I've been reading several sources on the location of the aerodynamic center
- John Anderson Jr., Fundamentals of aerodynamics
Many (such as for example Wikipedia) determine the aerodynamic center by writing out the equation for the moment for an arbitrary point, and then apply some definitions to get to the end result: the aerodynamic center lies at the quarter chord, see below:
However, I'm looking for a more physically intuitive explanation, probably starting from thin airfoil theory. The way I understand it, ultimately the aerodynamic center is determined by how the distribution of lift changes with angle of attack. Thus, the distance the center of lift moves w.r.t. the aerodynamic center cancels out the resulting moment due to the change in lift with angle in attack.
Can we explain why this point ends up to be at the quarter chord location?