Notes #13 MAE 533, Fluid Mechanics

Let (x, y, z) be a rectangular coordinate system, with +x in the direction of the undisturbed freestream flow velocity, +y normal to the plane of the thin wing, and z in the direction of the " span " of the wing. The wing is located on the y = 0 plane, " centered " at z = 0. We are given a large aspect ratio wing with the following information: Planform of the wing is described by c(z), the chord distribution. The " root chord, " c(0), is denoted by c o. The span of the wing (distance from wing tip to wing tip), is denoted by b. A large aspect ratio wing means b >> c o. Twist of the wing is described by α g (z), the distribution of the zero-lift angle of the wing (due to the camber of the wing cross-section). The overall angle of attack of the wing shall be denoted by α w. The goal of Prandtl's theory of finite wing is to find the lift and drag coefficients of this wing for low speed flight (M 2 ∞ << 1) as a function of the above information. There is no sweep to the wing under consideration.