14.2.1 Thin Airfoil Theory (2-D Inviscid Flow)
188.8.131.52 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.
184.108.40.206 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.