Betz Law

Albert Betz, a German physicist, published a book in 1919 where he concluded that only 16/27 of the winds energy (approximately 59.3%) can be used (in ideal conditions) by a wind turbine.  Ideal conditions do not actually exist, but we can imagine them in theory:  no friction; mass-less turbine blades; no eddies.  In these ideal conditions it seems like 100% efficiency could be achieved, but Albert Betz was smart enough to recognize that if we were to harness all of the winds power, the wind would not leave the blade and would therefore be in the way of the rest of the wind.

In fact Betz experimented and proved mathematically, under the previously mentioned ideal conditions, the best case scenario happens when approximately 2/3 of the winds power is extracted and 1/3 of it is not (allowing the air to move out of the way of the rest of the wind).  In this way Betz calculated a theoretical maximum power extraction for wind turbines.

When a wind turbine company reports that their turbine is 60% efficient, then, they mean that it is 60% of the 59.3% (Betz limit), or really only 35.6% efficient.  Because of mechanical losses, such as friction from bearings, noise and heat, the most efficient turbines available today produce about 80% of 59.3%, or you could say they are just over 47% efficient.

I participated in the Nelson Wind Turbine Project at Iron Range Engineering this fall and it was imperative to get an understanding of the Betz limit and how the wind turbine industry compares their efficiency.  The project provided excellent practice at applying engineering principles such as Impulse and Momentum, The Conservation of Mass, and The Conservation of Energy to a real world project.  It would take an hour to tell you everything that I learned during this project, but I hope I have clarified any misconceptions that you may have had about how Betz’s Law is applicable to wind turbine efficiency.

Written by Jim McCluskey    

Proofread by Charlie Schuh