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On airfoiltools.com website, for example: NACA 2412, they give airfoil data. One of it is the moment coefficient of the airfoil vs the angle of attack of the airfoil. However, these moment data could not be measured against the aerodynamic center of the airfoil. So, where could they measure the moment coefficient?

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As information supporting the answer by @PeterKämpf, Abbott and von Doenhoff (1) summarize data from the NACA regarding wind-tunnel tests of NACA 24-series airfoils, and show that for these airfoils of 12 to 18 percent thickness, at a Reynolds Number of 6 million, the moment about the aerodynamic center is at about the quarter chord, slightly more or slightly less, to within about one-percent of the chord length.

(1) Theory of Wing Sections. Dover Publications, Inc. New York. 1959

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There is no need for a reference point of a moment. The force vector, however, must be referenced to a specific point which is the quarter point for all decent airfoil data. We have already an answer that explains this in detail here.

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