Analytical Analysis of Lock-on Range of Infrared Heat Seeker Missile

Transcription

1 Ausralian Jurnal f Basic and Applied Sciences, 3(4): , 2009 ISSN Analyical Analysis f Lck-n Range f Infrared Hea Seeker Missile Mhammad Syuhaimi Ab-Rahman and Mazen R. Hassan Cmpuer & Newrk Securiy Research Grup Faculy f Engineering & Buil Envirnmen Deparmen f Elecrical, Elecrnic and Sysems Engineering, Universiy Kebangsaan Malaysia (UKM) Bangi, Selangr, Malaysia Absrac: The lck-n range, R, f infrared (IR) hea seeker missile has been sudied in deails. An analyical expressin frm f R has been derived in erm f arge (assumed as aircraf h meal ailpipe), amsphere and infrared (IR) deecr parameers. The R is represened in erm f Lamber W funcin and as a funcin f arge emperaure, T, and amsphere exincin cefficien, á, and als he nise equivalen irradiance (NEI) f he deecr. Assuming clear sky backgrund, he simulain resuls shw ha a high value f R can be achieved when he emperaure f aircraf engine is high especially in akeff case where he engine hrus is large. The R can be decreased by (1) increasing he aenuain cefficien f he prpagain medium, i. e. by cling he aircraf h engine r any her bscurans ha absrb r scaer he IR radiain (2) r by decreasing emissiviy, å, f he arge surface which depends n he applied caings / painings. Hwever, he R f can be increased by reducing he NEI f he IR deecr. Key wrds: Hea seeker missile, infrared, lck-n range. INTRODUCTION Infrared (IR) hming is a passive sysem in which hea generaed by he arge is deeced and hmed n. Typically, i is used in he ani-aircraf rle rack he hea f je engines. I has als been used in he anivehicle rle wih sme success. This means f guidance is als referred as "hea seeking". The IR hea seeker missiles have explied echniques acquire and inercep airbrne arges, by passively deecing heir IR energy. Develpmens in IR deecin and racking have led he increasing effeciveness f IR guided missiles (fire and frge), which are nw prable such as MANPADS (Man Prable Air Defense Sysems) and easily available. IR hea seeker missiles have been respnsible fr he majriy f aircraf lsses since heir inrducin in service during he 1960s. Sme saisics sugges ha hea-seeking missiles have been respnsible fr mre han 80% f all cmba aircraf lsses ver he las 40 years (Tiern, D.H., 2006), see Fig. 1 fr example. There are hree main ypes (generains)f IR hea seeker missiles accrding he ype f reicle (pical mdular) (Kpp, C., 1982) and he deecr(in missile head): spin-scan, cnical-scan, and imaging. The laer is he ms advance ne because I cann be easily fled by cuner-measure echniques. The IR hea seekers deec he difference f IR energy beween he arge and back grund, i..e. cnras. Thus, IR sealh echnlgy aims, ideally, make his difference zer by reducing he arge IR signaure level (IRSL). Hea seeker missile uses amsphere windws fr deecing and racking. Thse windws are specified bands f wavelengh in elecrmagneic specrum ha characerized by lw IR aenuain. In addiin, hse windws are ineresing he seeker designers because hey include he IR radiain f h urbje aircrafs. In an effr redress he balance beween he aircraf and he missile, researches in sysems ha culd be uilized defea seekers have been widespread. The develpmen wrk has fllwed w main pahs: defensive sysems such as flares; and acive sysems such as jammers. Thse cunermeasures are designed decreases he lck-n range, R, by increasing he aenuain f IR arge. In his paper, we invesigaes he lck-n range, R, f IR hea seeker missile in deails. A mdel is presened fr lck-n range in erm f arge, which is cnsidered as pin surce, amsphere and deecr parameers. We slve he R equain in erm f Lamber Crrespnding Auhr: Mhammad Syuhaimi Ab-Rahman, Cmpuer & Newrk Securiy Research Grup Faculy f Engineering & Buil Envirnmen Deparmen f Elecrical, Elecrnic and Sysems Engineering, Universiy Kebangsaan Malaysia (UKM) Bangi, Selangr, Malaysia syuhaimi@vlsi.eng.ukm.my, 3703

2 Fig. 1: Damage caused by a missile. The lucky par was ha he missile hi he wing. W funcin. The simulain resuls shw ha lck-n range, R, can be decreased by aenuaing IR energy f he arge r decreasing he arge emperaure. In addiin, he lck n range can be decreased als by decreasing he emissiviy f arge surface. This can be achieved using special applied caings/ painings (Mahulikar, S.P., e al., 2008). IR Radiain and Signaure: The specral radian emiance (SRE) f blackbdy* can be wrien as funcin f wavelengh, ë, and emperaure, T (in Kelvin ( K)), accrding Planck's lw as (Hudsn, R.D., 1969) (1) where -2-1 S ë is he specral radian emiance (Wcm ì ) c 1 is firs radiain cnsan, c 1 = Wcm ì 4 c is he firs radiain cnsan, c = ì K. 2 2 The SRE f blackbdy fr differen values f emperaures is shwn in Fig. 2. Mre general represenain f SRE f black bdy is shwn in Fig. 3. I can be seen ha SRE increases as emperaure increases and he maximum SRE peaks lie ver he range f shr wavelenghs. Principally, he range f emperaures (500 K- 900 K) is very impran hea seeker designer because i includes he IR energy h meal ailpipes f urbje aircraf (Hudsn, R.D., 1969). The peaks f SRE crrespnding abve emperaure range lie beween wavelenghs 3ìm -5ìm ha ms f hea seekers are designed rack and lck-n he arge. Inegraing he abve equain wih respec he wavelengh frm zer infiniy gives us an expressin fr he radian 2 emiance, i.e. he flux radiaed in hemisphere abve blackbdy 1 cm in area, which can be wrien as (2) where -2 S is he radian emiance (Wcm ) ó is Sephan-Blzman cnsan, ó = W cm K

3 Fig. 2: Specral radian emiance f black bdy fr differen values f emperaures. Fig. 3: (a) Specral radian emiance f black bdy vs. emperaure and wavelengh (b) he crrespnding cnur pl shw differen pimum value curves f specral radian emiance. The abve law is knwn as Sephan-Blzman law (Hudsn, R.D., 1969). Sephan-Blzman law prvides a sandard cmparisn; i describes an ideal radiar, i.e. blackbdy which can be used cmpare he radiain f any her surces. A facr can, be added, s i can be applied surces ha are nn blackbdies. This facr is called emissiviy, å, (Hudsn, R.D., 1969) (3) Therefre, SRE f any surce can be wrien as (4) surce where å is he emissiviy f he surce a specified emperaure and wavelengh. Fig. 4 shws he radian emiance as a funcin f emperaure, T, and fr differen values f emissiviy, å, where he curve f å = 1 has he highes radian emiance (black bdy). I can be shwn ha radian emiance decreases as å decreases. 3705

4 Fig. 4: Radian emiance fr differen values f emissiviies. General represenain f Sephan-Blzman law is shwn in Fig. 5 where i can be cncluded ha he arge having high å emis high radian emiance which can be lcked n by IR hea seeker. Fig. 5: (a) General represenain f radian emiance and (b) he crrespnding cnur pl which shw he curves f differen pimum values f radian emiance. Researches in he prcess f develping an elecr chrmic plymer. These hin shees cver he aircraf s whie skin and sense he hue, clr and brighness f he surrunding sky and grund. Amsphere Aenuain: IR energy is generally ls he amsphere mainly by absrpin and scaering. Absrpin is he energy lss due vibrain and rain f mlecules (Barbara Suar, 2004). Scaering is he energy lss due redirecin away frm he deecr. In general, he ransmiance f amsphere can be represened as (Hudsn, R.D., 1969) where R is he range beween he IR surce and he deecr and á is exincin (r aenuain) cefficien which can be wrien as (Mahulikar, S.P., e al., 2008) (5) 3706

5 á = a + ã (6) where a and ã are he absrpin (due waer vapur) and scaering (due fgs and cluds) cefficiens respecively. The amspheric windws are characerized by high ô a, i.e. lw á (aenuain). The presence f high humidiy, cluds, fg r smke can dramaically influence IR absrpin. IR Signaure Level (IRSL) f he Targe (Aircraf): Fr miliary sysems, generally he arges are aircraf, missiles, ships, grund vehicles, anks ec. The surces f radiain in miliary arges are mainly he h engine pars, he exhaus plume and he high emissiviy meal skin. The engine and exhaus plume prduce a large amun f hea and makes he exhaus secin as a main surce f hermal radiain. The ypical surces f radiain in je aircraf, as shwn in Fig. 6, are he h-meal ailpipe, he exhaus gas plume, meallic skin and he aerdynamic heaing which increases wih he speed f aircraf. Fig. 6: Surces f IR radiain in an aircraf. The h meal ailpipe and he sream f h exhaus gases knwn as he plume. Exhaus gas emperaure (EGT) is ne f he ms impran crieria f engine perfrmance. The emperaure f he plume a he meal ailpipe is given as T 2 = 0.85T EGT (7) where T EGT is he EGT. The ailpipe behaves ypically as a graybdy wih al emissiviy f abu 0.9, wih emperaure equals he EGT and an area equals ha f exhaus nzzle. The higher EGT f he aircraf is in akeff case where he engine hrus is maximum. This high radiain f ailpipe can be easily deeced by even less sensiive hea seeker missile. In his paper, we will assume ha he hermal radiain is emanaing frm a single pin, i.e. aircraf plume ha radiaes in hemisphere. Accrding ha, he radiance f he arge can be wrien as where -2-1 N is he radiance f he arge (W cm sr ), sr is he sld angle. -2 S is he radiance emiance f he arge (Wcm ) å is he emissiviy f he arge T is he emperaure f he arge which we will cnsidered in C. Ne ha he relainship beween he radiance, N, and he radian emiance, S, is N = S/ð (Mahulikar, S.P., e al., 2008). In addiin he radian emiance f arge backgrund shuld be aken in accun where he hea seeker deecin depends n he difference f radian emiance, i. e. cnras, beween he aenuaed IR radian level f he arge and is backgrund. The radiance f arge backgrund can be mdeled as a graybdy wih specified value f emissiviy (8) 3707

6 (9) where -2-1 N b is he radiance f backgrund (W cm sr ). -2 S b is he radiance emiance f backgrund (Wcm ). å b is he emissiviy f he backgrund T is he emperaure f backgrund ( C). b Hea Seeker Missile: The acical missile sysem used agains aircraf includes hree main secins: he guidance and cnrl, he warhead and he prpulsin secins as shwn in Fig. 7. The guidance and cnrl sysem is lcaed in he frn par f he missile and cnsiss f he seeker, he guidance cnrl uni and he rudders. Seeker head receives he IR radiain emied frm a heaed surce, ypically he engine f aircraf, and cnvers his energy in an elecric signal. The signal is prcessed in he guidance cnrl uni ha calculaes cnrl signals used fr direcing he missile via rudders and ailfins. Fig. 7: IR hea seeker missile. The blck diagram f seeker head is shwn in Fig. 8. I is cmprised f he fllwing majr cmpnens: (1) IR dme fr precin frm he aerdynamic frces and weaher, (2) pical sysem (mirrrs) fcus he IR arge energy n deecr, (3) reicule (r pical mdular) prvide direcinal infrmain fr rack (4) deecr, cnver he IR energy elecrical signal Als pical filer may be pu in frn f he deecr pass nly specified narrw wavelengh band fr lcking-n and rejec backgrund nise. Fig. 8: Blck diagram f seeker head. 3708

7 Lck-n Range: The lck n range f hea seeker missile can be wrien as (Mahulikar, S.P., e al., 2008) (10) where he definiin f abve parameers wih heir values used in calculain are 2 A is he arge area, ( 3660 cm (aircraf nzzle)) D is he diameer f pics, (3.8 cm) NA is he numerical aperure f he pics (0.25) ô is he ransmiance f he pics (0.81) * 10 1/2-1 D is he deeciviy f deecr, (5 10 cm Hz W ) -5 ù insance field f view, ( sr) Äf is he elecrical bandwidh, (200 Hz) SNR is he signal- nise rai, (3) Recalling ha he ransmiance f amsphere,ô a, is funcin f he range, R, herefre i appears difficul slve he abve equain fr R. Previusly he auhrs have used eiher numerical mehd such as Newn Raphsn slve his nnlinear equain. In his paper we presen exac and full analyical sluin. Subsiuing equain (5), i.e., in equain (10) and re-arrange he erms, n bains (11a) where (11b) where we cnsider he lck-n range, R, is a funcin f emperaure, T, crrespnding he emperaure f he cnras, N (T)-N (T), seen by he hea seeker. b The sluin f equain (11a) can be wrien as (12) where W(.) is he Lamber's W funcin. The lck-n range, R, is calculaed as a funcin f emperaure f arge and fr differen values f exincin cefficien f he amsphere as shwn in Fig. 9. The arge is assumed as graybdy wih å = 0.9, i.e. aircraf ailpipe. In addiin he backgrund is assumed as a graybdy wih T = 10 C and å = Accrding equain -2-1 (4) he value f backgrund radiance, N b, is W cm sr. As shwn in his figure, lck-n range, R, increases as he emperaure, T, f arge increases, herefre, h pars f arge fr insance, he nzzle and ailpipe f je aircraf, can be deeced by he seeker frm lng disance. In addiin, he R decreases as amsphere exincin cefficien increases. In addiin, as shwn in Fig. 10, he highes lck-n range is bained a aircraf akeff case because he emperaure f aircraf ailpipe is high where exhaus gases emperaure (EGT) reaches 635 C. While i is 515 C and 485 C in cninuus and cruise cases respecively. Accrding abve values f emperaure, he lck-n range will be Km, Km and 31.6 Km respecively where he maximum lck-n range is bained in aircraf akeff case. Frm her hand, lck-n range decreases as exincin cefficien increases. 3709

8 Fig. 9: Lck-n range f hea seeker agains he emperaure f he arge (ailpipe f je air craf) fr differen values f amsphere exincin cefficien. Fig. 10: Lck-n range f hea seeker missile agains exincin cefficien fr differen aircraf flying siuains, i.e. differen ailpipe emperaure. General calculain f lck-n range versus emperaure and exincin cefficien is shwn in Fig. 11. The decreasing f IR signaure level f aircraf will decrease he lck-n range f hea seeker missile and prvide lnger ime he aircraf maneuvre, i.e. increase he prbabiliy f survivabiliy. Lck-n Range in Term f NEI: In his secin, we express he lck-n range, R, shwn in equains (10) and (12) in erm f nise equivalen pwer (NEP) and hen nise equivalen irradiance (NEI) f he deecr. The NEP (W) is he radian flux necessary give an upu signal equal he deecr nise while he -2 NEI (Wcm ) is he radian flux densiy (irradiance) necessary give an upu signal equal he deecr nise. Generally NEP and NEI can be relaed each her as 3710

9 Fig. 11: (a) Lck-n range f IR hea seeker missile agains exincin cefficien and aircraf ailpipe emperaure. (b) The crrespnding cnur pl shw differen curves fr differen pimum values f lck-n range f hea seeker. (13) 2 where A d is he deecr area in cm. When he deecrs are cmpared, he bes deecr is he ne wih he lwes NEP and in urn he lwes NEI. Therefre, he lck-n range f hea seeker missile is expeced be increased as he NEI decreases (will be shwn laer). The deeciviy f deecr can be expressed as (Mahulikar, S.P., e al., 2008) (14a) In addiin, he deecr area can be wrien in erm f field f view,ù, and he equivalen fcal lengh f he pics, f, as Subsiue (14b) in (14a), yields (14b) (15) Furhermre, he numerical aperure, NA, f he pics can be expressed in erm f D and f as (16) Subsiue (15) and (16) in (11b) and afer sme simplificain, ne bains (17) 3711

10 Subsiue he abve equain in (12), ne bains analyical expressin f lck-n range, R, in erm f NEP. In addiin, by subsiuing (13) in (17), yields (18) where i is in erm f NEI and he rai f arge--deecr areas. Frm (18) and (16), i can be readily shwn ha as NEI decreases, R increases, herefre, he hea seeker missile having a deecr wih lw NEI represens serius danger he aircraf arges. Figure 12 shws he effec f reducin f NEI n he lck-n range, R. As shwn in his figure, as NEI decreases R increases fr he specified value f amsphere exincin cefficien. Develpmens in IR-deecin echnlgy are aiming reduce he NEI, fr insance, new generain f IR deecrs are based n quanum well infrared deecr imprve he deecin abiliy f IR missile. Fig. 12: Lck-n range f hea seeker missile agains arge emperaure fr differen values f missile NEI deecr. Mre general deails abu he effec f NEI n R is shwn in figure 13. This figure gives us a clear picure abu he develpmen effrs n he w sides. Frm ne side, f he aircraf designers ry reduce he IR signaure f miliary arges by reducing he emied hermal radiain. Frm he her side hea seeker missile designers ry imprve/develp he deecin abiliy f IR seeker by reducing he NEI using advanced IR deecrs. Fig. 13: (a) Lck-n range f hea seeker missile agains arge emperaure and NEI f he deecr fr á = (b) The crrespnding cnur pl shw differen curves fr differen pimum values f lck-n range f hea seeker. 3712

11 Fig. 12: Schemaic represenain f aircraf je engine Exhaus gases plume. In addiin absrpin by amsphere, he IR flux energy can be reduced by cling he h exhaus gases plume. One f he mehds used in aircraf precin is he reducin f je engine IR energy via cling he exhaus gases plume. This can be dne by injecin waer he exhaus sream. This leads decrease he ransmiance parameer, ô a due increasing f aenuain cefficien, and hen decrease IR signaure level. This can be schemaically represened by assuming ha he exhaus gases plume will pass he cling medium befre he amsphere ne as shwn in Fig. 12. Thus, he IR signaure received by he seeker head will be -ár -ácr -(á+ ác)r aenuaed by e e = e where ác is he aenuain cefficien crrespnding he cling medium (r any her aenuaed medium such as smke bscurans). REFERENCES Barbara Suar, Infrared specrscpy: fundamenals and applicain, Wily. Harshavardhan, M., " Hide and Seek: The Ar f Sealh", Aerspace Engineering Assciain, 1: 1. Hudsn, R.D., Infrared sysem engineering, Wiley, Kpp, C., Hea-Seeking Missile Guidance, Ausralian Aviain. Mahulikar, S.P., e al., "Infrared Signaure Sudies f Airbrne Targes", Prceedings f he Inernainal Cnference n Aerspace Science and Technlgy. Tiern, D.H., Develpmen f Infrared Cunermeasure Technlgy and Sysems, chaper f he bk Mid-infrared Semicnducr Opelecrnics, Springer Berlin / Heidelberg. 3713