A thin cambered airfoil has a zero-lift angle of attack $\alpha_{L=0} = -2^\circ$. According to thin airfoil theory, what is its lift coefficient $C_L$ when operating at an angle of attack $\alpha = 3^\circ$? (Take theoretical lift curve slope $2\pi \text{ rad}^{-1}$, round off to two decimal places).

Answer Key:

0.55

### Solution: Effective angle of attack $\alpha - \alpha_{L=0} = 3^\circ - (-2^\circ) = 5^\circ$. In radians: $5 \times \frac{\pi}{180} = \frac{5\pi}{180}\text{ rad}$. Lift coefficient: $C_L = 2\pi \left(\frac{5\pi}{180}\right) = \frac{10\pi^2}{180} = \frac{\pi^2}{18} \approx \frac{9.8696}{18} \approx 0.548 \approx 0.55$. Correct: 0.55 (range 0.53 to 0.57).

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