Hydro · Waterwheels
A well-built overshot wheel converts 85 percent of the energy in falling water into rotation, which beats a good many turbines. Then it does it at ten revolutions per minute, and that single number explains everything else about where wheels belong.
A correction worth making
Almost every introduction to micro-hydro repeats that waterwheels are charming but inefficient, and that turbines replaced them because they extract more from the same water. The first half of that is wrong.
A review of gravity waterwheels in Renewable and Sustainable Energy Reviews, drawing on historic data, modern experiments and numerical modeling, reports maximum efficiency of overshot and undershot wheels at around 85 percent, with breastshot wheels between 75 and 80 percent depending on how the water enters[1]. Those are hydraulic efficiencies measured on real machines, and they are competitive with modern low-head turbines.
A wheel is a genuinely good hydraulic machine. What it is not is a convenient one.
In 1704 Antoine Parent published a theory of jets that put the hydraulic efficiency ceiling for all waterwheels at 14.8 percent. The analysis was mathematically incorrect and did not apply to every wheel type, but it was influential, and one consequence was that the undershot wheel came to be preferred over better designs largely because it was the simplest to build[2].
Three centuries later the correction has reached the journals and not much of the popular literature. If you have read that wheels manage 20 or 30 percent, that figure has a long and mistaken history behind it.
The three types
The distinction is not decorative. It determines whether the wheel is driven by the weight of water sitting in its buckets or by the momentum of water striking its blades, and that in turn sets which sites each type suits.
Water enters buckets at the top of the wheel and turns it by weight as it descends. The most efficient of the three, and the one that needs the most drop.
Generally used for head differences up to about 6 meters, with maximum flow around 150 to 200 liters per second per meter of wheel width[3]. The wheel diameter is set by the available head, which is the constraint that matters most.
Water enters near the level of the axle, roughly halfway up. A compromise that works where there is some drop but not enough to feed a wheel from above.
Measured efficiency of 75 to 80 percent, varying with the inflow arrangement[1]. The nineteenth-century Zuppinger and Sagebien designs are refinements of this type and remain the reference for very low head work.
Water passes beneath the axle and pushes against the blades. Described by Vitruvius in 27 BC and the oldest arrangement with a horizontal axle. It needs the least drop of the three and, in its simplest form, sometimes none at all.
Properly designed undershot wheels reach around 75 percent efficiency and hold it across a wide band of flows, roughly a fifth of maximum flow up to full flow[4]. That tolerance of variable flow is a real advantage on a stream that changes through the year.
Waterwheels can operate on head as small as half a meter, a range where most turbines either perform poorly or become disproportionately expensive[4]. If the flat-site problem from the impoundments guide describes your property, this is the machine that addresses it without building a dam.
The real drawback
A wheel cannot simply be spun faster. Experimental work identifies a critical rotational speed above which efficiency falls away, because water starts being flung out of the buckets before it has done its work. Below that speed efficiency holds steady at its maximum. Above it, output declines in a straight line[3].
That critical speed depends on diameter, and the working approximation from the literature is straightforward.
Critical speed in rpm ≈ 30 ÷ wheel diameter in meters
Two published estimates give 31.3 divided by diameter and 27.2 divided by diameter, so 30 serves as a practical rule of thumb[5].
A three meter wheel is therefore limited to roughly 10 revolutions per minute. A four meter wheel, 7.5. These are not numbers you improve with better engineering. They are what the machine is.
A generator producing standard alternating current typically wants somewhere near 1,800 revolutions per minute. Getting there from 10 rpm takes a step-up of roughly 180 to 1, and from a four meter wheel, closer to 240 to 1.
That is not one gearbox. It is usually several stages of gearing or belt drive, and each stage takes its percentage, adds a bearing to maintain, and introduces something else that can fail in the middle of February. The wheel arrives at 85 percent and the drivetrain spends a good deal of it.
This is what the Department of Energy means in saying waterwheels are still available but not very practical for generating electricity because of their slow speed and bulky structureMicrohydropower Systems">[6]. It is a judgment about mechanical convenience, not about hydraulic performance, and reading it as a verdict on efficiency has misled a lot of people.
Where a wheel wins
The entire disadvantage of a waterwheel is the conversion from slow rotation to fast rotation. Remove that requirement and the disadvantage disappears, which is precisely what wheels did for two thousand years before anyone wanted alternating current.
Grinding grain, sawing timber, pumping water, driving a line shaft in a workshop. All of these want torque rather than speed, and a wheel supplies torque abundantly at ten revolutions per minute. No gearbox, no generator, no inverter, no batteries, and no losses in any of them.
Below a couple of meters of drop, turbine options thin out and get expensive. Wheels work down to half a meter, and the flat sites that frustrate every other approach in this section are the ones where wheels are the sensible answer.
A well-designed undershot wheel holds near its best efficiency from a fifth of maximum flow up to full flow[4]. Most turbines are matched to one operating point and lose efficiency either side of it. On a stream with a wide seasonal swing, that tolerance is worth a great deal.
Large open buckets turning slowly in the open air deal with leaves and twigs that would block a fine intake screen. The low rotational speeds, large buckets and free-surface operation are also why wheels are regarded as more environmentally accommodating than enclosed high-speed turbines.
A wheel runs in the open where a person can watch it. A bucket that is not filling, a bearing running hot, a blade that has worked loose, all of these announce themselves to anyone standing nearby. Compare that with diagnosing a sealed runner at the bottom of a penstock. For a household maintaining its own equipment, being able to understand a machine by looking at it has a value that does not appear in any efficiency figure.
Worked example
The creek followed through this section has 60 feet of head, which is 18 meters, three times what an overshot wheel can use. Building a wheel there would mean discarding most of the site's best asset. That property should run a penstock to a turbine, and the rest of this section explains how.
So consider a second site instead. An old mill race on flat ground, the kind of thing found across the eastern United States wherever there used to be a grist mill. Head of 2.5 meters, about eight feet. Flow of 100 liters per second, near 1,600 gallons per minute, through a wheel one meter wide.
100 liters per second across one meter of width sits inside the 150 to 200 liters per second per meter that an overshot wheel handles. The site fits the machine, which is the first thing to establish.
1,000 × 9.81 × 0.10 × 2.5 = 2,450 watts of hydraulic power, using the same physics as the equation in the run-of-river guide.
At 85 percent hydraulic efficiency, roughly 2,085 watts of mechanical power at the shaft, turning at about 10 revolutions per minute for a three meter wheel. If the job is grinding or pumping, this is where the accounting stops and the work begins.
Allowing 85 percent through the drivetrain and 85 percent at the generator leaves roughly 1,500 watts electrical. A quarter of the wheel's mechanical output is spent getting from 10 rpm to generator speed.
The Department of Energy shortcut on the same site: 8.2 feet of head, 1,585 gallons per minute, divided by ten, gives 1,300 watts.
Against 1,500 watts from the physical calculation, the two sit about 14 percent apart, with the shortcut lower. That is the expected direction, since divide-by-ten assumes an efficiency near 53 percent and a well-built wheel with reasonable gearing does better. Two independent methods bracketing the answer is what a usable estimate looks like.
Note what happens if the same wheel drives a mill stone or a pump directly. The 585 watts lost to gearing and generation stay in the system, and the wheel delivers its full 2,085 watts to the task. For a household that wants to grind its own grain or lift water to a cistern, that is the whole argument for a wheel over anything else on this site.
Honest limits
A three meter wheel is a three meter structure with water in it, needing a foundation, an axle, bearings that carry the load, and a headrace delivering water to exactly the right point. The turbine that replaces it would sit in a crate.
An open wheel in a cold climate accumulates ice on buckets and spray freezes on everything nearby. Wheels have run through northern winters for centuries, and doing it takes design attention and a person willing to go out and deal with it.
A loaded wheel carries enormous torque and cannot be stopped by hand. Ten revolutions per minute is slow enough to look approachable and strong enough to be indifferent to anything caught in it. Guarding matters, and it matters most around children who find the thing fascinating.
Bucket count, bucket shape, filling ratio and inflow geometry all move the efficiency figure substantially. The 85 percent belongs to a properly designed wheel. A wheel assembled by eye can perform very much worse while looking identical from the bank.
Common mistakes
A wheel can only use drop roughly equal to its own diameter. On a site with 60 feet of head, a wheel discards most of what the property offers. Head that large belongs to a turbine.
Above the critical speed, water leaves the buckets early and efficiency falls in a straight line. Speed has to come from gearing, not from driving the wheel harder.
Bucket shape, bucket count, filling ratio and the geometry of the inflow all carry real percentages. Two wheels that look alike from the bank can perform very differently.
The load is the wheel plus the water in it, applied continuously for years. Bearings sized by optimism are the most common reason a working wheel stops working.
If the wheel exists to pump water or grind grain, converting to electricity and back to motion throws away roughly a quarter of the output and adds several things that can break.
Next
Run-of-river, impoundments and wheels cover how water gets to the machine and back to the stream. What converts it is the next question, and for the great majority of properties with real head the answer is a turbine rather than a wheel.
The turbine guide comes next, matching Pelton, Turgo, cross-flow, propeller and pump-as-turbine machines to the head and flow figures measured in the first guide.
The configuration most properties with usable head should build.
Read the guideThe flat-site alternative, and what storing water costs in obligations.
Read the guideWhether your head suits a wheel at all is a question the tape measure answers.
Read the guideSources
Efficiency figures are laboratory and field measurements of properly designed wheels and should not be assumed for a wheel built without attention to bucket geometry, filling ratio and inflow. Head, flow and output in the worked example are illustrative. The critical speed relationship is an approximation drawn from two published estimates.