Question

A thin cambered airfoil has lift coefficient $C_l=0$ at angle of attack $\alpha=-1^\circ$. Estimate $C_l$ at $\alpha=4^\circ$, assuming stall occurs at much higher $\alpha$. (round off to two decimal places)

Hint:

Thin airfoil theory predicts slope $2\pi$ per radian. Always convert degrees to radians before applying formula.

Answer 1

Step 1: Thin airfoil theory.
\[ C_l = 2\pi (\alpha - \alpha_{L=0}) \] where $\alpha_{L=0}$ is zero-lift angle.

Step 2: Convert angles.
Given: $\alpha_{L=0} = -1^\circ = -\frac{\pi}{180} \approx -0.01745 \,\text{rad}$ At $\alpha=4^\circ = \frac{4\pi}{180} = 0.06981 \,\text{rad}$

Step 3: Substitute.
\[ C_l = 2\pi (0.06981 - (-0.01745)) = 2\pi (0.08726) \] \[ = 6.283 \times 0.08726 = 0.548 \approx 0.55 \] \[ \boxed{0.55} \]