# Aerofoil layout

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#### Regdor

##### Well-Known Member
Supporting Member
Regarding the laying out of the data points of a NACA Aerofoil..
Given: The data points are referenced to a percentage of the chord (“x” axis) line….

Question, are the ordinates (+/-)of the “y” direction, given perpendicular to the chord line, or are
they given as a perpendicular direction to the local slope of the mean line, from the
mean line at that Percentage of the chord line ??

Question, when scaling the Chord Line, are the (+/-) “y” data points scaled with the
same scale factor as the chord line, or must a complex function be used to generate those
data points ??

#### Aerowerx

##### Well-Known Member
The coordinates are given as a fraction of the chord line. They are perpendicular to the chord line.

Simple arithmetic scaling is used. To scale, just multiply the coordinates by the desired chord length.

#### Groundhog Gravy

##### Well-Known Member
They are perpendicular to the chord line.

This is not correct. It is perpendicular to the camber line. It's made very clear in the Wikipedia article: NACA airfoil - Wikipedia

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##### Well-Known Member
Supporting Member
There's some confusion here.

1) The NACA coordinates of a "complete airfoil" (thickness + camber, e.g. 2412), as given in tables, are, as Aerowerx said, a fraction of the chord line, and scaling is trivial as described.
2) The derivation of the NACA coordinates applies a thickness profile perpendicular to the camber line, so if you're trying to e.g. recreate the 2412 by applying the 24xx camber line to the 0012 thickness profile you need to know this.

And, since it will come up,

3) The Riblett airfoils you'll see discussed on this site extensively are, in large part (a) applying the NACA thickness profiles perpendicularly to the chord line instead, while (b) using slightly modified camber lines with a bit steeper leading edge camber.

#### Groundhog Gravy

##### Well-Known Member
I see. Yes, the top and bottom ordinates are perpendicular to the chord line. The ordinates are derived by applying the thickness, as determined by formula, perpendicular to the camber line, but that's not what was being asked. My mistake.

#### Retiree

##### Well-Known Member
If you want to "layout" a set of airfoil coordinates. That is create a 24" airfoil section, then you can scale the x and y coordinates by 24 (assuming the maximum x coordinate is 1.0)
If you want to create a NACA 2418, you cannot scale up a 2412. You have to use the proper formulas to add 18% camber to a 2400 symmetric section.

#### Scottiniowa

##### Well-Known Member
If you want to create a NACA 2418, you cannot scale up a 2412. You have to use the proper formulas to add 18% camber to a 2400 symmetric section.
Always enjoy how quickly things get added to, adjusted and turned into another direction.

If the question was, similar to this- " how does one make a simple wing profile, that has a 54" cord line, into a 60" cord line profile" That answer was one of the very first ones, with simple interpolation of the whole set of numbers. (for that airfoil)
i.e if your going larger, in this case 54 to 60 , simple math says a factor of 1.11 larger. or 11.111111% larger- like wise, if you were going smaller, 54 to 27 for a factor of --.5 thus (50%) smaller

Now if it (the question) was truly how to create a DIFFERENT airfoil, with a DIFFERENT Camber, and end up with different cord line? there are some that have spent a lifetime trying to do this, with little means to prove in real life. The slower the plane the harder to prove. Has it been done? certainly, Has it been done by many, not so much.

BJC

#### wsimpso1

##### Super Moderator
Staff member
Regarding the laying out of the data points of a NACA Aerofoil..
Given: The data points are referenced to a percentage of the chord (“x” axis) line….

Question, are the ordinates (+/-)of the “y” direction, given perpendicular to the chord line, or are
they given as a perpendicular direction to the local slope of the mean line, from the
mean line at that Percentage of the chord line ??

Question, when scaling the Chord Line, are the (+/-) “y” data points scaled with the
same scale factor as the chord line, or must a complex function be used to generate those
data points ??
When you have a known full airfoil (Appendix III of TOWS), all combinations have been done and all numbers in % chord. X and y coordinates for a particular chord are obtained by multiplying the values in the tables by chord/100. Excel is your friend here.

The other discussions come into play when one attempts to roll your own foil from a camber line and thickness distribution. The camber line moves the min cd point to some cl, which is usually our design point (cruise in a traveling airplane, racing speed in a racer, etc) and influences stall behaviour. The thickness distribution also influences stall behaviour and makes the rest of the foil's characteristics. They are separate and the foil should be created by picking a camber curve, scaling between two appropriate thickness distributions, then combining them.

Simply scaling between two foil coordinates messes with both the camber curve and the thickness distribution, and is just plain wrong way to do it, as the resulting camber curve and thickness distribution will both be altered.

Billski

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##### Well-Known Member
Supporting Member
I would strongly suggest using the Foil Design functions of XFLR-5 (an open-source application). You can pull Selig .dat format files from www.airfoiltools.com, refine, scale and or interpolate between foil geometries as you need, analyze as you need to as well, export as .dat files, and you will be on your way.

Always trust but verify, but this saves time. It worked very well for my project so far. Best of luck!

#### BJC

##### Well-Known Member
Supporting Member
Now if it (the question) was truly how to create a DIFFERENT airfoil, with a DIFFERENT Camber, and end up with different cord line? there are some that have spent a lifetime trying to do this, with little means to prove in real life. The slower the plane the harder to prove. Has it been done? certainly, Has it been done by many, not so much.
The late Orion fielded multiple questions abour airfoil selection. One response is here In need of professional help....
He had a paper on his business web site that would have stunned many people who spend months trying to get the last bit of airfoil performance for a sport airplane (not talking about an unlimited sailplane).

He was retained by Glasair in their early days to analyze their G-III airfoil selection. He concluded that it was sub-optimal. They stuck with their original section. The Reno record of G-III’s clearly shows that the sub-optimal airfoil, combined with the entire aircraft and a good race engine, beats the one-off dedicated design aircraft.

BJC

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#### Aerowerx

##### Well-Known Member
Question:

If you are creating a new cambered airfoil, are the +/-Y coordinates perpendicular to the camber line (which would involve some messy math), or perpendicular to the chord line but offset by the camber (which is a lot simpler)?

#### Shayde

##### Well-Known Member
If it's not clear yet, you can't just scale NACA cambered airfoil coordinates. I fell for this trap a while ago. You need to find the camber line height (which is midway between upper and lower y), subtract it from the upper and lower y coordinate, then do your y scaling, finally adding the camber line height back in.

Edit: I should have clarified; this is when scaling a NACA airfoil from one thickness to another.

Another gotcha I hit is you can't just linearly interpolate the NACA thickness from root to tip of a tapered wing if you want your wing to be straight. For instance, if a spec says the wing is NACA 2414 at the root, and NACA 2410 at the tip, interpolating 14 -> 10 along the wing length does not do what you want.

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#### Aerowerx

##### Well-Known Member
If it's not clear yet, you can't just scale NACA cambered airfoil coordinates. I fell for this trap a while ago. You need to find the camber line height (which is midway between upper and lower y), subtract it from the upper and lower y coordinate, then do your y scaling, finally adding the camber line height back in.
Since the scaling is linear, why would you have to do this?

Isn't the camber line defined as a percentage of the chord? With what you mentioned, I would think that you would also have to scale the camber line also.

Perhaps if you posted an example it would be more clear.

#### Groundhog Gravy

##### Well-Known Member
Since the scaling is linear, why would you have to do this?
Judging by the later remarks, I think they mean, "You can't just scale the thickness of a NACA airfoil (and get a thicker airfoil of the same family)."

#### Norman

##### Well-Known Member
The OP's question was answered in posts #2 and #4. The published ordinates are simple x,y offsets where y is a percentage of x. The NACA way of designing an airfoil takes the tangent of the mean line into account but the published coordinates are for plotting on a square grid without having to draw the mean line and find tangents. Scaling an NACA airfoil up by simply multiplying the y ordinates will distort it away from the derived shape of the properly derived thicker version but not very much if you're only increasing it by 1 or 2%. If you need an NACA airfoil section twice as thick as the one you have then simply scaling by multiplying the y ordinates will get pretty weird and you should get the official coordinates from a catalog or computer program. XFoil and the programs derived from it do the simple y * (a scaling factor) but also include a proper NACA airfoil generator in the foil design menu so you don't have to find a given shape in a catalog. JavaFoil also includes an airfoil generator but with a lot more airfoil families than the XFoil based programs. The attached drawing is a very crude example of 2 airfoil sections designed the NACA way and the thin airfoil scaled to the double thickness by multiplying the y ordinates by 2. It's an extreme example but you can see the tangents of the NACA way yield a different shape than simply multiplying y. This would be really tedious to do by hand.

#### Shayde

##### Well-Known Member
Judging by the later remarks, I think they mean, "You can't just scale the thickness of a NACA airfoil (and get a thicker airfoil of the same family)."

Sorry, yes, you are correct. It was in the context of scaling an airfoil to a different thickness.

#### Groundhog Gravy

##### Well-Known Member
XFoil and the programs derived from it do the simple y * (a scaling factor) but also include a proper NACA airfoil generator in the foil design menu

I wrote a Python tool to generate NACA airfoils, and was frustrated when checking it against Xfoil — until I realized that Xfoil does not generate NACA airfoils correctly. It applies the thickness perpendicular to the chord line instead of the mean line. I didn't know the internals of Xfoil well enough or know enough Fortran to fix it, and never got a response to the bug report I sent.

#### WonderousMountain

##### Well-Known Member
The decision to scale incorrectly is NACA cannon, their foil, their call.

#### Marc W

##### Well-Known Member
Use the Riblett method and happily scale away evermore!