Now since the center of pressure is at c/4 regardless of angle of attack (as long as the angle of attack is small, like below 10 degrees or so), the pitching moment about this point (c/4, or quarter-chord) must be zero, regardless of angle of attack.

The Aerodynamic Center

The aerodynamic center of an airfoil is the point located such that the pitching moment about that point is independent of angle of attack.

 

The moment about c/4 is zero regardless of angle of attack, so this qualifies as the aerodynamic center.

Thus, for a symmetric airfoil, the center of pressure and the aerodynamic center are both at the quarter-chord in low-speed flow.

Note that camber changes the above result and usually moves the center of pressure aft.

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