INTERIOR BALLISTIC STUDIES OF POSSIBILITIES FOR LAUNCHING AIRCRAFTS ROCKETS FROM GROUND. Slobodan Jaramaz and Dejan Micković

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1 3 RD INTERNATIONAL SYMPOSIUM ON BALLISTICS TARRAGONA, SPAIN 6-0 APRIL 007 INTERIOR BALLISTIC STUDIES OF POSSIBILITIES FOR LAUNCHING AIRCRAFTS ROCKETS FROM GROUND Sobodan Jaraaz and Dejan Micović University of Begrade, Facuty of Mechanica Engineering, Weaon Systes Deartent, Krajice Marije 6, 0 Begrade 35, Serbia In ast years haens that soe tye of aircrafts are no ore in use fro different reasons, but the stocs of aunition for the are enoous. In soe cases the question of ossibiities of aunching aircraft rocets fro ground arises. Coony, for ground aunching of aircraft rocets the need aears for increase of initia aunching veocity in order to rovide required rocet range and recision. In this aer different interior baistic ossibiities are studied as candidates for aroriate aunching. Interior baistic concets of oen-aft auncher, cose-aft auncher, cose-aft auncher with additiona charge, oen-aft auncher with additiona charge and counteass and auncher with nozze and additiona roeant charge are anayzed. Aroriate atheatica odes and couter codes are deveoed. Resuts for 57 aircraft rocet show ossibiities of different interior baistic concets to fufi secified requireents. INTRODUCTION Today soe tyes of aircrafts are no ore in use fro different reasons, but the stocs of aunition for the are enoous. Then the question of ossibiities of aircraft rocets aunching fro ground (for exae, for ight uti tube rocet auncher) arises. Coony for ground aunching of aircraft rocets the need aears for increase of initia aunching veocity in order to rovide required rocet range and recision. In this aer different baistic ossibiities are studied as candidates for aunching of 57 aircraft rocet BR-0/57 (rocet initia ass g, ass of doube base roeant -,g) with increased initia veocity. Foowing interior baistic concets are anayzed: oen-aft auncher, cose-aft auncher, 45

2 46 INTERIOR BALLISTICS cose-aft auncher with additiona roeant charge, oen-aft auncher with additiona roeant charge and counteass, and auncher with nozze and additiona roeant charge. For a these interior baistic concets infuence of auncher ength is studied. MATHEMATICAL MODEL The atheatica ode for oen-aft auncher with additiona roeant charge and counteass is given in this aer. A other odes for different interior baistic concets can be treated as secia cases of this ode. The scheatic reresentation of oen-aft auncher with additiona roeant charge and counteass is given in figure. Figure. Scheatic reresentation of oen-aft auncher with additiona roeant charge and counteass The atheatica ode [] is coosed fro foowing equations: equation for foation of roeant gases due to cobustion of additiona roeant charge dac ρacsacu ac n () where are: ac - ass of additiona roeant charge, t - tie, ρ ac - density of additiona roeant charge, S ac - instanteneous burning surface of additiona roeant charge, u ac - coefficient in burning aw of additiona roeant charge, - ressure in auncher, n ac - exonent in burning aw of additiona roeant charge, fow through the rocet nozze

3 Interior baistic studies of ossibiities for aunching aircrafts rocets fro ground 47 case a) ( ) + where are: - ressure in rocet otor, - secific heat ratio of roducts of rocet roeant,. Deteination of ocation of noa shoc wave in nozze using assution ( - ressure behind the wave) M + ( ) M + () where is: M - Mach nuber in front of the shoc wave in the rocet nozze. Based on nown /, M is deteined by iterative rocedure.. In the case of shoc wave ocation outside the nozze, we assue that it is in the nozze exit section. The axiu vaue of M deteines by iterative rocedure fro the exression: + ( ) Ssh + M St M + whereare: S sh - area of shoc wave, S t - nozze throat area, M - axiu Mach nuber, 3. Deteination: M in(m, M ). 4. The cross-section area in the nozze on the ace of aearing shoc wave Se St + M M +, 5. Deteination of ex : - -, + M ex where ex is ressure in the nozze exit area, 6. Deteination of V ex :, + ( ) Vex f ex (6) where are: V ex - gas veocity in the nozze exit area, f - rocet roeant force, (3) (4) (5) 7. Deteination of ass fow rate through the nozze & :

4 48 INTERIOR BALLISTICS + & S + t f (7) case b) > + V ex - ex, S e S t (8) f + & St f (0) equation for foation of roeant gases due to cobustion of rocet charge d n ρsu () where are: ρ - density of rocet roeant, S - instanteneous burning surface of rocet roeant, u - coefficient in burning aw of rocet roeant, n - exonent in burning aw of rocet roeant, equation of conservation of ass in the auncher dρ dz dw ω out + W & & ρ () where are: ρ - density of gas ixture in auncher, W - auncher voue between rocet and counteass, z- reative burnt web of additiona roeant charge, ass of additiona roeant charge and igniter ω ωac + ωi (3) where are: ω ac - ass of additiona roeant charge, ω i - ass of igniter of additiona roeant charge, equation of change of free voue in the auncher dw dz S dx ω dx c + + ac (4) ρ where are: S - cross-section area of auncher, x - rocet ath in auncher, x c - counteass ath in auncher, equation of energy conservation in the auncher (9)

5 Interior baistic studies of ossibiities for aunching aircrafts rocets fro ground 49 dt c W c f dz ω c & T + c T & S V+ V vρ R g dc v dρ dw T + + c v ρ W ( ) out c where are: T - teerature of gas ixture in auncher, c v - secific heat under constant voue for gas ixture in auncher, c - secific heat under constant ressure for roducts of burning of additiona roeant charge, c - secific heat under constant ressure for gas ixture in auncher, V - rocet veocity, V c - veocity of counteass, cobined force of additiona charge and its igniter ω acfac + ω if i f (6) ω where are: f ac - force for roeant of additiona charge, f i - force for igniter of additiona roeant charge, ass fow rate through the aft-end of auncher when the counteass eaves the auncher & ϕ S out + + R T where are: ϕ - nozze coefficient, - ratio of secific heats for gas ixture in auncher, change of burnt web dz e e de ( / e0 ) f + f + f 3 3 (8) e0 e0 where are: f, f,f 3 - coefficient of geoetry shae of roeant of additiona charge, e - burnt web of roeant of additiona charge, e 0 - initia web of roeant of additiona charge, equations for ixture of gases in the auncher dc v ε d c dε dε v + c v ( cv cv ) (9) where is ε - ass share of rocet roeant gas in gas ixture in auncher, ω z ε (0) ω z+ g (5) (7)

6 430 INTERIOR BALLISTICS dc v ε ω z+ () c ε c + ε c () c ε c + ε c (3) ω v v v dz ( ω z+ ) z& out ( c c ) (4) v v R ε R + ε R (5) g g g equation of state for ixture of gases in auncher ρ R T (6) g equations of rocet and counteass otion dv F+ S (7) t ( ) where is (t) - instanteneous rocet ass, dvc S (8) c where is c - ass of counteass, dx V (9) dx c Vc (30) equation for rocet thrust force + cosβ F η ef & Vex + S Se ( ex ) (3) where are: η ef - coefficient of oss of tota ressure in rocet otore, β - ange of divergent art of nozze. Based on these equations the couter rogra ROMOCM is created. For soution of syste of ordinary differentia equations of deveoed syste the fourthorder Runge-Kutta ethod is used. COMPUTATIONAL RESULTS During evauation of ossibiities of different interior baistic concets for aircraft rocet 57 BR-0/57 the foowing iitations are introduced:

7 Interior baistic studies of ossibiities for aunching aircrafts rocets fro ground 43 axiu ressure in auncher ust not exceed the vaue of 0 bar; on that way we rovide the conditions for reguar wor of rocet otor for a interior baistic concets, auncher ength was iited on 3. ; this ength was consequence of deands for acing rocet and eeents of different concets and acheiveent of required initia rocet veocity, fo one side, and syste ass, fro other side, for additiona charge can be used ony aready deveoed doestic tyes of roeants. Tyica resuts for the interior baistic concet of oen-aft auncher with additiona roeant charge and counteass are given in figures and 3. These resuts are obtained for counteass ass of 3 g and additiona charge coose of 30 g of tubuar, nitroceuose roeant. Figure. Change of ressures in auncher and rocet otor for oen-aft auncher with additiona roeant charge and counteass Figure 3. Change of rocet veocity and acceeration for oen-aft auncher with additiona roeant charge and counteass

8 43 INTERIOR BALLISTICS Siiar curves are obtained with ather interior baistic concets. Soe of coutatitiona resuts are cofied by exerienta data.the highest initia rocet veocity is obtained with the concet of cose-aft auncher with additiona roeant charge (70 /s). In the case of recoiess concets the highest initia veocity is acheived with the concet of auncher with nozze and additina roeant charge (65 /s). CONCLUSIONS Based on revious considerations we can ae foowing concusions:. In ast years haens that soe tye of aircrafts are no ore in use fro different reasons, but the stocs of aunition for the the are enoous.. Coony for ground aunching of aircraft rocets the need aears for inccrease of initia aunching veocity in order to rovide required rocet range and recision. 3. Foowing interior baistic concets are anaysed: oen-aft auncher, cose-aft auncher, cose-aft auncher with additiona roeant charge, oen-aft auncher with additiona roeant charge and counteass, and auncher with nozze and additina roeant charge. 4. The atheatica ode for oen-aft auncher with additiona roeant charge and counteass is given in this aer. A other odes for different interior baistic concets can be treated as secia cases of this ode. 5. The highest initia veocity for aircraft rocet 57 BR-0/57 is obtained with the concet of cose-aft auncher with additiona roeant charge (70 /s). In the case of recoiess concets the highest initia veocity is acheived with the concet of auncher with nozze and additina roeant charge (65 /s). REFERENCES [] S. Jaraaz, D.Micovic, Interior Baistics, Facuty of Mechanica Engineering, Begrade, (00)