A wind turbine can never capture more than the Betz limit of 59.3% of the kinetic energy flowing through its swept area — beyond that the air couldn't leave the rotor plane fast enough to make room for more. Real rotors fall short of even that, and how far short depends on two control variables: how fast the rotor spins relative to the wind (tip-speed ratio λ) and how the blades are pitched (β).
λ = ωR / V (rotor tip speed ÷ wind speed)
Cp(λ,β) = 0.5176(116/λᵢ − 0.4β − 5)e^(−21/λᵢ) + 0.0068λ
1/λᵢ = 1/(λ + 0.08β) − 0.035/(β³ + 1)
P = ½ ρ A V³ Cp (A = πR², ρ = 1.225 kg/m³)
This is the same empirical Cp(λ,β) surface (Heier's approximation) used in wind-turbine control-system design. At β = 0° the curve peaks near λ ≈ 8, close to the theoretical optimum for a modern 3-blade rotor — a real turbine's controller constantly adjusts blade pitch and generator torque to chase that peak as wind speed changes, which is exactly what "wind energy optimization" means in practice.
- Pitch angle β — feathering the blades (raising β) spills lift and is used above rated wind speed to cap power and protect the drivetrain; it also visibly rotates the blades in the 3D view.
- Tip-speed ratio λ — a variable-speed turbine's generator sets rotor speed to hold λ near its optimum for the current pitch; too low and the blades stall, too high and drag losses dominate.
- Hub height — wind speed grows with height following the power-law wind-shear profile V(h) = V₁₀·(h/10)^0.14, so a taller tower reaches faster, steadier wind — one of the real trade-offs in siting a turbine.
- Optimize button — sweeps the (β, λ) grid at the current wind speed and hub height to find the combination that maximizes captured power, then moves the sliders there.