Archimedes' screw

The Archimedes' screw, also known as the Archimedean screw, hydrodynamic screw, water screw or Egyptian screw,^[1] is one of the earliest documented hydraulic machines. It is a reversible hydraulic machine that can be operated both as a pump or a power generator.

An animation of the Archimedes screw as a water pump

An animation of the Archimedes screw as a generator

The origins of the water screw are unknown; Archimedes of Syracuse is traditionally credited with inventing the water screw, but other academics argue Archimedes found the Egyptians already using the screw. Moschion between 250–220 BC details the screw used as a bilge pump in a ship, with Posidonius reporting that the water screw was used for drainage in Spanish mines. Archaeological remains of the screw in Europe and Asia suggested that screw was diffused across the territories of the Roman Empire, though it fell out of use in the third century BC.

As a machine used for lifting water from a low-lying body of water into irrigation ditches, it lifts water by turning a screw-shaped surface inside a pipe. In the modern world, Archimedes screw pumps are widely used in wastewater treatment plants and for dewatering low-lying regions. Run in reverse, Archimedes screw turbines act as a small hydroelectric powerplant that can be applied even in low head sites. Such generators operate in a wide range of flows (0.01 m³/s to 14.5 m³/s) and heads (0.1 m to 10 m), including low heads and moderate flow rates that are not ideal for traditional turbines and not occupied by high performance technologies.

History

Origins

A sketch of Vitruvius's description of the Archimedes screw in De architectura.

The origins of the water screw are unknown;^[2] Archimedes is credited with inventing the water screw, but others have contested this.^[3] According to Posidonius, Archimedes invented the screw when he visited Egypt, possibly during Ptolemy II Philadelphus's reign between 283–246 BC. Other academics posits that Archimedes possibly found Egyptians already using the screw, though Canadian archaeologist John Peter Oleson notes that "no explanation is ever provided for the subsequent identification of the device with Archimedes or for the total lack of any literary or archaeological evidence for the existence of the water-screw before ca. 250 BC", and argues that there may have been confusion over the term used by Posidonius.^[4]^[a]

A modern mini reconstruction of Archimedes' screw at the Kotsanas Museum of Ancient Greek Technology, in Athens.

Assyrianologist Stephanie Dalley proposed that the water screw was used to irrigate the Hanging Gardens of Babylon, one of the Seven Wonders of the Ancient World.^[7] A cuneiform inscription of Assyrian King Sennacherib (704–681 BC) has been interpreted by Dalley to describe casting water screws in bronze some 350 years earlier.^[8] This is consistent with Greek historian Strabo, who describes the Hanging Gardens as irrigated by screws.^{[citation needed]}

Antiquity

The screw pump is the oldest positive displacement pump;^[1] Moschion reports in Treatise on the Great Ship of Hieron of Syracuse, written between 250–220 BC, that the screw was used as a bilge pump in a ship built for Hiero II of Syracuse.^[9] Posidonius also recorded water screws in Spanish mines used for drainage.^[9] Oleson notes that archaeological remains of the water screw were found in the territory of the Roman Empire such as Egypt, Spain, France, and Italy,^[10] whilst literary texts and inscriptions describe the screw to be present in Mesopotamia, Egypt, Syria, and Spain, though the lack of screws in Rome and northern Europe suggests that the screw was not utilised much there as irrigation and mining were less prioritised in those regions.^[11] By the late 1st century BC or 1st century AD, there were not many records mentioning the screw, according to Oleson's investigation in Fayum; he posits that they were either uncommon in the city or were not taxed, and hence were not recorded.^[12] The earliest depiction of the water screw is a fresco at the Casa di P. Cornelius Teges in Pompeii dating earlier than 79 AD, which shows an Egyptian screw.^[13] Archimedes' screw continued to be used in Europe until it fell out of use in the end of the third century, though Oleson hypothesises that the Arabs continued using the screw in north Africa and may have reintroduced the screw to Europe following the conquest of Spain in the 8th century.^[11]

Archimedes never claimed credit for its invention, but it was attributed to him 200 years later by Diodorus, who believed that Archimedes invented the screw pump in Egypt.^[1] Depictions of Greek and Roman water screws show them being powered by a human treading on the outer casing to turn the entire apparatus as one piece, which would require that the casing be rigidly attached to the screw.

Development and modern use

German engineer Konrad Kyeser equipped the Archimedes screw with a crank mechanism in his Bellifortis (1405). This mechanism quickly replaced the ancient practice of working the pipe by treading.^[14] The world's first seagoing steamship driven by a screw propeller was the SS Archimedes, which was launched in 1839 and named in honor of Archimedes and his work on the screw.^[15] Developments in maritime transport occurred over the next 180 years from the Fawcett, Preston and Company double blade design and patents by Sharrow Marine to address rotary propulsion and flow control on boating vessels through loop propellers. Electricity generation through hydropower pumps such as the Meriden project operated by New England Hydropower also uses Archimedes screw to direct water into the top, rather than the bottom, of the screw which forces it to rotate.^[16]^[17]

Modern Archimedes' screw which have replaced some of the windmills used to drain the polders at Kinderdijk in the Netherlands

Archimedes screw as a form of art by Tony Cragg at 's-Hertogenbosch in the Netherlands

Archimedes screws are used in sewage treatment plants because they cope well with varying rates of flow and with suspended solids.^[18] Screw turbines (ASTs) are a new form of generator for small hydroelectric powerplants that could be applied even in low-head sites. The low rotation speed of ASTs reduces negative impacts on aquatic life and fish. This technology is used primarily at fish hatcheries to lift fish safely from ponds and transport them to another location. An Archimedes screw was used in the successful 2001 stabilization of the Leaning Tower of Pisa. Small amounts of subsoil saturated by groundwater were removed from far below the north side of the tower, and the weight of the tower itself corrected the lean.

Other inventions using Archimedes screws include the auger conveyor in a snow blower, grain elevator, concrete mixer and chocolate fountain.

Design

The Archimedes screw consists of a screw (a helical surface surrounding a central cylindrical shaft) inside a hollow pipe. The screw is usually turned by windmill, manual labor, cattle, or by modern means, such as a motor. As the shaft turns, the bottom end scoops up a volume of water. This water is then pushed up the tube by the rotating helicoid until it pours out from the top of the tube.

In an Archimedes screw, there are several parameters to consider, mainly the external and internal parameters. The external parameters include the outer diameter of the screw ( $D_{O}$ ), the length of the screw ( $L$ ), and the inclination angle of the screw ( $\beta$ ), whilst the internal parameters include the screw's inner radius ( $D_{i}$ ), the number of blades ( $N$ ), and the screw's pitch ( $S$ ).^[19] The contact surface between the screw and the pipe does not need to be perfectly watertight, as long as the amount of water being scooped with each turn is large compared to the amount of water leaking out of each section of the screw per turn. If water from one section leaks into the next lower one, it will be transferred upwards by the next segment of the screw.

In some designs, the screw is fused to the casing and they both rotate together, instead of the screw turning within a stationary casing. The screw could be sealed to the casing with pitch resin or other adhesive, or the screw and casing could be cast together as a single piece in bronze.

Studies show that the volume of flow passes through Archimedes screws is a function of inlet depth, diameter and rotation speed of the screw. Therefore, the following analytical equation could be used to design Archimedes screws:^[20]

$D_{O}={\sqrt[{3}]{\frac {16\pi Q}{\sigma \omega (2\theta _{O}-sin2\theta _{O}-\delta ^{2}(2\theta _{i}-sin(2\theta _{i}))}}}$

where $D_{O}$ is in $(m)$ and:

$\omega$ : Rotation speed of the Archimedes screw (rad/s)

$Q$ : Volumetric flow rate $(m^{3}/s)$

Based on the common standards that the Archimedes screw designers use this analytical equation could be simplified as:^[21]

$D_{O}\approx \eta Q^{3/7}$

The value of η could simply determinate using the $\eta$ graph or $\Theta$ graph.^[21] By determination of $D_{O}$ , other design parameters of Archimedes screws can be calculated using a step-by-step analytical method.

Variants

An Archimedes' screw seen on a combine harvester

A screw conveyor is a similar device which transports bulk materials such as powders and cereal grains. It is contained within a tube and turned by a motor to deliver material from one end of the conveyor to the other and particularly suitable for transport of granular materials such as plastic granules used in injection moulding. It may also be used to transport liquids. In industrial control applications, the conveyor may be used as a rotary feeder or variable rate feeder to deliver a measured rate or quantity of material into a process.

A variant of the Archimedes screw can also be found in some injection moulding machines, die casting machines and extrusion of plastics, which employ a screw of decreasing pitch to compress and melt the material. It is also used in a rotary-screw air compressor. On a much larger scale, Archimedes's screws of decreasing pitch are used for the compaction of waste material.

Reverse action

If water is fed into the top of an Archimedes screw, it will force the screw to rotate. The rotating shaft can then be used to drive an electric generator. Such an installation has the same benefits as using the screw for pumping: the ability to handle very dirty water and widely varying rates of flow at high efficiency. Settle Hydro and Torrs Hydro are two reverse screw micro hydro schemes operating in England. The screw works well as a generator at low heads, commonly found in English rivers, including the Thames, powering Windsor Castle.^[22]

Footnotes

^ Posidonius says in an unknown work that "οὓς Αρχιμήδης ὁ Συρακόσιος εὗρεν, ὅτε παρέβαλεν εἰς Αἴγυπτον... θαυμάσαι δ ̓ ἄν τις εἰκότως τοῦ τεχνίτου τὴν ἐπίνοιαν οὐ μόνον ἐν τούτοις, ἀλλὰ καὶ ἐν ἄλλοις πολλοῖς καὶ μείζοσι, διαβεβοημένοις κατὰ πᾶσαν τὴν οἰκουμένην, περὶ ὧν τὰ κατὰ μέρος,ὅταν ἐπὶ τὴν ̓Αρχιμήδους ἡλικίαν ἔλθωμεν, ἀκριβῶς διέξιμεν", which translates to "they draw off the streams of water with the so-called Egyptian screw, which Archimedes the Syracusan invented when he visited Egypt... One might reasonably marvel at the inventiveness of the craftsman not only in this, but also in many other even greater inventions celebrated throughout the whole world, each of which we shall discuss carefully in turn when we come to the age of Archimedes".^[5] Oleson argues that the term "εὑρίσκω" means "'discover – in its subsidiary sense of 'invent'",^[4] and that "τεχνίτου" (craftsman) may be a reference to Archimedes or an inventive human.^[6] Oleson also argues that the academics with the opposing viewpoint interpret Posidonius's statement as Archimedes finding the screw when he came to Egypt.^[4]

Sources

^ ^a ^b ^c Stewart, Bobby Alton; Terry A. Howell (2003). Encyclopedia of water science. USA: CRC Press. p. 759. ISBN 0-8247-0948-9.
^ Dalley & Oleson 2003, p. 24.
^ Nuernbergk 2023, p. 1.
^ ^a ^b ^c Oleson 1984, p. 292.
^ Oleson 1984, pp. 91–92.
^ Dalley & Oleson 2003, p. 20.
^ Dalley & Oleson 2003, p. 16.
^ Stephanie Dalley, The Mystery of the Hanging Garden of Babylon: an elusive World Wonder traced, (2013), OUP ISBN 978-0-19-966226-5
^ ^a ^b Oleson 1984, p. 291.
^ Oleson 1984, p. 293–294.
^ ^a ^b Oleson 1984, p. 294.
^ Oleson 1984, p. 293.
^ Koetsier & Blauwendraat 2004, p. 294.
^ White 1962, pp. 105, 111, 168
^ "SS Archimedes". wrecksite.eu. Archived from the original on 2 October 2011. Retrieved 22 January 2011.
^ HLADKY, GREGORY B. "Archimedes Screw Being Used To Generate Power At Meriden Dam". courant.com. Retrieved 2017-08-01.
^ "Meriden power plant uses Archimedes Screw Turbine". Retrieved 2017-08-01.
^ Ben Finio (July 11, 2019). "Lift Water with an Archimedes Screw". Scientific American.
^ YoosefDoost & Lubitz 2021, p. 3–4.
^ YoosefDoost & Lubitz 2021, p. 10.
^ ^a ^b YoosefDoost & Lubitz 2021, p. 11.
^ BBC. "Windsor Castle water turbine installed on River Thames" bbc.com, 20 September 2011. Retrieved: 19 October 2017.

Bibliography

Dalley, Stephanie; Oleson, John Peter (2003). "Sennacherib, Archimedes, and the Water Screw: The Context of Invention in the Ancient World". Technology and Culture. 44 (1): 1–26. doi:10.1353/tech.2003.0011. S2CID 110119248.
Koetsier, Teun; Blauwendraat, Hendrik (2004). "The Archimedean Screw-Pump: A Note on Its Invention and the Development of the Theory". International Symposium on History of Machines and Mechanisms. doi:10.1007/1-4020-2204-2_15. ISBN 978-1-4020-2203-6 – via Springer.
Nagel, G.; Radlik, K.: Wasserförderschnecken – Planung, Bau und Betrieb von Wasserhebeanlagen; Udo Pfriemer Buchverlag in der Bauverlag GmbH, Wiesbaden, Berlin (1988)
Nuernbergk, Dirk Michael (2023). Hydropower Screws: Calculation and Optimal Design of Archimedean Screws. Germany: Springer. doi:10.1007/978-3-031-27642-2. ISBN 9783031276446.
Nuernbergk D. M.: "Wasserkraftschnecken – Berechnung und optimaler Entwurf von archimedischen Schnecken als Wasserkraftmaschine", Verlag Moritz Schäfer, Detmold, 1. Edition. 2012, 272 papes, ISBN 978-3-87696-136-1
Nuernbergk, D. and Rorres C.: „An Analytical Model for the Water Inflow of an Archimedes Screw Used in Hydropower Generation", ASCE Journal of Hydraulic Engineering, Published: 23 July 2012
Oleson, John Peter (1984), Greek and Roman mechanical water-lifting devices. The History of a Technology, Dordrecht: D. Reidel, ISBN 90-277-1693-5
Oleson, John Peter (2000), "Water-Lifting", in Wikander, Örjan (ed.), Handbook of Ancient Water Technology, Technology and Change in History, vol. 2, Leiden, pp. 217–302 (242–251), ISBN 90-04-11123-9{{citation}}: CS1 maint: location missing publisher (link)
P. J. Kantert: "Manual for Archimedean Screw Pump", Hirthammer Verlag 2008, ISBN 978-3-88721-896-6.
P. J. Kantert: "Praxishandbuch Schneckenpumpe", Hirthammer Verlag 2008, ISBN 978-3-88721-202-5.
P. J. Kantert: "Praxishandbuch Schneckenpumpe" - 2nd edition 2020, DWA, ISBN 978-3-88721-888-1.
Rorres C.: "The turn of the Screw: Optimum design of an Archimedes Screw", ASCE Journal of Hydraulic Engineering, Volume 126, Number 1, Jan.2000, pp. 72–80
White, Lynn Jr. (1962), Medieval Technology and Social Change, Oxford: At the Clarendon Press
YoosefDoost, Arash; Lubitz, William David (December 2021). "Design Guideline for Hydropower Plants Using One or Multiple Archimedes Screws". Processes. 9 (12): 2128. doi:10.3390/pr9122128.

External links

The Turn of the Screw: Optimal Design of an Archimedes Screw, by Chris Rorres, PhD.
"Archimedean Screw" by Sándor Kabai, Wolfram Demonstrations Project, 2007.
"Archimedes Screw Examples Various sources, 2021

[7] Posidonius says in an unknown work that "οὓς Αρχιμήδης ὁ Συρακόσιος εὗρεν, ὅτε παρέβαλεν εἰς Αἴγυπτον... θαυμάσαι δ ̓ ἄν τις εἰκότως τοῦ τεχνίτου τὴν ἐπίνοιαν οὐ μόνον ἐν τούτοις, ἀλλὰ καὶ ἐν ἄλλοις πολλοῖς καὶ μείζοσι, διαβεβοημένοις κατὰ πᾶσαν τὴν οἰκουμένην, περὶ ὧν τὰ κατὰ μέρος,ὅταν ἐπὶ τὴν ̓Αρχιμήδους ἡλικίαν ἔλθωμεν, ἀκριβῶς διέξιμεν", which translates to "they draw off the streams of water with the so-called Egyptian screw, which Archimedes the Syracusan invented when he visited Egypt... One might reasonably marvel at the inventiveness of the craftsman not only in this, but also in many other even greater inventions celebrated throughout the whole world, each of which we shall discuss carefully in turn when we come to the age of Archimedes".^[5] Oleson argues that the term "εὑρίσκω" means "'discover – in its subsidiary sense of 'invent'",^[4] and that "τεχνίτου" (craftsman) may be a reference to Archimedes or an inventive human.^[6] Oleson also argues that the academics with the opposing viewpoint interpret Posidonius's statement as Archimedes finding the screw when he came to Egypt.^[4]

[Stewart-1] Stewart, Bobby Alton; Terry A. Howell (2003). Encyclopedia of water science. USA: CRC Press. p. 759. ISBN 0-8247-0948-9.

[FOOTNOTEDalleyOleson200324-2] Dalley & Oleson 2003, p. 24.

[FOOTNOTENuernbergk20231-3] Nuernbergk 2023, p. 1.

[FOOTNOTEOleson1984292-4] Oleson 1984, p. 292.

[FOOTNOTEOleson198491–92-5] Oleson 1984, pp. 91–92.

[FOOTNOTEDalleyOleson200320-6] Dalley & Oleson 2003, p. 20.

[FOOTNOTEDalleyOleson200316-8] Dalley & Oleson 2003, p. 16.

[9] Stephanie Dalley, The Mystery of the Hanging Garden of Babylon: an elusive World Wonder traced, (2013), OUP ISBN 978-0-19-966226-5

[FOOTNOTEOleson1984291-10] Oleson 1984, p. 291.

[FOOTNOTEOleson1984293–294-11] Oleson 1984, p. 293–294.

[FOOTNOTEOleson1984294-12] Oleson 1984, p. 294.

[FOOTNOTEOleson1984293-13] Oleson 1984, p. 293.

[FOOTNOTEKoetsierBlauwendraat2004294-14] Koetsier & Blauwendraat 2004, p. 294.

[15] White 1962, pp. 105, 111, 168

[16] "SS Archimedes". wrecksite.eu. Archived from the original on 2 October 2011. Retrieved 22 January 2011.

[17] HLADKY, GREGORY B. "Archimedes Screw Being Used To Generate Power At Meriden Dam". courant.com. Retrieved 2017-08-01.

[18] "Meriden power plant uses Archimedes Screw Turbine". Retrieved 2017-08-01.

[19] Ben Finio (July 11, 2019). "Lift Water with an Archimedes Screw". Scientific American.

[FOOTNOTEYoosefDoostLubitz20213–4-20] YoosefDoost & Lubitz 2021, p. 3–4.

[FOOTNOTEYoosefDoostLubitz202110-21] YoosefDoost & Lubitz 2021, p. 10.

[FOOTNOTEYoosefDoostLubitz202111-22] YoosefDoost & Lubitz 2021, p. 11.

[bgTham1-23] BBC. "Windsor Castle water turbine installed on River Thames" bbc.com, 20 September 2011. Retrieved: 19 October 2017.

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