Each windmill's four sails sweep a disc of area A = πR². The power available in the wind passing through that disc is Pwind = ½ρAv³ (ρ = 1.225 kg/m³ air density). Only a fraction of that, the power coefficient Cp, can actually be extracted — Cp depends on the tip-speed ratio λ = ωR/v and the sail reef angle β (how much canvas the miller has unfurled), via the standard turbine curve:
1/λi = 1/(λ + 0.08β) − 0.035/(β³+1)
Cp(λ,β) = 0.22·(116/λi − 0.4β − 5)·exp(−12.5/λi)
Taero = ½ρAR·(Cp/λ)·v² (aerodynamic torque)
I·dω/dt = Taero − Tload − Tfriction
The rotor's moment of inertia I (∝ R⁴, heavier sails resist speed changes) integrates torque into angular velocity every frame. With the millstone idle the rotor free-wheels up to its natural equilibrium speed; engaging it adds a load torque that rises with ω² (grinding resistance), pulling λ down toward the sweet spot where Cp — and mechanical power — peaks. Reefing the sails (raising β) is the miller's real-world way of shedding power in high wind instead of over-speeding the rotor.
- Tip-speed ratio λ — traditional four-sail windmills are drag/lift-limited and run efficiently at low λ (roughly 1–3), unlike modern fast three-blade turbines.
- Milling rate — proportional to the load torque actually being absorbed, converted to an illustrative kg/h grain-throughput figure.
- Energy converted — running integral of mechanical power output, in kWh.