# Thin Airfoil Theory (2-D Inviscid Flow)

14.3.1.1 Incompressible Flow (M0 = 0)

A thin airfoil with parabolic camber line d {x) = 4d c {1 – x) is moving with velocity U in a uniform atmosphere of density p. The chord of the airfoil is c, d = 0-086. Give the expression of the Fourier coefficients A0, A1, A2,An, for this airfoil. What is the angle of adaptation or ideal angle of attack? Sketch the corresponding flow. How is the flow at the leading edge?

Calculate the incidence of zero lift, a0 in deg. Show that the moments Cm, o = Cm, a.c. in this case.

Estimate the upper limit of the weight (in N) that a wing of chord c = 0.368 m and span b = 4.877 m could lift at Ci = 2 if the 2-D solution were applicable at take-off velocity V = 10.5m/s (use p = 1.225kg/m3). What would the take-off mass be in kg?

14.3.1.2 Supersonic Linearized Theory (M0 > 1)

A biconvex profile of equation z = 2e| {1 – f) equips a fin moving through the air at M0 = 2 and a = 1°.

Calculate the wave drag coefficient {Cd)a=0 and give the formula for Cl (a) and Cd (a) in terms of a and calculate the values for the given incidence and for a 10 % thickness ratio e = 0.1.

Estimate the upper limit of the lift and drag forces (in N) on the fin if c = 0.1m, b = 0.2 m and V = 633 m/s at z = 6000 m altitude (pair = 0.657 kg/m3).