Betz's law

Betz's law states that no wind turbine can convert more than 59.3% of the kinetic energy of the wind into mechanical energy turning a rotor. This limit is known as the Betz limit or Betz's coefficient, and is derived from the principles of conservation of mass and momentum of the airflow through an idealized "actuator disk" that extracts energy from the wind.

The law was published in 1919 by German physicist Albert Betz. While Betz's law dictates a theoretical maximum, real-world wind turbines are subject to further inefficiencies, typically achieving peak efficiencies between 30% and 45%. These inefficiencies arise from factors such as blade design, aerodynamic losses, generator efficiency, and mechanical friction.

The derivation of Betz's law involves considering the wind as an incompressible fluid flowing through an area defined by the rotor blades. By applying conservation of mass, the amount of air entering the rotor area must equal the amount exiting. However, the wind speed must decrease as it passes through the rotor, as energy is being extracted. Applying conservation of momentum, the force exerted on the rotor can be related to the change in momentum of the air. Combining these principles, along with the concept of power being the product of force and velocity, allows the derivation of the maximum theoretical efficiency of 59.3%.

While unattainable in practice, Betz's law provides a crucial benchmark for evaluating the performance of wind turbine designs and understanding the limitations inherent in wind energy conversion. It highlights the fundamental physical constraints governing the extraction of energy from moving air.