Maximum lift-to-drag ratio airfoils at moderate supersonic speeds.

Maximum lift-to-drag ratio airfoils at moderate supersonic speeds are determined using linear theory and second-order theory. Two cases are investigated: 1) given length and thickness and 2) given length and enclosed area. The indirect methods of the calculus of variations are employed, and it is shown that the optimum airfoil is a diamond shape for case 1 and is biconvex for case 2. If linear theory is employed, the maximum lift-to-drag ratio airfoil has maximum thickness at mid chord and is symmetric with respect to the chord. Its geometry is identical with that of the minimum drag airfoil and is totally insensitive to changes in the Mach number. If nonlinear theory is used, the maximum lift-to-drag ratio airfoil has maximum thickness in the rear half and is asymmetric with respect to the chord (the upper contour is thicker than the lower contour). Its geometry is different from that of the minimum drag airfoil and, for a given surf ace-aver aged friction coefficient, is only slightly sensitive to changes in the Mach number.