A Water Wheel form 5 is a horizontal-axis tub wheel — a vertical-shaft runner with angled blades sitting in a wooden tub, driven by a jet of water from an inclined chute. Small grain mills across Scandinavia, the Faroes, and the Scottish Highlands relied on this form for centuries because it drives a millstone directly, no gearing required. The chute concentrates head into a single high-velocity jet that strikes the blades tangentially, spinning the runner and the stone above it on the same shaft. A typical tub wheel produces 1-3 kW from 2-4 metres of head and grinds 20-40 kg of meal per hour.
Water Wheel (form 5) Interactive Calculator
Vary head, flow, efficiency, and stone speed to see jet speed, hydraulic power, shaft power, and direct-drive torque.
Equation Used
The calculator estimates available water power from net head and flow, then applies overall efficiency to get shaft power. Jet speed is the ideal gravity jet speed from the same head, and torque is the direct-drive torque at the selected stone speed.
- Fresh water density is 1000 kg/m3.
- Net head is the usable vertical head at the chute inlet.
- Overall efficiency combines chute, blade, splash, and bearing losses.
- Runner stone speed equals tub wheel speed because the shaft is direct drive.
Operating Principle of the Water Wheel (form 5)
The form 5 tub wheel is the simplest working water wheel ever built. Water enters through an inclined wooden chute — the millrace chute — which converts the available head into kinetic energy. The jet exits the chute at the bottom and strikes the angled blades of a horizontal runner sitting inside a circular wooden tub. The runner spins on a vertical shaft, and that shaft passes straight up through the bedstone to drive the runner stone. No gears, no belts, no bevel pairs. One moving part from water to flour.
Why build it this way? Because it solves a specific problem — you have a steep hillside stream with 2-4 m of head and a low flow of maybe 30-80 L/s, and you want to grind grain without any of the metalwork a vertical wheel requires. A vertical undershot or overshot wheel needs a horizontal shaft, gearing to turn the drive 90°, and a millwright who knows how to cut wooden cogs. The tub wheel needs none of that. The chute angle is typically 25-35° from horizontal — steeper than that and the jet overshoots the blades, shallower and you lose head to friction in the chute. Blade angle on the runner sits around 30-45° from the shaft axis to catch the jet cleanly.
When tolerances drift, you feel it immediately. If the tub clearance around the runner is more than 8-10 mm the jet escapes around the blades and torque collapses. If the shaft is out of plumb by more than ~1° the runner stone wobbles and the meal comes out unevenly ground. The most common failure modes are chute erosion (the jet eats out the wooden chute floor over a season), blade rot at the waterline, and bottom-bearing wear on the footstep — that footstep takes the entire weight of runner plus stone plus the downward thrust of the jet, and if it seizes the whole mill stops.
Key Components
- Millrace chute: Inclined wooden trough that delivers water from the headrace down to the wheel. Length is typically 1.5-3 m at 25-35° pitch, sized so the jet exits at 4-7 m/s. The chute floor wears fastest near the outlet — expect to replace planking every 2-3 seasons in hard-water streams.
- Runner (horizontal water wheel): The rotating disc carrying 8-16 angled blades, mounted on the vertical shaft. Blade angle 30-45° to the shaft, runner diameter 0.6-1.2 m for small mills. Out-of-balance above 5 mm radial runout causes shaft chatter and accelerates footstep wear.
- Vertical drive shaft: Single timber or iron shaft running from the footstep below the runner up through the bedstone to the runner stone. Must be plumb within 1° or the upper stone wobbles. On Norse mills the shaft is often a single oak baulk with iron caps top and bottom.
- Footstep bearing: The thrust bearing at the base of the shaft — carries the entire vertical load of runner plus runner stone plus jet thrust, often 200-400 kg total. Traditionally a hardened iron pintle running in a stone cup with tallow or beeswax lubrication. This is the single highest-wear component in the whole mill.
- Wooden tub: Circular casing that constrains the spent water and forces it to leave through the tail race rather than spraying out radially. Clearance to runner blades 5-10 mm — wider than that and efficiency drops sharply because water bypasses the blades.
- Runner stone and bedstone: The runner stone is keyed directly to the top of the vertical shaft and rotates above the fixed bedstone. Gap between stones controls grind fineness, typically 0.2-1.0 mm. Because there is no gearing, stone speed equals runner speed — usually 60-120 RPM.
Industries That Rely on the Water Wheel (form 5)
The form 5 tub wheel survives wherever you find steep, low-flow streams and a tradition of small-batch grain milling. It is not a power-station wheel — peak output is rarely above 3-4 kW — but for direct-drive grinding, churning, or pumping at the household or small-craft scale it is hard to beat. Modern revivals show up in heritage sites, off-grid homesteads, and craft food producers who want a mechanical drive that runs on nothing but gravity and water.
- Heritage milling: The Click Mill at Dounby in Orkney — a working 18th-century horizontal tub wheel grinding bere barley, restored by Historic Environment Scotland.
- Faroese grain milling: Traditional kvarnhús (mill houses) across the Faroe Islands — small turf-roofed buildings each housing a single tub wheel grinding 20-30 kg of barley per hour for household use.
- Craft distilling: Small Norwegian akevitt and whisky producers using restored tub wheels to grind malted barley on-site, drawing 2-3 kW from hillside springs at farms in Telemark and Hardanger.
- Agricultural museums: The Highland Folk Museum in Newtonmore demonstrating a working Norse mill (clack mill) for visitors, grinding oats at roughly 90 RPM under 2.5 m of head.
- Off-grid homesteads: Smallholders in the Pyrenees and Carpathians using owner-built tub wheels to drive grain mills and butter churns from spring-fed streams with 2-4 m head.
- Educational hydropower demonstrations: University fluid-mechanics labs using scaled tub wheels to demonstrate impulse-jet energy transfer without the geometric complexity of a full Pelton runner.
The Formula Behind the Water Wheel (form 5)
The useful number for sizing a tub wheel is shaft power — what you actually get out of the runner once you account for the available head, the flow rate, and the realistic efficiency of a wooden impulse wheel. At the low end of the typical operating range (2 m head, 30 L/s) you are looking at roughly 300-400 W — enough to turn a small quern stone but slow. At the high end (4 m head, 80 L/s) you are pushing 2.5-3 kW, which will drive a full 0.9 m runner stone at production pace. The sweet spot for traditional construction sits around 3 m head and 50 L/s, where wooden bearings and chute timbers last a full season without rebuild.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| Pshaft | Shaft power delivered to the runner stone | W | hp |
| η | Overall efficiency of the tub wheel (typically 0.40-0.55 for traditional wooden construction) | dimensionless | dimensionless |
| ρ | Density of water | kg/m³ (≈1000) | lb/ft³ (≈62.4) |
| g | Gravitational acceleration | m/s² (9.81) | ft/s² (32.2) |
| Q | Volumetric flow rate through the chute | m³/s | ft³/s |
| H | Net head from headrace surface to the jet exit | m | ft |
Worked Example: Water Wheel (form 5) in a small Hardanger akevitt distillery
A craft akevitt distillery in Hardanger, Norway, wants to restore an existing tub-wheel mill house to grind 30 kg/hr of malted barley for their mash. The hillside spring above the mill provides 50 L/s of steady flow, and the surveyed head from headrace surface to chute outlet is 3.0 m. The owner wants to know whether the wheel can drive a 0.8 m runner stone at the 90 RPM needed for clean grinding, and how the output changes if summer flow drops to 30 L/s or spring flood pushes flow to 80 L/s. Assume η = 0.50 for the restored wooden runner.
Given
- η = 0.50 dimensionless
- ρ = 1000 kg/m³
- g = 9.81 m/s²
- Qnom = 0.050 m³/s
- H = 3.0 m
Solution
Step 1 — at nominal flow 50 L/s, plug everything into the shaft-power formula:
Step 2 — work the arithmetic:
That is roughly 1.0 hp at the runner-stone shaft. For a 0.8 m runner stone grinding malt that is comfortable — you need around 500-600 W to keep the stone turning at 90 RPM under load, so you have headroom.
Step 3 — recompute at the low end, summer flow 30 L/s:
At 441 W the wheel still spins, but you are right at the edge of what the stone needs. Throughput drops to maybe 18-20 kg/hr and the stone slows visibly when you increase the feed rate. The miller will hear it — runner pitch drops from a steady whir to a labouring growl.
Step 4 — recompute at the high end, spring flood 80 L/s:
At nearly 1.2 kW the wheel is pushing well past the stone's needs. In practice the runner overspeeds toward 130-140 RPM and the meal comes out coarser because grain flies through the gap before it shears properly. Most traditional millers fitted a sluice gate at the chute head specifically to throttle flow back to the design point in flood conditions.
Result
Nominal shaft power is approximately 740 W (1. 0 hp) at 50 L/s and 3.0 m head — comfortably enough to drive a 0.8 m runner stone at 90 RPM and grind 30 kg/hr of malt. Across the operating range, output swings from 441 W at summer low flow to 1,177 W at spring flood, so the sweet spot sits squarely at nominal where the stone runs at design speed without throttling. If you measure shaft power 30% below the predicted 740 W, check three things first: chute-floor erosion has lowered jet velocity (look for scoured planking near the outlet), runner-to-tub clearance has opened past 10 mm letting water bypass the blades, or footstep-bearing drag from a worn iron pintle is eating torque before it reaches the stone. Any one of those will knock 100-200 W off the output.
When to Use a Water Wheel (form 5) and When Not To
The tub wheel is not the only option for a small hillside stream — you could also use an overshot wheel, or a Pelton turbine if you have higher head. Each makes different demands on head, flow, gearing, and budget. Here is how they compare on the dimensions that actually matter when you are sizing a small hydro install.
| Property | Tub Wheel (form 5) | Overshot Water Wheel | Pelton Turbine |
|---|---|---|---|
| Optimal head range | 2-5 m | 3-10 m | 20-500 m |
| Optimal flow range | 20-100 L/s | 20-200 L/s | 1-100 L/s |
| Peak efficiency | 40-55% | 60-70% | 85-92% |
| Typical shaft speed | 60-120 RPM (direct-drive stone) | 4-12 RPM (needs step-up gearing) | 500-1,500 RPM |
| Build cost (small mill scale) | Low — wood and one iron pintle | Medium — large wheel, axle, bearings, gearing | High — precision-cast runner, manifold, nozzle |
| Maintenance interval | Chute relining every 2-3 seasons, footstep every 5-10 years | Bucket repair every 5-7 years, axle bearings annual | Nozzle inspection annual, runner check every 5,000 hr |
| Best application fit | Direct-drive grain milling, small craft food production | Larger heritage mills, multi-stage gearing applications | Modern off-grid electrical generation |
| Mechanical complexity | Single moving part | Wheel + axle + gear train + line shaft | Runner + nozzle + governor + generator |
Frequently Asked Questions About Water Wheel (form 5)
Almost always the runner-to-tub clearance has opened up. As the wooden tub dries and shrinks between seasons, or as the runner blades wear at their tips, the gap grows past 8-10 mm and a portion of the jet escapes around the blades instead of striking them. You lose torque proportionally to the bypass area.
Quick check — shut the sluice, drain the tub, and feel the gap with a folded business card (about 0.4 mm). If you can fit two fingers in there, the wheel needs re-shimming or the tub needs a new inner liner. A second cause to rule out is blade-tip rot at the waterline, which produces the same symptom from the opposite direction.
That site is right on the boundary. The tub wheel wins if you want to drive a millstone directly — no gearing, no line shaft, the runner stone keys straight onto the vertical shaft. The overshot wheel wins if you want higher efficiency (60-70% vs 40-55%) and you need to drive multiple loads through a line shaft.
For a single-purpose grinding mill, take the tub wheel. The mechanical simplicity pays back every time something needs repairing — one shaft, one bearing, one set of blades. For a working farm with a saw, a thresher, and a churn all on the same drive, take the overshot.
Three causes dominate, and you can usually identify which one by where the energy is going. First, chute geometry — if the chute angle is below 20° or the chute is too long, friction in the chute itself eats 10-15% of the head before the jet ever reaches the wheel. Second, jet aim — the jet should strike the blade at the leading edge, not the middle. A jet hitting mid-blade wastes about 20% of the kinetic energy as splash. Third, tail-race backup — if spent water cannot leave the tub fast enough it pools around the runner and adds drag.
Stick a piece of dye-coloured paper at the chute outlet and watch where the jet actually lands. Nine times out of ten, the chute has settled or the runner has shifted, and the jet is no longer hitting the design point.
Yes, but only if the chute runs continuously. A flowing jet will not freeze down to about -10°C because the kinetic energy keeps the water above freezing through the chute. The failure point is the headrace pond and the tail race — both go slack water and freeze solid overnight. Faroese and Norwegian millers traditionally drained the headrace and pulled the runner out for the coldest months.
If you want winter operation, insulate the headrace, keep flow above 30 L/s minimum to maintain jet velocity, and check the footstep bearing daily — frozen tallow lubrication will cause the pintle to score the stone cup within hours of dry running.
Below about 0.4 m runner diameter the blade-jet geometry stops working properly because the jet width becomes a significant fraction of the blade width — you cannot get clean entry and clean exit on the same blade. Efficiency drops from the typical 50% range down toward 25-30% at runner diameters of 0.3 m or less.
For demonstration models below 0.4 m, switch to a Pelton-style cup runner instead of flat angled blades. The cup geometry tolerates the small scale because it captures the jet on a curved surface rather than relying on a clean tangential strike.
The vertical shaft is out of plumb. Because the tub wheel direct-drives the runner stone with no intermediate gearing, any wobble in the shaft transfers straight to the stone gap. A 1° tilt on a 0.8 m stone moves the gap by about 7 mm across a single rotation — the meal sieves coarse on the high side and fine on the low side.
Hang a plumb bob from the top of the shaft with the wheel stopped. If the bob does not return to the same point on the bedstone within 2 mm, the shaft needs re-truing. The usual culprit is the footstep cup wearing oval, which lets the shaft base wander.
References & Further Reading
- Wikipedia contributors. Watermill. Wikipedia
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