# Find the coefficient of lift and induced drag coefficients for this wing at an angle of attack of $$6^{\circ}$$.

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 $$6^{\circ}$$.

Asked on 11th August 2021 in
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 $C_{D,i} = \frac{C_{L}^{2}}{\pi AR}\left ( 1+\delta \right ) =\frac{\left ( 0.55656 \right )^{2}}{\pi \left ( 6 \right )}\left ( 1+0.03 \right )=0.0169$