The solution by lifting-line theory of problems involving discontinuities

Abstract

The report, which has been written as a preliminary to a later account of similar work in lifting-plane theory, describes how wing loading problems involving discontinuities are solved by lifting-line theory. The four discontinuities considered are (a) direction of leading or trailing edge, (b) incidence, (c) two-dimensional lift slope and (d) chord. As the effects of the first are of minor importance in lifting-line theory, attention is mainly confined to the last three, the solution being based on the use of a few terms of a Fourier series in conjunction with special functions tabulated elsewhere. The work is limited to straight unyawed flight and includes lift, induced drag, and pitching, rolling and yawing moments, all with or without deflected landing flaps and ailerons. The method of formation of the equations, and the solutions of a representative range of problems for a hypothetical wing, including loading due to incidence, symmetrical wing twist, uniform roll, and deflected flaps and ailerons, are fully described. An indication is given of how induced drag and yawing moment calculations will later be simplified by the use of special derived functions. Absolute values of wing properties as given by lifting-line theory are usually too high, but the specification of correction factors for viscosity is beyond the scope of the report.