The theoretical and computational basis of focused sonic booms

Abstract

For the past 20 years sonic-boom signatures in focus ‘‘superboom’’ regions have been computed using a method based on a scaling law by Guiraud [J. Mech. 4, 215–267 (1965)] and a numeric solution by Gill [Ph.D. thesis, Cornell University (1974)]. The method recognizes that the smooth caustic case treated by Guiraud and Gill is by far the most common focusing situation, and that smooth caustics caused by aircraft accelerations and turns and by atmospheric gradients are topologically similar. Gill’s numeric result for a shock may thus be treated as a canonical result, and scaled to arbitrary situations by Guiraud’s similitude. The process has been incorporated into an existing sonic-boom program. When a focus is detected, the program fits the solution by (a) computing ray and caustic curvatures required by the theory, (b) determining a matching position consistent with Gill’s boundary conditions, and (c) applying the scaled Gill solution to each shock. The computational requirements of this process are reviewed, together with empirical support for the results.