Limitations of Use of Busemann's Second-order Supersonic Aerofoil Theory

Abstract

The author has found the Busemann theory very rapid in use for the determination of pressure coefficients. It has been tacitly assumed in the past that Busemann's second-order theory of aerofoils at supersonic speeds was subject to the same limitations of wedge angle as the exact theory given by Lighthill and others, namely, the wedge angle at which the bow wave detaches. The range of angles for which Busemann's theory gives a pressure coefficient in error by less than 1 per cent is shown to be smaller than the angle range for the shock wave to be attached. There is also a limit to the application of Busemann's method to angles of expansion as well as to angles of compression, unlike the exact theory, which can be extended to expansive angles of tile order of one right-angle without breaking down, in fact far beyond the useful range. The limits of angle given for the use of Busemann's theory are conservative, since they give the pressures to 1 per cent, and tile force coefficients will be more accurately determined since the errors tend to cancel out when integrating pressures to obtain forces.