Waverider configurations according to thin shock-layer theory

Abstract

This paper shows that the thin shock-layer theory can be completed in an analytical manner when the shock wave is attached to the leading edges of a non-planar triangular conical wing. Discontinuities appear only in the derivatives and not in the functions. Thus, the second derivative of each body and the shock is discontinuous at one point, and the first derivative of the transverse velocity components and pressure are discontinuous at one point. Bodies for which the slope is discontinuous at one point are also possible. A differentiable shock wave is assumed known and the body is calculated. Thus, bodies with smooth differentiable cross-sections in the inboard which are attached to planar segments in the outboard are obtained while bodies having infinite slope at the central axis are also possible. It is found that a parabolic arc shock in the inboard cannot permit an attached shock solution but other higher order polynomials can. Surface pressure coefficient, coefficients of normal and axial force, and the lift and drag forces of waveriders constructed from these bodies are calculated in closed-form for a wide range of the flow parameters.