Click here for a short animation video in National Geographic on the operation of the Mullers-TLC
Click here for an overview of the live test scale 1:1 with a 2370 kilogram load
Click here for the article in the scientific journal ENiM Egypt 24 June 2022
Pyramid building clarified with a Tilt Levering Cage:
Well -known ship technology
Abstract
A Tilt Levering Cage (TLC) was composed of two regular bipod ship masts. Fixed atop and at the base, posts were laid over both girders as the loading floor. Transport stairs were on all sides of the pyramid alike the pyramid steps but larger, known as platforms. A loaded TLC on a platform was tilted with ropes at the top, side to side by manpower. With each tilt a girder was lifted and supported underneath by lading posts at right angles, known as box cribbing. As a result, the TLC became higher with each tilt on top of two side-by-side struts. Upon reaching the base of the next platform at an average of 2.5 metres height, the TLC was pulled a little slanted down for conviniance onto it, on roller posts. There it proceed to the unloading spot or the next lift was initiated. At the height of the construction there were several hundreds TLCs on as many platforms on all sides of the pyramid. All TLCs with their peaks waving back and forth were steadily loaded with building blocks on the way up.
Tilting heavy objects like keeling a ship and holding this position with struts must have been well -known techniques for bottom maintenance of ships in Ancient Egypt. This technique could also have been used for pyramid construction. A lever could be made of two, at the time regular, two -legged ship masts. The two tops fixed together and at the base posts laid over both girders as the loading floor, made a Tilt Levering Cage (TLC). The top was the attachment for ropes with which the lever structure could easily be tilted. When tilting side to side, a girder under the loading floor always was lifted and propped up. Through repeated propping up the TLC became higher and higher on two side-by-side struts. Struts were made of stackied poles at right angles in layers, known as box cribbing.
Pyramid steps are the stairs for the workers, they are too small for the two side-by-side struts of a Tilt Levering Cage. Several transport stairs alike pyramid steps but much larger, known as platforms, were on all sides of the pyramid. The stones to create the platform were parked left and right beside, looking like battlements. The platforms were in line at a possible height difference of an average of 2.5 metres, as can be deduced from Petrie’s Chart about the stone layers of Khufu. A TLC on struts was lifted slightly above the base of the next platform for easy pulling onto it, using roller posts. Afterward, it proceeded to the unloading spot or the next lift was initiated.
A TLC, struts and transport stairs offer a tested method for pyramid building for the first time. It meets the description in Historien of the Greek Herodotus 500 BCE among other things as a ‘Machine made of short posts’ and ‘There were a flight of stairs of platforms or battlements’. The image of a TLC loaded with a building block is the appropriate determinative of the hieroglyph with the sound characters for the verb lifting.
Using a TLC wasn’t new, existing techniques were used: two -legged ship masts, struts and the action of keeling a ship. A TLC explains pyramid building without unimaginable big and unstable ramps, “troubles at the top” and explains the applying the cover layer “top down”. Evidence can be obtained by research on the pyramid. The platforms were closed equal to the progress of the construction of the cover layer top-down. The parked stones next to the platforms were placed back in bond, but a longitudinal joint at the top layer, against the rear wall of the former platform, remains visible. The most perfect and exact instrument with which this joint, covert with sand and grafel, can possibly be visualized is a broom.
Table of Content:
When and why were the pyramids built?
The pyramid of Khufu
How-long-did it take to build and how many bricks were used?
How were the pyramids built?
What does desert sand look like?
What were mudstones used for?
Troubles at the top
Where did the stones for the construction of the pyramid come from?
Tools and rope from that time
How were the building blocks moved from the quarry?
Where did wood for construction come from?
How could they possibly have done it differently?
How-were the stones possibly transported vertically?
Were the Egyptians familiar with such wooden constructions?
How was the Tilt Levering Cage used?
Why were the pyramid steps not made big enough for a Tilt Levering Cage?
How was a Tilt Levering Cage used near the rib of the pyramid or near the top?
How was the lift secured of the Tilt Levering Cage due to tilting?
How did they use the Tilt Levering Cage?
How many people were needed for the used of a Tilt Levering Cage?
What did it look like from a distance?
Where were the stones that had been moved to make a niche?
How-was the whitish limestone covering applied?
How many giant stairs were there?
How were the unloaded Tilt Levering Cage lowered again?
How were the stones lifted that did not fit in a Tilt Levering Cage?
Is there evidence that this pyramid building method was used?
When and why were the pyramids built?
There are three pyramids on the Giza Plateau. These pyramids were built during the Bronze Age 4th Dynasty, between 2543 and 2442 B.C.E. The Bronze Age, but the Egyptians did not know the alloy bronze of copper and tin at that time. The three pyramids were all built in this relatively short time. In addition to their function as funerary monuments, they can be seen figuratively as symbols of prosperity of the early Egyptian state. They were built by the Egyptians and not by slaves. During the Nile flood season, the land was unworkable for four months and many more Egyptians were able to devote themselves to building pyramids. It is said that the pyramids were built oriented towards certain stars, which is only temporarely possible due to the constant change of the ‘firmament’. The cyclical changes in the position of the Earth’s axis due to tilt and precession and the change in the Earth’s orbit around the sun due to eccentricity means also that our starry sky is constant different and for sure 4500 years later.
The pyramid of Khufu
The largest pyramid, known as the pyramid of Khufu who ordered it, or the pyramid of Cheops (Greek) also the ‘Great Pyramid’ has a base of 230 by 230 meters. The original height was just over 146 meters with 203 stone layers with a special stone on top at the time, the Pyramidion. Limestone from a nearby quarries, was the main building stone. At the bottom of the pyramid these had a length of about 1.3 metre, a width of 0.8 metre and a height of 1.3 metre with a weight of about 2500 kg. More layers higher in the pyramid the building blocks were smaller most, with exceptions, with an average height between 0,5 and 0,6 metre. The Great Pyramid may have included about 2.3 million limestone building blocks.
How long did it take to build and how many limestone building blocks were used?
According to Egyptologists, the pyramid of Khufu may have been built in 20 years by about 20,000 people. These have brought the 2.3 million limestone blocks into their final place. On top the Pyramidion, this stone was coated with electrum, a mixture of several including precious metals. It has been calculated that on average a building block had to be placed every 4 minutes or 360 in daytime in order to be able to build the pyramid over a period of 20 years.
How were the pyramids built?
The current theory among Egyptologists is that the pyramids were built using a ramp straight up to the pyramid or from a certain height it turns into a upwards circulating stone ramp on the pyramid. Whether this could have happened remains to be seen due to the lack of evidence and the lack of a provable other method. In any case, the number of stones and the speed at which they were placed makes the use of a ramp very unlikely.
The pyramid of Khufu was 146 meters high at the time. A ramp with a rise of a few degrees would make it many miles long. The volume of the ramp would be many times greater than the volume of the pyramid itself to be built. The top of the ramp should have a decent width for passing, the pulling plows of many tens of meters in length and the returning men. The slope with its embankments and the fanning out at the beginning would have to be raised and tamped after each layer of stone for transport to the next layer of stone. With each increase, the slope not only became wider, but also tens of meters longer. There were 203 stone layers, which means that, over 20 years, the stone transport had to be interrupted every five weeks on average to raise and tamp the ramp. This makes the use of a ramp extremely unlikely. Interesting to know that no trace of the use of colossal slopes has ever been found, neither on site, nor in hieroglyphs or writings.
A ramp might have been built with desert sand also drifting sand, together with stones from the surrounding area. In desert sand the internal friction coefficient between the sand grains is significantly low. That is why the slope of the ramp should be chosen extra oblique. When reaching the top at a height of 146 meters of the pyramid of Khufu, calculations show that the ramp there would have a width of about two kilometres. This makes the use of a ramp extremely unlikely.
The common theory among Egyptologists is that the building blocks were dragged up the ramp on sledges over moistened desert sand. This could have caused problems for the ramp itself and for the pulling plows, who had to be able to push off themselves firmly in the sand to drag the loaded sledges.
It has been proposed to lift the 2.5 ton building blocks that long poles were used as a lever mechanism. Calculations and experiments show that such a pole, not springing like a fishing rod, should have a considerable length and diameter that its gets unmanageable. This makes this proposed method of lifting the building blocks up the piramide also extremely unlikely.
The Greek Herodotus who visited Egypt 500 B.C.E. describes a building method, from tradition, in which the pyramid itself formed the stepping stone to ever greater heights. He speaks of ‘stairs’ and ‘platforms’ and of a ‘machine made of short pieces of wood’. He has detailed several other specific customs of the time, some of which have only recently been endorsed. His descriptions of pyramid construction has been dismissed by Egyptologists as technically impossible.
What does desert sand look like?
Desert sand consists of very small grains of sand sorted by weight by the wind. Very small because only light grains of sand can be carried by the wind, sorted because light grains are more easily carried further away. This transported sand constantly collide and is therefore rounded. Under the microscope desert sand also drifting sand can look like smal or smaller damaged marbles. Desert sand can not be used as foundation sand let alone suitable for a enormous high ramp. If a ramp could be made of desert sand and then subjected to heavy loads, or if a wind or rain shower passed over it, how would the ramp behave? Does it collapse spontaneously or is the ramp blown away or washed away or does it collapse on its own like loose sand?
What were mudstones used for?
The circular part of a ramp on the pyramid, according to Egyptologists, could be made of mud stones. A mud stone is a sun-dried mixture of clay and a bit of straw for binding. The question is whether such a brittle stone can support many tons of weight and how does a mud stone holds during heavy use? How does a mud stone holds during a rainstorm? Another problem is how to pull a sled loaded with 2.5 tons or more around the corner on a circulating mud stone slope? Where could the pulling plows stand to drag the sledge around the corner?
Troubles at the top
How was the transport of the building blocks near the top? Was a straight or circulating ramp continued tens of meters beyond the top of the pyramid to give the plows enough room to pull there sledges? Under those circumstances, it is conceivable that the entire pyramid may have temporarily disappeared completely under the ramp of sand and mudstones. This does not solve the ‘troubles at the top’.
Where did the stones for the construction of the pyramid come from?
The limestones of the pyramid of Cheops came from several nearby open quarries. By splitting, hammering and chiseling, the building blocks were cut to size and transported to the construction site on sledges. The limestones from the nearby limestone quarries had the same origin and therefore the same stratification. The whitisch Tura limestone used to cover the pyramid as well for interior linings came from a region on the eastern side of the Nile and was transported by boat down the Nile. This rock was whitish due to a different circumstances at the time of sedimantation at the bottom of the ocean. The igneous granite used for the construction of the burial chamber was brought by ship from the Aswan region located upstream on the Nile.
Limestone is petrified sedimentary lime of mostly calcium carbonate. This calcium carbonate comes from, over millions of years, tiny calcareous dead sea organisms skeletons that settle on the bottom of the ocean. The petrification of this was caused by temperature and pressure deep in the bottom of the former Tethis Ocean. Due to tectonics, the movement, cracking and colliding of tectonic plates, this limestone has been pushed to the surface.
Due to cyclic changes in the position of the earth and its orbit around the sun, the limestone is stratified. The dark layers in the limestone due to more residual organic material are called sapropels. This retention of organic matter could occur in low-oxygen conditions on the ocean floor if fermentation was not possible as a result. The whitish Tura limestone may have formed under more oxygenated conditions. But processes deep in the soil with high temperatures and pressure can also cause the limestone to change color and structure.
The stratification can affect the splitting ability of the limestone and could be a determining factor in the choice of the height of the limestone to be mined. The limestone of the open grooves near the pyramid of Khufu has been pushed up by tectonics almost horizontally, so that the stratification is quite the same top down.
Boulders of the igneous rock granite came from the Aswan region and could be selected to the most suitable size due to natural shrinkage cracks and erosion (woolsack deterioration). The choice may have made the intensive processing of the hard stone somewhat easier. The granite was transported by boat down the Nile to Giza.
Tools and rope from that time
The wheel for transport or for use in a pulley was not known at the time. A hammer, saw, flint and brass tools such as chisels and drills enabled wood processing and the manufacture of solid wood joints. Wood connections as mortise and tenon with dowel(s), clamped with wedges or inlaid and lashed were known. Rope made of palm fiber or papyrus made it possible to pull in a plough and make lashings.
How were the building blocks moved from the quarry?
For horizontal transport, the building blocks were placed on wooden sledges in the quarry. These heavy loaded sledges were towed over sand to the buiding site, according to Egyptologists. There are images were water was poured over the sand from a pitcher, in front of the sledge possibly to facilitate sliding. Transport over roller poles can also be seen on drawings from that time. Horizontal transport could possibly be realised more easily be using long cedar trunks, 40-50 metres in length, laid like rails. These trunks could eventually be partially buried in the sand for fixation, sticking out just enough for the use of roller poles. All these transport movements were based on manpower. The whitish Toera blocks for cladding the pyramid and the granite stones for the inner chambers were transported by boat both downstream the Nile.
The method accepted among Egyptologists of dragging the sledges over sand using rolling poles is nevertheless highly improbable. Rolling posts on sand do not roll but get stuck in it. More likely is that the sledges were pulled on roller poles, along long trunks laid like rails.
Where did wood for construction come from?
Not many trees grew in Egypt that were suitable for sturdy and bigger wood structures. The most suitable wood for construction was the tough and durable cedar. This was expensive as it had to be imported from far across the sea. Cedarwood grew in abundance in the then vast forests of Lebanon, Syria and a smal part of Turkey, at the time called the Levant. Long straight cedar trunks up to 40 – 50 metres high, without significant side branches, could be taken from the dense forest. Curved pieces of cedar could be optained from a lonely and then widely branched tree. Wood was traded by Phoenicians and transported in rafts from the natural harbour Byblos to Egypt, up the Nile.
How could they possibly have done it differently?
What could be more logical than using the robust pyramid under construction itself as a stepping stone for transporting the building blocks to greater heights. Not an unstable slope with a volume many times the pyramid itself. No incredible scaffolding more than 160 meters high for lifting many heavy building blocks. Not a huge amount of extra limestone for a stable ramp. The method in which the pyramid itself forms the stair for transporting the building blocks upwards has been described by the Greek Herodotus who visited Egypt 500 BC. He wrote of a “stair” on the pyramid consisting of “platforms or some call it battlements.” He had heard this explanation from tradition from a priest. This method after Herodotus is still dismissed by Egyptologists as technically impossible as well as with the argument that the Egyptians no longer knew it, 2000 years after the pyramids were built.
How were the stones possibly transported vertically?
The stones may have been transported vertically through the use of controlled tilting. How this could possibly have happened, could in any case be taken directly from the shipbuilding and ship repair of the time. A construction of a load floor using two bipod ship masts, the act of keeling a ship and propping up offered the solution: the Tilt Levering Cage or TLC.
They made a good and sturdy lever construction by connecting two then common two-legged ship’s masts of at least seven meters, in a unique configuration. They attached the mast feet, more than a metre apart, to a girder about one and a half metres. Two of these triangular structures were then firmly lashed together with a crossbeam at the top at a slight angle and the girders were connected with more then one metre long poles on top to form a robust loading floor. This floor, with its two bipod masts, resembled a open pyramid with a high pointed top. Known wood constructions were, as mentioned, notched wood with lashings, tensile connections with wedges or mortise and tenon with dowels. The use of tough cedar wood from the Levant made the lever construction rigid and form-retaining. We call this patented device a Mullers-Tilt levering Cage or TLC or a Mullers Cage. The theory behind is mentioned the Mullers Pyramid-Building-Principle or MPBP.
The top of the Tilt Levering Cage was the point of attachment for ropes. By pulling the top with sufficient manpower, the Tilt Levering Cage was tilted over a ginder. This way of tilting must have been familiar as keeling a boat sideways for regularly maintenance of the bottom. By tilting a Tilt Levering Cage over a ginder, the other was lifted. This lift was consistently secured by propping it up with poles stakker at right angles in layers. By alternately tilting in opposite directions and time and again propping, the TLC was lifted in its entirety on this two struts.
Propping up was done by box cribbing. Two parallel poles were stacked in layers at right angles. The reclining poles of a box crib had the same length. At the bearing points, the poles were of equal thickness due to a appropriate round notch at the bottom. Appropriate, because the depth of the notch depended on the diameter of the pole there. These measures guaranteed a square straight and stable box crib. While working with a TLC, two struts of stacked poles ‘grew’ under both girders. The aforementioned Herodotus noted “a device made of short pieces of wood,” which rhymes well with a TLC and its poles for the box cribs. More on that later.
The lift with a Tilt Levering Cage depends on the degrees of tilting and the distance between the girders. Easily box cribbing will also have been decisive for the degrees of tilting. The optimum of these parameters will have been determined in practice. A Tilt Levering Cage stands stable on its two girders. If, due to an unforeseen cause, the power at the top is suddenly lost, the TLC automatically tilts back to its safe resting position.
Were the Egyptians familiar with such wooden constructions?
Making a wooden construction of a Tilt Levering Cage will not have caused any problems given the extensive experience that people had in shipbuilding at the time. The sailing ships of 30-40 meters or more in lengt had high, sturdy bipod masts placed transversely in the hull. The image below shows the top of a bipod mast with mortise and tenon connection with several dowels. Underneath, ten wooden transverse connections as slip holes for the lines to starboard and port for operating the square sail. The sturdy bipod masts placed transversely in the hull needed only rigging fore and aft. These bipod masts in ships could be considerably larger than the construction required for a Tilt Levering Cage. With tools for hammeting, sawing, drilling, chiseling and rope for lashing and with the knowledge of sturdy wood connections, building a Tilt Levering Cage must have been easy.
A pole used as lever is loaded in bending. And bending, in contrast to tensile and compressive forces, a pole can only offer limited resistance. A split fracture can happen quite easily and surprisingly unexpectedly. Rigging up a mast ensures that only compressive forces are exerted on it. With a Tilt Levering Cage, constructed as a lever, the poles are only loaded by tensile and compressive forces. As a result, this truss construction is extremely rigid and shape retaining.
How was the Tilt Levering Cage used?
For the use of a Tilt Levering Cage (TLC), larger stairs as platforms were created at fixed distances in line above each other on all sides of the pyramid. The pyramid steps are great for climbing the pyramid, but too small for the use of a TLC. The transport stairs were deep and wide enough for the two box cribs for a TLC. The stones out of the pyramid to make the platforms, were moved over the step and parked just to the left and right of the newly formed platforms.
At the very bottom of the pyramid, the largest stones had been used and a transport star with platforms could be made every other step; a bit higher in the pyramid smaller stones were used and a platform could be made by creating it in the 1st, 2nd or even the 3rd successive stone layer (see drawing below). In this way, sufficiently large enough platforms for a TLCs could always be made. The stones remover to form platforms were parked just left and right of the platform. From a distance, the platforms will have looked like battlements in line above each other. When a platform was no longer used, the parked stones were moved back restoring the pyramid step.
The height of the stone layer and the slope of the pyramid determine the depth of a step. The slope of 52 degrees was already determined at the start of construction. The height of a layer of stone was never less than about 20 inches or 52 centimeters. The corresponding step depth is approximately 40 centimeters. The minimum stone layer height could be due to the fact that stones did not have to be temporarily moved deeper than 3 stone layers in the pyramid for a sufficiently deep platform of [1 + 3] x 0.4 = 1.60 meters. The box cribs would not have been on the edge of a platform step. This suggests that box cribs may have had a square footprint of up to 1.50 meters.
The platforms, whether they were made in the 1st, 2nd or 3rd successive stone layer, all had approximately the same rise to the next platform. This amounted to about 2 to 3 metres, which is well within the margin for safe box cribbing. More on that later.
The first platform at the bottom of the pyramid with the highest stones used determined the largest rise to the next platform of 2.6 meters (2 x 1.3 meters). Higher in the pyramid the platform steps were smaller.
These stairs of successive platforms were placed on all sides of the pyramid at a convenant working distance of 15-20 metres from each other. Using these platform stairs, it was possible that hundreds of loaded TLCs were all at the same time on the way up.
The Pyramidion, the capstone, loaded into a TLC used at least 56 (146m height, divided by the maximum platform step height of 2.6m) successive platforms and passed all 203 pyramid steps. Herodotus who visited Egypt 500 years B.C. visited noted a ‘flight of stairs’ and wrote about ‘platforms or some call it battlements’. More on that later.
Why were the pyramid steps not made big enough for a Tilt Levering Cage?
The pyramid steps are aesily accessible for workmen to be able to move over the pyramid, what does not apply to the bigger steps of platforms. It might have required many thousands of wooden stairs with platform steps.
How was a Tilt Levering Cage used near the corner of the pyramid or near the top?
Near a corner or near the top of the pyramid there was not enough space to pull a Tilt Levering Cage. Then an extra bipod made of round wood was placed slightly oblique against the loadingfloor of the TLC. A rope connected the top of this bipod and the top of the TLC. The TLC could now be tilted by pulling down at the top of the bipod. To make pulling easier, workmen could sit or stand on the bipod as ballast at the right time. Or they walked up and down a gangway on the bipod like on a treadmill, back and forth. Instead of pulling, gravity was used to tilt a heavy loaded TLC. How easy could it have been. Near the top of the pyramid they worked with a 2nd extra bipod, placed on the other side of the loadingfloor. With the use of a TLC and an two extra bipods, no “troubles at the top”, not even to move the Pyramidion on top.
How was the lift secured of the Tilt Levering Cage due to tilting?
During tilting with a Tilt Levering Cage every lift was secured by repeatedly propping. This was done by box cribbing. That’s stacking two parallel poles at right angles in layers. Box cribbing is safe if the strut is not higher than three times the distance between the bearing points of the box crib. Experimentally, the Egyptians will also have agreed on such a rule at the time. When using a Tilt Levering Cage, the distance between the bearing points is approximately 1.3 metres. Box cribbing is safe then to a height of almost 4 metres. The maximum lift between platforms is at the base of the pyramid with the biggest building blocks. The necessary lift there between two platforms is there about 2.6 meters. This is well within the margin for safe box cribbing. When it came to heavier objects, it could be decided for safety reasons to stack with 3 or 4 parallel poles. Herodotus noted a ‘device made of short pieces of wood’. More on that later too.
How did they use the Tilt Levering Cage?
The first layer of stone was laid after sufficient horizontal leveling of the construction site. The stones for the first stone layer were pulled on sledes to their final destination using roller poles and manpower.
Tilt Levering Cages were used for the construction of the second and all further stone layers. Loaded TLCs were placed using roller poles at a sufficient working distance of 15-20 metres on all sides of the first stone layer or base of the Pyramid. These TLCs were then tilt lifted on their box cribs until they were slightly higher than the first layer of stone. Then the TLCs could easely, slightly inclined downwards, be pulled on roller poles onto the first layer of stone. While the box cribs were removed for the next transport, the TLCs were moved on roller poles just like sledges over the first layer of stone to the final location for their load: the building blocks. The unloaded TLCs weighing less then 100 kilos were lowered in its entirety or higher in the building proces eventualy in parts for the next lift run.
To be able to reach the third stone layer they created the first temporary platforms on the construction side for TLCs, on working distances of aformentioned 15-20 metres on all sides of the first stone layer. A few stones were left out of this layer, in such a way that a platform was created wide enough for 2 box cribs. These stones were parked left and right from the first platform on the construction side. A loaded TLC was placed in the middle and was tilt lifted a little higher than the second stone layer. The TLC was then pulled, slightly slanted downwards, onto the second stone layer for the construction of the third.
For the construction of the fourth and fifth stone layer, a TLC was tilt lifted and pulled onto the second stone layer in the first prepared temporary platform in the third stone layer. From there the fourth and fifth layer of stone could be reached. The stones to create this platform were parked also just left and right on the same step.
To reach the sixth stone layer and all higher, the TLC had to be tilt lifted from the first platform onto the next and so on.
Pyramid building was an interplay of tilt lifting with multiple TLCs, box cribbing and the use of many parallel transport stairs consisting of subsequent platforms. Herodotus noted 500 years B.C. ‘a flight of stairs’ and ‘platforms and some call it battlements’. More on that later.
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How many people were needed for the used of a Tilt Levering Cage?
The top of the Tilt Levering Cage could have a height of about 7.5 metres. A loaded TLC weighed about 2500 kg. The horizontal force required for tilting follows from the lever rule. The balance of the Power x Arm of the stone and leverage are equal. The building block with a weight of 2500 kg multiplied by the distance (the arm) from the center of gravity of the stone to a beam of 0.5 meters is 1250 Fm. 1250 Fm divided by the arm of the 7.5 meter lever gives a pulling force required at the top of the TLC of approximately 178 kg. If the top was pulled at an angle of 45 degrees, the required force according to Pythagoras 178kg x √2 is approximately 250kg. Tilting at an angle of 45 degrees must have been possible with about 10 men with 25 kilos of tractive force per man, if the angle of tilt was greater, the required tractive force became less and less. The latter is due to the fact that during tilting, the top of theTLC is increasingly pulled in a more favorable ‘perpendicular’ direction and at the same time the stone is increasingly moved towards the pivot point. Both changes reduce the force required to roll over the trajectory. Investigations have shown that construction would have been carried out in shifts of 40 at the time, which would be an appropriate number for the easy use of a TLC with its two box cribs. 25 Man on the ropes, 10 box cribbers, 3 foremen and 1 man for the lead and the overview with his second.
As an example of the degree of lifting, in the article in ENiM-Egypt (see the link at the top right of this article) a controlled tilt, from the horizontal, of 0.3 meters was chosen as a lift for one of the legs. The Tilt Levering Cage is then tilted by approximately 14 degrees and the stone has been lifted by 0.15 metres. At a tilt of 14 degrees, the top of the tilt lift cage swings out 1.5 meters and the stone is lifted about 0.15 meters. With a full tilt cycle from -14 to +14 degrees and then by the other shift in front of them from -14 to +14, the lift of the stone is 4 x 0.15 or 0.6 meters. The top of the TLC then travels 6 meters: 3 meters to one side and 3 meters back. In five tilting cycles the largest difference in height between two platforms of 2.6 metres (2,6 : 0,6) could be achieved. These calculations about forces, degrees and distances work with a TLC are calculation examples. It will be clear that working in a team in connection with a TLC is safe and relatively simple and does not require superhuman efforts. Let alone that the help of aliens was needed.
What did it look like from a distance?
From a distance, the successive platforms in line with each other, sometimes with small differences in width, with the striking stones parked on the left and right, would have looked like a great stair of successive battlements. Multiple staircases were built on all sides of the pyramid. On the platforms of these stairs, many teams were in action with TLCs. Tilting back and forth these TLCs all steadily crept up the pyramid. The Greek Herodotus recorded 500 B.C.E. ‘a flight of stairs’ and wrote about ‘platforms and some call it battlements’ on the pyramid. More on that later.
Where were the stones that had been moved to make a niche?
In order to make a sufficiently large platform, pyramid steps were enlarged in the next layer(s) of stone. The stones from a platform were moved over the step to be parked immediately to the left and right of the platform. From a distance, a platform and the stones next to it, sometimes on several steps, looked like two battlements. The stairs of platforms in line above each other looked like stairs of successive battlements. The platforms were maintained until the last transport with TLCs was completed. Then the parked stones were moved over its step back on the platform and the original pyramid step was restored almost invisible. The last activity with a TLC consisted of supplying the whitish Toera capstones for the pyramid’s cladding. These capstones were laid on the pyramid from top to bottom. As stated by Herodotus 500 years B.C. described ‘platforms and some call it battlements’ and about the cladding ‘they worked top downwards’. More on that later.
How was the whitish limestone covering applied?
Transporting the whitish Tura capstones for the covering layer of the pyramid was the last activity with Tilt Levering Cages on platform stairs. The top of the pyramid was covered with smoothly finished capstones, delivered initially by the last four platform stairs precise in the center of the sides of the pyramid. The capstones were stable laid, working top-down in broad horizontal layers, by overlapped stacking over 5 to 6 pyramid steps until the desired layer thickness was reached at the top of the stack with a perfect connection with the sloping capstone layer above. This overlapped stacking kan be seen very wel at the bottom of the remaining cap of the pyramid of Khafra. Subsequently, overlapped stacking in horizontal layers was started again from the corners of the pyramid in the direction of the now, at a lower altitude, multiple central transport stairs. If a platform was reached by the ongoing stacking, this platform was closed. This was done by restoring the pyramid steps to almost invisibility by replacing the stones in bond who were parked next to it. Then the overlapping stacking with capstones could be continued. And so it went on down to the base in horizontal layers from top to bottom, each time starting from the corners.
The whitish Toera limestone cap of the Pyramid of Khafre, which remains after stone robbers disappeared, rests stable on the pyramid. Photos of the bottom edge clearly shows the overlapped stacking of the cap stones.
Meidum’s pyramid was dramatically different, the capstones were stacked from the bottom up until increasing pressure exceeded the internal coefficient of friction at the base and the stack became unstable. A many minutes-long collapse of the entire cladding layer followed. The result can still be recognized by the accumulation of stone rubble around the entire pyramid. Many thousands of people will have died, their remains are certainly still under the rubble. A lesson had been learned, on the Giza Plateau they did things differently about a hundred years later.
The four faces of the pyramid of Cheops have a slight curvature towards the heart of the pyramid. This shape ensures a higher stability of the surfaces of the pyramid if pressure would arise from the inside.
There is a good reason why the cladding would not have been worked from the bottom up, as it would have involved using a different lift mechanism to transport the Toera stones, without the platform stairs. An other reason: if any stone or rubble fall during the application of the Toera top layer from top to bottom, as described above, it will fall on a pyramid step and remains there. Working from the bottom up could have resulted in dangerous situations from falling rubble and stones, not to mention damage to the carefully finished whitish Tura top layer.
Herodotus noted ‘after the structure was completed, they finished off the top tiers first and worked downwards so that the lowest tiers at the ground level were finished last’. More on that later.
How many transport stairs were there?
The pyramid of Cheops originally had a height of 146 metres. On average, the possible platforms of the transport stairs were about 2 – 3 metres above each other. What can be deduced from Petrie’s Chart about stone layers heights at the pyramid of Khufu.
From the middle of a side it was (146 metres divided by 2.5 metres) at least about 60 consecutive platforms to the summit. To prevent the work crews from getting in each other’s way while pulling, the platform stairs may have been spaced about 25 metres apart. Per side of the pyramid of 230 meters, 9 platform stairs could be built. After 12 platform steps, the outer stairs reached a corner of the pyramid. These platform stairs could therefore temporarily no longer be used for the transport of stones. Temporarily, that is, until the time of transport of the capstones for the cladding of the pyramid from top to bottom. For the stairs that subsequently reached a corner of the pyramid, this was after 24, 36 and 48 platform steps respectively.
Before the closure of the first 2 outer stairs, there were 108 platforms (9 stairs x 12 platform steps) available per side and 168, 180, 144 respectively for the time of the subsequent stair closures. At the peak of construction there were 180 platforms available per side, but on average over the construction period there may have been 100 per side. Set the occupancy rate of TLCs on platforms to 50%, a total average of 200 (4 x 50) platforms were in use on all sides. With TLCs left after use on the way back down, on hold or for repair, up to 300 (200 + 100) TLCs may have been available for transport. Research has shown that shifts of 40 people would have been worked, which means that for 300 TLCs there would have been at least about 10,000 people (200 TLCs on a platform x 40 people per team + 2000 other workmen) on and around the pyramid were working with TLCs.
How were the unloaded Tilt Levering Cage lowered again?
The Tilt Levering Cages that had unloaded their building blocks at their final location were lowered in a controlled manner, possibly dismantled, over a slide using ropes. After any repairs, the TLCs were used again for a subsequent vertical transport. A TLC made of the light and tough cedar wood weighed less than 100 kilos and could be carried easily, especially in parts.
How were the stones lifted that did not fit in a Tilt Levering Cage?
The largest stones in the construction of the Great Pyramid were used to line the interior spaces and for the ‘pressure-relieving’ ceilings above the burial chamber. These stones are certainly lifted with the same tilt lift method. But because these do not fit in a Tilt Levering Cage, more lined up TLCs were needed. Or it could be that a larger scaled-up TLC was used. It is also possible that a multiple lever construction was constructed on the heavy stone (see the sketch). Of course, considerably more people were needed to provide the pulling force for tilting, but by raising the top of the lever construction and bringing the pivot lines closer together, it was for sure possible to lift even the heaviest stones.
However, these stones were too large for transport over the aforementioned platforms. These stones were placed on the construction site where they were needed, but many tenth of metres higher in the pyramid yet to be built. At the same time as the construction progressed, the stones were lifted one stone layer at a time, after which they were pulled on roller poles onto the next stone layer. Then, after being lifted again, these stones were pushed back, but on the next stone layer. In this way, during the progressive construction of the pyramid, the large stones were lifted layer by layer to where they were definitively planned.
The fact that even the largest stones can be tilted and lifted in this way here a practical example: A fully packed motorcycle with its riders can easily weigh 500 kilos. Still, it takes the motorcyclist no effort at all to keep the bike in balance. The weight of the motorcycle is determined by multiplying the inertia by gravity. The gravity on Earth is about 10 m/s2. To keep the engine exactly in balance, only the mass inertia plays a role and that is 10% of the weight of the engine and that is here only 50 kilograms. Gravity plays an increasingly important role as the motorcycle becomes more unbalanced. It is greatest when the engine is on its side. Several people are then needed to get the motorcycle upright again. This example makes it clear that a 5-ton stone can be balanced without difficulty by a team of 10 men or a hundred for 50 tons!
Tilting a 50 ton stone with a height/width of 2 by 1 metre and a length of 9 metres is reduced by using a long vertical lever of up to 10 or 15 metres high. The force required for controlled tipping over the length of the stone can be calculated from the leverage rule in balanced situations of force is load x arm. The force required for tilting is then reduced from – 80% with a 10 metre lever to almost – 90% with a 15 metre lever.
Here a calculation example for the force required at the top of a 15 metre high lever to tilt a 50 ton stone: F(top) x 15m = 50,000 kg x 0.5 m (the arm is 1/2 of the width of 1 meter) makes F = 1,700 kilos. The tractive force per person is set at 20 kilos, which means that it must be possible for 85 men to tilt a 50-tonne stone for lifting. This example shows that tilt lifting can be realized relatively easily, even for the heaviest stones.
Is there evidence that this pyramid building method was used?
The Greek Herodotus has visited Egypt 500 years B.C.E. and wrote down all his experiences. He was told by a priest, by tradition, how the pyramids were built. The description of Herodotus corresponds aptly with the working method mentioned here in the construction of the pyramids using a Tilt Levering Cage. He noted about ‘raising the stones from the ground up to the first tier’, a ‘flight of stairs’, ‘ platforms or some call it battlements’ on the pyramid and ‘a device made of short pieces of wood’. He also reports on the construction of the white stones as cladding ‘top tiers first and worked downward’. And about the number of ‘devices’ he wrote ‘either they employed as many devices as there were tiers’ or ‘used one single device that was easy to move from one tier to the next after they had removed (? author) the stone.
There are hieroglyphs and drawings that have the meaning of a pyramid (see below). One of them resembles a Tilt Levering Cage loaded with a building block of the igneous rock granite. The contour at the bottom of the hieroglyph is a fence, according to the experts, but this may also look like a girder from a TLC. The hieroglyph’s load looks most like a single block of granite and less, which is the interpretation, as the bottom of a pyramid.
That it’s a block of granite can be recognized by the very coarse drawing of the black crystallized mica. This indicates a block of rock of a limited size. Mica’s have filled the space, which remain as feldspar and silicon dioxide crystallized out in the cooling magma. The hieroglyph shows a pointed and very high top that does not resemble any pyramid from that period. But this pointed top resembles that of a Tilt Levering Cage. The bar at the top in the hieroglyph, the reference to the pyramidion, is an essential part in a Tilt Levering Cage as a crossbar between the two bipod masts to obtain a sturdy construction that is form-retaining.
Is it possible that we have been looking at the solution of the most ancient myth for thousands of years? Could it be that the hieroglyph of a pyramid, resembling a sort of a Tilt Levering Cage, once had this meaning of a ‘good and sturdy construction’? Was the hieroglyph the ‘device made of short pieces of wood’? The Egyptians recorded in detail everything about their functioning over the centuries and about how pyramids were built explicitly nothing at all and by no one at all and that remained a secret throughout the centuries? That sounds extremely unlikely.
The Pyramid Texts 1650 is about the pyramid itself or the good, sturdy construction of a Tilt Levering Cage who made pyramid building possible?: ‘Any Gods who shall cause this pyramid and this construction of the King to be good and sturdy, it is they who will be vital, it is they who will be respected, it is they who will be impressive, it is they who will be in control … it is they who will take possession of the crown.’
Further evidence could be gleaned by examining the pyramid itself, looking for signs that might point to former platforms. Or investigate under the rubble at the pyramid of Meidum for remains of wood that could possibly indicate the use of some kind of a Tilt Levering Cage. But of course it is quite possible that after 4500 years there will be no recognizable traces of TLCs, not even under the rubble.
Is there more about how the pyramids were built from the hieroglyph writing? Since the number of people involved in the construction of pyramids and its duration of their construction, there is no question of confidentiality.
Egyptologist Huub Pragt pointed me to the hieroglyph who has the meaning of lifting. The determinative to this verb is classified in ‘Gardiner extended library’ among the home and burial furniture with the code Q33. That does not sound appropriate for the verb lifting what it should portray.
In the middle the hieroglyphs for lifting with its determinative. This determinative does not resemble a piece of furniture at all but has striking features of a lift mechanism of a Tilt Levering Cage. A lift mechanism as a TLC would further fit perfectly with the verb what the determinative should images: lifting. It must be realized that a TLC lift mechanism was unknown when drawing up “Gardiners List”.
In the top of the determinative, rope can be recognized, exactly as it can also be seen with the determinative V33 of a knotted bag. This includes the characteristic pyramid-shaped lever of the TLC and immediately below a horizontal rectangle which is the characteristic of a block of stone in “Gardiners list” with code O39. Furthermore, clearly in this determinative, the round wooden beam under the stone onto two clearly visible girders. Features are almost completely missing for a piece of furniture.
Incidentally, the determinative that is stored in Gardiners ‘extended library” shows a more vase -shaped ‘stone’ which does not match the rectangular shape that of the ‘stone’ seen in the carved hieroglyphs.
Further investigation should determine whether this is a historical error in the description of this determinative in ‘Gardiner Extensive Library’, perhaps caused by the unfamiliarity with a lifting mechanism such as that of a kind of Tilt Levering Cage.
succesful lift of 2370 kilos on the first try
(notice similarities with Mullers-TLC)
Successful experiments have been carried out in full size and at a scale of 1 : 10 and 1 : 30. A full size Tilt Levering Cage was made of two constructed round wooden bipod masts. The mastfoot were fixed to a girder. The tops of the two bipod masts were connected with a lashed crossbeam. The two parallel girders were connected with poles of more than one metre to forme the loading floor. The top of the TLC was pulled with ropes, at right angles to the girders.
The first and successful tilt lift experiment with 2370 kilos shows that large weights can easily be lifted with a device as a Tilt Levering Cage. Also it’s quite conceivable with the use of platforms and box cribs to build a pyramid. Herodotus’ description of a method very similar to a TLC is telling. An archaeological search on the pyramid may provide clarity. A broom is sufficient to reveal the longitudinal joint at the top of filled former platforms.
Bernard Mullers
mullers.bernard@gmail.com
Gallerij
The logo above with the 3 pyramids of the Gizeh plateau, the pyramid of Cheops at the front, can be ordered as a logo embroidered on jackets, polo shirts or caps in the colors black, grey, red or blue. The standard logo has the color of a pyramid. Below are some examples. (another color logo is available on request)