Blade Element Momentum BEM Calculator
Rotor aerodynamics & blade design: Calculate axial induction factor (a), tangential induction factor (a'), Glauert turbulent wake state correction, and Prandtl tip loss.
Blade Annular Element Geometry
Induction Factors & Aerodynamic State
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Frequently Asked Questions
What are the axial (a) and tangential (a') induction factors?
The axial induction factor a represents the fractional reduction in freestream wind speed at the rotor plane: u_rotor = u₀(1 - a). The tangential induction factor a' represents the induced swirl in the wake opposite to rotor rotation: ω_wake = 2 a' Ω. In the ideal Betz limit, a = 1/3.
Why is the Glauert correction required when a > 0.33?
Standard 1D momentum theory predicts that when a = 0.5, downstream wake speed drops to zero, and for a > 0.5 the thrust coefficient exceeds 1.0 and air would theoretically reverse through the rotor. In reality, a turbulent wake state develops where outer freestream air mixes with the wake; empirical Glauert equations correct for this high-thrust regime.
What is the physical cause of Prandtl's tip loss factor F?
Because a wind turbine blade has a finite span, high-pressure air on the windward face spills around the blade tip to the low-pressure suction face. This creates a bound-vortex shedding helix that reduces the effective induced velocity and power extraction across the outer 10% to 15% of the blade radius.