GATE 2022 AE – Question 54

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

Consider a thin symmetric airfoil at 2 degree angle of attack in a uniform flow at 50 m/s. The pitching moment coefficient about its leading edge is _____ (rounded off to three decimal places).

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Correct answer: -0.065 to -0.045

Explanation

For a thin symmetric airfoil, thin-airfoil theory gives:

The lift coefficient: $c_l=2\pi\alpha$.
The centre of pressure is at the quarter chord, so the moment about the **quarter chord** is zero, $c_{m,c/4}=0$.

**Moment about the leading edge.** The lift acts at $c/4$ from the leading edge and produces a nose-down (negative) moment about it:
$$c_{m,LE}=c_{m,c/4}-\frac14c_l=-\frac{c_l}{4}.$$

**Numbers.** $\alpha=2^\circ=0.03491$ rad:
$$c_l=2\pi\times0.03491=0.2193,\qquad c_{m,LE}=-\frac{0.2193}{4}=\mathbf{-0.055}.$$