2-D Inviscid, Linearized, Thin Airfoil Theories
22.214.171.124 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.
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..
126.96.36.199 Supersonic Flow (M0 > 1, в = ^M(J — 1)
Consider the thin parabolic plate of equation
d (x ) = 4dm —
where the relative camber is given to be dm/c = 0.14.
Give the lift coefficient C; (a) for this airfoil.
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?