Rapid Estimation of the Sonic Boom Characteristics from Supersonic Passenger Aircraft in a Standard Atmosphere Based on Analytical Solutions: Caustics in Nonsteady Flight Modes

Abstract

The exact solutions for rays and ray tube areas in a standard atmosphere made it possible to formulate a criterion for sonic boom focusing on the ground in supersonic turn mode, as well as to calculate the caustic–ground intersection line width in acceleration mode in elementary functions. The dichotomy method was used as the basis for simple algorithms to calculate the caustic–ground intersection lines (focusing lines) arising in the acceleration and supersonic turn modes of a supersonic passenger aircraft. The dependence of the geometry of the focusing lines on the main flight trajectory parameters has been investigated. In acceleration mode, these parameters are flight altitude and acceleration, and in the case of supersonic turn, flight altitude, Mach number, and trajectory curvature radius. The focusing lines “stabilization” effect with increasing acceleration in acceleration mode and Mach number in supersonic turn mode has been observed. It has been established that flight altitude has a significantly smaller effect on the focusing lines shape than other trajectory parameters.