THEORYOFRELAT/ONS BETWEEN rHEDETONATION

VELOC/TYOFSOLIDEXPLOSn/ESANDTHETHIC尺〃ESS

OFCASESORTHEDlAMETEROFTHECHARGES

(Rteelled1958.ArlrtL15)

R､hU＼110 HLヽO'

<･> -

^b､trACt

卓■ JntroJuL･tlOl1S2.Th帥ry(〉n theelLtFCLOrallenel○さurビ

≠lthlhCthlCkrLeSJr

貴.2-) .4､､umptzorLOfr印CrLqTtZOrLrい,lLh

､nrはblt'len8th書8nd thC SlZIbltlt)I)Ideton仙On

S2-2 ThecretlCAHorm ulaS与=-3. Cl)rrlFnrl50TLⅥlLhexrKrLmenLnldALa

oL Copp.'lrtdUbbtl｡htlca3. 1ht･orTo1日heC汀亡CtChht=rAdlu･Rt)∫

harechaTF:亡､

.～bstrllCt

A theoreLIC.llEormulELhasbeenprモ5紺【ed.

1･.hlCh de5CTlb<s rel8t)OrLS among the

m.lXlmum deton仙On CヽlocLtyD..,.1n)5tabltt

de【onaL)OnヽekN=lEy D.reacLlOrttlme∫.ln

rdtLtOlはtlOn) TeaCtlOrlWne.thethlckne550f

肌atlr,the＼e)ocltVCEtheshockwtllej日rL

the≠allmatertaltW aTldthemaxLmum re.TI-

号.31■. ＼551,m PL･rms3-2 TheOrelLftLHorm ulnzl与3-3 ComEnrL50Ztl川 hexpcrlrnentaldnla

魯4 Theor)OIlthee打ecL'OE casesaTld tht=rAdLUS≠hen tN)thlan

i5. Apl)lleZItl0nt〉ftheLheOr〉S.5-1. PrLrL⊂】plei5-2 ExLlmPle

与.丘 GenとrTLLTulとjlOrLLhrreaCl10r=Lmeratl0

IMI.I,ndt王te rc州10nとOnr】印gthmLlO.＼■_＼-

CkTlOl､ledgnenL

､ヽ･＼一一 ･･- ･-･一- ･･一

.lSSUmptlOnLS⊂OnS】Stenti)appllCd10hoLhthe

so-ca一ledthlnandltlLCklla】LAlsoatheore･

tlCAlfonyllll.i has 1光en prCSerL【ed,､vhLCh

descrzbcsrelaL10nS bet､,eeTID..,D,radLuS

oEacdrlrLdgeR,crlt】Calrュd)usR｡,below

＼､tlLChFLOdetonalLOtl ∝ CUrS.IE..theeT)EtCal

rent:LIOn tllne tc.lhcve)oC】lyOfsoundI-1

dcLOnat】Onpr(lducts叫.basedonthe.TtSSun-

pl･OnLhalthepartOf.1ChargearoLlndthe

ctlOnl】mC/" basedontt-easstlmPt10nLhnt crLlleLlldlaz-1C(eraCt与L15aCase. A gl3Zleral

thedural】OnOftheretICtlOtHlmelSCEoT柳 Le(I

b.Ithecx王SIZln亡t30fthesolld ､Vmll,､､ht･re

the ､､州 beglnStOm OYCOnl)tlflCraShock

､8､e,W hobC Vet()clty 15V-.hastr8､<1kd

LromtllCInnerhurfacetDtheouterO rLeThe

IThcバ】pporl】ヽ8yaklJCo.Lld sa.53m〇･mbぐhl,lBlnBE;UChlkeTl,J叩art

equ8tLOn lnWhzcht氾ththeLhlCknessoEa

caseandtnt:dlamclcroEch.lrgeSVary,hiLS

deemcollStruCtCdsuEX･rPOSmgthelnEOC.15eS

descrLhedabolc

the､alidLlyOftheFundamcnlalforl11ul8S,

≠hlCllCOntalllnC･arbLtr叩 COtlSlanLltlCOn-

tnsttolhepre､.ousformulasdescnbedby･

170 TheoryoErehlJOn5bch､eeTHhEZt-仙OrHrlocllyOholldrxpZo51YEJ EVo】1910.3andthHhlckneSSl)LぐれeゝOrthedlJIm亡leTOrth亡rhJ)TgeS㌧ar)ouiauthors,hLLVebeen eヽrJLle(ii)y -1 BS白umethattheth)cknessofCaSLng5rOr

呈er)eSOEexper】menlatdaLEHltJetoCoop. lherndlu50tchaff:I;aR chanが theTnaS3

Ubbetohde,CookctfL] equ8t】Onilo(hhemcmenLUmeqlj8tl()namong

I,.,/C,themnxImum re.lCLZOnヱOnele叩th tht.tundnmentaleqt,al･On50日helheor〉oE

-Yql.thecrLllC･l)reaCILOnZone)lmgth.V,have dcIOT"LIOn､Vh,le】n山･I)reSenH heory only

beenc.llculnledbyuseoElheミeloTTT'uTaS, tht･tnerg),equal】0,日約 -Tluencedb)rdnd

､､hlchmaybecalZcd"thevarmb-erea｡110-- R

己OT)e)engtt】LlleOTY'' X 机 7㌦.ireloun(ho (3) Jnlhetht･cnthS01Jones良 E)rlnR

bemuch)ongerthiLrLh机･eZ托enSupPOSt(h o T)0Strtllghl-rOmaTdequat上(】nStX･t≠eeLIDand

bebymanyprcv】OustheorleS

ThegerLCralequiLt)OnderlvedbythepTe-

s印ttheory]s

(DD=)'-I(tc一号)fl.･i::.lJ･(忘 )R･,･=,<･R一票

至l htrOdllCtioTl

(i) T.he Lheor】esproposed by ll

JOTleSl)')-)andH EyrJngl)舶Sume thc亡On･

-lLLnCyOIthelengthofthereLLCtlOrlZone∫､＼hl)elnthepresetltdleOry ､ヽhlchmzlybeC8日ed "the v8rlELble reacLlOn･20T)ヒ-)e71gth

theory."theknglhoftherenCtlOnZOrLelS

assumedtoUar)fromthemnxlmum rraCt]Or)zone)engtllX,..Whlchcorre叩Ondstothe

ma.xlmum delOnallOn ､Cloclty Dl tO l九e

mmlmurEIOrCrltlCAtre.lCttOnZonelength.1',

ThereれCtlOnulnelSalsotLSSumed,)nthe

preSenHhcory,LO Varyfrom themaxlmum

1-tOthemin)nun orcrltica】I.

(2) ThelhcorllZSOEJonesflndEynng

1)H jones PT∝ RoさS∝ ..A 189pPヰZ}ーi26(】917)

2)johnLCoppzndA 冗 Ubbe]oh】e Tr.'zlう.FArad8yS∝ XLEV 6J6-649()948)

3)IT▲ylor Dc10nJILIOnlnCoTldtn5d E叩lo･S)I,也 Oxford,TtleChrcndozIp-e≦一.p 柑C(1952)

.)HenryEyrJnE,Rl⊂hnrdEPowel1.Gt･oTgCHDuttcy,fhn50mBPArllnChtmlCJl】RevJ<WS,45.69-179(19･[8)

YorRRYEdeducedlnLtnulytleaLfomsand

llnumberofpracljCalformljla50FI)m 'leJ

tLPPllCatlOnhAヽebt*nsuggestedbtlSedoll

numerlca)叩prOX)mEiuOtl,thtls,tilereSUhs

were semL･CmpmCalcquRtlOnS COntalnlnぢ

some aTbltrdry 亡On5l.lnls Whose phさS･亡0･

ehemlCAlmeamnBS atenotneCeSSarll)ekaT

whlle)rLthepresemtheorytlleequaいOnSfor

D.YaJtdRcot)la】n nOarbLtrnryCOnSt帥I

zlndthev8r相blesCO】11aLrtCdlntheequal)orls

b机edelmlteph)blC()-Chemlcalmenmr)gsar)d

canbedclerm lnt･d71UmCnCa1h byaSerle且

oE t･xperlmentSOTIDaJldYor々

(一1) Inbclhcla弘tCAlLheorze'lhe EunL･

tlOnSOftheso･calledthln ＼ヽ･allandtlleLh)ck

orleared】n'erezlt lntheEormeTthelrlema

ofthe､､･且1lphySamaJnPartI)ndlnthe

kulerCasetheshockWaleWllhlntheⅥzl)I

p18〉S.TI ma)nPart､､もHelnthepresenttheory

lht･t･EfecISOfcorl翁TlemCntlrltnthcasesZlr.3

dueLOtheac110nOftLt･sh(Xk≠且､C,hol､eヽeE

thm thewallm8〉Oe.Al一dthecLfectoER

onD)らalso】nLeTPTetedasacol)Rnlnga亡tJ()n

oiashenlhofan explosL､,eChargearound

'lhecrltle8hadlusoLacartndgc"

The detects (1)-(4) ofthe I:lass]e8】

thecrreshtLVeCOr･elatlon5 0nceⅥCassume

(1)aCorLSt且n Va一ueolX (andI).whl亡h

mezln5Zlbedpos】tlOnOtChapnaJl･Jouguet

planc,the.1(2)theHugonLOtenergyequa

I】OrLCarln()1 bemodlrteddrastlCal】yand(3)

lht･cakul仙OnS .lXCOmC COmPllC81ed )ll

tka】1mg､ヽlththetwoequal】OnSthemnさSnod

momentum eqULtlLOnS,】nSteLI(IOfoneenergy

equaLzOnZlnd(A)10e.Yp】alrH hec打eclS0f

theTildzus thethlcknessolcnse号dl打ererLt

meCharHSmSandd】fferentequatLOnSmtlStde

】ntfoduCedlorlh)r)andlhlckWA)lsbeeLIUSt:

_ll(and/)15 nSSumedeonsIJlrLl TncontTZlSt

tolh)s lhepresenttheorytTtSSumCSLhzll.V

(an(】E)variesthusleadlngtOOne meehtm lSm

ora gerleTnleql18tlOn WhlCh roversall

eLrectsoftheradluS,thLnand山LCk､､･且115

(5) 冗 S⊂h811日dlSCuSSe(lthestAbll】tyoL

loヽlerde10nRtlOnVelocltyOntllCIl)pOtheS】S

t】1at]t''SPrOpOrt)Onal101ID ､､･hlZcIllthL･

pTeSerLtPiLpt･T.YISEISSUme(hobe lnere.lSJng

w】thD)

(6) ＼lA Cook■)tnlrOduCedtheldeaoL

thedetorLEmOrlheadorthegeoT71etrLeLLlrnodel

andassuTnedlhzlt

1-4cd′I3D

､'herecLSaprOpOrtlOnallt)COrLSttlntbet､veen

zeroand10tnanassu!叩tlOnA-lLl'-length

of(hedeton8tlOnhead,andd′ 15 emp】ne8lb.

(ourldtot光 ′t'-2J～106cm lnthepTeSerlt

theor)noarbltraT)COllSIanthlLSbeenuEed

lnderlVlngthetheorctJ(a)form ul閃.

(7) N MansorlT】dLSCUSSedtheビffeetof

RonD orlthebaSlSOftheerLtj印IrELd】tJS

belo､､nh!chnodetonat】orM ccurgfL)tho叩h

h)stheor〉d】dI101g】ヽeZlny(lescrlptZOnOn

5) Rud'SぐhR)1 ZellSChI"rnngewELnlhePhyゴIk,6.470-475(1945)

6)-1 ＼le)～-rLA Cook,G Shoot71lorble),W･SPEI'tr】dge.W 0 Ursezlba亡h J ChemPhysIC$24.め-67く1956)･

○)-2. Iゝ A Cook,EarleA MAy丘eld.lVSPaTlrzdge ∫ PRY Ch帥 59,C･7シム50

(1955).

6>3 1lA Cook.FemnA OIson A7ChE JotJrna11.39】-一oo(1955)

I) r1 118nSO'' ZeLLSCTlr】IELLJrEl亡ktro<hem■亡61,58も-592(1957).

thestructureofthereacl】On乙OlleWhl】e】ll

theprt･senH heor)thetrlllCalrtld'usL)lays

ade危nltepart]n thestTut=turCOEthere8C-

t10nZone

吾.2 TJleOry On th(･ etfcctof llll

erLClosurewlththl∋thlCklle89Y

32-】 ･tssumplzOTl OLreztcE10nZOnL･SW】LIl

､arzzlb)ekzlgthsaJld(hestabllLlyOf

deLOrlat三〇n

Forastzlblede10nAt10†1≠】ththedeEonal-On

･elocltyD there.san叩prOXlmatlOneqtlu-

tlOnJ)het､､,tenthedeton･ll10n､･eZocLtyD..Lmll

lhehenLOldetonat10m ¢ h

DJ--｣.-120m(I,.- 1) (2-1)JL･〇一Lr

lt≠epu(

0.-efleetl､edetonzlt】Onheatal,8llable

ondelOr･aTIOTlpa5SZ)gClnthecaseof

･10rHdealdetonatLOn,

thentheot冶erTeddelDnat】OrH e)cN=ltyD ls

determ】nednotb.I Q,.butb)Q.パhatlS.Q■

･rHhellugoniotenergy equaLlOnShouldtk

replacedby0,I)､､hlZe0.depen由 onthe

degreeofconLmemen1､､hlChm tl】rnLrlnue-

ncestheobSenedD

or 意寸書 (2-2'

QOニ-＼r-fr･lCtlOnOFheatUL･.,-do,-

dclOnatlOnpaSSELgC

(2-3)

ITIOthc日､ords,lokE･ePade10n.1tlOnvヽn､e

atacon51An= el∝lr〉D theCot15umpl】Or10r

theeffecLt､eenerg)0,isrequlred.therefore

8) (3)p69T8b]e22.

9)Kum且OH.no DeLDl,at10Zl､e)oc)IyOfexpl015-YesJourllaloE theTndu51…】Exp】osLVeSSocLCL).Japan(lrLJapanese)tl,46-71(】948).9.9-2)47-W (1948)

172 Theor,OTTr】AtlOn～tkt"eCnthc血omtlOn､LLlo叫 OElO】l(hxp】os"eh L＼･tlH 91Tto 3arLdrhetEtLekrt亡5ゝOfA:ASeSOl-thed‡ameL亡rOf lllCCh Tltrゝ

(2-2)ma)he descnkdaSIthttenerg〉con-

NmptlOnrt･latl0Tl

tuthough therelS nO IImLtatLOn la Lht･

m叩mttJdt･otreaCtlOrlJpO'lelt=ngth .I(and

reacLlOnI)meI)from thesLarLdpoln10Ethe

Ehcrmodvn且ml⊂al･h)drod.mamlealtt】eorさ Of

de10T18t10n rt･aCtlOTIZCneさhouldhzlヽeSORE

dcFmltelt･ngth.lrEnraplyt･nLIXp】osl､eCarl･

ndgcunderZIP､erH:OrLdiLLOn(caS･eradlU5･

londlnt;derLSLt〉) Belo" Tht5CerlnllH alue

of.rlht:e鮎 etL､e heateヽ01uLlOnmZl)nott妃

tllO叫hLOSLlPPOrtthCStnbhHletonntLOl… 心 le

zltカ＼elhl･Y.TIlueof_IthビeXP.lnilOnOfthe

Llt!t:ompose(Ie叩Eoslyem akt･btheL･IonFl'lLlOn

ot･ヽ一日TlpOささLble Y〔anlユr) 0､era､rlde

r.unge､Vheltcases0T Ih亡rZtdluSChAnJZeLJnLleraglヽertぐOr･dltl｡n･

.X'- coltSE=.V. (2-1)

Rt･a亡tlOnllmeIl王dL･､mkdb follol巧.

ForiILtl､･eneXp】oil､IL 1｣ .lrtda_ha､tt

tlXed､aluヒSITldeFKTldenLOEthビJeflrOが OE

tht･eortEITtemenLArLdtheradluSOrI:harpelTherefort三

(2:)=conゝ. (2-9,

0lforai:1､eneXplo51､etJnderll#il印

ぐOrldl【10n

･､.=( 'Yi!:I)I,=雪㌢(2-10)

(2･10)gL､･eS'lhe enerp.Isuppb rel仙On.

llhertl'Ehetlne叩)COnSumpいOnrel.ltlOrt''(2

2)andLtheeEIL･rg)SupPl.IrehlJOTl●●(210)

lirebalan亡LLd.ltpOlntl'.lnFIG1theStabl･

llt)oEdt=tonaLlOrH50btaulL･dl父eauSelE､､t･

triereaz't･thedetonatlOnヽ eI∝ it)D ら)a･matl

.TtrnOunt.therltheene巧〉COn5umPtIOneXCeed･

thとenerF)与upPlyarLd∫) L*pITutO Jet:rea'iE･

I=.TlD (215) .lrld､】亡etビrSu

Thenfora丘xedI-alueof.Vt

lだ.TlID (2-6)

[止Lu" lSjUITLe,tOtlft群Iapt)rOXlma-

llOn.th(lttheLraCtlOnOftheefEeClL､edl_LOnELL)011heat.llJtldbleotldetonn-ll(】llr).TIS53gC13''pr叩Ort10m.llto ttle

re.letLOnurnCI

･Y- oo:- /1- (2-7)

肌hert･ I_-rnnX!mUm rL:ユL･110ntl爪e

As thetoLd]ene碍)･lSut王1lZedtit

.V=.rl '■k omelt!1.亡'1mL･≠1lh

the t=on,tnrttrea亡tLOrL-ZOn亡11enBth●●

.1,51JmedlntheelむさtCdltr亡ユtmeTllOf

JonesandE)rln2▲CoTntllrLlng(2-5)ttlLh(2-7).

lV-.V_Y/?",-(封(DD･)(2-8)

iP ql pl,p■⊃t-"E鴇 品 ,

9･さ●t■■▲tl■lT11>一i17

FIgI Sltblllt〉COndlL;OnOfふLOlu tIOn

_4叩 】958コ KtJmaOH■no

lnド)A1lllecur＼e(1)sho､vs lhet･nergy

<onsuml)tlOnTCLnllOnr≠hlLecurves(2)and

(3)show Itht:cncrgySUpP]ire)at10n5 for

dlHerEntreltCL)OnZonelength5 rhe pout

YLlndl(:att･S theCaseoftheIdealdetonatloll

eヽloelL)"heremaxlmUm detonalLOn､eloCLt)

/)AlSObtllLnCd帆lthm:lXlmUmreaCtlOnZOr)e

length)II (.lndL九emaxlmtlm reZtL:lIOTl･【】me

WherLL Iz=(hlCknesscE≠爪LL

tJW=yビlocltyOlshockmlVe叫Lhn

≠a11

(2-ll)lsb.lSedontheれ!mLnPLzOn一hat(1)

anLnFlecmemo､emeTltOL…… ulloccursonly

atEthepo･n10FrnLtXlmumhcnlde､eEopmerLL,

ttl.lHS nLLhCt･ndofA re.1CtLOnZOne,(2)

the ､､･I)L(lotsnotnOVt:untll皿 SlrOng5hoCk

I_) ThecL)nC (3)shoⅥSanmle･rmedLale ､､a､e lle､ck･ped I)I n POt】llE propag.11ビS

ぐL'St'.､､hereb〉1'pOOrCOnflneTT'entOrbya throughltH.tO ZlnOuter5urf"et:ho≠e､erbmallerradlu50fz'charge,anlntermedlate th" the､､allma)t*

detonaLlOn ､eloclt〉 DllSObtaLne(INth J

ShorterreactlorL20TleleTlgth.1'.(.lnd.1きhorter

reactlOn-t】meh) Thecunt(2)r叩 rL･SentS

thecase≠herethe】帥 eSEpOSSlblede10natlOn

velotLt)(ttleCrLt】CilldetonatlOn eヽl∝lt))I)i

lsobltLll1edfor8I:ntユCalradluSOliLCharge

R ⅥrLh the m】FILmum re.lCtLOtlZOne

leTlgthortheerll】ぐ'ltreaCl】OnZOnClength

JY.(andH1C lTMllmun rCLICtlOn･11TT)I:Or

thecrLt･C.llrcncLl0"一t,nelc) Ikenleet】ng

pomlSOflhtll､､･OgroupsOfcuTl･eS(the

eneTg)C0--5Umpt･On･..ldsupply)gltlCEht:

correSEX}n(lLTlg detonat･on ､elocLt】eS D.ATld ∫), respct=L】､･ely Whzch arc st.lble

underrespcctLVeCOTldLllOmS

阜212 ′1heoreLlczllFomlu]as

1ltllepresenttht･or)noA)ScrlmLlt10n

beh､eenthe50-CaL)ed一h]n＼＼.lllan(l lhe

Eh,ck "allL5 rLt･CeSSaTT InFI甘2 亡LLSe

(1)sh 0､､3 abEIreCharge､､Ith renctlon

llne I. (reTLCL)OnZOne-一ength_＼｡) rhe

rtL(lluSOTabtlreChilrge]SR The cnse

(2)sho"弓110"alh･n"allelongatestht!

TeaCtlOrL-I)mt=andthereactlOT) Zoneb),

arHlmOUnl～ l'Tld.Xf拙reSPeCtllel､

The､aluL'OE Ir F7).1)beasSumCd10

tKAaSEo】Lo＼＼S

･-- i: (2-ll)

BeeauseoEilnビnTttme11rapldaet10nOf

thedeLon.lt10Tlt･＼erLIoTlhcth=1ll.1日th亡

mt_,rt川 0(tlle＼ヽ.1日llot.inotdcternlncthe

mo､erTlt･nLOflht･､､tl)IbuHheJ}rOl)3gabOnOf

LIShockⅥn＼eI:omeshrstTheTenCtlOn-ZOnC-

1engthLStt)ongatedbヽ-thefol】0､､IrltZamOurlL

l:;■-JT::ll.

･74 TL印ハ"OirtehE,a'iETcsk怒三ごTrn｡空とd.e三othN:ldO:霊 '㌫忠 霊 T;:sPlが 一一d 〔､10.1910,

.r_-/-D (2-12)

Ho､rever,bothl■nrtd1-Iha丁etheLrupPtlE

lLmltSrepresentedb) th亡fol】○"logequat】On 仰J.becausethetotalLLrn'eOfreaぐttOntLOrthe

lotaheact･on-zonelleng【h-V'car" otexceed

lhcmax】mum fCaCtl0】1-い1Tle/m.lrLdthemnxL-

mumreactlon-zo】一ClcllgLhreSpeCtLlCL)

Z･-1･･,.F/･･÷ ∠L- (2.3,

or y∠t:A:L一一I.) (2-13)∫

.1･.=,Y.+.Y.≠ ･.十I D∠ .1･. (2-14)Tr<

or y∠ 昔 (-V･一･1'･) (2-15)

'rht･com blTlrLt10nOftheI,rluat】OnS(2-2)

(2-7)and(2-13)gLleSthefollo≠叫:reln･

l10n

意 こ .,･＼=1㌢ -I/･羊YIT'./_

(2-16)

or (蕊 )'=･r･Bl- (2-.7,

Whereー _i-/./∫.. (2117)∫

7.A.',(tt.toI

T lゝlt-･pfr

･tll(18El▲liJtFlg 3.EErectoEthICkrtes50i机allortJetonAt101日el∝Il)(dl.ameler｡r

explosEleCOn5taTLt)mtlrrtreaCt

LOn-tlme I- and lh(:maj{lmurZtTeaCt1011･ZOr)ellcnglh

resTmEl､elyasfollowsknolllllgtheI.lIuesoLt7-andI)-

,hゴー.｣ (2-i9)′'._1【1rl

ll･V･=(2,I)tanl,. (2-19,,′ln

Flg3 thevalueof;I--I.'t-b eZLSllrFoun

d.therefore.ⅥemaytlndthereaetJOn-tlm

eI,OfabarechargeasEolloWsL.

-III_ (2120)The reaet10n-Zone-kTlgth .V,

forabareB=1I(vJ-) く2-17)〝 chargelS(蕊 )≡

-(-,It)+(忘 )r (2-17)′′,WhlleslコbstllulL叩 (2-

12)LnlO(2117)".､ヾehave(DDT)!-(三･号)+(警)(忘)}~(2-18)

Llg.1958⊃ KtlZnaEIHiRO

描■',l還 ▲二還覧上 ･

璽囲 .I

Flg l 一OLdAlTulLlllTla～l亡elc851TuI(R-253cm)(DユLJLorlTICopp

ltUbbct｡TIFlr)

隻2-3 ComparlSOnWl山 expcrlmentaldatzI

ofCoppandUbbelohde

ln Fig 4 expenmentald山aOn60/40

AmmalOt(TNT40>',eoユrSe:(H.NO.60%)

due lOCopp zLnd Ubt*lollden wzth lhe

F唱 5 SErU⊂tltrCOfhareEh rge5≠ho父Ttdlu}l■bJgJP=hrl th亡OretleltradllJJ

seCbヽ LlqeOrtheequ8110nOfJonesLhal15,

tわt:easeOE"thLCkWAllI

§3 TheoryonthecLft-ctnlthe

rLldlu8JfoEcharges

専3-1. AssumptLOll

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radrLL5R.ofa亡artndgebel0､､･ⅥhI亡hrLO

stユb!edeEorLatZOrt ∝ CurS At8rad】usorR.

radlLA OE 叩 loSLVeR-253cm m aSteel thedelOnatlOn､el∝ilyJSLhecnl】⊂aldctona･

caslnghAVebeenptoHedaCeOrd'ng10(2-17) tion､elo叫 D･ Alth▲sent.catFad,uS lh亡

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tBnLT=0872

Whtle D_=6080m/see

t1--5940m/SeC

x･-(農 )誌 2-117C-

l171-- 0608×10◆Se亡=193/useC

Atsotro机 FIB4

1-tJI_I-08131hereEore

7.-0843/_

-0843xL93Z163/t5eC

'.-I63xlOJ×05583'10-Z=09lemr.=･JJ:I_-I.)-0591(193-163)

=0178crEI

From F】gtlll1hfoundtobeO18m in

agoodagreementwl血 l!ヽt･CakuhtedvalLZe

FromCopp'5daln r.±02ぐrTI

Copp良 Ubt*lohdereEX)rttha= -331/I

reユCtiorlLIMBI.LStheshor【esIPOSStbleorte

A51heradltJ50EcArtTLdgesIncreasesb唱ger

than Reasl51HustmledlrtFlg5.thereac-

tionLimeI)ncreMSbytheamour)日-dut･

totheⅥ州 e打ectortheparto†8 Ca'trldBビ

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皇2,theouterド.l√tOEacaZtrldgeacES tlSi'

"auaround‥iLChaTgCOfmdLuSJL(cr'LlCal

radluS);beczLuBIHhedeEonAL'On､etOClt)D

ForA15determHledbyD lntheaxlalcore

Ⅵhert･D au4mSEhehlghesEYalueortthe

sectlOnOfa⊂arlndge ThentlleS】mllar

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eXPrとゝ >tOn

DD:一予飽 く3-1'/■≠ hen･

て.,-lel∝at)oEthe50urldmlelnde【ona-

tlOTtprOdu⊂ES

･6 1hcor霊rtchJ:I;OhTeSknLxiごcoelnCこと:;r.(:oLnhnEt'.0.nBXet.lrT誤記.5:llまぶspEosl､eS 〔､'0日 91｡3

FIP ･ E鮎nolTddJLLmEhrenltTtd即 ヽ l>,･･lZoJIJelOT)JLtIOIl

eヽl∝ll〉･･･-且 ID=岩 D (32)iIL､ヽ･h

ctet',I)ndtl.arcthespet:lrtい olumesoEdetomtlOTlprOdtJCt5andtheor唱ITlalexpEo

lSlヽe reSPeCtl､el)･ Toattrst叩PrOXIna

tLOnv.15LLSSumt･d10beaI:o

TISt.lrlt.Jt--Ft-R, (33)

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T.IczlrtrldgearoundaentLCa

lTlldlUSR-radlu5

0f(atotal)亡AnrldJZt･R.-cntICaIrad

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I(1,,I-) (3-5y'B-1(I.II) (3-5y′

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--(.)t●t (310

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178 I"-to㌔ notLErLehteA恕 nY三ごeoeEnciL::霊 otnhaelldOznaニeelleT誤記eS霊 ぷ BP'osllt" 〔vol附 ｡ 3

号4 ThcoryontheeErectSoEcaS四 書･5 ApplLCationofthetheor)A

andthemd▲uswhenbothI-Ary' 貴5-1. Pnnc'ple

AnequnllOnEoTthlSgeneT･1lcasemalte One ofthe appllCaいOnSOEthet1-eor-I.

easil.ideducedby SuPer叩 一叩 the亡aSeSfor Presentedm thLS Paper l=0抗nd-herela一

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I?～-/'r'(三17:(i) (4~1㌦ a憲 三n:ac.tGLc:ettcha:pep::n:S g:憲 芸

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"llhc鮎川gthlckne≦sY

Dq=n ax】mun detonat1011､eloぐlt)

L=erlt1Calreact1CZ)ume

R,-I(-R{ TlhtLrl!

R.=crlt)CatradllJi.

て.-lel∝】l〉OfSのund≠alClndt･tortatt｡n

productS

】一声thlcLme55OL 亡aSeS

て..= eヽl∝ lty･OEAShock lヽaヽem rrLat亡ml

otcaslnp

lれ=maX】mum reaCllOnttmC

(DDT)'-(/,-::)tL･-1'IIJl･(忘)′～ (4-2)

orは)2=.･BR (4-3)

vIhere･Lt=(,e-;I:)土.-=': ,1-(413y

β- 1 (= )′′lJ,I-

Theequatlon(2-17yJ'EorthelmEl･efLeC【

ar)alheequ.lLlOn(3-5)EoHheradluS-e鮎et

arethespeclfltC8S也 OEthegeneralequatJOn

(4-2)respecll､t･))～

lO) hlA Cook■tW.≡ Partlldge I PhヽCh<TT156tT一寸'5(7555).

10

FoTexamplektusconslderbare亡harges

(1) FlrLda【ktonatton ､cl∝ lt)Dlfor

radluSRlandD,torR,

(2) Calclllatelherna/1Imun detorlユ【'On

､elo:巾 D_OrflndlLb)experlmentStora

muchlargerrid)usR_

(3) Plot(DJDI)Iand (D'ID_)≡on

∫-aX】SR,andR,onthe,T一皿JSaSSho､､n

mFlg6 FromtheStratghtllneEF丘ndEhe

nunerLCal､aluesofLr,nrtdR.

ta- -B-1･.1/_ (5-1)

A-÷一意 (512,

IL山-V.(ん.-(.)+rt. (513)

(4) CiLkulatetlleI,elocLl),OLsoundlll

detOnaLlonprodljCtSLhenndd)nz)m)ぐ811.I0日o

atlrStaPprOXLmatlOllb〉theEoLlo､l･lrLgequa-

tlOn

t･--㌃ D- (5-4)

･5, DD;- 075(Cock) (5-5)

or (蓋)'-0563 (5-5,,

Tr10血ernOrdBllma)k sEa一eJthat●'the

uF l958⊃ KllmaOH■no

亡T.tLCn1mdlUSOfEKE,]05L､,eCharge- i.hc ThecrlhC.■lreactLOn-ZOne･】en#Lh

radulS"IwhLChE" EIrlrldgedetonates≠ltl

anI:斤t･cLLleheatOfdetotlatLOnllhlChlsこIbout.tc-Dft. (5-9〉

onehulEoLLhcmEIXLnum heュl0tde10n一 臥 useoftheproceduredeserlkdabo､ビ

ー10nLr ､､eln皿)ILhdthelmpOrtaT'tCharaeLer1SL'e50f

ThenTrom Fl居6 ､､ecdrLhdtht=crztLCa) C叩】05■､,eC･lrtndges,b)thelnmlmumnumhcr

r3dlL･SR, ofdetonatlOn､Cloc■tymeasurement5,､､hlCh

(6) ThecrltEC81reaCtlOntlmeI.王Sfourtd hztvL･greatpraCtLCaIarLd山eoretzcaltmpor･

ailfo一lows lance

From (SIR), 烏5-2 Example

l三 九 +凡 (5_6) ら.､.Jen,::h:S:700芸 ごこtnr,aLtteyPde=T Li:C/:me.;J':hOe-

experLmetlは1■dzllaOnJiaridD havebeen

From (5-3)･ foundaSShoIVn.nTabteI lnlhl,CaseD.

1.-E｡- 礼 -Rc-/.--- (517) mayb- Opposed【obe.

l),.芸3620M/See

lltlt'rC RN,"-uPper･】lmlL.thlぐknessofzlrt

exp】05LtC Shell nroIJnd aTabLel rTLmOrleXplosLte

ent】calrnd】115 R 亡m O185 1･25 1o O･0

(7) ThemLuLm｡m ,tact.｡n-Zone-lengLh DnlSeに' 2870 3210I3420 3｡2O

JY..-D-ん. (5-8) From FLg10 "ertnd

rltabk2 CAJCuhledchrユぐIerlSLlぐSOTreaCtlOnエ011eSLrtdt･lOnAlLOnOtLOlLdex ploslle5

ト

jBO rheOr､OETelat】on､bcITlt- -hcL1ヒtOnal10nVeloellyOfsol】tlcxpLosl､e5 rv(･= 9?＼8 3.'Lntllilelhl亡krleSSDLc.lSe30rthe()ILIm｡tt:TI)EtheElhargtb

I--LIIl

Re

Yl亡Ite'EtE一~_亡Lr

Flg 】O Perrn■ttedAmmonexpLo･1､t･(Jd 0g,cm'(lureCbTgC)

R戸059cm

:I;0365

B≠tzln/γ=0308

'rhen ･J.-0302×101cm/sac

/m-1075/1SeC

D,-0272×101cm/5eC

Vq-3S9cm

(5-6) tc-609FLSeC(5-7) J′-608/-see jLTe-ユ66cm

喜6 (;e"cr･Llmlesorbt71ereLIt.tJl川

tLmCmt)0 L爪/LcandtherellC-

110n20Tlele-1gthm t)oXJX,

]L≠ eassumethefoH0､､1mge7(peTJmentTL]

ru)a(6-1)zlmOngthecr)ll亡alaTldm.lX】mUm

deton.ll)OnVe】oclt),Ⅵt･m叩 fmdsomeruZビb

ofpractletLl lllSeFortheTeilCt】Ont】meZllt(I

止eTellCt)Onlone]e叩lh

D,/I)..=U75 (61)

(1) ReaLll】OnllmC r.mO

Therfll】00ftllemnXlmlHTlrt･｡lCtL()ntエme

ldtOthemlrHmum (cntlLnl)rt:actlOnt]mtt

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/;-(普)≡-(ol75p-,7S (62)

(2) HeaCtIOn20ne)ビr)g111r･,flo

TheT.ltlOOfthelrLaXJmtJm re.lC一LOnZone

lerlglh_ll,〟tothecr州C.Ll(mm･ml川1)reachOrl

∑or)t･length.Te)ら.15(0)lol.JS

音-DD-.(;=(?,;)(DDT)と-(普)A-(.1･/5)1-238

(6-3)

】nTable2 theresu)ts()ItileeRl(:ulal】Onb

bEISヒd or= lle presenttheory h'1㌧e bビtm

summElrlZedm comply)≦onWLLhthe､･alu｡b

ofthecor】StanEreac110nl】mtlIuIldtheLOn-

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cILZSSleal亡qUatlOn5SuchasJolle5tlndE〉rlng

ckrtow]cdgTTle‖t

TheauthorthanksProl H JolleS,PrL)f

A lモUbbelohdc.1ndPTOfM A Cookfor

help)71gTlTS researchbyhavH叩 Senthlrnthe-r

oヽvnreportsonthesubjヒCt(1t;scrLbedlntht:

pTtStnlpaperlie alsoappTt･nnteSthe]ntere･

･ゝLI'lg JISCUSSlDn Wh】ch hご 118d w)LhProf

Cookat･.heUnL＼t:rS)1),OLUL.11…-thespTm g

oE1956

12