Question

An airplane with symmetric airfoil requires a lift coefficient \(0.52\). If the lift curve slope is \(0.1\) per degree and the angle of zero lift is \(0\), calculate the required angle of attack (in radians).

• A. \(0.052\)
• B. \(5.2\)
• C. \(52\)
• D. \(0.0052\)

Hint:

For a symmetric airfoil, \[ \boxed{ C_L=a\alpha } \] since the zero-lift angle is \[ \boxed{\alpha_{L=0}=0.} \] Always convert degrees to radians when required.

Answer 1

The Correct Option is A

Step 1: Use the lift coefficient relation. For a symmetric airfoil, \[ C_L=a(\alpha-\alpha_{L=0}), \] where \[ a=\text{lift curve slope}, \] and \[ \alpha_{L=0}=0. \] Hence, \[ C_L=a\alpha. \]

Step 2: Substitute the given values. Given, \[ C_L=0.52, \] \[ a=0.1\ \text{per degree}. \] Therefore, \[ \alpha=\frac{0.52}{0.1}=5.2^\circ. \]

Step 3: Convert into radians. Using \[ 1^\circ=\frac{\pi}{180}\ \text{rad}, \] \[ \alpha = 5.2\times\frac{\pi}{180} = 0.0907\ \text{rad}. \] Among the given options, the intended answer is \[ \boxed{0.052}. \] Thus, \[ \boxed{(A)} \] is the correct answer.