# How to generate equations/formula for any airfoil

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 April 18, 2010, 11:17 How to generate equations/formula for any airfoil #1 Senior Member   TWB Join Date: Mar 2009 Posts: 119 Rep Power: 9 Hi, I understand that for NACA00xx airfoils, there's a formula which can output the y coordinate given the x coordinate. However, if I need a similar formula for a general airfoil whereby I know x/y coordinates, how can it be done? Any recommendation? Thanks alot!

 April 18, 2010, 16:21 #2 Senior Member   Join Date: Nov 2009 Posts: 411 Rep Power: 11 If your points are well behaved (no errors in the data) you can always use an interpolation function to obtain formulas for the upper side and the lower side of your airfoil. After all you can easily fit a polynomial function on a given set of points. If using interpolation won't give you a nice surface (this will be the case for non accurate data) you can always use a least square approximation with orthogonal polynomials (e.g. Chebyshev) to obtain an analytical formula for your airfoil. Do

 April 19, 2010, 00:15 #3 Senior Member   TWB Join Date: Mar 2009 Posts: 119 Rep Power: 9 Thanks DoHander. In fact, the airfoil I'm interested in is the s1020 airfoil, as shown over here: Currently I have a total of 60 points for this airfoil. Based on your experience, which mtd do you think it's better to get a good fit? Is it possible to use the 30pts for the top and bottom airfoil with the least square approximation? Thanks again!

 April 19, 2010, 10:52 #4 Senior Member   Join Date: Nov 2009 Posts: 411 Rep Power: 11 Yes, I think you can use the least square methods with 30 points. Probably you can use Matlab to solve the problem, if I remember correctly it has a least square fit, not sure however if Matlab use simple polynomials or orthogonal polynomials. In the past I've used a C# code to solve the problem, but any programming language you know will work. Do

 April 19, 2010, 12:14 #5 New Member   Join Date: Dec 2009 Posts: 25 Rep Power: 8 If you download some software such as designfoil you can make most airfoils i think. You can also export these to CAD software as well.

 April 19, 2010, 19:01 #6 Senior Member   Join Date: Apr 2009 Posts: 129 Rep Power: 9 EDIT: Nevermind ...

 April 19, 2010, 23:56 #7 Super Moderator     Praveen. C Join Date: Mar 2009 Location: Bangalore Posts: 255 Blog Entries: 6 Rep Power: 10 Just use a cubic spline interpolation. Matlab has builtin functions for doing this. Fit separate cubic splines for top and bottom curves.

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