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 \[C_{D,i}=\frac{C_{L}^{2}}{\pi AR}\left ( 1+\delta \right )=\frac{0.712^{2}}{\pi(8)}\left ( 1.054 \right )
\\=0.0212\]
