The solution of lifting-plane problems by vortex-lattice theory (with seven appendices)

Abstract

The report describes in detail the methods by which the principles of vortex-lattice theory, introduced in a previous report, R. & M. 1910, are applied to the calculation of the aerodynamic loading of wings by lifting-plane theory. The scope of the paper is limited to the application of these principles to symmetrical incidence solutions and symmetrical and anti-symmetrical wing twist solutions, for which standard solutions can be treated by comparatively simple loading functions. The effect of discontinuity of direction of leading or trailing edge cannot be avoided even in the simplest solutions, and it has been found necessary to include an investigation of this problem in order to cover the prescribed usage of the method. Special standard functions tabulated in another report are used to allow for the rounding off effects due to change of direction of leading or trailing edge. The general problem of discontinuities is under investigation and will be dealt with in a later report. A comprehensive set of solutions for a delta wing is included in the report in order to show the convergence of and relation between solutions of varying complexity, and to indicate which solution should be used in order to satisfy the accuracy prescribed for any given problem. The case of the delta wing is not completely general, and the exposition in respect to induced drag and yawing moment will be completed in a later report.