Wind Turbine Power

This equation estimates how much mechanical/electrical power a wind turbine can extract from moving air. It comes from the kinetic energy carried by the wind passing through the rotor area each second: the mass flow rate through the swept disk is proportional to air density, area, and wind speed, while the energy per unit mass grows with v^2, giving an overall v^3 dependence. The factor C_p captures the real turbine’s efficiency, since no rotor can remove all of the wind’s energy and practical designs are limited by aerodynamics and the Betz limit.

Use this formula when estimating turbine output from site conditions, comparing rotor sizes, or evaluating how changes in wind speed affect generation. It is also useful in renewable-energy studies, feasibility analyses, and turbine performance calculations.

• using rotor diameter instead of swept area A
• forgetting that wind speed is cubed, not squared
• choosing an unrealistic Cp greater than the physical limit or not matching the turbine design