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 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 \[C_{D,i} = \frac{C_{L}^{2}}{\pi AR}\left ( 1+\delta \right )
=\frac{\left ( 0.55656 \right )^{2}}{\pi \left ( 6 \right )}\left ( 1+0.03 \right )=0.0169\]
