Animation: Design of rotor blades for wind turbines

The following interactive animation shows how the shape of the rotor blade of a wind turbine can be calculated from the parameters of the so-called Betz formula.

The blade depth of a rotor blade can be represented as a mathematical curve. The parameters are summarised in the formula developed by Albert Betz. The parameters can be changed in the animation. The result is displayed as a curve and also as a 3D model.

The Betz formula defines the blade depth as a function of the distance from the rotor hub. The blade profiles used in the animation are NACA profiles, which are actually used in the construction of some wind turbines.

The Betz formula can be represented as follows (Hein 2013):

All parameters can be changed in the table:

  • Blade number Z
  • Lift coefficient Ca
  • Design speed n
  • Blade length l
  • Wind speed v in m/s

The lift coefficient is a parameter that can only be determined empirically or through simulation.

The design (rotational) speed determines whether it is more of a high-speed rotor with low torque or a low-speed rotor with high torque.

Note: To display the curve, double-click on the 3D model.

In the animation, wind turbines with up to 9 blades can be constructed, although it is computationally shown that turbines with 3 blades have the highest efficiency. Wind turbines with more than 3 blades are still used today for specific applications.

The wind speed depends on the local conditions. This value is obtained through measurements and statistical analysis.

Overview and download

TitleDesign of rotor blades for wind turbines
Target groupTeachers and lecturers
PlattformenMicrosoft® Windows®
FeaturesFull screen mode
lossless zoom
Large screens and projection screens supported
DownloadContact us


C. Hein, S. Rikowski

Source information

  • 3D engine for 3D model: Papervision3D 2.0
  • Wing profiles (NACA 4412, 4418, 4421):
  • Authoring tool (control elements supplied): Adobe Animate
  • Betz-Formula: Hein, Christian (2013): [without title]. URL: [last access: 18.02.2013].


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