World History

A New Consideration of the Construction Methods of the Ancient Egyptian Pyramids Author(s): Frank Müller-Römer Source: Journal of the American Research Center in Egypt, Vol. 44 (2008), pp. 113-140 Published by: American Research Center in Egypt Stable URL: http://www.jstor.org/stable/27801624 . Accessed: 09/09/2014 14:50

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A New Consideration of the Construction Methods of the Ancient Egyptian Pyramids

Frank M?ller-R?mer

Abstract

Despite the wealth of books and articles published on the pyramids of the Old Kingdom, and the wide variety of suggestions offered with reference to the construction process itself,

timing of the building schedule, technical devices, and workforce employed, no conclusive

explanation has been proposed so far.

All previous solutions involving ramps start from the assumption that the blocks were

hauled up by means of sledges pulled by bulls

or man-power. Such a transport method requires

long ramps with moderate inclination and large sledges; moreover, it raises the question whether enough workforce

was available. Hardly any convincing suggestions have been made

to explain how the works at the top were carried out or how the casing was dressed, nor are

there any convincing building time calculations. The main shortcoming of the previous pub lications seems to be that archaeological findings

are often not considered sufficiently.

I argue that for several reasons, perpendicular and spiral ramps are not likely to have

played a significant role in the construction of the Old Kingdom pyramids. Rather, from the pyramid of Menkaure onwards, steep ramps erected parallel to the sides of the

core steps were used to haul up building material with winches (rollers). In the following building phase,

a working platform

was attached to the pyramid's faces to enable safe laying of the

casing, setting of the pyramidion, and dressing of the casing blocks starting from the top, as they had been left in boss during laying.

Finally, schedule calculations are made for the construction of the Red Pyramid and the

Pyramid of Khufu. The resulting building times agree with the time frame currently sug gested for the reign of the respective rulers, and the building times as far as they are known

today.

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 facil

ities and logistic proficiency of the ancient architects.

Throughout the past centuries, Egyptologists, archaeologists, engineers, and amateurs have at

tempted to explain the techniques and processes involved in the construction of the pyramids. How

ever, 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 expla nations and calculations, but frequently they have overlooked important archaeological evidence.

113

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114 JARCE 44 (2008)

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 em

ployed 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 Pyramids1 of the Old Kingdom,

starting from current research in Egyptology and taking into account archaeological evidence, taking

particular care to avoid internal contradictions. 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 archaeological evidence pertaining to the pyramids of the Old Kingdom should be taken

into consideration comprehensively.

Any explanation should relate to the construction of the entire pyramid, including the setting of

the pyramidion and the smoothing of the casing.

Building time calculations should be presented for all pyramids discussed.

Aspects of construction technique and safety issues should be considered for the construction

process as well as for subsequent dressing.

Backsighting must have been possible on a regular basis throughout the building process; there

fore, accessibility must have been guaranteed.

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 ob

servation 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 indis

pensable. 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.2 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

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, tafia, and mortar. 2 Felix Arnold, The Control Notes and Team Marks. The South Cemetery at Lisht (New York, 1990), 14.

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M?LLER-R?MER 115

Fig. 1. The workman from the tomb of Ti

(drawing after Steindorff, Das Grab des Ti

[Leipzig 19131 pl 134).

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 build

ing site. Unfortunately, no construction reports are available

for the Third and Fourth Dynasties. However, a pictorial repre sentation 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.3

Considering the life expectancy of the ancient Egyptian rul

ers, the building schedule for the pyramid complexes was ex

tremely 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 craftsman

ship 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 con

clusions 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.4 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.5

Drills are shown on various representations from the Old Kingdom period. Borchardt, for ex

ample, 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 accu

rate 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 function

ing principle of cranks and rollers was already understood and put to practical use; the principle of

force intensification was therefore known implicitly. Rollers with rods positioned at right angles for power transmission (spills, winches) are also known

to have been in use for lowering and lifting of heavy weights throughout the Old Kingdom. For ex

ample, in the upper part of the antechamber of the pyramid of Khufu, semicircular grooves can be

3 Rainer Stadelmann, Die gro?en Pyramiden von Giza (Graz, 1990), 248. 4 Denys A. Stocks, "Stone sarcophagus manufacture in Ancient Egypt," Antiquity 73 (1999), 918-22.

5 Denys A. Stocks, Experiments in Egyptian Archaeology. Stone working technology in Ancient Egypt (London, 2003).

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116 JARCE 44 (2008)

HOLLOWS IN THETOP OF THE GRANITE WAIN3C0T OF THE WEST WALL OF THE ANTECHAMBER. GREAT PYRAMID SCALE tV

GROOVE RIDGE G R V e RIDGE GROOVE RIDGE

Fig. 2. Grooves in the wainscot of the antechamber in the pyramid of Khufu (drawing after Petrie, Pyramids and Temples ofGizeh, pi. 12.).

seen in the wainscot on the West wall, as observed by Borchardt,6 and measured by Petrie (fig. 2).7 If we interpret these grooves correctly, they served as rests for round cross beams positioned horizon

tally above the antechamber. These beams, or rollers, were part of a construction which was used first for controlled lifting of the plugging blocks in order to remove the supports, and then for lowering them to seal the tomb (fig. 3). Ropes were run through the plugging blocks, coiled around the roller

beams, and lead towards the Grand Gallery. The average weight of each of the plugging blocks is approximately 2.5 tons. The borings on these

blocks suggest that ropes were run down through them and back up. As there are four borings to

each block, each rope on either side would have held a weight of about 0.31 tons (half of 0.62 tons). If the ropes had a diameter of 5 cm, they had to bear a load of 15 kg/cm2. The palm raffia ropes that

were used at the time would have been adequate for such a load. If hemp ropes were used,8 which are even more tear proof, and also attested for the Old Kingdom, a smaller diameter of approximately 3 cm would have sufficed. By means of several coilings, as seen in winches on sailing boats, even

heavier loads could have been held with much less force than their weight would require without the

aid of such devices.

This assumption is corroborated by the fact that the rollers' diameter (approximately 0.3 m) is un

usually wide for its length (1.5-1.6 m), and much wider than the weight of the plugging blocks would seem to require at first sight. The ropes on the Southern side of each plugging block would carry a

load of only half the plugging block's weight (approximately 1.25 tons). When the ropes had been

tightened and the wooden supports removed from the ruts for plugging blocks, the ends of the ropes towards the South were uncoiled gradually as they ran across the respective roller several times, to

lower the plugging blocks. It was possible to tighten the ropes in order to remove the wooden sup

ports by moving one of the rollers against the lowering direction. The force necessary for this move

ment was achieved by moving rods that were attached at right angles with the axis of the rollers, as

spokes of a winch or a spill. In the present case, a power transmission ratio of 5:1 is possible (length of the rods: max. 0.95 m, radius of the roller approximately 0.2 m) or 10:1 (0.95 m as opposed to

a

radius of approximately 0.1 m). This is to say that a force of a mere fifth (0.25 tons) or tenth (125 kg)

of half of the weight of each plugging block (1.25 tons) had to be employed to tighten the ropes and start lifting the block. Then, the force needed for tightening the ropes?250 or 125 kg for a roller

diameter of 0.2 or 0.1 m?could be easily achieved by four men working at the spill above the roller,

h Ludwig Borchardt, Einiges zur Dritten Bauperiode der Gro?en Pyramide bei Gise (Berlin, 1932), pl. 4.

7 William M. Flinders P?trie, Pyramids and Temples of Gizeh (London, 1883), pi. 12. 8 Bj?rn Landstr?m, Ships of the Pharaohs (London, 1970), 82-84.

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M?LLER-R?MER 117

Fig. 3. Antechamber of the pyramid of Khufu (drawing after Borchardt, Einiges zur Dritten Bauperiode, pl. 4.).

together with further workmen pulling the rope's end in the corridor. A process such as this serves to

explain why a gap of approximately 1 m was left between the roller and the ceiling. 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 rollers with spokes (winches) should be taken into account when discussing

lifting and lowering of loads and transport across inclined planes. Such connections between the vari ous groups of archaeological evidence have not previously been discussed to satisfaction, and in the

absence of relevant material evidence, we are of course dealing with interpretations here. However, 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 explain

ing how the gabled roofs in the pyramid of Khufu, or the burial chambers built in open cut construc

tion 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. This construction method even allows for adjustment to the varying weight of the loads, or the height at which the blocks were brought into their definite

position: ramps sloping at various degrees, or several winches in a row could have been employed.

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 high-ranking official from

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118 JARCE 44 (2008)

Fig. 4. Transport of a statue?two bulls pulling a

carriage, from the tomb of Hetepherakhti (drawing after M?hr, The Mas

taba of Hetep-her-Akhti, fig. 3).

Memphis (Fifth Dynasty),9 two bulls are pulling a device possibly made from wood, upon which the statue is secured against falling or shifting (fig. 4).

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 remark

able number of Old Kingdom ramps connecting quarries and pyramid sites, and by the causeways.

Mostly, the angle of inclination is low so as to ensure that bull carriages and towing crews were able to move even very heavy blocks. Only the small Layer Pyramids of Lisht, Meidum, and Sinki have per

pendicular 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.10 Disposal sites attested in the pyramid area of Giza con

sist largely of a mixture of limestone, gypsum and ta?a without any obvious remnants of Nile mud.

They are usually interpreted as waste that was disposed of during the building of the pyramids.11 This being the state of archaeological research, one cannot but draw the conclusion that a build

ing 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.

At this point, it is illuminating to take a closer look at the descending and ascending passages in the

pyramids of the Fourth Dynasty. They can be regarded as steep ramps displaying a gradient ratio of

2:1 (horizontal : vertical), or a slope of 26?33'54", with only minor exceptions to this rule. The size of

the entrances (1.2 m width, 1.05 m height) argues strongly against the use of towing crews or bull car

riages for conveying building refuse from within the pyramid, such as chippings from the rock core, towards the outside. Indeed, even granite slabs with a volume of up to 3.2 m length, 0.95 m width and

0.7 m height for the lower burial chamber, each amounting to a weight of up to 6.5 tons, were moved on this route. Hence, steep ramps are attested in the Old Kingdom.12

9 Herta Therese Mohr, The Mastaba of Hetep-her-Akhti (Leiden, 1943), 36, fig. 3. 10 Rainer Stadelmann, Die ?gyptischen Pyramiden (Mainz, 1997), 226. 11 Mark Lehner, "The Development of the Giza Necropolis. The Khufu Project," MDAIK 41 (1985), 124 and 132. 12

J?rgen Becker, Die Funktion der Pyramidenkorridore als vermessungstechnische Einrichtungen, Sokar 6 (1/2003), 14-21.

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M?LLER-R?MER 119

Fig. 5. Brick ramp from the tomb of Rekhmire (drawing after Davies, Rekh-mi-Re, pi. 60).

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. 5). 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?).

Initially started as a mastaba, the Pyramid of Djoser was built in layers (two to each step), and is

therefore rightly referred to as Layer Pyramid. The basic techniques for the construction of such

Layer Pyramids were developed at that time. Blocks were arranged around the core, with inward

leaning layers. The pyramids of king Sekhemkhet and Khaba, of which only the stumps are pre served, and the small pyramids (possibly of Huni?) were built according to this principle. There is

practically no evidence for a smoothed casing here.13 The first Pyramid ofSeneferu at Meidum was built as a Layer Pyramid in several stages. In stage El

and E2, limestone blocks were used for the visible surface of the steps, and dressed after application. After the finishing of the Layer Pyramid in stage E2, the steps were filled with another layer (E3), so

that the facade now formed a constant slope, rather than a stepped outline. Afterwards, it was cased

with finely grained limestone. In this monument, we are able to witness the transition from a visibly

stepped Layer Pyramid to a pyramid with steps filled to form a facade with a constant slope ("true

pyramid'). This development took place parallel to the construction of the Bent Pyramid. The cult

pyramid of Meidum was also built as a Layer Pyramid. It is virtually impossible to offer an archaeologically sound explanation for the construction pro

cess of the Bent Pyramid, especially its inward structures. The start of its construction is usually dated to twelve to fifteen years after the start of the construction of the Meidum pyramid, and at this time, no severe difficulties had occurred with the Layer Pyramid style. It is therefore likely that the Bent

Pyramid was initially designed as a Layer Pyramid as well. When the first stage of construction was

completed, backing and casing blocks were added in the next stage to form a constant slope in its

lower half. When the additional casing had been finished, the pyramid's construction was continued

from a height of 90 cubits (47 m) onwards with a less steep slope. Moreover, the construction tech

nique was modified: the stone courses underneath the casing were then set horizontally, that is to say the degree of inward leaning was lessened as the building gained height. Also, the stone blocks used

were smaller than those used in the casing below.

The casing of the lowest step of the small pyramid at Saujet el-Meitin is an exception to this rule.

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120 JARCE 44 (2008)

The design of the attached Satellite Pyramid then followed the "new," modified construction prin

ciple with horizontal courses of stone blocks. This might have served as a test for the construction

technique later adopted in other pyramids. To sum up, the transition from the principle of inward-leaning layers, as seen in the Layer Pyra

mids, to construction by means of horizontal courses, the latter being characteristic for the Fourth

Dynasty, took place during the reign of Seneferu. Having been pinned down to the building process of the upper half of the Bent Pyramid, the attached cult pyramid, and the Red Pyramid, it

can be

explained from the difficulties that occurred during construction of the Bent Pyramid. The Red Pyramid is the first to display fully horizontal courses of casing blocks. Due to its good

state of preservation, archaeologists have not been able to obtain any definite information as to the

structure of its core. However, it is hard to imagine that the core would consist of inward-leaning lay ers after the disturbing experiences made during the building of the Bent Pyramid.

Another significant change took place during the construction of the Red Pyramid, because the

large blocks familiar from the Giza pyramids are used here for the first time. Consequently, new

transport techniques must have been developed for these blocks. Considering the chronology of

Seneferu 's reign, the pyramid's construction started relatively late, and it is possible that the builders

were pressed for time, so that changes in the construction technique were at least partly dictated by

tight schedules. If a pyramid is built with stepped core and casing, it is possible at various stages of

construction to proceed on all four sides of the pyramid, so that much time can be saved. It is not a

far-fetched thought that the first and foremost way of improving construction techniques to such a

degree as to enable the building of the Great Pyramids was to collect solutions developed from diffi

culties encountered previously in this epoch characterized by intense pyramid building activity. Therefore, we may conclude that the core of the Red Pyramid consists of steps with horizontal

courses, marking the beginning of the Step Pyramid style. Scholars generally speak of a transition from the so-called Step Pyramids (as the Layer Pyramids

are often mistakenly called) towards the "true" pyramid during the reign of Seneferu. However, the

actual circumstances of this transition are hardly ever considered. Within eighty years after the erec

tion of the first pyramid by Djoser, the "classic" pyramid was developed as the type of royal burial

that should dominate the ancient Egyptian necropolis throughout the upcoming centuries. Seen

from an evolutionary perspective, the development of Egyptian burial structures first started from

the mud brick mastaba, moving on to the Layer Pyramid and the Step Pyramid and reaching a climax

in the "classic" pyramid with a constant slope. Observations made on the breach in the South face of the pyramid of Khufu and in the tomb rob

bers' tunnel on the North side, and also on the breach in the North face of the pyramid of Menkaure

(fig. 6) suggest that the horizontal courses of the casing do not match those of the core. In both pyr

amids the filling within the core walls that form the steps consists of roughly hewn stones of various

sizes and shapes piled on top of each other irregularly, and joined by mortar. Some of these are

clearly unworked quarry stones.

Production, transport, and laying of the stones for the core would have required less effort than for

the casing. The stepped core served to improve the inner stability of the building, while also increas

ing its resilience against external damage. However, the actual structure of the core of the Khephren

pyramid remains unknown up until today. The foundations of the casing were leveled out and measured permanently. The same is true for

the other courses of the casing and their respective offset. It was essential to maintain the same

height of the steps in order to achieve a constant batter. Depending on the quarrying, the stone lay ers may have had different heights. Under such circumstances, exact monitoring of the batter

was the

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M?LLER-R?MER 121

Fig. 6. Cross-section (S-N) of the pyramid of Menkaure with steps archaeologically attested in the breach on the north face

(drawn lines) and the other steps of the core reconstructed by analogy (dotted lines).

only viable way to check the angle of inclination, on which the height of the pyramid depended. The

fact that the pyramids' exact slopes vary is most likely a result of different designs, or else just slightly inexact measuring. Besides, it has to be admitted that today, the angle of inclination can often be only

roughly determined due to the pyramid's state of preservation. It seems likely, however, that the

actual height of the pyramid was not included in the initial design, rather, in effect, it resulted from

the added offset of all steps. The Step Pyramid style was kept in use throughout the Fifth and Sixth Dynasties, as is attested by

archaeological findings on all pyramids of this period, including the cult pyramids and Queens' Pyra mids. The pyramids of Menkaure and Userkaf mark the beginning of a period of pyramids with less

monumental dimensions than those of the Fourth Dynasty. The development continued in this direc

tion until the end of the Sixth Dynasty (Pepi II). However, the technique used in constructing the

steps changed during the Fifth and Sixth Dynasty. The stepped core walls of the steps consist of an

outer wall executed in well-hewn stones with slight batter, while towards the inside, we find a filling of blocks of various shapes and sizes that are only roughly hewn and mixed with mortar and rubble.

Thus, by using smaller blocks, it was possible to lower the expenses for production and transport in

comparison to the pyramids of the Fourth Dynasty. The courses of large well-hewn stones casing blocks characteristic of the Fourth Dynasty pyramids

disappear, making way for smaller backing stones of irregular shape filling the spaces between the

steps and the outer limestone casing. As a result, when the casing was stripped, the mortar was exposed to the elements so that parts of the core masonry collapsed. Stadelmann, Lehner, and others speak of

slack workmanship here; similarly, Maragioglio and Rinaldi attribute the state of the building to the

inferior quality of the masonry. However, I should like to argue that this construction technique was

the result of experiences made in pyramid building to the extent that in smaller pyramids, a stable

outer casing would have sufficed to protect the core from weathering or erosion. Surely, experience

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122 JARCE 44 (2008)

in pyramid building would have become increasingly profound over the years. Moreover, in order

to keep within tight building schedules while also minimizing the costs, the small pyramids did not

receive such a closely-fitted casing as the pyramids of the Fourth Dynasty, whose inner casing ma

sonry even resists the weather and most of the erosion when much of the outer casing is stripped. To sum up, all pyramids of the Old Kingdom have stepped cores (layered or stepped construc

tion). 14 In the immediate surroundings of the pyramids, no ramps have been attested by archaeologi

cal evidence that could have been used for building the pyramid itself rather than for transport of

stone blocks to the construction area. The pyramid of Seneferu in Meidum is the one notable excep tion to this rule.

The pyramids of the Old Kingdom were planned and built over a period of roughly four hundred

years, and a broad spectrum of construction techniques must have been invented and applied, while

the techniques themselves were improved continually.

Some Previous Explanations of Pyramid Building

Nearly all explanations of pyramid construction have been formulated with respect to the pyramid of Khufu. As stated above, with a view to archaeological evidence, the techniques did not change much throughout the period of four hundred years (Third to Sixth Dynasty), during which roughly

twenty-five pyramids were built, with the one notable exception of the transition from Layer to Step

Pyramid during the reign of Seneferu. Other improvements were introduced in a less dramatic way and can hardly be traced nowadays. Therefore, we have good reason to assume that any theories on

the building of the pyramid of Khufu should also serve to explain the building of other pyramids of

the Old Kingdom. An analysis of the suggestions published so far with reference to the building of the ancient pyra

mids in general, and the pyramid of Khufu in particular, yields the following three categories: solutions involving perpendicular ramps, solutions involving ramps built along the pyramid's sides, and

solutions making use of lifting or towing devices.

Any discussion of the subject should fulfill the prerequisites listed below, otherwise it does not measure

up to the requirements of the situation, and thus fails to meet the standards of academic discussion.

Basic prerequisites for solutions suggested for the construction of the pyramids

1. Only such tools, transport and techniques as are proven by archaeological evidence to have been available in the Old Kingdom are considered.

2. The archaeological evidence pertaining to the pyramids of the Old Kingdom is taken into con

sideration comprehensively.

3. The solution relates to the construction of the entire pyramid, including the setting of the pyr amidion and the smoothing of the casing.

4. Building time calculations are presented in order to allow comparison with other concepts. 5. Aspects of construction technique and safety issues are considered for the construction process

as well as for subsequent dressing. 6. Measuring must have been possible on a regular basis throughout the building process; there

fore, accessibility must have been

guaranteed.

14 In the case of the Bent Pyramid, the Red Pyramid, and the Pyramid of Khephren, this has not previously been proven.

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M?LLER-R?MER 123

In order to briefly review the extant literature, I shall now present three types of solutions to the

issues of construction techniques presented by the respective authors.

Perpendicular ramps as suggested by Arnold,15 Stadelmann,16 Lauer,17 Lattermann,18 and others can be excluded as a means of construction on the grounds of the following observations:

1. The ramps require continuous increase in height and, accordingly, width. This leads to regular

disruption of the construction works, or at least considerable delays. 2. The volume of the ramps would have been enormous, easily reaching or even exceeding the

volume of the pyramid itself, depending on the design of the ramp. 3. No archaeological evidence has been offered that cogently proves the existence of ramps or

appropriately large rubble deposits. 4. Free-standing ramps built from clay or mud bricks sustain their own weight only up to a height

of 120 m.

5. Archaeological evidence from the Step Pyramids, notably the pyramid of Menkaure, contradicts

the hypothesis that the core was erected layer-wise, casting doubts on an idea that is crucial to

the ramp models.

6. Due to safety concerns and aspects of construction technique, the application of the casing and

dressing required scaffolding or other attachments to the pyramid's facade.

Spiral ramps, as proposed by Goyon,19 Lehner,20 Klemm and Klemm,21 Houdin,22 and others can

also be excluded as a method of construction on the grounds of the following observations:

1. At the corners of the pyramid, spirals ramps would have necessitated transport of building material at an angle of 90?, even if the corners were chamfered. This

was hardly possible, and

even if it was, it would have been an excessively time-consuming task. Also, no feasible solutions

have been offered as to the redirection of the traction force.

2. The idea that the core masonry was laid layer-wise is not corroborated by archaeological evidence.

3. The limited transport capacity of the spiral ramp leads to a schedule for the pyramids' construc

tion that by far exceeds the attested time frame.

4. As stated above with reference to the other ramp models, due to safety concerns and aspects of

construction technique, the application of the casing and dressing required scaffolding or other

attachments to the pyramid's facade.

5. Exact measuring throughout the building process would have been difficult as spiral ramps are

thought to have enclosed the pyramid, partly obscuring its outer face and corners. It would have

been very difficult indeed to ensure a constant batter.

Furthermore, the authors suggesting ramps often omit calculations of transport capacities, thus fail

ing to set their solution in relation to the time frame suggested by archaeological evidence, which in

the case of the pyramid of Khufu is a maximum of twenty-three years total.

15 Dieter Arnold, "?berlegungen zum Problem des Pyramidenbaus," MDAIK 37 (1981), 15-28.

16 Stadelmann, Giza, 266-275.

17 Jean-Philippe Lauer, "Le probl?me de la construction

de la grande pyramide," RdE 40 (1989), 91-111. 18 Walter Lattermann, Der Bau der Cheopspyramide (Munich, 2002). 19

Georges Goyon, Die Cheopspyramide (Augsburg, 1990). 20

Lehner, "Development," 109-43. 21 Rosemarie Klemm and Dietrich Klemm, "Die Integralrampe als Konstruktionselement gro?er Pyramiden,"

in H. Guksch,

ed., Stationen. Beitr?ge zur Kulturgeschichte ?gyptens. R. Stadelmann gewidmet (Mainz, 1998), 87-94.

22 Jean-Pierre Houdin, Cheops. Die Geheimnisse

um den Bauprozess der Gro?en Pyramide (Mainz, 2007).

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124 JARCE 44 (2008)

The solutions offered by Arnold,23 Isler,24 and Graefe,25 who propose constructions involving steps

leaning against the pyramid's faces at right angles, are no more convincing. These models pose static

problems because the steep slope would have required upward leverage of the stone blocks, which

was practically impossible. Several hypotheses about pyramid building (Graefe, Landt,26 H?lscher) share the idea that

from

the stepped core of the pyramids, which is archaeologically attested, it can be deduced that ramps were used which ran in line with the steps7 lateral surfaces, and whose slope was adjusted to the trans

port method chosen for the respective material. On the broad lower steps, several ramps could be

installed on all sides of the pyramid, so that even the vast amount of material needed for the lower

area of the pyramid could be transported and laid within an economical frame of time and effort.

Keyssner suggests that stepped construction platforms were attached to the sides of the pyramid, with winches positioned on the steps to enable hauling up of the stone blocks.27 Again, we must hold

against this that the concept of layer-wise building of the core employed in this model is not corrob

orated by archaeological evidence.

Most hypotheses start from the assumption that traction force was employed, which is to say, bull

carriages or workmen were used for hauling. If the loads were heavier than usual, or the ramp slopes

steeper, larger carriages or more workmen would have been required, and also increasingly long ramps.

Some suggestions concerning the transport of building material for the pyramids are based on

rather complex construction processes, so that one may wonder whether the ancient Egyptian archi

tects would have indeed employed such sophisticated methods. What is more, the issues of construct

ing the top of the pyramid, setting the pyramidion, casing, and dressing often suffer neglect. The

same applies to safety concerns. From all this, we cannot but draw the conclusion that yet another

construction method was used which neither involved perpendicular, nor spiral ramps, nor quite so

large quantities of material, nor a

step construction.

My suggestion, which I shall outline in the following section, combines the idea of ramps set out

parallel to the pyramid's sides and that of hauling devices with winches in connection with ramps with a steeper slope. Again, I should like to emphasize that I have incorporated only such techniques and

procedures which are supported by archaeological evidence.

Ramps and Winches in the Construction of the Pyramids

Starting from archaeological evidence, I shall propose an explanation for the building of the pyra mids 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:

23 Arnold, "?berlegungen

zum Problem des Pyramidenbaus." 24 Martin Isler, "On Pyramid Building," ?ARCE 22 (1985), 129-42, and Martin Isler, "On Pyramid Building II" JARCE 24

(1987), 95-112. 25 Erhart Graefe, ?ber die Determinanten des Pyramidenbaus bzw. Wie haben die Alten ?gypter die Pyramiden erbaut? at ?.www.uni

muenster.de/Philologie/laek/PYRyy. 2() Ernst Landt, Ein neuer Kampf um die Cheopspyramide (Berlin, 1923). 27 Heinrich Karl Keyssner, Baustelle Giza. Kritische Untersuchung zum Bau der Cheopspyramide (Karlsruhe, 2007).

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M?LLER-R?MER 125

1. 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.

2. Next, from the lowest course of casing upwards, a stepped structure is erected around the pyra

mid which serves as a working platform.28 The platform enables the workers to perform in one

continuous process the laying of backing and casing blocks. 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.

3. 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.

The point of my argument is that on the one hand, the stepped core was built using steep ramps and

winches, while on the other hand, a working platform was employed for the positioning of the pyra midion and the laying, working, and dressing of the casing, which was again made possible by steep

ramps and winches running simultaneously on the four sides of the pyramid. Thus the complete build

ing process including the setting of the pyramidion can be understood as one continuous process.

Winches 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 winches), it certainly could have been available in the Old Kingdom and is there

fore 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. 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 simul

taneous 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 build

ing 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 pyra

mids of the Old Kingdom, with individual modifications.

In the Queens' Pyramids of Menkaure, which are also Step Pyramids, 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. 7) 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 con

sists not of a core masonry wall with filling, but rather from well-hewn blocks that were installed in

alternate courses, as can be seen at the top of the pyramid of Khufu.

28 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.

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126 JARCE 44 (2008)

Fig. 7. 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 if at any point loose rubble raised suspicions

about the static quality of the ground, these areas 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

cu

bits?).29 Also, the base line of the lowest layer of the casing was fixed at 196 200 cubits (102.2

104.6 m).30 At the same time, the construction of the passages and chambers was planned, and build

ing started.31 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

29 V. Maragioglio and C. A. Rinaldi, L'Achittetura delle Piramidi Menfite, Band 6 (Turin, 1967) 38; (dergl. Addenda,

Taf. 4,

Abb. 2). 30

Maragioglio and Rinaldi, LAchittetura delle Piramidi Menfite.

31 In the present context, it is impossible to discuss why the entrance to the antechamber was later closed, and whether this

should be seen as a subsequent change of the original building plan, or whether the structure in question had been

a transport

pathway for granite slabs for the wainscot of the burial chamber.

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M?LLER-R?MER 127

could only be achieved by exact laying of backing and casing blocks. Starting from the blocks in the

lowest layer of the casing, an exact 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 incli

nation 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 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 pyramids, together with the respective filling material (stones of

various sizes and shapes, gravel, tafia, 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. Their design is illustrated by figure 8.

Several possibilities exist for the design of the transport way on the ramp:

1. The surface was made from smoothed limestone.

2. Ruts were engraved along the ramp surface, lined with mortar and filled with dolerite pellets. The ruts were slightly wider than the sledge runners.

3. The surface consisted of dolerite pellets embedded in mortar.

4. The surface was engraved with horizontal grooves into which wood beams were fitted.

One possible arrangement of ramps on the core steps is shown in figure 9. 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. 8), ramps can be positioned on each side of

the pyramid as follows:

step 1: 2 ramps

step 2: 2 ramps

step 3: 1 ramp

step 4: 1 ramp

step 5: 1 ramp

step 6: 1 ramp

Figure 10 gives a view from above to illustrate the positioning of the ramps. The dimensions of the core steps have been added (in meters).

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 trans

port capacity emerges which is significantly higher than that of perpendicular or spiral ramps. A perspective drawing of the ramps seem from South West is shown in figure 11.

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128 JARCE 44 (2008)

ili _+_17.00_+_?lML_t1'00*

Fig. 8. Suggestion for a transport ramp.

Fig. 9. Arrangement of ramps on the first to sixth core step.

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M?LLER-R?MER 129

Fig. 10. All ramps on the core steps as seen from above. For the sake of greater clarity, I have used

a base length of 104.6 m

here, and in fig. 11.

Let us now take a closer look at the transport system. We are dealing with transports on 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 winch is positioned at the side opposite

the sloped surface. Figure 12 illustrates what these winches may have looked like.

The winch consists of wooden beams that are crossed and bound together, then firmly planted into the ground. The roller lies on top of them. The largest blocks have sizes of approximately 2.3 m

1.4 m at a height of 0.6 m (weight 4.5 tons),32 which means that the rollers' supports can be posi tioned with as much space in-between as to allow the sledge to be drawn right up onto the platform

together with its load.

The front supporting beam of the roller is weighted with a maximum pressure of 3500kN (kilo

Newtons). In order to ensure that the back supporting beam is not dislodged from its bracings when

it is pulled upwards towards the roller with a force of approximately 1200kN, it is fastened on the

Blocks in the steps of the outer wall of the core.

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130 JARCE 44 (2008)

Fig. 11. Ramps used for construction of the stepped core (perspective drawing).

ramp with additional ropes. 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 min

imum, so that we safely may discount it.

The hauling vehicles, presumably sledges or similar devices made from wood, are likely to have

measured approximately. 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 pur

pose 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). To estimate the maximum necessary traction force for transport of the heaviest supposed load of

4.5 tons (see above), we base our argument on the following assumptions: one block measured approxi

mately 2.3 m 1.4 m 0.6 m. Several ropes were fastened to it, which were then led through a winch

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M?LLER-R?MER 131

5.00_._17.00_+_LuM_tl, 00

Fig. 12. Design of the winch at the top end of the ramp.

with 0.3 m roller diameter, coiled several times, and safely lodged to avoid slippage. On either side of

the winch there were eight or more spokes with an average length of 2 m, on whose end a rod was

fastened horizontally, or else the spokes were connected with wooden struts. The power transmis

sion amounts to 0.15 m (roller radius) per 2 m spoke length, that is to say 1:13. Four men can work

on each spoke with a force of 30 kp (kiloponds) (force directed downwards or forwards), moving 120

kp 13 = 1560 kp. If there are two spoke levels altogether,

one on either end of the winch, a total

traction force of 3100 kp is available.

This 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 of 0.25, that is to say the force

needed in the least favorable circumstances. Supposing that sledges or other wood devices with less fric

tion were used, or horizontally embedded wood beams,33 fine sand strewn over the sloped ground,34

or another kind of support covered with dolerite pellets, a traction load of a mere 2200 kp has to be

achieved,35 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, several coilings of the rope, and

a traction force along the ramp down to its base. The rope is led

back to the base of the ramp, where the workmen ensure that it is always pulled tight. At the same

point, a safety device would have prevented the load from slipping if, for example, a spoke snapped;

that is to say, a stopper (wood post firmly lodged in the rock) could hold the rope when it was in dan

ger of snapping back.

33 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. 34 The favorable effect of fine sand is comparable to the lowering of rolling friction by

means of stone pellets. 35 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.

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132 JARCE 44 (2008)

Fig. 13. Working platforms attached to the faces of the pyramid of Menkaure.

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 fill

ing. 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.

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 blocks36 and the

casing37 were completed starting from the base of the pyramid as a rule.38 In some pyramids, like the Queens' Pyramids of Menkaure G III b and G III c, only the core was

finished.39 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 pyra mid, for no other solution ensures the safety of the workplaces. In figure 13, I have sketched a solu

36 By backing, or backing blocks, 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. 37 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.

38 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, Die ?gyptischen Pyramiden, 226). 39 Peter J?nosi, Die Pyramidenanlagen der K?niginnen (Wien, 1996), 85.

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M?LLER-R?MER 133

tion involving working platforms attached to the pyramid's sides. 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 work

ing 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 pyra mid 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 approximately 5 m, 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 con struction 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 exe cuted vertically, but rather to fit the situation found on-site. This kind of work 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.40 To illustrate how the stone surfaces were smoothened, see figure 14 with a

representation from the tomb of Rekhmire (TT 100, Thebes West).41

By measuring the length of the sides of a finished course of casing blocks at the pyramid stump from one corner stone to the other, it was possible to ensure that the angle of inclination of the corners and the batter of the side faces of the pyramid still followed the designed course. Exact mea

suring of the base of the pyramid of Khufu has proven that this kind of measuring posed no insur mountable difficulties, in spite of the rock spur enclosed by the pyramid, which prevented diagonal measuring.

40 Herodotus reports that the pyramid was finished top down (Herodotus, Hist?ri?? 11.125, translated by Alfred Horneffer, Herodot Historien. Deutsche Gesamtausgabe [Stuttgart, 1961]). According to Diodorus, the construction of the pyramids involved earth walls (mud bricks) along the outer face of the pyramids (Wilhelm von Bissing, Der Bericht des Diodor ?ber die Pyramiden [Berlin, 1901])). Pliny mentions a terrace system (Goyon, Die Cheopspyramide, 173).

41 Norman de Gavis Davies, Rekh-mi-Re, PMMA 11 (New York, 1943), pi. 62.

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134 JARCE 44 (2008)

Fig. 14. Smoothing of stone surfaces, representation from the tomb of

Rekhmire (drawing after Davies, Rekh-mi-Re, pi. 62).

Calculating the Building Time of the Pyramid of Menkaure

In calculating the efforts made in building the pyramid for Menkaure, and the resulting building

time, we must use rough estimates in some points, especially as far as the block sizes are concerned,

which are different in each layer. However, as the burial chambers of the pyramid of Menkaure are

located below the core steps, estimating these numbers is comparatively straightforward. The measures of core and backing blocks are approximately 1.3 m 1.3 m 0.7 m (1.2 m3), thus

their weight amounts to approximately 3 tons, as the specific weight of limestone is 2.4 tons per m3.42

This calculation accounts for the fact that the core stones have slightly smaller dimensions than those

of the outer walls of the core. These numbers serve the purpose of transparent reckoning, as the

average block size will be used in the calculations of sledge loads and towing below.

For the stones of the casing, the mean measure is 0.7 m 0.7 m 1.1 m (0.54 m3, approximately 1.5

tons). Two of these blocks would form a sledge or hauling load.

Transport efforts as calculated here account for the building itself with core and casing, as well as

the attached working platform. Moving of the winches would only become necessary occasionally, de

pending on the number of transport units. Therefore, I have excluded this task from my calculations.

Also, the flat rate stone volume assumed for spaces filled with mortar, sand, and so forth, is negligible.

Throughout the construction process, a broad range of transport and building tasks was employed.

After upward transport, the stones had to be moved horizontally into their definite position. Due to

the limited number of ramps, upward transport required far more time than horizontal transport within one layer, as a greater number of workmen could be set to the latter task simultaneously. Horizontal transport may therefore be regarded as comparatively irrelevant to the building sched

ule, compared to ramp-dependent transport. Consequently, I have only taken into account ramp

dependent transport.

My model of transport of a sledge load, or a hauling process, up to a height of one step, is based

on the following practice-based assumptions: the duration of transport up to the next step amounts

to approximately 5 minutes, that is a towing speed of approximately 5 meters per minute, amounting to five winch turns per minute. For fastening and releasing of the ropes from the sledge

or the block, the shifting of the sledge or respectively the load, and the back transport of the empty vehicle, rope and so forth, 10 minutes should suffice. Therefore, a unit duration of 15 minutes is realistic.

42 Dieter Arnold, "Kalkstein," Lexikon der ?gyptischen Baukunst (D?sseldorf, 1997), 119.

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M?LLER-R?MER 135

Further to the schedule calculation, we need to keep in mind that the blocks for the upper steps

had to be moved over several ramps, which was a more time-consuming procedure. On the other

hand, if we start from the assumption that a block was conveyed continuously from one ramp to

the next to its final destination, it follows that a new block would reach the construction level every

15 minutes, be it via sledge or hauling. The additional effort necessitated by the greater height that

had to be overcome could be compensated by an increased workforce. The assumed average values

for block weight and unit duration directly influence the estimated building time. If these sizes are

altered, a new schedule will result. Obviously, calculations such as these are always more or less hypo

thetical, depending on the numbers inserted above.

The respective volumes of the six core steps add up to a volume of 140,736 m3, that is 117,280

stone blocks at a volume of 1.2 m3 each and an equivalent number of sledge loads. The seventh step

with its volume of 900 m3 was built at a later stage when the platform had been installed (see above).

Further to a calculation of the building time of the core, we propose that a sufficient workforce

was available on three hundred days of the year, ten hours per day (shift work), which means that

under the circumstances outlined above (15 minutes per load), a total of 12,000 units were conveyed in a year. Therefore, the building of the core took 1.7 years. We still have

to add construction and

removal of the ramps on the first to sixth step, that is thirty ramps at a total volume of approximately 9000 m3, requiring a total of 0.4 years, if work took place

on all sides of the pyramid. Therefore the

entire core could have been readily completed in just 2.1 years.

My calculation of transport volume and building schedule for the working platform attached to the

outside, plus the seventh core step, backing and casing, covers a volume of 157 728 m3 or 17,486 work

units. If again we base our calculations on the availability of the workforce as outlined above,

a total

1.5 years results. Next, the ramps and the platform need to be removed, and the stones left in boss

need to be dressed. The removal of said structures requires 0.5 years in keeping with the framework

set out above.

Only a rough estimate can be offered for the dressing works on the facade. A time frame of about

0.5 years seems realistic in the light of the following considerations. Firstly, the lowest sixteen layers

were left partly unfinished (granite wainscot). Secondly, we may assume that on one day (10 hours of

work in shifts) one team of workmen succeeded in dressing a facade area of 1.0 m 1.0 m (Tura lime

stone from the seventeenth layer onwards). In the case of the granite wainscot, the area would have

only been 0.5 m 0.5 m.

Then, in order to calculate the schedule for the dressing works, the outer face of the pyramid is

divided into eight stumps (arranged in steps as in figure 13, for measures

see figure 7). Next, the

circumference of each is measured and the respective area is calculated. Thus, the number of days

spent on the task can be determined. In order to avoid intruding on one another's workspace, there

is a minimum distance between two work teams amounting to 1 m. From this, there results the num

ber of teams set to work on each pyramid stump and the number of days needed for dressing. By

employing up to 170 teams, the same work process can be undertaken in the lower part of the pyra

mid, on all four sides at the same time. The number of teams can be increased steadily, and new

teams can be trained and broken in continually. At a height of 65 m, excluding the eight lowest layers, an approximate duration of 155 days

or 0.5 years results. However, we must still keep in mind that

the removal of the working platform and the ramps must be coordinated with the dressing and

disruptions must be dealt with. To account for such unforeseeable circumstances, another 0.5 years

are added.

The debris accumulated during removal of the ramps and the working platform, largely mud

bricks, amounted to roughly 60,000 m3, that is approximately 25% of the pyramid's volume. While

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136 JARCE 44 (2008)

mud bricks could be distributed for use on the surrounding agricultural domains, the rest of the

debris was stored on the north eastern slopes of the desert plateau and in the area towards the south

of the Giza plateau. The building of the pyramid of Menkaure, not counting the time spent on pre-construction prepara

tions, therefore took approximately 4.6 years. All in all, an average volume of 202 m3 of stone or 186

blocks were moved per day.

Towards a Comparison of the Building Times of the Red Pyramid and the Pyramid of Khufu

How does the schedule proposed for the pyramid of Menkaure compare to that of the other pyra mids? In the following section, I propose for comparison some calculations for two other pyramids, for which a good enough time frame is widely acknowledged. Again, my calculations are based on

estimates in some instances. I base my arguments on the points made above with reference to the core steps, ramps, and unit duration. Similarly, the construction of backing, casing, and working plat form is assumed to follow the same principle as illustrated above.

Building time calculation for the Red Pyramid

In order to estimate the building time for the Red Pyramid, we need to first establish a frame

work of data that can only partly be verified by archaeological evidence due to the pyramid's state

of preservation.

The height of the respective steps is assumed to be 10 m. Therefore, the pyramid has a total of ten

steps.

The average size of the backing and core blocks is approximately 1.1 m 1.0 m 0.7 m,43 which is

a volume of 0.77 m3, or a weight of 1.9 tons.

Although the ramps are slightly longer, the duration of a single unit can be fixed at 15 minutes, because the average weight is lower in the Red Pyramid than in the one previously discussed.

The number of working days per year and hours per day is equal to that discussed above.

The building of the two burial chambers is not taken into account, as these are subterraneous

structures.

These assumptions are illustrated by a cross-section of the Red Pyramid which reveals the stepped structure of the core (figure 15).

Our estimation of the building schedule of the Red Pyramid, not counting the preliminary prepa rations, will again start from the assumption that construction works took place on three hundred

days of the year, on ten hours of each day, in shift work. It follows that a total of 12,000 transport units of 15 minutes each could be carried out per year. Thus, the construction of the core of the Red

Pyramid took 9.9 years. The time needed for the construction of the working platform, backing and

casing, adds up to 4.8 years. For subsequent removal of ramps and platform, and dressing of the

43 John F. Perring, Pyramids, vol. 1 (London, 1893), has measured the height of twenty-one steps of backing blocks starting

from the bottom step. In total, their height is 21.4 m, which leads to an average step height of 1.02 m. The width is said to be

0.9 m. V. Maragioglio and C. A. Rinaldi, L'Architettura delle Pyramidi Menfite, vol. 3 (Turin, 1963), 126, and also Addenda, pi. 19,

fig. 6, suggest the heights of the stones are 0.5 to 0.7 m and their depth 0.9 to 1.2 m. Ranier Stadelmann, "Die Pyramiden des

Snofru in Dahschur. Erster Bericht ?ber die Ausgrabungen an der n?rdlichen Steinpyramide," MDAIK 38 (1982), 380-81, writes that the height of the corner blocks of the backing, up to a point at two thirds of the height of the pyramid,

was 1 to

1.3 m. Richard Lepsius, LD 1, texts (Berlin, 1897), 206, describes the blocks of the core masonry to be altogether ". . . maybe

not quite as large as in Giza. . . ."

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blocks left in boss, 1.7years should suffice. The time frame for dressing comprises approximately 223

work days or 0.75 years. If we assume that this time must be added to that needed for the removal of

the working platform and so forth, the actual building time of the Red Pyramid results at 16.9 years,

during which in total an average of 443 m3 of stone, or 576 blocks, were moved each day.

Building time calculation for the pyramid of Khufu

Again, as in the case of the Red Pyramid, some assumptions have to be made with reference to the measurements and the number of the core steps that are partly impossible to corroborate by archae

ological evidence as yet.

My starting point are my own observations and studies. In the tomb-robbers' tunnel the structure

of the core masonry changes abruptly in layer seven (lower edge at 7.06 m over foundation level), about 15 m behind the entrance. Considering the horizontal measures of the outer wall of the first core step (1 m) and of the casing which is not preserved (approx. 3 m), and also the inclination of the outer wall of the core steps (80?), there results a base length of the first step of the core of approxi

mately 197 m (375 cubits).44 The height of the steps is likely to be 11 m and the number of steps twelve.45 The width of the steps accordingly is 5.75 m, if we take into account the alignment of 54?30' along

the steps' edges on the lateral surface.

The unit frequency differs the pyramid of Menkaure, because the ramps are significantly longer, thus approximately 20 minutes.

44 This is an assumption based on calculation, which does not include the streaks of solid rock that reach the backing. The same is true for the suggested ramp arrangement on the first step of the core.

45 Graefe, Determinanten, proposes eleven steps at a height of 13 m each for the core steps, at a width of 7.35 m. Thus, the

line of the steps' edges on the lateral surface also reaches 54.5.

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138 JARCE 44 (2008)

The volume of the bed rock core in the base of the pyramid is assumed to amount to 7.9% by Haase,46 and 7.7% in more recent studies, i.e., 200,000 m3.47 Goyon supposes a volume of 127,000 to

160,000 m3.48 I shall use the volume of the rock core given by Haase. Further construction data as the number of working days per year and the size and average weight

of the stone blocks and so forth are the same as for the pyramid of Menkaure.49 To illustrate these suggestions, figure 15 shows the pyramid of Khufu with its stepped core. In order to estimate the building time of the pyramid of Khufu, not counting the preliminary prep

arations, we again assume that a sufficient workforce was available on three hundred days of the year, ten hours a day, in shift work, so that at a duration of each transport unit of 20 minutes a total of 9000 rounds per year could be achieved. Accordingly, for the core of the pyramid of Khufu, the time

needed for transport of blocks amounts to 13.1 years, or just 12.4 years if we subtract the volume of the bedrock core. The building time for the working platform, backing and casing amounts to a total of 6.0 years. Finally, the ramps and the platforms need to be removed, and the blocks left in boss

require dressing, which all in all takes 1.8 years. As the time spent on dressing amounts to approxi

mately 286 work days, or one year. If we assume that this must be added to the removal of the work

ing platform and so forth, the actual building time of the pyramid of Khufu results in 21.2 years, during which an average amount of 393 m3, or 327 blocks per day were moved.

I should like to emphasize again that these observations are based on rough estimates for the block

sizes and weights, and to be precise, they ought to be modified by adding some more detailed expla nations, for example as to how the large limestone blocks over the entrance on the North side of the

pyramid, or the granite blocks of various shapes (Grand Gallery, burial chambers, stress-relieving chambers, plugging blocks) were moved (figure 16).

It may well be the case that in the lower area at the various pyramids' East some tangential ramps with a less steep inclination were erected in order to convey the larger blocks with a weight of up to

60 tons, which were delivered along the causeway. On the other hand, it is quite possible that the

causeway was continued at an even inclination (10:1) towards the base of the pyramid or into the

actual building site, reaching a height of 40 to 45 m above base level, at which height the ceiling slabs

could be conveyed further upwards. These considerations, however, are best discussed elsewhere.

Starting from his own observations on the topographical situation at the SW corner, Lehner shows

that the ramp, approaching the pyramid from the Southern Quarry, would have met the pyramid at

about 30 m above base level.50 Furthermore, we should not go without mentioning a solution for

heavy load transports during the building of the pyramid of Khufu which Haase has published

recently.51

Summary of Results

Several solutions that have so far been offered for issues of the construction of the ancient Egyp tian pyramids by Stadelmann, Arnold, Lehner, Goyon, Klemm and Klemm, Lattermann and Houdin,

46 Michael Haase, "Der Felskern der Cheopspyramide," Zeitschrift f?r Arch?ologie und arch?ologische Grenzwissenschaften

(1/1993), 5-13. 47 Michael Haase, Eine St?tte f?r die Ewigkeit. Der Pyramidenkomplex des Cheops (Mainz, 2004), 17. 48

Goyon, Die Cheopspyramide, 117. 49 In a number of publications, an average volume of lm3 is assumed for each stone block, from which an hypothetical

volume of the pyramid of 2.3 10b m3 results. The solid rock core, cavities, and the spaces filled with mortar and rubble are

neglected. 50

Lehner, "Development," 109-43. 51 Michael Haase, "Eine Rampe f?r Schwertransporte beim Bau der Cheops-Pyramide," Sokar 15 (2/2007), 48-49.

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M?LLER-R?MER 139

le 16.41 t_197,18_^ 16,41 ̂ _230, 00_.

Fig. 16. Arrangement of ramps for the building of the core of the pyramid of Khufu.

which are based on the assumption that perpendicular or integrated ramps were used. Other expla nations involve steep ramps running parallel to the core steps (Landt, Graefe) have also been noted. Still other authors suggest the use of winches, for example Riedl, Pitlik, and Keyssner. However, most

of these authors assume that the core was built layer-wise; moreover, many do not offer solutions as

to how the pyramidion was set, and how safety was ensured when the casing was applied and dressed.

Building time calculations are only offered occasionally. The observations which I have presented here and elsewhere, lead to the conclusion that difficul

ties encountered in building the Bent Pyramid prompted the architects of the Red Pyramid to revise their construction methods in order to control the threat to the pyramid through ground erosion and

earthquakes. At the same time, it was crucial to keep the building time as short as possible to meet

the king's request for swift completion. As a result, a stepped core was erected, to offer more stability on the one hand, and on the other hand to enable ramps to be positioned on all four sides of the

pyramid parallel to the core steps, in order to allow for material transports in a shorter time frame.

Also, larger stone blocks were used. Subsequently, during the building of the pyramid of Khufu, the same methods were employed, and the size of the blocks was increased still further, in order to finish

the vast building as soon as possible.

My hypothesis for the building of the Step Pyramids of the Old Kingdom involves combined use of

ramps and rollers, which are both archeologically attested, in a device commonly known as winch.

Compared to previous suggestions involving transport of material by towing crews, the ramps were

positioned in line with the steps of the core and to the working platform and were thus built with a

steeper slope. As we have seen in the case of the pyramid of Menkaure, there is no longer a need

for perpendicular ramps, or integrated ramps with less slope. Under these circumstances, we may

dispense with any more complex solutions for the constructions. The use of several ramps with a

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140 JARCE 44 (2008)

steeper gradient ratio (26.5?, 2:1) on the core steps and the platform, on each side of the pyramid,

leads to a steady and frequent influx of material, thus emerging as the best time-saving device that has

been proposed so far.

Following the construction of the core and the removal of the respective ramps, backing and casing

were applied layer-wise, after stepped working platforms with ramps had been installed around the

pyramid, all of which were removed as the dressing of the casing proceeded top down. This

same

platform also offers a convenient solution for works at the pyramid's top including the pyramidion.

The calculations of the transport effort and the resulting building time are based on the least favor

able circumstances in terms of block size and weight, the ramp surface's friction, and transport unit

duration. If any of these conditions are found to be more favorable, either the number of ramps could be reduced, or the building could be finished sooner. I have occasionally mentioned

alternative

solutions to some details, such as the ramp surfaces, but these do not have a significant effect on the

overall construction method.

A calculation for the building times of the pyramids of Menkaure, Seneferu (Red Pyramid), and

Khufu would realistically render the following results:

Pyramid of Menkaure: - planning and preparation?1 year - building time, including dressing?approximately 4.6 years52

- total 5.6 years.

Red Pyramid: - planning and preparation?2 years

- building time, including dressing?approximately 16.9 years

- total 18.9 years.

Pyramid of Khufu: - planning and preparation?2 years - building time, including dressing?approx. 21.2 years

- total 23.2 years.

These building times fit well within the accepted dating of the reign of Seneferu (thirty-five

years),53 Khufu (twenty-three years),54 and Menkaure (twenty-eight,55 or six,56 years). The present article offers a solution that has been developed from archaeological evidence.57 It is

centered around the idea of "pyramid building with ramps and winches." The solution involves steep

ramps positioned in line with the steps of the pyramid's core, equipped with rollers in the form of

winches for transport, and superseded by a working platform attached to the pyramid's sides to en

able safe setting of the pyramidion and dressing of the casing.

Ludwig?Maximilians?University, Munich

52 The dressing of die casing is not quite finished. 53

According to new results, thirty-three years, Rolf Krauss and David A. Warburton, Ancient Egyptian Chronology (Leiden,

2006), 490. The building of the Red Pyramid was begun in year fifteen of the reign of Seneferu. 54

According to new results, twenty-six years, Krauss and Warburton, Chronology, 491. 55

J?rgen von Beckerath, Chronologie des pharaonischen ?gypten (Mainz, 1997), 188. 5b

According to new results, only six years, Krauss and Warburton, Chronology, 485. 57 pranr; M?ller-R?mer, Pyramidenbau im Alten ?gypten (M?nchen, 2008), published electronically

at http://archiv.ub.

uni-heidelberg.de/propylaeumdok/volltexte/2009/349.

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