Wind Turbine Power Output Calculator
Calculate the theoretical power output of a wind turbine from wind speed, rotor diameter, and air density using the Betz limit.
输出功率
2,128.0 kW
Power Output vs Wind Speed
公式
## Wind Turbine Power Physics Wind turbines extract kinetic energy from moving air. The available power depends on the cube of wind speed, which is why small increases in wind speed produce large gains. ### Formula **P = 0.5 x rho x A x V³ x Cp** Where rho is air density (kg/m³), A is the rotor swept area (pi x r²), V is wind speed (m/s), and Cp is the power coefficient (efficiency). The Betz limit states that no turbine can capture more than 59.3% of the available wind energy.
计算示例
A turbine with 80 m rotor diameter operates in 12 m/s wind at 40% efficiency.
- 01Swept area = pi x (80/2)² = pi x 1600 = 5,026.5 m²
- 02Wind power = 0.5 x 1.225 x 5,026.5 x 12³ = 5,316,045 W
- 03Turbine output = 5,316,045 x 0.40 = 2,126,418 W = 2,126.4 kW
- 04That is 2.126 MW of electrical output
常见问题
What is the Betz limit?
The Betz limit (59.3%) is the theoretical maximum fraction of wind energy a turbine can extract. Real turbines typically achieve 35-45% efficiency.
Why does power scale with the cube of wind speed?
Kinetic energy is proportional to velocity squared, but a faster wind also delivers more mass per second. Combined, power scales with V³.
What wind speed do turbines need?
Most turbines have a cut-in speed around 3-4 m/s, reach rated power at 12-15 m/s, and shut down above 25 m/s to prevent damage.