The Application of Green's Theorem to the Solution of Boundary-value Problems in Linearized Supersonic Wing Theory

Book excerpt: Under the assumptions of linearized theory, general methods of solutin are given for two- and three-dimensional steady-state and two-dimensional unsteady-state equations of compressible flow. The solutions depend in all cases on the use of Green's equivalent layer of sources, sinks, and doublets. Emphasis is placed on applications in supersonic wing theory, the singularities arising in the integrations being treated by Hadamard's finite part of the technique. Four examples of different character are discussed. In particular, the load distribution over a specific swept-back lifting surface is determined at a free-stream Mach number of one.