๐ช๏ธ Wind Turbine BEM & Betz Limit Sizer
Calculate wind turbine aerodynamics with Blade Element Momentum (BEM) theory: power coefficient Cp, Betz limit, tip-speed ratio lambda, thrust load, and AEP.
โก Fortran 90 Engine
Double Precision (IEEE 754)
โ ISO / ASME Validated
Turbomachinery
๐ Solver Telemetry
โ ACTIVE
๐๏ธ Views
41
โก Solves
31
๐พ Downloads
479
๐ฆ Fortran Code
5.2 KB
๐
Released
Jun 2026
โฑ๏ธ Latency
< 1 ms
๐ช๏ธ 3-Blade HAWT Rotor, Tower & Streamline Wake Deflection
Real-time visual simulation: Free-stream wind deceleration through disk, induction factor a, and wake expansion๐ Configuration & Presets
๐ NREL 5MW Offshore
โก Giant 8MW Deepwater
๐๏ธ Commercial 3MW Onshore
๐ก 50kW Community Turbine
BEM Theory & Betz Formulation:
โข Tip Speed Ratio: ฮป = (ฯ ยท D ยท N / 60) / Vโ
โข Betz Theoretical Limit: Cp,max = 16/27 โ 59.26%
โข Aero Power: Paero = ยฝ ยท ฯ ยท A ยท Vโยณ ยท Cp(ฮป, ฮฒ) [MW]
โข Rotor Thrust: T = ยฝ ยท ฯ ยท A ยท Vโยฒ ยท CT [kN].
โข Tip Speed Ratio: ฮป = (ฯ ยท D ยท N / 60) / Vโ
โข Betz Theoretical Limit: Cp,max = 16/27 โ 59.26%
โข Aero Power: Paero = ยฝ ยท ฯ ยท A ยท Vโยณ ยท Cp(ฮป, ฮฒ) [MW]
โข Rotor Thrust: T = ยฝ ยท ฯ ยท A ยท Vโยฒ ยท CT [kN].
๐ Performance Results
Configure inputs and click Compute to view results.
๐ Calculation Methodology & Wind Aerodynamics Standards
Blade Element Momentum (BEM) Theory
BEM couples 1D momentum conservation across the rotor streamtube with 2D sectional airfoil lift and drag properties, resolving axial and angular flow induction factors $a$ and $a'$.
Betz Limit & Glauert Correction
Albert Betz proved that no wind turbine can capture more than 59.26% of kinetic energy. The Glauert correction handles high thrust states ($a > 0.33$) where momentum theory breaks down due to turbulent wake vortex mixing.
Key Engineering Assumptions
- IEC 61400-1 wind turbine design standards.
- Rayleigh/Weibull annual wind speed distribution.
- Widely used for onshore and offshore wind farm power rating and fatigue thrust analysis.