Wind Turbine Betz Limit & Power Coefficient Calculator
Calculate aerodynamic power coefficient (Cp), Tip-Speed Ratio (TSR), Betz law theoretical maximum limit, rotor aerodynamic torque, and thrust force.
Rotor Dimensions & Inflow Wind
Atmospheric Air Conditions
Power Coefficient & Aerodynamic Forces
| Power Coefficient (Cp): | -- (Max Betz: 0.593) |
| Tip-Speed Ratio (TSR λ): | -- |
| Total Kinetic Wind Power (P_wind): | -- kW |
| Theoretical Betz Maximum (P_betz): | -- kW |
| Blade Tip Speed (V_tip): | -- m/s (-- km/h) |
| Aerodynamic Rotor Thrust (T): | -- kN |
| Low-Speed Shaft Aerodynamic Torque: | -- kN·m |
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Frequently Asked Questions
What is Betz's Law and why can no wind turbine exceed 59.3% efficiency?
Formulated by German physicist Albert Betz in 1919, Betz's law applies conservation of mass and momentum across an idealized actuator disk. If a turbine extracted 100% of kinetic energy, air behind the rotor would come to a complete standstill (zero velocity), preventing upstream air from passing through. The optimal balance occurs when wind velocity behind the rotor drops to exactly 1/3 of upstream velocity, yielding a maximum theoretical power coefficient Cp = 16/27 ≈ 59.26%.
What is Tip-Speed Ratio (TSR) and why does an optimum value exist?
Tip-Speed Ratio (TSR or lambda = V_tip / V_wind) is the ratio of blade tip rotational speed to incoming wind speed. If the rotor spins too slowly (low TSR), wind passes through the swept area without interacting with blades. If it spins too rapidly (excessive TSR), blades act as a solid wall creating excessive aerodynamic drag and turbulence. Modern 3-bladed utility wind turbines achieve peak efficiency at an optimum TSR between 7.5 and 8.5.
What is the physical cause of the large axial aerodynamic thrust on wind turbine towers?
As the rotor extracts kinetic energy, static pressure rises in front of the rotor and drops sharply behind it. This net pressure differential acting over thousands of square meters of rotor swept area produces an enormous horizontal overturning force (often 300 to 800 kN on a modern multi-megawatt turbine), dictating the structural design of the tower and foundation.