Al-Jazari's Third Water-Raising Device: Analysis of its Mathematical and Mechanical Principles

Five pumps or water-raising machines are described by al-Jazari in his monumental treatise of mechanics Al-Jami' bayn al-‘ilm wa 'l-‘amal al-nafi' fi sina'at al-hiyal (A Compendium on the Theory and Useful Practice of the Mechanical Arts). The following long article is a detailed study of the third of these water-raising devices. The study presents a detailed analysis of the mathematical and mechanical principles of this sophisticated machine and explains its functioning. Further, the various components of the pump are reconstructed via computer assisted design. A profusion of 3D graphics and 3D animations show the device in different angles and helps in viewing it in operational mode.

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By Salim T. S. Al-Hassani* and Colin Ong Pang Kiat**

Table of contents

Preface: Summary and Objectives of this Research

I. Characterisation of the tradition of Islamic Technology
  1. Beginning of Islamic Science and Technology
  2. Islamic Technology
  3. The Teaching of Islamic Engineering
  4. Comparison of Islamic and Modern Engineering Concept
  5. Transmission of Islamic Studies

II. Al-Jazari: Outline of his Biography and of his Work's Historical Context
  1. Al-Jazari's Life and Personality
  2. Al-Jazari's Work: The Book of Knowledge of Ingenious Devices
     2.1. Why is Al-Jazari's Work so Important?
     2.2. Why was there so Limited Works by other Scholars?

III. Water-Raising Devices: History and Technical Principles
  1. What Led to the Development of Water Raising Devices?
  2. Ancient Water Raising Devices
     2.1. The Shaduf
     2.2. The Archimedean Screw or Water-Snail
     2.3. The Noria
     2.4. The Saqiya

IV. Al-Jazari's Third Water-Raising Device
  1. A Revolutionary Idea
  2. Description of the Device
  3. Possible Problems Encountered

V. Research and Analysis
  1. Scoop-Wheel or Water Turbine
     1.1. How did al-Jazari Invent the Scoop-Wheel Design?
     1.2. Why did he Use the Scoop-Wheel Instead of the More Common Overshot Wheel?
     1.3. Why did he Convert the Undershot Scoop-Wheel to an Overshot Scoop-Wheel?
     1.4. Comparison between the Undershot Wheel and the Overshot Wheel?
     1.5. John Smeaton Experiment
  2. Cogwheel and Lantern Pinion Gears
  3. Analytical Interpretation of the Gears Found on al-Jazari's Illustration
     3.1. Why is it Elliptical in Shape?
     3.2. Why do the Gears have Sharpened Teeth?
     3.3. Possible Relationship to the Saqiya Gears
     3.4. What did the Actual Gears Look Like?
     3.5. Will the selected Gears be able to Transmit High Torque?
     3.6. What are the Methods Used to Enhance its Efficiency?
  4. Sindi Wheel
     4.1. Possible Problems Encountered?
     4.2. What are the Methods Used to Enhance its Efficiency?
  5. Where Does Water from the Lower Chamber Flow?
     5.1. Possibility 1
     5.2. Possibility 2
     5.3. Possibility 3
  6. Rudimentary Components and Materials Used by Al-Jazari
     6.1. Bearings
     6.2. Axle
     6.3. Lubrication
     6.4. Pipes
     6.5. Fittings
     6.6. Materials
     6.7. Jackwork or Jack Figures
  7. Weights and Measurements

VI. Mathematical Analysis

  1. Analysis of the Total Head of Water Jet
  2. Analysis of the System of the Third Water Raising Device
  3. Assumptions and Considerations
     3.1. Deflection Angle for the Bucket
     3.2. Maximum Weight Of Water Being Raised

VII. 3D Graphics and Animations
  1. Identification of Parts
  2. Front Perspective Close-Up View
  3. Rear Perspective Close-Up View

VIII. Conclusion

IX. References
  1. General
  2. References for Mathematical Analysis

* * *

Preface: Summary and Objectives of this Research

The following study investigates an ancient water raising device invented in the 13th century by an Islamic inventor and engineer, al-Jazari. This invention is known as the Third Water Raising Device, which is found in the important treatise of al-Jazari Kitab ma‘rifat al-hiyal al-handasiya (The Book of Knowledge of Ingenious Devices) [1]. We explore hereinafter thoroughly the origin and genius of the inventor, al-Jazari, and his invention, with in-depth research and discussion from the evolution of the invention to the rudimentary components used.

The study is composed of 7 chapters and 12 appendixes (which can be navigated by using the Table of Contents below). In addition, mathematical analysis and 3D animations of the system are also included to further aid the reader in understanding the concept of the invention.

Chapter I introduces a brief history on technology in Muslim heritage. The scope of interest is focused on the various branches of Islamic technology, its educational system and the possible transfer of knowledge to the West. A comparison of Islamic and modern engineering concepts is also investigated.

In Chapter II, the life and environment of the inventor, al-Jazari, and his factors of innovation are investigated. All of which contributed to the compilation of his important work, The Book of Knowledge of Ingenious Devices. The importance of al-Jazari’s work as an engineering document is attributed to the various ingenious components and concepts included, most of which are of relevance and are used in modern-day engineering.

In Chapter III, the origin and development of the ancient water raising devices are summarised. These devices were invented as early as 2500 BCE and were driven by either animal or water power. The relevance of some of these designs to al-Jazari’s invention are discussed in Chapter V.

In Chapter IV, the evolution of the inventions is discussed, followed by a description of the system of the inventions. The possible problems that might be encountered during its operation are also discussed. The technical and mechanical aspects of the inventions are discussed in Chapter V.

In Chapter V, components ranging from the large scoop-wheel to the rudimentary bearings that al-Jazari used are investigated and discussed. References are made to relevant components of the ancient water raising devices. The materials available and unit scales, which he used to define measurements, are also discussed.

In Chapter VI, the mathematical analysis of the system of the invention is derived and discussed. The formulas derived have been programmed into a Microsoft Excel programme to estimate the head of the water jet, the force capable of raising the water and the weight of the water raised.

In Chapter VII, 3D graphics and animations are constructed, using 3D Studio Max R3.1, based on the findings on the research and mathematical analysis done. The 3D animations consist of a 360° rotational view movie file and another one that shows the movement of individual components during its operation.

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Figure 1: A miniature depicting a traditional scene of instruction.

They also knew the book of Mechanica by Hero of Alexandria and the book of Pneumatica by Philo of Byzantium. These and other Greek and Alexandria works served as a basis for their research in this domain [10].

The Alexandria school teaches a series of writings on various mechanical devices, gadgets and automata. This branch of science is called the ‘ilm al-hiyal’ in Arabic and had attracted the imagination of Muslims, fascinated with the unusual, ‘ilm al-hiyal’ itself has always been related in the Muslim mind with the occult sciences and magic, as the word itself whose roots means stratagem or ruse, shows.

In addition, many Muslim scholars also learn from the works of their predecessors. In accordance, a series of works describing complicated machines and gadgets can be found in various important works. From the treatise of the Banu Musa on the balance ‘qarastun’, those attributed to Ibn Sina such as the ‘Mi‘yar al‘uqul’ (The Standard of the Intelligence), to the work of the 13th century AD author Ibn al-Sa‘ati who describe the clock of Damascus [11].

Another important feature of the thinking behind many of the devices described in the treatises is the preoccupation of the Arab engineers with controls, particularly with controls that would allow a given machine to continue working for a long period of time without human intervention [12].

The above mentioned might also be the basis of teaching for al-Jazari and he in turn will also contribute to this method of teaching through his work, ‘Kitab fi ma‘rifat al-hiyal al-handasiya’ (The Book of Knowledge of Ingenious Mechanical Devices).

The Book of Knowledge of Ingenious Mechanical Devices is a compilation of writing on automata and the like, which were a source of wonder and served as pastimes for princes and rulers. It consists of six parts, fifty complicated mechanical devices such as clepsydras and fountains, some of practical use and others more for amusement, following the tradition of the Alexandrines. The treatise was translated from Arabic into Persian as late as the 19th century and because of the variety of its content and beautifully illustrated manuscripts found in relative profusion, has become the best-known work of its kind in the West after it had been studied by historians of science and of art since the 19th century [13].

4. Comparison of Islamic and Modern Engineering Concept

There are a few areas whereby there is notable difference between Islamic and modern engineering concept, namely in what concerns the use of mathematical analysis, the lack of sufficient resources and the use of various sources of power. These are further elaborated as follows.

4.1. Calculation (Mathematical Analysis)

The assumption for the Modern Engineering Concept is that engineering tasks must be accompanied by rigorous mathematical analysis. Whereas in the Islamic Engineering Concept of the past, most of the mathematical relationships that underlie the physical phenomena had not been identified, and engineers had to draw upon a large fund of practical experience. This is to say that the Muslim engineers of antiquity most probably didn’t do many calculations at all and obtain the best results through trial and error methods.

Of course, not all the work of Muslim engineers was so laborious; they had a clear understanding of arithmetic, plane geometry, and measurement, and they used these sciences to the full in the construction and assembly of their devices. But when a set of mechanisms was particularly complex and delicate, final assembly and adjustment were done by painstaking trial and error [14].

4.2. Limited Resources

The Muslim engineers most probably needed to have at their command all the contemporary scientific and technical skills available in order to obtain the best possible results from the limited resources at their disposal.

4.3. Source of Power

The Modern Engineering uses fossil fuel, water pressure, air pressure, nuclear energy etc. for its source of power whereas Islamic Engineering was essentially bases only upon the use of the effects of water pressure and air pressure.

5. Transmission of Islamic Studies

Islamic Studies obtained most of its knowledge from various ancient civilisations (see Fig. 3), and subsequently the transmission of knowledge from Islamic Studies to Europe was mainly by literary means and occurred on a large scale. However, the situation is completely different for Islamic Engineering, there are very few works in Arabic dealing with engineering, and the treatises that have survived were never translated into Latin nor, until recent time, into any modern European language.

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Figure 2: Two shadufs used to raise water from a river in Egypt.

2.2. The Archimedean Screw or Water-Snail

The Archimedean Screw or Water-Snail was probably invented by Archimedes, its origin are datable to about 250 B.C. and by Roman times it was widely used [43]. It consists of a helical wooden blade rotating within a barrel-like wooden cylinder with the lower end of the screw dipping into the water source while the upper end discharges into an irrigation ditch. The angle of the screw therefore determines its water output (see Fig. 5).

However, unlike the Shaduf, the device has not retained its popularity although it was still in common use in Upper Egypt and other parts of the Arab world in 1965, but had since disappeared from the Delta region [44].

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Figure 3: A giant Noria Wheel at Hama, Syria.

2.4. The Saqiya

The Saqiya, which is driven by animal power, was almost certainly invented in Egypt in the third century BC [47], and was known by Roman times, from about the start of the Christian era. It is probably the most widespread and useful of all the water-raising machines that medieval Islam inherited and improved (see Fig 7).

It consists of a chain-of-pots or potgarland, driven through a pair of gears by an animal moving in a circle. The animal pushes a drawbar through the circle, turning an axle whose pinion meshes with a cogwheel gear. This gear then turns the chain-of-pots, which consists of suspended earthenware pots between two ropes, carrying water. The chain-of-pots is optimal for raising comparatively small amounts of water from comparatively deep wells [48].

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Figure 4: Another depiction of al-Jazari's pump for raising water in a manuscript of copy held in Topkapi Sarayi Libray in Istanbul. (Source).

2. Description of the Device [51]

The Third Water-Raising Device was intended as a decorative attraction near an ornamental lake [52], with an element of mystification about it. Thence an ornamental lake erects an elegant open structure, with only its automata working parts visible to spectators, thus leaving the spectators curious on how the device is powered (see Fig. 8).

Consider the nature of al-Jazari’s working environment, it is most likely erected in the King’s garden, where it caused wonder and aesthetic pleasure to courtly circles and raised water for irrigation to the garden at the same time.

It was however, simply an elegant development of a utilitarian device that was used for supplying water for irrigation and domestic purposes. A development of the Saqiya, having the main difference of the device being powered by waterpower instead of animal power.

The structure itself is quite small, being divided into 2 sections; the lower chamber whereby the water driven mechanism is ‘hidden’ under the ground and upper chamber whereby the automated mechanism above the pool was made visible.

It consists of a copper pool with an escapement, whereby water flows into the lower chamber and drives the Scoop-Wheel. The rotating Scoop-Wheel in turn rotates the Cogwheel and Lantern Pinion gears, driving the vertical hollow copper pillar with an iron stanchion beneath it. The rotating pillar in turn rotates the second set of gears in the upper chamber, driving the Sindi Wheel that raises water to the head tank (this is seen in Fig 8 and in the reconstructed depiction in Fig. 9) [53].

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Figure 5: A 3D graphic of the Overshot Scoop-Wheel.

The first description of the Scoop-Wheel was by Philo of Byzantium. In his work, he introduce a water-raising device whereby a chain of buckets is driven by an Undershot Wheel with a series of spoon-shaped spokes arranged in a circle around the hub (see Fig. 13). In addition, Philo remarks that the wheel “can be applied to many other uses” [61].

It seems that Al-Jazari might have studied Philo’s work [62] and noticed the ingenious Undershot Wheel of unusual design set up to work a string of pots by a chain drive [63]. Later, Al-Jazari improved on its design by converting it from an Undershot Wheel to an Overshot Wheel and later echoed Philo’s remark by incorporating the Scoop-Wheel design as part of his striking mechanism in his various devices [64].

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Figure 6: A small low-powered Pelton wheel of the 1890s.

1.1. How did al-Jazari Invent the Scoop-Wheel Design?

Assuming that al-Jazari was ignorant of Philo’s work, as we claimed earlier, then it would be a reasonable assumption that he derived his Scoop-Wheel design from the principle of the Overshot Wheel and the Noria, which had a wheel for lifting water with buckets scoops fixed to its outer rim. However, even though we consider that he had based this design on Philo’s work, he must had to rely on the mechanism of Scoop-Wheel to power his invention.

1.2. Why did he Use the Scoop-Wheel Instead of the More Common Overshot Wheel?

The reason is that Al-Jazari was interested only with the innovative and ingenious water wheels, whereas ordinary wheels, such as the Overshot Wheel, were taken for granted and evoked no interest [66]. However, it is interesting to note that according to John Smeaton’s experiments, impact between a stream of water and a flat plate resulted in a marked loss of energy in the form of spray and turbulence. Thence leaving us to wonder did al-Jazari know about this or was it by a stroke of luck that he happened to use the curvaceous Scoop-Wheel instead of the flat-plated Overshot Wheel?

1.3. Why did he Convert the Undershot Scoop-Wheel to an Overshot Scoop-Wheel?

As mentioned before, al-Jazari had expressed awareness for the need to develop machines with a better design and greater output than the traditional ones. He might have done experiments on his own and most probably obtained the similar results [67]. Furthermore, his concept of the invention is to hide the lower chamber of the driven mechanism, allowing only the flow of water down, hence the Overshot Wheel design would have been more appropriate in this case.

1.4. Comparison between the Undershot Wheel and the Overshot Wheel?

First of all, we know that both wheels have been around since Vitruvius (100 BCE) who described them in his work