What Is the Wind Turbine Betz Limit & Aerodynamic Power Calculator?
The Betz limit establishes the upper physical limit on power extraction from an open fluid stream.
How Does the Wind Turbine Betz Limit & Aerodynamic Power Calculator Work?
To extract 100% of wind energy, air would have to come to a complete stop, blocking airflow behind the turbine.
Wind Turbine Betz Limit & Aerodynamic Power Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
P_{\text{wind}} = \frac{1}{2} \rho A V^3, \quad P_{\text{Betz}} = \frac{16}{27} P_{\text{wind}}, \quad P_{\text{rotor}} = C_p P_{\text{wind}}
Wind power cubic velocity scaling, Betz theoretical limit, and aerodynamic rotor power.
How to Use the Wind Turbine Betz Limit & Aerodynamic Power Calculator
- Input rotor diameter, upstream wind velocity, air density, and aerodynamic power coefficient Cp.
Step-by-Step Example Calculation
3 MW Commercial Wind Turbine
Input Values:
rotorDiameterMeters:100
windSpeedMPerS:12
airDensityKgPerM3:1.225
powerCoefficientCp:0.44
Worked Steps: Predicts 8.31 MW unconstrained wind stream power, 4.92 MW Betz ceiling, and 3.66 MW captured rotor power.
Understanding Your Result
Shows swept area in m², available wind power, Betz theoretical ceiling, and captured output power in MW.
Factors That Affect the Result
- Power scales with the cube of wind speed (V^3) and square of rotor diameter (D^2).
When Should You Use This Calculator?
- Wind farm site resource assessment, turbine selection, and power curve modeling.
Assumptions & Limitations
- Actuator disk theory assuming 1D inviscid steady flow with no wake rotation.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Derived by Albert Betz in 1919.