GATE 2021 AE – Question 51
An elliptic wing has aspect ratio 10, section lift slope $2\pi$ per radian and angle of attack 5°. Its induced-drag coefficient is (three decimals)
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: -0.003 to 0.017
Explanation
**Finite-wing lift slope** (elliptic loading, Prandtl's lifting-line theory):
$$a=\frac{a_0}{1+a_0/(\pi AR)}=\frac{2\pi}{1+2\pi/(\pi\times10)}=\frac{2\pi}{1+2/10}=\frac{2\pi}{1.2}=5.236\ \text{per rad}.$$
**Lift coefficient** at $\alpha=5^\circ=0.08727$ rad (for a symmetric wing with zero lift at $\alpha=0$):
$$C_L=a\alpha=5.236\times0.08727=0.4569 .$$
**Induced drag coefficient** for elliptic loading ($e=1$):
$$C_{D_i}=\frac{C_L^2}{\pi\,AR}=\frac{0.4569^2}{\pi\times10}=\frac{0.2088}{31.416}=\mathbf{0.0066}.$$