Explain thin airfoil theory and its limitations.

Thin airfoil theory uses potential flow to predict 2D airfoil characteristics by representing the airfoil as a vortex sheet along the camber line. Key results: lift curve slope is 2*pi per radian, zero-lift angle equals negative of mean camber line slope, and pitching moment about quarter-chord is constant. Limitations include: neglects viscous effects (no drag prediction, no stall), assumes small angles and thin profiles, doesn't capture thickness effects, and fails at high Mach numbers. It provides a good first approximation and physical understanding.