Survey of acoustic characteristics of bullet shock waves

Abstract

The extensive literature on characteristics of shock waves provides fundamental relationships for amplitude and length which hold over a large range of projectile size. However, the discussions are spread through many publications and employ varying notation in mathematical exposition. The frequency spectrum of the shock-wave signature has received much less attention than the wave shape, although it is important in engineering applications such as bullet detection. This paper emphasizes engineering aspects. It combines data from a number of publications first to give a qualitative description of the N wave generated by bullet passage and the geometry associated with N-wave measurement. Formulas with consistent notation for calculating N-wave amplitude, length, and frequency spectrum are given. Computed values are compared to results of experimental measurements reported in the literature and carried out at Bissett-Berman. Effects on frequency spectrum of distance and shadowing by interfering objects are illustrated. It is shown that various theoretical and experimental results are consistent and produce a body of knowledge from which the characteristics of shock waves, generated by projectiles and other supersonic bodies, can be confidently predicted mathematically and accurately measured with available equipment.