# Does the aerodynamic center always have to lie on the chord line?

A lot of resources online state that the aerodynamic center is the "point on the body of an airfoil with respect to which the moment coefficient does not change with angle of attack." However, does this necessarily imply that the aerodynamic center must lie on the chord line? Of course, we can resort to thin airfoil theory and prove that it lies on the chord line, but what about for highly cambered airfoils?

This answer (Why does the aerodynamic center exist?) explains the existence of the AC, but resorts to inviscid, incompressible, thin airfoil assumptions. What about in general though? So, is the aerodynamic center present on the chord line in general for all flows? If not, when does it deviate from chord line and why?

• I don't know enough about the mechanics of aerodynamics to provide a thorough answer, but isn't the aerodynamic center given as a % of MAC? Therefore it wouldn't be on the chord-line unless it was 100% of MAC.
– Noah
Oct 25, 2019 at 0:49
• Yeah, I don't understand how the aerodynamic center could be anywhere but along the chord line. How could it be somewhere else? Oct 25, 2019 at 15:00

No, there is no reason why aerodynamic center (AC) have to lie on the chord line. As the OP correctly pointed out, Thin Airfoil Theory (TAT) result indicates that the AC:

1. Exists, and
2. Lies on the chord line 1/4c away from the leading edge.

However, this is only because the TAT makes the fundamental assumptions that the airfoil is thin, the mean deviation of the camberline is small relative to the chord, and small free-stream incidence (AOA). As shown in the diagram below, the vortex sheet is assumed to lie on the chord line instead of the mean camber line. (I should mention, however, that the slope of the mean camber line is accounted for in the theory to construct the tangent boundary condition on the airfoil). And, of course, TAT doesn't account for drag. (Diagram cited from Anderson, Fundamentals of Aerodynamics.)

The vertical offset is small, however, at least until the drag rise associated with flow separation or when flow incidence becomes large. If there is a large vertical separation between the center of pressure and the chord, then AC will not exist and this manifests as nonlinearity in the Cm curve.

I've included the pitching moment coefficient about 1/4 chord of NACA0010, Clark Y and NLF(1)-0115 analyzed with Airfoil Tools, which were analyzed with xfoil using panel method + boundary layer equations. The plots included Reynolds number of 500,000 and 1,000,000 with Ncrit transition of 5 and 9. Note that AC exists locally where Cm has a constant slope. For NACA 0010, AC exists up to 10 deg AOA at 1/4c; near stall, the drag rise occurs and the Cm becomes nonlinear. For Clark Y and the NLF, the AC is pretty close to 1/4 for small AOA, then shifts to a point further aft until drag rise.

Therefore, while the concept of AC is useful for theoretical derivation of stability relationships in linear aerodynamics, it's not a good enough for precise modeling. In engineering modeling, we generally measure the pitching moment (from wind tunnel) at 1/4c, and account it as a function of AOA.

• A legend for the graphs would help for completenes. But still, I struggle to see how could the conclusion ("AC exists up to 10 deg") be derived from these graphs.
– Zeus
Oct 28, 2019 at 0:15
• @Zeus Right above the graph, "Note that AC exists locally where Cm has a constant slope."
– JZYL
Oct 28, 2019 at 0:17
• Yes, but what about the bends at, say, 3-5° for NACA? I think they need an explanation, otherwise it's rather confusing...
– Zeus
Oct 28, 2019 at 0:23
• @Zeus I think you're referring to the NLF? I think it's the end of the laminar bucket. But I can't be sure why it's doing it. I mentioned above that the AC shifts aft past small AOA.
– JZYL
Oct 28, 2019 at 0:25
• My point is simply that most people looking at these graphs will not find anything special at 10°, but will find many other 'interesting places'...
– Zeus
Oct 28, 2019 at 0:39