THE O RY OF T〟g B U R Nl NC RA TE O F / N Du S T R Z A L S A F E TY F u S E

FIP'

JOUJLA'jLLOFLTJ

I

^{EJNDuSTRIJLLエXPLOSJyJS SOCJETY.JJLPA.V ORJCI^rjuPJW ER}

THE O RY OF T〟g B U R Nl NC RA TE O F / N Du S T R Z A L S A F E TY F u S E

(RtcelYedJAntnr

y

19.1954) By KUITAO l･llNO

(TheAsaLLlborAtOry,TheI(叩TXInI(a)AktlCoLtd)

^汚CmJICr)叩Lrle.llLorllttlh 帆hLChrepTCSCntSthercl爪tl01日lmOtlgburEl'rlg

r a

te.PreSStJTeOE LIOmbustl0r)pTOducLSAZlddeZuLtyOEbJzICkpoVdl:rI:Orel】Pre5entetl

UTltl亡rthe亡OTldltzoTIOfStAtlOnAryburTILElgWblChlSr伽IIle(Hn routlnetesと川tbeopen

LItmOSPherecquatlonSforthercIBtLOnSnrnOng thc托mOllntOrlEIter81discharge.AJEhII LIJSChJlrgeOfcombllStLOllpr(KluL.tSJITldtbctlIstADCetrAVellcdbycombustlDTIErotltArcderlヽ･CtL

Thcrneth伽ltoreTnPmCilldttcrmlnAtlOr…Ltheco{爪亡let)tSlnVOhedizHhecqt)JIuOnSArc d亡〜CTlk l

^ zlquALIOnlSderLVedEorthetlIt･AltlmeOfeOmbtlBtiorltorA恥(叫 fuseo†且gL＼,CTl lcTlgthtJndertheeondltlOr)OEIALerdly coTnpleteLAmpll1g WhichLJZ=eZLrJy r

e J L l ‡ L e d川

pr■cucL h deLnbcreb｡leLFrom thisTelJLtioユtbeeJEpOtletlt■ZHheburn.T)ど ttEeequAtlOn

eat)bedetcT771ined EmplrtCZLITed tIWhi亡hoon丘rmtheqluLIOn■Ared亡父rlbd tuthdlト

c

^{tlJnOnOnthest･&blJltyofbtlrElltlg}

ln of

T

h

en,thetwo‑Lerrm ftmctlOn Which maybecalled a''Linearformuh ●'has WhllesaLetyfusehastmnwldelyused beenpresented

lndustn;llblaStlngfor the )gnlt】On black powperdlarge Or detonatiOrL caps.notheorerlCalann)ysISOnitscorn‑ buStioncharactrIstlCShaskenattempt‑ ed From the pDlntSOEvleWOEsafety andefrlCIenCylnbhst

l

ng,aSafetyFuse mustberellableln Itsuruformlty.lnd stablLltyOf rLlteOEburnlng ､Vhlch are greatly lnnuenced by cozldltEOnS under lVhlchltlSbllrnt

Thcory 1PrcsstJreandburnlngrate

From thepractJCalpo】nlofv

l

ew.the burnlngヽelocICty(vcrn/see)ofasolld explosIVehasbeen expressedbyprevlous a

u t

h

o

rs,as こlfunctlOtl Of pressure (pkg/cmZ)aIWhlch )tburns

M

ostoL tlleSe runCt10mS have ben emplnCnl although some thecretICal deductlOnS haveLmnattem咋d̲

The mostclassical but l:OnVenlent EuncnonisthefollowingwhICh mayh巳 calledns''n･thpolVeTformulaI.

tr.‑azpl (1)

t ･ . ‑

4'+A,p (2) From the stalldplnt of the klnetlC theory of

g

as,the folloWlng functlOn ヽl'hlCh may tX CaLl

e d

"propcrnonal formula●●hasL治enSuggCSted

vF bTP (3) LEIthe present atJthorJs a oplrHOnL) TlOneOfthe three equal)onsdescrlbed above ci一n represent thebehavIOur Of pressure‑T;lteCurvesOverWlderangeol pressureandhesu皇geStedamorege†leral funcLlOn,that】S.

LFa'Pl+L･.p (一I) Tt'sconslderedthat(3)holdsfoThIgh pr6Sure mnge lvhlle (2) holds ln medlum Pressure range exClud)ng near zeroprB Sure For lo､v pTe弘 urerange mcludlTlgrteこlrZeroPrBS

u

∫e.thefuJICt10n (1)lSthemostrnt10Jnlandconvenlent aHeaSta一Pn巴はnt

JL TernlXratureOEcombustionandburn.

lograte

JJltheauthor●sslmpli丘edassurnpt!on

hIart=h.1954〕 加^rnJngVetocltyOrSaf叫'Fuse

overlolVpressurera

n

ge,theactlVat10n ofsollde〉叩losIVeSurhCebythecolllSIOIl ofcombustion productsplaysasltlaller partforcombustlOnWh)1ethe･lCtlV･ltlOn bytherュd)atLOnfroTnhotgasestocool surfacepLaysamajorroll ThlSeIlergy transfer maybeexpressedto the first approxlmatlOnbyp≠Tん,whereTISthe temperatureoftheburntgasesForthe TこIdlatlOnFrom SOlldbody(thecombus‑ ttonresldue),7J‑0,/‑‑1.whlleforgase･ ousCO,').'l‑1/,,A‑35,forgaseousJ

l ･ .

0,

〜

‑‑/R,l･‑3andothergasessuchasO=. N:,shownoremLlrkableradlatlOn

For hlgh pressurer'l

n

ge.theactlVa‑ ttonofcoolsurfaceby thecolllSIOEtOf actlVegaseous moleculesplaysaTnaJOr p

a

rt,theref

o

re.thetemper.ttureOfcom･ bustlOnT mlghtaffect thecombl▲StLOEl ratebytherelationPC‑I/I"､Vherei,･kac‑ tlVatlOn energyandA‑gas constant Theretorlngeneral.

V‑a,r･1)I+b,1"‑lNr u∫■■tl■■■r ウニ.∴̲ t1‑

‑

^{vJ' ･.‑UT.}

一匹] _{｣ L} ^‑ 一 一 ^V･

^し

⁶

^‑

ローv レ B

Flg1 Arrat)gemenEOfpo"dergralnS

alollg二日目はLSOfaLTu5e

皿 LoadlngdensltyandburrHngT'ate ltmaybcasstlmed thatagralnOf powderunderdlSCuSSIOnlSaら(】Ildcube whosesldele【lgth

l

^SI,,and thatthe dlStanCe

b

etヽVeentlVOgratnSalongthe dlreCtlOnOfburnlnglSI.as ISSChcma‑ tlCallysholVnlnFJg1rnF)g1,tl.and I,｡representthellnearburrltngVeloc】tleS

throl】ghthesolldgralnprOperandthrough gaseousproductsalongthedlrectlOnOL burntngrespectively

ltlSaSSurnedtha= he propagat10Z10f combust10nfromonegra】ntoanotherlS through gaseousmed^lum F

l r

St,1fthe denslty OfcoreAg/cmllS.lSSulnedto be1,andthenllmtXerOflayersoEgralnS

wlthln 1 clnalongtheaIこLSOfasafety fuse.lSe)咋ressed byM.then wehave,

JII(l

.

十J.)=lcm

TlmeOfcolnbustlonfor1cm th上(^:kneSS

ISrepresentedbyI

JII(lpj･1‑ILlJiL+

｣ U

i

=

(

IfW

e

traIISfelthe

d

ensltyA

.

^t

^o

then t

l l

e

t o

talth1(:kn

e s s

of tlle

I : l J. I s o l i d

becom

e S

LVり(,.､Vhllet

h a t o

fgase

o

^usspace

decreases

t o

r,l

り

車 ^ l/ク

Tfヽveta

k e

∠70

‑

1.A‑

Ad

, then

‑ ､′吾,巨

q

lli･;‑

j '

′q(:;i

･ : : )

‑▲､′Al(鴇

.

^吉 )=箸 ･苛 AA orburnlngVeloclty

t･C‑/sec‑チ‑｣,∫(Lp晶^.Aま),

wllh‑hesubsrltut

l O nNq L q . +

:

J

qE･‑1"e

obtaln･

I

毒 ‑ウE･

I l l t 4

V=V.十

｣ V l . ( . I . ‑ ‑ I . )

dl

lFtherealdensltyOfthe solld lSln‑

dECatedbySg/

c T

n'.therLSl/N'‑AB

‑

1

.

therefore,JlfLFS‑i

わ‑両

^{莞 ) AI s ‑ ‑ ㌻}

⁽⁵⁾

･ r ‑ L t ^轡

Flg2 Pro亡ed一lreOf】uSいflC8tlOn fortrg>t･.

InFlg2,tlVOp】eCeSOfa safetyfuse, each pleCebelng10cm lnler)

g

th,are separatedbyadlStanCeIalongthedzrec･ tlOnOfbllrntngWhenI‑10cm,thetotal tlmeOicombustlOnlSabout254sec for atyplCalbrandofsafetyfuse,ヽlhllethlS EtlSe､Vlthalerlgthof20cmburnswlthln

1 3

ZLI Kunuo

f l l

n

O

〔Vo115,hlo I

≡

t

=citeB;h

t a h t

%

e e

:lee,a.sc

; t y e m

.;n;:こ;vaega;::

V = a r A p l (

評 ^(9,′

through space

】

s atl

e

as‑ 戸品 ‑25 or ･

= ･

11

･ ･

⁽部 ^(9)"

c

m/

sec･w

nht h a

tfor

t h

efu

s e

^pr‑ rl steadybuzTMngCfaSafelyfuse

t=芸‑08 c

n V s e c

^.lher

e f o

re･wem ay a らl Ex阿 ‑enCeha,,h｡wnthatan.｡｡Lutm｡1

su

m e

that

L

.

>t･

.

(6) ThenヽleObtam

r ‑ L ･ ( A

S)l

( 7 )

R SchWabq has derlVeda dttferent EuncLLOnfortheEel?̲tlonbetweenloadlng densltyllnddetonatlOnVelocltyOfpoIV‑ deryexplosIVeSaSSumlngforthatcase

l g < t

,

(

⁸⁾

Frornthee:叩larLatTOrlabovedescn

kd

, thegeneraHormuhforburnlngVeloclty l】uybelヽrlltenasEolloヽvs

L ･

‑(仰

･

わ

ー

晶

p l (

^{三)i (9)}

r < l f C l t r p J t ･ ‑ 1 o eL L t J ･ ｢ 止 J l 一 ‑ ph r l c d L

4‑gこらor■ b

F】g3D151rlbtltlOT‑O

tdtschlrged

gasfrom asafetさfusc safetyfuseburnswlthunif

orm burnlng ratelnopen atmospherewhlc

h lSthe CaEselxacnrtlysOutFklnaetkests

l

ng,therelationbel､､een the to

talbuTnlngLLndthetotal一ength ofafuse

Lmlghtbeexpressedby L‑J一十B.L

IVhere .1,

andB.arecotlStaJltS

･lspractlcal

ty ‑lllSVerySmall,ヽヽ,amay assulTLC

IVlthoutserlOuSerrortllこItt‑B‑

/･.that

lSltheburnlng】SSte･17dy Th

ed】stanceofthetT｡hVeloFacom‑

bllSt‑On

frorlt】SmeasuredlTOmthe】gnlt‑ ed

endand】slndlCatedby2cm ForこICert

LTIlnPerJOdafterthelgnltlOn, thegaseo

usproductsofcombushonare lTLalnly d

tschar苦edfrom Thelgnlledend

Lx=Cause

laLeralresIStaIICefor the dlS･ chargeo

fgasIS greaterthanthatLor axlaldisc

hargeThlSprIOdmaybedesI crlhed

n

s"

cnd‑dlSChargel氾rlOd".whlle after

th千spemodthedlSChargelSCarned out

throughthehterltlporous＼Vallof a lu

sc andtJllSSecondstagemaybc callcd''1ater.ll(lisch;lrgCfnr)

Od一° ThetlrnOuntOfdlSCharge Gr,p

erurHt tlm

e

lS.aCCOrdmgto thertLles

ofther‑

motIy

o･

n't

=

Tn,

l

,CS,aSFollows

I

( L i l ) A ‑ 1 ‑ / L 2 i k l T ,

^I,I

1 ,( l l

) WhereA‑raい

ooFthespeclttcheatsof thegaseousprod

ucts.lrCOnStantPressure tothatntcons

t.TntVOl

u n

^.̲C,ど‑thecon‑ stantolg

ravlty,J･'‑effectlVeSeCt10nal arep･of

dtschユ

T ‑

ge,p‑gasCOllSt

a

nt.T‑

temIXra

rureOfgas.9‑pre弱ureOfgas, andや】Sth

eCoeL7icICntOEresistance

f

^o

r

d)scharglng L7olV Asthe resistanceE or gfuasseeouInCs drealSCh',.rgc alongthe axisota

SCS.TISthecombust10nproceeds. TnthepresentpaFX:ruhlchdea

･ll瓜eh･

1

⁹⁵

4 ⊃

^{Bt･rmz)gVeI∝‑I)ofSJlfelyFuse}

1Vherev〜lSthevalueofゥりat正‑0)E1denotestheeffectlVeareaforhtemldlSChargethroughporousstnlCruTeofthes.de､ValloEafuseforl'nltlength(ユcrrL)oEこlf

u

se,thenthetorateEfectlVeareaavallabletorthedlSChaTgCOflllegaseousProductsmaybeeL･preSSedby7rD

t/J I+

岬,WhereDISthedlarneteroEtheseetIOnOfapoヽvdercore Thercforeatanydlstancea: vJ‑‑中●(7rD!/4+q.I)/(1+b)(13)Jnsteadystate()fbuTEllngthevalueoEpj●shouldbeindependentofthedlStanCeI.rhuslヽeObraintheLolloW･lJlgCOndltlOn throughlateralWF.1日s

o

･‑甲｡

iT bxKp =恥

議ム''･(19) 01couTちethereht10n(7㍉=0.+0.holdsForThetotaHenslhoEafuseLcmthelotaJamountofgas O'L‑(恥F.I(

p

)

L

(20)

theamountoEdlscharsefromJgmtedend

oJ ‑∫:

仙這正人坤軸F

.A‑I,)･ t

L一三芋10g(l･

b

L)i(2.)

Theamount｡tlateraldlSCharge

･ ･ . ‑

苧 I ^｡4'

G J Zl . ' 恥 ∫ 7 ‰

‑

lfI]SSrn?.l

l

V,I‑ pl=p･(汀.D圭

p

.I.(15)

､､'here I･'‑secnonalareaof thepoll,der core

lf之･S一arge pF'‑9･‑若 (15) く15)an(l(】5)Imean thatshortlyafter thelgnJ【lOnthedzschargeoEgasISmalnly reLIHzedthroughan lgnlted endlVhlLe

･

lfter･lCertLllnTXnOdthegas】sdlscharg‑ edrhrough tllate

r

alヽvall

(a)AmountofdlSl:bargeln‑̀crld‑dIS‑ ch?.rget光rJOd'■

･E､､･ede

h c ^ ･

=

(

k

三

1

) l i l . /

k

e

g.J1.,ll",

‑(恥]･^

' p

^)乙㌘ 1｡g(1･bL) (22)

‑f､､edeheo?.Ji

‑T

,

thenr･1=S:JLi=憲 …4.‑% (23) A

s theranOI Or7･+1areeasllyd^e‑

lefmlnCdbyslrnPLeexpeTlment;ItlOn,We caJILtndthevalueofthecoe打1Clentb (ら)AmourttofdJSChargelTla川Iateral dlSCharge叩rlOd

TotalamountofgaseounsdlSChargelS thesamelVlththatJnCase(a),thLltlS.

Gr,(I‑(恥FOKt,)L (20) TheaTnOuntOFa:くIaldischargerem111nS r】‑esITIITt.e <TlfLer先>x.ヽVhere才,denotes (iLPOWdeTCOnSrnnt) (16) rhc lcngth whlChcorrespondsto the

､vhcreA‑125.Rr

‑

(.(foICCOfpowder) PerlOdofen'ldlSCharge thcll＼VeObtaln

oJ･‑(Q,oF

J l ‑ p ) t a t ‑

²¹³⁰³

･og(1･bx.))‑ const(24)

Theamountoflateraldlschargc after エ>2.1SaSfollows

Gr./A

‑

(,[〜).I.JJz･)L

‑

(tPoJ･oKp)

(

2･)等 310g(1IbI.)I

F(伽f'+A,p)L‑Const (25) V VelocllyOfburnmg lna StatlOnary

l:OndlI10n 15

･

,‑3

,

oi c‑/scc

lnsteadyburnlngthetotalamountof gilSeOuSdLSCh.lrgeperunlttllnelS

O,=(中｡F.EIzJ く17) AmountoEdlSCharge perunlt time

throughtheJgnltedendlS

G･印

｡ F･ r 完

L,

7

･ (18) Amoullt OEd】scharge lXrunlt tlme

rfWedenotethedensltyofpolヽdercore by 4 the WelghtoFpowderperunlt lengthofafuse^ls7r/4D亡AIfafuseburns lVlthburnlng VetOClt

y

1,the仙eZghrOf powderburntperuruttl111e^l

S ; t / ⁴

D=Al IrlSteadyburnlngthlSWetghHSthesame wlththetotLH amountofdlSChargeper unitt

Z

me,thatlS^0.‑,/bll

.

Kp,】Ewea5‑ sllmeThereremalnSnOSOlldresidue Tf Therelssomesolzdresldue,thlSamount canbet'lketlInto(:alculatlOnmOdlfylng thevalue^{of (p}o

ThusIVeObta)n ,p.Ji'p‑Al･

･vlththerelatl｡nV=･J

p

ⁿ(

A ^S

^{‑)舌(9)′′･､､,e}

f

indpoKp‑･lJ)≠SiA言,theref

o

re

,

p

i

欝 )

t A

^{l (26)}

｡rv=.JTT･(V,aK)亡

s i 未

如き(告) (27)

A s

^IS

^{S h}

^ownby

t

^he

^e

^{quation(27),vls}

l

n d

^epe

^{r L d} e n

^{tof the d】}

^a

^{meter of the}

p

o I V

^der

^{c o}

^{】e Wlth}

^{t h}

^e

^s

^ll

^{b s t}

^{ltutlOn Of}

K

‑

芳 lntO

( 2

7)Iw

e

obtazn

v=(2

07

‑ pq

, O ‑ ^{･ ･ L L}

卓4'q五

㌧

中 (27)′ Forexam

p

一e,lfweassume〜‑05,/1‑2 forJ‑CTA,jL‑0

3

8V.Twherel'.zsthe speclflcvoJurneorgas atnormaltem‑

peratureandpress

u

re,ヽvefind

I . ‑

吐

I ,

些二

‑ L t

^{C ,I},.MTl･SMTA9,･ (27)′′ ThereL乙IrlOn(27)′′Elves eStlmatlOn On theeffectsOfvarlOuSfactors such as

,

temperatureOEcombustlOnT,realdenszty of po､vderS,frlCtlOnalcoe抗clent

9 】 . ,

specltlCVOlurrLCOLgasVD,andthe load

‑

1ngdenslty∠J 恥 dependsnotonlyon thestructureOEafusebutalso on the natureand:lmOuntOfsolldresldueafter burn

l

ng,andtheadhesIVepropertyOFthlS resldueagalnStthelnSldewanoffuse thre;lds Moreo

v

er, m a commerclal safety f

u

se.Core threads and lnSlde threadsofafusecontrlbutesomearnotlntS

oEgasestothetotalamountofgaseous products WhlChare producedfrom the powderproper Thesecorrectionsmust betakenIntoaccountbymodlfymgthe ヽ,nLueoFthel:Oe朽clentや.

Ⅵ BurnlngvelocltyOfsafetyfuseunder laterallycornpletetamplng

lnprこICtlC三ll

u

se,1tlSmoreCOmmOnthat asafetyfuselSlgnLtedWhllelt】Slateral‑ lytampedlnaI)orehole,thecompleteness oftamplngnuCtuatlngfrom casetocase TnthlSC

a

se,theburmngoccuzTSnOTnOre understat10naryCO】1dltlOnbutaccelerat‑ JrLglSreall

z

ed,theref

o

re,thescLlutlOnOf lheproblem lSpraCtlCallyImportant

Tncompletetamplngqtendsto zero. therefore,the amotlntOfdlSChargeper unLttmleatthelengthofafuseェ

o･

=駕 砦 (28) InequatlOn(28),the valueofp IVlthでhcd】stance2,Ontheother

VarleS

hand, theamountofgasproducedbyburnlnglS

o{‑JIo･.1,〜(i)主A‑Fo･11,

¶

^{SをA書 (29)}

AlthoughthevalueoFpln(29)varleS WlththedlStanCea,the amount(28) correspondswlththatof(2g)atarblt‑ r

a

ry3,t^hereforelVeget

q'iJioi'p‑FJp"S}A3

orp‑(響 )fi(1咄 声 (訓, V‑‑1ti‑ I

z

,〜(芸)古

=(

‑

^{二や IA 抑 (1‑ 辛}

+, T

^k(,poEIT'･S

志 A

惜

) ) I

(1十

b i E

)

1

一･ (31) rfWedenotethevalueofvata‑ 0,by lo.thenl･omeansthebl汀n】ngVelocltyln freealllVlthoutlateraltaTnplng

l.=L｡(1+La).I. (32)

hhr叫 1954〕 LIurnLtlgVcloc▲t〉,ofSafet).Fust, 17

Ifl'‑05.then

ll.‑γ.(1+b才) (33) rEIPraCt

l

Ce.the totaltlmeOfcombus･ tIOnI.lsImportantfor､vh]Chweobtaln

J= =旦二且 1̲.

･ ･ ‑

I川.(

1 . b

^X).,(.一

･ ,

^{(ト2,.)bL.｡}

( ( l ･ b I / . ‑ : : ‑

^{i) (3"}

rf ll‑05.then

Lz‑I

｡

^{窒 ‑tlJ"(1･b'･)‑}

ぢ堅担

g

(1+bL)

r

J

l ⁽³⁵

)

且 ErnplrtCalResultsand Calculatlon foramounts0EllaS

ETnplrlCalResultsObtalne(lforthetwo klndsofcommerclalsafetyfuses,brand 1and2,are tabtllこIted lnTable 1and plotted lnFlg5

･L

l

_cy^{.TT T}_llEdtT 二二

≒ ' ･ ･ i

巨 r･

Aslle areable toflnd thevalueo

f

AbythelnethoddescrltcdlnrV,､veea一一 fmdthevalueofIzbyplort

m

^gf.

‑

^I,for

aglVenValueofbtryJngViLr]OuSassumed valuesfornlVhlCharetobelnt】】erarlge bel:lVeetl1ごIndzeroThenuTnCrlCatValue ofI,Ln(3Jl)】sveryserlSlt)VetO the帆l

l

mutech:LngeO

F

l･,theref

o

re,weareabl

e

^rd)

to(letermlneTheexponent71WlthConst

‑

derユbleaccurこICy

ErJ)erJn(･ntnl I Experlnlentalprocedure

The.TtpParntuSeSused】ntheexperlrnent

EoabrSL,鷺 iatrniiu:(5hfr,ili;:uouilisLl'ol漕 i'(?jf E喜;≡…≡≡‡…貢 重 義 ?;rnEtnc,ogEeg‑

TZ‑eprocedureemployedISVerySLmple (a)LWeLSu,lng吋】,Ode,

･lndl【maye:lSllyt光 understoo(tfrortl Fzg4 AT)r‑ LL‑ EormcjLAUrlng thelllustTarlOnlnドl雷 1 AmOtJn一OfdL5ChLLrgedgas

Table1 TorAIAmOuZltbfp与(G.(･)andamot.nto[etltld'9,hユrger￠J.)

18 ⅠくumAO

H 叩 0

⊂Volz5.̲〜,o 1 Flg 5 shoWsthatforbrLtnd 1after

rJ

=

B.‑30cm (forbrand2.L=x.=20cm) theamountofenddlSChargetcJ一dstoa constant va

l

ue, therefore Eor brand 1,xF 30crn)sthebound:ユrybetweenend‑ dISChargeperlOd and lateral‑dlSCharge perlOdForbrand1ntL=30crrt

M 3lL'vh .t7lZH (V'1さtofNJd p 血･日 中 )

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Table2Tot瓜】tlmCOr｡OTllbtLStZ

O

I】 lAteTAllycomT)lctctJITZlp

h ]

g

(Ll) Otz.e°ed

名臣 121･hL‑030,b,=0015

Thesmoothcurves shownlnFI尽 5 arecalculatedbythefolloWmgeqtxLrlOn

( ;

.

L

='p

J ‑ ･ A , , ･

,

(

L一三

欝 o g (

1÷bL,)(21, whllethevalueof(伽fl人,p)1SCalculated bytheEollo､vlugrehtlOn

(,pJ･'J{7･)

‑ O iL l

(20)

TtmaybcscanfrolnFJg5tha‑agree･ mentbctweeIltheObservedandcalculilt･ edresultsISgood

皿 EmplrlCalresultsfor burnlng WJth latemltalnplngilndcalculatedresults SaEetyfusebrand1､､‑aslrlSulated ag･ alnStlalernld】schargeofgasbyCoverlng t】ghtlythesldeotlいvlth】nsulatlngtape Eore]ectrlCCodeandthin(̲opfNer Wlre To;､scermln thIlt there tx=nolateral

eSCaPeOf

g

ag,ttlCtotalamountofgas dlSChargednxlatly from the 】gnJtederLd Was =L150meaSured For varioustOtこll IengthsoFthesafety f

u

se,brand1,とhe relatlOTlt*tlヽ,eCnthetotaltlmeOEcom･ bust10n EJandthetota一lengthof the fuseI.lvasmc.lSurCd forthlSStateOF latenltycompTetetamp

l

ng,the results belngShoIVnlnTab一e2andFlg 6

ThetheoTet】Calrelat】onbehveenhand r.At)rttoILlHcngthor托 fuseIITlth

㌃完 ー ㌃l w

^{言 完 二 ,Lb,.芸og}

.ht

A

rch.1954⊃ 伽TnLngVelocltyoESAfct^y Fl娼e 19 I lsasfolloIVS･

t･‑(1 ‑2'i去

( (

^1+bL声^{‑1) (叫}

8ythemeasurernenloF total一lmeOE bu‑ 1ng Ofa fuse for aglVenLength

｡叫当此又tqF輔が､uT.{F︼g6DeteTm‑1nuOtlOftheexpqentnbyll⊃erehuJEIT)bモIVeet)tOultlnleofcoTtlbtStlOIl且ndtotA

HeTlgtbofAlll父

LwithlzLter山ayc o mpleteLAmplng(L=100⊂mlnthlSexample)wlthoutlateraltampln g,lVeObtained

r

･

=

農

芸 ‑0833cmlsec･

lVithsubstit1

0n()fassurr.㍗ edvaluesf

or

,

^‑I‑113㌢nto (35).wecal

cuhtetherela

‑

ttonbel:wee

n L.andLWlt

h

thevIl

luea‑ 0065cm 1 'rhecalcuh

tedresultsar

e

Shown lTI

Table2arLdl

n

Flg6 Ther

esultsIn°‑la

t

^e

th.ltII芦0231 JS th

e most probable

J)iscu

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^Sion

1 Stablllty

OfcoFtlbustlO

n

EnpractzCa

l

u

se,thest

a ･

blIItyOfcoT

nbustionlSOne ofthemo

st】mprtantr

e ‑

qulSitesforsafet^{y FtlS}eS

0. = (

恥F

●R1‑a,p (17)′ WhlLethe amountof

gasevolvedat combustlOnfrontbyburn

lngOfapowder peru

rLILt)rTleis

O.=(FJ tl)‑(F..LSi

A

i

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0 ,

p' (36) Steadybum ingcanbere

allZedatpres‑

s

u r e

p.a= hecombust10n

Fr

o

n

t .

p‑t光lng deterrtllnedbythecrossing

po)ntp.oFthe stralghEllne(17yandacurv

e(36)coltCaVe downwardasareshown

z

_n

0‑

prel

at】ons lnF1flg 7ally SmalldlSturba

ncecausesll】t IncreaseOfthlsstar)ona

rypressurep., say,tolJ.+6p,thentherat

eofgasevolu･ tlOElby burLl川g Wlll

belnCrea5edby6Ge‑1･C'tJI‑16p(37)therelatlOnfoundcasllybydlEfe rentlatlng

(36)bwlelngth respecttop.lVhlletheこI

TnOulttOf dlS‑ char苫eWlll

beIoncreasedby

‑GF Olep (38) The^lrldexfortlleStabili

tyofcortLbus‑

t10nmayberepresented

bythespeedoE readJuStmeAtOEthisdis

ttubed pressure

p.+etJtOtheoriginalp,

This^Speed

. l

d

,

maybeassumedtobe

proportlOnalto thed!fferenCebe

tween(60,一dG.) TheaT

nOuntOf gas0.

dlSChargedperunl= 1rnelS FI古7 STAB;】Ilt,OfcomblBtl

On

t

orvnrlOt即‑

repr6entedasafunctior10t a.̲rate｡fgAHVOlt!…zlb)bt'rnlZ'gOf

T泊､rlterc̲山scc pressurepbyequat10El(17) 0,‑raSCOEtot^a一g^asdl父tLB^tgeI

:

亡加｡

J<unuoH .710 ⊂VollS.No T

11']‑con

s t ( S

G.leGr｡) (3()) IEtheslgnbefore(39)LSrl‑Copposlte tothatofthedlSturbanceonpress

u

re,

+

l)^p,t

h

en,the sttltlOnarypressureCan againk estabIIS

h

cd.､､'hlleLnitnOpPOSlte caseanysm.ill(llSturbancewilleont)nl】e to enlarge lcndl)lg tOan aCCClerat1‑1g conbust

L

On,Orm CaseOfnegatlVedls‑ ttLrbance(‑62')le:ldlrLgtOfadlngOutOF colnbuslloll

Fortunat

e

ly,lrLpmC

r l

Ce,the s)gn of J【LIStheopposltC tO thatofagLVen dlSturbance67)こIStSSho､vnlnドL

g ?

, case(1),(2),く

3 )

,､､･h‑1ethecase

(

1

) ,

Wherethec).poncnr7LOfburnlngVeloclty )slargerthan1,doesnotexist

̲I(I‑const(CI‑IIC･J)'L1)67, (Ilo) It zs obviousth:lt For the case(3) 71=Othestabllltyistheb

e

st,､vhllefor thecase(2),wherelJisnearz

e

ro,rue stabllzty】sfairlygood lnthecase(1) 1ヽ･herelr一1thesl.lblllty terldstoWo

r s e

, theref

o

re,l爪prこIC

L L

CliL,､VC Shoulddeslgn asafetytusesoasLO realize iLSl‑1こ11ler valueohL,

a

nd,lfposs

】 b

le,"shouldLx:

zeTOWhlChlSthec.TISeOfa''gasIcssf

u s

e‑I Thee)叩Onent71maybcurlllZedユSa pr=LCIICallnde)LOLstごIbllltyOfcombustlOZI otasafetyfuse

JlErfectsofthestructureof:lfuscon stablllryOfcombustlOrl

Makoto Klmurこ1こlrld Kazuo Kudol) havefoundthe(･xponents†ItorVar10uS klndsofsafetyfuses bythe tcchnlque ntldthetheor^y developedbythepresellt author

Someofthe resultsobtained W】11be dlSCuSSedfrom rhcpresentauthor●Spolnl ofvleW

AccordlngtOthesllllPlllZe^dassum^p

t l O

ⁿ

preseIltedlil

t

hlSp;ll)eZ, thee)こPOlle

n rl

I

､vllLtendto毒forH･.0 vapourI一lCO

m

･

bust･OnpTOdu

C

ts.､vllllcfor

C

O 三,'JIS去 1ftheenergy tr:lTlfeTtO the unburnt l泊Ⅵderfrom theco】rLbustlOnproductsls lllalnlythroughsolldresl

d

ue,thenthe c).ponentllWllltendto2:e

r O

produceIleo bee.,tuscltCOrlSIStSOfpotas‑ slum llltrate KNO..S111phur S .lnd charcoal(malnLy C)､､‑hlle 】n こI COm merclatSafetyfusethecorethreadsand thelnnermOStThreadsofこIEusedecom‑ 7nSeandburn",lrh‑hepo､vder･therefore, the〟erfecいVepOヽ､der‥Incl

u

de.tosoTne ext

e

nt.hydrogczIEro】1日､,hlChHの vLIPOur couldbepzoduce(lznこしquantltymoreOr

less

lrtTable3(a)7'decreases､､herbc

l l r

b

o r L

becorLleST‑lChlnthepo､､der,､vhllH､･hen KhTO, ln‑Creases,theH三O vapourfrom heTnpytlrnthreadmay be lnCreaSed･"

beconllngb)gger

lnT.lble3(b)7HnCreaSeS"henK

N

O

,

becomes richer,lncreaslngthe:‖110unt ofll,0 from thecombusnonorheTnP yarnthre.lds

r.ITable3(C)7日 nCr

e

a

S

eS､VhetHhe degrees ofcarbonLZユtlOn OfchalCOal decrease,1nCreaSmg the contentsOr hydrogenlrLCharcoals

lnTable3(a)7'mCreaSeS､､,henThe

､､‑eightofpo､yder permeterOfaftlSa lIICrea

S

eS,mCre乙lSIIlgtheaznountO‖一cmp‑

yarllburl一tbytllepO､､(】er

paPerthreadlSmoreeaSllyburntthan heTnpy.lrEl.therefore,‑heamodJ1‑0日tO produced tsgreaterLn Case OFpaper threadLhnnHlCaseOfllempyarnTable 3(e)sho､､,sth.1日=nC.easesaSthemLl‑ terlalsofthreadschaTlgefrom hcmT)yこIrEl Intopaper

Tf､vecha咽ethema‑erLalsohhesecotld layerOfafuse(seCortdtothelllnermOSt layer)from paperEntOCOttOn,The

e

x

l 氾

･ nen日日ndlCateSr)0nhangeasLS

S

^tlOl＼n

lnT.lble3(b).(heresultsh0､､,logttlat thesecondlayerdoesnotlnterLcrewlrh thecombustionofthepowderltSelf

Thecoverlr'gbyasphaltonthesecond layerdoesllUtalso乙llfecttlleCXPOllent TlaSISShownltlTable3(g),the

r

eason may be the same､viththatdcscrlbed above

Tf〜te Changethe InnermostlhreLlds Into nOn‑COmbustlble glass‑wooly

a

rn

,

thenonlythe black powderburnswlth no

J

ltO nll(lll,LthrlChcarbon こIlldsolld

}lArCh.t954⊃ J3tLrmngVcl∝It)lo【SaEet) l･lLSe 2L

mllC7‑sITLaller Table3(h)sho＼､sthat (f) E打ectotsecontthyer

Tablc3 ReEntLOnbetwccnttle叩 nent Coml楓 LO

n

‑ u‑IthestrtleturCOEsafety

ky ･ 0 1 l s ･

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ruseS･

i S2 0

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65 20 15 0126

70 20 10 0139

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50 20 30 0.C504

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^cknowledgc一rlCrtt

Theauthorwould lLkctoexpresshls thanksto Messrs lくazltO1(liland Sel･ 1ChlYamiltle forthelr VLllùLblehelp m

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