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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
LetusassumelhzltthereexL515ZICnt)eat
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
FromF.gLIWeLlnd
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
Le■dueto【ht・WallefkctofthepartoEa
cartTldgeRl,that)I,、、ema)assume,aSLn
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
ユTPmentabln喜2 leads toLhleIotlo≠lnき
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)
whereR■芦Lhlt:knessoEnn outerSheH o
T.IczlrtrldgearoundaentLCa
lTlldlUSR-radlu5
0f(atotal)亡AnrldJZt・R.-cntICaIrad
JuSD-deIOnZltlOnVet∝tt)(orarzL
d[usRD■-maxl爪um (or】deal
o=htOTt・llCal)dt:I()rld
t)On、eloぐlt)I■≠mzIX}murnreael10ntime
I,-CrltlCal(ornlllLmuTT))
reacLl0】111mt・(a/I)
I)I-(∫.,(..)+(R-Ju/(
1・.∫..) (3日or (D/D_).=lI.I一一II./(1・./-)] A.
A.A-ll・・■'■土・r∫・Flパ 7 50/50AmaTOl(tmr亡 Chzlrgt・)(DAt8
EromColIkc一hl・1-÷(,El号), (・1,--t・-::)'JrLoptlleI:rLtlt:alrea亡LIOrltln e.
,.=_4,.十Jtt.+
1.・.tanLr -.
・.1‡.T..--D-Ll・t-D・
,E・(票)D
6
7
8
9
3
㌻
3
3
I-(,+R・(39y
:lbthe10
Lltlreactl(】nLIMEIC.lLlntJteXt;I.tiLdぅ+亡1I(;・ん )コ/I (3-5) themtlX'mum reZICE'On
tt■加/- "erlnd.or (I)D_)7-.1+BR
(3-5y"here :1-I,I_-R.
I(1,,I-) (3-5y'B-1(I.II) (3-5y′
JThequat'on(3-5)'srepre,iCnled ZLS
ast17Hghtlm e、川hrespecttO(a/D
.)landRn FtE 6 The、aluesof.IartdB川(
35)′rnDyt妃 eaSll)・fou'ld川 F.g6 Th亡reEore・
(.-(.+pLlゝL-OrR-上1.(I
--(.)t●t (310
)Aboヽe8Certam rad・usJL.thedl!lOnRLMn、el∝ tl)・D do也 nOtlnL.Tt:3Ljrt="henR
lnLre・ates The zヽLlueoIR.■⊃
t!lヽt・nら)je.-(〟-)..-
Ao月I95g KumaoHmO
、vht!rt・ It.=upJXr-lLTTnt
-radluS告3-3 ConpnnsonWJth
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
阜2 (thee鮎ぐtOECases)andi3 (the L10nSt*1、・eenthedetona110nYetOC】l}・D(and
eだeCtOrtheradiusOTcanrldgeS)itsf01lo"5・ thedetona110n pressuret'nwhEChtsorprac-tlCallEnpOrtanCeErorrlthestaTldFN)】ntOfthe
I?~-/'r'(三17:(i) (4~1㌦ a憲 三n:ac.tGLc:ettcha:pep::n:S g:憲 芸
yher亡 thedLamelerOfcharges氏ErorrLeXTXLr'menLt
I)-deto"atJOn 、et∝lt)atradlU5Rュnd asfe"asposstbte
"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
/.JSaSfol】oヽ\5
/;-(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-
もtantreact)OnZOZICLerLgthc・Tt)cul・1kdb)tht=
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