I am a glider pilot and instructor with a master’s degree in actuarial mathematics. I teach aerodynamics every winter for upcoming glider pilots.
As you surely know, the aerodynamic center is the location where the aerodynamic moment remains constant regardless of the angle of attack – the leverage of the lifting force acting through the center of pressure gets larger for decreasing angles of attack while the force acting through this location gets smaller.
Although I find it easy to understand the mechanisms behind the aerodynamic center, I struggle with understanding how it can exist? How can we be sure that there is such a point in the wing? I know that by definition it is a fixed point, but will it be exactly fixed in practice or just approximately fixed?
Is it not possible to construct an airfoil which will somehow have a discontinuity in center of pressure leverage but delivering the same lifting force in the two situations, yielding non-constant moment around the aerodynamic center?