Equivalent Area Targets for Inverse Design Optimization With Changing Low-Boom Cruise Conditions

This paper provides theoretical and numerical justifications for inverse design optimization of reversed equivalent area (Ae,r) of low-boom supersonic aircraft when the cruise condition changes during the optimization iterations. A modified linear theory for steady flow around a supersonic projectile is used to establish the accuracy of Ae,r-based body-of-revolution approximation of a low-boom supersonic aircraft for undertrack sonic boom analysis using computational fluid dynamics off-body pressure. As a result, designing a low-boom shape of the off-body pressure at three body lengths below the aircraft is equivalent to designing a low-boom Ae,r shape. A Bezier curve with eight control points is used to define an Ae,r target for inverse design optimization of Ae,r of a supersonic aircraft. To make an Ae,r target matchable by a low-boom supersonic aircraft, the Ae,r target must have the minimal perceived level of decibels (PLdB) for sonic boom and satisfy two constraints defined by the cruise condition, effective length, and two nondimensional parameters. Numerical results are used to verify that, for different cruise conditions, all optimized Ae,r targets with PLdB below 70 can be approximately generated by scaling one of them if the targets have the same nondimensional parameters and approximately the same effective length.