# Water wheel A **water wheel** is a wheel turned by falling or flowing [[Water|water]], used for most of recorded history to grind grain, saw timber, drive bellows and hammers, and lift water — the original machine of [[Hydropower|hydropower]]. Water can push a wheel with its speed or turn it with its weight, and which of the two a wheel uses decides how much of the water's [[Energy|energy]] reaches the shaft: a well-made overshot wheel, filled from above, delivers about 85% of the hydraulic power available, while flat blades pushed by a current can never deliver more than half.[^mk2004][^barmeir-6] On the Thury spine the water wheel is the first working machine of [[Fluid_dynamics|fluid dynamics]], and at St. Anthony Falls on the [[Mississippi_River|Mississippi]] it built Minneapolis.[^nps-ch6] <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Water_wheel.html" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" allow="accelerometer; gyroscope" title="Water wheel — p5.js microsim"></iframe> </div> *Microsim (THY-053): switch between undershot, breastshot and overshot wheels and change the flow and head; the bars show how much of ρgQH each type turns into shaft power. ILLUSTRATIVE: efficiencies are held at their best-point values.* Videos: [16:9](https://wikitube-3d-microsims.netlify.app/media/Water_wheel_16x9.mp4) · [9:16](https://wikitube-3d-microsims.netlify.app/media/Water_wheel_9x16.mp4) ## Types Water wheels are classed by the axis they turn on and by where the water meets them. Horizontal-axis wheels, which turn in a vertical plane, are the familiar mill wheels; vertical-axis wheels turn flat in the stream like a crude turbine. Among vertical wheels the entry point runs from the bottom (undershot) through axle height (breastshot) to the top (overshot), and the higher the entry, the more the wheel works by the weight of the water rather than its speed. ### Summary of types In the classic ordering, efficiency rises with the height of entry: flat-bladed undershot wheels are the least efficient, breastshot wheels are intermediate and overshot wheels the most efficient. Laboratory and field measurements put well-designed overshot wheels near 85% and improved undershot designs near 75%.[^mk2004] ### Vertical axis A vertical-axis wheel, the horizontal mill of many mountain regions, sits in a fast chute of water and drives a millstone directly above it with no gearing. It is simple and cheap, but most of the water's energy passes it by. ### Stream A stream wheel simply dips its paddles into a flowing river and is pushed by the current, with no dam or channel to create head. It uses only the kinetic energy of the flow, so its output is small and follows the river's speed. ### Undershot wheel An undershot wheel is struck near its bottom by water running in a channel. With flat blades it works as an impulse machine: the momentum given up by the water pushes the blades, and the best it can do is to move at half the water's speed, where the efficiency peaks at one half — the same result that the Pelton analysis gives when the water is not turned back.[^barmeir-6] Curved blades and close-fitting channels raise the figure well above that limit.[^mk2004] ### Breastshot wheel A breastshot wheel receives water at roughly axle height, usually from a sluice that directs it onto the blades as they descend inside a close-fitting curved breast wall. It combines the push of the flow with the weight of water held against the wall, and was the usual choice for heads too low for an overshot wheel. ### Overshot wheel An overshot wheel is fed at the top from a flume, and its buckets carry the water down one side so that its weight turns the wheel. Because it uses nearly the whole fall and releases the water gently at the bottom, the overshot wheel is the most efficient traditional type; properly designed ones have an efficiency of about 85% over a wide range of flows.[^mk2004] ### Backshot wheel A backshot (or pitchback) wheel is fed near the top like an overshot wheel but turns in the opposite direction, so the water leaves in the same direction as the tailrace flow. It suits sites where the tailwater level rises, because the wheel is not slowed by backing water as much. ## History Water wheels spread across the Mediterranean world and China in antiquity and remained the main source of industrial power until steam engines and then water [[Water_turbine|turbines]] displaced them in the nineteenth century. They drove the first factories as well as mills, and many of the principles later formalized in [[Hydraulic_engineering|hydraulic engineering]] were first worked out by millwrights. ### China In Han-dynasty China, water power drove trip hammers and the bellows of iron furnaces, among the earliest uses of water wheels for metallurgy. ### Roman Empire The Roman architect Vitruvius described a vertical water wheel driving a millstone through gears in the first century BC, and Roman engineers built mill complexes and water-powered stone saws. ### Islamic world In the medieval Islamic world, water wheels powered mills for grain, sugar and paper across a region from Spain to Central Asia, and wheels fitted with pots lifted water for irrigation. ### Medieval Europe Medieval Europe multiplied water mills along almost every usable stream, applying them to grinding, fulling cloth, sawing, forging and pumping. ### Modern developments In the nineteenth century engineers measured wheels systematically and learned to shape blades and channels for efficiency, just as enclosed turbines were taking over. In the twenty-first century slow, fish-friendly water wheels have returned for small, low-head sites, and modern tests confirm the efficiencies of well-built historical designs.[^mk2004] ## Efficiency The efficiency of a wheel is the shaft power divided by the hydraulic power ρgQH of the water it uses. An overshot wheel keeps its buckets full on the descending side and loses little: measured efficiencies reach about 85%. Undershot wheels with improved blade shapes reach about 75%, while the simplest flat-bladed undershot wheels, which work only by impulse, are limited to 50% by momentum alone.[^mk2004][^barmeir-6] ## The power of a wheel The power available to any water wheel is set by the flow Q and the head H, the height the water falls while in contact with the wheel: P = ηρgQH, where ρ is the [[Density|density]] of water, g the acceleration of [[Gravity|gravity]] and η the wheel's efficiency. A wheel passing a quarter of a cubic metre per second through a 4 m fall has about 9.8 kW available; at 85% it delivers about 8.3 kW to its shaft. ### Formulae Hydraulic power: P_h = ρgQH. Shaft power: P = ηP_h. For a flat-bladed impulse wheel moving at speed u in water of speed U, the momentum result is η = 2(u/U)(1 − u/U), with a maximum of one half at u = U/2.[^barmeir-6] ### Rules of thumb Overshot wheels suit falls roughly as high as the wheel's diameter; breastshot wheels suit lower falls; undershot and stream wheels suit sites with little or no fall and plenty of water. ## Minnesota *This section is specific to Wikitube.* At St. Anthony Falls in Minneapolis, soldiers from Fort Snelling built the first mills between 1821 and 1823, Franklin Steele opened commercial sawmilling in 1848, and water power from the falls drove the flour mills that made Minneapolis the country's leading flour producer from 1880 for about fifty years; output rose from 193,000 barrels in 1870 to 2,051,840 barrels in 1880.[^nps-ch6] The same falls later drove the country's first central hydroelectric station in 1882.[^mnopedia1882] ## See also - [[Hydropower]] - [[Water_turbine]] - [[Pelton_wheel]] - [[Hydraulic_head]] ## Explanatory notes - The worked power figure in *The power of a wheel* is arithmetic: 1000 kg/m³ × 9.81 m/s² × 0.25 m³/s × 4 m ≈ 9.8 kW. ## Citations [^mk2004]: Müller, G.; Kauppert, K. (2004). "Performance characteristics of water wheels." *Journal of Hydraulic Research* 42 (5): 451–460. https://doi.org/10.1080/00221686.2004.9641215 [^barmeir-6]: Bar-Meir, Genick (2025). *Basics of Fluid Mechanics*, version 0.7.5, §6.3 "Machinery Unitizing Momentum" (Euler turbine equation; Pelton wheel), pp. 253–261. https://open.umn.edu/opentextbooks/textbooks/basics-of-fluid-mechanics [^nps-ch6]: National Park Service, Mississippi National River and Recreation Area. "River of History — Chapter 6." https://home.nps.gov/miss/learn/historyculture/river-of-hisory-chapter-6.htm [^mnopedia1882]: Huber, Molly. "Hydroelectricity in Minneapolis, September 5, 1882." *MNopedia*, Minnesota Historical Society. https://www.mnhs.org/mnopedia/search/index/event/hydroelectricity-minneapolis-september-5-1882 ## General references - Bar-Meir, Genick (2025). *Basics of Fluid Mechanics*, v0.7.5 — [OTL record](https://open.umn.edu/opentextbooks/textbooks/basics-of-fluid-mechanics); on the [[PORTAL_WT!Thury_Hydrodynamics_Compendium|Compendium]] Fluid core shelf. - Murphy, Tom W., Jr. (2021). *Energy and Human Ambitions on a Finite Planet* — [eScholarship](https://escholarship.org/uc/item/9js5291m); on the [[PORTAL_Energy]] shelf. ## External links - [Water Power Technologies Office](https://www.energy.gov/eere/water/water-power-technologies-office), U.S. Department of Energy ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Water_wheel) : [Wikitube](https://en.wikitube.io/wiki/Water_wheel) · pinned revision [1373015832](https://en.wikipedia.org/w/index.php?oldid=1373015832) · 2026-09-10 ## Previous hub tags Hubs: `Life_Physics`, `Systems`. Portals: [[PORTAL_Thury_Hydrodynamics_Apex_Spine]], [[PORTAL_Energy]]. --- *Thury station wave · 2026-09-10 · drafted · microsim THY-053 (p5.js) · parent [[Hydropower]].*