Compressible potential flow with circulation about a circular cylinder

The potential function for flow, with circulation, of a compressible fluid about a circular cylinder is obtained in series form including terms of the orders of m(4) where m is the Mach number of the free stream. The resulting equations are used to obtain pressure coefficients as a function of Mach number at a point on the surface of the cylinder for different values of circulation. The coefficients derived are compared with the Glauert-Prandtl and Karman-Tsien approximations which are functions of the pressure coefficients of an incompressible fluid. For the cases considered, the values of the pressure coefficients computed from the theory were found to be somewhere between the two approximations, the first underestimating and the second overestimating it

The application of Green's theorem to the solution of boundary-value problems in linearized supersonic wing theory

Following the introduction of the linearized partial differential equation for nonsteady three-dimensional compressible flow, general methods of solution are given for the two and three-dimensional steady-state and two-dimensional unsteady-state equations. It is also pointed out that, in the absence of thickness effects, linear theory yields solutions consistent with the assumptions made when applied to lifting-surface problems for swept-back plan forms at sonic speeds. The solutions of the particular equations are determined in all cases by means of Green's theorem, and thus depend on the use of Green's equivalent layer of sources, sinks, and doublets. Improper integrals in the supersonic theory are treated by means of Hadamard's "finite part" technique

A special method for finding body distortions that reduce the wave drag of wing and body combinations at supersonic speeds

For a given wing and supersonic Mach number, the problem of shaping an adjoining fuselage so that the combination will have a low wave drag is considered. Only fuselages that can be simulated by singularities (multipoles) distributed along the body axis are studied. However, the optimum variations of such singularities are completely specified in terms of the given wing geometry. An application is made to an elliptic wing having a biconvex section, a thickness-chord ratio equal to 0.05 at the root, and an aspect ratio equal to 3. A comparison of the theoretical results with a wind-tunnel experiment is also presented