The effect of wind tunnel interference on the characteristics of an aerofoil

Abstract

The effect of the walls of the enclosure on the measured values of the lift and drag experienced by an aerofoil is quite appreciable and it has been known for a considerable time that correction must be applied to wind tunnel result before they can be applied to free air conditions. Prandtl* investigated the effect on an aerofoil in a free jet or circular tube both in the case where there is a uniform lift distribution, and in the case where there is an elliptic distribution of circulation. The elliptic distribution is of importance because it gives the minimum drag for a given lift. Glauert by means of an approximate method found the induced drag and lift in a rectangular channel when there is a uniform distribution of lift. Terazawa modified Glauert’s method and obtained the exact solution for an aerofoil with uniform distribution of circulation in a rectangular channel. It is The object of this note to extend these results and to obtain the induces drag and lift in a rectangular channel when there is an elliptic distribution of lift. In addition, the discussion of Prandtl is briefly gone through because Prandtl’s results are usually given as the first few terms of an infinite series, and it has not been noticed that the result can be obtained exactly. Glauert’s work on the effect of plane barries is briefly re-examined because, in his analysis, approximate expression were summed over an infinite series of points, and at first glance it appeared that this would introduce some error of the same order as the result. In this note the summation is carried out rigorously and the approximations to the actual values. The small divergences from Glauert’s result obtained by Terazawa in two numerical cases are, in effect, the result of a slightly more accurate approximation. From the practical point of view the results of this paper add little to what is known already, for the major corrections are given by the results of the approximate methods, but this note should fill in some small gaps in the theory of wind tunnel interference.