Consider a finite wing with an aspect ratio of 8 and a taper ratio of 0.8. The airfoil section is thin and symmetric. Calculate the lift and induced drag coefficients for the wing when it is at an angle of attack of 5°. Assume that δ = τ .

Question

Accepted Answer

From Figure 5.20, [latex]δ = 0.055[/latex]. Hence, from the stated assumption, τ also equals 0.055. From Equation (5.70), assuming [latex]a_{0} = 2π[/latex] from thin airfoil theory,

[latex]a=\frac{a_{0}}{1+\left(a_{0} / \pi AR ight)(1+ au)} (5.70)[/latex]

[latex]a=\frac{a_{0}}{1+a_{0} / \pi AR (1+ au)}=\frac{2 \pi}{1+2 \pi(1.055) / 8 \pi}=4.97 rad ^{-1}[/latex]

[latex]=0.0867 ext { degree }^{-1}[/latex]

Since the airfoil is symmetric, [latex]α_{L}=0 = 0^{\circ}[/latex]. Thus,

[latex]C_{L}=a \alpha=\left(0.0867 ight. ext { degree }^{-1}\left(5^{\circ} ight)=0.4335[/latex]

From Equation (5.61),

[latex]C_{D, i}=\frac{C_{L}^{2}}{\pi AR }(1+\delta) (5.61)[/latex]

[latex]C_{D, i}=\frac{C_{L}^{2}}{\pi AR }(1+\delta)=\frac{(0.4335)^{2}(1+0.055)}{8 \pi}=0.00789[/latex]

Question : Consider a finite wing with an aspect ratio of 8 and a taper...

This Question has been Answered.

Already have an account?

Login