The result from Problem 12.6 demonstrates that maximum lift-to-drag ratio decreases as the Mach number increases. This is a fact of nature that progressively causes designers of supersonic airplanes grief as they strive toward aerodynamically efficient airplanes at higher supersonic Mach numbers. What physics is nature using against the airplane designer in this case, and how might the designer meet this challenge?

Data problem Problem 12.6:

Consider a flat plate at an angle of attack in a viscous supersonic flow; i.e., there is both skin friction drag and wave drag on the plate. Use linear theory for the lift and wave-drag coefficients. Denote the total skin friction drag coefficient by C _f , and assume that it does not change with angle of attack. (a) Derive the expression for the angle of attack at which maximum lift-to-drag ratio occurs as a function of C _f and freestream Mach number. (b) Derive the expression for the maximum lift-to-drag ratio as a function of C _f and freestream Mach number M.