A mill’s wheat throughput in kilograms an hour equals the watts reaching the stone divided by the energy it takes to grind a kilogram, about 15-60 Wh/kg; divide again by 27.2 kg per bushel for bushels. On that arithmetic one horse grinds 0.24-1.5 bushels an hour, a 3 m, 0.2 m3/s overshot wheel 1.9-7.6, sails of 20 ft in a 6 m/s wind 1.5-6.1, and a hand quern 0.1-0.2, so any quoted rate must name the watts behind it.
Part of Community Grain Mill
The arithmetic that turns a power source into flour: grinding energy per kilogram, watts at the stone for each source, the resulting bushels an hour, and a check of the rates quoted elsewhere in the wiki.
Throughput Is Power Divided By Grinding Energy
Grinding turns shaft work into meal and heat, so the flour a mill makes in an hour is the work delivered divided by the work each kilogram takes:
kg per hour = watts at the stone / (Wh per kg ground)
and bushels per hour = kg per hour / 27.2 for wheat (60 lb x 0.4536 = 27.2 kg; the 60 lb bushel is the standard US weight, recalled). Watts at the stone means after the gear train: two wooden stages at 0.90 each leave 0.81 (Power Transmission).
The Grinding Energy Has Three Anchors And Is Not Measured Here
No mill on this wiki has been put on a dynamometer. The 15-60 Wh/kg planning band comes from three independent estimates:
| Anchor | Working | Wh/kg |
|---|---|---|
| Hand quern, carrier row of 0.1-0.2 bu/h (2.7-5.4 kg/h), person at 50-100 W (recalled) | 50 / 5.4 to 100 / 2.7 | 9.3-37 |
| A rule that a 4 ft pair takes about 3-5 hp for 4-6 bu/h (recalled from millwrighting practice, unchecked) | 3 x 745.7 / (6 x 27.2) to 5 x 745.7 / (4 x 27.2) | 14-34 |
| A small modern electric stone mill, about 360 W for about 6 kg/h of fine flour (recalled) | 360 / 6 | 60 |
Coarse meal sits at the low end and fine flour at the high end. The planning band starts at 15 rather than at the quern’s lowest 9.3 on purpose: understating the power a mill needs is the costly error, so the band leans toward needing more watts. Treat all three anchors as unconfirmed and replace the band with your own figure as soon as you have measured one (see Method).
Watts At The Stone For Each Source
| Source | Working | At the stone |
|---|---|---|
| Hand quern | person at the handle | 50-100 W |
| Horse in a gin | 490-735 N x 1.0 m/s x 0.81 | 397-595 W |
| Ox in a gin | 589-883 N x 0.56-0.83 m/s x 0.81 | 267-594 W |
| Overshot wheel, 0.05 m3/s, 3 m head | 1,000 x 9.81 x 0.05 x 3 x 0.65 x 0.81 | 775 W |
| Overshot wheel, 0.2 m3/s, 3 m head | 1,000 x 9.81 x 0.2 x 3 x 0.65 x 0.81 | 3,099 W |
| Undershot wheel, 0.5 m3/s, 0.91 m head, 25% | 1,000 x 9.81 x 0.5 x 0.91 x 0.25 x 0.81 | 904 W |
| 20 ft sails, 3 m/s | 0.5 x 1.225 x 117 x 27 x 0.2 x 0.81 | 313 W |
| 20 ft sails, 6 m/s | 0.5 x 1.225 x 117 x 216 x 0.2 x 0.81 | 2,505 W |
| 20 ft sails, 8 m/s | 0.5 x 1.225 x 117 x 512 x 0.2 x 0.81 | 5,939 W |
The animal pull is 10-15% of body weight (500 kg horse, 600 kg ox), a recalled draft rule; the wheel and wind derivations are in Water Wheel Design and Siting, Windmill Power for Grain Milling and Animal-Powered Mill. The wind capture fraction of 0.2 is a recalled planning value.
Wheat Per Hour For Each Source
| Source | kg/h at 60 to 15 Wh/kg | Bushels/h |
|---|---|---|
| Hand quern | 2.7-5.4 (carrier) | 0.1-0.2 |
| Horse | 6.6-39.7 | 0.24-1.5 |
| Ox | 4.5-39.6 | 0.16-1.5 |
| Overshot, 0.05 m3/s | 12.9-51.7 | 0.47-1.9 |
| Overshot, 0.2 m3/s | 51.6-206.6 | 1.9-7.6 |
| Undershot, 0.5 m3/s | 15.1-60.3 | 0.55-2.2 |
| Sails, 3 m/s | 5.2-20.9 | 0.19-0.77 |
| Sails, 6 m/s | 41.8-167.0 | 1.5-6.1 |
| Sails, 8 m/s | 99.0-395.9 | 3.6-14.6 |
For the carrier’s village of 68 kg of grain a day (100 people x 1.5 lb), the 0.2 m3/s overshot wheel needs 68 / 206.6 = 0.33 h to 68 / 51.6 = 1.3 h of running, which is the “1-2 hours” the carrier promises. One horse needs 68 / 39.7 = 1.7 h to 68 / 6.6 = 10 h.
Checking The Carrier’s Throughput Table
The carrier’s rates, with the stone power each needs at the best case of 15 Wh/kg:
| Row | Quoted | Stone power needed | Source supplies | Verdict |
|---|---|---|---|---|
| Hand quern | 0.1-0.2 bu/h | 41-82 W | 50-100 W | Consistent |
| Animal | 2-4 bu/h | 0.82-1.63 kW | 0.40-0.60 kW (horse) | Too high by 1.4 to 4 times, or more at fine flour |
| Undershot wheel | 3-5 bu/h | 1.22-2.04 kW | needs 0.67-1.13 m3/s over 0.91 m head | Needs a big stream |
| Overshot wheel | 5-10 bu/h | 2.04-4.08 kW | needs 0.13-0.26 m3/s over 3 m | Plausible |
| Windmill, good wind | 4-8 bu/h | 1.63-3.27 kW | 2.5 kW at 6 m/s, 5.9 kW at 8 m/s | Plausible in a fresh breeze |
The undershot flow comes from 1.22 kW / 0.81 / (9.81 x 0.91 x 0.25) = 0.67 m3/s up to 2.04 / 0.81 / (9.81 x 0.91 x 0.25) = 1.13 m3/s; the overshot flow from 2,041 / (9,810 x 3 x 0.65 x 0.81) = 0.13 m3/s up to 4,082 / 15,495 = 0.26 m3/s.
At fine-flour energy (60 Wh/kg) every requirement is four times higher. Only the animal row fails even at the best-case energy; the quern row, which is consistent at 15 Wh/kg, would need 163-327 W at 60.
Two Other Pages Fail The Same Check
- A grain-mill page states that a 1.2 m mill takes 80-100 W at full load (Power Transmission) while another gives 150-250 kg an hour for 1.2 m stones (Grain Mill Design). At 100 W and the lowest 15 Wh/kg the mill could grind 100 / 15 = 6.7 kg an hour, so the page’s 150 kg/h is 150 / 6.7 = 22 times higher. The 150 kg/h needs at least 150 x 15 = 2.25 kW.
- The mill-construction page says a site with 30 L/s and 1.5 m of head can run a mill grinding 50-100 kg an hour (Mill Construction). The water’s own power is 1,000 x 9.81 x 0.03 x 1.5 = 441 W even at 100% efficiency, and 50 kg/h at 15 Wh/kg needs 750 W, so the rate is out of reach before any wheel loss.
Method: Measure Your Own Mill
Step 1: Weigh a sack of clean, dry grain of known mass, say 25 kg.
Step 2: Measure the power at the source. For a gin, hang a spring balance or a weighed counterweight on the sweep arm to read the animal’s pull in newtons, and time laps to get the speed. For a wheel, measure flow and head as in the siting article.
Step 3: Grind the sack at the grade you want and note the time in hours.
Step 4: Compute the energy per kilogram: e = watts at the stone x hours / kg. Then use your own e in place of 15-60 for every later plan.
Step 5: Repeat at coarse and fine settings, because e rises with fineness.
Common Mistakes
- Quoting bushels with no watts. Every rate in this batch carries its power; a rate without one is a guess.
- Using volume-measured bushels for other grains. Oats weigh about half a wheat bushel.
- Using the spring flow in the dry season. Power follows flow; see the siting article.
The drive you cannot stop from where you stand
A mill that turns at several kilowatts cannot be stopped by hand. Name the stop for each source: the sluice gate or a disengaged stone nut for water, the sail brake for wind, the driver at the animal’s head for a gin, and for hand drives a person at the crank who can let go. The coast time is set by the runner’s stored energy (Runner and Bedstone Mechanics). Keep flame out of the mill, because flour dust explodes in a cloud, and never test for dust with a flame.
What’s Next
- Learn next: Throughput and Operations - fitting these rates into a milling week
- Combine with: Mill Power Sources - choosing among the sources