Why do wind turbines keep getting enormous? Because power grows with the cube of wind speed and the square of rotor diameter — small changes pay off big.
Wind Turbine PowerLive
the Betz limit
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Wind power scales with the cube of wind speed and the square of rotor diameter — which is why turbines keep getting bigger and why a windy site is worth so much more. No turbine can extract more than 59.3% of the wind's energy (the Betz limit); real machines reach about 45%. Below cut-in and above cut-out speeds they produce nothing.
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How it works
A turbine's power is ½·ρ·A·v³·Cp: air density times swept area times wind speed cubed times the power coefficient. No machine can capture more than 59.3% of the wind's energy — Betz's limit — and real turbines reach about 45%. Below the cut-in and above the cut-out wind speed they generate nothing at all.
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