Explain the concept of the Betz limit in wind energy.

• A. The Betz limit is the maximum fraction of wind energy extractable by a rotor, about 59.3%.
• B. The Betz limit is the minimum rotor diameter to capture wind energy.
• C. The Betz limit states no energy can be extracted from wind.
• D. The Betz limit relates to solar irradiance conversion efficiency.

Answer: (A)

The idea behind the Betz limit is that there’s a fundamental cap on how much wind energy a rotor can convert into usable power. In an ideal, frictionless flow, a rotor can capture at most about 59.3% of the wind’s kinetic energy.

This limit comes from applying conservation of mass and momentum to air moving through the turbine. The rotor must slow the wind to extract energy, but the air that has passed through the rotor still needs to continue moving downstream. If you try to extract more energy by slowing the air even more, you end up choking the flow and reducing the amount of wind that reaches the rotor, so the overall power can’t keep increasing. The optimum slowdown occurs when the induced velocity through the rotor balances these effects, yielding a maximum power coefficient of 16/27, which is about 0.593.

In the real world, blades aren’t lossless—there are friction, tip losses, and wake mixing—so actual turbines achieve lower efficiencies, typically around the 0.4–0.45 range. But the Betz limit sets the ceiling for what any rotor could theoretically accomplish.

This idea isn’t about rotor diameter, nor is it saying no energy can be extracted, and it isn’t related to solar energy.