Methods for calculating the lift distribution of wings subsonic lifting-surface theory

Abstract

This report contains some fairly simple and economic methods for calculating the load distribution on wings of any plan form based on the conceptions of lifting-surface theory. The computer work required is only a small fraction of that of existing methods with comparable accuracy. This is achieved by a very careful choice of the positions of pivotal points, by plotting once for all those parts of the downwash integral which occur frequently and by a consequent application of approximate integration methods similar to those devised by the author for lifting-line problems. The basis of the method is to calculate the local lift and pitching moment at a number of chordwise sections from a set of linear equations satisfying the downwash conditions at two pivotal points in each section. Interpolation functions of trigonometrical form are used for spanwise integration both in setting up the downwash equations and in getting the resultant forces on the wing from the local forces. The preliminary chordwise integrations for the downwash are predigested in a series of charts (Figs. 1 to 6) ; it is these which make the method a practical computing proposition. The theory is outlined in sections 2 to 5 ; section 6 deals with the solution of the linear equation and section 7 with the resultant forces on the wing. Some examples are worked out in section 8 to compare with other methods; one solution is given in full detail in Tables 8 to 30 as a guide for computers. Appendices I to VI discuss more carefully some salient points of the mathematical theory, and AppendLx VII is intended to instruct the computer how to carry out the steps of the calculation.