Analytical model for sound of explosives and firearms

An analytical model is presented for approximate prediction of the waveform and the sound level spectrum of blast waves generated by explosives and firearms. The model is based on numerical results for spherical blast waves, with overpressures between 10 kPa and 100 MPa, and a nonlinear propagation theory for blast waves. The matching of the numerical results and the nonlinear propagation theory is investigated, and compared with results from the literature and results of calculations with a nonlinear propagation model. The analytical model presented here assumes a Friedlander waveform, from which formulas are derived for the 1/3-octave band spectrum of the sound exposure level. The formulas take into account the nonlinear effect of pulse broadening, and the corresponding frequency shift. For firearms, the muzzle blast levels vary in general with the emission direction, and the model takes into account an empirical directivity correction. Apart from the directivity correction, the model has no empirical parameters. The waveform and the spectrum follow directly from the explosion energy or the explosive charge mass. Model predictions are in good agreement with measurement results of explosives and firearms, with the explosive charge mass ranging from 0.4 g to 4 kg TNT.