GATE 2023 AE – Question 56

Aerodynamics · Airfoils and wings: coefficients, Kutta-Joukowski theorem, thin airfoil theory, finite wing theory, critical and drag divergence Mach numbers · 2 marks · Numerical answer

A thin cambered airfoil has zero lift at −1.1°. Below stall, its lift coefficient at 4° (two decimal places) is _______.

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Correct answer: 0.55 to 0.57

Explanation

For a thin airfoil, **thin-airfoil theory** gives a lift curve that is linear below stall:
$$c_l=2\pi\,(\alpha-\alpha_{L=0}),$$
with the angles in radians.

**Numbers.** $\alpha=4^\circ$ and $\alpha_{L=0}=-1.1^\circ$:
$$\alpha-\alpha_{L=0}=4-(-1.1)=5.1^\circ=5.1\times\frac{\pi}{180}=0.0890\text{ rad}$$
$$c_l=2\pi\times0.0890=\mathbf{0.56}.$$