A windmill with four 20 ft sails turns a millstone with about 0.31 kW in a 3 m/s breeze, about 2.5 kW at 6 m/s and about 5.9 kW at 8 m/s, because the power in wind rises with the cube of its speed. That makes it a good mill where the wind is steady and strong and a poor one where the average is light, so measure the site for a month and keep a hand or animal backup for calms.
Part of Community Grain Mill
Using wind to drive a grain mill: how the cube law sets the power, what the carrier’s sail sizes deliver at the stone, and how tower and post mills differ.
The Cube Law Makes The Site Everything
The power in moving air passing through the swept circle of the sails is P = 0.5 x air density x swept area x wind speed cubed (Wind Power gives the same relation with air density 1.225 kg/m3). Double the wind speed and the power is eight times larger. No rotor can take all of it: the Betz limit caps extraction at 16/27, about 59%, and the corpus puts simple home-built rotors at 25-35% of that ceiling.
For a cloth-sailed mill the capture fraction is lower again. This article uses 0.2 of the available power as a planning value. That figure is a recalled estimate for traditional sails, not a measurement, and a poorly set or ragged set of sails does worse.
What The Carrier’s Sail Sizes Deliver
The community grain mill note gives four sails, each 15-25 ft long (4.6-7.6 m) and 4-6 ft wide. Taking the swept circle’s radius as the sail length (a small overestimate, since the hub has no sail) a 20 ft sail is 6.1 m and the swept area is pi x 6.1^2 = 117 m2.
| Wind | Power in swept area | At 0.2 capture | At the stone (x 0.81) | Wheat ground (15-60 Wh/kg) |
|---|---|---|---|---|
| 3 m/s | 0.5 x 1.225 x 117 x 27 = 1.9 kW | 0.39 kW | 0.31 kW | 5-21 kg/h, 0.19-0.77 bu/h |
| 6 m/s | 0.5 x 1.225 x 117 x 216 = 15.5 kW | 3.1 kW | 2.5 kW | 42-167 kg/h, 1.5-6.1 bu/h |
| 8 m/s | 0.5 x 1.225 x 117 x 512 = 36.7 kW | 7.3 kW | 5.9 kW | 99-396 kg/h, 3.6-14.6 bu/h |
The 0.81 is the two-stage wooden gear train (0.90 x 0.90); the grinding energy per kilogram and the 27.2 kg bushel are derived in Bushels per Hour by Power Source. The carrier’s 4-8 bushels an hour “in good wind” for a 36-48 in stone fits the 8 m/s row and the top of the 6 m/s row, not a light breeze.
Because the power at 3 m/s is one-eighth of the power at 6 m/s, the miller’s skill is using the strong hours. A site that averages 3 m/s over a month gives far less flour than one averaging 6 m/s, and the monthly average hides the calm days entirely. See Wind Measurement for logging the site before building.
Tower Mill Or Post Mill
- Tower mill: a stone or brick tower with a rotating cap carrying the sails. It is the most durable, and only the cap turns to face the wind.
- Post mill: the whole timber body turns on a central post to face the wind. It is simpler to build and cheaper, but the whole structure must be turned by hand, usually with a tail pole.
Either way the sails drive a horizontal shaft, a great gear on that shaft turns a small pinion on the vertical stone spindle, and the gap between the stones is set exactly as in a water mill (see Runner and Bedstone Mechanics).
Method: Running A Windmill Day To Day
Step 1: Face the sails into the wind. Turn the cap or the whole body so the sails square to the wind before releasing the brake.
Step 2: Set sail cloth to the wind. In a strong wind reef (furl) part of the cloth so the mill does not run faster than the stones and gears can take; in a light wind spread the full area.
Step 3: Re-set the stone gap as the wind changes. The runner slows in a lull and grinds finer, and speeds up in a gust and grinds coarser; check the flour at the spout and move the gap by feel and sound, as in a water mill.
Step 4: Feed steadily. A hopper that runs dry lets the stones run bare, which heats them and strikes sparks (see the danger block).
Step 5: Brake and turn the sails out of the wind before leaving. Never leave a loaded mill running unattended.
Common Mistakes
- Building before measuring. A mill on a site averaging 3 m/s runs at one-eighth of the power of the same mill at 6 m/s.
- Counting on the swept area alone. Torn or loose sail cloth throws away most of the capture fraction.
- No backup. The carrier says to pair a windmill with a hand mill; a village that depends on wind alone eats nothing in a calm week.
Sails, brake and dust
Moving sails pass close to the ground and can strike a person without warning, so keep a clear ring around the mill and never stand in the sail plane. The stop is the brake on the great gear, worked from the mill floor, and the sails are large enough to coast on for some time after it is applied; never reach for the gears or the stones until the sails are stationary and tied. Flour dust in the mill air can explode when a spark, a bare running stone or a hot bearing ignites it: sweep dust often, ventilate, and use no open flame inside. Do not test for dust with a flame.
What’s Next
- Learn next: Runner and Bedstone Mechanics - what the shaft power turns
- Combine with: Hand-Cranked Backup Systems - the calm-day backup