Copyright © 2015 Bernard Paul Badham. All rights reserved.
No portion of this article may be reproduced, mechanically, electronically, or by any other means,
includingphotocopying, without written permission of the author.
Original Height: 146.5 m
Base: 230.4 m
Number of Blocks (of average 2.5 tons): 2.3 million
Estimated Total Weight: 6.5 million tons
Construction Time: 20 years
Many theories abound for the construction methods of the Great Pyramid and there have been numerous attempts by modern Egyptologists to solve the problem of moving heavy stone blocks using the tools available to the ancient Egyptians, as far as we know they were not aware of the mechanical advantages of using pulley systems to lift heavy stone. Historical records of their construction methods have not been discovered, but there are some interesting clues as to how they achieved the incredible tasks of cutting hard stone and its transportation. In this article I propose a method for moving and lifting stone that the ancient Egyptians probably used for the construction of the pyramids of Egypt.
Construction of the Pyramids According to Herodotus
The Greek historian, Herodotus (484 - 425 BC) informs us in ‘The Second Book of Histories’ how the pyramids were constructed:
‘124. Down to the time when Rhampsinitos was king, they told me there was in Egypt nothing but orderly rule, and Egypt prospered greatly; but after him Cheops (Khufu) became king over them and brought them to every kind of evil: for he shut up all the temples, and having first kept them from sacrificing there, he then bade all the Egyptians work for him. So some were appointed to draw stones from the stone-quarries in the Arabian mountains to the Nile, and others he ordered to receive the stones after they had been carried over the river in boats, and to draw them to those which are called the Libyan mountains; and they worked by a hundred thousand men at a time, for each three months continually.
Of this oppression there passed ten years while the causeway was made by which they drew the stones, which causeway they built, and it is a work not much less, asit appears to me, than the pyramid; for the length of it is five furlongs(1.006 km) and the breadth ten fathoms (18.29 m) and the height, where it is highest, eight fathoms (14.63 m), and it is made of stone smoothed and with figures carved upon it. For this, they said, the ten years were spent, and for the underground chambers on the hill upon which the pyramids stand, which he caused to be made as sepulchral chambers for himself in an island, having conducted thither a channel from the Nile.
For the making of the pyramid itself there passed a period of twenty years; and the pyramid is square, each side measuring eight hundred feet (243.84 m, modern measurement 230.4 m), and the height of it is the same (the modern estimate of original height with casing stones is 146.5 m). It is built of stone smoothed and fitted together in the most perfect manner, not one of the stones being less than thirty feet in length.
125. This pyramid was made after the manner of steps, which some call ‘rows’ and others ‘bases’ (horizontal courses): and when they had first made it thus, they raised the remaining stones with machines made of short pieces of timber, raising them first from the ground to the first stage of the steps, and when the stone got up to this it was placed upon another machinestanding on the first stage, and so from this it was drawn to the second upon another machine; for as many as were the courses of the steps, so many machines there were also, or perhaps they transferred one and the same machine,made so as easily to be carried, to each stage successively, in order that they might take up the stones; for let it be told in both ways, according as it is reported. However that may be, the highest parts of it were finished first (polishing the outer stone of white Tura limestone) and afterwards they proceeded to finish that which came next to them, and lastly they finished the parts of it near the ground and the lowest ranges. On the pyramid it is declared in Egyptian writing how much was spent on radishes and onions and leeks for the workmen, and if I rightly remember that which the interpreter said in reading to me this inscription, a sum of one thousand six hundred talents of silver was spent (a talent is about 27 kg, therefore, 1600 talents is equal to 43.2 metric tonnes equivalent to a modern value of 22.5 million dollars); and if this is so, how much besides is likely to have been expended upon the iron with which they worked, and upon bread and clothing for the workmen, seeing that they were building the works for the time which has been mentioned and were occupied for no small time besides, as I suppose, in the cutting and bringing of the stones and in working at the excavation under the ground?’
‘126. Cheops moreover came, they said, to such a pitch of wickedness, that being in want of money he caused his own daughter to sit in the stews, and ordered her to obtain from those who came a certain amount of money, how much it was they did not tell me; but she not only obtained the sum appointed by her father, but also she formed a design for herself privately to leave behind her a memorial, and she requested each man who came in to her to give her one stone upon her building: and of these stones, they told me, the pyramid was built which stands in front of the great pyramid in the middle of the three, each side being one hundred and fifty feet in length.’
‘127. This Cheops, the Egyptians said, reigned fifty years; and after he was dead his brother Chephren succeeded to the kingdom. This king followed the same manner as the other, both in all the rest and also in that he made a pyramid, not indeed attaining to the measurements of that which was built by the former, this I know, having myself also measured it, and moreover there are no underground chambers beneath nor does a channel come from the Nile flowing to this one as to the other, in which the water coming through a conduit built for it flows round an island within, where they say that Cheops himself is laid: but for abasement he built the first course of Ethiopian stone (Aswan granite) of divers colours; and this pyramid he made forty feet lower than the other as regards size, building it close to the great pyramid. These stand both upon the same hill, which is about a hundred feet high. And Chephren they said reigned fifty and six years.’
‘128. Here then they reckon one hundred and six years, during which they say that there was nothing but evil for the Egyptians, and the temples were kept closed and not opened during all that time. These kings the Egyptians by reason of their hatred of them are not very willing to name; nay, they even call the pyramids after the name of Philitis the shepherd, who at that time pastured flocks in those regions.’
‘129. After him, they said, Mykerinos (Menkhaura) became king over Egypt, who was the son of Cheops; and to him his father's deeds were displeasing, and he both opened the temples and gave liberty to the people, who were ground down to the last extremity of evil, to return to their own business and to their sacrifices; also he gave decisions of their causes more just than those of all the other kings besides. In regard to this then they commend this king more than all the other kings who had arisen in Egypt before him; for he not only gave good decisions, but also when a man complained of the decision, he gave him recompense from his own goods and thus satisfied his desire. But while Mykerinos was acting mercifully to his subjects and practising this conduct which has been said, calamities befell him, of which the first was this, namely that his daughter died, the only child whom he had in his house: and being above measure grieved by that which had befallen him, and desiring to bury his daughter in a manner more remarkable than others, he made a cow of wood, which he covered over with gold, and then within it he buried this daughter who, as I said, had died.’
‘134. This king also left behind him a pyramid, much smaller than that of his father, of a square shape and measuring on each side three hundred feet lacking twenty, built moreover of Ethiopian stone up to half the height.’
The ‘wooden machines made of short timber’ mentioned by Herodotus is the only information we have about how they lifted the stone blocks and it is interesting that each machine was responsible for lifting stone up one step and it is quite likely as the levels of horizontal courses of stone went up, that they placed a ‘machine’on each level and on each side of the pyramid. Stone blocks would have been brought to the base of the pyramid from the quarries on sledges. We know from archeological evidence that the ancient Egyptians used mud-brick ramps and inclined causeways, but the shallow inclines of such ramps could not have been used to construct a major monument of significant height.
Remains of a mud brick ramp - note: the stone at the top was polished first
Levering methods are considered to be the most probable solution to complement ramping methods, partially due to Herodotus’ description; and partially to the Shadoof; an irrigation device first depicted in Egypt during the New Kingdom, and found concomitantly with the Old Kingdom in Mesopotamia.
The shadoof is basically a lever and consists of an upright frame on which is suspended a long pole or branch, at a distance of about one-fifth of its length from one end. At the long end of this pole hangs a bucket, skin bag, or bitumen-coated reed basket for lifting water out of the Nile. The short end carries a weight (a stone) which serves as the counterpoise of the lever. When correctly balanced, the counter weight will support a half-filled bucket, so some effort is used to pull an empty bucket down to the water, but only the same effort is needed to lift a full bucket. A similar system may have been adopted in Herodotus’ ‘machines’ and may have comprised of two such levers (or more), one at each end of a stone block. Such lever machines could have been used for lifting stone to the next level.
Sledge from mortuary complex of Senwosret I. Middle Kingdom. Dynasty 12, reign of Senwosret I, ca. 1961–1917 B.C.
The University of Amsterdam investigated the forces needed to pull weighty objects on a giant sled over desert sand, and discovered that dampening the sand in front of the primitive device reduces friction on the sled, making it easier to operate. To make their discovery, the researchers picked up on clues from the ancient Egyptians themselves. A wall painting discovered in the ancient tomb of Djehutihotep, which dates back to about 1900 B.C., depicts 172 men hauling an immense statue using ropes attached to a sledge. In the drawing, a person can be seen standing on the front of the sledge, pouring water over the sand. Adding water to the sand, increased sand’s stiffness, and they found that sleds were able to glide more easily across the surface. This is because droplets of water create bridges between the grains of sand, which helps them stick together.
I have studied this picture before and came to similar conclusions, except for two more important observations, the picture:
The men standing in front of the statue are pouring a liquid (water or oil) from a jar onto the ground in front of the sledge. The hauling ropes are attached to a thicker rope at the front of the sledge. Three other men are carrying yokes with two jars of water/oil each, while other men walk behind the statue, behind them three men are carrying what appears to be a large lever or wooden beam.
There is more to this picture than has been interpreted, let us go through the observations one at a time before drawing any further conclusions:
1. Man standing on the legs of the statue: he carries what appears to be a bag over his shoulders and is depicted in the action of clapping. This we assume was a worker beating out time to keep the men pulling on the ropes in correct rhythm for each pull.
2. Man pouring water-oil: on the front of the sled a worker pours a liquid to the ground directly in front of the sledge, this we presume is for lubrication between the rails of the wooden sledge and the ground surface.
3. Man holding two wooden mallets: in front of the sledge is a worker holding what appear to be two wooden mallets and is in the process of clapping them together, again this would be to beat out the time for the three teams of pullers. It may be that he was simply amplifying the beat set by the man clapping on the statue.
Notice: not all the men in the towing teams are looking forwards; some are looking back for obvious guidance to beat and maybe directions.
4. Workers carrying water pots: at the side and near the front of the sledge are three workers each carrying a yoke with two water pots, thus supplying the liquid needed for lubrication of the sledge.
5. Workers carrying a wooden beam: it has been suggested by some that the long wooden beam carried by three men was used as a lever, but I think not, careful observation shows that the top edge of the beam is jagged while the lower edge is smooth. This difference must have been depicted for a reason. I believe theses timbers, even only one is depicted were laid out in the ground as rails in front of the sledge and were positioned at right angles to the rails of the sledge, hence only the top edge needed to be smoothly planed. Dry wood on dry wood would produce a lot of friction, but if the sledge rails and the wooden track were lubricated with oil of water the friction would have been much reduced. The sledge could simply glide over the laid wooden timbers.
Evidence for such a road of tracks is also in the accompanying text:
‘Following the statue of 13 cubits in stone of Hetnub. Behold, very wonderful was the road upon which it came, more than anything. Behold, wonderful to the minds of men was the dragging of valuable stone along it on account of the stone and already difficult for a mere square block of sandstone. I caused to come troops of goodly youths in order to make for it the road, together with guilds of tomb-sculptors and quarrymen, the foremen with them knowing how to point out the strong-armed. I came to bring it, my heart enlarged, the townsmen all rejoicing: exceeding good was it to see more than anything.’
6. The twisted rope: this clue is very important as to possibly solving one of the great pyramid construction mysteries. Three loops of twisted rope secure the almost seven metre high statue to the sledge, careful observation shows that the rope was twisted tight by six inserted winding sticks.
This technique of tightening rope by twisting with a stick is remarkable and clever in itself and so I wondered was the same technique ever used to move stone? Without prompting I asked my father who was a retired ‘hewer’ (miner of Welsh coal), if he ever had the need to move large stone obstacles underground, he replied as if it were common knowledge. ‘Simple,’ he said, ‘if a large immoveable stone fell in our way, we placed a loop of rope around it and around an adjacent upright roof supporting timber, with a stick we twisted the rope and moved with ease the incumbent stone out of the way (as rope is twisted, it gets shorter).’ I have tried this method and it works, the twisting of the rope gives a mechanical adavantage, the same as a lever, in essence it is a machine:
Lifting Model Pyramid Stone Blocks Using Twisted Rope
It had been on my mind for some time to test out this method of moving stone, and so with some molding plaster I made myself two ‘stone’ blocks and tried the technique. To my surprise it took less than 20 turns to lift both stone blocks up a distance greater than their own height.
The following photographs demonstrate lifting two stone blocks by the twisting of rope, each one counterbalances (counterpoise) the weight of the other, thus simultaneously on opposites ides of the Pyramid workers could easily lift two stone blocks at a time.
Only a simple method of twisting rope and counterpoise is demonstrated here, but the ancient Egyptians could easily have improved and adapted the technique with wooden cradles to carry the stone and a central A-frame type winding mechanism.
A Simple Machine Winding Mechanism
The picture below shows a simple lifting mechanism, the winding cylinder lies on a wooden mount where the wood on wood contact could be lubricated with oil. This model shows one lifting rope which could have been easily pulled by a single team of men, to make things easier another rope wound around the cylinder in the opposite direction would allow two teams to simply lift two counter-weighted stone blocks at the same time in a matter of minutes.
A Two Team Lifting Mechanism
Bernard Paul Badham
Please give credit to the author if referenced
Copyright © 2015 Bernard Paul Badham. All rights reserved. No portion of this article may bereproduced, mechanically, electronically, or by any other means, including photocopying, without written permission of the author.