Agree 100% with Henra. Thin aerofoil theory in an ideal fluid shows that the pitching moment coefficient Cm is independent of the lift coefficient C
L at the quarter-chord point. For finite thickness wing sections in a real fluid, the point (which will be near to the quarter-chord point) can be found such that Cm about this point is independent of incidence. This point, where d Cm / d C
L is zero, is called the aerodynamic centre. Note that this is where the first differential, the
rate of change of pitching moment with incidence, is zero. The pitching moment coefficient itself at that point will have a constant value, denoted by the term Cmo.
The aerodynamic centre is useful because when you construct the equations of longitudinal static stability for the whole aircraft, taking moments about that point eliminates any variation in the wing pitching moment with incidence. It makes the equations simpler, although when you see them you'd be hard pushed to believe it.
Acknowledgements to the wonderfully clear 1963 lecture notes from the late F.G. Irving (1925-2005).
