Supersonic Bangs

Abstract

SummaryThe non-linear theory of supersonic bangs, obtained in Part 1 for a body accelerating along a straight path, is extended to include curved paths. The basic theory remains the same. The important parameter, which appears in the theory, is the acceleration component along the ray, the rays being lines drawn from points on the flight path at an angle cos-1(1/M) with the direction of motion. It is found that the only essential effect of the curvature of the path is in the modification of this acceleration component to include a term due to the transverse acceleration. With this modification the main results are formally the same as in Part I.The strength of the bow shock is obtained, and it is found that the effect of the curvature of the path is more pronounced at points on the inside of the curve, and in general it becomes greater as the distance from the body increases. A simple asymptotic formula is obtained which predicts the strength of the shock with an error of less than five per cent, at distances of the order of a hundred body-lengths. Finally, the theory is compared and contrasted with the recent work by Warren.