COMPARISON OF SONIC-BOOM RISE TIME PREDICTION TECHNIQUES

An important quantity in determining the loudness of sonic booms outdoors is the rise time. In the absence of turbulence, the rise time is dictated by frequency-dependent loss mechanisms in the atmosphere including relaxation, viscosity, and thermal conduction. Two techniques have been used to predict rise times of sonic booms. The technique developed by Pestorius and Blackstock numerically steps a weak shock through the atmosphere accounting for frequency-dependent absorption and time-dependent wave steepening independently at each step. This technique has been extended by Bass and Raspet to include absorption and dispersion by the vibrational relaxation of N2 and O2 in the presence of H2O. The second technique is to apply the augmented Burgers' equation to determine a steady-state asymptotic shock profile. This approach is strictly valid only for a plane shock wave with a duration much greater than the rise time. This letter compares predicted rise times using these two approaches. The input waveforms were assumed to be N waves with a linear rise at the front and rear of the shock. These calculations show that N waves of duration greater than 100 times the rise time can be treated as steady-state shocks. The rise time for shock waves of shorter duration cannot be determined using the steady shock assumption.