# Comparison of pitching moment at different locations

I've conducted some numerical simulations of a pitching airfoil at three different locations of the pitching axis along the airfoil. The locations (from the leading edge of the airfoil) are: $$0.25c$$, $$0.4c$$, and $$0.75c$$. where $$c$$ is the chord length of the airfoil.

Each simulation computes the pitching moment coefficient using the pitching axis itself as the reference point. That is, In, the first simulation the pitching moment is computed about $$0.25c$$ axis, and in the second simulation the pitching moment coefficient is calculated about $$0.4c$$, etc.

My questions are:

• Is it OK to compare all three moment coefficient together given that the reference points are different?
• Do I have to change the reference point to $$0.25c$$ for the two last results? if so, how can I achieve that without restarting the simulations and specifying the $$0.25c$$ as reference point?

• Depending on the target audience, it may be more intuitive to show the movement of the Centre Of Pressure (COP) with different AOAs Aug 6 '20 at 17:11

Is it OK to compare all three moment coefficient together given that the reference points are different?

No, it's not ok. The pitching moment will be different at different reference locations, unless lift is 0.

Do I have to change the reference point to 0.25c for the two last results? if so, how can I achieve that without restarting the simulations and specifying the 0.25c as reference point?

The industry standard for reporting and comparing pitching moment is quarter chord, because the classic Thin Airfoil Theory concludes that infinitely thin airfoils in subsonic flow have their aerodynamic centres at quarter chord.

That being said, there is absolutely nothing wrong gathering the pitching moment data about any other point, as long as you stay consistent when comparing to other data (or more importantly other people's data). You can convert the pitching moment from one point (say $$x_0$$) to any other point ($$x$$) via:

$$M(x) = (L\cos\alpha+D\sin\alpha)(x-x_0) + M_0 \approx L(x-x_0) + M_0$$

where $$L$$ is the measured lift, $$D$$ is the measured drag, and $$M_0$$ is the measured pitching moment at $$x_0$$. The approximation works great at small AOA ($$\alpha$$).

• Thank you for the detailed answer. What about the sign in $M(x)$ formula? is $x$ the same as $d$ in the figure above? Jul 27 '20 at 17:19
• @izri_zimba x is positive toward TE. M is positive CW.
– JZYL
Jul 27 '20 at 17:35
• @izri_zimba You need lift. M_0.25 = (0.25 - 0.75)*L + M_0.75
– JZYL
Jul 27 '20 at 18:04
• Yes, thanks, I made a typo. but shouldn't Lift multiplied with something like $\cos(\alpha)$? what about drag contribution? Jul 27 '20 at 18:16
• The airfoil is pitching from -15° to 27°. So I think lift should be multiplied by the cosine of angle of attack. am I wrong? Jul 27 '20 at 18:26