# Consider a wing with a thin, symmetric airfoil section in a Mach 2 airflow at an angle of attack of 1.5°. Calculate the lift coefficient

Consider a wing with a thin, symmetric airfoil section in a Mach 2 airflow at an angle of attack of 1.5°. Calculate the lift coefficient

(a) For the airfoil section.

(b) For the wing if it is a straight wing with an aspect ratio of 2.56.

( c) For the wing if it is swept at an angle of 60°, with an aspect ratio of 2.56 and a taper

ratio of unity.

(a) \[M_{\infty}=2; \alpha = 1.5^{\circ} = 0.02618\,rad\]

\[C_{L}=\frac{4\alpha }{\sqrt{M_{\infty}^{2}}-1}= \frac{4\left (0.02618 \right )}{2^{2}-1}=0.0605\]

(b) \[C_{L} = \frac{C_{l}}{\sqrt{1+\left ( \frac{a_{0}}{\pi\,AR} \right )^{2}}+\frac{a_{0}}{\pi AR}}=\frac{0.0605}{\sqrt{1+\left ( \frac{2\pi}{\pi 2.56} \right )^{2}}+\frac{2\pi}{\pi 2.56}}=0.02951\]

(c) \[AR = 2.6; TR = 1; \wedge = 60^{\circ}\]

\[ \beta =\sqrt{M_{\infty}^{2}-1}=\sqrt{2^{2}-1}=1.732\]

\[Tan \wedge = Tan 60^{\circ}=1.732\]

\[AR\,Tan \wedge = 2.6\times 1.732 = 4.503\]

\[C_{Na} = \frac{4.1}{1.732}=2.367\, per\,rad\,= 0.0413\,per\,deg\]

\[\Rightarrow C_{L} = C_{Na}\alpha= 0.0413\left ( 1.5 \right )=0.062\]