According to classical thin airfoil theory in incompressible potential flow, a symmetric airfoil operates at an angle of attack $\alpha = 4^\circ$. What is the sectional lift coefficient $c_l$? (Take $\pi \approx 3.1416$, and round off to two decimal places).

Answer Key:

0.44

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Lift Slope:** For any thin airfoil in incompressible flow, $\frac{dc_l}{d\alpha} = 2\pi \text{ rad}^{-1}$. 2. **Stage 2: Zero-Lift Angle:** For a symmetric airfoil, $\alpha_{L=0} = 0$, so $c_l = 2\pi \alpha$. 3. **Stage 3: Radian Conversion:** $\alpha = 4^\circ \times \frac{\pi}{180} = 0.069813\text{ rad}$. 4. **Stage 4: Evaluation:** $c_l = 2\pi (0.069813) = 0.43865 \approx 0.44$. 5. **Stage 5: Tolerance:** 0.42 to 0.46.

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