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A new approach to the numerical solution of the equation of subsonic lifting surface theory

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Author: Zandbergen, P.J. · Labrujere, Th.E. · Wouters, J.G.
Publisher: Nationaal Lucht- en Ruimtevaartlaboratorium
Institution: National Aerospace Laboratory NLR
Source:NLR TR G.49
Rights: (c) 1967 National Aerospace Laboratory NLR


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.