Consider a wing with elliptic planform, of span b and chord c(y) = c0A/1 – (2 y/b)2. The wing has constant relative camber d(y)/c(y) = d/c = const and has washout given by t(y) = -4tx(2y/b)2, where -4tx is the twist at the wing tips.
Calculate the coefficients A1, A2,… ,An, n = 1, to. Hint: Write Prandtl integro – differential equation, where the circulation in the l. h.s. is represented by the Fourier series, and the wing geometry is introduced in the r. h.s. Use the change of variables y = -§ cos t, 0 < t < n and the identity 4cos21 sin t = sin t + sin 3t.
From the equation for A1 give the equation of the lift curve CL(a). What is the incidence of zero lift, a0?
Calculate the induced drag if a = 3tx – 2d/c.
6.14.1 Design Problem
Considering the lifting problem, design a rectangular wing of span b and chord c, (AR = b/c), with zero twist, and equipped with parabolic thin airfoils, such that the circulation is elliptic at the given lift coefficient CL, des = 0.5. Furthermore, at the design CL, des the wing has an adapted leading edge.
Find the relative camber distribution d(y)/c that will satisfy all the requirements. Where is the maximum camber located along the wing span? Calculate the value of the maximum camber.
Give the value of the geometric incidence at design, a, in terms of CL, des and AR. Show that at a different incidence, в = a, the circulation is no longer elliptic.
If viscous effects limit the maximum local lift coefficient to a value Ci, moa, which is the same for all profiles, where will stall occur first on the wing?
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