eff AT'*

A-APMC~fUtA~R' DPTH

oB-m -go',.wA 7 CRTR NSHL

to-' -. * -1!l,

* -- a- ~ ,I V - J-

. we

4 a4

aa0 1. 30

At to

4 '

3 CAto'

A A -. - - go ~Via* ~ . .I 7

10 2

a 46

'5 5 to05~~' 0'052" 5 2

4j '4c

39ca

-100~* -t -8 7- -6 3o20 -01de ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ -- ISO 11.1..A. f. KRA

NOMOGAPH 011 RATE

6 BAIC FRO StrFCC 51 APAET4RTRI C

- -7

-- -- -~ ---- ------

0' ) _

15~ 2

3 lo,7

o -4 0. -10

4S2 4

23

33 1 5 2

6 , 4

o~~~~~~ 3__ _ _ _ _ _ _ _ _ _ _ _ _ _ 2

to 2. 2-/2o- 1, a

-W 70 50 -3

05. oI -0 -to 5 -20

ItI

3 - -

lot

.33

10 4

~. ,~ to' 3

I, -I0

.3 4 3 43-

332~. 2 . 7

is 3. Is 2 3

it 3

to- 2 .9

-P0 0 -5' -0 -2 -IC 0 4Z-OCPTN~0`; 3f4ILOfCA

6 0-2U.CAt'Rf4jSN M G A H F R C A E

*10 PLA, 6W47. -0 -40 -0 -20 -1 0 .4

0 - TRU. CRAEW RADIU.

---s

I.A.

-. , 0

44

'0'4.

41 .6S 4I- vS 24

-, 4S

ii '- 2 -- .. V2

V~~ 4-4 .

OS~~1 0 05 -1 -S 2

41-

-Ico -30 -60 -70 -00 --50 -40- -30 -0 4 , 12- EFTN Or "UIA4. OW CKw.,,q. FT o

0-TRU C RATltR AA 'NOMOGRAPH FOR- CRATERi-TRUE CRATIER, DEPTH ANDRDU

MOC AT POYI A.I TRUE' CRTER IN DRY--CLAYr6ANOF URNC

* ': 15,2 -~-~w

V77

3 41

S..... 99 ~99 I " .

-

4 - 2 3 " 5 1,2 3

"9 9 4 15- a 4 I

2 2

4

I... ." '"op A .2o

7 7 ^ 7 o t :

..

.9

.

.

I3 "S ..

a 0

2 2 72

6

5 2t

4

32

40'

20 20 7

,9 ', I5 4

05 1-05

-2 10 2 a

*'-'-

SS , 1' F:.. r 'I I I " *"T -r---~-r---" -- Tr ;.:-'' r-I - l" '* *

-,-I00 -0 -

-70 -60 -"0 ,.# -30 -20. -10 0 I0 F ui4 O I4RG.F

0- TRUJE CRATEfl R/U NOMOGRAPH FOR CRATER

t- TRUE CI.,,R DfPTH.. DEPTH AND RADIUS" 5F OA TA P t.O TT1 # -, E

t.

"05 TAO 40 o. Er cr 4 TRUE CRATER IN

01BASALT 2

1' X2

10 '9 ',P L A T E 6 6

-3

99,- O

- T E R S NSifit

4 4 2- 1, -- -6O1

2 4

4 4

3. Lo

b, 5 -2i00 . ef- I5 2-

910 4B * B

0g , 4!!3t10

~-24 -5N4

I- 34 3

V 2 4- 3

Do- 1020' 2 *'1 '

1 7

5 41515 4 4

3 4

3.1- , i

IO~~~lll7~l - -7|0 I'l'l2 a Ol

-816

5 5 -5 . 0o05 u -05 -10 -I -29,

110

.9'S. .', -

T_ I'

-100 -90 -60 -70 ::-s0 -50 " -40 -30 -20P9 -10 0 10S-DEPTH or BURIAL OliP CKARE, FT.

0- TRUE CRATER RAI, IS NOMOGRAPH FOR CRATERb- TRUE C-AAtERDEPTH DEPTH AND RADIUSNOTE DATA PLrjrTED A00VE;WERE1/t

-. OTAIN.TO ,oU RrEwENC a TRUE CRA~TR IN CHALK

PLATE 67

S ... . 1 , ) : ;, . .. . ....

---- - - 5 3

,4 !2 3i0 .4,. 0 0 05 2"

0 0.

0 --

0 4'&15 15

-I-. 2,53 10*S.... . 4 5

100

0 0 !0 2:

A 30 040

4 o ' 3 o tO1o~ A 4

3 1 1 2

~2 2 1

0 5 4 .4

,o' o . " . -z . 3o. "

- 9, -11'-... "100 ID 2

g 8

0 0 - 0 100 t10

/77

5 30

* A . ..

tOO -20 so0 -0 "t 60 0 -5o 0 -30 - 20 710O 0 10I - DT. OF' WAIAL OF CHARGE ,FT

0 - tAW,_ .AL - .RAIL RADJU' NOMOGRAPH FOR CRATER : -; A TWI,, CRATE. R . DEPT:H A N D R A D IUS ,..

0 OT , TE O XP, WFAL TRU E CRA I- LH IN G RA N IT E

u--

2 4 . "

i .PLATE 68 ,

10',..i* .' uC): '..

It 3 13 .' '.

0 3 .5Do

7 t, -10,

5 7

3

* 9 4

It 5

I-0 4;.~a 2

ef 33 . . 5

10 2

v 100 10,

7 6

IS 415. 43

10 . . .l~t 2 10

7 . 3

1776 66

.5 0 . 05 -10 -1 s -20

xc

T

-10 9 0 _50 -7 26 50 40 30 -20 ,-o' 1Z-DcprCe orB~A F HRE T

0-~~~~~~~lfo TRECAE -U ~ ORPFRCAE.,61 TRU CRTEA EPT DEP H. ND R DIU

40TE ~ ~ ~ ~ ~ 1 DAAPOTE DV, EE 1

OBAMTFRMWtRLC TU CRATER INU N GAP O CARATOER

* ~ ~ ~ ~ ~ ~ ~ ~ ~ LT 69R0 RTE e ETHADRDU

M,~ 1/14A

0 .4

-. 10

3 ( 3

.

2 QQ 0 0 3 24i1 . I),J 00 t122 7- 10''O

0 70-- 4 064 ..

4D .3.

0 .22- 3

2

-0

0' -2

* 5 4

4 3.-02 40

a-'~ 2C* , S IS

1cp

* S 40

-10 -IS -2

Is as7*.

-1,00 -00 -au i0 -s0 -50 -40 -30 -20 -I0 0 la2 - DEPTH OF SUPIAL Oe CKHARGE, FT

0. 0- TRUEI CRATERRADIUS *NOMIOGRAPH FeOR CRATERr~urCRAER DPTHDEPTH'AND RADIUS

NOTE DATA Pl0outr. ASOVE WEREOBTAINED FRO0M REFERENCES TRUE CRATER IN -SANbSTQNE

..PLATE 70 , *

IF"

6.4-3

7* 10'

5 374a

- 3 4-N 4. 2, 3~10" -W lop 1.-

2 *'* . IS9

4 -104

2 6j41 ..X. G

7 -. 44

3'' 2

0 ---- t~--: 7- - -2

44~~~~~~~) X , ... . .. ,7 '

'4~ -24 4

. .*~- ~ __ .. NOOGRPH FR CATENO~rDAT PLTTCOAa~~ TUE RATE IN'SIAL2

O~~~TAINE0~0- 2U~~E -D PH A D R DU9 I-4

444 . . ..4.,.-' , PL A~h. 1 ' .-3

4 ,. /7

ff~4

4 ' 4__ ___ ___ __ ___ ___ __ ___ ___ ___ __ ___ ___ __ ___ __-2____

____ ____ ___ ____ ____ ____ ___

-10 -t 7 4'0 ( 0'. -,. 0 -3 20 0 0 10

.44,44 CRTE DEPTH

.. NOT DAAPOTD4SV EET U RT RIOBTAIED FOM REERENE 47

PLA 71

INo of '

Address, ;' Copies

-Army.

Chief of Rese~trch & Dee pmen' ~-Wsig 25, D!-1.ATTV: Atoniic~,',Air".D',ense..&.Missile Division,

Chief of Engi~'eers, DA,: Wahi "tS M 25, D. C.1.AT:ENGTO-

ENfl,', '2

Commanding (;enbral,, U. S. Continental,-Army Commaxnd, Ft. Monroe' Va. 1Commanding General, AberdeenProving .Groxind, Aberdeen, Md. 1ATTN. Director, pallistics Laboratoi~y

Commanding General)4 The Engineer Center, Ft. Be~voir., Va. ,,2ATTN: Asst. Commandantr,. Erngineer "School

C ommandrinc 'Off'icer., :Engineer Research- &, Deve'lopiiiefit Laboratory'I.*Ft. Belvoir-, Va. ATT1N: -Chief, Tech. Support Branch

Commndig Offi~~', . S Ary Cold Regi'on,Research and--Engineering 1Labbratory, Wilmette','Ill.~. A'ITN: -Mr. "K.' BoydDirector,. Waterways Experiment, Station, P.' 0. Box 6 3i Vicksburg, 1Miss-. AITN: Library.

.

'.. ' . Address ,C~ opiesNavy -(Continued)..:

Director,, Navy,.Radiological Defense Laborat 9 ,ry ."**ATTN: U. 3, Army, 1.ialsor Of f ier..

Air Force.Assistant for Atomic Energy,. Headquarters, USAF, Washington 25,'\D. C.

*.Director' of Plans., HeadquArtois, .USAF,, Washington 25, D. C. ( 1-ATTN,-. Wdr P1Lans Division. '

Director of. Research & .Dcve lopmenx-t AHeadqtarters b,- USAF, 'weshi~ngton. 25, D. C. A'TTN:. Cqoibat Components DivisionCommander-in-Chief, Strategic Air CoimnAnd, Offutt AFB, Nebr,.-~ATTN: OAWSCommander, AF Spec ia1-W-feajxcnx C enter,,Kirtland A1S, "N. 'Mex.1ATITN:,, 'LibraryTheRanld Corp., 1700 Main St., $anta.Moni~ca, .Clf

(oNuclear Energy DivisiLn. Clf . '1Ih~ssistant Chief-of' Staff'. "Installations, Headquarters', USAF,1-Washington 25, D. C."" ATTN: AVCIE-E ' '

' ~~Other DOD--Agencies ''./Assistant Secretary-of 'Defeiipe (Res 'earch&' &Engineeri ,ng),Wash~ington. 25, D. C. ATITN: Tech. Library

U. 3. Document's Officer, .Office of the United States National1Mi] i1tary :Re'pre'sentat ive, SHAPE, APO 55, New York, N. Y.Qor rflande, .Fi Old Comm and, DASA, P. 0. lox 5100,1

..Albuquer~qud, N. Mex.

Commander, Fiel~dComma4nd, DASA, P. Box 5100,,"P 2Albuquerque, N. Mex. ATTN:' Training' Diviqion

CheDefense Atomic SuppoA Agency, Wsshington 25, 5CASTIA;',Docunent 3ervice Center, Arlington Hall 1tto, I 10Arlington i2, Va. ATTN: 'TIPDR'

Others,The Sandia Corp., -SandiaBase,, Albuquerque, ,N.' Mex. ' ,ATTN:, Classified'"Document Division (For Dr. Mel 'Merr~itt, Ddpt.

Supe'rintendent,..Eastern Experiinerit Station, U,"6. Bureau of, Mines.. 1 4tColjege 1Park,. Md. ATTN,: Dr. Leonard Obert)The Univeri-sty of Illinois, Civil Enginee~ring, Room 207- Talbo't Lab, 1Urbana',. Ill. (For Dr. N.. M.-Ne~nmark) ." *

~~2,

A, _ _ __ _ .

* :~ ,II...No. ofAddress dopi&Q-

Others jqontinued)Mpssdchuse'tts Itiute of Tlec'hnolog}'il Dept' of Civil,& SanitaryEngineering, (Thrbridge 39,'!Mass. AN D.C C-Hi Norris 1. .... .

Dr. R. V. Whitman' *~Amherst College,, De6pt. of, Physics' 46zherst4, 'Mass,:. 1A'l'32N: 'Dr. A.-B. Aroyns. .Mr.- C. W. Livingston, Barodynamics, Inc. BP Bx 432",Georgetown, 1Cob p

3` 0*

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