# Perimeter of airfoil

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#### plncraze

##### Well-Known Member
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What is the formula for calculating the perimeter of an airfoil? I was working with a wing torsion formula and I can't find this in the books. Many thanks and I hope this isn't as stupid a question as it seems.

#### wsimpso1

##### Super Moderator
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I do perimeter, Ixx, Iyyy, and J of the skin or the cross section numerically from the coordinates of each airfoil. Once you have these for one chord size, perimeter scales with the chord, cross section area scales with chord ^2, and the I's and J scale with chord ^4 and the skin thickness.

Bill

#### pwood66889

##### Well-Known Member
Zis in closed form, Bill???

#### wsimpso1

##### Super Moderator
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Zis in closed form, Bill???
I do not understand? Full sentences help with conveying meaning to those of us who are old, socially difficult, slightly dyslexic, and engineer types.

Every foil has a different shape, cambers vary, material forward and aft of the thickest spot varies, so has a different perimeter, A, I's and J, centroid locations, etc. Not only that, many of us put on control surfaces so the wing skin only goes to a lip, many with the top and bottom skins ending in different places. Then when you add in the main spar, drag spar, maybe even a leading edge spar, you get a bunch of other A's, I's, J and their centroids to use to make a total wing or tail A, I's, J, etc. Wing skins are not usually symmetric either, their centroid is usually somewhere near the chord line giving a bigger z above than below.

Best scheme is to run your airfoil cross section at some chord and skin thickness, then if you are doing any kind of taper to the wing, scale for the terms. Or run the math at many different chords. I prefer to scale, the math is simpler. You can do this by using the basic coordinates for your airfoil, then scale it to some size in the middle of your use range. Then you can do a piecewise calculation of area and x and z position , find centroid, then go back and compute values for all the pieces... Or you can model it in SolidWorks and let Mass Properties tell you the characteristics.

This is all a first principles run through beam section calculations and then parallel axis theory. If you do not believe that I's and J correlate with skin thickness and chord^4, then run four different chords and run Linest(). Skin perimeter will fit perfect with C, and skin cross section area will fit perfect with C and t, I's and J will fit perfect with chord^4 and t, and centroids will fit perfect with C as well. Done it, have a program, sorry, you have to do your own homework. I will check your math if you ship me the Excel and/or SW files on a PM and ask nice.

Billski

#### flyboy2160

##### Well-Known Member
The method depends on what tools you have and know how to use.

IF you have the equation of the airfoil, AND IF you can use calculus or a numerical method, you can use those to get the length.

IF you have a CAD system, you can build the shape and just query the perimeter.

(As always, sanity check these as ~ 2x chord + 1x max thickness.)

IF you're really old school, you can use an analogy to the Thomas Edison light bulb volume method: You DRAW or PRINT OUT the airfoil on something (size doesn't matter, you can scale your result). Then you can physically measure the perimeter by one of several methods. You can use one of those little wheeled length measuring drafting gizmos. You can lay something flexible along the curve, like fishing line, then measure that. If you're really, really cool, you can use lofting ducks to help you hold the curved thing (but tape will work ok)!

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#### Topaz

##### Super Moderator
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XFOIL calculates all sorts of neat parameters for you.

To do it, load up your coordinates file in XFOIL, and type the command "BEND". You'll get full structural parameters for the loaded airfoil section. Perimeter is given as "Slen", as a function of a unit chord. So if Slen = 2.055565, the perimeter is that value times the chord length of your wing at that station. If you've modified the section, created your own, or otherwise played with the GDES tools, be sure to NORM (normalize to unit chord) the section before you run BEND.

Here's a screen-grab of the "BEND" data for the Eppler 662 airfoil:

#### Aerowerx

##### Well-Known Member
I have in the past created an Excel spreadsheet that uses published airfoil coordinates.

By calculating (dX^2+dY^2)^0.5 and summing all the points it gives the circumference.

By calculating dX*dY and summing it gives the cross sectional area.

For a constant taper wing, you can calculate the circumference at the mid-half-span and multiply by the span to get the surface area. Multiply the cross section area by the span to get the wing volume.

For what I was doing at the time this was close enough.

#### mcrae0104

##### Well-Known Member
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What is the formula for calculating the perimeter of an airfoil? I was working with a wing torsion formula and I can't find this in the books. Many thanks and I hope this isn't as stupid a question as it seems.
If you are using AutoCAD (flame suit on) it can give you the perimeter length once you have constructed the foil shape from the ordinates. Also it can give you Ix-x and J. More here.

#### Lendo

##### Well-Known Member
I've used flyboy's methods and used Auto Cad, (add root and Tip)/2 = average - to find surface area.
George

#### pwood66889

##### Well-Known Member
In other words, Billsky, the answer is no. Flyboy and Topaz have good approaches; I did not see parameter in McRae's screen shot.
My best bet would be to measure the real wing I have and go from there. I appreciate your time.

##### Well-Known Member
IF you have a CAD system, you can build the shape and just query the perimeter.
Very true. When I designed my foils, I built up a .scr file to import them into AutoCAD as a polyline. After I imported them as block files into the master drawing (scaling as appropriate, because all my foils are 1" in original form), I was able to pull the perimeter information accordingly, as @mcrae0104 is showing a couple entries above.

Correct me if I am wrong, fam, but you can pull perimeter and centroid data on a foil using XFLR-5, correct? Howabout OpenVSP?

#### wsimpso1

##### Super Moderator
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In other words, Billsky, the answer is no.
I like to point out that an appropriate response is encouraged by a well thought through question.

Sarcastic responses to a well intended reply is discouraging of the sought after help. Additionally, this is a forum. Other folks read the responses looking for information on topics. I like to think that we can write generally to help all of the folks reading a thread.

Billski

##### Well-Known Member
I did not see parameter in McRae's screen shot.
See second line under Regions. Below "Area".

#### pwood66889

##### Well-Known Member
See second line under Regions. Below "Area".
Thanks - missed that. Now, how did they figure it?

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