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}.
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 beC_{L} = a\left ( \alpha – \alpha _{L=0} \right ) = 0.0773\left ( 6^{\circ}-\left ( -\left ( 1.2^{\circ} \right ) \right ) \right )=0.55656Induced 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
