Question

If the Aspect Ratio of a wing is doubled, what will happen to the Induced Drag Coefficient, assuming the lift coefficient and efficiency factor remain constant?

• A. Remain same
• B. \(50\%\) increase
• C. \(50\%\) decrease
• D. \(100\%\) increase

Hint:

Induced drag coefficient: \[ \boxed{ C_{D_i} = \frac{C_L^2}{\pi e\,AR} } \] Hence, \[ \boxed{ \text{Higher Aspect Ratio} \Longrightarrow \text{Lower Induced Drag}. } \]

Answer 1

The Correct Option is C

Step 1: Write the induced drag coefficient formula. The induced drag coefficient is \[ C_{D_i} = \frac{C_L^2}{\pi e\,AR}, \] where
• \(C_L\) = lift coefficient,
• \(e\) = Oswald efficiency factor,
• \(AR\) = aspect ratio.

Step 2: Determine the effect of doubling aspect ratio. Since \[ C_{D_i}\propto\frac1{AR}, \] doubling the aspect ratio gives \[ C_{D_i,\text{new}} = \frac12 C_{D_i}. \] Thus, the induced drag coefficient decreases by \[ 50\%. \] Therefore, \[ \boxed{\text{50\% decrease}} \] is the correct answer. Thus, \[ \boxed{(C)} \] is the correct answer.