Parameters
Rotor radius R50.0 m
Blade count B3
Design TSR λ7.0
Design lift coeff Cl1.00
Lift-to-drag ratio Cl/Cd80
Wind speed V∞10.0 m/s
Airfoil profile
Spanwise elements N20
BEM Equations
Inflow angle and induction factors iterate until convergence:
$$\phi = \arctan\!\left(\frac{1-a}{(1+a')\lambda_r}\right)$$ $$a = \frac{\sigma C_l \cos\phi}{4F\sin^2\!\phi + \sigma C_l \cos\phi}$$Power coefficient:
$$C_p = \frac{8}{\lambda^2}\int_0^\lambda \lambda_r^3 a'(1-a)\,d\lambda_r$$
Betz limit: Theoretical maximum Cp = 16/27 ≈ 0.593 (ideal lossless rotor)
0.000
Power Coeff Cp
0.0 kW
Power P
0.0 rpm
Rotor Speed
0.000
Mean Solidity σ
Cp-λ Curve
Blade Shape Distribution
BEM Design Key Equations
Optimal chord: $c(r) = \dfrac{8\pi r}{B C_l}\cdot\dfrac{\sin^2(\phi/2)}{\cos\phi}\cdot\dfrac{1}{3}$
Optimal twist: $\beta(r) = \dfrac{2}{3}\arctan\!\left(\dfrac{R}{\lambda r}\right) - \alpha_d$
Prandtl tip-loss factor: $F = \dfrac{2}{\pi}\arccos\!\left(e^{-B(R-r)/(2r\sin\phi)}\right)$
Engineering note: Modern offshore turbines (10–20 MW) run at λ ≈ 7–9, Cp ≈ 0.47–0.50. Blades 80–120 m long have max chord ~5–7 m near root and <1 m at tip. Root twist ≈ 20°, tip twist ≈ 0°.