NASA NTRS1994
One common method of extrapolating sonic boom waveforms from aircraft to ground is to calculate the nonlinear distortion, and then add a rise time to each shock by a simple empirical rule. One common rule is the '3 over P' rule which calculates the rise time in milliseconds as three divided by the shock amplitude in psf. This rule was compared with the results of ZEPHYRUS, a comprehensive algorithm which calculates sonic boom propagation and extrapolation with the combined effects of nonlinearity, attenuation, dispersion, geometric spreading, and refraction in a stratified atmosphere. It is shown there that the simple empirical rule considerably overestimates the rise time estimate. In addition, the empirical rule does not account for variations in the rise time due to humidity variation or propagation history. It is also demonstrated that the rise time is only an approximate indicator of perceived loudness. Three waveforms with identical characteristics (shock placement, amplitude, and rise time), but with different shock shapes, are shown to give different calculated loudness. This paper is based in part on work performed at the Applied Research Laboratories, the University of Texas at Austin, and supported by NASA Langley.