Perfect Turbine or Pipe Dream?

Wind turbines operate within the limits of Betz’ Law. Simply put, if you try to capture 100% of the energy available in the wind, the wind is stopped—it cannot move the blades. On the opposite end of the scale, the wind just goes around a fixed obstruction. In either case, the result is the same—no energy is extracted.

The Betz limit says that capturing 59.6% of the energy in the wind is the best compromise between stopping the air and letting it pass through the turbine unaffected. Maintaining the flow of air is the compromise any wind machine must make, whether it is a horizontal-axis (a traditional-style turbine) or a vertical-axis turbine; with many blades or few. All turbines are subject to the Betz limit.

The “Energy Output” table shows the amount of energy you can reasonably capture per rotor swept area at several average wind speeds. You can multiply by the swept area of the turbine you’re considering to see if the manufacturer’s claims are even possible!

However, comparing the “model” wind turbine columns with manufacturers’ claimed production data from four reputable manufacturers’ turbines, none are as good as claimed. Numbers in the “Model Turbine” column are based on an average efficiency of 35%. It is not terribly likely that you’ll find a wind turbine that is more efficient than this. Remember: If it’s too good to be true, it may very well be!

The table shows the energy (KWH) per month that a “perfect” turbine designed to Betz’ law could produce, and what a real-world model turbine could produce, taking inefficiencies and design into account. The table assumes a Rayleigh wind distribution at sea level.

Let’s try an example. If you have a turbine with a swept area of 10 square feet in a 10 mph wind, you’ll find that the “model” turbine value per square foot of rotor is 2.08. Multiply it by 10 because you have 10 square feet of rotor. If the manufacturer is claiming that the turbine can put out more than 20.8 KWH per month, the turbine is probably too good to be true. Next, multiply the Betz limit value of 3.5 by 10. If the manufacturer claims you can generate more than 35 KWH per month, then they are claiming to have broken the laws of physics.

—Mike Klemen