Egyptian pyramids: how and in how many years ?
Whoever goes to Egypt, stops at least one day in Cairo to go and see the Giza Plain, with the Sphinx, the three great pyramids and what remains of the other structures of the sacred area and of the ancient necropolis.
By standing at the foot of the great pyramids, looking to the summit of the enormous geometric structure that lies in front of us, some inevitable questions come: "how" and "why". Only a few more experienced visitors, those who already have some knowledge of the Egyptian mysteries ask themself, "How long?"
The technical-cultural adventure that I propose to you consists in seeking an acceptable answer to that question: "in how many years ? ".
No certainties, only hypotheses based on objective findings.
1 - RAMPS AND PYRAMIDS
At the beginning of each design project a crucial question is always: "What is it for?"
This first question is followed by other questions with the aim to define, with the maximum possible precision, which needs must meet the object that has to be realized.
At this point the designer must know where the well-defined object is to be constructed and, only at that point, he begins to think about how to build it.
It is clear that the "how to build it" requires a lot of information regarding the available materials, the techniques and the applicable technologies.
Nowadays, the next question would refer to the "spending budget".
Any modern designer will tell you that if the financial availability is not known, the risk of designing something too expensive or too poor compared to the customer's expectations is too high.
If we try to understand how and why the great pyramids of Giza and its surroundings were built, we are forced to reverse the order of questions that are part of the design process.
It is crucial to establish how long have been needed to built the pyramids, to imagine their "intended use", since we are not convinced by the hypothesis that each pyramid was built for a single Pharaoh and was created to be a "tombs and only a tombs". This hypothesis does not imply only an identification of finality, but also imposes a very short time of realization, definitly lower than the life expectancy of the reigning king.
Once the location and the materials to use have been defined and the available technologies identified, we must "only" try to understand "how and in how many years", simply not?
Once the challenge is accepted, we must make our head's work, without ever forgetting that the given conditions must be respected, otherwise it is not valid.
The great pyramids of Giza are not the only great works carried out in ancient Egypt, but those pyramids differ not only in their size and incredible precision, but also for the use of large blocks of hard stone.
The three pyramids are similar in the external shape but substantially different in the internal structures, in the used materials and in their dimensions.
This detail is at the origin of many of the questions that have helped to maintain the charm of ancient Egypt over the centuries.
One of the questions, in my opinion still without a satisfactory answer, is represented by the construction methods of the three pyramids, as those large blocks of stone have a weight that varies from about two to a few tens of tons.
Most of the blocks were excavated in limestone quarries found a few hundred meters from the place where the pyramids were built, the white stone of Tura comes from a quarry located on the east bank of the Nile, while the granite blocks come from the quarries of Aswan, almost a thousand kilometers from Cairo.
To accomplish those impressive monuments, several problems have been addressed and solved.
For example, today we would say that a logistic problem had to be solved, that is, after having dug and squared them, it was necessary to let those blocks flow near the construction site when they had to be installed.
It is really difficult to hypothesize that those blocks were stacked in the vicinity of the "construction site" and then picked up when they were used. It would have required as an area similar to a modern harbor equipped with containers, it means large squared area with rails, reinforced at the base, on which huge cranes move.
Here we are talking about hundreds of thousands of blocks, with an average weight of twenty five quintals each, transported and lifted by men who had neither pulleys, nor steel cables, nor carts with wheels, let alone cranes.
Once again, the today's technology and the consequent mental training leads us to "take for granted" things that are not obvious at all.
Only a few decades ago, in the industrialized world, a system of distribution of raw materials, semi-finished products and finished products that tends to avoid storage has been introduced.
But without a phone, without a computer, without an effective transport network with certain journey times, with a speed of information dissemination linked to the speed of a donkey, as far as we know, "jast in time" is not possible. As you can see, another mystery that, at first sight, is not known, but there is.
Based on the archaeological findings found in excavations carried out in Egypt, Egyptologists say that the work's tools of the pyramid era were made mainly of wood, chipped or polished stone and little copper, while they could have good quantities of cordage made of vegetable fibers .
I have recently heard that the blocks of about one cubic meter, used to build the Great Pyramid, are not 2.5 million, because under the pyramid there is a small hill. The surveys carried out in the internal structures have allowed us to define the height of the hill in about 7 meters above the base of the pyramid, this means that it consists of about 150 thousand cubic meters of limestone.
The volume of the pyramid, including the small hill, is 2.580 million cubic meters, so that even removing the approximately 100 thousand cubic meters of hill, there are still more than 2.4 million cubic meters of blocks, so it does not change the order of magnitude of the problem.
Lets continue and recall that some of the blocks used to build the King's Chamber and the overlying "discharge chambers" weigh over 50 tons and were placed at over 50 meters in height.
These are the terms of the challenge to intelligence launched by the ancient builders: "How did they do it, how long?"
1 "Just in time" - it is a model for organizing the flow of raw materials and semi-finished products that avoids the need for storage and / or warehouse stocks - the obvious aim is to save the cost of storage and related movements.
2 - BUT ... WHICH RAMPS?
The presumption of having discovered the "mystery of the Pyramids" is far away from me, the exercise that I set myself to face, together with you, only helps to clarify the conditions of the problem, to understand why those questions continue to fascinate generations of men through the centuries, indeed, the millennia.
On the "how" the pyramids were built, several hypotheses were presented, some of them are really extravagant, I adopt the one shared by the majority of Egyptologists: "the construction of the pyramids may have been built using large ramps to bring the stone blocks used in construction ". In this regard, I recall the opinion of an Egyptologist who has all my respect, I.E.S.Edwards:
"The Egyptians had a single system for lifting large weights, that is to say by means of ramps of bricks and earth that sloped upwards from the ground level to any desired height."
I join in with all those who do not fall into the trap inherent in the words of Herodotus when he spoke of machines made with "short woods" when it came to the construction of the pyramids:
"This pyramid (of Cheops) was built in steps that some call steps and others call stairs; after they had built it in this form, they raised the remaining stones with machines formed with short beams, raising them from the ground on the first order of steps ... "
Above all, it seems appropriate to emphasize that the use of "machines made with short woods" was only hypothesized for the assembly of the covering slabs, neglecting to take an interest in the construction of the pyramid.
The first attempt
The attempt to re-invent that machine has sparked the creativity of dozens or hundreds of "experts" who have hypothesized everything and even more. If from those ingenious solutions iron is eliminated, some pulley for "referrals", some cable with an inadequate "breaking load", remains little and with low credibility.
On the question of how they did, dozens of hypotheses are available, one more brainy than the other and F. Cimmino, in his book "Storia delle Piramidi", reported a beautiful sample, I present three of them ..
Frankly, it is impossible to imagine how it could have been possible to bring the water there, ever harder imagine how it was possible to make the "dam" that should have contained water up to the height of 145 meters.
The second attempt
In the second case, even if the hypothesis refers to the placement of only the blocks of the covering, it is not clear how the pins necessary for the references and the winches have been constructed.
The third attempt
In this case the lifting of the blocks would have occurred using wooden "gondolas".
By tilting the gondola, a plug is inserted so that the block has gained a higher height with the straightening.
In this illustration we have played on the dimensions, in fact if the block has a side of about one meter, the gondola should be at least two meters big, moreover, once raised from the first stopper, one should continue with inclinations and insertions made with "plugs" "always larger that had to ensure stability and that they had to withstand compression. If the cap represented in the drawing was made of wood, it is crushed, if it was made of stone, the inflator is crushed.
Once opted for the use of ramps, there is a choice to make. You could make linear ramps, orthogonal to the facades, made to grow together with the pyramid, or you could build ramps adjacent to the facades, made so that they wrapped the pyramid.
3 - The Wrapped Ramps
The use of enveloping ramps is a solution that seems credible until it is subjected to the examination of logic and the limits imposed by the given conditions, which cannot be modified.
To achieve a perfect alignment, capable of respecting a completely Egyptian precision standard, for all the more than 10,000 square meters of each facade and for the nearly 190 meters of each of the four edges of the pyramid, continuous alignments of control were needed.
The wrapping ramp
Furthermore, the enveloping ramps re-propose the problem of the amount of cubic meters needed, because in order to pull the sledges with relative blocks, we will see that hosts of men were needed who, however arranged, occupied tens of meters in length and in width.
How wide were the ramps in the curves?
To obtain curves that allow the towing of large blocks serve ramps that are well over a hundred meters wide, a considerable commitment due to the volumes of stone blocks and raw bricks necessary. A commitment that however does not avoid the other impediments connected to the choice of enveloping ramps.
4 - SLOPE
Our considerations have led us to opt for linear ramps, now we need to define the slope.
The slope of linear ramps
The ramps are used to make up an inclined plane, along which the sledges on which the blocks that must rise in height are to be towed.
The ramp cannot exceed 10% of slope to be usable, a greater slope would make the towing of the blocks difficult, while a lower slope would "lengthen" the ramps beyond measure. Some authors solve the problem of ramps by proposing drawings that show that, all things considered, the use of ramps was a simple solution.
I reproduced the drawing found on a book published in the USA, to show you how the problem is addressed.
A design like this is not a fake, it is a "little story" for very young children. With a slope between 30 % and 40% it would not be possible to climb even with a crawler, it would run the risk of toppling backwards, while a man would find it difficult to climb without even carrying any weight. It is a slope from "ladders", why do you think that it could be fine for people who dragged weights of several tons for 10 hours a day? The drawing below represents a ramp with a slope of 10% and the proportion between the volume of the pyramid and that of the ramp appears immediately evident.
But still not enough. From the level of the temples to the valley, in front of which it is very probable that the waters of the Nile arrived, involved up to that point using canals, at the base of the pyramids there are 40 or 50 meters in altitude. So another five hundred meters of ramp, which at the moment we do not consider to simplify our calculations as much as possible and to work on a decidedly underestimated hypothesis.
The use of a ramp with a 10% slope is an acceptable solution without forgetting that for every meter of elevation, you need 10 meters of length of the same ramp.
When we arrive at the last course of blocks and we will be at an altitude of 145 meters, the ramp will be over 1450 meters long, with the inevitable use of an enormous amount of materials.
The material available on site in sufficient quantity was the dry sandy soil of the Giza plateau, although this type of material has a "natural slope angle" of 1.75, which means that, if we try to accumulate this material close to a wall, for every meter of height of the heap, we will have a base of 1.75 meters. In other words, when the pile that will constitute the ramp, will have reached 145 meters, on both sides of the ramp we will have scarps 254 meters wide each.
It is clear that such a ramp would end up overflowing from the sides of the facade of the pyramid, preventing the necessary alignments as well as constituting an unstable base for the passage of the blocks placed on sled and for the work of the men involved in the towing, it was therefore necessary to resort to the use of limestone blocks the size of those used in Saqqara in the pyramid of King Djoser.
If the ramp is 220 meters wide at the base, when it reaches 1450 meters in length, it has a volume greater than 7 million cubic meters, against 2.5 of the pyramid itself.
5 - The men
Men who pull weights placed on sledges, with "sliding friction" on an inclined plane with a slope of 10% for whole days of work, cannot tow more than 20 kilograms of stone each; this means that for each 2.5 ton block, we need teams of 125 men, remember that the towed weight must be increased by another 500 or 600 kilograms for the sled and the tow ropes, so the towed weight becomes about 25 kilograms per capita. It seems to me an insurmountable limit.
125 men, lined up by 4, are arranged on 32 rows, with a distance of at least one meter and a half between one row and the other, plus the space occupied by the sled which must have slides of suitable size to distribute the weight on the ramp. A little space between each sled and the next, so that stopping a block does not cause the entire row to stop immediately. We arrive at least 100 meters between one block and another.
Indeed, to think of more than a hundred men pulling a sled can seem an easy exercise, but fortunately in this case we can resort to a suggestion provided by the Egyptians themselves of about 1900 BC, found in the tomb of Dehutihotep in Deir el Bersha.
Deir el Bersha. On a wall of the tomb of the official Dehutiothep, approximately 1900 BC, the towing of a huge statue was depicted.
There is depicted the towing of a huge statue, a few tons heavy, placed on a sled. There are four large ropes attached to the sled, at each rope there are about twenty pairs of men. Around this expanse of drivers other figures of the organization move, conveyors of large beams to be placed in order to facilitate the journey of the sled, others transport containers of liquid that is poured in front of the sled, in order to reduce friction. Grazing that slows his progress, others still move to the edge of the sled, perhaps waiting to replace the men involved in the process. In total, more than 150 men can be counted in tow, while about a hundred people move around the sled, which advances on horizontal terrain.
If we make the appropriate proportions with the towing of the blocks used for the construction of the pyramid, we realize that ours was a deficient calculation.
The only sure thing here is that for the large blocks of over 50 tons, used to make the King's Chamber and its "unloading chambers", the number of men had to rise in a frightening way.
Now we have enough data to calculate how many blocks arrived, on the pyramid under construction, for every hour of work.
To cover those hundred meters, it could take about 10 minutes, including stops, which means that in an hour, about 6 blocks of 2.5 tons arrived at an altitude.
We are consciously neglecting the problem of blocks of around 50 tons, we will resume the subject later, for the moment there are still some details to be clarified.
The measures of the King's Chamber and the "Unloading Chambers".
(Detail of the Tablets by V. Maragioglio and C. Rinaldi which also show the measurements taken by F. Petrie).
7 - Volumes
The three pyramids of Giza have volumes of 2.598, 2.188 and 0.291 million cubic meters of stone respectively, for a total of about 5 million blocks of one cubic meter, weighing 2.5 tons. each of media.
To allow men to line up for 4, plus those who worked on the sides of the sleds, we need a base at least 10 meters wide, suitably reinforced to allow the slide to slide without planting itself in the ground and without the ramp crumbling underneath men's work.
In fact, if we consider the long summer periods during which the climatic conditions of Giza become prohibitive for several hours a day, for men working on the edge of the desert, if we keep in mind the possible accidents for men who worked moving enormous weights, the diseases etc., the turnover of the workers had to be rather rapid, involving a decidedly large number of people, there had to be around 50,000 valid men in the area to ensure continuity of work.
All this while others cut the blocks, others shaped them in the desired dimensions and others carried them near the beginning of the ramps, arranging them on the sledges, ready to be dragged up by teams of about 250 men, where others still arranged them with precision in the right place. In the meantime there were also those who thought about the corridors, the halls, the Great Gallery, the "ventilation" ducts and, finally, the "unloading chambers".
Now you understand why I have bored you with these calculations.
It seems right to me that we really understand the meaning of: "they have used ramps". Put like this, it seems a solved problem. Instead, if you calculate the volume of material moved and placed with great skill to avoid collapse, we can realize that those ramps cost an impressive amount of work, even higher than the construction of the pyramids .
If you try to calculate how many blocks of 20 X 20 x 50 cm were used to build the ramp and to continue to adapt it to each successive level of blocks and then how many men were served to take them to altitude and place them, you realize that around the pyramid tens of thousands of men worked.
8 - Times
The subsequent calculation, referring to the time required to build the pyramid, is based on the fact that 2.5 million blocks of an average cubic meter were to be brought up and placed.
On the basis of the parameters established in the previous pages, in our hypothesis 6 blocks were placed for every hour, 60 blocks every day, 21 thousand each year, so it took about 237 years to bring in quota and place the 5 million blocks used to make the three pyramids.
A calculation for global averages, lends itself to criticisms of all kinds, I invite you to leave out the details and see if the overall reasoning on large numbers can be adopted to define the order of magnitude.
We keep in mind that in the calculation, the times to realize the "preparation of the site", the leveling of the base on which the first course of blocks was placed, the times to realize the Sphinx, the Elevated Roads, the funerary temples were not counted. The temples in the valley, the pits for sacred boats and all the other structures that certainly required enormous amounts of work.
It should be remembered that when Herodotus visited the Giza esplanade, the Raised Great Pyramid Road was still in good condition and the Greek historian was able to comment:
"... Road that is certainly not much less than the pyramid itself as it seems to me: ... It was covered with polished stone and figures had been carved in it. "
It can always be said that while the pyramids were being built, the other buildings were also realized, but such reasoning involves a massive use of people and, in a country with less than two million inhabitants, almost all engaged in agriculture, this assumption has insurmountable limits. If the social order itself and the survival of the state were not to be compromised, whose boundaries were however defended with timeliness and effectiveness even while the Great Pyramids continued to be built.
There is still time to make the coat of the pyramids knowing full well that this is not a secondary commitment. Only for the Great Pyramid, it was a problem of positioning 115,000 blocks of white marble, weighing about 10 tons each, putting them in place with extreme precision, not leaving even "the space to insert a pocket knife blade".
We have not forgotten the large blocks of about 50 tons and, if it is not clear how they did it, we must still think that it took a lot of work and a lot of time during which the towing of the middle blocks had to be suspended.
Therefore the evaluation of a total duration of about 250 years, seems to me not only an acceptable hypothesis but also a reductive one, thinking also that, while the works continued on the Giza plain, the various Pharaohs built also the other pyramids, attributed to the IV dynasty, and their individual tombs, placed in locations with greater possibility of "going unnoticed" than the pyramids themselves.
9 - More ramps for each Pyramid?
To bring the construction time back into the lifetime of the kings, a problem of speed in placing the blocks also emerges.
Let's consider the Great Pyramid that should have been built in about 20 years, Erodoto says that:
"Ten were the years used for the construction of this (causeway) and underground rooms on the hill on which the pyramids stand, which Cheops built as tombs on an island ...
For the pyramid itself they say that twenty years went by until it was built ... "
It is appropriate to point out the contradiction, Herodotus speaks of a construction time of 30 years, 10 for the preparation and 20 for the pyramid, while the kingdom of Cheops was defined in 23 years by the official chronology.
However, in twenty years, assuming you work 365 days each year, assuming you work 10 hours on average a day, there are 4,380,000 minutes in all. Since about 2.5 million blocks had to be placed, it means that a block had to be placed every minute and forty-five seconds.
An assembly-line rhythm to Charlie Chaplin's "Modern Times" to keep for 20 years at an average of 10 hours every day, does it seem credible to you?
To reduce the speed of that infernal mechanism, instead of hypothesizing a single ramp, some Egyptologist has hypothesized the use of two or three ramps for each pyramid. .
The reasoning is not a wrinkle, if with a ramp a block had to be brought up every minute and 45 seconds, with two ramps, you could go down to 3 minutes and 30 seconds, with four ramps at 7 minutes for each block. It is still a remarkable rhythm, but less and less dizzy and the pyramids could have been made during the reign of every Pharaoh.
It just seems to talk about the usual short blanket, if on one side you cover your shoulders, below your feet stay out.
In fact, if the pace slows down with more ramps, and the construction times are compatible with the theory that says "the pyramids are tombs and only tombs", on the other hand the volumes involved in building those ramps increase, and all the other parameters in proportion.
As you have seen from the data shown in the previous chapters, the ramps represented a grueling commitment, and when it is stated that the architects had an unlimited workforce, we are actually neglecting conclusions from the previous chapters, with respect to a population lower than two million inhabitants.
As I said, a good challenge! There are spaces and volumes that cannot be compressed beyond an insurmountable limit, the time remains that, if it is not compressible, is certainly expandable, in the sense that more can be used to accomplish the same job. withstand the challenge with the logic of construction, you can work on the time factor. One can always think that it took longer than the sum of the durations of the kingdoms of the three Kings indicated by modern Egyptology.
But if the construction of the pyramids required more time, it means that we are facing an overall project for which the full Pharaonic Theocracy has taken charge, definitely not a single Pharaoh for each single Pyramid.
But we are looking for a credible hypothesis, so we accept the only idea that seems acceptable to us.
That is, the pyramids of Giza were built using ramps, made with raw bricks and smaller limestone blocks and more manageable than the blocks used in the pyramids, in this way the ramp may have been made with slopes of the side slopes slightly higher than those of the pyramid, so as to leave the edges of the facades free for the necessary and repeated alignments.
The material used for the ramp of the first pyramid, may have been reused for the subsequent ones, and finally for all the other structures relating to the various temples and the raised roads. Moreover, to complete the structures of the Third pyramid, also raw bricks were used, perhaps the "leftovers" of the materials used to build the ramps in the previous pyramids.
10- Machines and ramps to raise the stones
It is undeniable that the use of large blocks, a few tons of weight each, has been decisive in guaranteeing the durability of those buildings.
"How they did it". This is the question that caused many scholars to squeeze their brains, also because they, the Egyptians, did not leave enough clues to reconstruct the method actually used.
Almost all the activities of the ancient Egyptians have been depicted on the walls of the tombs. On those walls, everything is rappresented: hunting, fishing, farm work, crafts, towing statues, etc. etc. . But pyramids are not shown on those walls. Since on those walls almost exclusively activities to be carried out after the death have been depicted, it means that the construction of pyramids was not foreseen for "the after death world". We do not know why, but it is certain that the construction of the pyramids is excluded from post-mortem activities and we remain with our curiosity.
As we have seen, among the many hypotheses the most acceptable, in my opinion, are those based on the realization of ramps, the Frenchman Jan Philippe Lauer thought of linear ramps, placed in an orthogonal position with respect to a facade. The characteristic of Lauer's study seems to me interesting because it foresees a ramp that varies, for width and slope, while the pyramid grows.
While the ramp is wide for the lower courses, so that several slides can pass at the same time, the ramp narrows while the pyramid rises and decreases the number of blocks involved for each course.
11 - Still some reflections
At this point it seems right to me to still face two problems:
- the transportation of the granite blocks used to build the King's Chamber and the so-called discharge chambers;
- the times for raising the ramp to adapt it to the next level.
Lauer's solution is logical and does not call into question our calculations related to the volumes and time required to build the ramp in blocks and raw bricks, but it is appropriate to include two tricks:
First - it was possible to build a ramp with a slop of 5% up to a height of 60 meters, to more easily transport the Cyclopean blocks of the King's Chamber and the overlying Exhaust Chambers, and then continue with a ramp with a 10% slope for take the blocks in height to make the remaining part of the pyramid, without forgetting the large cusp, the benben that probably completed the Pyramid;
Second - to avoid having to interrupt the towing of the blocks to adapt the ramp to the new height, it was possible to create two adjacent parallel "tracks" so that while one was in use, one could work to prepare the other for the new height, in order to avoid interruptions of the works that would have caused a further lengthening of the times.
It seems to me that Lauer's idea is valid, but it is useful for "not expanding construction times" any more, not "to reduce them".
It is evident that even these last "reflections" are the result of logic but, we have arrived to the same conclusions too ...
12 - The great project
Our hypothesis is based on technical analysis relating to the "construction sciences" and on a comparison between the "short chronology" adopted by modern egyptology and the convictions of the first Egyptologists of the modern era who preferred to think of a "long chronology". Champollion considered reliable the data attributed to the priest Manetone, based on which the dynastic began about in 5850 BC.
Therefore, either pharaohs belonging to the III, IV and V dynasty have been involved, or the durations of the kingdoms indicated by Manetone are valid, which determine the presence of a long chronology, but this is another story and deserves to be examined separately.
