Constant‐Velocity Aerofoils: Theoretically‐derived Profiles of Thin Sections Suitable for High Speeds

FOR aerofoils intended for use at high speeds, it is evident that the maximum lift on the back, consistent with a given maximum intensity of suction, will be attained when the suction, and hence the velocity, over the back is uniform; in other words, for a given mean lift on the back, the greatest suction will be a minimum, and so will the greatest velocity. On the hypothesis that compressibility stalling and compressibility effects generally depend on the amount of the greatest velocity at any point, such an aerofoil will have the ideal shape for high speed work. Interest, therefore, attaches to the theoretical solutions which are possible giving the form of an aerofoil having this property, particularly in view of the success of the theory in predicting velocity and pressure distributions for the ordinary range of aerofoils. When the thickness is finite somewhat involved problems in conformal representation require to be solved, although there is no fundamental difficulty in working out the solution. For thin aerofoils of small camber, such as those considered by Glauert in his classical theory, the problem is much simpler and it is known that the results of this theory are actually applicable to aerofoils such as are used in practice. Glauert himself considered only the case of infinitesimal thickness; this gives one solution of the problem here considered. Others are obtained by extending the theory to thicknesses of the same order as the camber, the order of approximation remaining the same. A particular case which will be treated here is that of an aerofoil having a flat face, i.e., camber equal to half the thickness.