NACA-TN-925

Abstract

INTRODUCTION <br>The distribution of lift over the span of a wing in uniform motion is determined, according to the Prandtl theory of the lifting line, as the solution of a singular integro-differential equation the mathematical complexities of which are such that exact solutions have been obtained only in very special cases. While several methods have been devised for obtaining approximate solutions to this equation, it is felt that a new procedure based on a method of least squares which was presented in reference 6 may be of practical interest. <br>In the usual procedures' an approximation to the lift function is assumed .as the sum of a finite number of appropriate approximating functions with undetermined coefficients, after which the coefficients are determined in various ways so that the lifting-line equation is approximately satisfied, While it might be expected that the determination of these parameters would be nest efficiently accomplished by a method of least squares, the only application of such a method known to the writer (reference 2) was not well adapted to numerical computation ,for arbitrarily varying chord and angle of attack. In addition, the single case treated was that of awing with discontinuous angle of attack, for which the procedure as given in reference 2 failed to give satisfactory results. <br>The purpose of the present paper is to present least-squares procedure in which the major-part of the numerical calculation can be readily carried out on a computing machine, and in which the amount of labor involved is not dependent upon the nature of the variation of the chord and the ,angle of attack. Since all the previous procedures are notably inadequate for the analysis of wings with discontinuous spanwise variation of angle of attack or chord, an explicit treatment of such cases is included. <br>This investigation, conducted at the Massachusetts Institute of Technology, was sponsored by, and conducted with financial assistance from, the National Advisory Committee for Aeronautics.