A Form 7 water wheel is a high-breastshot gravity wheel where the headrace delivers water onto the rim above the horizontal centreline but below the crown, filling closed buckets that drive the wheel by weight rather than impulse. The Cromford Mill auxiliary wheel in Derbyshire is a classic example. It exists to extract usable shaft power from medium-head sites of roughly 2 to 4 m where neither an overshot nor an undershot wheel fits cleanly. Well-built Form 7 wheels run at 60 to 75% hydraulic efficiency and deliver 2 to 20 kW of steady mechanical power.
Water Wheel Form 7 Interactive Calculator
Vary bucket water mass, wheel radius, working angle, efficiency, and speed to see gravity torque and shaft power for a high-breastshot water wheel.
Equation Used
The article diagram gives the gravity torque relationship tau = m g r sin(theta). This calculator applies that ideal bucket torque, then multiplies by efficiency to estimate delivered shaft torque and power at the selected wheel speed.
FIRGELLI Automations - Interactive Mechanism Calculators.
- Torque is for a representative filled bucket or water packet on the working arc.
- Gravity torque dominates; inlet impulse and splash losses are not included separately.
- Efficiency is applied after ideal gravity torque.
Operating Principle of the Water Wheel (form 7)
Form 7 sits between the overshot and the breastshot in the family of gravity water wheels. Water arrives through a controlled penstock or launder and enters the buckets at a point above the shaft centreline — typically between the 9 and 11 o'clock position on a wheel rotating clockwise when viewed from the inlet side. From there, the weight of trapped water in each bucket pulls the rim downward, and the wheel converts the falling mass into shaft torque. There is a small impulse component from the inlet velocity, but 80 to 90% of the work comes from gravity acting on filled buckets across roughly 120° of arc.
The geometry matters more than people think. The buckets must be shaped so water enters cleanly without splash-back — a curved or angled lip is standard — and they must empty fully before the rim reaches the tailwater. If the bucket dumps too early, you lose head. If it carries water past the bottom and into the tailrace, you lift dead weight back up the rising side and pay an efficiency penalty of 5 to 15%. Bucket pitch is usually 250 to 400 mm of arc length, and bucket depth runs 200 to 350 mm depending on flow.
What causes a Form 7 wheel to fail or underperform? Three things, in order of frequency. First, tailwater drowning — if the river level rises into the lower buckets, you create back-pressure and efficiency drops below 50%. Second, shroud leakage — the side plates (shrouds) and the inner cylindrical sole plate must seal the bucket on three sides, and rotted timber or a warped iron shroud lets water spill sideways before it has done its work. Third, inlet misalignment — the headrace sluice should deliver water onto the bucket lip with no more than ±20 mm vertical scatter, or you get splash losses and irregular torque that shows up as shaft pulsation downstream of the gearing.
Key Components
- Headrace and Sluice Gate: Delivers a controlled flow onto the wheel above the horizontal centreline. The sluice opening is typically sized for 0.05 to 0.5 m³/s, with a spillway parallel to it for flood overflow. Gate seal clearance must stay below 5 mm to prevent leak-through during shutdown.
- Buckets: Closed cells around the rim that trap water and convert its weight to torque. Bucket count typically runs 32 to 60 around the rim, with internal volume sized so each bucket holds 60 to 75% of its theoretical capacity at design flow — overfilling causes spill-out at the inlet.
- Shrouds (Side Plates): Two annular plates that close the buckets on either side. They must run true to within ±3 mm of the sole plate to prevent side-spill. Cast iron shrouds are standard on 19th-century survivors; modern restorations use 6 mm steel plate.
- Sole Plate: The cylindrical inner skin that closes the bucket on the rim side. A continuous timber or steel band running the full circumference. Any gap larger than 4 mm bleeds water out the back of the bucket and costs efficiency.
- Shaft and Bearings: Carries 100% of the wheel's weight plus the unbalanced water load. Plain bronze or white-metal bearings are traditional; modern restorations often use sealed spherical roller bearings rated for the combined static load of typically 5 to 30 tonnes including water.
- Tailrace: Carries spent water away from the bottom of the wheel. The tail water surface must sit at least 100 to 200 mm below the lowest point of the bucket discharge, or the wheel drowns and torque collapses.
Where the Water Wheel (form 7) Is Used
Form 7 wheels show up wherever the available head is awkward — too little for a clean overshot but too much to waste on a low breastshot. Heritage restorations dominate the modern installed base, but a handful of off-grid and craft-industry projects have specified new-build Form 7 wheels in the last 20 years because they tolerate variable flow better than turbines at this scale.
- Heritage Milling: The restored corn mill at Cromford, Derbyshire runs a 4.2 m diameter Form 7 wheel driving a single pair of millstones for visitor demonstrations.
- Craft Distilling: A 3.6 m Form 7 wheel at the Annandale Distillery feeds an auxiliary cooling-water pump and a malt elevator, salvaging mechanical work from a mill stream the licence won't let them dam further.
- Off-Grid Workshops: A timber-frame joinery in the Welsh Marches uses a 2.8 m Form 7 to drive a line shaft for a band-resaw and a pillar drill, sized for 3 m of head off a hillside leat.
- Educational Demonstration: The Beamish Living Museum operates a half-scale Form 7 wheel as a working teaching exhibit on bucket geometry and gravity-driven hydraulic efficiency.
- Small Hydroelectric: Several micro-hydro installations in the French Massif Central use Form 7 wheels with belt drives to 5 to 15 kW permanent-magnet generators, chosen over Pelton turbines because the 2 to 3 m head is too low for a turbine to be efficient.
- Agricultural Pumping: A heritage farm in Saxony drives a piston irrigation pump through a 12:1 reduction off a 3.0 m Form 7 wheel, lifting water 18 m to a hilltop reservoir.
The Formula Behind the Water Wheel (form 7)
The shaft power available from a Form 7 wheel comes from the rate at which gravitational potential energy is delivered to the buckets. What matters in practice is how the answer changes across your operating range. At the low end of the typical 0.05 to 0.5 m³/s flow band, the wheel runs at low torque and the bearing friction eats a noticeable fraction of output. At the high end, you start to spill water at the inlet because the buckets fill before they finish entering the headrace, and efficiency drops back. The sweet spot for most Form 7 wheels sits at 70 to 85% of design flow, where buckets fill to about 70% of geometric capacity and the wheel runs at 4 to 8 RPM rim speed.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| P | Useful shaft power output | W | hp |
| η | Hydraulic efficiency (typically 0.60 to 0.75 for Form 7) | 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 of water onto the wheel | m³/s | ft³/s |
| H | Effective head (vertical drop from inlet to bucket discharge point) | m | ft |
Worked Example: Water Wheel (form 7) in a heritage paper mill in Hampshire
A heritage paper mill on the River Test in Hampshire wants to restore a Form 7 wheel to drive a Hollander beater for hand-papermaking demonstrations. The site has 3.0 m of usable head between the headrace inlet and the tailrace surface. The licensed abstraction is 0.20 m³/s nominal, with the brook running between 0.10 and 0.35 m³/s seasonally. Target hydraulic efficiency is 0.70 based on similar restored wheels in the area.
Given
- H = 3.0 m
- Qnom = 0.20 m³/s
- Qlow = 0.10 m³/s
- Qhigh = 0.35 m³/s
- η = 0.70 dimensionless
- ρ = 1000 kg/m³
- g = 9.81 m/s²
Solution
Step 1 — compute nominal shaft power at the licensed abstraction of 0.20 m³/s:
That's enough to drive a half-tonne Hollander beater through a 15:1 belt reduction with comfortable headroom for the loaded paper stock.
Step 2 — at the low end of the seasonal range, summer flow drops to 0.10 m³/s:
You lose half the power and the wheel will struggle to turn over a fully loaded beater. In practice the operator either runs the beater at half charge or accepts a longer beat cycle. The wheel itself still runs cleanly because efficiency is largely flow-independent down to about 30% of design flow.
Step 3 — at the high end of the seasonal range, winter flow climbs to 0.35 m³/s:
Note the efficiency dropped from 0.70 to 0.60 in this calculation — that's deliberate. At 175% of design flow the buckets overfill and spill at the inlet lip, so real-world efficiency falls. You'd typically bypass the surplus through the spillway rather than try to capture it, which means the practical winter ceiling is closer to 4.5 to 5.0 kW with the sluice held at design opening.
Result
Nominal shaft power is about 4. 1 kW at the licensed 0.20 m³/s abstraction. That's a comfortable working figure — enough to run the beater steadily at the rated 28 RPM beater-roll speed without bogging when fresh stock enters the trough. Across the seasonal range the wheel delivers 2.1 kW in summer drought and a practical 4.5 to 5.0 kW ceiling in winter spate, with the sweet spot at the licensed flow. If you measure 3.0 kW at the shaft instead of 4.1 kW at design flow, look first at sole-plate gap (anything above 5 mm bleeds enough water to cost 15 to 20% efficiency), then check tailwater level — a winter rise of 200 mm into the discharge zone is enough to drown the bottom three buckets and cut output by a quarter, and finally inspect the inlet sluice for partial sediment blockage which reduces effective Q below the assumed value.
Water Wheel (form 7) vs Alternatives
Form 7 sits in a crowded field. Below it on head, you have undershot and Poncelet wheels; above it, you have overshot wheels and small Pelton turbines. The choice depends on head, flow stability, and what you're driving.
| Property | Form 7 High Breastshot | Overshot Wheel | Crossflow Turbine |
|---|---|---|---|
| Optimal head range | 2 to 4 m | 3 to 10 m | 2 to 200 m |
| Hydraulic efficiency | 60 to 75% | 70 to 85% | 75 to 85% |
| Typical shaft RPM | 4 to 8 RPM | 3 to 8 RPM | 300 to 1500 RPM |
| Tolerance to flow variation | Excellent — runs cleanly at 30 to 130% of design Q | Good — efficient down to 40% Q | Poor — narrow efficiency band, needs guide-vane control |
| Capital cost (5 kW class) | £15k to £40k restoration, £25k to £60k new build | £20k to £50k new build | £8k to £20k turbine plus civils |
| Maintenance interval | Annual shroud and bearing inspection | Annual bucket inspection | 5,000 hr bearing service |
| Service lifespan | 50 to 150 years (cast iron and timber) | 50 to 150 years | 20 to 40 years |
| Best application fit | Medium-head heritage and craft sites with 2 to 4 m drop | High-head sites with stable flow | Variable head, electrical generation focus |
Frequently Asked Questions About Water Wheel (form 7)
You're hitting tailwater drowning. When the receiving river or tailrace rises into the discharge arc of the wheel, the lower buckets fill from below and have to lift water on the rising side instead of dumping it cleanly. Two or three drowned buckets is enough to cost 20 to 30% of shaft output, and it gets worse fast.
The diagnostic check is simple — measure the vertical distance from the lowest point of bucket travel down to the tailwater surface during the flood. If it's less than 100 mm you're drowning. The fix is either a deeper tailrace cut downstream of the wheel or a tail-gate that lets you draw the level down by 200 to 300 mm during high flow.
At 3.5 m you're in the overlap zone, and the deciding factor is usually the geometry of the headrace approach, not the head itself. An overshot needs the water delivered above the crown of the wheel, which means your inlet launder has to climb above the shaft height plus the wheel radius. If your hillside doesn't give you that elevation cleanly, a Form 7 with the inlet at 10 o'clock saves you 0.6 to 0.9 m of launder height and a lot of civil work.
Overshot is 5 to 10 percentage points more efficient on paper. Form 7 wins on flow tolerance — if your stream varies by 3:1 across the year, the Form 7 holds efficiency better at part-flow because the buckets fill more progressively across the inlet arc.
You're probably calculating from the assumption that the buckets fill 100% — they don't. Real-world bucket fill is 60 to 75% of geometric volume, because water entering at the inlet has to displace air, the bucket lip catches some flow, and a fraction always splashes off. So your effective Q at the rim is lower than your headrace Q.
Check by measuring depth in three or four buckets as they pass the 9 o'clock position with the wheel running at design load. If you see less than 60% fill, the inlet sluice is misaligned or the headrace velocity is too low to fill the buckets in the time they spend under the inlet. Raise the headrace water level by 50 to 100 mm and re-measure.
Yes, but you need to respect the wheel's torque ripple. A Form 7 produces a roughly sinusoidal torque variation of ±5 to 10% as each bucket enters and leaves the loaded arc. That's fine for a millstone or a Hollander beater that has its own flywheel inertia, but a permanent-magnet generator running into a grid-tie inverter will see that ripple as voltage flicker.
The standard fix is a heavy flywheel on the intermediate shaft sized for at least 3° the wheel's own moment of inertia, or a belt-drive primary stage that decouples the slow wheel rotation from the high-speed generator and adds its own damping. Don't direct-couple a generator to the main shaft.
Two usual suspects. First, inlet splash — if your sluice gate sits more than 50 mm above the bucket lip, water free-falls onto the bucket instead of flowing in cleanly, and you get a slap on every bucket. The cure is a curved approach lip that guides water tangentially into the bucket at near-zero relative velocity.
Second, bucket harmonic resonance. If the bucket plates are unstiffened sheet steel they ring like a bell at the bucket-passing frequency. Heritage wheels almost always use riveted construction with internal stiffening ribs that detune the resonance. Add a stiffener bar across the back of each bucket and the noise drops by 10 to 15 dB.
More than people expect. A 5 mm gap between the shroud edge and the sole plate, running the full circumference of a 3 m wheel, is a slot of roughly 0.047 m² in cross-section. Under the small head present inside a loaded bucket (typically 0.15 to 0.25 m of water column), that slot leaks something like 0.02 to 0.03 m³/s — which is 10 to 15% of typical design flow.
That maps directly onto efficiency. A 10% leak is a 7 percentage point drop in overall hydraulic efficiency, which is the difference between a wheel running at 0.70 and one running at 0.63. On the Hampshire example above, that's the difference between 4.1 kW and 3.7 kW. Tighten the shrouds.
References & Further Reading
- Wikipedia contributors. Water wheel. Wikipedia
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