GATE 2021 AE – Question 26
For a cambered airfoil in thin-airfoil theory, which are correct?
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Show answer and explanation
Correct answer: (A) The lift coefficient for an airfoil is directly proportional to the absolute angle of attack.; (B) The aerodynamic center lies at quarter chord point.
Explanation
Check the statements for a cambered airfoil in thin-airfoil theory (incompressible, inviscid, 2-D).
- **A. $C_l$ is proportional to the absolute angle of attack.** True. $C_l=2\pi(\alpha-\alpha_{L=0})=2\pi\alpha_{abs}$. ✓
- **B. The aerodynamic center is at the quarter chord.** True. The pitching moment about $c/4$ does not change with $\alpha$. ✓
- **C. The center of pressure is at the quarter chord.** False. It moves with the angle of attack for a cambered airfoil.
- **D. The drag coefficient is proportional to $C_L^2$.** False. In 2-D inviscid flow there is no induced drag (and no drag at all, by d'Alembert's paradox).
Answer **A and B**.