Eccentric two-target model for qualitative air combat game analysis

An air combat duel with all-aspect guided missiles between a Harrier type and a faster conventional fighter aircraft is modeled as a two-target game between a homicidal chauffeur and an aggressive pedestrian. The firing envelopes of the missiles are approximated by eccentric circles in the faster airplane's coordinate system. The qualitative two-target game analysis is a nontrivial combination of two zero-sum pursuit-evasion games with eccentric circular target sets. The analysis confirms the need for large angle missiles for the less maneuverable aircraft and the great sensitivity of the solution to firing envelope parameters. Nomenclature A = aspect angle a,b = eccentricity of the fast and slow aircraft capture circle, respectively ^ = fast aircraft JC = slow aircraft (Harrier type) L = off-boresight angle R =best turning radius of the fast aircraft S = switch function of the fast aircraft control t = time Vl9 V2 = velocity of the fast and slow aircraft, respectively x,y = Cartesian coordinates in the coordinate frame of the fast aircraft a,/3 = radius of the fast and slow aircraft capture circle, respectively 7 = velocity ratio (V2/V1)< 5 = parameter in the terminal manifold 0 = angular parameter of the target sets , =costate variables T = retrograde time, =tf — t fa/ = control of the fast and slow aircraft, respectively Subscripts a,b = fast and slow aircraft target set, respectively / = final value p - value at the intersection of the target sets s = value at the stagnation point'' uoi,u/3 = boundary of the usable part of the fast and slow aircraft target set, respectively