03-1 Model of reference

I have long asked myself: from which documents did this huge construction, involving thousands of people for 20 years on an area of 1,000 km, is based on?

My experience in the industry, based on paper documentation and printing plans, misled me. For some time, this documentation system has been replaced by a digitized one, completely virtual, that is not historically stable. Another system could have existed before it.

No need to remind you that the ancient Egyptians became masters in the art of cutting into stones, even the toughest of all, all sorts of objects of complex forms with absolute precision.

I therefore propose that the pyramid’s “construction file” would never have been in “papyrus” form but in 3D model form, as we do today, but not digitized and transformed into electromagnetic impulses on a microscopic device, accessible only with a well-defined type of computer, and all of which could disappear effortlessly and completely instantly.

No, the 3D model I’m thinking about would have been in the form of carved stone objects representing the same objects in the pyramid on a reduced scale and serving as a model for the stonemasons, who had only to make what they had on hand on a 1:1 scale.

For example, the upper chamber, entirely made of granite, could have had two identical scale models, one on the construction site at Giza and another at the quarry of Aswan, 1,000 km to the south.

The one at Aswan served as a model to cut the blocks, and the one at Giza was used to check them and guide the construction project.

These model scales are precise and solid; rain cannot destroy them, only clear them; wind cannot blow them away. There is no need to know how to write, read or even speak the same language; only how to measure and reproduce suffices. Each approved piece wore the project manager’s seal. They were probably made of granite, diorite, or some other very hard stone that only specially equipped workshops could produce.

This system could not be counterfeited and slowed well-known trends of the design office for constantly changing the plans to “improve” the finished product because the decision to do so was in the hands of the modeling workshop that guaranteed the pyramid’s integrity and was placed under the watchful authority of the project manager.

Moreover, there was immediate technical validation since a design error would be immediately visible and verifiable by all authorized parties examining the new model before approving it.

The “design office” was in the fresh air; the hammer and the chisel were the pencil, the stone was the paper, and the eraser was a blow of the hammer, and here we go again!

I think that only the crafted part of the pyramid was represented this way, i.e., the chambers, the galleries and the siding—less than 1 % of the pyramid volume. As for the 99 % of the volume left, the pyramid siding, the workers built the courses more or less like dry-stone walls builders did, which have almost disappeared and whose work can still be admired.

The difference was that the stone could not be held in the hand and could weigh several tons. The observation of the course 201 of the Great Pyramid would discourage protesters from using such an analogy.

Besides, laying out as you go along requires solid logistical organization for handling a flow of 400 very heavy blocks a day. No documents were needed; a routine was established.

Only some of the filling blocks needed to be re-cut, probably on the bedding where it had been laid, to fit the masonry and siding dimensions, but no documentation was produced; the stonemason’s skill was sufficient.

Quarry men worked to cut a small wall whose thickness was equal to the course “of the day” and as wide as the bedrock from which it was cut.

Instructions about the width were given daily, with no precision requirement, and depended on the flaws of the cutting bench. For the rest, a “giant battering ram” broke the small wall into smaller pieces, like we would break sugar.

The model, once assembled, showed all the inner parts connected to each other and their support, the central masonry. Each of these parts could be pulled out to be examined and served as a model for the stonemason.

A mini-pyramid cut exactly along its north-south axis was placed next to the model of the inner volumes; this explains why the axial plan of the inner galleries shifted 14 cubits to the east of the pyramid’s north-south axis. This plan allowed the east-west positioning dimensions of all the objects to be placed in the pyramid.

Only the upper and lower chambers, the grotto and the mortuary complex could be cut in two by this plan; the western part was embedded in the central plan, displaying the interior of both the east and west sides.

This 14-cubit shifting suggests that the reduction ratio had to be 14/1, leaving a one-cubit space to move between the central plan and the masonry to take measures. This model would have been 20 cubits high and 31 cubits and 12 fingers (or a big claw) on the sides, leaving a significant inner volume to hold, in the shadows, the office of the architect on site!

The bigger pieces, like the beams closing the ceiling of the upper chamber, would have weighed just 10 kg for about one cubit long. They could easily be manipulated and serve as a model of reference for both the production and the preparation of the handling.

This mini pyramid had to be placed to the south of the pyramid under construction so that the sun, the point of reference, would not be blocked by the pyramid. This way, the very precise orientation towards the south could be adjusted, which allowed geometricians to practice using the edges and faces of the pyramid in the sun’s shadow at certain times of the day, on certain days of the year, to check the alignments.

03-2 Rope-deflecting rollers

The use of rope was limited on the construction site. It was used to lift the freshly cut blocks about 0.5 m from the cutting bench and place them on their bearings, raising the ballast up to six meters to operate the east shaft located on the pavement access to the pyramid. Once the pyramid was finished, the rope was also used to haul up the filling stones to the last cage at 140 meters high and then control their descent from there.

All these tasks required rope-deflecting rollers. Nowadays, pulleys would be used, but at that time, pulleys had the same disadvantage as the wheel when it came to withstanding loads of several tons:

It required an axis that could support this charge, which is not easy with wood or copper. But that is not all. There was also the pulley rotation problem on this axis, which would have had to be of a considerable diameter and therefore would have generated significant friction, which, absorbing too much energy, would have worn out rapidly.

One might argue that an oil could be used to lubricate the pulleys’ rotation on their axis, which could have been a solution. But on a construction site in the open air, frequently exposed to the winds from the nearby desert, sand would mix itself with the oil or grease, turning the lubricant into an abrasive paste.

Nonetheless, a hundred or so rope-deflecting rollers, at the most, were enough. This meant that builders could “tweak” them by reusing the technology used to operate the cone rollers of the autonomous roller skate.

Below, I represented the rollers in a 5-cm-diameter round section, 10 cm wide, but coned rollers could do the trick, hewn into granite or diorite, with an axial hole to hold the axis that will serve to hold the cord “links” together.

The “links” don’t have to exert any effort; they simply keep the rollers at the right distance.

Inside the caterpillar track, there is the pulley’s axis, and the rollers spin above. Each roller does a rotation on itself at the same time and moves along the axis’ surface, making the pulley.

A second caterpillar track is placed further on the axis, the whole resting on a semi-opened support, and we obtain a beautiful roller bearing pulley with a low rotation resistance since there is no friction and only a small distortion of the axis where the roller meets the axis.

For better output, it is best to have a support made of hard stone, such as granite or diorite. I represented it here in a semi-round shape, but that is a luxury; a V- or U-shaped support could do the trick!

The ancient Egyptians could have made such a device.

If the load is very heavy, all it takes is to increase the diameter of the axis and add rollers to the caterpillar track inside a bigger support.

03-3 Wood

Wood was used for the big floats (the bearing’s road?) and for various frames.

As Egypt was not a renowned wood producer, records of its expeditions to Lebanon to procure quality wood have come down to us despite its ancient origins.

The boat found in detached pieces in a trench at the base of the pyramid tells us that Egyptians knew how to work wood with precision on a large scale.

Frames measuring just a few meters in length and a few dozen centimeters in cross-section would have been part of the professional carpentry routine at the time, as would roller tracks manufactured in assembled sections.

The strategic piece of the roller track is the hammer-hardened copper. Wood could have been used to support the copper, but this function could just as easily have been performed by limestone masonry in fixed pavements, such as that linking the Nile or the quarries to the pyramid.

On the other hand, on the course, the track needs to be constantly moved in small sections, and I can only see Wood doing that very well.

The large floats had all the functional characteristics of large ships that the Egyptians knew how to make, and although a watertight float is a rather special craft, there’s no doubt about their ability to make them.

The sight of the “solar boat” found at the foot of the Cheops pyramid, however, casts doubt on the technique used to build floats.

The planks are joined with ropes, which doesn’t seem to provide a sufficient watertight seal, let alone the airtight seal required for first- and second-generation floats.

I think that the float may not have been a marine construction but could have been an assembly of hardwood pieces with a density close to one and filled with low-density material, probably cork (density 0.25), both resin-coated so as not to absorb water, which would have upset the hydrostatic balances, which had to be very precise.

As the weights of these had to be variable, a 0.5 x 05 m interior chimney, opening to a volume at the bottom designed to receive copper bars as ballast, was needed as these volumes were underwater.

As for the air volume of the “bell” needed for the good operation of the first- and second-generation floats, it could have been made of a whole set of pork bladders or something similar instead of an air pocket waterproofed with resin that would have then been placed into the float’s structure that is naturally water- and air-proof.

This construction technology would be perfectly consistent with the frontispiece of the pyramid design office:

Bold, simple, effective, reliable and cheap.

03-4 Copper

This may surprise readers, but copper was, for the pyramids, a strategic resource of first importance.

Give it the credit it deserves; without copper, the pyramids would have never been built.

Despite common conceptions and what some archaeologists claimed, copper was never used to directly cut the stone; it is not hard enough for that.

But copper alloy might have been used for the support and drive of the hard stone cutting edges, which first had to be embedded in a copper support pad.

But foremost, the main interest in copper for the construction site is its density of 8.9.

Builders used it as ballast, and they needed dozens of tons of it to make the elevator floats function and to power the driving force of the pendulum.

Phenomenal quantities of copper were used, probably in the form of bars weighing around 40 kg that could be easily handled and stacked up.

The consumption was so heavy that a permanent logistic road was established between the Sinai mines and the construction site, as attested by recent searches of Wadi el-Jarf led by P. Tallet from the Sorbonne.

The copper was also used to build roller tracks to ensure the transportation of the blocks.

By examining the cone roller characteristics, we notice that these rollers could, in contact with the ground, rapidly exert a pressure that exceeds the nummulites limestone filling stone resistance, which is around 40 N/mm2; it exceeds that of Turah quarries, evaluated around 60 N/mm2, and even that of Aswan granite, around 220 N/mm2. The copper is hammer-hardened and has a constriction resistance of around 320 N/mm2. Copper is then completely hammer-hardened and has a compression resistance of 320 N/mm2.

The ancient Egyptians could therefore have used this property to harden copper into the furrows that guided the rollers on the stone transport pavements.

According to recent archaeologists ‘searches, the copper available at that time was “pure” with a certain impurity degree of arsenic, depending on where the ore was mined and how it was obtained. Bronze, an alloy of copper and tin, was not yet in use.

For the study, I will keep the physical characteristics of hammer-hardened copper, whether it is referred to as bronze or copper.

The compression elastic limit is 300 N/mm2, the Young’s modulus is 125 Kn/mm2, and the density is 8.9 T/M3.

The alchemical symbol of copper is strangely close to “Ank”, the key to life that the Egyptian gods held in their hands.

03-5 Stones issue

Granite for the upper chamber, refined limestone for the siding, or coarse limestone for the filling—no matter its aspect, stones are the primary resource for the pyramid.

Granite:

The upper chamber masonry is made of granite extracted from the Aswan quarries, 900 km to the south, and precisely cut. I did not go to the extent of explaining the extraction and manufacture processes of these blocks, sometimes gigantic, but I gave more details about their handling from Aswan to their final position in a chapter dedicated to the megaliths.

Casing:

The siding blocks were extracted from Turah quarries, 20 km to the south of the construction site. I don’t mention their extraction either; however, the extraordinary “Merer’s journal” unearthed by P. Tallet provides us with significant information about the fluvial transportation of the blocks.

Filling:

The filling blocks are made of nummulites limestone; they represent 96 % of the total volume of the pyramid. The entire operational problem of the stone treatment is about this material.

For all that, is it well known?

To my regret, despite the considerable number of measures taken on these pyramids, I failed in finding hardness, density, or compressive force measures for these stones.

This lack of information about the physical characteristics of the stones reveals how little effort was made by the authors of the different studies to really understand the work involved in building these monuments.

In addition, we found many geological studies about the constitution and composition of stones but very few measures about their physical characteristics.

Lacking anything better, I fell back on a nummulites limestone that can be found in stores in France, whose density varies from 2.1 to 2.5 T/M3 and compressive force between 30,000 and 60,000 Kn/M2.

For my calculation, I arbitrarily retained the following values: 2.4 T/M3 and 40,000 Kn/M2.

To dig furrows into the rock, there was no other way but to use a tool with a cutting edge at its end to exert a pressure that exceeded the compressive force of the rock to break it and smash it to dust.

Therefore, to break the stone with a cutting edge, a pressure must be exerted on it that equals the rock’s compressive force multiplied by the contact surface of the tool.

It breaks the rock down bit by bit.

The energy consumed by the cutting is the result of the movement of the tool, and the volume of broken rock is the result of the contact surface of the cutting edge.

Therefore, the cutting movement of one meter on a 1M2 surface breaks 1M3 of the rock down and meets a 40,000 kN resistance and consumes an energy of 40,000 KJ, or 11.1 kWh.

To realize this work in an hour, it requires a power of 11.1 kW.

Whether it is made in one big cut or in smaller cuts, it still has a power of 11.1 kW.

Needless to say, the cutting edge has to be harder than the nummulites limestones to obtain this result, so it doesn’t warp.

This requirement disqualifies the metals available at that time, including copper because its hardness is the same as limestone’s.

This means that the cutting edge must be either a gemstone like corundum, quartz or diamond, either amorphous stones like basalt, flint or obsidian or compound stones such as granite or diorite.

In all these cases, these hard stones will disintegrate quickly with repeated, hard shocks.

A solid tool is efficient since there is no wasted time replacing it.

Therefore, the stone must be gradually cut without inflicting shocks on the cutting edge.

Extracting blocks

03-6 Hydraulic Elevators

Despite many common hypotheses, neither ramping methods nor the Herodotus machine were used to build the pyramids.

For the six Great Pyramids, 99 % of the stones were hauled up by millions thanks to counterweights descending along the opposite face, steered by a winch.

This method is particularly quick and efficient, but it was limited to a load of seven tons because of the ropes’ resistance.

Meaning that the very heavy monoliths, especially the rafters of the vaults, the beams of the five ceilings of the upper chamber, and those of the real burial chambers, were hauled up by sliding floats in wells filled with water and are left to be discovered in the “BIG VOID”.

The stepped pyramid of Saqqara, attributed to Djoser, brings the novelty of oscillating floats to lift the big slabs of rock. These floats are directly inspired by naval architecture; actually, they are specialized vessels for a vertical trip, not a horizontal one. They have a heavy counterweight in their bottom part to stabilize the load put higher above the deck, which means that the load is relatively low, and they operate very slowly.

The following pyramids, Meidum and Red, respectively 2.3 and 6 times bigger than the first one, hid three well shafts; six of them are visible in the rhomboidal pyramid instead of 12 in the first. To lift heavier stones, a second generation of submersible floats saw the light of day.

These floats are more efficient than the first ones, and will be used, not exclusively, for all the Great Pyramids, from Meidum to Khafre’s.

Nonetheless, these floats’ performance was limited to charges of two or three dozen tons, but we found some megaliths weighing approximately 30 to 70 tons inside Cheops; some of them were to be raised 60 meters above the base.

These rocky monsters exceeded the submersible floats’ capacity; it would have required a gigantic plateau as big as that of the “trench of the sun boat”, located on the plateau to the east of the pyramid so that they could be lifted.

Credits to Maraglioglio & Rinaldi

For such a surface inside the pyramid, the builders ran out of solutions to hold the pressure with stones.

A chamber is like a bathyscaphe that overcomes the compression stress inside the pyramid. The lower chamber of the Great Pyramid is under pressure, corresponding to a depth of 300 meters under the sea.

The biggest masonry chamber of the seven pyramids is Cheops’s upper chamber; it is 50 m2, and its ceiling is broken!

Despite a well-shaft of low section regarding the pyramid size and the stones to lift, another float method had to be found, one that could act as springs of tremendous strength while being height adjustable.

The pyramid of Cheops features three chambers, each of which is a water reservoir supplying a float elevator shaft; only the upper chamber obviously shows its associated shaft, covered up as a “harrows chamber”. This shaft has a 1.5 m2 section and is supplied by a 50 m2 chamber, meaning we can calculate the section of the two other, still undiscovered to this day, which are fed by two other chambers whose free water surface is known, namely 71 m2 for the lower chamber and 120 m2 for the horizontal gallery and the underground cave.

A thorough examination of the lower chamber niche allows us to guess that the two other shafts containing the first and second stories’ floats are within masonry to the east of the chamber.

The detailed operation of these elevators will be described floor by floor later.

03-7 Winch course

The electric motor is the slave of our modern era; it is so common that we don’t pay attention anymore. How many engines did you count in your car or in your home?

In antiquity, the only available motor was men or, in some cases, animals.

No matter the method used, the driving force always comes from men, i.e., a single power of 80 w for one workday that can come up to 200 w for several hours and more than 2 kW for seconds.

We will see later how the ancient Egyptians could use this driving force to make a surprisingly powerful engine!

But the archaeologists who wrote and published about the pyramids settled for a single man pulling loads with a rope as a driving force.

A single walking man pulling a load can only produce a traction force inferior to his weight multiplied by the friction coefficient of his feet, which were bare at the time; the coefficient can vary around 0.3 depending on the nature of the ground.

To transport a block, the authors suggested putting it on a wooden sled that slides on a wooden track, lubricated with water.

The friction coefficient of wood on wood in these circumstances is around 0.2. It means that to drag a block on a sled, the operator’s weight must be the same as the load’s weight, while considering that when working in groups, there is swelling, hence a loss of strength.

So, to lift a load on a ramp with such a method would amount to lifting the load up twice, in addition to the wasted effort made to overcome the sliding resistance and the energy consumed by walking.

As a result, the energy efficiency is catastrophic—around 30 %, whereas the energy consumed while hauling could reach 200 W.

In my study, I suggest a different approach. The maximum strength a single man can always exert is his weight. So, I imagine a system in which the operator falls either with the load, for when the float needs to be sunk, or on a rope that will transfer his strength to the wheel, activating a winch or a cutting-disc.

Let’s take the example of a winch that is put on the course and drives the counterweights with six operators in charge. It can produce a strength of 1 ton to block ascending at a speed of 1.5 m/s. Its driving wheel spins at a tangential velocity of 2.5 m/s, and its axis is 2.5 m high. A fly rope has been weighed down and coils three or four round-turn knots on the wheel, suspending the operators on the tight side, and the weight of the rope on the slack side is enough to tightly lock the rope onto the wheel cylinder.

The operator jumps to take the rope at 2.5 meters high into both his hands, then quickly goes down with his hands at the level of his solar plexus, even his knees. Once down, he lets go of the rope at 0.5 meters and lands on a slide that takes him to the operator before him, who catches him and helps him get back on his feet before going back in line to start over.

There is a delay of 0.8 seconds between each operator, so they have time to get themselves into position to catch the following operator. At the landing, there are three operators: one who catches then goes back in line, another gets into position, and the last one waits.

The rope moves at a linear speed of around 2.5 m/s, and it could take 0.8 s to go two meters down. Once the rope is in the hands of an operator, another operator takes it back at 2.5 m, and so on…

It has a very fast rhythm worthy of a music-hall spectacle.

It is a gesture worthy of a trained athlete. If an operator were to be weighed down to 1 KN while descending along the rope for two meters, he would have given a potential energy of 1×2 = 2 KJ with a 0.8 second recovery to the driving wheel and would have exerted a power of 2 / 0.8 = 2.5 kW.

This equals the power generated by a javelin thrower, a shot putter, a weightlifter, or a jumper, a gesture brief but intense.  To maintain a bearable rhythm of 200 W for a few hours before the relief, an operator had to wait in line for at least 10 s. So to operate the device, the line had to be at least 10/0.8, resulting in 13 people waiting in line.

At full power, there were always three people on the rope; therefore, the power of the driving wheel could be 2.5 × 3 = 7.5 kW, and the winch, being equipped with two wheels, produced a power of 15 kW at most.

Depending on the weight of the block to be lifted and the counterweight, the winch didn’t have to be operated at full power all the time. For example, the length covered by the previous operator simply had to be increased from 0.6 to 1 meter before the next operator took hold of the rope to reduce power from 15 to 12 kW.

03-8 HUMAN RESOURCES

We don’t have much information about the human resources of the project. The latest available information from the excavation of the workers’ village at Heit el Ghurab, at the foot of the Giza plateau, was provided by Mark Lehner, director of the excavation, who reported a maximum of 2,000 workers on the pyramid site.

Labor and the Pyramids: The Heit el-Ghurab “Worker’s Town” at Giza 

Mark Lehner, University of Chicago and Ancient Egypt Research Associates

Excerpt: A Colloquium Held at Hirschbach (Saxony), April 2005

Volume V, page 471

VizierAnkh Haf, half-brother of Cheops, was identified as the main organizer of the work, andHemiunu, also a member of the royal family, was named architect. The mastabas around the pyramid containing their statues have been found.

Their tombs sheltered their statues, some writings, and engravings on the walls, but no information about the pyramid, unlike the empty chambers of the pyramid.

Thanks to Lehner’s searches in the builders’ village, which covered an area of 150 000 m2, different types of housing were uncovered: luxurious villas for the managers and dorms for the workers (called NFRW-neferu). These dorms were organized by “gangs” of four “phyles,” grouping five “divisions” of ten individuals, that is to say 200 workers. To conclude, 21 people managed 200 workers.

Considering that the workers were sleeping in dorms, after cross-referencing, Lehner concluded that there were 1,600 to 2,000 workers who lived in this village.

Giza Reports 2007, volume 1

In the town of Heit el Ghurab, for every 1,600 to 2,000 workers, almost as many are needed for supervision, food logistics, administration, care, and entertainment.
While the NFRWs were undoubtedly bachelors, the surrounding staff most likely came as families with children, bringing the population up to a total of 3 to 4,000.

According to Lehner, the searches covered 10 % of the entire site, which gives a population density of approximately 4 to 5,000 inhabitants per km2.

This number is closed to the population densities of medium-size cities in Bangladesh, for example:

For cities with a population density of around 140,000 inhabitants, there is a density** of around 3 to 4,000 inhabitants per km2.

**http://sedac.ciesin.columbia.edu/data/set/gpw-v3-population-density/data-download

According to Lehner’s comment, this is a high estimation of the workers’ number.

The site of Giza was far away from any living center. At that time, there were no roads or subways, and the staff lived on site. The village had its own supply chains; traces of port facilities and many remains of food revealed that workers were well-fed. A nearby necropolis allowed archaeologists to discover that they received medical attention when injured.

What emerges from these facts is that workers were not that many after all regarding the task, but well supervised, well-fed, and kept motivated.

Many scientists, including archaeologists, estimate the workforce at 36,000 individuals (Borchardt and Croon, 1937). Stadelmann, 1985), even to 100,000 for some working intermittently on the site! Did they ask themselves where they could be housed? Who could have supervised them?  I think these numbers are pure fantasies from these scientists; they don’t rely on any discoveries made.

In terms of the energy management of my study, we can wonder what can be expected in terms of strength and, finally, in terms of energy production from this 2,000 NFRW population?

02-9 Strength production

Employing workers to pull on ropes while walking to drag loads on sleds (sliding or rolling) limits the strength produced to 20% of their weight. Asking more from them would make them go backward, sliding on their feet instead of pulling forward.

The employed method used the workforce’s weight by making them go down on a platform; the resulting force is five times more powerful than hauling; the only effort to make was to climb the stairs to the platform or to swing!

The 2,000 workers of Heit el Ghurab with an additional weight of 100 kg, represented a cumulated potential strength of 2,000 kN.

There is little archaeological data, but nonetheless, it seems plausible to think that these workers were elites due to their physical capacities; they were selected, well supervised, and well-fed; they could be compared to professional athletes today.

Long-term effort specialists claim that with these conditions, a worker could deploy a strength of 80 W without tiring himself out for a 12-hour workday.

Meaning a production of 1 kWh per day by NFRW,

2,000 kWh per day for the total workforce.

Many other theories, based on the idea of gliding sleds on oiled tracks, have condemned the workers to the tiring task of pulling 65-ton megaliths for 12 hours a day, every day, under the Egyptian sun, and sometimes in groups of thousands of people.

Did they really think, comfortably seated at their desks, that the “slaves” could have endured for years these work conditions, even if they were well-fed?

The work conditions described in my study are certainly strict. But there is a difference between pulling heavy loads for 12 hours with rope on sliding dusty tracks and going up the stairs in small groups along the pyramid’s face, probably in the shade, and who knows? Maybe there was some music and a drink once they arrived at the course.

A large wall, 200 meters long, 30 meters high, and 10 meters thick, with a door embedded in it, separated this village from the construction site. It is called the “Wall of the Crow”, and it might have been well protected. So, the entrance and exit of the site were severely controlled. I think this is where workers were weighed and given their ballast, so they had the “standard weight”, probably in the form of a vest with copper weights.

Copper was as precious as gold at the time; it abounded everywhere on the site. It is understandable that while leaving the yard, workers were weighed again to make sure they did not take some copper weights.

Let me introduce you to the model NFRW, mister kWh, “recruited” to the land of Punt: