CLH292 History of Ancient Technology and Engineering
by V Carliell
by V Carliell
Reconstruction of a Fifth Century AD Roman Waterwheel
The waterwheel I have constructed is a horizontal axis overshot wheel and is based upon the Athenian Agora wheel. Horizontal wheels were more efficient than the vertical axis wheel, and overshot more efficient than undershot. This suggests that the horizontal overshot is a development of the more primitive vertical mills, but there is no evidence to prove which came first. This type of waterwheel would have been used to power a water mill, with gearing to convert the horizontal motion of the axle into motion about a vertical axis to turn the grind stones. My wheel is fed by an overshot channel, requiring water to be brought to the top of the wheel. Originally wheels were placed directly in rivers, making them undershot and powered by the kinetic energy of the water, which had to flow at a rapid pace to turn them. The undershot wheel could generate about 1.5kW of power. The overshot wheel was more efficient because it used not just the kinetic energy from the flow of the water but also the potential energy from the height of the water. Cotterell and Kamminga (1990) estimate that for overshot wheels the power output is doubled, and that the Athenian Agora wheel-upon which my wheel is based, would have had an output of 3kW.
The situation with the literary evidence is little better. There are some scattered references to waterwheels, but most of these are brief, mentioning at most the paddles turning, or the water flowing. From these we can deduce whether the wheel was undershot or overshot, but little else. A poem written by Antipater of Thessalonica at the end of the first century BC celebrates the watermill as the end of women’s labour grinding corn. It is useful in dating the introduction of the waterwheel (as used in a watermill), for the fact that it was written at all suggests that it was a relatively new invention and therefore worthy of critical appraisal. Diocletian’s edict of AD 301 sets the price of 4 different types of mills. It includes watermills, which were quoted as the most expensive kind, suggesting that they were not common. But in reality the expense would not have been that much greater than animal mills; the watermill produced more power than the hand or animal mills and it did not have the added expense of feeding, stabling and eventually replacing the animals.
The growing importance of the
waterwheel to grind flour is demonstrated by the fact that when the Goths
attacked Rome and blocked the aqueduct to the watermills on the Janciulum,
floating watermills on ships anchored in the Tiber had to be constructed to
prevent starvation. Whereas five centuries previously a similar
bread shortage had been caused by Caligula commandeering
Whilst these provide useful evidence for the existence and development of the waterwheel there is little that would help a reconstruction. The best evidence comes from Vitruvius, but even he is of limited use. He provides a detailed description of water-lifting devices, but his description of a waterwheel is more concerned with the gearing that connects it to the grindstones of the mill. There is debate about the translation and interpretation of that particular passage, as scholars are unsure whether it indicates step-up (as in later European mills) or step-down gearing. However we can gain important evidence for a reconstruction by assuming that the information he gives for water-lifting wheels is general for all waterwheels. This tells us that the axle was wooden and round (having been turned on a lathe or compasses) but its ends were capped with iron sheeting, the drum was made of planks joined together and the whole thing was mounted on beams, with iron bearings for the axle ends.
I have scaled down the Athenian Agora wheel to make a scale model roughly a third of the size of the original. Thus the diameter of my wheel is 1m and its width 0.17m. I have also been able to base the axle on the existing measurements of 3.5m long and 0.2 diameter. The reconstructed axle is 0.045m diameter but only 0.4m long. I have not kept the length proportional because originally it would have extended past the wheel to connect to the gearing mechanisms, but I only need sufficient length to demonstrate the wheel without the gears.
Unfortunately these were the only dimensions that could be deduced from the Agora wheel, the rest of the wheel had to be designed from educated guesswork. An account by Philo of Byzantium describes a water-powered whistling wheel saying ‘The central part of the wheel ought to have a diameter equal to one-third the diameter of the wheel.’This seems a reasonable proportion, so my central hub is a third of the diameter of the wheel, with a 0.3m diameter with a 0.045m hole in the centre for the axle. Given the paucity of detailed ancient information I had to widen my sources and even look at modern waterwheels to complete the design. There is a carving of a treadmill used to power a crane that shows 14 spokes for the wheel, more modern designs had 12 or even 8 spokes. However Arthur Parsons describes the Agora wheel as probably having many long spokes and it made sense to have a spoke for each rim compartment, so I settled on two sets of 16 spokes.
The Agora wheel also gave evidence for the overshot channel. Parsons reports that ‘the gradient indicated by the floor tiles will bring the channel, restored, to the wheel race at a height of ca 1.40m above the wheel. This is certainly too high for the water to fall uncontrolled onto the wheel.’ This suggests that the final stages of the channel (after running almost level) were steeply sloped to utilise the force of the water. This was somewhat unusual as normally the water for overshot wheels fell only a short distance, and ‘Only in the case of small undershot or horizontal turbine wheels’is the steep incline used.
In constructing the wheel I tried, as far as possible, to use only tools and techniques that would have been available to ancient Romans.
Screws were not yet in use in woodworking so I have used nails to secure the wood, as well as mortice and tenon joints where the spokes are inserted into the planks of the central hub. ‘Woodworking in the Roman period involved the use of tools, such as saws, drills and chisels, and different types of joints.’
I used a handsaw to cut the wood, and a plane and file to smooth the finish; this is probably the same as the ancient Romans, who used a type of plane, the adze, for ‘trimming rough timbers and shaping and smoothing the surface of timbers.’ I also used a simple hand drill and cut out the sockets in the bearing blocks with a mallet and chisel.
When it came to materials it was harder to keep to those available to ancient Romans. I needed relatively large areas of wood for the rim, bucket compartment dividers and faces of the central hub, but unfortunately I had to cut these from sheets of plywood due to the expense and unavailability of large sheets of hard wood.
In Vitruvius’ description of waterwheels he says that they were ‘pitched ship fashion’ and ‘made tight with pitch and wax’. There is also evidence to show that bitumen was used as a water-proofing agent. It was applied as a protective coat of paint on wood and other materials. Pliny says that ‘The ancients coated the monuments with bitumen…I do not know if it is a Roman invention but it is said that it was done at Rome first.’
There is no evidence to show what
the Romans used to waterproof their wheels, or indeed whether they covered the
whole wheel or just the seams. The
practice in ancient shipbuilding was to caulk the seams, using bitumen, tar or
pitch and to paint the rest of the planks.
I think it is likely that the waterwheels would have been treated in a
similar fashion, with the thick bituminous substance applied only to gaps and
seams, and have therefore waterproofed the reconstructed wheel in this
The authenticity of the waterproofing agent was limited by modern improvements; I was unable to find any kind of pitch or bitumen in its pure form, the closest substance was bitumen based roofing sealant.
The frame that supports the wheel is not intended to be an ancient reconstruction. The wheel at the agora was set against a stone wall, with the other end connected to the gears and millstone. Therefore this frame is only intended to support the wheel and deliver a constant flow of water to it. The overshot channel can be set at two heights. One is almost level, and demonstrates the gradient that would have supplied most large overshot waterwheels. The other is set to approximate the gradient of the Agora wheel (see above), it is roughly 1:1.5 or 67%. This should show if the gradient made any actual difference to the turning speed of the wheel. However I found that the use of a pump to circulate the water and provide a constant flow cancelled out any effect from the gradient, because the water travels down the channel at the speed created by the pump rather than the slope. This is borne out by my measured observations; the wheel achieved an average of 38 turns per minute at both gradients.
The wheel was tested by counting the number of complete turns per minute, to thereby calculate the speed.
Mean turns per minute = 38 (this was the same for both gradients)
Speed = distance / time
Distance (of one turn) = circumference of wheel Ţ C = 2Pr
distance = 3.14 x 38 (mean number of turns)
speed = 119.32 / 60
It is also possible to determine the force of the wheel.
Force = mass x acceleration
Mass = 12.5kg x 9.81 (gravity)
= 122.6 N (
The wheel is moving at a constant velocity due to the constant flow of the water
therefore acceleration = 1
Force = 122.6 x 1
= 122.6 N
The speed and the force of the wheel can be used to determine the power, and therefore efficiency, of the wheel.
Power = Force x Speed
= 122.6 x 1.99
= 243.974 W
Cotterell and Kamminga have estimated the power output of the Athenian Agora wheel, upon which my wheel is based, at 3kW. I can test the accuracy of the reconstruction by comparing its power output to that of the original wheel. The reconstructed wheel turns at roughly 244 W, which is 12 times less powerful than the original Agora wheel. The difference in power does not necessarily mean that the reconstruction is flawed, but is probably caused by the size of the wheel; a smaller wheel produces less power. It is also due to the water supply; although we know the probable gradient of the overshot channel we do not know the quantity of water that flowed through it, or the velocity, so the water flow of the reconstruction is unlikely to match it. The water flow rate affects the speed and therefore the power of the wheel. Lastly with such imprecise evidence for the Agora wheel it is impossible to say with any certainty the exact power it generated. When these factors are taken into account the difference in power is not very significant.
· Cotterell, B and Kamminga, J (1990) Mechanics of pre-industrial technology, Cambridge University Press, Cambreidge
Forbes, R J (1955) Studies in Ancient Technology volume 1, E J Brill,
Humphrey, J W, Oleson, J P and Sherwood, A N
(1998) Greek and Roman Technology: A
Moritz,L A (1958) Grain Mills and Flour in
· Parsons, A W (1936) ‘A Roman Water-mill in the Athenian Agora’ Hesperia, Vol. 5, No. 1, The American Excavations in the Athenian Agora: Ninth Report 70-90
Books On Architecture, translated
by Morgan, M H (1926) Harvard University Press,
· Wikander, O (1984) Exploitation of Water-Power or Technological Stagnation? CWK Gleerup
Woodworking Taken from the
 Excavated by the Americans and published by Arthur W Parsons (1936) in Hesperia
 This is described in Vitruvius, on Architecture 10.5.1-2 and is discussed below.
 This is usually achieved by aqueducts, for example the watermills on the Janiculum, but could also be achieved by damning a river.
 Cotterell and Kamminga (1990) 43
1st-2nd Century Roman Wheel rim, in Gallery 69 in the
 This wheel is referred to by Parsons (1936) 76
 eg Lucretius, On the Nature of Things 5.517, Strabo Geography 12.3.30 as well as poems: Latin Anthology 284. All taken from Humphrey, Oleson and Sherwood (1998) 31
 Diocletian Edict xv.54 taken from Moritz (1958) 102, 138
 Moritz (1958) 139
 Cotterell and Kamminga (1990) 43, believe it was geared down as does Landels (1978) Engineering in the ancient world 24
 Vitruvius On Architecture 10.4.1-4, 5.1
 Parsons (1936) 80
 Vitruvius On Architecture 10.4.1 ‘its (the axle) ends capped with iron sheeting.’
 Parsons (1936) 82
 Cotterell and Kamminga (1990) 27 record an Egyptian Chariot from 1400BC that had animal fat on its axles as evidence for the fact that animal fat was used as a lubricant in antiquity.
 Cotterell and Kamminga(1990) 40
 see the illustrations at http://www.waterhistory.org/histories/waterwheels/
 Parsons (1936) 81. unlike the small and chunky wheels (eg the Venafrum wheel) that were designed to turn rapidly in a fast-running stream.
 Parsons (1936) 82
 Parsons (1936) 82
 Vitruvius on Architecture 10.4.3
 As quoted by Forbes (1955) 86