A finite wing has aspect ratio of $6$ and taper ratio of $0.8$. The airfoil constituting this wing has a lift slope of $0.102$ per degree, and angle of attack at zero lift of $-1.2^{\circ}$. Assuming that $\delta =\tau$ and equals approximately $0.03$ , find the coefficient of lift and induced drag coefficients for this wing at an angle of attack of $6^{\circ}$.

The relation between lift slopes for an airfoil and wing is $$a = \frac{a_{0}}{1+\left ( \frac{a_{0}}{\pi AR} \right )\left ( 1+\tau \right )}$$ Here, $a_{0}$ = lift slope for an airfol, $a$ = lift slope for a wing, $AR$ = Aspect ratio,
$\delta = \tau = 0.03$

$0.102\, per\, degree = 5.8442\, per\, radian$
Therefore, $$a = \frac{5.8442}{1+\left ( \frac{5.8442}{\pi \left ( 6 \right )} \right )\left ( 1+ 0.03 \right )}$$ $$\Rightarrow a = 4.43\,per\,radian = 0.0773\,per\,degree$$

Coefficient of lift for this wing will be $$C_{L} = a\left ( \alpha – \alpha _{L=0} \right ) = 0.0773\left ( 6^{\circ}-\left ( -\left ( 1.2^{\circ} \right ) \right ) \right )=0.55656$$ Induced drag coeffcient for this wing will be $$C_{D,i} = \frac{C_{L}^{2}}{\pi AR}\left ( 1+\delta \right ) =\frac{\left ( 0.55656 \right )^{2}}{\pi \left ( 6 \right )}\left ( 1+0.03 \right )=0.0169$$