A water wheel is a machine for converting the energy of flowing or falling water into more useful forms of power, a process otherwise known as hydropower. In the Middle Ages, waterwheels were used as tools to power factories throughout different counties. The alternatives were the windmill and human and animal power. The most common use of the water wheel was to mill flour in gristmills, but other uses included foundry work and machining, and pounding linen for use in paper.
A water wheel consists of a large wooden or metal wheel, with a number of blades or buckets arranged on the outside rim forming the driving surface. Most commonly, the wheel is mounted vertically on a horizontal axle, but the tub or Norse wheel is mounted horizontally on a vertical shaft. Vertical wheels can transmit power either through the axle or via a ring gear and typically drive belts or gears; horizontal wheels usually directly drive their load.
A mill pond is formed when a flowing stream is often dammed of water. A channel created for the water to follow while flowing to or from a water wheel is a mill race (also spelled millrace) or simply a "race", and is customarily divided into sections. The race bringing water from the mill pond to the water wheel is a headrace; the one carrying water after it has left the wheel is commonly referred to as a tailrace.
See main article: Watermills.
In ancient Mesopotamia, irrigation machines are referred to in Babylonian inscriptions, but without details on their construction, suggesting that water power had been harnessed for irrigation purposes. The primitive use of water-rotated wheels may date back to Sumerian times, with references to a "Month for raising the Water Wheels", though it is not known whether these wheels were turned by the flow of a river.
The early history of the watermill in India is obscure. Ancient Indian texts dating back to the 4th century BC refer to the term cakkavattaka (turning wheel), which commentaries explain as arahatta-ghati-yanta (machine with wheel-pots attached). On this basis, Joseph Needham suggested that the machine was a noria. Terry S. Reynolds, however, argues that the "term used in Indian texts is ambiguous and does not clearly indicate a water-powered device." Thorkild Schiøler argued that it is "more likely that these passages refer to some type of tread- or hand-operated water-lifting device, instead of a water-powered water-lifting wheel."
Irrigation water for crops was provided by using water raising wheels, some driven by the force of the current in the river from which the water was being raised. This kind of water raising device was used in ancient India.
Around 1150, the astronomer Bhaskara Achārya observed water-raising wheels and imagined such a wheel lifting enough water to replenish the stream driving it, effectively, a perpetual motion machine.
The construction of water works and aspects of water technology in India is described in Arabic and Persian works. During medieval times, the diffusion of Indian and Persian irrigation technologies gave rise to an advanced irrigation system which bought about economic growth and also helped in the growth of material culture.
The earliest clear evidence of a water wheel comes from the ancient Greece and Asia Minor, being recorded in the work of Apollonius of Perge of c. 240 BC, surviving only in Arabic translation. Mithradates VI Eupator of Pontus had a water mill at his palace at Cabira before 71 BC. In the 1st century BC, the Greek epigrammatist Antipater of Thessalonica was the first to make a reference to the waterwheel, which Lewis has recently argued to be a vertical wheel. Antipater praised it for its use in grinding grain and the reduction of human labour:
Hold back your hand from the mill, you rinding girls, even if the cock crow heralds the dawn, sleep on. For Demeter has imposed the labour of your hands on the nymphs, who leaping down upon the topmost part of the wheel, rotate the axle; with encircling cogs it turns the hollow weight of the Nisyrian millstones. If we learn to feast toil-free on the fruits of the earth we will taste again the golden age.
Modest numbers of water wheels have been identified in various parts of the Greek and Roman World, and they may have once been much more extensive than historians have recognised. Most towns and cities had good aqueducts, and it would not have been difficult to harness part of the supply to driving water wheels for milling, fulling, crushing and sawing wood and stone such as marble. The Romans used both fixed and floating water wheels and introduced water power to other parts of the Roman Empire. The basic construction is described by the engineer Vitruvius writing in 25 BC in his work De Architectura.
The Romans were known to use waterwheels extensively in mining projects, with enormous Roman-era waterwheels found in places like modern-day Spain. They were reverse overshot water-wheels designed for dewatering mines. A series of overshot mills existed at Barbegal near Arles in southern France where corn was milled for the production of bread. The Roman poet Ausonius mentions a mill for cutting marble on the Moselle. Floating mills were also known from the later Empire, where a wheel was attached to a boat moored in a fast flowing river.
Chinese water wheels almost certainly have a separate origin, as early ones there were invariably horizontal waterwheels. By at least the 1st century AD, the Chinese of the Eastern Han Dynasty began to use waterwheels to crush grain in mills and to power the piston-bellows in forging iron ore into cast iron.
In the text known as the Xin Lun written by Huan Tan about 20 AD (during the usurpation of Wang Mang), it states that the legendary mythological king known as Fu Xi was the one responsible for the pestle and mortar, which evolved into the tilt-hammer and then trip hammer device (see trip hammer). Although the author speaks of the mythological Fu Xi, a passage of his writing gives hint that the waterwheel was in widespread use by the 1st century AD in China (Wade-Giles spelling):
Fu Hsi invented the pestle and mortar, which is so useful, and later on it was cleverly improved in such a way that the whole weight of the body could be used for treading on the tilt-hammer (tui), thus increasing the efficiency ten times. Afterwards the power of animals—donkeys, mules, oxen, and horses—was applied by means of machinery, and water-power too used for pounding, so that the benefit was increased a hundredfold.
In the year 31 AD, the engineer and Prefect of Nanyang, Du Shi (d. 38), applied a complex use of the waterwheel and machinery to power the bellows of the blast furnace to create cast iron. Du Shi is mentioned briefly in the Book of Later Han (Hou Han Shu) as follows (in Wade-Giles spelling):
In the seventh year of the Chien-Wu reign period (31 AD) Tu Shih was posted to be Prefect of Nanyang. He was a generous man and his policies were peaceful; he destroyed evil-doers and established the dignity (of his office). Good at planning, he loved the common people and wished to save their labor. He invented a water-power reciprocator (shui phai) for the casting of (iron) agricultural implements. Those who smelted and cast already had the push-bellows to blow up their charcoal fires, and now they were instructed to use the rushing of the water (chi shui) to operate it...Thus the people got great benefit for little labor. They found the 'water(-powered) bellows' convenient and adopted it widely.
Waterwheels in China found practical uses such as this, as well as extraordinary use. The inventor Zhang Heng (78–139) was the first in history to apply motive power in rotating the astronomical instrument of an armillary sphere, by use of a waterwheel. The mechanical engineer Ma Jun (c. 200–265) from Cao Wei once used a waterwheel to power and operate a large mechanical puppet theater for the Emperor Ming of Wei (r. 226-239).
See also: Timeline of Muslim scientists and engineers. Muslim engineers employed water wheels as early as the 7th century, excavation of a canal in the Basra region discovered remains of a water wheel dating from this period. Hama in Syria still preserves one of its large wheels, on the river Orontes, although they are no longer in use.  The largest had a diameter of about 20 metres and its rim was divided into 120 compartments. Another wheel that is still in operation is found at Murcia in Spain, La Nora, and although the original wheel has been replaced by a steel one, the Moorish system during al-Andalus is otherwise virtually unchanged. The flywheel mechanism, which is used to smooth out the delivery of power from a driving device to a driven machine, was invented by Ibn Bassal (fl. 1038-1075) of al-Andalus, who pioneered the use of the flywheel in the chain pump (saqiya) and noria.
The industrial uses of watermills in the Islamic world date back to the 7th century, while horizontal-wheeled and vertical-wheeled water mills were both in widespread use by the 9th century. A variety of industrial watermills were used in the Islamic world, including gristmills, hullers, paper mills, sawmills, shipmills, stamp mills, steel mills, sugar mills, and tide mills. By the 11th century, every province throughout the Islamic world had these industrial watermills in operation, from al-Andalus and North Africa to the Middle East and Central Asia. Muslim engineers also used crankshafts and water turbines, gears in watermills and water-raising machines, and dams as a source of water, used to provide additional power to watermills and water-raising machines. Fulling mills, paper mills and steel mills may have spread from Islamic Spain to Christian Spain in the 12th century. Industrial water mills were also employed in large factory complexes built in al-Andalus between the 11th and 13th centuries.
Muslim engineers developed two solutions to achieve the maximum output from a water wheel. The first solution was to mount them to piers of bridges to take advantage of the increased flow. The second solution was the shipmill, a type of water mill powered by water wheels mounted on the sides of ships moored in midstream. This technique was employed along the Tigris and Euphrates rivers in 10th century Iraq, where large shipmills made of teak and iron could produce 10 tons of flour from corn every day for the granary in Baghdad.
Cistercian monasteries, in particular, made extensive use of water wheels to power watermills of many kinds. An early example of a very large waterwheel is the still extant wheel at the early 13th century Real Monasterio de Nuestra Senora de Rueda, a Cistercian monastery in the Aragon region of Spain. Grist mills (for corn) were undoubtedly the most common, but there were also sawmills, fulling mills and mills to fulfill many other labor-intensive tasks. The water wheel remained competitive with the steam engine well into the Industrial Revolution.
The main difficulty of water wheels was their inseparability from water. This meant that mills often needed to be located far from population centers and away from natural resources. Water mills were still in commercial use well into the twentieth century, however.
Overshot & pitchback waterwheels are suitable where there is a small stream with a height difference of more than 2 meters, often in association with a small reservoir. Breastshot and undershot wheels can be used on rivers or high volume flows with large reservoirs.
The most powerful waterwheel built in the United Kingdom was the 100 hp Quarry Bank Mill Waterwheel near Manchester. A high breastshot design, it was retired in 1904 and replaced with several turbines. It has now been restored and is a museum open to the public.
The biggest working waterwheel in mainland Britain has a diameter of 15.4 m and was built by the De Winton company of Caernarfon. It is located within the Dinorwic workshops of the National Slate Museum in Llanberis, North Wales.
Modern Hydro-electric dams can be viewed as the descendants of the water wheel as they too take advantage of the movement of water downhill.
Most water wheels in Great Britain and the United States are (or were) vertical wheels rotating about a horizontal axle, but in the Scottish highlands and parts of southern Europe mills often had a horizontal wheel (with a vertical axle).
The wheel is usually mounted inside the mill building below the working floor. A jet of water is directed on to the paddles of the water wheel, causing them to turn. This is a simple system, usually used without gearing so that the axle of the waterwheel become the spindle of the mill. This system is sometimes called the Norse mill. In a sense it is the ancestor of the modern turbine.
A vertically-mounted water wheel that is rotated by water striking paddles or blades at the bottom of the wheel is said to be undershot. This is generally the least efficient, oldest type of wheel (with the exception of the poncelet wheel). It has the advantage of being cheaper and simpler to build, but is less powerful and can only be used where the flow rate is sufficient to provide torque.
Undershot wheels gain no advantage from head. They are most suited to shallow streams in flat country.
Undershot wheels are also well suited to installation on floating platforms. The earliest were probably constructed by the Roman general Belisarius during the siege of Rome in 537. Later they were sometimes mounted immediately downstream from bridges where the flow restriction of arched bridge piers increased the speed of the current.
A vertically-mounted water wheel that is rotated by falling water striking buckets near the centre of the wheel's edge, or just above it, is said to be breastshot. Breastshot wheels are the most common type in the United States of America and are said to have powered the American industrial revolution.
Breastshot wheels are less efficient than overshot wheels (see below), more efficient than undershot wheels, and are not backshot (see below). The individual blades of a breastshot wheel are actually buckets, as are those of most overshot wheels, and not simple paddles like those of most undershot wheels (the Poncelet design being a notable exception). A breastshot wheel requires a good trash rake and typically has a masonry "apron" closely conforming to the wheel face, which helps contain the water in the buckets as they progress downwards. Breastshot wheels are preferred for steady, high-volume flows such as are found on the fall line of the North American East Coast.
A vertically-mounted water wheel that is rotated by falling water striking paddles, blades or buckets near the top of the wheel is said to be overshot. In true overshot wheels the water passes over the top of the wheel, but the term is sometimes applied to backshot or pitchback wheels where the water goes down behind the waterwheel.
A typical overshot wheel has the water channeled to the wheel at the top and slightly to one side in the direction of rotation. The water collects in the buckets on that side of the wheel, making it heavier than the other "empty" side. The weight turns the wheel, and the water flows out into the tail-water when the wheel rotates enough to invert the buckets. The overshot design can use all of the water flow for power (unless there is a leak) and does not require rapid flow.
Unlike undershot wheels, overshot wheels gain a double advantage from gravity. Not only is the force of the flowing water partially transferred to the wheel, the weight of the water descending in the wheel's buckets also imparts additional energy. The mechanical power derived from an overshot wheel is determined by the wheel's physical size and the available head, so they are ideally suited to hilly or mountainous country.
Overshot wheels demand exact engineering and significant head, which usually means significant investment in constructing a dam, millpond and waterways. Sometimes the final approach of the water to the wheel is along a lengthy flume or penstock.
A backshot wheel (also called pitchback) is a variety of overshot wheel where the water is introduced just behind the summit of the wheel. It combines the advantages from breastshot and overshot systems, since the full amount of the potential energy released by the falling water is harnessed as the water descends the back of the wheel.
A backshot wheel continues to function until the water in the wheel pit rises well above the height of the axle, when any other overshot wheel will be stopped or even destroyed. This makes the technique particularly suitable for streams that experience extreme seasonal variations in flow, and reduces the need for complex sluice and tail race configurations. A backshot wheel may also gain power from the water's current past the bottom of the wheel, and not just the weight of the water falling in the wheel's buckets.
A recent development of the breastshot wheel is a hydraulic wheel which effectively incorporates a weir into the centre of the wheel. This was developed by the French inventeur Michael Fonfrede and is commercialised as the Aqualienne by  Estimated hydraulic efficiency 67% (max 76%).
A parallel development is the hydraulic wheel/part reaction turbine that also incorporates a weir into the centre of the wheel but uses blades angled to the water flow.The WICON-Stem Pressure Machine (SPM) exploits this flow.  Estimated efficiency 67%.
The University of Southampton School of Civil Engineering and the Environment in the UK has investigated both types of Hydraulic wheel machines and has estimated their hydraulic efficiency and suggested improvements, i.e The Rotary Hydraulic Pressure Machine. (Estimated maximum efficiency 85%). 
These type of waterwheels have high efficiency at part loads / variable flows and can operate at very low heads, < 1 metre. Combined with direct drive Axial Flux Permanent Magnet Alternators and power electronics they offer a viable alternative for low head hydroelectric power generation.
Although traditionally water wheels have been made mostly from wood, the use of iron or steel in overshot (and pitchback) wheels allows faster rotation (possibly reducing the need for gearing) without extreme reductions in available torque. A wooden wheel with a wooden axle that can easily turn low-speed, high-torque loads such as a run of millstones cannot necessarily sustain high speeds such as are needed for hydroelectric power generation.
Until around 1820 water wheels in North America were generally built with a wooden axle (usually from seasoned white oak) with 3 or more of the spokes extending through the wood axle and interlocked inside. Additional spokes attached to pocket holes in the axle and were wedged inside the wood axle. These wheels generally had metal gudgeons held in place on the ends of the shafts using wedges and steel hoops which allowed the wood axle to have a small metal tip on the end. These metal tips or “journals” would then ride on wood or stone bearings. A water wheel made this wheel was called a Compass Wheel . Sometimes a wood axle would need to be replaced after only a year or two prompting the development of “hybrid wheels”. After 1820 water wheels began to have steel hubs and later steel axles with wood spokes, rims, and paddles. These hybrid wheels eliminated the often problematic wood axle and allowed the addition of more spokes. Later they went to cast Iron water wheels and eventually they went to all steel water wheels. Overshot (and particularly backshot) wheels are the most efficient type; a backshot steel wheel can be more efficient (about 60%) than all but the most advanced and well-constructed turbines. Nevertheless, in some situations an overshot wheel is vastly preferable to any turbine.
The development of the hydraulic type water wheels with their improved efficiency (>67%) opens up an alternative path for the installation of waterwheels in existing mills, or redevelopment of abandoned mills.