Kulfan Airfoil Visualizer

Interactive visualization of CST (Kulfan) parameterized airfoils. Adjust parameters to see real-time updates.

Kulfan Airfoil Theory (CST)

The Class-Shape Transformation (CST) method, developed by Brenda Kulfan, represents airfoil geometries by multiplying a Class Function by a Shape Function. This approach allows for smooth, versatile geometry definition with a minimal number of parameters.

General Formulation

$$\zeta(\psi) = \sqrt{\psi} \cdot (1-\psi) \cdot \sum_{i=0}^{N} A_i \cdot \psi^i + \psi \cdot \zeta_T$$
$\psi = x/c$ (chord position)  •  $\zeta = z/c$ (vertical coordinate)  •  $\zeta_T = \Delta \zeta_{TE}/c$ (TE thickness)

Class Function

The term $\sqrt{\psi} \cdot [1-\psi]$ is called the "Class Function" $C(\psi)$. It defines the fundamental shape (e.g., round nose, sharp trailing edge), with the general form:

$$C_{N2}^{N1}(\psi) = (\psi)^{N1} [1-\psi]^{N2}$$

Shape Function

The "Shape Function" $S(\psi)$ is a simple, well-behaved analytic equation that defines the detailed profile features:

$$S(\psi) = \sum_{i=0}^{N} A_i \cdot \psi^i$$

Key Geometric Relations

Specific airfoil properties are directly related to the unique bounding values of the shape function:

$$S(0) = \sqrt{2 R_{LE}/C}$$
Leading Edge Nose Radius ($R_{LE}$)
$$S(1) = \tan \beta + \frac{\Delta Z_{te}}{C}$$
Boat-tail Angle ($\beta$) & TE Thickness

Thanks Brenda!

View Kulfan Whitepaper →
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CST Configuration
N1: 0.5
N2: 1.0

Geometry Scaling

Shape Function Parameters (Bernstein Weights)
Bernstein polynomial coefficients defining the surface curvature.

File & Database

Export Tools

Kulfan Parameters