Sonic Boom Propagation Revisited: a Nonlinear Geometrical Acoustic Model

An analytical model which can accurately propagate a near-field sonic boom pressure signature down to the ground in a stratified atmosphere is presented. The pressure perturbations are limited to the vertical plane below a supersonic aircraft flying at constant horizontal speed. The proposed model employs geometrical acoustics to propagate the boom and combines a nonlinear treatment of both its amplitude and distortion, supplemented by the "area rule" for shocks fitting; ray-tracing equations are derived to calculate the ray trajectory and the ray-tube area, considering the Standard Atmosphere. Although simple, this combined method allows a very efficient and accurate prediction of the boom propagation and can be considered a useful tool for the aerodynamic design and multi-objective optimization of low-boom supersonic aircrafts via CFD methods. Whitham's aeroacoustic theory, here proposed in an "inverse mode" formulation, and classical geometrical acoustic theory are recalled and critically compared with the proposed model in order to assess its features and qualities. Comparisons with recent experimental data and previously published results obtained via well established sonic boom propagation codes are also provided and explained.