# Problem 2

14.2.1 Thin Airfoil Theory (2-D Inviscid Flow)

14.2.1.1 Incompressible Flow (Mo = 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.

Define the lift and moment coefficients, C; and Cm, o in terms of the dimensional quantities p, U, c, L, M, o, where L and M, o are the lift (N/m) and the moment (Nm/m) per unit span.

Use thin airfoil theory results to express the Ci and Cm, o in terms of a, the incidence angle (rd) and d the relative camber.

Given d = 0.086 find the angles of incidence in degree for which C; = 0.5, Ci = 2.0 and calculate the corresponding moments Cm, o.

Find the location of the center of pressure pp in both cases.

Show on a sketch the position of the center of pressure relative to the aerodynamic center.

14.2.1.2 Supersonic Linearized Theory (M0 > 1)

The same airfoil as in 1.1 is moving at supersonic speed.

Give the expression for the lift coefficient C; (a) in supersonic flow.

Give the expression for the moment coefficient Cm, o(a) in supersonic flow and

calculate (Cm, o)a=0.

Express x3L in terms of a.