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An inverse solution of the exact partial differential equations for three-dimensional inviscid flow was obtained by finite-difference techniques for the subsonic-transonic flowfield over a generalized class of blunt-body shapes at up to 40° angle of attack. The formulation led to the development of an IBM 7094 computer program capable of handling either perfect gas or real equilibrium air. The causes of the inherent and induced instabilities and removable singularities which arise in the solution are presented; and the procedures adopted for handling these difficulties are explained. Results are shown for several cases, one of which is the real-gas flowfield for the Apollo Command Module at 22° angle of attack. The results represent the first real-gas angle-of-at tack flowfield predictions for this shape computed by the inverse method with particular attention being focused on the flowfield behavior around the small radius shoulder region. The computed behavior of the stagnation streamline is found to be in agreement with theoretical predictions by Hayes for rotational stagnation point flow. Nomenclature speed of sound; shock coefficient constant in Hayes theory shock equation parameter; constant in Hayes theory specific enthalpy a / g h p = i = grid coordinate defining value of r i r = unit vector along direction of increasing r i x = unit vector along x axis i$ = unit vector along direction of increasing 9 j = grid coordinate defining value of 6 k = integration plane index M = Mach number n = shock equation parameter n = unit vector normal to shock surface p = pressure r = a body-oriented radial coordinate (Fig. 1) S = function describing shock, Eq. (7); entropy T = temperature U = total velocity u = velocity in the x direction v = velocity in the r direction v -transformed velocity defined by Eq. (8) w= velocity in the 6 direction w = transformed velocity defined by Eq. (9) X = oblique curvilinear coordinate (distance measured from the shock surface in the x direction) x, y, z = body-oriented Cartesian coordinates (Fig. 1 ) Presented as Paper 66-413 at AIAA.x', y'j z' = freestream-oriented Cartesian coordinates ( Fig. 1) a = angle of attack; Hayes parameter e = density ratio across shock B = a body-oriented cylindrical coordinate (Fig. 1) p = density cf > = a stream function defined by Eq. (31) \f/ = a stream function defined by Eq. (32) Subscripts B e 9= evaluated on body surface = equilibrium = shock coefficient identification index = normal to shock; shock coefficient identification index r = partial derivative with respect to r s = behind shock; partial derivative at constant entropy t = tangential to the shock X = partial derivative with respect to X x = partial derivative with respect to x y = partial derivative with respect to y 0 = partial derivative with respect to 6 co = freestream

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