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Airfoil generation using CST parameterization method

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Generates an airfoil shape using CST method



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CST method is a powerful parameterization method because of its simplicity, robustness, and its ability to be generalized into various possible shapes of aerodynamic bodies. CST with low order polynomial is also suitable for airfoil preliminary design and optimization purpose since it only needs few parameters to give specific shape of airfoil. CST build the airfoil by summing the individual contribution of its basis function that is built by Bernstein Polynomial. The code is easy to use and also very easy to be modified for your own needs.

The input to CST_airfoil.m is the following:
- wl (lower surface weight)
- wu (upper surface weight)
- dz (trailing edge thickness)
- N (number of airfoil coordinates)

Where the output is a set of x and y coordinates of CST generated airfoil.

As a demonstration, you can try the following:

CST_airfoil([-1 -1 -1], [1 1 1],0,400)


CST_airfoil([-0.1294 -0.0036 -0.0666], [0.206 0.2728 0.2292],0,400)

The latter will gives coordinates that resembles the shape of Clark-Y airfoil.

You can also easily add the order of CST by simply adding additional weight value on wl or wu inputs. For detail information you can refer to the original paper by Brenda Kulfan:

Kulfan, Brenda M. "A universal parametric geometry representation method—CST." AIAA Paper 62 (2007).

Comments and Ratings (7)


IDEA (view profile)

how to build a 3D-airfoil with CST in MATLAB ?Do you have the code for 3D ?

@Niyati Chokshi

Indeed, this program only generates the airfoil shape. For meshing, I typically use open source meshing-code (Try GMSH).

It only gives the co-ordinates. How do I create a mesh around the airfoil?

@Thomas Hansen,

I am sorry for the late reply. For trailing edge thickness, you can just adjust the dz parameter.

But if you want to control the thickness of the entire airfoil, I suggest to approximate some existing airfoil and then found its CST parameters. By that way you can easily correlate the CST parameters and the thickness of an airfoil. Or another approach is that you can multiply the unit airfoil with some defined thickness.


Thomas Hansen

Nice implementation.

How do one control the max/min thickness of the airfoil?

Regards Thomas

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