Analysis of sonic boom data to quantify distortions of shock profiles

Researchers at Penn State have been examining some sonic boom waveforms recorded during overflights by the Air Force which have become available to NASA and its contractors. The quality of the digitized data and the supporting meteorological data was such that one could test the applicability of molecular relaxation theories. In the late sixties, it had been supposed that the finite rise times in the absence of turbulence had neglected the vibrational relaxation of nitrogen molecules. Bass et al. have demonstrated that molecular relaxation definitely gives the correct order of magnitude of the observed rise times. However, the Air Force data in conjunction with the recent steady-state shock profile model theory of Kang and Pierce give the first opportunity to make a detailed quantitative assessment of the molecular relaxation hypothesis. Currently an investigation is ongoing to establish a method of quantifying the distortion of a sonic boom wave from a classic N-wave shape using the Air Force data taken at Edwards AFB in 1987. Using the premise that energy will be conserved approximately for a sonic boom wave both before and after the boom passes through the Earth's turbulent boundary layer, a classic undistorted waveform is constructed from the distorted signature received at the ground. A correlation between the mean-squared deviation of the distorted and undistorted waveforms and the distance the boom travels through the turbulence is sought.