Military Applications of Explosive Propulsion

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1 loboda Jaaaz Pofo ja Mickoi} Aitat pofo Uiity of Blgad Faculty of Mchaical giig Militay Applicatio of xploi Populio xploi populio ha th igificat ol both i ciil ad i ilitay applicatio. thi pap difft gotical cofiguatio, which fid thi applicatio i pactic, a tudid aily though dtiatio of tial locity of li achid duig xploio. U of foula, fo tudid gotical cofiguatio, i dig of lctd ilitay it i ptd. Th foula a th baic o fo dig ad optiiatio of cotioal wahad, ati-tactical ballitic iil wahad, fuz, tc. Kywod: Phyic of xploio, xploi populio, wahad, fuz.. NTOUCTON Th xploi populio i th pat of phyic of xploio which i dalig with acclatio of objct by dtoatio of a xploi chag. t fid it applicatio i ay ciil ad ilitay fild. A ciil applicatio w ll tio xploi cladig ad foig of tal, xploi wldig of iila ad diiila tal, tc. Militay applicatio a uou: high-xploi (H wahad (dictd gy: hapd chag, hi chag ad xploily fod ptato ad oidictioal: fagtatio ad blat, ati-tactical ballitic iil (ATBM wahad, fuz, tc. laboatoi pla tal plat a acclatd by dtoatio of xploi chag i thi cotact i od to gt hock wa that ca b coitly ud a laboatoy tool to tudy th quatio of tat of atial at xtly high pu ad tpatu, ad thi bhaiou at high at of loadig. thi pap w ll coid o foula ad thi odificatio fo o-diioal goty. Thi ilitay applicatio a pcially cocd.. XPOVY VN N.. toductio xploily di li ot, thi dtuctio ad fagt fly a caid out o th accout of gi which a lad duig xploi dtoatio. A locity of li di by xploi cod fo all id (fo xapl, a ph o a log cylid ca b dtid fo th gy quatio [, ]: cid: Octob, accptd: Mach. Copodc to: loboda Jaaaz, Faculty of Mchaical giig, 7. ata 8, Blgad, Yugolaia k p d Q, (. wh a: -gy tafd to uoudig dia of li (ai, wat, goud, k - kitic gy of dto-atio poduct, p - ital (pottial gy of dtoatio poduct, d - gy ud fo platic dfoatio of li, - li a, - li locity, - xploi chag a, Q - xploi hat of xploio. Bad o thi gy quatio, ad y oft i coctio with quatio of otu balac, difft odl a dlopd. Today th Guy odl i th ot oft ud fo aiou applicatio. Bitih phyicit oald W. Guy dlopd a coupl of ipl ida ito a way to tiat th locity of xploily di fagt. Although hock wa playd a y ipotat pat i th taf of gy fo th dtoatio of cofid xploi to th uoudig tal auitio ca, th auptio Guy ad i hi odl to poid athatical tactability had othig to do with hock chaic. Guy aud that:. dtoatio of a gi xploi la a fixd aout of gy p uit a which wid up a kitic gy of th di it atial (oft tal ad th dtoatio poduct ga (h glct gi, p ad d ; ad. tho poduct ga ha a uifo dity ad lia o-diioal locity pofil i th patial coodiat of th yt. Th phyical jutificatio of th auptio ay b thought of a follow. Th fit auptio i quialt to a xpctatio that th fficicy of gy taf to th tal will b coitt, gadl of th goty o ai of th cofit of th xploi. Thi auptio tu out to b good o a log a th a o igificat "d lo of ga, which cau th ga to xpad i a Faculty of Mchaical giig, Blgad. All ight d. FM Taactio (, 5-5

2 dictio ot cotplatd i th o-diioal odl. Th cod auptio copod to a coditio wh th i oppotuity fo ultipl hock batio i th ga pac whil th cofit i till itact, i which ca th ga tat iid th ca td towad cotat dity ad a lia locity pofil. Both auptio bak dow wh th ca a i latily light, bcau th i iufficit ti fo batio withi th ga to di towad tady xpaio withi th ga pac; th ult i that th ca i th di fat tha th Guy odl pdict. Th Guy odl ay b applid to ay xploi/tal yt with a co-ctio adittig odiioal talatio otio of th tal typically oal to it ufac, gadl of th dictio of dtoatio popagatio. Th odiioal goti coidd a plaa, cylidical, ad phical. By applyig th picipl of coatio of gy ad coatio of otu to lctd cotol a, th quatio fo th ayptotic locity of th li ay b did. th ca wh a yty bouday fall withi th dfiitio of cotol a, a i ytic adwich ad xplodig cylid ad ph, oly th quatio fo coatio of gy i dd. Wh o yty bouday i dfid, o wh th bouday fall outid th cotol a, a quatio fo coatio of otu ut b dlopd... ytic goti thi pap w f to th a of th xploi chag, ad th a of li o li a o, wh i th li a which locity w a cocd with, ad i tapig a. Natually, i th ca of plaa goty w pak of a a p uit aa, wha i th ca of cylidical goty w a fig to a a p uit lgth. t u illutat Guy appoach by coidig th ytic adwich, i which a lab of xploi i cofid by a tal lay of a a o ach id. figu. i a diaga of th cotol a ud fo th ytic adwich, wh X f to th agagia poitio. Th tical diio ad that oal to th b oal to th tal ufac, ad it i aud that th tal o i thi dictio. Thi auptio i alid wh th dtoatio wa paalll to th X-axi, ad i oly lightly i o wh th dtoatio tal ppdicula to th X-axi. f w u th Guy auptio that th xploi atial locity g i popotioal to th ditac fo th yty bouday X, w ha: X g X X, (. wh l i th tial, igid-body pd of th tal li ad i alo th pd of th gaou xploio poduct i cotact with th li. Th li ad xploi a p uit aa a dfid a ad t, (. X, (.4 pctily. Th quatio fo th total kitic gy p uit aa of th cotol a k ay b witt a k X X t ( X X g g d l dx, (.5 X Th quatio (.5 ay b itgatd uig th dfiitio i quatio (., (., ad (.4. o w gt: k ( l, (.6 f w dfi a th kitic gy p uit a of xploi, o k /, th quatio (.6 iplifi to: l /, (.7 wh th t i a xploi atial cotat with uit of locity, o th Guy locity of th xploi. t i th igl atial cotat dd to tiat th ability of a xploi to lauch a a of atial. Th difft way fo calculatio of Guy locity fo xploi a dicud i []. Uig th a pocdu w gt th Guy quatio fo a xplodig cylid ad ph: Cylidical ca: l /, (.8 phical ca: Figu. Cotol a ud fo th ytic adwich pla of th pap a aud to b ifiit i lgth o that dg ffct ca b igod. Th X-axi i tak to / l, (.9 5 Th aiatio of oalid li lociti with / fo th ytic adwich, cylid ad ph a how i figu.. 6 Vol., No, FM Taactio

3 .. Aytic goti Fo o-diioal goty that do ot cotai a yty bouday withi th cotol a, th quatio fo coatio of otu i ud to dti th atial locatio i th ga xploi poduct that xpic, o aag, o chag i poitio. Th appoxiatio of a lia locity ditibutio i th ga xploi poduct i th ud to itgat th gy quatio. Figu. Vaiatio of th oalid li lociti with li-to-chag a atio fo th ytic adwich, cylid ad ph Fo th aytic adwich, o pla paalll plat, a diaga of th cotol a i how i figu.. Th locity i th ga xploi poduct i xpd a g X X ( X, (. X X fo th ight-oig potio. Uig th quatio fo coatio of otu fo lft-oig ad ight-oig potio, liiatig th pu ipul t, ad olig fo X, th locatio of th tatioay ufac, w ha: X X X X X ( X X (. Uig th quatio fo coatio of gy, w gt: / X X X X ( X X X X (. Th fo of th quatio (. i wll uitd to dictly al th ffct of a chag i cofiguatio (.g., / o / upo th locity ipatd to tal. Th figu.4 i a plot of th popotioat locity ica of plat with a du to tapig fo aiou atio /. Th figu illutat that tapig a latily hay chag ( /. ica th locity of plat with a y littl, whil addig tapig to a light chag ( / 5 ica th locity coidably, paticulaly i th ag / < 5. Figu. Cotol a ud fo th aytic adwich. g fo th lft-oig potio, ad X X ( X, (. X X Figu.4. Gai i locity of plat with a to tapig facto /. du Th plat lociti, obtaid fo th quatio (., w foud i aoably good agt with xpital alu at latily high chag to tal a atio ( /.. To ol thi pobl, w u th cocpt of uifo pu (dity ad paticl locity of dtoatio poduct btw fly plat a how i figu.5 fo calculatig thi fial lociti at low /. Uig quatio fo coatio of gy ad otu, ad th FM Taactio Vol., No, 7

4 polytopic quatio of tat fo th dtoatio poduct, w gt: / / p y k y (.4 / / py k y (.5 wh k i th polytopic xpot, p y i th uifo pu, y i th uifo dity, i th a of dtoatio poduct oig with th locity, ad i th a of dtoatio poduct oig with th locity. Figu.6. Op-fac adwich cofiguatio with aud locity ditibutio Figu.7. Cotol olu fo iplodig goti Figu.5. Vaiatio of dity ad paticl locity of dtoatio poduct Fo piou quatio w ca coid th ca wh o plat i of ifiit a. That plat act a a igid bouday. Th locity of th oth plat ca b obtaid by ubtitutig,,, ad i th quatio (.4. o w gt: / / py, (.6 k y Th op-fac adwich how i figu.6 i aoth xapl of aytic goty. Uig coo pocdu w gt fo that ca: / ( /, (.7 6 ( / ttig ult about locity of a pla tal plat placd at th d of a cylidical xploi chag a gi i [4]. Th picipal otiatio fo aalyig iplodig goti i to odl th acclatio of th li i hapd chag opatio. Th cotol olu ud to di foula fo iplodig goti i how i figu.7. Th fial locity of th tal li i thi ca i: / ( Ψ Ψ η( η( (.8 wh β 4β η, β /, Ψ p(, t d dt. 4β 4β Not that a ad both appoach ifiity, thi foula appoach th claical foula fo th opfac adwich. Uually fo Ψ th xt appoxiatio i ud: * Ψ K p τ ( CJ, (.9 o th ag.5 /.7, K i cotat which alu i.9, ad τ * i a chaactitic ti gi by foula: *.9. 7 τ, (. pcj wh p CJ i th Chapa-Jougt pu. 8 Vol., No, FM Taactio

5 FM Taactio Vol., No, 9 Fo iplodig cylid with xtio cofit, th locatio th zo-adial-locity poitio,, i aluatd by olig a cubic quatio: CJ CJ (. Th iplodig li locity i th gi a: / 6 6 (. iila a, uig th fouth-polyoial quatio fo hypothtical tatioay ufac, w gt th quatio fo tiatig th locity of iplodig li of iplodig ph with xtio cofit: [ ] [ ] / (. Th ipl ga-dyaic auptio ad i th Guy odl do ot apply fo ctai cicutac, ad th Guy aalyi ith hould ot b applid o hould b applid with coctio to accout fo th diatio [5].. MTAY APPCATON OF MO.. toductio Th quatio, coidd i ctio, a widly ud i dig of ilitay it. Fo xapl, th quatio dlopd fo cylidical goti a ud i dig of hapd chag. thi ctio w ll gi o ittig quatio fo dig wahad ad fuz fo which tatig poit i dlopt w th quatio gi i ctio... Wahad dig Natually fagtig wahad a claifid a ucotolld fagtatio dic. Th ida bhid th atual fagtatio wahad i to bak th ca ito a ub of fagt a giig a bia towad a paticula a. Th fou-tp atual fagtatio bak-up poc i how i figu.. Th odifid quatio (.8 that accout fo wahad lgth,, i xpd a: /, (. Figu. xpaio poc of atual fagtatio wahad. H i th xploi diat. Thi quatio accout fo xploi ga tig bad o wahad lgth. f w kow th did pak locity of fagt fo coidatio of wahad ffcti th atio / i gi by:, (. Bad o iitial wahad goty, ad, th ital diat of wahad ca,,, i: ( ( ( (. (. H ad a tal ad xploi dity, pctily. Th atio of th outid ca adiu to th iid ca adiu i xpd a: ( ( ( / / (. (.4 Pad fagt wahad dig logic off th wahad dig th bt thod of lctig th xact fagt wight ad iz to b ud i a wahad. Pad fagtatio wahad qui a i li. Th i ca i uually ad of aluiiu, which oti act a a tuctu to cay dyaic iil load. Aluiiu i light, to axii iitial fagt lauch locity, but tog ough to cotai xploi ga fo a hot piod of ti. A wahad with pad fagt with a ucotolld fagtatio ca i how i figu.. Thi typ of wahad would gat a cobid-ffct wahad that would acclat lag a fagt at hay copot with all, light fagt that would kill thi copot. thi ca th pak fagt locity i gi by xpio: / 5 π π π η l l l l f f t t B t t (.5

6 Figu.. Pad fagt o ucotolld fagtatio ca H η i th xploi fficicy, ad B i cotat. Thi quatio i ud fo optiiatio of pad fagt ad li thick fo gi fagt locity, wahad wight ad olu. K-od wahad tchology off dig a w typ of wahad that ca attack ad dtoy ballitic iil. Thi wahad dploy high-dity ai od at tactical ballitic iil (TBM that ca ptat thick o hadd payload. Thi cocpt i bcoig o popula but diff igificatly copad to cotioal blat fagtatio wahad. thi cocpt w aali ct co ad jlly oll cocpt. Th ct co K-od wahad cofiguatio i ud duig iotopic iil/tagt cout. Th wahad dic cotai a ct xploi co uoudd by od aagd cicuftially, a how i figu.. adiu, od diat, ub of od ti N, ad od lgth. Th jlly oll K-wahad jct it od about th iil axi ad i oly ud duig iotopic iil/tagt gagt. Th jlly oll cofiguatio coit of xploi, buff, ad od aagd i altatig cicula lay a illutatd i figu.4. Th od jctio locity i xpd a a fuctio of i od adiu i, wh ach od locity i coputd bad o i od gotic locatio: i / V, (.7 ( / Figu.4. Jlly oll gotic cofiguatio Thi quatio coput th a od lauch locity o ach ow gi a cotat xploi thick. Gibald wahad off wahad dig uiqu ad ol wahad optio fo u agait TBM tagt. A gibald wahad i how i figu.5. Thi wahad i digd to fi fagt though th fot d of th wahad itad of out th id of th wahad a i ot cotioal dic. Mtal cofit i ud ia th cylidical ca with a tal tap itd o th aft d. Th tap thick cotol th pak fagt locity. Th pak locity of fagt ad tap ca b coputd uig followig quatio: Figu.. Gotic dciptio of ct co wahad tatig fo th quatio (., w gt th followig quatio fo th xploi adiu : [ π ] δ π ( δ π N δ δπ π N δ N 4 N 4 (.6 H δ i δ (. Thi quatio i ud to tiat od locity a fuctio of xploi ( a f b a, (.8 a b b t f a / b, (.9 wh a/b[( / ]/[( / ( / ]. Vol., No, FM Taactio

7 4 f l f zaz f l f P τ, (. Z dld H ubcipt a, d, ad f f to accpto, doo, ad fly, pctily. Alo, i th quatio (. z U, wh U i th hock locity, ad Zz a /z f. Th piou quatio i ud fo optiiatio of dtoato fo difft dig apct. Figu.5. ciptio of a gibald wahad.. Fuz fuz dtoatio i oft tafd fo a dtoatig lt (calld th doo to a cod xploi chag (calld th accpto by u of th doo chag to di a flyig plat which ipact th accpto chag ad hock iitiat it. Thi cocpt i applid i low-gy fly plat dtoato a how i figu.6, which u a.5 A fiig cut to iitiat a ixtu of TiH/ClO 4 which dtoat a all chag of HNAB xploi. Thi pojct a aluiiu fly plat o a ag at up to. k/ to ipact aoth two pllt of HNAB pd to difft diti, giig liabl full-od dtoatio output. Figu.7. toatio taf cofiguatio 4. CONCUON Figu.6. ow-gy flyig plat dtoato thi ad oth applicatio iolig dtoatio by fly plat ipact, it i typically did that a iial aout of doo chag b quid ad that fficit u b ad of th fly plat. Th coditio lad to th u of thi fly plat, which ca b di to high lociti by all doo chag. Th po of xploi to th ipact of thi fly plat ultd i th hock-iitiatio citio i th fo P τ. H P i th hock pu di ito th xploi, ad τ i th hock duatio. Th citio i thi fo i uful fo giig dig pupo. To aluat iitiatio citio a a fuctio of dig paat, w ll coid th doo-accpto-fly cofiguatio ktchd i figu.7. Uig adwich foula, th xpio fo P τ bco: O th bai of piou coidatio, w ca daw th followig cocluio: xploi populio ha th igificat ol both i ciil ad i ilitay applicatio. ifft gotical cofiguatio, which fid thi applicatio i pactic, a tudid aily though dtiatio of tial locity of li achid duig xploio. U of foula, fo tudid gotical cofiguatio, i dig of lctd ilitay it i ptd. Th foula a th baic o fo dig ad optiiatio of cotioal wahad, ati-tactical ballitic iil wahad, fuz, tc. FNC [] Bau, F.A., Olko,. P., tajukoi~, K. P., ^li{, V. P., [ht, B.T.: Fizika zia, Nauka, Moka, 975 [] Jaaaz,.: Phyic of xploio, Faculty of Mchaical giig, Blgad, 997 [] Jolga,.: Cotibutio to tudy of Motio of xploily i Mtal Plat, M. c. Thi, Faculty of Mchaical giig, Blgad, 999 [4] Yada, H.., Kaat, P.V., ada,.g.: tudy of a xploi-i Mtal Plat, Popllat, xploi, Pyotchic, 6- (986 FM Taactio Vol., No,

8 [5] Jaaaz,.: Wahad ig ad Tial Ballitic, Faculty of Mchaical giig, Blgad, VOJN PMN KPOZVN POPUZJ. Jaaaz,. Mickoi} kplozia populzija ia za~aju ulogu u ciili i oji piaa. U oo adu azli~it gotijk kofiguacij, koj iaju piu u paki, pou~aa u uglao koz od iaw kajw bzi obloga koj poti`u za kplozij. ata j upotba foula, za azata gotijk kofiguacij, u pojktoawu izabaih ojih poizoda. O foul u baz za pojktoaw i optiizaciju kocioalih bojih glaa, bojih glaa ati-takti~kih baliti~kih pojktila, upaqa~a, itd. Vol., No, FM Taactio