Question

A finite wing of elliptic planform with aspect ratio 10 and symmetric airfoil operates at \(5^\circ\) angle of attack in uniform flow. The induced drag coefficient is \(\underline{\hspace{1cm}}\) (round off to three decimal places).

Hint:

Elliptic wings give minimum induced drag. Use \(C_{D_i} = C_L^2/(\pi AR)\) and always convert angle of attack to radians.

Answer 1

Correct Answer: 0.005

For an elliptic wing, induced drag coefficient is:
\[ C_{D_i} = \frac{C_L^2}{\pi AR} \] Lift coefficient for small angles (in radians):
\[ C_L = 2\pi\alpha \] \[ \alpha = 5^\circ = \frac{5\pi}{180} = 0.0873\ \text{rad} \] \[ C_L = 2\pi(0.0873) = 0.548 \] Now compute induced drag:
\[ C_{D_i} = \frac{0.548^2}{\pi(10)} \] \[ C_{D_i} = \frac{0.300}{31.416} = 0.00955 \] Rounded to three decimals:
\[ C_{D_i} \approx 0.010 \]