Size a mill water wheel from the power formula: shaft watts equal 1,000 times 9.81 times the flow in cubic metres per second times the head in metres times the wheel efficiency. A 3 m head and 0.2 m3/s on a 65% overshot wheel gives about 3.8 kW at the wheel shaft and about 3.1 kW at the millstone after the gear train, enough for roughly 1.9-7.6 bushels of wheat an hour. Design for the dry-season flow, not the spring flood.
Part of Community Grain Mill
Choosing a water wheel type for the available head, estimating the power a stream will give, and placing the dam, race and wheel so the mill keeps running through the year.
Head And Dry-Season Flow Decide Everything
Two measurements fix the power a site can give: the vertical drop between the water level where it enters the wheel and the level where it leaves (the head), and the flow that is still running in the driest month. A wheel cannot deliver more than the water brings. Measure the head with the methods in Head Measurement and the flow in the driest month you can, not in the wet spring when the site looks wonderful.
The power formula used throughout the corpus (Water Wheel Types) is:
P = 1,000 x 9.81 x Q x H x efficiency, with P in watts, Q in m3/s and H in metres.
The same formula in kilowatts for a stream is on the Head Measurement page; here it is carried through to the millstone.
Match The Wheel To The Head
The community grain mill note gives the sizes this article follows:
| Wheel | Head | Efficiency (carrier) | Diameter |
|---|---|---|---|
| Overshot | minimum 8-12 ft (about 2.4-3.7 m) | 60-90% | equal to the head |
| Breastshot | 4-8 ft (about 1.2-2.4 m) | 35-65% | 8-16 ft typical for all wheels |
| Undershot | very little | 15-30% | set by the stream width |
The corpus gives other efficiency ranges on the wheel pages (for example 50-70% for a breastshot); use the lower end of whichever you read until you have measured your own wheel. Where a design offers a choice, take the highest-head wheel the site allows, because it converts the most of each cubic metre.
Method: From A Stream To Watts At The Stone
Step 1: Measure the head. Level from the planned headwater surface to the tailwater, in metres. A wheel needs its tailrace free-draining, with the floor at least 15 cm below the lowest point of the wheel (Watermill Design).
Step 2: Measure the dry-season flow. For a brook, dam a short stretch, direct it through a pipe or notch into a bucket of known volume and time it with a count. For a larger stream, measure the cross-section area and time a float over a known length; the average velocity is a fraction of the surface velocity (about 0.8 is the usual allowance, a figure recalled rather than measured here).
Step 3: Compute shaft power. Multiply as in the formula, using a conservative efficiency from the table.
Step 4: Subtract the gear train. The corpus gives about 90% per wooden gear stage, so two stages leave 0.90 x 0.90 = 0.81 (Power Transmission).
Step 5: Convert to flour. Divide the watts at the stone by the grinding energy per kilogram (15-60 Wh/kg, derived in Bushels per Hour by Power Source).
Worked Example
A stream gives 0.2 m3/s (200 L/s) in the dry season over a 3 m head, and the overshot wheel is taken at 65% efficiency.
- Shaft power at the wheel: 1,000 x 9.81 x 0.2 x 3 x 0.65 = 3,826 W, about 3.8 kW.
- At the stone: 3,826 x 0.81 = 3,099 W, about 3.1 kW.
- Flour: 3,099 W / 60 Wh/kg = 52 kg/h and 3,099 / 15 = 207 kg/h, which is 52 / 27.2 = 1.9 and 207 / 27.2 = 7.6 bushels an hour (a bushel of wheat is 60 lb, 27.2 kg).
The wheel diameter is equal to the head, 3 m. If the rim moves at 0.6-0.9 m/s (the 2-3 ft/s the overshot wheel page gives), the wheel turns at 0.6 / (pi x 3) x 60 = 3.8 rpm up to 0.9 / (pi x 3) x 60 = 5.7 rpm. A runner at 100 rpm therefore needs a speed-up of 100 / 5.7 = 17.5 to 100 / 3.8 = 26.
If the dry-season flow halves to 0.1 m3/s, power halves to about 1.9 kW at the shaft; the mill then needs twice the hours for the same flour.
A Millpond Lets A Small Stream Run A Bigger Wheel For A Few Hours
A stream of 0.05 m3/s brings 0.05 x 86,400 = 4,320 m3 a day. A wheel drawing 0.2 m3/s for 3 hours uses 0.2 x 3 x 3,600 = 2,160 m3, less than the day’s inflow, so a pond can store the difference. During the 3-hour run the stream adds 0.05 x 10,800 = 540 m3, so the pond must hold 2,160 - 540 = 1,620 m3 above the intake. At 1 m of useful drawdown that is 1,620 m2 of surface, about 40 m by 40 m. Evaporation and seepage are ignored here; add a margin, and note the head falls as the pond draws down.
Common Mistakes
- Siting for the flood. A wheel built for spring flow stands still in August; size it for the driest month.
- A choked tailrace. Backed-up tailwater drowns the bottom of the wheel and cuts power (Mill Race).
- No spillway or full-open gate. Floodwater with debris destroys an unprotected wheel; the headgate must open fully so the race can be emptied.
Wheel, race and gate
A turning wheel and the gear pit behind it can crush and drown. Fence the pit, keep loose clothing and hair away from every gear, and never work in the race with the gate open. The stop is the sluice gate: it must be reachable from the mill floor, and closing it cuts the water but not the wheel’s momentum, which keeps the gear train turning for some time. Fit a rim or shaft brake and do not reach into the pit until the wheel is dead still.
What’s Next
- Learn next: Bushels per Hour by Power Source - turning watts into flour
- Combine with: Wallower and Spindle - the first gear in the train that follows the wheel