jeudi 18 août 2011

Nouvelles considérations sur les techniques de construction des anciennes pyramides égyptiennes, par le Professeur Frank Müller-Römer

Le Prof. Dr.-Ing. Dr. phil. Frank Müller-Römer (né en 1936) est président du Collegium Aegyptium, dans le cadre de l’Institut d’égyptologie et de coptologie de la Ludwig Maximilians Universität de Munich (Allemagne).
Ce spécialiste en techniques de communications, de réputation internationale, a fait ses études à l’Université technique de Stuttgart, où il a obtenu son diplôme d’ingénieur en 1962. Il a ensuite occupé différentes fonctions chez Siemens AG à Stuttgart, Reutlingen et Munich. Il a été Directeur technique de la Bayerischer Rundfunk (Radio bavaroise) de 1975 à 1994. Il a toujours œuvré pour le développement permanent de la radio et de la télévision, notamment en participant à plusieurs groupes de travail créés par les stations de radiodiffusion de la République fédérale d’Allemagne. 
Il est l’auteur de nombreux articles et de monographies publiés dans l’Europe entière.
Au terme de sa vie professionnelle, il a entrepris de se consacrer à l’égyptologie. Ses recherches ont fait l’objet de publications en langue allemande, dont une “dissertation” (thèse de doctorat) sur les pyramides de l’Ancien Empire : “Pyramidenbau mit Rampen und Seilwinden – ein Beitrag zur Bautechnik im Alten Reich“ (2008). Une synthèse en anglais de cette publication a été publiée sous le titre “New considerations on construction methods of the Ancient Egyptian pyramids”.
Le Professeur Frank Müller-Römer m’a accordé, à titre exceptionnel, l’autorisation de reproduire ce texte dans son intégralité (il fera l’objet de plusieurs notes successives de ce blog).
Qu’il en soit très cordialement remercié.

“The pyramids of the Old Kingdom have always fascinated visitors of Egypt by their astonishing size and the vast proportions of the stone blocks. Not only do they leave a lasting impression, but they also prompt questions such as why did the ancient Egyptian kings build such gigantic burials ? In searching for answers, we have grown accustomed to viewing the construction of the pyramids in the context of the religious mindset and the society of the time, and also in relation to the technical facilities and logistic proficiency of the ancient architects.
Throughout the past centuries, Egyptologists, archaeologists, engineers, and amateurs have
attempted to explain the techniques and processes involved in the construction of the pyramids. However, as Egyptologists and archaeologists are not usually specialized to deal with the technical aspects of the construction process, many assumptions widely acknowledged in the academic world are flawed in this respect. On the other hand, authors without conventional training in Egyptology have made interesting contributions to the discussion of construction issues, adding remarkable explanations and calculations, but frequently they have overlooked important archaeological evidence. Consequently, the suggestions of ‘non-archaeologists’ are, as it were, less than well accepted among academic Egyptologists.
With reference to issues such as construction process, timing, technical devices, and workforce employed in the construction of the pyramids of the Old Kingdom, no conclusive explanation has been proposed so far, despite the wealth of books and articles published on the subject.
In the present study I shall suggest a new solution to the construction of the Step Pyramids (1) of
the Old Kingdom, starting from current research in Egyptology and taking into account
archaeological evidence, taking particular care to avoid internal contradictions. (2) I base my
analysis on the following assumptions :

- only tools, transport devices and construction techniques proven by archaeological evidence to have been available in the Old Kingdom can sensibly be assumed to have been employed ;
- the same applies to the architectural characteristics and construction techniques of the Old Kingdom pyramids ;
- not only technical aspects should be taken into account, but also safety issues concerning the casing and its subsequent smoothing, as well as secure accessibility of the respective construction site ;
- backsighting must have been possible on a regular basis throughout the building process ;
- building time calculations based the construction hypothesis developed in the following discussion are presented for several pyramids.

Construction techniques in the Old Kingdom
The laws of statics and mechanics were neither explored in theory nor by scientific experiments throughout the Old Kingdom. There is no evidence for any sort of static reckoning similar to that which we are accustomed to today. Proficiency in construction, as in other crafts, was developed through observation of nature and by experience, and thus brought to perfection. The techniques employed in the production of columns, architraves, obelisks, and so forth, as well as the relevant means for building and transport, continued to evolve, culminating in the Late Kingdom. For example, alterations in work processes or construction techniques would emerge on the grounds of experiences made with different types of material like local bedrock. Indeed, if one may say so, solutions to construction issues tend to be as ‘simple’ as the available techniques.
On the other hand, the construction of the pyramids is unthinkable without extensive preparation and detailed plans. Exact schedules for each task and a highly sophisticated infrastructure were indispensable. Choosing quarries yielding adequate material and finding a site suitable as a harbor for the shipping of material, surveying the pyramid’s base area and orienting it, calculating and providing, marking and storing of building material were tasks that required an experienced and exceedingly well-organized team. We have evidence that in the Middle Kingdom stone blocks were inscribed with precise descriptions comprising the date of production, the mason in charge, the transport pathway, the storage area, and so forth. (3) It seems reasonable to assume that a comparable level of organization also existed in the Old Kingdom.
Preparations for work in the entire construction area required painstaking organization. Similarly, regulations were needed for transfer of material from the quarries and the harbor, and also for the recruiting and maintenance of the workforce. Just looking at the number of blocks and the building time as such, we must inevitably conclude that some sort of ‘just in time’ principle was employed to coordinate quarries, harbor, storage, and building site.
Unfortunately, no construction reports are available for the Third and Fourth Dynasties. However, a pictorial representation from the tomb of the royal architect Senedjem-jb Inti, dated to the late Fifth Dynasty, can be regarded as proof that the owner of the tomb was in charge of a plan for the pyramid complex of King Djedkare Isesi. (4)
Considering the life expectancy of the ancient Egyptian rulers, the building schedule for the pyramid complexes was extremely tight. Works at several stages of construction must have been carried out in various areas of the site at the same time.
Much information pertaining to ancient Egyptian craftsmanship can be found in pictorial representations, notably reliefs in tombs of the kings’ relatives and officials. Such representations can be compared to other archaeological evidence, and conclusions can be drawn with reference to the reconstruction of long-forgotten techniques. Below, I shall discuss some construction techniques that have emerged from such research with reference to the relevant archaeological findings and sources.
Notably, the sarcophagus of Khufu, the first known sarcophagus of the Old Kingdom to be made from granite, has been extensively studied, and it has been proven that copper saws in combination with sanding were used to accomplish its remarkable exterior design. (5) Further to this, Stocks has published an in-depth study of the usage of saws, including documentation of experimental approaches and other aspects of stone working. (6)
Drills are shown on various representations from the Old Kingdom period. Borchardt, for example, refers to a picture of a drill for carving hollow vessels from the Fourth Dynasty. The drill has a forked shaft, and pieces of flint could be inserted as drill bits depending on the required diameter. At its upper end, an arched crank handle is attached, together with two stones on ropes that serve as weight and flywheel at the same time. If pressure is kept constant, the stone weights assure an accurate centering of the drill’s working end. In the tomb of Ti in Saqqara, a workman is depicted with a drill of this type (fig. 1).
The simplest lifting device attested from the Old Kingdom onwards is a wooden lever beam. It enables the user to lift heavy weights attached to the shorter arm with relatively little force by moving the longer arm of the lever. This method was used to loosen stone blocks from the bedrock in the quarries of Giza, and also for laying and adjusting stones for the pyramid’s core and casing.
The usage of drills and lever beams bears witness to the fact that in the Old Kingdom, the functioning principle of cranks and rollers was already understood and put to practical use ; the principle of force intensification was therefore known implicitly.
Fig. 1 The workman from the tomb of Ti (7)

There is ample evidence for devices needed for lowering and lifting of heavy weights in Ancient Egypt. The earliest evidence is a bearing stone used to erect building elements by means of rope deflection. It was found on the site of the Valley Temple (possible harbour area) of Menkaure and is dated to the Old Kingdom (fig. 2). (8)
Fig. 2 Bearing stone

Arnold suggests that it was used in a wood structure. (9)
Fig. 3 Bearing stone in use, as reconstructed by Arnold

In the upper part of the antechamber of the pyramid of Khufu, semicircular grooves can be seen in the West wall, which served as rests for wooden rollers used for lowering the plugging blocks. (fig. 4)
Fig. 4 Grooves in the wainscot of the antechamber in the pyramid of Khufu (10)

Thus, on the basis of archaeological finds (rollers embedded in semicircular grooves - fig. 4 -
together with fixed rope redirection devices - fig. 2 and fig. 3), it can be argued that the principle of force redirection was known the Old Kingdom. Furthermore, mobile disk wheels (sheaves) are attested for the Fifth Dynasty. Therefore, mobile wooden rope rolls, functioning according to the winch principle, may already have existed in the Old Kingdom.
Consequently, while pulleys as such are not documented for the Old Kingdom, they cannot be
discounted altogether. (11)
In a tomb at Lisht North, three wooden rope rolls were found, which were obviously used for guiding two ropes each (unpublished information, fig. 5). Arnold initially dated them to the late Twelfth Dynasty, that is, to the Middle Kingdom. (12) Later, they were used for lowering a limestone slab which displays two drill holes for attaching the ropes. This is the earliest evidence for rope redirection by means of a roll revolving on a roller. However, one of these rope rolls kept at the Metropolitan Museum in New York is now dated to the Nineteenth or Twentieth Dynasty. (13)
Fig. 5 Wooden roll with two guide grooves for ropes (dated either to Twelfth or Nineteenth toTwentieth Dynasty)

Rolls such as these can be used to construct a pulley. Further similar rope rolls, including some larger ones, are documented for the New Kingdom (fig. 6). (14) At Deir el-Medina, in tomb no. 1353 which is dated to the Eighteenth Dynasty, a revolving roll on a roller, or respectively a winch, with a raffia rope was found.
Similarly, Lauer describes a wooden rope roll discovered at the site of the pyramid of Djoser at Saqqara, which was apparently intended to revolve on a roller, and thus used for rope redirection (fig. 7). (15) However, Clarke and Engelbach argue for a Roman dating of this redirection roller, (16), while Arnold dates it to the Late Period. (17)

Fig. 6 Rope roll (Eighteenth Dynasty)

Arranged on a round beam with a diameter of approx. 8cm, it served as a kind of sheave in a bearing device. The round beam seems to have rested on supports at either end. From this model, a clearance of approx. 60cm can be deduced as a basis for the following calculations.

Fig. 7 Rope roll from the site of the pyramid of Djoser

In order to estimate the force which the rope roll is intended to redirect, I base my calculcations on a maximum resistance to bending stress of 1000 kg/cm² for hardwood (18) and 750 kg/cm² for nile acacia. (19) A total diameter of approx. 10cm can be deduced from the rope roller’s width and from the fact that it would have needed to rest safely on the round beam. Resistance in the rope roll’s middle must therefore be at least 125 cm³ ([radius 5 cm]³), so that the resulting bending moment amounts to 125 000 (hardwood) or respectively 93 750 kgcm (nile acacia). (20) Thus, the maximum force to be redirected amounts to 4 167 or 3 125 kg respectively. (21) For a redirection roll with an integrated roller and an estimated diameter of 15 cm, the maximum force to be deflected amounts to 14 067 or respectively 10 547 kg.
Rope rolls of this type in various designs and measurements were used in Ancient Egypt for force redirection, including heavy loads and transport on sloping ground. The pyramid of Khufu is the first building in which rollers were employed for controlled lowering of plugging blocks. Later, in the antechamber of the pyramid of Menkaure, the same principle was employed.
Therefore, the use of redirection rollers should be taken into account when discussing lifting and lowering of loads and transport across inclined planes. Such connections between the various groups of archaeological evidence have not previously been discussed to satisfaction, but it emerges that a well-functioning system of lifting devices must have been available in the Old Kingdom from the Fourth Dynasty onwards at the very least. In fact, the combination of lifting devices and an inclined plane is virtually the only way of explaining how the gabled roofs in the pyramid of Khufu, or the burial chambers built in open cut construction as used in the pyramids of the Fifth and Sixth Dynasty, or even the gabled roof in the burial chamber of Djedefre in Abu Roash were built. Constructions such as these require lifting devices combined with slopes or ramps (inclined plane).
Building material and similar objects were conveyed on a level plane by means of sledges. Several pictorial representations from tombs of officials of the Old Kingdom show transports of statues and other goods on sledges. In a relief from the tomb of Hetepherakhti, a highranking official from Memphis (Fifth Dynasty), (22) two bulls are pulling a device possibly made from wood, upon which the statue is secured against falling or shifting (fig. 8).

Fig. 8 Transport of a statue – two bulls pulling a carriage, from the tomb of Hetepherakhti

One of the principles of Egyptian construction technique was to pull, rather than lift, large or heavy stone blocks. This was the case for transports to the building site, and for bringing the blocks into their definite position. An inclined plane, or ramp, was commonly used, as is attested by a remarkable number of Old Kingdom ramps connecting quarries and pyramid sites, and by the causeways.
When towing crews or draught animals are employed to pull loads on ramps, it is a necessary
precondition that frictional force R

R = (μ [coefficient of friction] (23) · Q [load] · cos α [Angle of elevation of the plane])

exceeds the gravity forces on batter, for only then backwards sliding of the sledges can be prevented, as they stop automatically whenever the towing crew pauses or a rope tears. Striction of each transport object is determined by the contact surfaces and the normal force exerted on its support by the object. In the present case, it has to exceed kinetic friction by about 20%. However, it is easily overcome when additional thrust is applied, or by means of leverage.
Thus, a maximum slope of approx. 15° results for our ramp when we take into account the coefficient of friction applicable when stone blocks are conveyed on ramps covered with sand or gravel. (24) Transport ramps with a lower coefficient of friction (smooth stone surface, wet surface, facilitation of bull carriage towing by round beams positioned on the track horizontally (25) may not exceed a slope of 8° with a view to prevention of backwards sliding, as explained above. Accordingly, the slope of the ramp at the Mortuary Temple of Menkaure is approx. 7°, the ascent from the Valley Temple of Khafre and his pyramid is 6°26 and the angle of the ramp running from the quarry in the South toward the pyramid of Khufu is 6° (with a slope of 10%). (27) Under such circumstances, it is easily explained how bull carriages could haul stone blocks weighing up to 200 tons to the Mortuary Temple of Menkaure, or respectively blocks of up to 425 tons to the Mortuary Temple of the pyramid of Khafre. (28) Stops were possible whenever necessary, as stiction would prevent slippage.
Only the small Layer Pyramids of Lisht, Meidum and Sinki have perpendicular ramps which were used in building the pyramid itself. Other than that, only ramps that delivered material to the area surrounding the immediate construction site are attested. No sufficient amount of ramp material has been found in the necropolis areas, not even in the case of pyramids that were abandoned in mid-construction. (29) Disposal sites attested in the pyramid area of Giza consist largely of a mixture of limestone, gypsum and tafla without any obvious remnants of Nile mud. They are usually interpreted as waste that was disposed of during the building of the pyramids. (30)
This being the state of archaeological research, one cannot but draw the conclusion that a building technique was used during the Old Kingdom which did not depend on perpendicular ramps that required enormous amounts of building material as their height had to be gradually increased throughout the construction process.
Steep ramps displaying a gradient ratio of 2:1 (26°33’54’’) with only minor exceptions to this rule are used in the pyramids of the Fourth Dynasty for downward and upward bound corridors. Hence, steep ramps are attested in the Old Kingdom. (31) However, in these cases it is unlikely that the loads were pulled by towing crews and bulls.
In the Debeheni Mastaba at Giza, dating to the early Fifth Dynasty, a depiction of a ramp with a gradient of 2 : 1 from the Old Kingdom is preserved (Fig. 9). (32)

Fig. 9 Ramp from the tomb of Debeheni as published by Hassan

It is also interesting to consider the picture of a ramp from the tomb of Rekhmire (TT 100 Thebes West) although it is dated to the Eighteenth Dynasty (fig. 10). To the right, three walls or columns can be seen, the intervals between which are filled with brick walls. To the left, a ramp runs towards a building under construction, apparently enabling upward transport of stone blocks to the next layer. The gradient ratio of the ramp is 10:5, or 2:1 (26.5°)
Fig. 10 Brick ramp, from the tomb of Rekhmire (33)

à suivre : deuxième partie

(1) With the term ‘Step Pyramids’, I refer to buildings with a stepped core, resembling a series of platforms built one on top of the other, each smaller than the preceding one. The outer walls of the steps consist of large, finely hewn blocks with a batter of about 80°. To fill the core, stones of varying format were used, and also rubble, gravel, tafla, and mortar.
(2) Müller-Römer, F. 2011. Der Bau der Pyramiden im Alten Ägypten. Utz, Munich.
(3) Arnold, F. 1990. The control notes and team marks. New York, 14.
(4) Stadelmann, R. 1990. Die großen Pyramiden von Giza. Graz, 248.
(5) Stocks, D.A. 1999. “Stone sarcophagus manufacture in Ancient Egypt,” Antiquity 73, 918-922.
(6) Stocks, D.A. 2003. Experiments in Egyptian Archaeology. Stone working technology in Ancient Egypt. London.
(7) Steindorff, G. 1913. Das Grab des Ti. Leipzig, pl. 134.
(8) Reisner, G.A. 1931, Mycerinos. The temples of the Third Pyramid at Giza. Cambridge MA : Harvard University Press, 276 pl. A.
(9) Arnold, D. 1991. Building in Egypt. Oxford: Oxford University Press, 283.
(10) Petrie, W.M. Flinders 1883. Pyramids and Temples of Gize. (London, 1883), pl. 12.
(11) Stadelmann, R. 1990. Die großen Pyramiden von Giza. Graz, 135.
(12) Arnold, D. 1991. Building in Egypt. Oxford: Oxford University Press, 71 and 103 with n. 56 (text pertaining to note 55).
(13) &OID=100027095, accessed 24 October 2010, 11:30 am.
(14) Bruyère, B. 1937. Les Fouilles Deir el Médineh 1933-1934. Cairo: Institut Francais, 122 fig. 54.
(15) Lauer, J.-P. 1936. La Pyramide à Degrés. Vol. 1: L’Architecture : Texte. Cairo: Institut Français d’Archéologie orientale, 52.
(16) Clarke, S. and Engelbach, R. 1930. Ancient Egyptian Masonry. London: Oxford University Press, 44 n. 2.
(17) Arnold, D. 1991. Building in Egypt. Oxford: Oxford University Press, 71.
(18) dos Santos, A. 1998. “Theorien zur Bautechnik der Großen Pyramide” In Kemet 7 (3) 27 sqq. – According to Croon, African Bulletrie wood resists strains of up to 2000 kg/ cm2 (Croon, L. 1925. Lastentransport beim Bau der Pyramiden. Dissertation. Hannover : Buchdruckerei des Stephanstifts)
(19) Croon 1925, 42 sqq.
(20) The bending moment is defined as the resistance moment multiplied by bending strength.
(21) The maximum force to be deflected results from dividing bending strength (125 000 bzw. 93 750 kgcm) by half the clearance (30 cm).
(22) Mohr, H.T. 1943. The Mastaba of Hetep-her-Akhti. Leiden: Brill, 36 fig. 3.
(23) The friction coefficient for a smooth surface (wood or stone) is 0.6 (wood on stone) or 0.3 (stone on sand or gravel).
(24) Dörnenburg, F. 2008. Pyramidengeheimnisse ? Enträtselte Mysterien. Munich: Brose, 148.
(25) These round beams can be compared to railroad sleepers in that they are lodged firmly in a ballast bed (limestone chips, small stones). They are able to carry considerable weight, because the ballast functions as solid underground which precludes sideways slippage by canting of the stones.
(26) Stocks, D.A. 2007. “Das Bewegen schwerer Steinobjekte im Alten Ägypten.” In Sokar 15 (2), 74 sqq.
(27) Lehner, M: 1985. “The Development of the Gisa Necropolis : The Khufu Project.” In MDAIK 1985, 127.
(28) Maragioglio, V. and Rinaldi, C.A. 1966. L’Archittetura delle Piramidi Menfite, vol. 5. Torino : Officine Grafiche Canessa, 64 sqq.
(29) Stadelmann, R. 1997. Die ägyptischen Pyramiden. Mainz: von Zabern, 226.
(30) Lehner, M: 1985. “The Development of the Gisa Necropolis: The Khufu Project.” In MDAIK 1985, 124 and 132.
(31) Becker, J. 2003. “Die Funktion der Pyramidenkorridore als vermessungstechnische Einrichtungen. ” In Sokar 6 (1), 14-21.
(32) Hassan, S. 1943. Excavations at Giza, 1932–1933, vol. 4. Cairo, Fig. 122.
(33) Davies, N. de Garis 1943. The Tomb of Rekh-mi-Re at Thebes, vol. 2. Egyptian Expedition vol. 11. New York : Publications of the Metropolitan Museum of Art, pl. LX.