samedi 20 août 2011

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

Première partie 
Deuxième partie

Ramps and redirection rollers in the construction of the pyramids (50)

“Starting from archaeological evidence, I shall propose an explanation for the building of the pyramids and an estimate of the necessary time frame, using the pyramid of Menkaure as an example.
I have chosen this pyramid because its stepped construction, the laying technique of inner and outer casing, and its measures are easily accessible, and therefore subject to archaeological documentation and discussion.
My hypothesis involves the assumption that construction took place in several phases, which can be summarized as follows :

• First, the stepped core is built up to the sixth step. Transport of stone blocks takes place via ramps with a gradient ratio of 2:1 positioned on all four sides of the pyramid on the step platforms of the core, in line with the sides of the pyramid. These ramps are removed as soon as the core is completed.
• Next, from the lowest course of casing upwards, a stepped structure is erected around the pyramid which serves as a working platform. (51) The platform enables the workers to perform in one continuous process the laying of backing and casing stones. Transport of stone blocks for this purpose runs via steep ramps with a gradient ratio of 2:1 positioned on the working platform which, as we have said, surrounds the pyramid on all sides.
• After the setting of the pyramidion, the stepped surrounding structure (working platform) is removed, and at the same time dressing takes place starting from the top of the pyramids, proceeding downwards.

Pyramid of Menkaure

The point of my argument is that on the one hand, the stepped core was built using steep ramps and redirection rollers, while on the other hand, a working platform was erected around the pyramid’s circumference to enable the positioning of the pyramidion and the laying, working and dressing of the casing, which was again made possible by steep ramps. In both cases, the building process would continue simultaneously on the four sides of the pyramid. Thus the complete building process including the setting of the pyramidion can be understood as one continuous process.
Redirection rollers allow even heavy loads to be hauled up over steep ramps without large towing crews. What is more, because this method combines two construction techniques that are archaeologically attested (ramps and rollers), it certainly could have been available in the Old Kingdom and is therefore a likely candidate.
At first glance, it may seem contradictory to install two independent ramp systems and to remove both in the course of the building process. However, the archaeological evidence does suggest that the core was built in a distinct phase preceding the application of the casing. To quote another example, the Queens’ Pyramids near the pyramid of Menkaure also consist of the core only, as the casing was not finished. Furthermore, in the breach at the North of the pyramid of Menkaure, we can observe that the backing stones were fitted into the outer masonry of the core. This evidence plainly excludes layer-wise simultaneous laying of core, backing and casing with the aid of one single ramp. It is probable that static concerns prompted the separate building of the core. The intention was to avoid damage to the building through earthquakes or ground shifts by combining stable outer core walls with a filling.
If the solution I have offered holds true for the pyramid of Menkaure, it is applicable to all pyramids of the Old Kingdom, with individual modifications.
In the Queens’ Pyramids of Menkaure, it can be observed that the heights of their single steps are roughly equal, apart from the lowest step, which is not quite as high as the others. Therefore, we may assume that in the pyramid of Menkaure, two more steps exist below the breach. The total height of these two steps is about 16.39 m, and thus not quite as high as that of the uppermost steps. This characteristic is comparable to the construction principles of the Queens’ Pyramids. The reconstruction shown below (fig. 12) suggests that the core consists of seven steps. The heights of the fifth to seventh step and their batter are inferred from the measure attested for the third and fourth steps (height 8.5 m, width 4.2 m). It is also possible that the seventh step consists not of a core masonry wall with filling, but rather from wellhewn blocks that were installed in alternate courses, as can be seen at the top of the pyramid of Khufu.

Fig. 12 Stepped core of the pyramid of Menkaure

The building phases
Once a decision had been reached on the pyramid’s construction, planning was completed and
the site chosen. Then the building site was leveled and areas presenting loose rubble were supported with stone slabs. The transport ways connecting the quarries and the newly-built harbor were determined and equipped with the necessary facilities. Furthermore, the pyramid’s base was fixed and aligned towards the North. The length of the base line on each side is about 80 m according to Maragioglio and Rinaldi (150 cubits ?). Also, the base line of the lowest layer of the casing was fixed at 196 x 200 cubits (102.2 x 104.6 m). At the same time, the construction of the passages and chambers was planned, and building started. (52) As soon as these preliminary works were finished, that is, approximately a year later, the building of the actual pyramid began.

Building of the core
Archaeological evidence suggests that the second to fourth steps of the core masonry are slightly divergent in their height and width. There is no unified alignment of the steps’ edges, at the best about 54°30’, but this measure does not cover all of the edges in question, for example the edge of the second step is situated further inwards. The same divergence in term of step height and width can be found in the Queens’ Pyramids G III c and G III b. Thus it becomes clear that a constant slope could only be achieved by exact laying of backing and casing blocks. Starting from the blocks in the lowest layer of the casing, a continuous batter had to be kept on the side faces as well as at the corners. In fact, this seems to be the reason for the outer angle’s always being slightly smaller (51°30’) than that formed by the edges of the steps of the core masonry (54°30’). Consequently, the outer angle of inclination could be determined separate from the core, and it was not necessary for the upper edges of the steps to be positioned as precisely as the corner stones of the backing and casing.
Right from the start of the building works, the lowest courses of blocks of the core walls were laid simultaneously at all sides of the pyramid, together with the respective filling material (stones of various sizes and shapes, gravel, tafla, sand, mortar). The stones were conveyed from one layer of blocks to the next by means of ramps which grew higher as the building increased in height. As one layer of the core walls after the other was finished, and as the respective filling was completed, the ramps were increased in height, and thus in length. However, the part of the building that had already been completed, did not require changes on the ramps. The winches however had to be moved upwards.
The transport ramps probably had a slope of 26.5°, at a ratio of base to height of 2:1, with a width to match that of the respective steps of the core (4.8 m on the first two steps, and 4.2 m on the other steps). As mentioned above, a gradient ratio of 2:1 (26°33’54) can be observed in all passage systems of the pyramids of the Fourth Dynasty. The ramps consist of the actual transport way with a set of steps running alongside it, adding up to a total width of 3 m, which corresponds to the total width of the respective step of the core. Fig. 13 illustrates a ramp combined with a roller.
Fig. 13 Transport of blocks by a revolving redirection roller

Several possibilities exist for the design of the transport way on the ramp :
– the surface was made from smoothed limestone ;
– ruts were engraved along the ramp surface, lined with mortar and filled with loose dolerite pellets. The ruts were slightly wider than the sledge runners ;
– the surface consisted of dolerite pellets embedded in mortar ;
– the surface was engraved with horizontal grooves into which wood beams were fitted, which would revolve under the block which was hauled, and return to their initial position as soon as the load had moved on.
One possible arrangement of ramps on the core steps is shown in fig. 14. On the first to sixth step, ramps could be positioned on each side of the building.
The outer faces of the ramps consist of finely hewn blocks, forming a stable wall with a slight inward slope comparable to the outer shell of the core masonry. The interior of the ramps was filled with roughly hewn stones and mud bricks.
Considering the measures of the transport ramps (fig. 14), ramps can be positioned on each side of the pyramid as follows :
- step 1 : 2 ramps
- step 2 : 1 ramp
- step 3 : 1 ramp
- step 4 : 1 ramp
- step 5 : 1 ramp
- step 6 : 1 ramp
This serves to illustrate once more that construction works on the steps of the core may have well been carried out simultaneously on each side of the pyramid, using one or two ramps. Thus, a transport capacity emerges which is significantly higher than that of perpendicular or spiral ramps.

Fig. 14 Position of the ramps for redirection rollers on steps 1 to 6 of the core

The following remarks are intended to clarify what I refer to as the principle of transport by means of a steep ramp. I have had to adopt some common sense parameters, as there was no opportunity to confirm them by practical experiments. On the uppermost platform of each ramp (length : 5 m), a redirection roller is positioned at the side opposite the sloped surface fig. 15.

Fig. 15 Ramp with redirection roller

The redirection roller consists of wooden beams that are crossed and bound together, then firmly planted into the ground, while the roller is resting on top of them. As the largest blocks have sizes of approx. 2.3 m x 1.4 m at a height of 0.6 m (weight 4.5 tons), (53) the rollers’ supports have to be positioned with enough space in-between to allow the sledge to be drawn right up onto the platform together with its load. However, we have not taken into account the weight of the roller itself. Through use of hardwood and greasing of the roller’s rests, the frictional force can be kept at a minimum, so that we safely may discount it.
The hauling vehicles, presumably sledges or similar devices made from wood, are likely to
have measured approx. 2.5 m (length) to 1.5 m (width). On the other hand, it is quite possible that the stones themselves were pulled up on the ramp without further supporting devices. For that purpose however, a sufficient traction force would have been needed. The advantage of this method would have been that the time consuming tasks of loading and unloading of the stone blocks, and also the transport of the sledges back down, were not needed. In any case, the hauling devices must be designed in such a way as to ensure that they can be pulled in both directions (change of direction at the top of one ramp to be pulled towards the base of another).
3100 kp is the traction force necessary for transport of a stone block over a smoothed limestone ramp with a gradient ratio of 2:1 or with a slope of 26.5°, and a friction coefficient of 0.25, that is to say the force needed in the least favorable circumstances. 45 workers are needed. Supposing that sledges or other wood devices with less friction were used, or horizontally embedded wood beams, (54) fine sand strewn over the sloped ground, (55) or another kind of support covered with dolerite pellets, a traction load of a mere 2200 kp has to be achieved, (56) which may be further lowered when smaller blocks are moved.
Then again, friction is necessary to ensure that the roller does not spin freely under the coiled rope. This is guaranteed by the use of a roughened wood surface, the natural roughness of the ropes, and a traction force (workers) along the ramp down to its base.
Horizontal transport of a block on either end of the ramp towards its definite position in core or casing, or towards the starting point of its transport to the next level, would be carried out by means of levers or stone pellets. As in the pyramid G III c (Menkaure), layers are also visible in the core filling. It is therefore quite possible that the blocks were moved across a surface covered with loose stone pellets. Furthermore, we have reason to assume that the uppermost horizontal layer of the ramps was covered with dolerite pellets on the first few meters after the ending of the slope, in order to allow the sledges or the blocks to be rotated if necessary, and to await further transport as they were sitting on a bed of stone pellets.
The building phases of the core construction by means of tangentially positioned ramps and
redirection rollers are illustrated by the following drawings.

Fig. 16 Laying of the second layer of the first step of the core. Note the rock spur in the
middle which is enclosed by this step

Fig. 17 The first step of the core is complete

Fig. 18 The second step of the core is complete

Fig. 19 The fourth step of the core is complete

Fig. 20 The core’s six steps are complete

As soon as the sixth step of the core is finished, the ramps are removed (fig. 21).

Fig. 21 Finished core after removal of the ramps

Application of the backing blocks
In many pyramids it is still obvious today that measuring and laying of the base course of the casing was carried out most meticulously. This supports the assumption that the backing blocks (57) and the casing (58) were completed starting from the base of the pyramid as a rule. (59)
In some pyramids, like the Queens’ Pyramids of Menkaure G III b and G III c, only the core was finished. (60) I should like to put particular emphasis on this fact at is rules out virtually any other model than that involving separate construction phases for core and casing.
Exact laying and working of backing and casing blocks requires a platform surrounding the pyramid, for no other solution ensures the safety of the workplaces. Ramps would have been erected on these platforms to match those suggested with reference to the core construction phase (see above).
As can be seen in the breach on the North side, the core steps were filled out with backing stones to match the respective batter. This process is technically impossible without an attached working platform. The same is true for laying and working the stones of the casing. Only an attached working platform enables the workmen to fit the blocks quite so neatly into the given spaces. Also, this model explains how the pyramid’s surface could be dressed top down during removal of the attached working platforms. Up until then, these blocks would not only have been as yet unsmoothed, but also parts of them would have protruded from the pyramid’s walls. Their rough surfaces would have ensured safe lodging of the ramps leaning onto the pyramid with blocks resting on the surface of the pyramid’s outermost masonry. As the ramps are built layer by layer, the ramp blocks facing the pyramid are safely positioned in this manner, lending sufficient security to the ramps walls.
For the transport of blocks on the respective steps of the platform, I would suggest ramps with
a width of approx. 5m, similar to the core ramps, made from mud bricks or smaller stones, with outer flanks made up from stone walls. These brick ramps display a gradient ratio of 2:1, and they grow with the platform from layer to layer. Within one layer, first the backing is completed and then the casing is laid, each new course of casing blocks on top of the previous one. The working platform may well have served for the construction of the seventh step of the core also (if indeed there was one), and of course for the setting of the pyramidion.
The blocks of the casing were worked with remarkable precision even before transport on their horizontal faces. Their fronts, however, were left undressed. The sides of these blocks were often cut very finely, partly during laying. As can be seen in several instances, some of the cutting was not executed vertically, but rather to fit the situation found on-site. This kind of work also requires a platform attached to the pyramid’s face, because only then, the required sawing on both sides would have been possible in safe circumstances. Only very closely fitted casing blocks could prevent leakage of water and sand into the masonry, thus offering protection from damage through erosion. Before a casing block was fitted, the slope of the pyramid was sketched on the previous block so that later, dressing could start from this mark in keeping with the exact slope. Dressing of the outer faces of the casing blocks previously left in boss, starting at the top of the pyramid and proceeding downwards as the platform was removed, was feasible because the brick ramps were dismantled when work at the top had been completed. (61)
The building phases and subsequent removal of auxiliary structures (working platforms, ramps) as seen in the construction model that utilizes redirection rollers are illustrated in fig. 22 to 24.

Fig. 22 Finished working platform 1 with ramps

Fig. 23 Finished working platform 3 with ramps

Fig. 24 Positioning of the pyramidion following completion of the uppermost working

Fig.25 Positioning of the pyramidion

As soon as the pyramidion has been positioned, the working platform is used for top down dressing the outer casing. At the same time, it is removed step by step (fig. 26).

Fig. 26 Removal of the working platform and the outer ramps while dressing is carried out

Fig. 27 Finished pyramid following dressing

à suivre : 4e et dernière partie

(50) Müller-Römer, F. 2011. Der Bau der Pyramiden im Alten Ägypten. Utz, Munich, 335.
(51) A working platform attached to the pyramid on all sides enables best possible access to the construction site, and safety issues are thus taken care of satisfactorily. Both are necessary concerns during the laying of the casing, notably the on-site fitting of backing and casing blocks’ sides to match their finely-hewn horizontal surfaces.
(52) Due to the constraints of this paper, I will not further discuss the question whether the access to the antechamber which was later built over constituted an expansion or change to the original plan, or whether it could have served as a transport way for the granite slabs for the burial chamber’s wainscot.
(53) Blocks in the steps of the outer wall of the core.
(54) This technique is archaeologically attested only from the Middle Kingdom onwards, but then again, the principle of the roller is known already from the Old Kingdom.
(55) The favourable effect of fine sand is comparable to the lowering of rolling friction by means of stone pellets.
(56) As I am only aiming at a rough outline at present, I have not taken into account the minimal friction caused by the roller’s rests.
(57) By backing, or backing stones, I mean the horizontal layers of stone blocks between the steps of the core and the casing, which consists of Tura limestone and Assuan granite.
(58) The blocks of the casing from Tura limestone or Assuan granite were left in boss at the stage of fitting the casing, to be dressed later.
(59) Stadelmann has noted that in the Bent Pyramid, the casing was laid right at the beginning, together with the core. In that case it was laid starting from the base, moving towards the top (Stadelmann 1997. Die ägyptischen Pyramiden. Mainz, 226).
(60) Jánosi, P. 1996. Die Pyramidenanlagen der Königinnen. Wien: Verlag der Österreichischen Akademie der Wissenschaften, 85.
(61) Herodotus reports that the pyramid was finished top down (Herodotus, Historiae II.125. Herodot Historien. Deutsche Gesamtausgabe 1961. Translated by A. Horneffer, Stuttgart : Kröner). According to Diodorus, the construction of the pyramids involved earth walls (mud bricks) along the outer face of the pyramids (von Bissing, W. 1901. Der Bericht des Diodor über die Pyramiden. Berlin: Duncker). Pliny mentions a terrace system (Goyon, G. 1990. Die Cheopspyramide. Augsburg, 117).