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The science
Lift on a blade section
Air over the curved upper surface speeds up and its pressure falls, while the flatter lower side slows it; the pressure difference gives lift. At a radius r the blade moves at Ωr and meets the wind (1 - a)U, so the relative flow makes an angle φ = atan((1 - a) / ((1 + a′) λr)) with the rotor plane, and the angle of attack is α = φ - (twist + pitch). Thin-airfoil theory gives Cl ≈ 2πα until stall.
Blade element momentum
For each of 60 annular elements, momentum theory (axial induction a, tangential induction a′, Prandtl tip-loss factor F) is solved together with the blade forces, a = 1/(4F sin²φ/(σ Cn) + 1) and a′ = 1/(4F sinφ cosφ/(σ Ct) - 1), by fixed-point iteration (σ is the solidity). Summing the torque gives the power coefficient Cp = P/(½ ρ πR²U³). An ideal actuator disc gives Cp = 4a(1 - a)², maximal 16/27 = 0.593 at a = 1/3: the Betz limit.
Honest simplifications: a made-up tapered blade and twist, a toy lift and drag polar with a smooth stall, a Glauert correction only for heavy loading, no rotational stall delay, no wake rotation losses beyond the induction terms, no turbine controller (power is not capped). It is a teaching model, not a certified design tool.
What to try
- At the Design point (pitch 0, tip-speed ratio 7) Cp is high and the angle of attack is nearly constant along the blade.
- Pick Slow rotor or Stalled blades: the attack angle exceeds the stall line near the root and the power collapses.
- Sweep the tip-speed ratio with the slider and see the Cp curve peak; it never exceeds the red Betz line.
- Choose Storm, pitched out: pitching the blades to feather them cuts the power in high wind.