Chapter 12, Problem 12.6P

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. Answers: (a) $\alpha ={\left(C_f\right)}^{1/2}{\left(M^2-1\right)}^{1/4}/2;$ (b) ${\left(c_l/c_d\right)}_{\max }={\left(c_f\right)}^{-1/2}{\left(M^2-1\right)}^{-1/4}$