HOW THE EGYPTIANS BUILT THE PYRAMIDS

BY RICHARD KOSLOW

If people can lift water with a counter weight, why not use the same principle to lift stones, huge stones, like the ones used to build the pyramids? Back in ancient Egypt, a device called a shadoof was commonly used to move water. A shadoof is a long pole, weighted at one end, perhaps with a stone, and a vessel on the other end, used for raising water to irrigate the land. They pulled down the vessel, filled it under the water, and then easily lifted it by the counter weight. These water lifting machines showed that the Egyptians knew something about weights, fulcrum, and balance long before they built the pyramids .

This method of lifting heavy stones with a counter weight is an idea that I am sure Historians may have thought of in the past, but dismissed because there is no evidence that it was ever done with huge stones.
So, how did they lift a five-ton block of stone to build the pyramids? We know that at the time of the first pyramid the Egyptian culture was well developed and they were knowledgeable in some methods of building and construction. To get the blocks so close and in such perfect order would be extremely difficult using just man power. It would be impossible to assemble enough men around a 9,000 pound stone that is perhaps three and a half feet by three and a half feet, by five feet long to move it. To lift this stone onto a barge and off a barge, and then to maneuver it in place on the pyramid would take ten men, three on each side and two at each end. This placement means that each man, if all lifted equally, would be lifting 900-pounds. Obviously such a miraculous display of strength not only seems impracticable, but impossible.

The most commonly held solution for moving these large blocks is to slide skids under the blocks so that many men would pull the skid along the ground and up ramps built around the pyramid to the level required. Pictured is a hieroglyphic panel showing the use of skids. Getting the block off the skid would be laborious enough, but moving the 5-ton block and placing it in its proper position in the pyramid by pushing and shoving seems inconceivable.

Perhaps the Egyptians rolled the stones by placing them on platforms and used round logs under the platform to push the stones along. However, the same difficulty of getting the 5-ton block off and on the platform exists.

At the time of the first pyramid, basic devices to pull heavy stones such as the windlass were very much in use. The windlass is a wheel and axle machine where the axle is fasten to the wheel. On both sides of the axle are large wheels, poles, or bars much larger than the axle. Let us say that the diameter of the wheel is ten feet and the diameter of the axle is one foot. By winding a rope around the axle and turning the wheel a mechanical advantage equal to the ratio of the diameter of the wheel to that of the axle is realized. Therefore, in this case the ratio would be one to ten. With a windlass ratio of 1:10, and considering the bearings as frictionless, a 2000-lb load could be lifted by applying a 200-lb force. With suitable bearings, bedding, and geometry, even a smaller force would be required to slide the load. Thus, it would require 900-pounds of force to pull a 9,000-pound stone, or six men applying a force of 150-pounds each. By putting the stone on a skid and using the windlass, 6 men could move the stone across the surface much easier. Also, by putting the windlass on the level of the pyramid they are working on, the 6 men could hoist stone up the side of the pyramid on a narrow ramp. However, they would still face the challenge of placing the stones on and off a skid or barge, and lifting them into place.

Although the use of skids or rolling platforms may have been the method to get the stones to the barges, the Egyptians must have had a better method for putting them on the barges. Also, they must have had a method of lifting the blocks off the barges onto the platforms at the pyramid site. They recorded nothing about how they lifted the stones to the level they wanted them once the stones were delivered to the pyramid.

To lift a five-ton stone using a shadoof, the counter weight would have to weigh almost as much as the stone to be lifted. So how could the workers produce a counter weight to lift the stone almost the same way the shadoof lifts the water?

When I started to seriously think about how the Egyptians could accomplish the counter weight problem I came up with a method the Egyptians could have used to lift a five-ton stone. Why not use a material that they had plenty of - SAND?

The first thing would be to build as many as four towers with four legs each out of heavy timbers and ropes, with all the legs meeting near the top. They would be approximately ten to twenty feet high, with perhaps a stone spool at the top. The base would be a solid platform of logs to give it stability.

The legs would extend a foot or more below the platform to allow for uneven terrain. The platform would also serve to hold bags of sand if needed for additional steadiness. The tower can be constructed as a system of multi-connected tetrahedrons if internal bracing is provided. Such a structure would be rigid, or stable, and could support significant loads with appropriate dimensions, timber, and foundation.


Tetrahedron

The spool would resemble a spool of thread, except the area where the thread is wrapped around would be cut deeper to guide the ropes. A hole through the center of the spool as in a spool of thread would allow it to turn freely as the ropes move. A large substantial log would be placed through the hole at the center of the spool and tied firmly on top and between the legs of the tower. These towers would be set at each corner of the pyramid or one tower at one corner at the level being worked. A rope would be tied around the stone block on the ground and brought up to the level on which the men are working. Then the rope was swung above the tower and tied on the other end to a basket at the center height of the tower. The basket was filled with sand until the basket's weight was equal to or more than the weight of the stone. Once the basket was full, it was moved down the side of the pyramid, thus lifting the stone easily up the adjacent side. The purpose of hanging the basket five or ten feet up from the base of the tower was to insure that the stone clears the edge of the level to which it was lifted. The spool would be set at an angle so that the ropes would fall on the adjacent sides. If the spool was not used then the workmen could have greased a groove in the log at the top and swung the rope over it. The pyramid was built so there would be a substantial size landing on every block level. As the pyramid rose stepping stones were placed on each landing so the sand carriers could bring sand to the tower level, fill the baskets, and return for more sand.

Several men would push the basket with sand over the side of the pyramid and then pull on the ropes to lift the stone from the ground, using the counter weight of the basket to help them. Other men would be stationed all the way down on each of the landings with long poles to keep the basket from hitting the sides of the pyramid and insure a smooth ride to the ground. Additional men would be on the adjacent side with poles to keep the stone blocks from hitting the pyramid on the way up.

When the stone was on the level of the tower and was placed on a skid or platform, the ropes around the stone were untied and the sand in the basket on the ground was emptied. The empty basket could then be pulled back up to the tower with the other end of the rope going to the ground, and the process started again. Once the stone was on the level desired, it than could be rolled to its location. A smaller tower would be used to lift the stone into place using the same method. This method could also have been used to put the stones on or off the barges. The Obelisk can be lifted and put into place by lifting it at the center to balance it and turn it to a vertical position.

One cubic foot of sand weighs approximately one hundred ten pounds. A 9,000-pound block of stone would require eighty-two cubic feet to equal or exceed the weight of the stone. A basket just 4½ feet by 4½ feet by 4½ feet high would do it. A fifteen-ton stone block would require two hundred seventy-three cubic feet of sand to equal or exceed the weight of the stone, or a basket 6½ feet by 6½ feet by 6½ feet high. It would take actually on site conditions to accurately determine how many men they would need to carry the sand and pour it into the basket, how long it would take to lift the stone, and the time to repeat the process. While the stone was being untied the workmen would pull up the empty basket, and other workers would wait to pour their sand into it. To do the same job in the same time by building ramps and rolling the stones up the sides of the pyramid would take many more thousands of people to accomplish the same results.

Why are the measurements of Khufuís Great Pyramid such odd figures like 432 cubits for each base? The cubit, about 21 inches long, was the standard measure of the Egyptians. It seems reasonable that the architect would have used an even number like 400, 450, or 500 cubits for the bases. Imagine Khufu asking his architects to build a pyramid 300 cubits high or 525 feet, so it would be the greatest monument ever built. (I doubt that he would have said, ìBuild the pyramid 275.43 cubits high.î) The architects would then need to know two things: the angle of the pyramid and the length of each of the four sides of the base. The most manageable size block of stone at the time was about two cubits by two cubits, so the pyramid would be 150 stones high to equal 300 cubits.

The Egyptian architects would draw a number of pyramids on paper as the most likely design. By laying out blocks on paper and starting with the top block, the designers concluded that there are three most natural methods of building the triangular shape. The building blocks were of approximately equal size and square, 2 cubits high by 2 cubits wide by 3± cubits long. Using the squared side as the face of the pyramid, the first block would be placed on half of each of the blocks in the row below. See figure 1 below.


Pyramid Figure 1

The next layer down would be placed the same way forming a brick pattern. Note that the second row down would contain two blocks, the third row down would contain three blocks, and so on, until 150 blocks high would equal 150 blocks for the base, or 300 cubits high by each base at 300 cubits long. This would form an equilateral triangular shape that would have been considered too steep, perhaps from the experience of the Bent Pyramid, or the landings would be too small for the sand carriers or the stone masons to do their work.

Secondly, by placing the top block on top of the block directly below, with two blocks placed on either side, the second layer would have three full blocks on that row. See figure 2 below. The third layer down would have five full blocks in that row, and the forth row would have seven full blocks. Carrying this down to the 150 blocks level, there would be 290 blocks at each base, or 580 cubits, or 1,015 feet for each base of the pyramid. This isosceles triangle appears to be too flat, and this area of 1,015 feet by 1,015 feet is much too large for the area and would require many more stones.


 Pyramid Figure 2

The third and seemingly best design would be to put the top stone one and a half cubits in from the face of the stones on the second level. See figure 3 below. The second row would have two and one half stones, the third row would have four full stones, the fourth row would have five and one half stones, and so on. Carrying it down to the 150 block level, there would be 225 blocks at the base, or 450 cubits. This measurement would be 787.5 feet at each base of the pyramid, making the pyramid 300 cubits high and 450 cubits at each base. These are numbers I can understand.


Pyramid Figure 3

Each step of the pyramid would measure three and one half feet with a landing of 31½ inches. The sand carriers and stonemasons would have room to easily climb up and down the pyramid and to do their work. Assuming the architects used this design, the Great Pyramid would have originally been 31½ feet wider at each base and 43 feet higher than the present figures indicate. The vandals and looters may have taken more stones to build Cairo than previously thought.

To build the landings, the angle, and the smooth exterior surface of the pyramid, the foundation was first laid out and the size of the base determined (as noted above, this would have been 450 cubits). They set the corners at right angles from the first line and measured the distance of the line so all sides would be of an equal length. Pegs were inserted at each corner and a rope with knots tied every cubit and a half (31½ inches) were wrapped around the pegs. After wrapping the rope, the first block would be placed into position at the edge of the rope. All the corners would be positioned first and with a block that was cut approximately three and a half feet high, three and a half feet wide, and three to six feet long. This measurement would be equal to a block measuring two cubits by two cubits by three cubits. Then the perimeter would be filled from corner to corner with blocks cut to the same measurement and adjusted as they reached the center. The bottom of each block was carefully placed along the rope line. This was important as it determined the angle of the entire pyramid. When the perimeter was complete, the center of the level was filled in with various blocks to an approximate height of the top of the outer core of blocks or to the top level of the perimeter blocks.


After the first course or foundation was laid and one and a half cubits were deducted from each side, pegs were inserted at the top of corners of the first course and wrapped with the knotted rope. The number of knots on the rope should be equal on all four sides. A line could have been drawn exactly one and a half cubit in from the top of the stone, but the planners still needed to be sure all sides were equal.

This method would make the second course one and a half cubits shorter than the one below it on each side. By using a cubit and a half instead of one cubit, the stones were laid in order to give the workmen a 31½ inch platform to work on. It gave the sand carriers and workmen easy access, using stepping stones, to the level on which they were working. Cutting the outer stones from base to base also gave the pyramid a satisfactory angle to rise from the ground to the top.


Figure 1. For detail of circled item see figure 2

As in the first course they would lay the outer most stones, made of limestone, starting at the corners and laying the base of each stone on the rope or line. Again they would fill in the center to the height of the outer stones. They were building a pyramid with steps, three and half feet high and thirty-one and half inches wide. They would repeat this until they reached almost to the top of the pyramid.




The artist rendering show sand and stone ramps used to roll or pull the platforms or skids with the stones on them up the sides of the pyramids, but I do not believe that the Egyptians ever built any ramps. It is my opinion that the men climbed the side of the pyramid to deposit their sand in the basket.They could have made this climb easier by placing stepping stones on top of each of the large blocks creating a crude stairway.


Figure 2

Two stones would be placed on each 31½ foot landing, one 14 inches high, the other 28 inches high. The length and width could vary. Thus, every landing would have three steps to the top of the next level, each step no more than fourteen inches high.

As the workmen built up the various levels, moving the towers up was necessary as they went.  When they filled in the levels to the height of the perimeter stones, in order to

fill in the area under the tower they tilted the tower over on its side onto logs, and rolled it a cubit or so away. They filled in the tower area with blocks of stone previously brought up, rolled the tower back, and lifted the tower to its upright position. When the top was reached, it was time to install the cap stone. The cap stone would also be two cubits high, but it was cut into a small pyramid one and a half cubit short on all four sides of the base on which it was placed. The pyramid would be built up to this level. As the pyramid got smaller as they approached the top, they would remove the log platform of the tower they were using and wedge the four legs onto the top of the pyramid. Then they would hoist the balance of the stones and the cap up. After the cap was in place, the tower would be discarded. Now it would be time for the stone masons to start the work of cutting the stone into a smooth finish. They would start at the base of the cap on top of the pyramid and cut down to the outer base of the next row of blocks. It would be a rough cut at first, but as they got nearer to the proper angle they would use a straight edge or straight piece of wood as a guide. When the surface from the base of the cap to the outer base of the lower stone was smooth, the masons would step down to the next level, standing on the thirty-one and a half inch ledge, that is on every level. They used this ledge and the step stones where necessary as a scaffold while cutting the stones. As they came down, they would discard the stones making up the crude stairways used by the sand carriers. The masons would then start to cut the limestone from the base of the stone just completed at the level above to the outer base of the next row of stones below. When the stonemasons finished chiseling away a row of stones then they would grind and polish the surface to a smooth finish, probably using a granite stone the size of the palm of their hand. If they laid the stones exactly one and a half cubit from the edges, then the cutting and smoothing of the surface would automatically give the pyramid its approximately 53°± angles.

There is no real mystery as to why and how the shape of the pyramid was used for the tombs of the pharaohs. The purpose was to build a monument that would last forever, be at a great height for all to see, serve as the burial place of the pharaoh, be relatively easy to build, secretly hide the burial chamber, keep visitors out, and discourage robbers from desecrating the tomb.

If you ever watched a child playing with blocks, you noticed that the child quickly realizes that a structure built by placing one block on top of another becomes very unstable the higher the structure goes until it falls. However, the child notices that when building the blocks in a triangular shape, the structure becomes very stable. Obviously, the architects of the day must have arrived at the conclusion that the monument to be very stable should have a pyramid shape. This shape was easier to build than one straight up on all sides and allowed for the sand carriers to bring their sand up to fill the baskets, and enabled the stonemasons to work from the top down to give the structure a smooth finish. Given enough stones and workmen, a pyramid could be built to almost any height the Pharaoh wished by changing the size of the base and the angle of its sides. It could be built with secret passage ways and tombs within the structure. The architects would have the sides cut smooth finish to keep people from walking on the structure and damaging it, and it would discourage robbers from climbing around looking for the entrance. The shape of a pyramid was the most logical one to use.

I think that this method of building the pyramid worked for the first few hundred years until the weakest areas, the filled in entrance, may have begun to show wear and reveal itself.

These are my theories as to how the Egyptians could lift the stones, how they laid the stones, how they determined the size and angles, and how the exterior was finished to a smooth surface. I believe these methods are much more feasible than building a ramp almost as large as the pyramid itself.

There is a good reason why there is no evidence that the shadoof method was used. After they built the pyramid, there was no reason to keep the towers. They consisted of wood and rope and in time would totally disappear. Historians, seldom, if ever, record how a picture is painted, how a building is built, or how a tradesman did his work. It appears that only the results count. This picture was painted by . . . This is the work of . . . I have been looking, but I have yet to find a picture of a pyramid in any ancient Egyptian art.

These pyramids built by the Egyptians 4,000 to 4,500 years ago are one of the seven wonders of the world. If there were any references to any machines used in building the pyramids they may have burned in the fires of the Alexandrian Library. I believe I have given Egyptologists and Historians completely new ideas to think about. Considering the vast amount of information still available, perhaps the scholars really did not know what to look for. Perhaps the scholars will now revise their thinking on how the Egyptians built the pyramids.

Richard Koslow
5950 Pelican Bay Plaza, # 1102
Gulfport, Florida 33707-3961
Phone: 1-727-347-3327
E-mail: rkoslow@tampabay.rr.com

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