Wind Turbine Power Calculator
Estimate the power output of a wind turbine from wind speed, rotor diameter, and efficiency.
Turbine Power Output
630.5 kW
Turbine Power Output vs Wind Speed
सूत्र
## Wind Turbine Power Wind power depends on the cube of wind speed and the swept area of the rotor. ### Formula **P_available = 0.5 rho A V^3** (total wind power) **P_output = 0.5 rho A V^3 Cp** (extracted power) where rho is air density, A is the swept area (pi D^2/4), V is wind speed, and Cp is the power coefficient. The Betz limit states maximum Cp = 16/27 = 59.3%. Practical turbines achieve 35-45%.
हल किया गया उदाहरण
An 80 m rotor diameter turbine in 8 m/s wind, Cp = 0.40.
- 01Swept area = pi x 40^2 = 5,027 m^2
- 02Available power = 0.5 x 1.225 x 5027 x 8^3 = 0.5 x 1.225 x 5027 x 512
- 03Available = 1,576,461 W = 1,576 kW
- 04Output = 1,576 x 0.40 = 630.6 kW
अक्सर पूछे जाने वाले प्रश्न
Why does power depend on wind speed cubed?
The kinetic energy in wind is 0.5 m v^2. The mass flow rate through the rotor is rho A v. Power = energy x flow rate = 0.5 rho A v^3. So doubling wind speed increases power 8-fold. This is why site selection (average wind speed) is critical.
What is the Betz limit?
Albert Betz proved in 1919 that no turbine can extract more than 59.3% of the kinetic energy in the wind. This is because the wind must continue flowing downstream; extracting all energy would require stopping the wind entirely.
What wind speed is needed for viable wind power?
Annual average wind speed above 5-6 m/s is generally required for economic viability. Most utility-scale turbines are rated for 10-15 m/s wind and cut in at 3-4 m/s.
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