F-Function Lobe Balancing for Sonic Boom Minimization
The early sonic boom theory defined the F-function distributions for two-shock (bow and tail) signatures with minimum impulse, minimum overpressure, or minimum bow-shock overpressure. The cross-sectional area distributions for wing-body wind tunnel models were derived using the iterative methods. But these methods have a disadvantage that a two shock ground signature, which being the worst case of the system is optimeised by these methods. the ground-signature parameter is physicaly minimised by the use of the bow- and tail-shock strength minimisation and keeping them as close to the aircraft as possible. when this coalescence occurs closer to the ground, the Less than optimal two-shock signatures are resulted. Also, a unique equivalent body of revolution is determined by the F-function lobe. And it does not produce a unique aircraft geometry. The constrained optimization is used by the aircraft shaping methods. a realistic aircraft shape is where the process starts with and in the end, cross-section area and lift distributions is produced.

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