Aeroelastic Problems of Low Aspect Ratio Wings: Part II. Aerodynamic Forces on an Elastic Wing in Supersonic Flow

A method is presented for calculating the aerodynamic forces acting on an elastic supersonic wing having arbitrarily swept straight leading edges and a supersonic trailing edge. The loads are presented in matrix form in terms of the geometrical incidence effective at given wing structural stations. It is thus possible, by combination with the corresponding structural matrix, to determine the steady state aeroelastic loading and final shape of the wing. It is shown how the distribution of loading associated with the placing of incidence on a small quadrilateral area within the wing plan form may be calculated. This loading is broken down into point loads acting at the required structural stations by graphical integration. The loading due to each small area is built up by superposing solutions obtained from linearized supersonic control surface theory. The sweep of the hinge line, and its relation to the wing Mach lines and leading edges are the main parameters of the problem. Twelve formulae are presented, giving the loading in each of the various regions likely to occur for practical wings. By a proper combination of the loads acting on symmetrically opposed stations on each side of the wing, the symmetric or anti‐symmetric aerodynamic matrix can be formed, corresponding to pitching and plunging, or rolling motions of the wing respectively.