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Shape Optimization with F-Function Balancing for Reducing the Sonic Boom Initial Shock Pressure Rise

A shape optimization methodology for reducing the initial shock pressure rise (ISPR) on the ground of a supersonic aircraft is presented. This methodology combines elements from the linearized aerodynamic theory such as Whitham's F-function with elements from the nonlinear aerodynamic theory such as the prediction of lift distribution by an Euler or a Navier-Stokes flow solver. It also features a concept of F-function lobe balancing that locates suitable positive and negative lobe pairs of the F-function, and modifies the shape of the aircraft to balance the areas of these lobes. The latter feature accelerates the convergence of the optimization procedure and forces it to generate an aircraft shape with a multi-shock ground signature, which reduces further the ISPR. This shaping technology is illustrated with an application to the Point of Departure aircraft developed by Lockheed-Martin for Phase I of DARPA's Quiet Supersonic Platform program. At M∞ = 1.5, a twenty-fold reduction of the ISPR on the ground, from 1.616 psf to 0.083 psf, is demonstrated while maintaining constant length, lift (weight), and inviscid drag. At M∞ = 2.0, a six-fold reduction of the ISPR on the ground, from 1.866 psf to 0.324 psf, is also demonstrated while maintaining constant length, lift (weight), and inviscid drag.