# HD Animation: Design of rotor blades for wind turbines

The animation shows how to calculate the ideal rotor blade shape of a wind turbine from the parameters of the Betz formula. At the base of the rotor, the blades are wider and flatter, while they become narrower towards the tip.

Various requirements are taken into account, such as the number of rotor blades and the average wind speed at the installation site. The precise calculation of the blade depth is a prerequisite for the highest possible energy yield.

Several parameters can be changed in the animation. The result is displayed both as a curve and as a 3D model.

## Note on use

As with all animations, the windows can be enlarged or reduced by clicking on them.

The rotor of the wind turbine can be viewed from several predefined perspectives:

After starting the application, you can view the animation in full-screen mode. To do this, click on “View” and then on “Full screen”:

To exit full screen mode, press the Esc key.

## Explanations

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:

• Lift coefficient Ca
• Design speed n
• 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 can be constructed with up to 9 rotor blades, although it can be shown mathematically that turbines with 3 rotor blades have the highest efficiency. Wind turbines with more than 3 rotor blades are still used today for special applications. One example is the operation of pumps. The limitation to 9 rotor blades is for technical animation reasons, because the high number of polygons exhausts the computing power of a normal PC.

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

 Title Design of rotor blades for wind turbines Target group Teachers and lecturers Plattformen Microsoft® Windows® Features Full screen modelossless zoomLarge screens and projection screens supported Licence Freeware Download Contact us

## Contributors

C. Hein, S. Rikowski

## Source information

• 3D engine for 3D model: Papervision3D 2.0
• Wing profiles (NACA 4412, 4418, 4421): http://www.ae.illinois.edu/m-selig/ads/coord_database.html
• Authoring tool (control elements supplied): Adobe Animate
• Betz-Formula: Hein, Christian (2013): [without title]. URL: http://www.unimuenster.de/imperia/md/content/fachbereich_physik/technik_didaktik/energietechnik_nutzung_windenergie.ppt [last access: 18.02.2013].

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