Exact and approximate solutions to the oblique shock equations for real-time applications

The derivation of exact solutions for determining the characteristics of an oblique shock wave in a supersonic flow is investigated. Specifically, an explicit expression for the oblique shock angle in terms of the free stream Mach number, the centerbody deflection angle, and the ratio of the specific heats, is derived. A simpler approximate solution is obtained and compared to the exact solution. The primary objectives of obtaining these solutions is to provide a fast algorithm that can run in a real time environment.