· · · Aerospace Engineering reports

An approximate method for the calculation of the aerodynamic forces on a wing of arbitrary planform in a subsonic non-viscous-flow has been given. The presented method can be considered as a modification of Multhopp's well-known lifting-surface theory with the view on the application of digital oomputors. Numerical results ere given for a swept-baok wing and the circular wing. Extensive comparisons of these results- for the circular wing with exact results were already made in the first author's thesis (ref.4) some years ago.

The present report deals with the numerical treatment of the linearised lifting surface theory through a method which is based upon the representation of the pressure distribution on chordwise direction by a series of Chebyshew polynomials according to Laschka, and upon the determination of the spanwise integral involved by means of trigonometric polynomials such as also appUed by Multhopp. When calculations are performed using Multhopp's method the results show strong variations with increasing number of the spanwise stations and chordwise points, to which the boundary condition is applied. This makes it impossible to obtain a plausible solution. Hence a new method has been developed, where the representation of the pressure distribution in spanwise direction is separated from the representation of the regularised kernel function in spanwise direction. This makes it possible to obtain accurate integrals for a given distribution of pivotal points and leads to results which show a rapid decrease of variation as either the number of spanwise stations or the number df chordwise points or both are increased. This is demonstrated by including a number of results for some well-known wings. As the method allows of the possibility to take arbitrary positions for the pivotal points, some computations have been performed for different distributions of spanwise stations. The results indicate that further investigations may be useful.

It was decided to develop a universal programme for the calculation of aerodynamic forces using Laschka's theory. Because of the storage capacity of the computer in use at the HLR the programme has heen split up into three parts. The first and third part are presented in this report in the form of an Algol programme; the second part, determining the solution of a set of linear equations, is not presented because an autocode programme was used. The results of some calculations carried out with these programmes have been published in ref.5.