AERONAUTICAL RESEARCH COUNCIL REPORTS AND MEMORANDA Velocities on Two-Dimensional Closed and Semblnfinite Aerofoils at Zero Incidence

An attempt is made to clarify the position as to the comparative two-dimensional velocity distributions on a thin doubly symmetrical aerofoil and on the corresponding senli-infmite body, the front part being the same ill the two cases. It is shown that the approximate linear method may be used with advantage to investigate the problem. The method provides a simple general proof that the supervelocity at the mid-chord station of a closed doubly symmetrical profile of any shape is approximately halved when the rear half is replaced by a semi-infinite parallel body. No such simple relationship applies to the entire chordwise distribution on the front part. All exact solution of the velocity distribution has been obtained for one particular semi-infinite profile and several alternative examples have been studied by the linear method. It is found that the ratio of maximum supervelocities may often considerably exceed 0-5 and sometimes rise to nearly 1.0. 1. Introduction.-In a recent discussion the question was raised as to the comparative two-dimensional velocity distributions on a thin doubly symmetrical aerofoil and the corresponding semi-infinite body. The purpose of this report is to investigate the matter. It has been found, using the well-known linear perturbation theory of thin symmetric aerofoils, that the value of the supervelocity at mid-chord station on any thin doubly symmetrical aerofoil gets very nearly halved when the rear half is replaced by a semi-infinite parallel body. No such simple rule, however, applies to the entire chord-wise supervelocity distributions in the two cases. At more forward stations, the ratio of corresponding supervelocities may assume values considerably in excess of 0.5, often not much lower than 1. This is shown below not only by general reasoning but also by working out complete velocity distributions by the linear method in several examples, including the biconvex parabolic profile, the ellipse, one very blunt oval, and one oval with particularly thin rounded nose. An exact solution has been found for one semi-infinite profile which is found to have rather exceptional properties in that the maximum supervelocity occurs at mid-chord for both the closed and semi-infinite aerofoil. In many other cases of doubly symmetrical profiles, the maximum may occur not at mid-chord but further upstream, either for the semi-infinite profile, or for both closed and semi-infinite ones.