Tables of multhopp and other functions for use in lifting-line and lifting-plane theory

Abstract

The report gives the derivation and computed tables of two classes of functions suitable for the solution of problems of spanwise aerodynamic loading of wings either by lifting-line or lifting-plane theory. The functions are based on lifting-line theory, but, by a consideration of the connection between lifting-line and lifting-plane theory through the application of I~nnk's stagger theorem to the calculation of induced drag, it is deduced that the functions must be equally suitable for lifting-plane theory. The first range of functions, called Multhopp or M functions, is associated with discontinuities of induced downwash, while the second, called P functions because of the polygonal representation of induced downwash, is connected with discontinuities in rate of change of induced downwash. Examples are given of the combination of functions to produce given curves of induced downwash, and evidence of the close relation between the results for a continuous and stepped downwash curve suggests that the functions tabulated will be sufficient to cover almost any problem in wing loading.