Al-Jazari's Third Water-Raising Device: Analysis of its Mathematical and Mechanical Principles By Salim T. S. Al-Hassani* and Colin Ong Pang Kiat** 1. 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) . 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. Considering the vast areas of the Muslim World, the history of engineering in Muslim heritage, particularly that which relates to agriculture, must be very rich. Yet the materials or treatises available are very limited, considering the minute effort being spent in this field, except the works published so far by Eilhard Wiedemann, Fritz Hauser and Donald Hill. The latter being the most important contributor to this research, whereby most of his works are emphasised on al-Jazari's Fi ma‘rifat al-hiyal al-handasiya (The Book of Knowledge of Ingenious Mechanical Devices) . However, despite all the research undertaken in the last decades, the field of Islamic technology is still under-investigated. In this regard, Donald Hill declares: "As far as I am aware, there has been no archaeological study of medieval Islamic technology, nor any detailed technical examination of those machines, which still exists, such as the noria at Hamat, Syria." Our aim in this study is to contribute to this investigation by analysing al-Jazari's Third Water-Raising Device, showing the technological innovation represented by the invention of this machine. One of our main tools in that will be to rely on the construction of 3D graphics and animations as visual aids for better understanding of the device. This work was carried out by undertaking the following tasks: * Research into technology in Muslim heritage; * Research into al-Jazari's life, environment and work; * Research into the development of the water-raising devices; * Analysis of al-Jazari's Third Water-Raising Device; * Analysis of the innovation of the invention of this machine; * Analysis of the technical aspects of the invention; * Analysis of the mechanical aspects of the invention. * Mathematical analysis of the invention; * Construction of 3D graphics and animation; * Evaluation. Table of contents 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 End Notes  The treatise survived under another title: Al-Jāmi‘ bayn ‘l-‘ilm wa ‘l-‘amal al nāfi‘ fī sinā‘at al-hiyal,. [A Compendium On The Theory And Practice Of The Mechanical Arts]. For more details, see FSTC, 800 Years Later: In Memory of Al-Jazari, A Genius Mechanical Engineer.  Even though the machinery in the lower level was hidden from viewers and the cow was a wooden dummy, the pump was an entirely automatic design, powered either by the water turbine in the lower level, the upper horizontal axle drove the sindi wheel carrying the yellow belt with its attached water-pots to lift water to the upper level.  For more details, see Appendix 1. * Foundation for Science, Technology and Civilisation, Chairman of the Board, and Emeritus Professor at the University of Manchester. ** Final Year Student (2001), Mechanical Engineering, MACE, University of Manchester, UK.