Wind Turbine Power
Wind Turbine Power
A wind turbine captures a fraction of the wind’s kinetic energy flux, set by the swept area, wind speed cubed and a power coefficient.
The power is P = ½·ρ·A·v³·C_p. where ρ is air density, A the swept area, v the wind speed and C_p the power coefficient.
Inputs
rho := 1.225 kg/m^3=1.23 kg/m^3
A := 5000 m^2=5000 m^2
v := 12 m/s=12 m/s
C_p := 0.4=0.4
Apply the wind-power equation.
P := 0.5·rho·A·v^3·C_p=2.12e+06 W
Results
Power scales with the cube of wind speed, so a small speed increase yields far more energy. The Betz limit caps C_p at 0.59.
Assumptions & limitations
- Power coefficient below the Betz limit (0.59).
- Uniform wind over the rotor.
- Steady wind.