The Mechanical Water Clock Of Ibn Al-Haytham

The Foundation for Science, Technology and Civilisation (FSTC) announces their new achievement in the history of Islamic clocks. For the first time, the work of Ibn al-Haytham on the water clock (Maqala fi ‘amal al-binkam) is uncovered and edited from two manuscripts. Whilst work is currently  undertaken to produce a critical edition of the text in a book that will be published in 2015, we are proud to publish a glimpse of this pioneering work of Ibn al-Haytham’s contribution on mechanical clocks. In this article Professor Salim Al-Hassani, President of FSTC, summarises the text and publishs its draft English translation. In addition, he describes the mechanism of the water clock and produces engineering diagrams as well as a 3D animation video of its working procedure. To verify the technical details of the description of the clock, a mathematical analysis was also carried on. Although rudimentary at this stage, this analysis, in conjunction with the drawings and video animation, should be useful in design replicas or models of this clock. This ground breaking article precedes the full historical editing work which is to be published by Professors Al-Hassani and Mohammed Abattouy in due course.

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by Professor Salim Al-Hassani, President of FSTC


This work would have not been achieved had it not been for the assistance of a number of people. Of special mention are: Prof. Mohammed Abattouy for his valuable assistance in editing the manuscript and in historical research, Prof. Hamza Kandor for providing digital copies of the manuscripts, Sara Tahboub for helping with the translation, Dr Stephen Burley for his assistance and advice with the mathematical analysis, and Abdul Kader Jahjah for his assistance with the drawings and interpreting of old Arabic engineering terms. We mention also the financial assistance received from from Zuhair Fayez and Dessert publishers, for which we express our thanks and gratitude.

Table of contents

1. About Ibn al-Haytham’s Life
2. The Manuscript Copies
3. Remarks about the English Translation
4. Description of the Clock
5. Mathematical Analysis of the Clock
6. Discussion and Concluding Remarks
7. The English Translation of Maqala fi ‘amal al-Binkam
8. Details of the Mathematical Analysis
9. References

Imaginary potrait of Ibn al-Haytham (Source)

1. About Ibn al-Haytham’s Life

Abu ‛Ali al-Hasan Ibn al-Haytham (965-1039 CE) was born in Basra, Iraq, around the year 965 CE (354 H). His scientific career began in Basra, but most of it flourished in late 10th and early 11th- centuries Fatimid Cairo, founded in 972 CE. Also known in Europe by the name Alhazen, since the translation of his works into Latin in the 12th century, he completely changed his contemporaries’ understanding of light and vision. In searching for knowledge and truth, Ibn al-Haytham questioned and tested on many subjects, in physics and astronomy, especially in optics. His opus magnum Kitab al-Manazir (The Book of Optics) influenced the scientists who came after him in the Arabic and Latin traditions, from Kamal al-Dinal-Farisi (d. 1319) until Johannes Kepler (d. 1630). He died in Cairo in around 1040 CE (431 H).[1]

Ibn al-Haytham is most renowned for his achievements in optics, although he made considerable contributions to mathematics, astronomy, medicine and chemistry. According to Ibn Abī ’Usaybi‛a, the author of Tabaqat al-Atibbā’, Ibn Al-Haytham left some 200 treatises, including commentaries on the works of Greek scholars and Galen. Besides physics and optics, Ibn Al-Haytham wrote nearly in every subject, in botany, medicine, engineering, mathematics, logic and metaphysics, warfare, ethics, and even in religious issues. He also wrote tracts on moonlight, starlight, and the determination of the direction of the Qibla.

From the lists of his works quoted by Ibn abi Usaybi’a and Ibn al-Qifti and based on modern historical studies, it is not known that Ibn al-Haytham authored other texts in engineering than the Maqala fi al-Binkam. That is why this piece of his writing is of rare value and very important.

2. The Manuscript Copies

The manuscript under consideration is the Maqala fi ‘amal al-Binkam. It is extant in two copies preserved in the Süleymaniye Library in Istanbul, under the following shelf marks: Atif Efendi collection, MS 1714, item 8, folios 77r-82v and Fatih collection, MS 3439, item 8, folios 138r-140r. Extracts from both manuscript copies are produced below in figures 1 and 2.

Fig. 1. First page of Ibn al-Haytham’s Maqala fi ‘amal al-Binkam in MS Fatih 3439, folio 138r

Fig. 2. First page of Ibn al-Haytham’s Maqala fi ‘amal al-Binkam in MS Atif 1714, folio 77v.

The two copies present the same text, with significant variant readings, and they complete each other for the reconstruction of an excellent scientific text on the description, use and functions of a specific water clock, which has no other similar specimen in the Islamic tradition of technology.

3. Remarks about the English Translation

The English translation of the text is based on the critical edition of the Arabic version. There were a number of challenges, which had to be met before a final acceptable English version has been reached. There was a need for not only the usual editing methodology but also for expertise in old Arabic terminology for engineering technical terms. In a number of instances we had to resort to several old texts such those by Banu Musa, Ibn Ridhwan al-Sa’ati and Al-Jazari to converge onto an acceptable meaning of a particular term. The result is a reasonable translation, which we hope will add to knowledge in this important field.

The full text of the translation is given below in an Appendix at the end of the article, at section 7.

4. Description of the Clock

In his description, Ibn al-Haytham gives details of the water clock. He describes it as a new invention in that it gives hours and minutes, which no other clock gave before his time. He refers to making and manufacturing as well as testing by trial and error, as well as calculations.

We notice that he uses a cylinder with a small hole at its base as the prime mover for telling the time. As this cylinder sinks downwards into another tank, which contains sufficient amount of water, it resembles an inflow clepsydra.  This is unlike the clepsydras used of the Antiquity, which were later adapted by Muslim engineers Al-Muradi, Ibn Ridhwan al-Sa’ati and Al-Jazari, all of which were outflow clepsydras. It is interesting that Ibn al-Haytham should use this technology for the control of his clock instead of the outflow clepsydra, which should have been well known in Cairo at the time when he was in Egypt.

The sinking-bowl water clepsydra seems to have been invented in India in the early 5th century CE. Inflow clepsydras appeared in China during the Han dynasty (206 BCE-8 CE), soon after the time of Ctesibios, though there is no known connection. Tan Zheng produced inflow clepsydra that survived for a millennium, and which were drawn and described in the 11th century. Chinese engineers also struggled with the problem of keeping the flow uniform. It is therefore, possible that Ibn al-Haytham based his design on ideas coming from the East, which he acquired whilst he was in Basra. This city was an active seaport, where such technology could have reached. The Indians call the inflow clepsydra “Ghatika Yantra.”[2]

The use of the inflow clepsydra is not new but Ibn al-Haytham has used it to determine hours and minutes and designed the scale for telling the time, overcoming the problem of non-uniform motion of the sinking cylinder.

Basically the sinking cylinder is attached to a rope/string, which after passing over pulleys is connected to a shaft and a bearing onto which a circular disc is mounted.  As the cylinder sinks vertically and concentrically into an outer cylindrical tank, the string rotates the disc about its own horizontal axis, see figures 3 and 4.

Fig. 3.  A sketch of the clock based on the description of Ibn al-Haytham.

Fig.4. A line diagram shows the circular disc connected to the cylinder via a rope/string.

Ibn al-Haytham graduated the disc into 24 divisions that can tell the hours with subdivisions to reveal a fraction of an hour up to minutes. He calibrated each division such that one hour elapses between one division and the next. The cylinder is designed to sink in 24 hours. The marked division on the disc pass by a pointer to tell the time, see fig.5. A close up view of the divisions showing minutes is given in fig.6

Fig. 5. The upper portion of the disc passes by the pointer to indicate the time.

Fig.6. A close up view of the divisions showing, half, quarter and minutes.

The pointer is fixed separately from the disc. It is possible that the disc is placed inside a box which holds the pointer. The cylinders may be placed further away from the disc container so that the observer only sees the disc box. The string can be made sufficiently long to allow for the distance.

Fig.7. A pointer is mounted on top of the clock box. The circular disc protrudes from the top of the box. The distal end of string is connected to the cylinder, not shown in the diagram.

The calibration of the clock is thoroughly explained. Ibn al-Haytham goes through an elaborate method of calibrating the time using another one hour “Binkam” (possibly a clepsydra), with the help of two observers. By trial and error and with the use of small copper weights dropped into the inner cylinder (now used independently in another shallow outer tank, he fixes the duration of the sinking such that the cylinder hits bottom after one hour. He would also enlarge the diameter of the orifice to make it sink faster.

If however, the sinking has to be slower he suggests plugging the hole and drilling another larger hole nearby in the base. He also uses a small stopper tube at outer mouth of the hole at the bottom of the cylinder. This will stop dirt, gathered at the bottom of the outer tank from going inside the cylinder. When the cylinder is calibrated (hole diameter fixed and added weight attached), the cylinder is mounted into the big outer tank and the rope/string attached at one end to  the top of the cylinder and the other to the bearing shaft of the circular disc passing around appropriate pulleys.

The marking of divisions on the circular disc is explained in a slightly confusing manner as there is reference to celestial sphere, the full celestial cycle,  armillary sphere, ruler (sometimes to mean the scales on the outer periphery of the disc) and sometimes to divisions and subdivisions.  The two observers used in the calibration process communicate with each other at the time when each hour is passed so that an appropriate mark is made on the disc. This then is divided into sub-divisions for parts of the hour and for minutes.

Ibn al-Haytham divides the full 360 degrees into 24 sectors, making each sector subtending 15 degrees. He takes great care in ensuring accuracy of the divisions of the hours and minutes to allow for the changes due to the slightly non-linear motion of the cylinder. He mentions that the cylinder goes faster as it goes deeper; hence the divisions become larger nearer the 24hour end. He does, however, mention that the variation is almost unrecognisable. 

Ibn al-Haytham solved the problem of the need for the inner cylinder to move concentrically inside the outer cylindrical tank by using a framework inside which the inner cylinder slides, see Fig.8.  The framework is constructed from two rings separated vertically by 4 metal vertical spacing bars to form a cylindrical frame. The rings are made from copper bars of rectangular cross section and bent and welded into a full circle.  The lower identical ring is connected to 4 other bars, which radiate outwards, see Fig.10. The ends of each of these radial bars are welded to the lower ring. The distal ends of each radial bar will be welded onto the inner wall of the outer cylinder. The fixed frame now allows the inner cylinder to loosely slide and down inside the rings:

Fig.8. Method for ensuring concentric sliding motion of inner cylinder using rings and bars.

Fig. 9. The guide metal frame before welding onto the inner surface of the outer tank.

Ibn al-Haytham had to face the challenge of the need for continuous un-interrupted time by making two identical clocks resting next to each other, see Fig.10. As the first clock nears the 22nd hour, he would start the second clock synchronised with the first such that when the first one reaches 24 hours the second clock reaches the beginning of its cycle. In this way he avoids down time for resetting the clock.

By using two clocks, Ibn al-Haytham was able to avoid down time for resetting the clock. The second clock is synchronised to coincide with the first clock at the latter hours.

Ibn al-Haytham does not explain how the water removed from the cylinders. He could have used the string to pull the inner cylinder out. This would require the use of the pulleys and some crank arm to winch the filled cylinder. This could be a heavy load to bear by the pulleys. There is no reference to a draining orifice in the outside cylinder. It would take too long time to drain the inner cylinder through the small orifice hole. Used for allowing the inflow. On the other hand he could have used siphons to empty both the cylinders. The latter seems the easiest and it could have been used. 

The Clock in 3D Animation

All the engineering line diagrams of the clock were based on Ibn al-Haytham’s description, see Appendix. The engineering drawing drawings were then used to produce 3D animations of the clock. The animations are produced in a video film. To see it in action, press Ctrl and click on Fig.11.

Fig. 11. 3D animation video of the reconstructed model of Ibn al-Haytham’s clock. Click to see film.


5. Mathematical Analysis of the Clock

The simplest mathematical model to consider is that for a cylinder of thin walled metal opened at the top and closed at the base by a circular disc. The disc has a small diameter hole at its centre. The whole is first plugged in so that when the cylinder is placed in water it sinks to a height of equilibrium. This equilibrium is reached when the buoyancy force equates the combined total weight of the cylinder and the base plate.

If the hole is unplugged the water will start filling the inner space of the cylinder and the cylinder commences to sink towards the bottom.  The analysis is rudimentary and uses a simple model of the cylinder without allowing for the friction forces between the guide frame and the outer surface of the cylinder nor between the rope and the pulleys nor between the disc mounting and its axil.

The cylinder is closed by an end plate of thickness b. The cylinder is sunk initially under its own weight below the water surface. As the water goes into the cylinder through the orifice hole, the water level inside it reaches a value labelled, depth, with the surface of the water is now below the water surface outside the cylinder. The difference between the two surfaces levels is labelled, head, see Fig. 12.

A sketch of the model used in the mathematical analysis.

The outer cross-sectional area of the cylinder is Ao The outer diameter is Do . The cross-sectional area of the inner cylindrical space is Ai and the cross-sectional area of the wall material thickness is At . The total length of the cylinder is, len.

The list of variables and the full analysis are given in an Appendix at the end. In this analysis a practical case is chosen for evaluation.

The equations use the force balance between the weight of the cylinder and the buoyancy forces as well as the fluid flow rate through the orifice hole to predict the variation of the depth with time for the duration of 24 hours.  

6. Discussion and Concluding Remarks

This paper gives a rapid examination of the clock that Ibn al-Haytham describes as being unique and “none like it before”. He actually gives an important view on all previous clocks that they do not produce accurate timings not have sufficient information on hours and minutes. Because of this shortcoming he decided to embark upon making this clock.

Both manuscripts were produced in modern Arabic fonts and then a single critical edition is produced. The full work is the subject of a separate book to be published shortly.

It is not known why Ibn al-Haytham chose to use an inflow clepsydra type instead of the out-flow type which was frequently used by the Greeks.  It could be that he was in Basra when he described his clock, where Indian technology would have reached. It is also difficult to explain why Muslim engineers who came after him did not refer to this clock.

Ibn al-Haytham goes to great length to describe in detail the manufacturing method and materials of each component of the clock. He describes the calibration technique and the trails and errors of each run so that the clock can reflect time accurately in the form of hours, half hours, quarter hours and minutes.

He mentions that the cylinder sinks at a faster speed as it gains more water inside it. He allows for this by calibrating the rotating disc dial such that the spacing’s between the hour divisions become larger nearer the end of its rotation. However, he mentions that the difference is negligible.

We have attempted to produce engineering drawings of this clock and its various components based on our understanding of his description.  In order to clarify its working mechanism, the clock was produced in rendered 3 D animations which were made into a video in colour.

In order to verify the workings of this clock and check that our understanding of the mechanism described by Ibn al-Haytham, we carried out a mathematical analysis of the motion of the sinking cylinder.

The parameters for the practical case chosen were fed into the analytical model. The model predicted the variation of the depth with time.

We notice that the chosen cylinder sinks almost in a uniform speed during the 24 hours period. The degree of non-linearity is small. This confirms the statements of Ibn al-Haytham.

A more sophisticated model is required. However, the governing parameters are related through equations and hence the design can easily be varied to suit different materials, sizes, etc. This then can be used to produce clock models of different sizes. For more sophisticated analysis a  “Finite Element” computational fluid-solid interaction model should be built.


The English Text of Maqala fi ‘amal al-Binkam

"In the name of Allah, the Most Gracious, the Most Merciful.

May God ease this task and end it with goodness."

The Epistle of Al-asan Ibn al-Hasan Ibn al-Haytham on the Water Clock

One of the indispensable means of telling the time, estimating the movements and calculating the parts of time is the water clocks by which t