Algebraic Prediction of Pressure and Lift for High-Angle of Attack Supersonic Asymmetric Delta Wings Based on Geometric Similarity

The need for simpler, yet accurate and physically sound, methods to predict the lift and pressure distributions over asymmetric delta wings, particularly at high angles of attack with attached shock wave, motivates the development of an alternative approach presented in this paper. By employing a geometric transformation and postulating a functional similarity between linear and nonlinear solutions, a straightforward algebraic technique for pressure estimation is developed. This approach bridges the solution in the central nonuniform flow region to the exact solutions in the uniform flow regions with attached shock waves near the leading edges, in a manner analogous to methods used for supersonic starting flow at high incidence. The method is shown to reproduce established results for both symmetric and yawed delta wings within a limited error. It yields a compact, explicit expression for the normal force coefficient, formulated as a weighted average of the pressure coefficients from the two uniform flow regions. A pathway for extending the approach to the upper surface, where the uniform flow is governed by swept Prandtl-Meyer relations is also outlined. Although classical analytical approaches for delta wings were established decades ago, the proposed method provides a tractable alternative tool for modern fast engineering analysis.