I know this is digging up an old post, but OCD compels me
The method shown is how to find the aerodynamic centre, not centre of pressure. They're different.
page 61; Aerodynamics Aeronautics and Flight Mechanics;McCormick B. W. 1995
"Do not confuse the aerodynamic centre with the centre of pressure. Again, the aerodynamic centre is the location about which the moment is constant, and the centre of pressure is the point at which the resultant lift acts."
At the centre of pressure (or centre of lift, whichever you'd prefer to call it) there will be zero moment due to aerodynamic forces, as the resultant vector is acting through that point (so zero moment arm -> zero moment).
The centre of pressure moves as the angle of attack changes (usually forwards with increasing AoA). Because AoA frequently changes, centre of pressure is not a very useful quantity.
There is a point on the wing called the aerodynamic centre which, if lift is measured there, has a constant moment. It is (usually) located at (around) 25% chord. As AoA increases and lift increases, the centre of pressure moves forwards (toward the aerodynamic centre) which reduces the moment arm - resulting in a constant moment around that point.
Because the aerodynamic centre is fixed, it is much more useful. It only needs to be found once for an airfoil or wing. The wing may be treated as though lift acts through that point with a constant moment also acting.
Center of Lift Formula
in Performance, Aerodynamics & Structure
Posted
I know this is digging up an old post, but OCD compels me
The method shown is how to find the aerodynamic centre, not centre of pressure. They're different.
At the centre of pressure (or centre of lift, whichever you'd prefer to call it) there will be zero moment due to aerodynamic forces, as the resultant vector is acting through that point (so zero moment arm -> zero moment).
The centre of pressure moves as the angle of attack changes (usually forwards with increasing AoA). Because AoA frequently changes, centre of pressure is not a very useful quantity.
There is a point on the wing called the aerodynamic centre which, if lift is measured there, has a constant moment. It is (usually) located at (around) 25% chord. As AoA increases and lift increases, the centre of pressure moves forwards (toward the aerodynamic centre) which reduces the moment arm - resulting in a constant moment around that point.
Because the aerodynamic centre is fixed, it is much more useful. It only needs to be found once for an airfoil or wing. The wing may be treated as though lift acts through that point with a constant moment also acting.
I hope that's clear.