Electricity From the Wind: The Cube Law and a Rotor on a Dynamo

A small permanent-magnet DC motor is also a generator: turn its shaft and it makes a voltage proportional to speed. Print a three-bladed rotor 300 mm across in PETG, with a hub that presses onto the motor shaft, each blade twisted — steep near the hub, flatter towards the tip — because the tip moves faster through the air than the root. Mount the motor on a dowel mast clamped to a plywood base, with the rotor facing the fan. Wire the motor's terminals to a 330 Ω resistor as a load, with the multimeter across it. Add an LED in series if you want to see it light.

Stand the box fan 1.5 m away, facing the rotor. Measure the wind speed at the rotor with the anemometer before fitting the rotor, at each fan setting. Fit the rotor, run the fan, and read the voltage across the resistor once it is steady. The electrical power is **V² ÷ R**. Record wind speed and power for each fan setting. Plot power against wind speed cubed. It should be roughly a straight line — not exactly, because a small motor's own losses take a bigger share at low speed. Then divide your power by the notebook's power passing through a 0.3 m disc at the same wind speed. That ratio is your rotor's power coefficient, and the Betz rung shows the most it could ever be.

**Charles F. Brush, Cleveland, Ohio, 1887–88** — a 17 m, 144-bladed rotor on a tower about 18 m (60 ft) high driving a 12 kW dynamo through step-up gearing, charging batteries that lit his house; it ran for some twenty years. Brush had already built the arc-lighting dynamo in this catalogue. No patent number is asserted here. In Denmark from 1891, **Poul la Cour** tested rotors in a wind tunnel of his own and found that fewer blades turning faster made better use of the wind than many slow ones — the direction every modern turbine took. **Honest limits.** The wind stops; a wind generator needs storage or another source behind it. Its output swings with the cube of a quantity that changes by the minute. And a large rotor is a serious hazard: it must be able to stop itself in a storm, as the Halladay windmill's governor in this catalogue already could.