Solution of Subsonic Nonplanar Lifting Surface Problems by Means of High-Speed Digital Computers

Abstract

The method proposed in this paper is based on an approximate solution of the integral equation which represents the potential flow about a finite wing, with no restrictions beyond those necessary for linearization. After assuming the usual series representation of the wing surface vorticity distribution, the solution is achieved by approximating portions of the kernels of the transformed integral equation by single and double Fourier series and performing termwise integrations analytically. This is followed by the routine inversion of the aerod3mamic influence coefficient matrix, after satisfying appropriate boundary conditions at selected control points. In this procedure the number of control points used is limited only by the storage capacity of the computer. Control points may be located so as to cover the entire wing surface, with due regard to certain physical requirements, permitting the accurate representation of complicated mean surface shapes. An evaluation of the proposed method is included. Comparisons with other theoretical methods and electrical analogy tank results are used to substantiate the accurac} of the proposed method when applied to plane wings. A final evaluation involves a comparison of calculated surface pressure distribution with wind-tunnel measurements on a swept, tapered wing with a cambered and twisted mean surface. The agreement evidenced in the latter comparison has the same order of overall accuracy as similar comparisons on plane wing planforms. In either case, the results given by the proposed method are within the accuracy requirements for most aircraft design studies.