# Where does the main CoP move when deflecting the elevator up & down and trimming?

I recently asked a question and in the comments I got this response

"The CP changes with angle of attack, so it is not a useful point in terms of stability. The NP does not change with angle of attack. Your intuition about distance from CM applies to the NP. When an aircraft is trimmed (at some alpha), the elevator has been adjusted such that the CP is at the CM."

My question was how does the CoP go to exactly where the CM is when trimmed? Wouldn't that mean the aircraft is far more unstable than if the CoP was still behind the CM by a bit?

(I didn't go to aeronautical engineering school or anything like that so if you could kind of put the response in layman's terms I'd appreciate that)

• There's a lot of terminology there that must be well understood before proceeding: do you understand the meaning of Neutral Point, Centre of Pressure and pitching moment $C_m$ (I suppose of the wing)? For example: although only slightly, Neutral Point does change with AoA. And what's the "distance from CM"? There's no distance from a moment... Oct 5, 2023 at 6:17
• @sophit Here he is quoting me using CM to refer to the center of mass, not the moment coefficient. I shouldn't have done it, but I think it matched the OP's usage in the original question. Oct 5, 2023 at 15:09
• @RobMcDonald haha I didn’t know that you’d see that. Thought this deserved a whole new question. Oct 5, 2023 at 15:14
• @RobMcDonald: ah ok, thanks for the clarification Oct 5, 2023 at 15:35

The center of pressure is the point where the aerodynamic moments go to zero. If you sum about this point, the pressures produce a pure force and zero moment.

If the center of pressure is not located at the CG, the aircraft will rotate. Therefore, if an aircraft is trimmed, then the CP has been positioned to coincide with the CG. We never think of it this way, but it has to be true.

*This argument ignores the moment caused by the engines. And technically, the CP applies only to pressure, so it also ignores the moments caused by viscous shear forces. But, the inviscid pressure forces dominate an aircraft -- they are what we use to hold it up (lift) and to control it (roll, pitch, yaw moments).

The CP changes with angle of attack -- and also with control surface deflection. So, trimming an aircraft requires simultaneously finding the angle of attack and control surface deflections to achieve the desired lift coefficient (target trimmed airspeed) and zero moment. Fortunately, for the most part, these equations are linear and we can solve this with a simple system of two linear equations. Typically written as a 2x2 matrix equation.

Since the CP moves with angle of attack, it is not useful for the stability discussion. Instead, that focuses on the aerodynamic center or the neutral point.

AC and NP are pretty much analogous terms. We usually use AC when talking about 2D airfoils and also 3D wings in isolation. We usually use NP when talking about a 3D aircraft as a whole. The NP is a weighted (by area) average of the AC's of all lifting surfaces (wing, tail, canard) for an aircraft.

The AC and NP are defined as the point where the moment is constant as you change angle of attack. This is only true in the linear, well-behaved region of flow. When you approach stall (for example), this falls apart.

• oh okay so basically the lift from the tailplane combined with the change in AoA of the wing will move the CoP to the CM? Oct 5, 2023 at 15:51
• @Wyatt Yes. When a perturbation hits, a stable aircraft will return to the equilibrium point, and an unstable aircraft will diverge from the equilibrium point. Oct 5, 2023 at 18:07
• Ahh, okay makes sense. Thanks for all of your help! Oct 5, 2023 at 18:12
• Last question, say there is a pitch up disturbance, wouldn't that move the CoP forward, and because of a higher AoA making more lift forward of the CM, making the plane pitch up? Oct 5, 2023 at 18:24
• (In a stable plane with a restoring moment) Oct 5, 2023 at 18:31