2-D Inviscid, Linearized, Thin Airfoil Theories

14.10.1.1 Incompressible Flow (M0 = 0)

Profile Camber Estimation

A wing profile lift curve, calculated with a numerical method, gives a value of the lift coefficient to be (Ci)profiie = 2.1878 at a = 4°. Using the result of thin airfoil theory, find all the Fourier coefficients of a thin parabolic plate equivalent to this airfoil. Estimate the relative camber dm/c of the thin parabolic plate. Check your result as the rest depends on it.

Take-Off Incidence

For this equivalent thin parabolic plate, find the incidence in deg. for which the lift coefficient is Cl = 2.5.

Nose Pitching Moment Coefficient

Give the pitching moment coefficient Cm, o(a) for the parabolic plate. Predict the nose pitching moment coefficient of the wing profile (Cm, o)projile at a = 4°. Compare with the calculated result of -0.935.

Aerodynamic Center Pitching Moment Coefficient

Give the definition of the aerodynamic center. Give the pitching moment coefficient about the aerodynamic center Cm, a.c..

14.10.1.2 Supersonic Flow (M0 > 1, в = ^M(J — 1)

Consider the thin parabolic plate of equation

X

d (x ) = 4dm —

c

where the relative camber is given to be dm/c = 0.14.

Lift Coefficient

Give the lift coefficient C; (a) for this airfoil.

Drag Coefficient

Calculate the drag coefficient (Cd )a=0 and give the expression of Cd (a) for this airfoil.

Pitching Moment Coefficient

If the profile is allowed to rotate freely about an axis placed at the quarter-chord, find the equilibrium incidence aeq in deg. (Hint: Use the change of moment formula to evaluate Cmf/4). How would you qualify the equilibrium situation: stable, unstable, neutral?