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Energy, electricity and mechanics

Power of a wind turbine

Power available in the wind and useful power of a wind turbine based on rotor diameter and wind speed.

m

Diameter of the circle swept by the blades.

m/s

Average speed at rotor height.

Fraction of the wind's power captured by the rotor. Real small wind turbines: 0.25-0.40. The physical limit (Betz) is 0.593.

%

Electrical and mechanical losses of the generator and drivetrain.

kg/m³

1.225 kg/m³ at sea level and 15 °C; decreases with altitude and temperature.

Result

Power available in the wind
— W
Useful power generated
— W
Energy in one day at constant wind
— kWh

How it is calculated

Area swept by the rotor: A = π × (diameter ÷ 2)². Power available in the wind: P = 0.5 × ρ × A × v³ (ρ air density, v wind speed).

Useful power: P_useful = P × Cp × generator efficiency.

Energy in one day if the wind blew constantly at that speed: kWh/day = P_useful × 24 ÷ 1000. In practice the wind varies, so this is a theoretical maximum, not real output.

Keep in mind

  • Power grows with the cube of wind speed: doubling the speed multiplies the available power by 8. Small errors measuring the wind change the result a lot.
  • Always install a braking or regulation system for strong winds: above the design speed the rotor can destroy itself.
  • The tower and its anchoring must be designed for the extreme wind loads of the site, not just normal operation.

See also

More tools in “Energy, electricity and mechanics”