Sławomir Stępień Stanisław Szajnar Michał Jasztal. 1. Introduction

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1 Aricle ciion info: Sępień S, Szajnar S, Jaszal M. roblems of miliary aircraf crew s safey in condiion of enemy couneracion. Eksploacja i Niezawodnosc Mainenance and Reliabiliy 07; 9 (): 6, hp://dx.doi.org/0.75/ein Sławomir Sępień Sanisław Szajnar Michał Jaszal roblems of miliary aircraf crew s safey in condiion of enemy couneracion roblemy bezpieczeńswa załogi wojskowego sku powierznego w warunkach przeciwdziałania przeciwnika* The presened paper consiss ouline of he probabilisic mehod of evaluion of miliary aircraf crew s safey, which ook ino considerion enemy couneracion. The specific enion was focused on esimion of durabiliy of ejecion se, which is a means of pilo s emergency escape from aircraf. The basis of he presened model is probabiliy of pilo s danger o life for single sorie caused by enemy. Formuled differeniion equion characerises process of incremen of successful sorie number. The equion afer ransformion ino parial differenial equion served for esablishing of successful sorie disribuion funcion and subsequenly for calculion of crew safey indicors. Keywords: miliary aircraf crew, safey, ejecion se, durabiliy, probabiliy. W arykule przedsawiono zarys probabilisycznej meody oceny bezpieczeńswa załogi wojskowego sku powierznego uwzględniającej niszczące działanie przeciwnika. Największą uwagę skupiono na szacowaniu rwałości foela kapulowego jako środka do awaryjnego opuszczania samolou przez piloa. odsawą prezenowanego modelu jes prawdopodobieńswo powsania zagrożenia dla życia piloa w pojedynczym locie sku powierznego spowodowane przeciwdziałaniem przeciwnika. Sformułowano równanie różnicowe charakeryzujące w ujęciu probabilisycznym proces przyrosu liczby udanych loów bojowych sku powierznego. Równanie o po przekszałceniu w równanie różniczkowe cząskowe, posłużyło do wyznaczenia funkcji rozkładu udanych loów bojowych, a nasępnie wskaźników bezpieczeńswa załogi. Słowa kluczowe: załoga wojskowego sku powierznego, bezpieczeńswo, foel kapulowy, rwałość, prawdopodobieńswo.. Inroducion Miliary aircraf crew s safey is a very complex problem. The complexiy of he problem emerges from necessiy o rescue pilo s life in dynamic emergency condiion, when ime for making a decision is shor [, 8-9, 6-7,]. Therefore, elemen of human facor, canno be overlooked [, ]. World lierure on his issue has an inerdisciplinary nure and reles o hese mers in a general way, ofen purely descripive. In aviion, pilo s life rescue in emergency siuion is realised wih use of special devices which are called ejecion ses. They are mouned only on miliary aircraf, wh can resric an access o informion abou heir usage. Hence, specialised lierure on his issue is no oo exensive. In oland, sudies of a pracical and applicion nure in hese field were mainly carried ou in he Air Force Insiue of Technology and years ago also in he Insiue of Aviion, however analyical sudies were performed in he Miliary Universiy of Technology, Miliary Insiue of Aviion Medicine and Warsaw Universiy of Technology as well as oher research cenres worked on aerospace echnology e.g. Rzeszow Universiy of Technology. World lierure consis publicion reled o differen areas of ejecion process. Some of hem raise anhropomeric quesion conneced wih ejecion [], medical quesion as well as condiioning which may occur during ejecion process [,, 7, 0-, -]. ublicions reling o colleced comb experience also occur [, ]. One of he line of research is compuer modelling of ejecion process [5, 6, 9, 5, 5, 6], which enable o simule various scenarios of he process, analysis of condiions of safey escape from an aircraf as well as examinion of facors h affec pilo s organism in differen siuions of emergency escape. Huge diversiy of he publicions confirms inerdisciplinariy of he subjec area. In he domesic lierure, major par of he papers concern medical problems of ejecion process and was published by scieniss from he Miliary Insiue of Aviion Medicine [, ]. Opering and mainenance manuals for paricular ype of ejecion ses are also available. However, papers such as h on quaniive evaluion of crew safey wih regard o ejecion se usage, are exremely rare [8]. In oday s world, various ypes of ejecion ses are employed in differen ypes of miliary aircraf. The ejecion ses differ in heir design soluion, dimensions (size, weigh), esablished sabilision sysem, survival equipmen and accessory. [7, 9]. The direc inspirion for researching in he field of ejecion ses developmen was necessiy of perpeual modernision of miliary aircraf owards performance and effeciveness improvemen, which in urn involves indispensabiliy of emergency escape subsysem perfecion []. In he course of modernizion, he quesion arises: how o assess pilo s safey for miliary aircraf equipped wih paricular rescue sysem? Currenly, abou he idea of wh ype of ejecion se is insalled in paricular aircraf decides more ofen han no: ype of an aircraf (who is a manufacurer), acical and echnical capabiliies as well as (*) Teks arykułu w polskiej wersji językowej dosępny w elekronicznym wydaniu kwaralnika na sronie Eks p l o a a c j a i Ni e z a w o d n o s c Ma i n e n a n c e a n d Reliabiliy Vo l.9, No., 07

2 economic condiions. I also happens h, various ypes of ejecion se manufacured by differen producers are insalled on he same ype of aircraf. Furhermore, each of producers have in his ender from several o over a dozen ypes of ejecion ses, resuling significan diversiy of possible echnical soluions [9]. For an analysis of miliary aircraf crew safey, dispariy of asks in ime of peace and war mus also be coun. Hence, furher quesions need answers: How o evalue aircraf crew safey? Wh ool for such assessmen apply? Thus, auhors of presen paper proceeded o sudy of he mehod (echnique) which allows such an assessmen, and is helpful in uilision planning as well as aircraf and heir rescue sysems modernision. resened mehod bases on probabilisic calculion, which ake ino considerion aircraf and ejecion se reliabiliy. Carried ou soluions do no exhaus he problem, bu represens disinc progress in he ques for answers o he quesions raised and provide he inspirion for formulion furher quesions conneced wih ejecion se usage for aircraf crew life rescue. Ejecion ses represens very complex echnical objecs, which are essenial elemens of he aircraf equipmen and enable pilo o escape from an aircraf in very shor ime in emergency siuion. So, i was assumed h pilo s safey during fligh depends on: ) aircraf reliabiliy; ) ejecion se reliabiliy; ) pilo healh and calmness in emergency siuion []. Addiionally, in case of enemy couneracion, following elemens have influence on pilo s safey: ) miliary aircraf vulnerabiliy; ) abiliy o self-defense; ) effeciveness of enemy impac on aircraf in order o desroy i during fighing; ) qualiy of air raffic organision (dynamic of operion) and crew s skills [8]. ilo s safey was considered under he following assumpions: ) on airfield (miliary base) possibiliy of aircraf desrucion (as well as ejecion se) is negligible; ) aircraf is desruced by enemy during comb mission; ) probabiliy of aircraf desrucion during one sorie equals Q, and ejecion se remain operable (exis possibiliy o uilise he se); ) ejecion se durabiliy is he same as aircraf durabiliy. The leading role in pilo s safey evaluion plays aircraf durabiliy, which is defined as a number of sories or flying ime unil desrucion of aircraf in comb condiion. Lifeime of he ejecion se can be measured by he number of he aircraf successful flighs unil desrucion. The main subjec of he presened paper was deerminion of he ejecion se durabiliy in he above menioned scope and assessmen of crew s safey indicors.. Mehod of durabiliy assessmen wih use of difference equion This chaper presens mehod of deerminion of disribuion of successful fligh number for assumed ime range or for he whole aircraf s durabiliy in erms of fighing. Wih he disribuion of he number of successful flighs considered one ried o calcule ineresing parameers. The process of incremen of he number of successful fligh was considered as a funcion of ime or number of sories. I was assumed h he sories occurs randomly wih a cerain inensiy λ. Therefore, for he range following condiion is fulfil: λ, where: can be considered as a durion ime of one sorie. Above menioned condiion ses h aircraf do no fly coninuously bu here are exis random inervals beween consecuive sories. For he sake of compleeness, i was assumed h probabiliy of aircraf s desrucion during one sorie equals Q. Le U z, denoe he probabiliy h for he momen he number of successful flighs is z. For he applied symbols, he incremen of he number of flighs will be described in probabilisic way by he following difference equion: + ( ) Uz, + = λ Uz, λ QUz,. () The difference equion () means wh fallows: he probabiliy h for he ime + he number of successful flighs amoun o z is equal o he sum of probabiliies of he following evens: fligh did no happen during and aircraf have accomplished z successful flighs unil he momen, successful fligh was accomplished during, aircraf desrucion did no happened and aircraf have accomplished z- successful flighs unil he momen. Afer rearranging o he funcional noion: where: (, ) u( z, + )= ( λ ) u( z, )+ λ ( Q) u( z, ), () u z is a probabiliy densiy funcion of he successful flighs number for he momen. Taylor s expansion was used for above menioned equion. u( z, + )= u( z, ) !!! ) +... u z u z u z u( z )= u( z), (, ) (, ) ),, !!! For i is wo elemens of expansion, and for z hree elemens. Afer ransformion and rearrangemen of he equion (), here was obained: ) = Qu( z) Q u z, λ, λ + λ Q. () λ λ = λ ( ) Le inroduce he noions: c = Q: b= Q : a Q. Coefficien c indices aircraf desrucion inensiy. Then coefficien b and a despie he same descripion have somewh differen meaning, b is an average incremen of he number of successful flighs in he ime range, insead a is an average square of incremen of he number of successful flighs in he ime range. Convergence of he descripions for a and b resul from he fac h in he ime range can occur increase only by one fligh, so an incremen and square of incremen are equal. Then: ) = cu ( z, ) b u( z ), + a. () To presen soluion of equion () auhors made use of equion s soluion of he Fokker-lanck ype [] in he following form: Eks p l o a a c j a i Ni e z a w o d n o s c Ma i n e n a n c e a n d Reliabiliy Vo l.9, No., 07

3 ,, + a u( z ) =b u( z ). (5) We search for he soluion of he paricular equion (5), which, by 0 is concurren o he so-called Dirac funcion: u( z, ) 0 for z 0 and u( 0, ), bu in his way h he inegral of funcion (, ) u z equals a uniy for all > 0. For above menioned condiion, he soluion of equion (5) akes he form []: u( z, )= π e z b ( ). (6) Having aken accoun of hese considerions one can presen paricular soluion of equion () which akes he form: (, ) c (, ) u z = ce u z. (7) In order o verify he correcness of he soluion, following ransformions have been made: ) c c ) = c e u( z, )+ ce = c + b z b u( z ) u( z ), c = ce, c = ce z b + ( z b) = u( z, ), = + Having pu above relionships ino (), one ges: ( z b) u ( z, ). u ( z, ), 0 = dzd Having deermined he disribuion of he number of aircraf successful flighs (densiy funcion (8)) i is possible o obain: ) average value of he number of aircraf successful flighs: a) for he lifeime; b) for he finie period of ime; ) for esablished number of successful flighs z : a) probabiliy h he number of successful flighs is less han or equal o z ; b) probabiliy h he number of successful flighs is greer han z as a funcion of ime. Expeced value of he number of successful flighs for ime less han : b c Q E[ z]= zu( zdzd ) = ( + c ) e c =, Q 0. Q + λq e λ. (9) If we ake ino accoun longer ime period, i.e. ime, we received well known relionship which describe average value of he number of successful flighs for he aircraf lifeime: ET [ z] ( Q) =. (0) Q Hence, he number of successful flighs for finie range of ime is described by equion (9). robabiliy, h he number of successful flighs is less han or equal o z for ime wih possibiliy of aircraf desrucion is represened by: z () z ( )= u( z, ) dzd. () 0 ( ) + + ( )= ( ) c b z b z b z b ( ) z b c b + a + u ( z, ). a Then, afer arrangemen: ( ) + + ( )= + c b z b z b c b z b ( z b) + u ( z, ). robabiliy, h he number of successful flighs is greer han z for ime wih possibiliy of aircraf desrucion is represened by: z ( u z dzd )= (, ). () 0 z robabiliy, h in he range of ime (0, ) aircraf will no be desroyed has following form: As seen, lef side of he relionships is equal o righ side, which proves he correcness of his soluion. Finally, he disribuion of he number of aircraf successful flighs was obain: = = ( ) c () z = + z ( ) ce d 0 c = e = c + = c e e 0 () u( z, )= ce c π e z b ( ). (8) Funcion (8) has feures of densiy funcion since: I can be demonsred h specified probabiliies bring he oal number o one. () + + =. z z Eks p l o a a c j a i Ni e z a w o d n o s c Ma i n e n a n c e a n d Reliabiliy Vo l.9, No., 07

4 The equion () can be wrien down in he form: where: k Qk k = e, () = λ - number of sories performed unil ime. robabiliy h in he range of number of sories (0, k) aircraf will be desroyed adops he following form: Qk Qk k = e. (5). Ouline of he pilo s safey assessmen In case of rise o loss of he ship hazard, pilo for he sake of saving one s own life is forced o rigger ejecion se. The success of ejecion process depends mainly on he following facors [8]: ) ime o reach a decision abou ejecion; ) course of ejecion (including pilo s landing afer ejecion process); ) condiions of he ejecion process; ) ype of aircraf and ype of ejecion se; 5) behaviours and skills of pilo during ejecion process. In real siuions ime for reaching decision abou emergency escape is predominanly very shor. Addiionally, in his kind of siuion pilo ofen ries o remedy he hre o aircraf. Gre influence on making he righ decision abou ejecion has human facor and oher facors which deermine pilo s menal se. Taking decision abou ejecion necessies he implemenion of a series of aciviies which influence ejecion process. These aciviies are more or less auomed. Reliable performance of he operions has significan influence on he resuls of ejecion. As menioned in he inroducion above, reliabiliy of he emergency escape depends on aircraf s and ejecion se s ype. Emergency escape does no always end successfully, o a large exen he resuls depends on condiions in which i occurred. robabilisic evaluion of he pilo s safey can be, depending on he assumpions and simplificions, more or less accure. In his paper, model is limied by aking ino accoun aircraf and ejecion se reliabiliy. Reliabiliy of an aircraf and ejecion se, by virue of assumpions, are considered as a separe ses of evens: RS + QS =, (6) RF τ + =, (7) QF τ where: R - probabiliy h, in he ime range (0, ), aircraf was no desroyed or he desrucion of an aircraf occurred and pilo survived hanks o use of he operable ejecion se. robabiliy of loss of pilo s life during sories in he ime range (0, ) akes he form: Q Q Q = () S F τ, (9) where: Q - probabiliy of loss of pilo s life during sories in he ime range (0, ). Dependency (8) shows h pilo s safey depends on reliabiliy of an aircraf and reliabiliy of ejecion se. Dependencies (8) and (9), how easy i is o check, bring he oal number o one, which proved he correcness of he above formulas for he assumpions made. Equion (8) for exponenial disribuion as a funcion of number of sories has following form: R = e + e R τ, (0) k Qk where: k number of sories. Qk F. Illusrion of he calculions Due o lack of available and reliable da reling o comb use of aircraf, which are indispensable for evaluion of required resuls, below hypoheical da were used. Inpu da for he calculions: sories inensiy λ = [ / day ]; probabiliy of aircraf desrucion during one sorie Q = 0,05 [-]. The inpu da illusre siuion, where sories are curried ou wice daily, and probabiliy of aircraf desrucion during one sorie equals 0,05. Figure presens changes over ime of an average value of he number of successful flighs E[z] (calculed according o (9)) and dashed line presens sionary value E T [z] pursued by E[z] (calculed according o (0)). E T [z] = 9. While, figure presens changes over ime of probabiliies ( ) z ( ( ), ) z ( ), ( ) ( ) calculed according o he equions (), () and (). where: RS ( ) - aircraf reliabiliy in he ime range (0, ); QS ( ) - unreliabiliy i.e. probabiliy of he aircraf desrucion for he ime range (0, ); RF ( τ ) - ejecion se reliabiliy he ime of is use; QF ( τ ) - ejecion se unreliabiliy he ime of is use. The above equion (6) refers o he aircraf, and equion (7) o he ejecion se. Using formulas (6) and (7), probabiliy of pilo s survive in he ime range (0, ) can be deermined in he following form: R = RS()+ QS() RF ( τ ), (8) Fig.. Average value of he number of successful flighs Eks p l o a a c j a i Ni e z a w o d n o s c Ma i n e n a n c e a n d Reliabiliy Vo l.9, No., 07

5 ( Fig.. Graphs of calculed probabiliies: ) z ( ) probabiliy, h he number of successful flighs is less han or equal o z =9 for ime, ( ) z ( ) - probabiliy, h he number of successful flighs is greer han z =9 for ime, ( ) ( ) - probabiliy, h in he range of ime (0, ) aircraf will no be desroyed 5. Summary The requiremens of he modern blefield in he field of aircraf engineering forces us o seek reliable (no only inuiive) answers o imporan quesions: wh effec should be expeced on blefield as a resul of aciviy of specified ype of one s own or enemy aircraf, and how aircraf engineering should be formed in order o achieve a goals for assumed probabiliy and under paricular condiions. Furhermore, References very imporan aspec of effeciveness evaluion of miliary aircraf usage is assessmen of aircraf durabiliy and crew safey during comb mission [0]. I seems h presened mehod of crew safey evaluion in erms of he enemy couneracing can be used for he preliminary assessmen of pilo safey wih specific rescue sysem applied o he aircraf. Addiionally, he mehod suppors decision-making during comb mission as well as facilies obaining required indicors in he field of safey and reliabiliy for comb use of aircraf. Wih he use of disribuion of he number of successful flighs obained in presened work i is possible o deermine average value of he number of successful flighs (as presened figure ) as well as probabiliy of achievemen esablished number of successful flighs and probabiliy of aircraf endurance for specified ime (figure ). resened numerical example shows possible uiliarian aspecs of use he mehod oulined in he work.. Borgoń J. Niezawodność i bezpieczeńswo sysemu pilo - sek powierzny. Informor Insyuu Technicznego Wojsk Loniczych 987; 69/87.. Chiou W Y, Ho B L, Kellogg D L. Hazard poenial of ejecion wih canopy fragmenion. Aviion, Space, and Environmenal Medicine 99; 6(): 9-.. Davis J R, Johnson R, Sepanek J, Fogary J A (Ediors). Fundamenals of Aerospace Medicine. rd Ediion. Lippinco, hiladelphia: Williams & Wilkins, Edwards M. Anhropomeric measuremens and ejecion injuries. Aviion, Space, and Environmenal Medicine 996; 67(): Głowiński S, Krzyżyński T. Modelling of he ejecion process in a symmerical fligh. Journal of Theoreical and Applied Mechanics 0; 5(): Grzesik N, Czapla R. Aircraf crew escape sysem assisan. Safey and Reliabiliy: Mehodology and Applicions. CRC ress 0: Hearon B F, Thomas, H A, Raddin J H. Mechanism of verebral fracure in he F/FB- ejecion experience. Aviion, Space, and Environmenal Medicine 98; 5(5): Lewis M E. Survivabiliy and injuries from use of rocke-assised ejecion ses: analysis of cases. Aviion, Space, and Environmenal Medicine 006; 77(9): Maryniak J, Maryniak A, Ładyżyńska-Kozdraś E, Fole U. Kapulowanie - możliwości, problemy i modelowanie. Nauka, Innowacje, Technika 00; 5 (7): McBrney C M, Rush S, Kharod C U. ilo ejecion, parachue, and helicoper crash injuries. Journal of special operions medicine 0; (): Moiseev I B, Srakhov A I, Churilov I K, Vovkodav V S, Radchenko S N. Medical oucomes of emergency ejecions from Russian aircrafs in Aviion, Space, and Environmenal Medicine 0; 8(): Newman D G. Survival oucomes in low-level ejecions from high performance aircraf. Aviion, Space, and Environmenal Medicine 0; 8(0):06-065, hps://doi.org/0.57/asem Osborne RG, Cook AA. Verebral fracure afer aircraf ejecion during Operion Deser Sorm. Aviion, Space, and Environmenal Medicine 997; 68(): 7-.. Rainford D J, Gradwell D (Ediors). Ernsing's Aviion and Space Medicine. 5h Ediion. CRC ress Ramm A G, Kaleps I. Modeling of he ejecion process. Mhemical and Compuer Modelling 99; 0: 95-0, hps://doi.org/0.06/ (9) Szajnar S W. Diagnozowanie w podsysemie opuszczania sku powierznego. Informor Insyuu Technicznego Wojsk Loniczych 995; 0/95: Szajnar S W. Ocena bezpieczeńswa i modelowanie w sysemach awaryjnego opuszczania samolou wojskowego. Warszawa: Wojskowa Akademia Techniczna, 0. Eks p l o a a c j a i Ni e z a w o d n o s c Ma i n e n a n c e a n d Reliabiliy Vo l.9, No., 07 5

6 8. Szajnar S W, Tomaszek H. roblemy wyznaczania wskaźników rwałości foela kapulowego i bezpieczeńswa załogi wojskowego sku powierznego w warunkach działań bojowych. Zagadnienia Eksploacji Maszyn 00; (7): Szajnar S W, Wojkowiak M. roblemy bezpieczeńswa załogi sku powierznego w syuacjach awaryjnych". Warszawa: BIL-GRAF, Tomaszek H, Wróblewski M. odsawy oceny efekywności eksploacji sysemów uzbrojenia loniczego. Warszawa: Dom Wydawniczy Bellona", 00.. Tomaszek H, Żurek J, Jaszal M. rognozowanie uszkodzeń zagrażających bezpieczeńswu loów sku powierznego. Radom: Wydawnicwo Naukowe Insyuu Technologii Eksploacji, Williams C S. F-6 pilo experience wih comb ejecions during he ersian Gulf War. Aviion, Space, and Environmenal Medicine 99; 6(9): Wojkowiak M. Adapacja usroju do działania przyspieszeń w kapulowaniu rzeczywisym i pozorowanym. Lekarz Wojskowy 97; :0-5.. Wojkowiak M. Wpływ pozycji piloa na urazy kręgosłupa podczas kapulowania. Medycyna Lonicza97; : Yu J, Lin G, WU M. Numerical Simulion of Decelerion erformance of Ejecion Se. Aca Aeronauica e Asronauica Sinica 006; 7(6): Yu J; Lin G, Mao X. Numerical Simulion of Ejecion Se and Analysis of erformance Under Adverse Aiudes. Aca Aeronauica e Asronauica Sinica 00; (0): Sławomir Sępień Sanisław Szajnar Michał Jaszal Miliary Academy of Technology ul. Gen. Sylwesra Kaliskiego, Warsaw, oland s: ssępień@w.edu.pl, sszajnar@w.edu.pl, mjaszal@w.edu.pl 6 Eks p l o a a c j a i Ni e z a w o d n o s c Ma i n e n a n c e a n d Reliabiliy Vo l.9, No., 07