Power available in moving air scales with the cube of wind speed and with swept area. A turbine only converts a fraction of that, the power coefficient Cp — capped in theory by the Betz limit (Cp ≤ 0.593), and by roughly 0.45 in practice once mechanical and electrical losses are included.
P = ½·ρ·A·v³·Cp
A = π·(D/2)², ρ ≈ 1.225 kg/m³ (air density)
Cp_max ≈ 0.45 (Betz theoretical ceiling: 0.593)
Below cut-in speed there isn't enough torque to turn the rotor, so output is zero. Between cut-in and rated wind speed, blades sit at their optimum pitch (0°) and power climbs with v³. Above rated speed the generator is already at its design limit — so pitch control rotates ("feathers") the blades to deliberately spill lift and hold Cp down, keeping power flat at the rated value instead of letting it keep climbing. Turn pitch control off above to see what happens without that regulation: power keeps rising past the generator's rated capacity, which real turbines never allow. Past cut-out speed (~25 m/s) the turbine shuts down entirely regardless of pitch, to protect the structure from excessive loads.
- Wind speed — moves you across the four regions: cut-in, cubic ramp-up, pitch-regulated plateau, cut-out shutdown.
- Rotor diameter — bigger swept area means more power at every wind speed, and raises the rated-power ceiling.
- Pitch control — toggling it off removes the regulation above rated speed, exposing the uncapped cubic curve pitch control exists to prevent.
- Gusty wind — layers turbulence on top of the base wind speed so the operating point drifts across regions the way it does on a real site.