I think we're on the same page here. To get c.p. you sum all the pressure on the airfoil and divide that force by the observed moment at 1/4c. To get Cm you separate the pressure force on the top from the bottom and calculate the couple about the 1/4c. So Cm has 2 shortSo, if I understand correctly, instead of summing Y forces and using the resultant force to create a moment around the AC, we keep both Y+ and Y- components, and use that instead, now we always end up with a moment even with zero lift.

__real__leaver arms and c.p. has one long

__imaginary__arm.

Both methods show the same data if that's what you mean by "stays the same". Cm is the product of those 2 short arms. c.p. is the product of taking the measured lift force and the measured moment and calculating the arm that would produce that moment.And since both magnitude and chordwise position are moving depending on alpha, the moment at ac stays the same.

My math skills and memory never were very good and have gone down the toilet with age so I put a simple little formula to find the actual AC in a spreadsheet years ago.Regarding the ac position, I finally found a paper explaining a method to find it in a manner I can understand:

View attachment 103136

It used to be (before 1940) that different labs put their force balance pitch axis at different places but now the 1/4 chord point is standard. Computer programs should all use 1/4c.Would you say it looks right? If so, how do I know where on the x axis was Cm measurement taken, for instance on the graph below:

Cm is only constant in a small range of AoA, and boundary layer conditions can really obscure it. Often when the Cm over alpha graph looks like that it's because of a laminar separation bubble on the lower surface. Forcing transition at 75 or 80% on the lower surface will usually give a flatter curve as in the attached graph. Notice that the Cm at zero lift doesn't change much, if at all.View attachment 103137

The Cm value being all over the place means it's not Cm measured at the ac but at some other point, correct?

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