# Consider a finite wing of aspect ratio 4 with an NACA 2412 airfoil; the angle of attack is 5°. Calculate (a) the lift coefficient at low speeds (incompressible flow) using the results of Prandtl’s lifting line theory, and (b) the lift coefficient for \(M_{\infty}\). Assume that the span efficie

Consider a finite wing of aspect ratio 4 with an NACA 2412 airfoil; the angle of attack is 5°. Calculate (a) the lift coefficient at low speeds (incompressible flow) using the results of Prandtl’s lifting line theory, and (b) the lift coefficient for \(M_{\infty}\). Assume that the span efficiency factor for lift is e1 = 0.90.

(a) Lift coefficient at low speeds(incompressible flow), \(a_{0} = 6.016/radian\)

\[ a = \frac{a_{0}}{1 + \frac{a_{0}}{\pi e_{1} AR}}\]\[a = \frac{6.016}{1+\frac{6.016}{\pi\left ( 0.90 \right )4}}= 3.927/radian = 0.0685/degree\]\[C_{L0} = a\left ( \alpha -\alpha _{L=0} \right )=0.0685\left ( 5-\left ( -2.2^{\circ} \right ) \right )=0.493\](b) Lift coefficient for \(M_{\infty} = 0.7\). \[C_{L} = \frac{C_{L0}}{\sqrt{1-M_{\infty}^{2}}}=\frac{0.493}{1-0.7^{2}}=0.6903\]