# Prandtl Lifting Line Theory

The WWII Spitfire was designed with an elliptic wing of span b = 11.2m and wing area S = 22.5 m2. It is equipped with a NACA2209.4 profile of 2 % relative camber (d/c = const = 0.02). The top speed in cruise is V = 170 m/s (378mph) with a take-off mass of M = 3,000 kg.

14.9.2.1 Vortex Sheet

Explain succinctly the key features of the vortex sheet (physically and mathemati­cally) and the effect it has on the flow past a large aspect ratio wing (lifting line).

14.9.2.2 Lift Coefficient

Given the above data, calculate the lift coefficient CL at top speed in cruise (take p = 1.2kg/m3 and g = 9.81 m/s2).

Assuming an elliptic planform, a constant relative camber and zero twist, calculate the induced drag CDi and the first mode amplitude A i in the Fourier Series expansion of the circulation

Г[y(ff)] = 2Ub ~1 An sin nd
y(Q) = —§ cos в, 0 < в < п

Write the equation for the lift coefficient CL in terms of aspect ratio AR, geometric incidence a and relative camber d/c.

Find a, the geometric incidence in cruise.