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Betz Limit Wind Turbine Aerodynamic Power Calculator

The Betz law establishes that no horizontal-axis wind turbine can capture more than 16/27 (59.3%) of the kinetic energy in an undisturbed wind stream.

Calculated Result
2.165 MW

Aerodynamic Extracted Power

Rotor Swept Area (A)

7854.0 m²

Total Incident Wind Power

4.811 MW

Betz Limit Efficiency

75.9% of Betz max

Calculation Breakdown

  1. Calculate circular rotor swept area A = π·(D/2)²A = π * (100 / 2)² = 7854.0 m²
  2. Evaluate third-power wind kinetic power equation P = 0.5 · ρ · A · v³ · CpP = 0.5 * 1.225 * 7854.0 * (10)³ * 0.45 = 2164.8 kW

Extracted Power vs Wind Speed (100m Rotor)

Interactive visualization based on your current inputs

MW
0.00.91.92.83.76 m/s8 m/s10 m/s12 m/sSpeed (m/s)Power (MW)

What Is the Betz Limit Wind Turbine Aerodynamic Power Calculator?

The Betz law establishes that no horizontal-axis wind turbine can capture more than 16/27 (59.3%) of the kinetic energy in an undisturbed wind stream.

How Does the Betz Limit Wind Turbine Aerodynamic Power Calculator Work?

The calculation evaluates user-provided measurements using recognized domain equations, converts between measurement units, and adjusts for real-world efficiency factors.

Betz Limit Wind Turbine Aerodynamic Power Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

P_{\text{shaft}} = \frac{1}{2} \rho A v^3 C_p, \quad C_{p,\max} = \frac{16}{27} \approx 0.5926

Power output scales cubically with wind velocity: doubling wind speed yields eight times the available aerodynamic kinetic energy.

How to Use the Betz Limit Wind Turbine Aerodynamic Power Calculator

  1. Enter your primary measurements in the input fields above.
  2. Select your preferred units (e.g. metric or imperial) if applicable.
  3. Review or adjust operational assumptions such as field efficiency.
  4. Click Calculate to instantly generate the full results breakdown and visual chart.
  5. Use the Reset button at any time to clear the form and test a new scenario.

Step-by-Step Example Calculation

100m Modern Utility Rotor at 10 m/s

Input Values:

rotorDiameterM:100
windSpeedMps:10
powerCoefficientCp:0.45
airDensityKgPerM3:1.225

Understanding Your Result

Your calculated result represents the realistic operational capacity or baseline output under the specified conditions. Comparing theoretical and effective outputs reveals the direct impact of turns, overlap, and practical downtime.

Factors That Affect the Result

Field terrain, operator experience, equipment maintenance, overlap margin, and weather conditions can significantly influence real-world output.

When Should You Use This Calculator?

Use this calculator whenever you need quick, verified estimates for job planning, budgeting, equipment sizing, or project timelines.

Assumptions & Limitations

  • Excludes mechanical gearbox and electrical generator losses (typically 90-95% electrical efficiency).

Frequently Asked Questions

Calculation Accuracy & Reference Note

This calculator implements verified, deterministic mathematical equations based on published standards. Results should be treated as professional engineering estimates; always verify critical operations with local equipment manuals and site inspections.

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