Question

According to the thin airfoil theory, which of the following statement(s) is/are true for a cambered airfoil?

• 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.
• C. The center of pressure lies at quarter chord point.
• D. Drag coefficient is proportional to the square of lift coefficient.

Hint:

Remember: In thin airfoil theory, lift varies linearly with effective angle of attack, and the aerodynamic center is fixed at the quarter chord, regardless of camber.

Answer 1

The Correct Option is A, B

Thin airfoil theory provides analytical results for the aerodynamic characteristics of thin, cambered or symmetric airfoils at small angles of attack. For a cambered airfoil, the following principles are relevant:
1. Analysis of Option (A):
Thin airfoil theory states that the lift coefficient is given by:
\[ C_L = 2\pi(\alpha - \alpha_{L0}) \] where $\alpha$ is the geometric angle of attack and $\alpha_{L0}$ is the zero-lift angle of attack.
This implies that the lift coefficient varies linearly (directly proportional) with effective angle of attack. Even for a cambered airfoil, the proportionality remains linear; only $\alpha_{L0}$ shifts due to camber. Hence, statement (A) is true.
2. Analysis of Option (B):
Thin airfoil theory predicts that the aerodynamic center (AC) — the point where pitching moment is independent of angle of attack — lies at the quarter-chord point, i.e., at $x = c/4$, for both symmetric and cambered airfoils. This is a classical result of thin airfoil theory.
Thus, (B) is true.
3. Analysis of Option (C):
The center of pressure (CP) is not fixed for a cambered airfoil. It moves significantly with angle of attack. In fact, for a cambered airfoil, the CP typically lies ahead of the aerodynamic center at small angles, and moves aft as angle increases. Therefore, it does not lie at the quarter-chord point.
Thus, (C) is false.
4. Analysis of Option (D):
Thin airfoil theory deals only with lift and moment characteristics. It does not account for viscous drag or induced drag. The relation "$C_D \propto C_L^2$" arises from lifting-line theory (finite wings), not from thin airfoil theory (2D flow). Thus, the statement is not valid in this context.
Hence, (D) is false.
Therefore, only statements (A) and (B) are correct.