# Is the aerodynamic center always on the chord line?

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#### Anna Tian

##### Well-Known Member
I'm wondering is the aerodynamic center always on the chord line? What if it is a highly cambered airfoil?

#### Autodidact

##### Well-Known Member
I assume you mean the 1/4 chord line. The definition of aerodynamic center is "the point at which the moment coefficient is constant regardless of the angle of attack. When you look at the moment coefficient on a NACA airfoil chart, there are two of them; one is CMc/4, and the other is CMa.c.. CMc/4 varies a little, while CMa.c. is almost constant, implying that the a.c. moves a little depending on aoa. In fact, the a.c. moves aft as aoa decreases and moves forward as aoa increases, which is why lower air speeds tend to make an aircraft less stable and high speeds make it more stable. You can calculate the location of the a.c, but it is really unnecessary since the moment about the quarter chord is more convenient for design calculations. For symmetric airfoils the a.c. is the 1/4 chord point, and the above doesn't apply.

#### Anna Tian

##### Well-Known Member
I assume you mean the 1/4 chord line. The definition of aerodynamic center is "the point at which the moment coefficient is constant regardless of the angle of attack. When you look at the moment coefficient on a NACA airfoil chart, there are two of them; one is CMc/4, and the other is CMa.c.. CMc/4 varies a little, while CMa.c. is almost constant, implying that the a.c. moves a little depending on aoa. In fact, the a.c. moves aft as aoa decreases and moves forward as aoa increases, which is why lower air speeds tend to make an aircraft less stable and high speeds make it more stable. You can calculate the location of the a.c, but it is really unnecessary since the moment about the quarter chord is more convenient for design calculations. For symmetric airfoils the a.c. is the 1/4 chord point, and the above doesn't apply.
I have highly cambered airfoil as shown in the attached picture. I'm wondering would the aerodynamic center be quite far from the 1/4 chord point? Will the arodynamic center be still on the chord line?

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#### BBerson

##### Light Plane Philosopher
HBA Supporter
The horizontal variation or the chord wise position is described in Theory of Wing Sections, page 182.
No mention of vertical position or vertical variation.

#### Anna Tian

##### Well-Known Member
The horizontal variation or the chord wise position is described in Theory of Wing Sections, page 182.
No mention of vertical position or vertical variation.
Anywhere I could find a clue regarding the vertical position?

#### BBerson

##### Light Plane Philosopher
HBA Supporter
Anywhere I could find a clue regarding the vertical position?
I never thought about it until now. From this site, it seems the Aerodynamic Center would more or less follow the chord line and move down with more camber (from extending flaps down). Extending the flaps down also moves it forward.
I don't know if the vertical position matters much.
Aerodynamic center - Wikipedia, the free encyclopedia

#### Synergy

##### Well-Known Member
A positively cambered airfoil moves the aerodynamic center of pressure upward. Its precise location is given by integration of the pressure distributions, and can be above or below the chord line. The influence of any vertical movement is absorbed and camouflaged by our inaccurate convention of assuming the pitching moment comes from lift rearward of the 1/4 chord line location, rather than in a forward direction above it, and this heresy moves the discussion from the practical to the silly in a hurry, since what's actually happening is not 2-D, either.

Curious as to why one would like to understand the physics rather than compute the desired result... onder:

#### Anna Tian

##### Well-Known Member
When people design aircraft, do they just simply use 1/4 chord point as the aerodynamic center to calculate the position of the neutral point?

For my case, as my highly cambered airfoil is not quite conventional, I’m afraid the 1/4 chord rule won’t work for my case. I have the CFD simulation results of my wing for different AoA. I’m trying to look for a way to give more precise location of the aerodynamic center or at least confirm that 1/4 chord rule also works for my case.

If the vertical location of aerodynamic center could also change, I’m wondering how shall I calculate the aerodynamic center location? Any formula or reference on that?

#### ultralajt

##### Well-Known Member
Anna, is the airfoil in your case an standard airfoil with known data ot it is designed by you?
From the drawing posted above, it seems to me it is an similar airfoil shape often used for axial compressors and turbines... (jet and steam turbines..)
What is the purpose of your airfoil..where it will be used?
Maybe the mission of this airfoil in your construction need actual and precise location, or maybe it is not of such importance. For instance in usage as an turbine blade, centrifugal force is the main concern..way above any torsion moment of blade itself....

So, what you are up to?

Regards!

Mitja

#### Dana

##### Super Moderator
Staff member
A positively cambered airfoil moves the aerodynamic center of pressure upward. Its precise location is given by integration of the pressure distributions...
Curious as to why one would like to understand the physics rather than compute the desired result... onder:
I think she's talking about the aerodynamic center (the point about which Cm is constant), not center of pressure (the point about which Cm is zero)... two different things.

Some people like to actually understand what's happening. With a computer, GIGO (garbage in, garbage out).

When people design aircraft, do they just simply use 1/4 chord point as the aerodynamic center to calculate the position of the neutral point?

For my case, as my highly cambered airfoil is not quite conventional, I’m afraid the 1/4 chord rule won’t work for my case. I have the CFD simulation results of my wing for different AoA. I’m trying to look for a way to give more precise location of the aerodynamic center or at least confirm that 1/4 chord rule also works for my case.

If the vertical location of aerodynamic center could also change, I’m wondering how shall I calculate the aerodynamic center location? Any formula or reference on that?
You don't use C/4 as the a.c.; you use C/4 because (or when) the airfoil data gives lift and drag through and moment around that point. C/4 is used because it's usually close to the a.c. so the moment changes will be small for small changes in AOA. And it's easier since C/4 doesn't move if, for example, you're comparing different airfoils.

The vertical location of the a.c. doesn't generally matter as for stability calculations since it's relatively close to the chord line so any moment seen by assuming a different point (drag times the vertical distance) will be relatively small.

Dana

The most valuable function performed by the federal government is entertainment.

#### Autodidact

##### Well-Known Member
Anna, that's a very unusual airfoil. I believe that people usually use the moment about the c/4 point when computing the neutral point of an aircraft (if they use the moment coefficient at all). The chord line is very arbitrary and really only a reference. This is an unusual airfoil and you have stated that the 1/4 chord rule won't work for you; can you give a more specific description of what you are designing? CFD results should allow you to find the vertical location.

PS, is this airfoil for a slat?

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#### Jimstix

##### Well-Known Member
Looks like a turbine bucket to me.

#### JamesG

##### Well-Known Member
The vertical location of the a.c. doesn't generally matter as for stability calculations since it's relatively close to the chord line so any moment seen by assuming a different point (drag times the vertical distance) will be relatively small.
It would be if such an exaggerated airfoil were pivoting in the spanwise direction. Esp. if it were free pivoting. The location of that rotation axis on the ideal a.c. would set the neutral point for its AoA.

#### Anna Tian

##### Well-Known Member
sorry that the airfoil picture I attached is misleading. I just use it as an example to tell that the chord line could be out of the airfoil geometry and asking would there be a vertical location for the a.c. It's an example and too much exagerrated. I'm not allowed to publish the airfoil I'm working on so I use an inappropriate one to explain my question. Sorry for wasting the time of the guys who tried to help me here.

#### JamesG

##### Well-Known Member
I'm sure someone did the research into this even if a practical formula was never created. Maybe for the all flying stabilator? That is what comes to my mind first when I read the original question. I'm sure its there somewhere but it might take some digging into the NACA/NASA or AIAA archives...

#### DangerZone

##### Well-Known Member
HBA Supporter
I'm wondering is the aerodynamic center always on the chord line? What if it is a highly cambered airfoil?
There is one thing you should consider also, the AC does not mean the same in American English and British English, they both sometimes exchange the CP with the AC. For example, in the US the AC is defined as the point on the section side view where most pitching moments are constant. However, if we read books written in English in Europe or UK (for example books that Darrol Stinton wrote) we might see that the AC (aerodynamic centre) is actually the center of pressure, not the neutral point of an airfoil. The same goes for some other differences between aerodynamic terminology coming from English and French, decalage has a different meaning depending on where you live and which books you started to read first. There are other confusing elements and quite a few books have the same problem with the AC, CP, CL (not to be confused with the Coeficient of Lift), NP and CG. The good thing is that CG is the same everywhere, but the others tend to vary depending on geographical region.

It might be wiser to present the problem you have to solve than ask people over here for defintions. Otherwise you might get some contradicting information and the people arguing will all be right.

Answer to question: No, the AC does not always have to be on the chamber line.

#### Norman

##### Well-Known Member
HBA Supporter
sorry that the airfoil picture I attached is misleading. I just use it as an example to tell that the chord line could be out of the airfoil geometry and asking would there be a vertical location for the a.c.
I was looking through some old notes and ran across these NACA standardized airfoil characteristic charts from the 1930s that show the X,Y position of the aerodynamic center. Looking at the catalog that I scanned these from it appears that for cambered sections, at least for the NACA 5 digit series, the AC is always above the chord line and usually between the mean line and the top surface. They even marked the AC outside the airfoil for some of the 5 digit sections. They also marked a few symmetrical airfoil sections this way. I haven't seen this notation on any charts other than those from NACA Langley nor have I seen any explanation of how they arrived at this but if it's simply a mater of integrating the pressure distribution then Xfoil, XFLR5, or any other program that plots the the pressure distribution, should be able to locate the X,Y position of the AC.

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#### BBerson

##### Light Plane Philosopher
HBA Supporter
I just noticed the vertical location of the AC is shown in Theory Of Wing Sections.
Each airfoil is different. The thick 4421 shown here is somewhat negative. Apparently moves with R.
Looks like the 23012 AC is close to the chord line.

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