#Airfoil generator matlab code code
Does it look difficult to you? No problem, you can download the MATLAB code at this article so you can understand and try it by yourself. Now we can define the complete equation of CST for an airfoil:Ĭool, the equation is now complete. Oh my, another creature named K, God had chosen someone to named it binomial coefficient which is expressed as: To alter the overall shape of airfoil then you’ve got to define the component shape function that is given as the following:
![airfoil generator matlab code airfoil generator matlab code](https://i.ytimg.com/vi/nILo18DlqAo/maxresdefault.jpg)
N in shape function expression is the order of the Bernstein polynomial (note that N1 and N2 are different things!) and A is the weight/curvature coefficient. Perfect, now you can make your own airfoil! Now I can give the expression of shape function: The shape function itself defines the specific shape within the airfoil. After you define an airfoil with class function surely you don’t want a boring shape of an airfoil, right? You want to create another airfoil by yourself so now the definition of shape function comes in handy. I explained class function, and then you ask what is the shape function. Now we consider N1 = 0.5, N2 = 1.0 and we will get a round nose and pointed aft end airfoil, exactly what we want for an airfoil. Gives N1 = 0.75, N2 = 0.25, you get a low drag projectile shape. Gives N1 = 0.5 and N2 = 0.5, you get a round nose elliptic airfoil. The general class function is defined as follows: N1 and N2 are two most joyful parameters of CST, you can play with these values and create various shapes with them.
![airfoil generator matlab code airfoil generator matlab code](https://www.mathworks.com/matlabcentral/mlc-downloads/downloads/3828d978-52a0-4b9a-87e3-a865fc2a3a92/59ede3b3-b43d-427d-ae77-767693c0f405/images/screenshot.png)
As you can see that class function takes x coordinate, N1, and N2 as its input. The class function is the part that defines the type of aerodynamic body that you want to build could be airfoil, nacelle, or even axisymmetric bodies.
![airfoil generator matlab code airfoil generator matlab code](https://www.researchgate.net/profile/Md-Akram-7/publication/349733159/figure/fig1/AS:997906110763014@1614930765414/The-C-type-mesh-for-the-baseline-airfoil-of-a-wind-turbine-at-an-angle-of-attack-AOA-of_Q320.jpg)
Trailing edge thickness is another term that completes the CST equation but for a preliminary purpose, it might be not that important. Roughly speaking, two main important parts of CST are the so-called class ( C) and shape function ( S). The upper and lower surface coordinate of CST are easily defined as follows:Ĭonsider that you don’t know what is the meaning of x, z, and c, those creatures are absis, the ordinate location of the airfoil, and chord length or airfoil. The good thing about Bernstein polynomial, and CST itself is that later you will see that the smoothness of its curve is beneficial for optimization purpose! Since the number of parameters can be tuned easily by altering the order of Bernstein polynomial, CST is suitable for either conceptual or preliminary design of airfoil.Īlright, let’s kick out the jams and move to the mathematical expression. Roughly speaking, you also don’t want a bumpy airfoil, well, except if you want to add some shock bump on your airfoil. For simplicity purpose, this simple article considers only CST for the two-dimensional shape of an airfoil.ĬST build the airfoil by summing the individual contribution of its basis function that is elegantly built by Bernstein Polynomial.
![airfoil generator matlab code airfoil generator matlab code](https://i.ytimg.com/vi/dv3wltBHDdU/maxresdefault.jpg)
The greatest thing from CST is that CST can be used not only for an airfoil, but it can also be extended further into the general shape of aerodynamic bodies. Those are some of the reasons of why Brenda developed CST that is very simple to be coded and also it doesn’t take such a long time to understand the concept of CST itself. So what’s the point of having another airfoil parameterization method? As it was pointed by Brenda in her paper (Brenda is a woman engineer, cool!), we want an intuitive, robust, smooth, and flexible parameterization method. The Class Shape Transformation (CST) parameterization method was first developed by Brenda Kulfan, an aerodynamic engineer at Boeing. Short note on CST method for airfoil parameterization ( MATLAB Code included)