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I understand that the Aerodynamic Centre (AC) is the point in the aircraft where the pitching moment never changes with a change in Angle of Attack (AoA). My understanding of the Centre of Pressure (CoP) is that it is the resultant pressure point in the airfoil and it slides rearward when AoA decreases and vice-versa, i.e. it changes its position with regard to the AoA.

Now the point is, how does the pitching moment (the force arm, i.e. the distance between the CoP and the AC multiplied by the force) remain constant when the CoP itself moves with the change in AoA?

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    – Pondlife
    Jun 28, 2018 at 13:54

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As the pitch of the wing increases moment arm decreases and at the same time lift increase, so the pitching moment stays constant.

In typical airfoils such as the wings of an airplane flying level sub-sonically the pressure center is at approximately 0.44 of the cord length, and the aerodynamic center is at 0.25 of the cord length.

When the AoA increases the lift increases linearly and at the same time the CoP moves forward closer to aerodynamic center in a way that reduction in the length of the pitch moment arm is cancelled by increase in the force (lift); so the pitch moment is constant.

In fact the location of AC is calculated by finding the point that the decrease in pitching arm is proportional to increase of lift, otherwise one could pick any arbitrary point along the cord and calculate the pitching moment at that point, but it would not remain constant for a different AoA.

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