The measured lift slope for the NACA 23012 airfoil is 0.1080\; degree^{−1}, and α_{L}=0 = −1.3^{\circ}. Consider a finite wing using this airfoil, with AR = 8 and taper ratio = 0.8. Assume that δ = τ . Calculate the lift and induced drag coefficients for this wing at a geometric angle of attack = 7^{\circ}.
The measured lift slope for the NACA 23012 airfoil is 0.1080\; degree^{−1}, and α_{L}=0 = −1.3^{\circ}. Consider a finite wing using this airfoil, with AR = 8 and taper ratio = 0.8. Assume that δ = τ . Calculate the lift and induced drag coefficients for this wing at a geometric angle of attack = 7^{\circ}.
Lift slope for the wing is a=\frac{a_{0}}{1+\frac{a_{0}}{\pi AR}\left ( 1+\tau \right )}.Here a_{0}=0.1080/\textrm{degree}=6.188\;\textrm{per radian}.\delta =\tau=0.054.Therefore a=\frac{6.188}{1+\frac{6.188}{\pi(8)}\left ( 1+0.054 \right )}=4.91/\textrm{rad}=0.0857\;\textrm{per degree}
Coefficient of lift is given as C_{L}=a\left ( \alpha-\alpha_{L=0} \right ) \\=0.0857\left ( 7-\left ( -1.3 \right ) \right ) \\=0.712
Induced drag coefficient is given as C_{D,i}=\frac{C_{L}^{2}}{\pi AR}\left ( 1+\delta \right )=\frac{0.712^{2}}{\pi(8)}\left ( 1.054 \right ) \\=0.0212
