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Blade Element Momentum BEM Calculator engineering
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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

Blade tip radius
Local blade station (typ. 0.8 R)
Airfoil chord width at station r
λ = Ω · R / u₀ (Design TSR)
Airfoil polar lift at angle of attack
Airfoil drag polar
Angle to rotor plane

Induction Factors & Aerodynamic State

Axial Induction Factor (a)
-
-
Prandtl Tip Loss Factor (F)
-
Tip vortex reduction factor
Tangential Induction Factor (a')
-
Wake swirl factor
Inflow Angle (ϕ)
-
Relative wind angle
Angle of Attack (α)
-
α = ϕ - θ
Local Rotor Solidity (σ_r)
-
B · c / (2 · π · r)

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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.