According to classical thin airfoil theory for an arbitrary cambered thin airfoil in subsonic incompressible flow, which of the following statements are TRUE?

(A) The theoretical lift curve slope is $C_{l\alpha} = 2\pi\text{ rad}^{-1}$.

(B) The aerodynamic center is located strictly at the quarter-chord point ($x_{ac} = c/4$).

(C) The pitching moment coefficient about the aerodynamic center ($C_{m,ac}$) is strictly zero regardless of camber.

(D) The center of pressure location varies with the angle of attack for a cambered airfoil.

Answer Key:

A, B, D

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Lift Slope Invariance:** In thin airfoil theory, $C_l = 2\pi(\alpha - \alpha_{L=0})$, yielding slope $dC_l/d\alpha = 2\pi\text{ rad}^{-1}$ for all thin airfoils (Statement A is TRUE). 2. **Stage 2: Aerodynamic Center Location:** The pitching moment about the quarter-chord is independent of angle of attack: $dC_{m,c/4}/d\alpha = 0$, so $x_{ac} = c/4$ (Statement B is TRUE). 3. **Stage 3: Camber Moment Behavior:** For a cambered airfoil, $C_{m,ac} = \frac{\pi}{4}(A_2 - A_1) \ne 0$. It is constant, but not zero (Statement C is FALSE). 4. **Stage 4: Center of Pressure Movement:** $x_{cp} = \frac{c}{4}\left[1 - \frac{C_{m,ac}}{C_l}\right]$. As $\alpha$ changes, $C_l$ changes, causing $x_{cp}$ to travel along the chord (Statement D is TRUE). 5. **Stage 5: Official Reference:** Abbott and von Doenhoff, *Theory of Wing Sections*, Chapter 4.

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