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sci.wind-turbine-Betz-limit Calculator
Calculates the Betz limit maximum theoretical power coefficient Cp_max = 16/27 ≈ 0.593 from actuator disc theory and derives optimal axial induction factor a = 1/3. No wind turbine can extract more than 59.3% of wind kinetic energy — modern large turbines approach Cp = 0.48–0.50.
Inputs
V Wind M S
Rate of movement. 1 m/s = 3.6 km/h = 2.237 mph.
D Rotor M
Distance across a circle through its centre. Always confirm units match the rest of the calculation.
Cp
Rate of energy transfer (W). P = V×I (electrical). P = F×v (mechanical). 1 horsepower ≈ 746 W.
Results
available wind power P_wind (kW)
Sample size or count used in the calculation.
turbine output P (kW)
Sample size or count used in the calculation.
Betz limit power P_Betz (kW)
Reference formula or conversion factor shown for context.
Betz efficiency (Cp/0.593)
Useful output divided by total input, as a percentage. True 100% efficiency is impossible — losses appear as heat. LEDs: 30–50%. Electric motors: 85–97%. Switching supplies: 85–95%.
P = ½ρAv³ × Cp
Reference formula or conversion factor shown for context.
capacity factor estimate
A dimensionless multiplier applied in the calculation.