Atmospheric turbulence effects on shaped and unshaped sonic boom signatures

Atmospheric turbulence is known to randomly distort the "N-wave" sonic boom signature emitted by conventional, unshaped supersonic aircraft. To predict the effect of turbulence on the signature from shaped aircraft, a numerical model has been developed based on the nonlinear Khokhlov-Zabolotskaya-Kuznetzov (KZK) propagation equation coupled with an approximate atmospheric turbulence model. The effects of turbulence on an archetypal N-wave and a shaped signature are compared via a series of numerical experiments propagating the signatures through multiple random realizations of turbulence in varying atmospheric and propagation conditions. The simulated results generally show that the variance of the Stevens Mark VII perceived level metric related to loudness is decreased by boom shaping and that the shocks in the shaped signature are less distorted than for the N-wave. Additionally, the probabilities of high-level and high-amplitude signatures are decreased for the shaped signature. Thus, the model predicts that boom shaping results in a signature with more consistent loudness and amplitude after propagation through turbulence.