Downwash and induced drag corrections for a lifting wing at low speeds in a circular‐section wind tunnel

Abstract

Analytical solutions for the downwash and induced drag wall corrections are given for a finite lifting‐rolling wing at low speeds in a circular test‐section wind tunnel. The spanwise lift distribution is represented by a Fourier cosine series instead of the Fourier sine series as has been the general practice in the literature so far. Unlike the sine distributions, the cosine distributions do not produce a singularity in shed vorticity at the wing tips and hence these are considered more realistic in mimicking actual lift distributions. For a given lift, comparisons are made for tunnel corrections for uniform, elliptic, and parabolic lift distributions (the last being an example of cosine distributions) to highlight the fact that tip loadings have a primary influence on the magnitude of tunnel corrections at large wing span: tunnel test‐section diameter ratios, and thus must be correctly represented. Similar comparisons are made for a given rolling moment at zero lift for the simplest of the antisymmetric Fourier sine and cosine lift distributions.