SUMMARY

A method of successive approximations to the ideal flow around airfoils at high supersonic Mach numbers is developed, based on the concept of Crocco's stream function. Taking the undisturbed flow as a starting-point, a second approximation to the flow in the whole region surrounding the airfoil is derived, and the results for velocity and pressure distribution at the airfoil surface are compared with the corresponding expressions obtained by potential flow theory. The flow behind a plane shock wave is next chosen as zero-order approximation in order to obtain better results for the flow in the vicinity of the leading edge. The first approximation gives expressions for the shock-wave curvature and for the derivative of the pressure coefficient at the leading edge, which check similar results obtained by other investigators. The second approximation yields expressions for the derivative of the shock-wave curvature and for the second derivative of the pressure coefficient at the leading edge. Nomenclature A, B, C constants denned by equations (78). G, H, L constants denned by equations (56). &y, btj coefficients in expansions of velocity perturbations. c speed of sound, in units of limiting velocity. cc specific heat at constant volume. cp pressure coefficient. g{x) airfoil profile. G(z) airfoil profile form function. ^«v- ̂ s&o airfoil and shock curvature at leading edge, respectively. M Mach number. P function of w, denned by equation (11). Ptf coefficients in expansion of P in powers of tfiv and <jix. •f Abstracted from a doctoral dissertation submitted by the author in the Departmen