My SimulatorEngland / Wind Power

English Windmill Simulator

Catch the wind. Turn grain into flour.

Interactive 3D • Norfolk

Educational model with simplified aerodynamics; values are illustrative, not engineering advice.

Lab & science

Drag to orbit, wheel / pinch to zoom. Space = start / stop milling, R = reset, G = gears.

Setup

Simulation clock (x real time)

Camera

Graphics (High on every device; Low = fewer wheat plants, 1x pixel ratio)

Live readout (model values)

Missions

Mission 6: what is the largest fraction of the wind's kinetic power ANY rotor can extract (Betz limit), in percent?

The science

What you see

A Norfolk-style brick tower mill, cut open. Wind turns four cloth-covered sails. The sail shaft turns the brake wheel, which drives the wallower and the upright shaft; the great spur wheel drives the stone nut and the runner millstone above the fixed bedstone. Grain falls from the hopper through the shoe into the eye of the stones; the flour leaves at the rim. The fantail on the tail pole turns the cap so the sails face the wind.

Equations

Wind power through the swept disc  P_w = 1/2 rho A v^3 ,  A = pi R^2 ,  R = 8.8 m
Rotor power                         P = P_w Cp(lambda, theta)
Tip-speed ratio                     lambda = omega R / v
Power coefficient (model)           Cp = Cpm(theta) x exp(1 - x) ,  x = lambda / lambda_opt(theta)
  Cpm = 0.30 exp(-((theta - 25)/16)^2) ,  lambda_opt = 4.2 - 0.08 theta
  never above the Betz limit 16/27 = 0.593
Rotor torque                        T = P / omega = 1/2 rho pi R^3 v^2 Cq ,  Cq = Cp / lambda
Rotor dynamics                      J d omega/dt = T - b omega - T0 tanh(omega/0.03)
Gear train                          stones/rotor = (48/16)(48/24) = 6
Flour mass rate                     dm/dt = eta b omega^2 / e ,  eta = 0.8 ,  e = 162 kJ per kg
Cap alignment loss                  v_eff = v cos(error)   (so power ~ cos^3)
Gentle quality window               stones 60-105 rpm; above that flour heats

Assumptions & honest simplifications

The Cp surface is a smooth fit that peaks near 0.30 at a 25 degree sail setting; real cloth sails reach roughly 0.2-0.3 and depend on how much cloth is spread.
Sail angle is one number for the whole sail (real sails are twisted). Wind gusts are a sum of three sines; wind direction drifts and the fantail follows.
The cut-away is schematic: the big vertical wheel is drawn low in the tower so you can see it, a real brake wheel sits in the cap on the sail shaft. Teeth are real counts (48/16 and 48/24) but are drawn without exact meshing.
Grinding load is modelled as viscous (proportional to speed); the specific energy of 162 kJ/kg is typical for stone milling, not measured. The 75% flour extraction is typical for whole-grain to sifted flour. A storm brake closes at 60 km/h (model).
The simulation clock runs faster than real time so a batch of flour appears in about a minute. Fixed values, no weather forecast, no engineering advice.

Independent numerical checks

Also in node: node check.js.

Sources

Betz (1920) limit; classical wind-turbine theory (Burton et al., Wind Energy Handbook); historic tower and post mill descriptions (e.g. Rex Wailes, The English Windmill). Illustrative scene for a Norfolk tower mill.

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