Engineering

Pumps

The Six-Cylinder Water Pump of Taqi al-Din: Its Mathematics, Operation and Virtual Design

Salim T S Al-Hassani* and Mohammed A. Al-Lawati**

Table of Contents

1. Preliminaries

1.1. Preface

1.2. Structure of the Article

1.3. Nomenclature

2. Water Machines in the Lands of Islam

2.1. The Science and Art of Water Management

2.2. Three Water-Raising Machines in Al-Turuq al-Saniya

2.2.1. The Pump with Two Opposing Cylinders

2.2.2. The Spiral Pump

2.2.3. The Pump of the Rope with Cloth Balls

3. Taqī al-Dīn and his Treatise: Historical and Textual Context

3.1. Overview on the Treatise Al-Turuq al-Saniya

3.2. Description of the Pump with Six Cylinders

4. The Functioning of the Pump: Technology and Operation

4.1. How Does it Work

4.2. Historical Assessement of the Six-Cylinder Pump

5. Mathematical Diagnostics of the Six-Cylinder Pump

5.1. Pipes, Cylinders and Pistons

5.2. The Connecting Rod, the Pivot and the Cam

5.3. Complementary Parts

6. Virtual Reconstruction of the Pump

6.1. Modelling and Animation

6.1.1. Modelling

6.1.2. Creating Objects

6.1.3. Modifying Objects

6.1.4. Assigning Materials

6.1.5. Creating Lights and Cameras

6.2. Animation

6.3. Computer Softwares

6.3.1. MathCAD

6.3.2. 3D Studio MAX

6.4. The 3D Model

6.5. By Way of Conclusion

6.6. Acknowledgments

7. Appendices

7.1. The Evidence from the Manuscript

7.2. References

***

1. Preliminaries

1.1. Preface

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Figure 1: Drawing of the six-cylinder pump as it was depicted in Taqī al-Dīn in Al-Turuq al-Saniya fī al-'ālat al-rūhaniya (Chester Beatty Library in Dublin, Arabic MS 5232, p. 38).

The main objective of this study is to investigate into the six-cylinder water raising pump described around 1550 by the Ottoman Muslim scientist Muhammad Ibn Ma‘rūf, known as Taqī al-Dīn, in his treatise Al-Turuq al-Saniya fī al-'ālat al-rūhaniya. Our study of this important machine consists of three major parts. The first covers some historical facts that give knowledge about the role of engineering and engineers. The second is centered on an engineering analysis of the water pump. The last obtains all the dimensions of the machine and provides a graphical model which was then used to produce a virtual 3D animation of the mechanical workings of its various parts, including the water turbine, the cam shaft, the connecting rods, the reciprocating pistons and the cylinders. The study is focused on the pump in order to verify its ability to work using modern engineering analysis.

1.2. Structure of the Article

The study is composed of seven sections. The first one is introductory whilst the layout of the remaining sections is as follows. The second chapter contains a historical background about the Islamic tradition of engineering and water raising machines. The glimpses we present about Islamic engineering give an idea of how engineering was practiced and what were the working fields for engineers. Our aim in this short survey is to know how metals and some other materials were obtained or manufactured. This will help to decide the type of the material and select the suitable mechanical properties for it.

The third section presents a concise biographical sketch about Taqī al-Dīn and the contents of his treatise, with the English translation of the relevant portions on the pump from the original manuscript. The fourth chapter explains the working of the device. The fourth and fifth sections represent the core of this study as they describe the machine and its components, explain its mechanical function and the various materials used.

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Figure 2: Parallel views of the virtual reconstruction of the pump.

The fifth section is mainly devoted to mathematical analysis to verify the mechanical adequacy of the different components. This analysis and related calculations show how robust the pump was, and whether it was capable of delivering the water to the required height. All the equations and formulas in this section were obtained from the sources (3), (4), (5), (6) and (9) [see the list of references in Appendix 7.4]. The values for some physical constants such as the coefficient of friction and the drag coefficient were found in the Data Book of the Department of Mechanical Engineering, UMIST, Manchester , UK.

The sixth section covers the modelling and animation part. Modelling the pump and animating its motion gives a better insight of its operation and helps to properly understand its operation and the linkages and dimensions of each component. This section ends on a conclusion drawn from the research and also contains suggestions for further work.

Finally, the last section is devoted to appendixes: a reproduction of the three pages of the original manuscript and a list of the main references used in the study.

Click here to view animation.	Click here to view animation.

1.3. Nomenclature

In this section, we present the list of symbols assigned to the different physical and mathematical magnitudes involved by our description of the six-cylinder pump.

* Hon. Chairman Foundation for Science, Technology and Civilisation, UK and Emeritus Professor at the University of Manchester, UK.
** Engineering Graduate, UMIST, Manchester, 2001.

by: FSTC Limited, Mon 21 July, 2008