The point about which we choose to take moments is not an irrelevant thing.
We choose one point or another for a reason.
We can try to find about which point a given force has zero moment. If we find it, we can consider the force to be acting exactly on that point.
In the case of Lift, if we find the point about the moment of Lift is zero, we have found the CP
M = L * arm
(if we are in the point where Lift acts, the arm is zero, therefore M is zero)
If we find the point about which pitching moments are constant irrespective of lift, we have found the point about which the moment created by changes in lift is zero.
dM = dF * arm
When this arm is zero, the change in moment due to a change in Lift is zero. Therefore we have the point where changes in Lift are acting. That is the AC. I don't remember the mathematical formulae that show that theoretically this point is at the 25% of the chord (subsonic).
As for the aerodynamic moment, which confuses me:
- This moment is like that of a couple of forces, isn't it? the moment is always the same no mater what point you choose, right? It's like a "pure" moment.
- Why is it always zero when the airfoil is symmetrical?
- Does it changes with Lift in cambered airfoils? Why?