Acoustical model of small calibre ballistic shock waves in air for automatic sniper localization applications

Abstract

The phenomenon of ballistic shock wave emission by a small calibre projectile at supersonic speed is quite relevant in automatic sniper localization applications. When available, ballistic shock wave analysis makes possible the estimation of the main ballistic features of a gunfire event. The propagation of ballistic shock waves in air is a process which mainly involves nonlinear distortion, or steepening, and atmospheric absorption. Current ballistic shock waves propagation models used in automatic sniper localization systems only consider nonlinear distortion effects. This means that only the rates of change of shock peak pressure and the N-wave duration with distance are considered in the determination of the miss distance. In the present paper we present an improved acoustical model of small calibre ballistic shock wave propagation in air, intended to be used in acoustics-based automatic sniper localization applications. In our approach, we have considered nonlinear distortion, but additionally we have also introduced the effects of atmospheric sound absorption. Atmospheric absorption is implemented in the time domain in order to get faster calculation times than those computed in frequency domain. Furthermore, we take advantage of the fact that atmospheric absorption plays a fundamental role in the rise times of the shocks, and introduce the rate of change of the rise time with distance as a third parameter to be used in the determination of the miss distance. This lead us to a more accurate and robust estimation of the miss distance, and consequently of the projectile trajectory, and the spatial coordinates of the gunshot origin.