# Airfoil "Actual Location" of Aerodynamic center...(How to find it)

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#### WonderousMountain

##### Well-Known Member
A CP around 30 is not altogether uncommon,

In my opinion it's not good practice to place your spar at CP in D cell structures, because the rest of the D cell is forward. Better practice would be to place the beam at greatest depth or as far back as 40% depending on how substantial the D is.

On 'humble' airplanes sometimes minimum thickness becomes the primary design element, which is one reason theory and practice frequently differ.

LuPi

#### Pete Plumb

##### R.I.P.
Nope. By far the largest force the spar sees is bending and a round tube is not efficient at all for that. For a given height and length an I-beam will bend much less than a tube under the same load and it will also hold more weight before it fails. A D-tube consisting of a leading edge skin and an I-beam is the simplest way to get both the bending stifnes of an I-beam and the torsional rigidity of a tube.
Especially with a 2-30 series airfoil! Spars are for bending loads and skins (or struts) are for torsion.

#### Norman

##### Well-Known Member
HBA Supporter
Thats the way many wings are built. Infact, you cant have spar positioned at CP, as CP is dependant on AoA or CL if you will (not a fixed point). As you increase AoA, CP moves forward (that for airfoils with positive camber and negative Cm). In some extreme cases when flying at low AoA (high speed) CP goes back close to TE or even beyond... these are cases with huge torsion acting on wing; you see, we cannot fight that issue (torsion) by putting spar at any particular position - thats why we assume spar caries no torsion load, then optimize it for bending, and use other structural elements to bear torsion.

one interesting specific example was Daedalus human powered aircraft. Main structural element of its wing was tubular carbon section - it carried both bending and torsion, and yes it was position in CP (which was somewhere at 30-35%, exactly where max airfoil thickness was). However that particular airplane was built for single purpose, to set distance record in human flight, and it was intended to fly in specific conditions - at optimum AoA (around 3-5 degs), and Cl (around 1.1-1.4).

"real" airplanes have to be more operational and to have some useful flight envelope.
It doesn't help that we aren't all speaking the same language either. The notation from different labs can look a bit different and notations from different countries have changed over time. CP is probably the worst example of this drift over time. Before about 1935 everybody plotted the position of the center of pressure (c.p.) which leads to infinities because the pitching moment does not drop to zero when the AoA is such that the wing isn't producing lift. So by the mid 1940s all the labs had switched over to using the theoretical AC at c/4 and a moment coefficient (Cm) so the engineer has real numbers that he can do math with. Now we also have a new notation, Cp, that stands for "coefficient of pressure". Cp is the pressure distribution on the airfoil surfaces not the old c.p. but it's a similar looking notation so gets confused with the older notation.

Sorry this is kind of short and disjointed. I may wright something better after the holiday

#### Norman

##### Well-Known Member
HBA Supporter
So the airfoil shape could be Taylored ...using what tool ?
To keep the Aero Center on check.
Is this this pic from PPRuNe Forums - Professional Pilots Rumour Network right ?
Yes but it just shows that the pitching moment would appear different if you measured it at a different point on the airfoil. They used a Cm0=0 airfoil, such as the NACA 23112, but most airfoils aren't. If they had used an airfoil with some non-zero pitching moment part of the black line would still be horizontal but at some + or - value and * the colored lines would still diverge in a similar fashion. It also shows which way the actual AC is displaced when the linear part of the curve on a Cm/alpha graph is not horizontal**. The old graphs see attachments showed the position of the center of pressure. I've highlighted the C.P. curve and its scale in one of the graphs in case you haven't seen airfoil data presented this way before. As you can see from the attached graphs the center of pressure moves a lot on the cambered airfoil and is fairly stationary on the reflexed airfoil. The AC is assumed to be a fixed point, it's the distance between the AC and C.P. that causes the pitching moment.

You can convert Cm from modern polar data into C.P. and visa-versa with a little algebra.

The formula to find the distance of the C.P. from the leading edge is:

x_cp = 0.25 - cm/cl

You will have to repeat this several times to get enough points to draw a curve.

The formula to convert C.P. to AC is:

x_ac = 0.25 - (d cm/d alpha)/(d cl/d alpha)

(d) stands for "delta" which means you would have to find the slope of the line but since all modern data is presented as polars with the Cm data all you have to do is take the Cm and cl numbers at some point in the linear range and plug them into the spreadsheet I pointed to in post #2.

* transposition error / dumb-ass attack
** also backwards, apparently

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#### Birdman100

##### Well-Known Member
Norman, I think you misinterpret graph, they didnt use Cm=0 airfoil, but Cm<0 airfoil. See that horizontal black line (Cm about AC) is below x-axis

#### Norman

##### Well-Known Member
HBA Supporter
Norman, I think you misinterpret graph, they didnt use Cm=0 airfoil, but Cm<0 airfoil. See that horizontal black line (Cm about AC) is below x-axis
Thanks for catching that error. Do you have any other observations? I'm concerned that what I said about the lines showing the displacement of the AC is also backwards because I have another post-it note on my desk that says "if Cm vs cl curve has a negative slope the AC is aft of 25%c". I ran that aerodynamic center spreadsheet on two airfoil sections with opposite slope and it confirms my note. This is important for short coupled aircraft so I need to confirm it. Spreadsheet with XFLAR5 screenshot attached.

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#### Birdman100

##### Well-Known Member
yes, if Cm slope is negative, "real" AC is aft of the 0.25 c (or to be precise, aft from the point for which Cm graph is given). That stands both for "normal" airfoils, and reflexed (Cm>0). This is not contrary to graph in post 24. Everything is fine there.

I think you should try to skip calculating "exact" AC position, as this data is pretty much meaningless. XFLR Cm chart in respect to known-fixed point (25% chord) is all you need here and that is accurate - I mean the approach - program as such has its errors and limits of course.

there is one more thing regarding "real" AC position. Straight Cm line, whether tilted or horizontal, means there is AC in some fixed point. That is the only case there is sense to find AC position, though I dont see it as a practical approach either. However, Cm plot is straight just in theory (like idealized in picture shown), in reality it is often more or less curved, which means that AC moves with AoA. So, AC in most real airfoils is not a fixed point, but it does travel (not much but still does). Whenever you see bumpy - curvy Cm vs AoA chart keep in mind that that airfoil doesnt have fixed AC.

You can check that yourself. Take ronczs spreadsheet and try calculating AC for different spots: in cells D4 and D5 insert Cl and CM for other Alphas... 2, 5, 6, 10... and so on. If you insert CL and CM for AoA=4 (that is by default, but doesnt have to be that) you will just calculate averaged AC over domain from CL=0 - CL@AoA=4.

#### clanon

##### Well-Known Member
Thank you guys .Always trying to learn , here.

#### SpainCub

##### Well-Known Member
Sorry guys, I'm a little confused here, when working with a wing I thought AC was a little difference. (When I come here all I learn is, I don't know enough! )

This is from my notes. (Sorry no reference.)

Below is a graphical representation of how to find AC of a wing panel by using the Mean Aerodynamic Chord (MAC) or Geometric Mean Chord (GMC). This method will work for most wings, tapered or not. Take the lengths you found before and add the tip chord measure (C) in front of and behind the Root Chord (A). Next add the Root Chord (A) in front of and behind the Tip Chord (C). Draw a diagonal line from each end of the newly created lines and find where the two intersect. Now measure the distance of the GMC as seen in the picture below. Write this length down as it is important!

I also have in my notes to look up a graphical solution to finding the AC, but I could not finds anything other than:

We have just described an analytical method to find the AC. There are also graphical methods to find the AC. We won’t go into detail on those methods though.
Found here: http://www.aerostudents.com/files/flightDynamics/theAerodynamicCenter.pdf

Are we talking about the same thing here? I mean, Airfoil (2D) vs Wing (3D)?

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#### Norman

##### Well-Known Member
HBA Supporter
Are we talking about the same thing here? I mean, Airfoil (2D) vs Wing (3D)?
Those drawings show how to the find the centroid of a trapezoid and the chord that passes through the centroid is the mean geometric chord which is not exactly the mean aerodynamic chord (MAC) but close enough for a first approximation and usually isn't far enough off to be a problem. What we've been discussing in this thread is the fact that the aerodynamic center of MAC of a given airfoil cross section may not actually be at 25% but instead 1 or 2% forward or aft of that point. On airplanes with short chord wings and long tail arms it isn't a big issue although it does affect the size of the tail. In tailless airplanes it makes all the difference.

#### SpainCub

##### Well-Known Member
Those drawings show how to the find the centroid of a trapezoid and the chord that passes through the centroid is the mean geometric chord which is not exactly the mean aerodynamic chord (MAC) but close enough for a first approximation and usually isn't far enough off to be a problem. What we've been discussing in this thread is the fact that the aerodynamic center of MAC of a given airfoil cross section may not actually be at 25% but instead 1 or 2% forward or aft of that point. On airplanes with short chord wings and long tail arms it isn't a big issue although it does affect the size of the tail. In tailless airplanes it makes all the difference.

Thank you Norman, sorry I missed your reply earlier. BTW, do you know a source to access NACA airfoil wind tunnel test? You seen to quickly find the right test when engaged in any discussion.

Cheers!

#### Norman

##### Well-Known Member
HBA Supporter
Mostly I Google for specific modern airfoils and generate my own data for the older stuff with XFLR5.

"Theory of Wing Sections: Including a Summary of Airfoil Data" By: Ira H. Abbott, A. E. von Doenhoff has a very in depth collection of data from the late '30s and '40s. You used to be ably to buy it for $10 but this morning Amazon lists it for$17. I'm not sure if NACA-TR-824 has all the material in the book but it should be most of the wind tunnel data.

For stuff older than that I use a very dog eared copy of "Comprehensive Reference Guide To Airfoil Sections For Light Aircraft" from Aviation Publications. You can buy it from several book retailers but Aircraft Spruce And Specialty Co. has the forward and a few sample pages in a PDF. The book is exactly what the title implies (except that all the airfoils are antiques) 167 pages of old NACA 5 axis (1 X and 4 Ys) graphs of wind tunnel data. Most of those old wind tunnels, except for L.M.A.L., had high turbulence and ran at pretty low Reynolds numbers (less than three hundred thousand) the results are a bit skewed toward lower performance than can be expected at more realistic Re.

There's a lot of information on the University of Illinois at Urbana–Champaign Applied Aerodynamics site. Not a lot of wind tunnel data but good information.

There are newer books but most of the data is from computers not wind tunnels.

#### SpainCub

##### Well-Known Member
For stuff older than that I use a very dog eared copy of "Comprehensive Reference Guide To Airfoil Sections For Light Aircraft" from Aviation Publications. You can buy it from several book retailers but Aircraft Spruce And Specialty Co. has the forward and a few sample pages in a PDF. The book is exactly what the title implies (except that all the airfoils are antiques) 167 pages of old NACA 5 axis (1 X and 4 Ys) graphs of wind tunnel data. Most of those old wind tunnels, except for L.M.A.L., had high turbulence and ran at pretty low Reynolds numbers (less than three hundred thousand) the results are a bit skewed toward lower performance than can be expected at more realistic Re.
This is what I was looking for, thank you! All the best!!!