Wind Turbine

The power in the wind grows with the cube of the wind speed: twice the wind, eight times the power. But no turbine can catch more than 59.3% of it — the Betz limit.

EnergyWind powerBetz limit

Inputs

Input examples

The yearly energy assumes the wind speed follows a Rayleigh distribution around the mean you enter, the usual first estimate for a site.

The turbine

Rotor diameter

Rated power

Power coefficient Cₚ (%) — Betz limit 59.3

Cut-in wind speed

Cut-out wind speed

The wind

Wind speed now

Yearly mean wind speed

Air density

Catching the Wind

Moving air carries kinetic energy: the power through a rotor grows with the swept area and with the cube of the wind speed. A turbine cannot stop the air completely — it has to flow away behind the rotor — so Albert Betz showed in 1920 that at most 16/27 of the power can be caught. Modern turbines reach about 45–50%.

Above its rated wind speed the turbine turns its blades to spill wind and stays at full power; in storms it shuts down. Because the wind varies, a turbine on land produces on average 25–35% of its rated power over the year (the capacity factor).

v³2× wind, 8× power

59.3%the Betz limit

D²2× rotor, 4× power

25–50%capacity factor

Power Curve

turbine output

power in the wind × Betz limit

now

Result

Enter the values above

Key Relations

Power in the Wind

The kinetic energy of the air flowing through the rotor disc each second.

Example:

Betz Limit

Slowing the air to one third of its speed behind the rotor gives the most power.

Yearly Energy

The power curve weighted by how often each wind speed occurs (Rayleigh distribution with mean v̄).

Sources & Verification

References

J. F. Manwell, J. G. McGowan & A. L. Rogers, Wind Energy Explained: Theory, Design and Application, 2nd ed., Wiley, 2009 — chapters “Wind Characteristics and Resources” and “Aerodynamics of Wind Turbines”.
G. M. Masters, Renewable and Efficient Electric Power Systems, 2nd ed., Wiley, 2013