Supersonic Flow (M0 > 1, в = JM(2 — 1)

A thin airfoil with parabolic camber line d(x) = 4dmx (1 – x/c) is moving with Mach number M0 in a uniform atmosphere. The chord of the airfoil is c, dm = d/c = 0.086.

Pressure Distributions

Plot —C + and – C – versus x for this airfoil at a = 0. What is the corresponding lift coefficient Cl?

Lift and Moment Coefficients

Calculate the zero incidence moment coefficient (Cm, o) 0.

Give the values of the coefficients C; and Cm, o for the general case a = 0.

Equilibrium About an Axis

Calculate the moment Cm, D about an arbitrary point D along the chord and if the profile is allowed to rotate freely about point D, show that the equilibrium will be stable provided xD/c < 1/2 (neglect weight).

Give the equilibrium incidence, aeq in terms of xD.

Does aeq depend on Mach number?