Copyright © 2006 by Mike Molyneaux
New insights into ancient pyramid construction techniques presented in this article include the following:-
[1] The use of battering rams to create acoustic energy for quarrying, shifting and positioning stones.
[2] The use of counter-ramps with counter-weight principles for hauling massive stones uphill.
[3] The use of overlapping planks and rollers to create an auto-aligning, auto-braking system for the ramps.
[4] The use of leveraging towers with counter-weights for lifting stones out of a quarry and onto rollers.
[5] Submerging large stones in watery mud for transporting them down rivers or along canals.
[6] Partially completed courses of the pyramid forming a spiral staircase to support a ramp to the inner chambers.
Many tall stories have been told to explain the building of the pyramids, some involving aliens from outer space, or mysterious super-technologies of secret societies now lost in the mists of time, or a superhuman race now extinct as a result of a massive flood. However we don't need to invoke those Science-fiction sounding hypotheses when engineering insight can help de-mystify the ancient world. There are also dozens of serious scientific explanations but a close examination of all the practicalities and logistics involved in those explanations indicate that in practice the building project could never be completed that way within the historical timeframe. In our minds and dreams we can build pyramids the size of the Great Pyramid of Giza using only human power and a few primitive tools with amazing speed and success. But in the real world these amazing systems and inventions flounder at some practical obstacle or bottleneck along the way. Much more can be learned by real life experimentation and actual physical trials than by pure speculation. This article focuses on the Great Pyramid of Giza since that construction represents the greatest wonder and challenge. We need to explain the transportation and lifting of not only 1 and 2 tons stones but 20 and 70 tons stones as well and not only along a ramp but all the way from the quarry to the top of the pyramid.
A new, realistic set of trials and experiments using scale models or children have now revealed how easily large stones can be transported with rather primitive technology. The Nile River and flood plane would provide just the right environment for building a simple and efficient transportation system. The key to success for the ancient Egyptians would have been years of practical experience with the available media and technology as well as a number of "tricks of the trade." As it now becomes clear through experimentation, most of these "tricks of the trade" would only have been known by those actually plying the trades. Some of these tricks have been rediscovered through experience - practical trials and errors with scale models and this is why they are only now being published at this late stage of the debate. A realistic imagination, simple mathematical predictions and experimental modelling go a long way to understand the practical use of acoustics, mud canals, levers and counter-weight techniques for moving large stones. Experiments also suggest that rather than insisting on a single method or technique to move, lift and position stones, different techniques and combinations of techniques work best for different sections and stages of the project. Some techniques may only have been discovered by later dynasties.
The results of experiments with a scale model indicate that a team of around 20 men could quite easily generate just the right amplitude and energy of vibration as well as sufficient impact momentum to shift 5 ton stones the last short distance into the tightly packed formation of a pyramid. They could do that using a large 500kg wooden battering ram suspended by straps from poles that are shoulder yoked between pairs of men.
By swinging the ram back and forth like a pendulum slowly building up momentum until the ram impacts on one end of the stone, sufficient acoustic and mechanical energy is produced to shift the stone along the top of other stones without rollers. Some authors mention the way layers of gypsum were spread on completed courses for sliding the stones more easily and cementing them into position.
Mathematical predictions and the 1:1000 scaled down working model [220 gram wooden ram and 2400 gram concrete block] shows that although the stone shifts only in very small increments it can still be moved in a well controlled manner into a very precise position. For 10 ton stones 2 teams are needed each with a 500kg ram, 4 teams for 20 ton stones etc. - some simple technology that the ancient builders could have worked out by trial and error. No mystery or doubt about that - it's uncomplicated applied science.
For lifting stones relatively short distances up onto the lower courses of a pyramid, a variant of the shadoof lifting device with a counter-weight works very efficiently, provided the stones weigh no more than about 3 tons. The best way of setting up the shadoof would be to excavate round holes or sockets in the ground for securing tall tree trunks as the upright poles. In fact rows of sockets have been found in the ground around the perimeter of a few pyramids. Some authors have suggested that these sockets were used for surveying or for securing tent poles. But their size, location and spacing around the perimeter seem perfectly suited to securing the poles for shadoof lifting devices. 20 meter tall poles would be set in the sockets - a pair of poles for each shadoof. A 30 meter cross-beam tied to a fulcrum would be hauled up by ropes running over the top of the poles. Perched at the top of the poles, the beam would provide lift to a height of at least 15 meters above ground.
To facilitate the lifting operation, two counter-weights [each half the weight of the stone to be lifted] would be attached to one end of the beam in a two-stage operation. During the lifting procedure weights are removed or attached at either end in a sequence that ensures that at any time the difference in weights at opposite ends of the beam is always at most only half the weight to be lifted. That provides for good control over the operation with minimum manpower and avoids over-crowding the working area. A four-rope noose arrangement will grip the stone to be lifted around the sides in a self-tightening knot for hoisting up by the other end of the beam. One counter-weight always remains permanently dangling; the other is attached only during the lift. Before each stone is untied after setting it down on the platform above, another counter-weight at the ground level is secured [as a substitute] to an alternative rope attached to the lifting beam. Then a new stone waiting to be lifted can take its place. Using counter-weights in this way the shadoof could be easily operated by a team of no more than 18 men to lift 2.5 ton stones. A horizontal reach of nearly 20 meters from the pole would be achieved if another rope were also attached to the load and pulled from the growing summit of the pyramid. With 50 or more shadoof devices operating simultaneously, the stones could be delivered onto the platform at a rate of at least 200 per hour. The shadoof would not be strong enough to lift the large 11 ton casing stones so other transportation techniques described in later chapters would be required for those. Nevertheless just over 10% of the pyramid volume could be rapidly constructed with the help of the shadoof.
For moving longer distances along horizontal or near horizontal surfaces, large stones would need to be pulled on wooden sledges or rollers by teams of men or oxen as many others have pointed out. On horizontal surfaces, multiple parallel tracks overlaid with wooden planks and rollers would be the most efficient and practical. Spaces in between the wooden tracks would need to be provided for the labourers or teams of oxen to tread. It was also discovered through scale model experimentation that to start the block rolling, a single knock with a correctly sized battering ram was required to provide additional acoustic energy. This suggests that in the real world the use of levers and/or battering rams of different sizes would have played an important facilitating role in moving and hauling large stones around.
A shadoof will lift the smaller stones up to about 15 meters above ground. Other techniques are needed to take them beyond that height. For hauling up slopes, simple mathematical predictions and experiments with scale models [see details in following section] shows that 1 to 2.5 ton stones on rollers can be pulled up narrow gradually sloping wooden or stone and wooden ramps by 5 to 20 men hauling with ropes. Building several sets of gently sloping ramps built on the ledges that form the faces of the pyramid [zigzagging across the faces] supported on the layered steps has been suggested by others. The problem arises with much larger stones. The casing stones of the great pyramid are estimated to be around 11 tons before final shaping. These are more difficult to haul given the limited space on the edges of the pyramid for large teams of men and virtually impossible to haul around corners. However with massive stones the task becomes easier using a counter-weight and counter-ramp principle. This principle multiplies the force of the men walking and pulling the ropes down a steep ramp [stairway] on another side of the pyramid. Depending on the ratio of the slope of the upward ramp in comparison to the downward sloping ramp the anti-gravitational force on the stone will in effect be multiplied by 10 or 20 times the force that the men can generate by their body weight alone.
A stepped wooden structure or clay plastered over stone rubble and edged with wooden batons on other faces of the pyramid would provide the stairways needed for the men pulling the ropes to tread the shortest route down the side of the pyramid. All that we additionally require is a smooth round polished wood or metal pole mounted at the edge of the pyramid for the ropes to turn over. A refinement of this arrangement would be to grease the wooden or metal pole and then wrap it in a scroll of leather or beaten copper. The grease would allow the leather and rope to turn more freely over the pole like a roller and reduce friction of the rope on the pole without making the rope slippery.
A large labour force of men would be able to walk [in single file] back up the stairways to take over the pulling task at the top and replace those who leave the rope when they reach the bottom in repeated cycles. The journey of the stones would admittedly be slow compared with modern cranes but fast enough with sufficient hauling teams to complete the work in 20 years.
A 1:1000 scale model was built to test the effects of friction on a roller ramp system with a 1:20 slope. Strings of 70 gram lead sinkers were used to represent the weights of average men on the scale of the model. First, smooth urethane coated wooden board was used to construct the ramp, smooth round pencils for rollers and a highly polished steel pen was used as the turning point for the cotton thread [rope] to turn over. A 2400 gram concrete block was hauled up the ramp by 210 grams of lead sliding down the opposite 50 degree angle ramp made of glass wet with soapy water to represent the frictionless walking of men. This would be equivalent [in terms of the 1:1000 scale] to the weight of three men [70 Kg each] pulling downwards on a 50 degree angle stairway in order to haul a 2.4 ton stone up a ramp of this design. Or about 12 men for 11 ton blocks.
Next a more realist ramp was constructed with sawn Balsa wood planks, the rollers from dried twigs simply cut into lengths without trimming and the same steel turning point was used. The rougher material required 360 grams of lead and wire to haul the block up the ramp [i.e. five men of 70 Kg each to haul 2.4 tons].
When the rough realistic ramp was adjusted and fixed in the horizontal position 310 grams of lead was required to move the block [almost five men]. This shows that the force required to overcome the effects of friction and inertia is much larger than to overcome the effects of gravity [reduced in the 1:20 ratio] on a gently sloping ramp.
For sliding the block along a plain wooden horizontal track [with no rollers] 1900 grams was required to keep the block moving [i.e. 30 men to haul 2.4 tons]. Almost the same weight was required [1720 grams] when the block was mounted on a smooth thin piece of wood to act as a sledge. When the wooden track and sledge were saturated with vegetable oil or oil and water this reduced to just over 1100 grams [15 men to haul 2.4 tons]; however the movement along the track was irregular and characterised by constant jumps and starts. When sand was blown over the track movement was surprisingly improved by eliminating the jumps and starts and only 780 grams [11 men to haul 2.4 tons] was required to keep the block moving. When the wooden track was wet and covered with a 5mm deep layer of slippery wet clay this reduced to just over 980 grams [14 men to haul 2.4 tons]; however the movement along the track was extremely slow compared to rollers. A little sand mixed with the clay did not have any detrimental effect. A thicker layer of clay [10mm] improved the speed of movement initially as the block starts off but then a lot more clay slides out sideways from under the stone as it moves and the speed of movement slows down accordingly. For that technique to work in real life canals would be required to contain the large volumes of clay and retain the water content of the clay.
The next step in the experiment was testing a much larger scale model to see what the scaling factor would be. In other words to check if certain unexpected physical effects that are not operating with very small scale models could change the way large scale operations work in real life or vice versa. To check for this the experiment was scaled up by a factor of 50. Instead of 70 gram weights and a 2400 gram block, an athletic 31 Kg girl and a 40 Kg concrete slab was used. The girl was easily able to haul the slab across a horizontal wooden board. The slab was mounted on a flat piece of wood and hauled with a thick cotton rope. When the experiment was moved to an area with a 1:10 slope she was only just able to haul the slab up the wooden board, but not when more weight was added. Her rubber soles kept slipping on the concrete. Similarly a 75Kg man was able to haul no more than 100 Kg up the 1:10 wooden slope without slipping.
When the wooden track and sledge were saturated with vegetable oil and water the girl could not haul the load up the 1:10 wooden slope without slipping. But when the wood was sprinkled with sand over the oil she succeeded. She could haul 58 Kg [but no more] up the oil, water and sand covered wood. At least 30 minutes of rest was provided between each trial.
When the slab was supported on 25mm diameter wooden rollers and loaded with additional weights the girl was able to haul a total of 170 Kg up a 1:10 slope with rollers but only when the concrete slope was overlaid with smooth wooden boards. When the wood was removed she could only haul the 170 Kg slab on rollers up a 1:20 concrete slope.
These results show that the girl could haul almost six times her own weight up the 1:10 slope if it was supported on rollers but only a little over her own weight when rollers were not used. She could haul nearly twice her own weight up a 1:10 wooden track covered with oil, water and sand.
The counter-weight technique was tested at this scale using a smooth steel pole mounted on a frame for the rope to turn over. The girl simply dangled on the hanging section of the rope. Her own weight could NOT initially shift the 170 Kg load mounted on rollers. Friction between the rope and steel pole was considerable however a sharp knock with a pole sent the loaded slab moving up the smooth wooden board on the 1:10 slope. It was also quite obvious that once in motion, the loaded slab accelerated [with the girl dangling on the rope] to about twice the speed at which she could haul the load along on foot. The results of the real life, large scale tests were not much different to the very small scale working models.
Finally, experimenting with levers showed that dismounting a heavy block from a sledge in a controlled manner was very tricky and cumbersome. The use of unoccupied rollers placed next to the block to act as a fulcrum for a lever made the task easier and controllable. The ability to roll the fulcrum closer or further away was very convenient. It was even more tricky to lift a heavy block off a flat hard surface onto a sledge with levers and wedges. This experience suggests that the ancient Egyptians would have quickly realised the value and convenience of wooden poles in their natural state for use not only as fulcrums for levers but also as a transportation facility. It seems unthinkable that they would cut very useful round poles into less useful square beams for fulcrums and remain blind to the huge advantage of rollers over other methods of reducing friction.
Another trick discovered by experimentation was the way a stone block can be elevated using a set of rollers of different sizes. By placing the rollers on a flat surface parallel to one another and ranging in size from very thin to very thick the stone block can be pulled over the rollers from smallest to biggest moving it simultaneously forwards and upwards. This trick would be very useful for bringing stones up the last part of the journey to the very top of the pyramid.
Results of these experiments demonstrate quite clearly the superiority of the wooden plank and roller system over other techniques for moving large stone blocks. Wet clay or wood saturated with oil and water are not nearly as effective but better than hauling over dry wood, stone or dry sand. Furthermore, the wooden plank and roller arrangement has an added advantage on sloping ramps, namely, the auto-braking system as described in a later section. The use of clay or mud along a flood plane close to a river is quite feasible but building suitable containment canals for the watery clay on sloping ramps becomes impractical compared with the use of oiled timber or rollers.
Consider the obvious conjecture that the larger the stone to be moved, the longer the ropes needed to accommodate all the labourers. In practice when using long ropes, the stone jumps forward in fits and starts. This was noticed in the course of experimenting. The longer the rope the more the stone tends to jump. This problem makes it very difficult for the labourers to keep their balance and their grip on the ground, as the NOVA project discovered in Egypt a few years ago. Long ropes stretch more than short ropes when pulled. As the labourers begin to pull, the tension in the rope increases and the ropes stretch further. When the tension becomes sufficient to break the static friction between the sledge or stone and the surface it rests on, the stone lurches forward because kinetic [moving] friction is less than static friction by a good margin. The elastic energy in the rope is expended by pulling the stone forwards and the tension is released. That causes the stone to stop moving, but the labourers keep pulling so the rope stretches and the stone jumps again. Jumps of a few centimetres at a time with smaller stones are not particularly difficult to manage. But experiments indicate that with 50 meter long natural fibre ropes for hauling massive loads over 12 tons or more, the ends of the ropes would jump as much as half a meter. Using several shorter ropes would improve the situation but there's a limit to the number of teams that could work in parallel for really massive stones. Trials indicate that a load of 30 tons on sledges and wooden sleepers would need about 240 men to haul up a slope of 1:10. It's very unlikely that more than six ropes could be used to accommodate more than six teams of men hauling in parallel rows shoulder to shoulder. That means at least 40 meters of rope. Rear action battering rams or levers are not of much help. These are best used only to get the stone moving. But not when the stone jumps as much as half a meter at a time and then stops. Thicker ropes would improve the situation but there's a limit to the size of rope which labourers are able to grip in their hands and tie around stones or poles. A very effective solution is available. In the course of experimenting it became clear that the problem is eliminated when friction is drastically reduced through the use of rollers, fewer labourers and shorter ropes. The ancient Egyptians may have used primitive technology but they would have been very intelligent and experienced in their use of it.
In conclusion it appears that the use of wet clay or wet, oiled timber facilitates the transportation of smaller stones on wooden sledges along tracks and ramps for the construction of the more primitive smaller pyramids. For later pyramid designs using much larger stones the wooden plank and roller system would have been essential, especially near the top of the pyramid where working space for large teams of labourers is very limiting making some manoeuvres impossible. Remains of ancient brick and clay ramps have been excavated in Egypt with wooden beams partly submerged in the track at regular intervals like railway sleepers. Some authors assume these to be the tracks along which oiled sledges were drawn. The beams [sleepers] could just as well have been anchors for fixing planks or split poles in place for a roller ramp design as explained in a later chapter.
Experimental results indicate that there is no advantage of the counter-weight technique [in terms of the minimum number of labourers required for hauling a given load up a slope] compared to the simple hauling technique. However, there are four other advantages. Firstly, once set in motion the block moves faster up the ramp using the counter-weight technique. Secondly, the double ramp design means the labourers would not slip on the wooden planks since they have their own stairway to tread. On narrow ramps there is insufficient space for providing both wooden tracks and lanes of bare stone surface for good tread. For stones to move easily [with or without rollers] the wood needs to be constantly wetted and oiled and as such the labourers would not be able to get a good foot grip on slippery wood. The third advantage of the counter-weight system is that it allows strain on the muscles to be alternated from arms to legs so that the lifting operation can be sustained for longer before fatigue sets in. The simple uphill hauling operation continuously places great strain on both arms and legs whereas the counter-weight system strains mainly the arms while pulling on the way down and only the legs while walking back up. Fourthly, the counter-weight system allows blocks to be hauled very close up to the edge of the pyramid or ledge. This is important when one considers that the working space is very limited on the top of ledges, ramps and the summit particularly as the pyramid nears completion. Pulling down a stairway can bring the stone closer to the edge than when pulling around a corner. More significantly, there's a fundamental flaw in the square spiral ramp design described by other authors where the stone is pulled around a corner.
In the final stages of construction as the summit becomes much smaller, the distance along one side of the summit would not be long enough to accommodate the stone hauling manoeuvre without pulling around the corner. The minimum distance required along the edge of the summit for this manoeuvre is equal to the length of the stone plus the length of the hauling team plus that same distance [the stone and the hauling team] repeated in front of the team. The extra space [in front of the team] is needed to allow movement for the labourers to advance as they haul the stone from a lower level up to the summit; i.e. a total distance of nearly forty meters for hauling up casing stones. A detailed experimental test of this situation will make the point quite clear - when the summit becomes smaller than forty meters a corner is needed for the rope to turn around. The flaw is that the corner can only be built on each new course with blocks that have been hauled up to the precise elevation of that new and not yet built course. But how does one haul blocks up and around a corner that does not yet exist and cannot exist until that course is at least partially built? It's the chicken and egg situation.
Some published illustrations of spiral ramps show the last stretch of the spiral ramp transitioned to the horizontal position a good distance before the corner and then continued level with the summit to provide space to accommodate the advancing team of labourers. That eliminates the need to pull around the corner to bring the stone level with the summit. These illustrate only the early or middle stages of pyramid construction when the summit is still fairly large. However as already mentioned, a corner is needed when the summit becomes small.
A solution would be to erect a temporary but robust corner built with a stack of small blocks that can be pushed and hauled up by only four or six men, but that means making, breaking and remaking each corner on all the upper courses of the pyramid. Alternatively a temporary wooden corner could be built, however, the wooden frame would need to be secured in place with a stack of temporary stones to restrain it from toppling over due to the massive force exerted on the corner frame by the men hauling on the ropes. Such counter-productive methods of constantly making and breaking corners are unnecessary and do not credit the Egyptian engineers with sufficient practical intelligence.
The counter-weight technique would be a far more neat and secure arrangement. All it requires is a temporary wooden frame on the top part of the wooden stairway where it is secured in place by the weight of the men hauling down on the ropes rather than around the corner. The distance along the top edge of the summit for accommodating the manoeuvre would only need to be about six times the length of the block.
The conclusion reached by experimenting is that while large blocks can be simply hauled along wide gradually sloping ramps on rollers it becomes impractical to do that near the top of the pyramid. As the slope becomes steeper slipping becomes more problematic and the advantage of the counter-weight technique over the simple hauling technique becomes greater. Quite clearly, to complete the highest layers without massive external ramps, the counter-weight technique employed on narrow zigzag ramps would be the only safe and practical method and the only practical way of lifting the capstone into place. [Illustration of zigzag ramps follows]
Illustration to show how teams would work in the final stages of
pyramid construction. Some counter ramps are constructed on the
same face of the pyramid as the ramps for the stones
To transport both small and large stones up to the lowest courses, a relatively small primary ramp stretching beyond the base of the pyramid would be quite practical and efficient for accommodating several teams of labourers hauling stones in parallel tracks. This style of ramp would also be the only practical way of transporting those more unique and very largest of blocks for the construction of inner chambers. Once the lower layers and chambers are complete the stones used to construct the primary ramp could be recycled for use elsewhere i.e. transported up the secondary set of narrow zigzag ramps to level out the spiral course way or construct the rest of the pyramid higher up.
The small zigzag ramps could be conveniently and securely built on the ledges. The layered design of the pyramid is perfectly suited to supporting such small transportation ramps at all levels. The very lowest part of each ramp could be constructed from wood and the rest using a range of small size blocks, the largest being just shorter than the height of the ledges on which they rest. Relatively small quantities of stone would be required to build those secondary ramps, overlaid with wooden planks or split poles. The stones forming the ramps would have one roller left under the stone at one end, secured with split poles either side the roller to restrain movement. This way the stone can be easily set up on more rollers again, ready to move along the ledge when its function as a ramp has been completed. Such zigzag ramps can also operate simultaneously at the lowest levels of other faces of the pyramid without hindering movement up the primary ramp. For the sake of economy the stone material for the ramps [about 3% of the total volume of the pyramid] could be used for filling in the interior bulk of the pyramid when the ramps become redundant. So the ramps eventually end up hidden inside the pyramid. In the early stages of construction 12 or possibly 14 sets of zigzag ramps could be operating simultaneously on the four faces of the pyramid.
As the pyramid rises and the summit becomes smaller fewer ramps are required to reach the summit. Eventually only one set of zigzag ramps can be accommodated on each face. As some ramps become redundant, the wooden planks or poles and rollers can then be recycled for use at higher levels to extend ramps that need to be continued upwards. This economy in the use of ramp material works very neatly on a pyramid shape where the summit becomes progressively smaller as the pyramid becomes higher.
Some materials that become redundant are simply shifted across the ledges [the stones on rollers] onto the rollers of an adjacent operating ramp where they can be hauled upwards. Other materials that would be obstructed from entering a ramp by the down-coming counter-ramp if shifted horizontally have to be first lifted up to the next suitably orientated ramp higher up. Anyone who thinks logically and considers the details of dismantling the secondary ramps may ask how the stone from the redundant ramps that are obstructed would be transported upwards when those secondary ramps are being dismantled.
There are two possible solutions. One employs a set of rollers of different sizes to elevate the stones upwards as they roll forwards and backwards over smaller and then bigger rollers. That trick is described in a later chapter concerning restrictive work on a small summit.
The second solution uses only one ramp [for each face of the pyramid] made completely from wood in easily transportable sections, and deployed in the first instance at the bottom level. In addition one set of temporary wooden scaffolds is required [for each face of the pyramid] that can be mounted on the stepped face. The lowest obstructed ramp in a particular zigzag series of ramps would be dismantled first and hauled up the transportable wooden ramp and then onto the rest of the series of stone ramps above. Dismantling means using levers to re-insert extra rollers under the first group of these smaller stones, shifting them a few meters across the ledge on the temporary wooden scaffolds to provide space at the bottom of the remaining part of that ramp, inserting the first of the wooden sections into that space, then hauling the first group of stones upwards. Then temporarily shift the lowest wooden section for access, shift another group of stones backwards out of the way, set two sections of wooden ramps in their place and then haul those stones up and out the way and so forth using three then four wooden sections in place of stones until the obstructed stone ramp has been completely removed. The transportable wooden ramp and scaffolds that remain are then ready to be moved up for use on the next highest obstructed ramp. That next stone ramp is then dismantled in turn as described above and the wooden ramp and scaffolds are moved up again. In this step by step progression the whole system of ramps are removed leaving only the set of transportable wooden ramp sections and scaffolds. This same step by step progression would be employed for dismantling the last four zigzag series of ramps near the end of the project. It's quite possible that one very last zigzag ramp would be left operating on one face to complete the last upper courses near the top. The finding that the core stones of many pyramids become smaller near the top [but not the casing stones] is consistent with this technology. The ramps would be made from smaller stones and those stones from the ramps would be the last ones to be placed in the core. Both methods of dismantling zigzag ramps are slow but the procedures would not in any way disrupt other teams from continuing their operations on parallel ramps.
The task of building and dismantling the large brick ramps shown in many authoritative books and articles is not only very labour intensive but very obstructive. The ramp building, extending and dismantling program halts the rest of the pyramid building program. This is not well appreciated by theoreticians until attempted in practice. Ramps need to be dismantled during and NOT after the pyramid building project. That's because the ramps stand on and obstruct access to the casing stones that need to be chiselled to complete the pyramid. To build a 5-meter wide ramp sloping at 1:8 from mud brick and clay to raise five 2.4 ton blocks from the ground in parallel tracks onto a platform 1 meter above ground would require approximately 20 cubic meters of building material. To extend the size so that it can reach 2 meters above ground would require a total of about 60 cubic meters of building material. For another meter of height we need nearly 200 cubic meters of material, to reach 6 meters - over 4000 cubic meters of material and so forth for higher courses. So a building project requiring large brick ramps takes three times as long as one that doesn't use such ramps. Egyptian engineers would have known that through experience. Smaller external ramps for lower courses - yes, but for higher courses - internal ramps, to be explained later.
A Five-meter wide ramp that spirals around the external boundaries of a pyramid would require somewhat smaller volumes of building material but a bottle neck is created at the corners where the teams have to wait turns to haul around the same corner. More significantly, there's a flaw in the square spiral ramp design [as described in an earlier section]. Furthermore, covering the corners with ramps would obstruct the alignment surveys needed to check and ensure the corners of the pyramid will meet at the top to form an apex. In contrast, building and dismantling small zigzag ramps built mainly with the stone material for the pyramid itself is not only economical but it can also be done without disrupting other parts of the building program.
The most practical way of constructing the inner chambers would be as follows. Once the pyramid reaches the height required to start constructing the chamber, subsequent courses are only partially completed in certain pre-selected and staggered zones surrounding the chamber. They are partially completed in a stepped pattern creating a terraced surface in the fashion of a spiral staircase that leads up and around the chamber with four flat quadrants on each corner of the pyramid where the blocks can be turned as they progress up the staircase [see illustration].
Ramps can then be constructed on the spiral staircase using smaller blocks in graded sizes overlaid with planks or split poles to slope across each step. The ramp and counter ramp style could be an option. This structure [primary ramp followed by spiral ramp] serves as the perfect system for transporting the largest stones for the walls and roof of the chamber. The terraces and ramps appear in stages as construction of the chamber progresses. Once the inner chambers are completed the primary ramp can be dismantled and the stones comprising that ramp transported up the secondary ramps for building the remaining higher courses of the pyramid. While some authors have suggested the concept of a horizontally stepped pyramid as a preliminary stage of construction with ramps constructed on the steps in a spiral series, I believe the proposal that the interior parts of the pyramid courses themselves form the spiral ramp represents a new insight.
Other authors have not explained how to progress beyond the horizontal stepped stage for completing the pyramid. The problem is that as the steps are filled in to complete the pyramid, the very steps that supported the ramps for transporting the stone blocks no longer exist. The ramps have to give way to finish the pyramid itself; in fact their places are filled in with new stones and so the very means for transporting the stones disappears and no further progress can be made. If an attempt is made to incorporate the ramps and steps into the final structure by overlaying them with more stones to form new layers [layer upon layer] then the lowest ramp would have to be extended layer by layer as well to maintain a suitable gradual slope and still reach the new elevation of the latest course. That progression eventually ends up with the situation where the first ramp at the bottom [the only external ramp] would need to extend externally from the ground level to the very top of the pyramid. Quite clearly if one thinks the plan through carefully to the final conclusion, the partially completed stepped pyramid concept cannot be employed to complete the entire building project as some authors have suggested. It can only ever be employed for partial completion and other massive external ramps would be required for full completion. If massive external ramps are required, then there's no advantage of the partially completed stepped pyramid design in the first place. In contrast, small zigzag ramps and counter-weight systems provide a very practical and efficient way to complete the pyramid building project.
The counter-weight techniques as described above would be quite within the intellectual capabilities and physical strength capabilities of those ancient people, refined over many years of trials and errors. A team of 20 men would be required to haul 11 ton stones up a 1:20 ramp. To start the stone moving they would need the assistance of an impact with a suitable ram swung by 20 men from the team working at the bottom of the ramp. A well organised relay system would see the entire transportation system moving blocks forward ramp by ramp in a co-ordinated manner. It would be quite feasible for a total of about 200 teams to work simultaneously on 200 ramps on all the different layers of the great pyramid. With the counter-weight system the blocks would move along the ramps at walking pace. Thus 100 blocks arriving per hour on the lower levels is achievable and eventually only about 10 blocks arriving per hour on the smaller summit near the end of the project.
For speed of transportation the entire ramp system would be laid out with rollers in advance of the stones. While experimenting with a scale model a fascinating feature of a ramp overlaid with wooden planks [or split poles as a more primitive version] was discovered when the planks overlap half the length of the next plank like an upside down version of tiles on a roof. In the case of split poles, the same useful overlap feature can be achieved by laying the split poles parallel to one another with gaps between adjacent poles. All the thinner ends should point downhill. The next set of parallel split poles are laid with the thin ends set in the gaps near the thick ends of the previous set. Notches cut near the ends of the poles or planks would be needed to secure them between the stone supports.
A ramp system like this has 5 valuable properties. [1] Until the stone sets them in motion, the rollers lie securely waiting in the square discontinuity of the overlap at the upper edge of each row of planks or poles. There's no need for labourers to insert them as the stone moves forward. [2] The square discontinuity automatically resets the rollers in correct parallel formation after each movement to ensure trouble-free transportation of the stones. In the case of split poles on a horizontal surface, the slight gradient required to reset the position of the rollers can be achieved by cutting a notch near the lower end of each pole. [3] Each time a stone moves over the rollers they move up the plank and lodge in the next discontinuity or notch. This means that the rollers are automatically transported upwards to the top of the pyramid where they can be laid out on the next newly built ramp, ready for the next stones. [4] Overlapping planks create just the right smoothly curved transition in the direction of travel from horizontal to upward sloping. A ramp system without that smooth transition would make the slight change in orientation impractical since the leading edge of the stones are prone to catching on the ramp or bumping waiting rollers out of the way instead of rolling over them. [5] Probably most valuable of all, the overlapping planks [or poles] and rollers form a ratchet type system so that the stones are unable to roll backwards down the ramp. The degree of control that this auto-braking system provides is invaluable, preventing serious destruction and fatalities if a rope breaks or if the hauling team trips and loses control of the hoisting operation. Wooden ramps of this type would possibly qualify as the short wooden scaffolds described by historian Herodotus. Remains of ancient brick and clay ramps have been excavated in Egypt with wooden beams partly submerged in the track at regular intervals like railway sleepers. Some authors assume these to be the fixed tracks along which oiled sledges were drawn. The beams [sleepers] could just as well have been anchors for fixing planks or split poles in place for a roller ramp design as explained above.
As commonly claimed, the non-rectangular casing stones would be chipped and chiselled into final shape from the top down. Redundant ramps are dismantled one by one as the faces near completion making them accessible for the chiselling work. That finishing work could start on the four corners while the last upper courses are still being built. The chips could be collected on the ledges below and hauled up in baskets for use as fill material for the hidden interior higher up. More advantages of counter-weight techniques can be discerned. [1] Wooden sledges can be transported up the ramps like the stones, carrying rollers, wood and small stones for the higher ramps. [2] The sledges can then be tied to the ropes on the downward side to transport them back down while simultaneously helping to pull more stones uphill. [3] These sledges can also transport redundant rollers and dismantled wooden parts of the ramp back down again when the pyramid nears completion simultaneously helping to pull more stones uphill. In this manner, counter-weight technology provides a high degree of control over the movement of heavy items.
Another feature discovered while experimenting with scale models was the convenient way a stone on rollers can be directed to turn to the right or the left using a rear action battering ram either when the stone is stationery or being slowly hauled along. [1] This manoeuvre would be helpful for rotating and positioning 11 ton stones on the top of the structure after the ropes are removed for fit up and there's nothing to pull on. With limited space available for labourers to work from, the ram would become an essential tool particularly as the pyramid nears completion and working space becomes extremely limited. [2] A massive stone that accidentally tips off its rollers in the wrong place can still be moved using the ram. [3] The ram would also be useful to manoeuvre the stones off the rollers more quickly than with levers when the stones approach their final resting place. In fact experimentation shows just how difficult it is to remove the last roller underneath a very large stone. Scale models suggest that the use of both levers and a ram is the only practical way of doing that - the level to lift and the ram to bump off the lever onto the ground. A smaller set of rollers on the summit would act as intermediaries to facilitate the let down operation in stages. [4] Likewise a rather tricky operation is required to manoeuvre the stones across from the rollers at the top landing of one ramp [where the stones have to change direction] onto the parallel set of rollers at the bottom of the next ramp in the series. During that stage of the operation the only suitable space available for extra labourers to work from is the front or rear of the stone. The task can be accomplished with the second trailing rope attached to the rear of the stone. Using these ropes the stone can be pulled back and forth several times in zigzag motions. However that would be rather slow near the final stages of construction where the landings would be relatively short. At those locations a quicker method would be to tilt the stone with levers inserted simultaneously at the front and back of the stone and insert a small wooden roller under one side of the stone at the outer edge of the ramp. Then lift from the other inward facing side and insert more small wooden rollers underneath. The small rollers rest on and cross the track mounted rollers perpendicularly. In this way the stone can be rolled away from the outer edge of the ramp [on its auxiliary rollers] and onto the other parallel set of track-mounted rollers, first by pulling on the ropes and then when there's no more space for pulling by pushing. In the case of the massive casing stones the sideward move would be achieved by impacting the stone with the side of a battering ram held parallel to the stone. A gentle swing and impact would be enough to roll the stone sideways. The lower set of rollers are conveniently located and secured in the wooden track to act as fulcrums for the levers used to dismount the stones off the smaller set of rollers. With practice this manoeuvre at the transition could be executed quite deftly and quickly even in relatively cramped ledges.
The smaller the summit of the pyramid becomes as it nears completion the more tricky the task of hauling up stones. At a certain point the slope of the ramps becomes too steep and the working space too confined for a human workforce so the task becomes unmanageable even for battering rams and levers. Alternative methods are required. A larger than normal capstone could be pulled up one of the steep smooth finished faces on a wooden sledge. In other words the smooth pyramid face acts as a ramp with multiple ropes running up and over the summit and down on the other side. For such steep slopes friction is considerably less than for a similar sized stone moving up a gradual slope so the use of rollers is not helpful. To test this method at the 1:1000 scale, the 2400gram block was mounted on a 120 gram sledge. Two smooth concrete slabs were inclined at angles of 50 degrees and propped against each other like an "A"-frame to represent the smooth faces of a pyramid. Two smooth steel poles were set side by side on the apex. The combined 2520 gram load was hauled up sliding over the concrete surface by a 6900 gram block rolling down the opposite side on wooden rollers to represent the frictionless force of hauling men. Although the rope is relatively long, the stone does not jump. That's because the force of friction between the sledge and the pyramid face is much smaller than the force of gravity that needs to be overcome as the stone moves.
A comparable scenario was created by resting the 40 Kg slab on a wooden board inclined and secured at an angle of 50 degrees. The 75 Kg man was NOT able to slide the 40Kg slab up the 50 degree slope by hauling the rope along a horizontal concrete surface, until help was provided to set the slab in motion. Once in motion the man could keep the slab moving unassisted. Frictional resistance of the rope in contact with two steel poles is double the resistance generated when hauling the rope over one steel pole. Also a man can generate more force than his own body weight if required for short bursts of activity but the continuous strain on hands, arm and leg muscles is considerable and difficult to sustain.
These experiments indicate that the combined body weight of several hundred men would be required to exceed the weight of the heavy capstone. This indicates that apart from the availability of a long and massive ramp from the ground with a large extension on the opposite side of the pyramid, the counter-weight hauling technique is the only practical way of raising the capstone to the apex. Realistically each labourer would probably only be capable of continuously hauling one quarter of his own weight up the side of a pyramid for several minutes until the load reaches the top. That translates to about 60 men for every ton to be lifted. At any time when the labourers need a rest a counterweight could be attached to the ends of the ropes to replace the weight of the labourers.
Experimenting with scale models indicated another valuable advantage of the counter-weight hauling technique. When the stone reaches the edge of the summit there would be a check on alignment and possible adjustment using battering rams before the final haul to tilt the stone over the edge and onto the summit. The effect of friction means that the men holding the ropes [some on the counter-ramps and some at the bottom of the pyramid] would be able to rest their limbs while the check and adjustment is taking place. This is because the force exerted by the labourers on the rope to prevent the stone from moving back down the slope only needs to be about two thirds the weight of the stone itself. In other words, to lift the stone each man needs to be able to exert a force equal to the weight of about 17 Kg, but to prevent the stone slipping backwards he only needs to exert a force equal to the weight of about 4 Kg.
The stones for several of the final upper layers [perhaps the top 5 courses of the pyramid] could have been hoisted up on sledges in this counter-weight manner in preparation for the capstone.
There are many reasons for not employing this technique when building the lower layers of the pyramid. [1] It is not as safe and controllable when ropes break or when the labourers lose their grip or their footing. [2] It fully occupies the space on the summit and that means the stones could not be hauled up while other teams were simultaneously moving or placing stones in position on the summit. [3] It also means that all the frames mounted on the edge of the summit with rollers for ropes to turn over would need to be set up at each level, then removed after placing the stones for one course so that the most recently placed casing stones can be chiselled smooth, then all the frames need to be reset on the next level. [4] The casing stones would need to be chiselled and polished from the bottom up, so that would require temporary hanging wooden scaffolds to be built for the masons to work from. The reason is that the ledges for standing on while chiselling the most recently placed stones would have been chiselled away at the previous stage. [5] Every stone brings with it a sledge that needs to be transported back safely down. Quite clearly the program of constantly building and removing frames and hanging scaffolds would become far too disruptive and time-consuming. That technique of hauling up on sledges creates so much unnecessary additional work and disruption; it would only be employed as a last resort on the very top layers where no other techniques can work.
There is one other trick that could be used to elevate a massive stone block near the very top when space for zigzag ramps is too small - the trick described in an earlier chapter using a set of rollers of different sizes. By placing the rollers parallel to one another on the ledge, the stone block can be pulled up over the rollers from smallest to biggest until it is level with the next highest course. If space on the ledge is very limited then back and forth movement see-sawing from smallest to biggest rollers works just as well. Once level with the next highest ledge, a thin roller is place on the higher ledge, the stone is then swivelled around slightly, balancing on the largest roller until a corner of the stone rests on the thin roller waiting to receive it. The stone is then pulled over in stages onto the new set of thin rollers on the higher ledge. That procedure can then be repeated from one level to the next. This elevating technique was tested in practice at the 1:1000 scale using a spring balance hooked to cotton threads that were tied around the stone block as the only means of moving the stone. The model suggested that this elevating technique would require approximately the same manpower to operate as the zigzag ramp and counter-ramp technique but it is not as fast, safe and controlled.
While experimenting with clay and mud as the lubricating medium for transporting large stones it became clear that the best way of transporting large stones with this type of "plastic" medium would be to build canals to contain several feet of watery clay or mud. To test the idea in the 1:1000 scale model, a long narrow plastic tray filled with clay, pebbles and sand was used. The bottom of the tray was first filled with a 3cm layer of pebbles, then a 3cm layer of sand and finally a 5cm layer of mud from a river to represents a realistic riverbed. The most surprising [but in retrospect quite obvious] finding was that when the tray [canal] was filled with water until the 2.4 Kg block was completely submerged, the force required to keep the block sliding [under water] along the mud was as little as 210 Grams. This is less than half the force required to keep the stone moving along a layer of mud without submerging it in water.
Extrapolating the results from the model up to the real world implies that teams of only 14 men walking and hauling ropes along the banks of a canal would be able to haul 11 ton blocks sliding along the muddy bottom of a canal. It was also discovered that the 2.4 Kg block could be very easily hauled up from the mud onto a set of rollers on a stone ramp leading out of the water. Trial and error showed that the easiest technique was to submerge several thin rollers and place them in the mud [where they become stuck] at the bottom of the ramp. As the block [still under water] slides over the rollers they began to roll forwards onto the ramp, thereby lifting the block up and out of the mud. At that stage the force on the rope had to be doubled to break the suction of the mud underneath the block. This shows that another 14 men would be required just for the mud to ramp manoeuvre. Thereafter only 14 men are needed again to continue the rest of the journey along the typical roller and plank course way. This simply and highly efficient submerged transportation technique may have been discovered by the Egyptians after an event when a quarry became filled with flood waters or if heavy blocks needed to be recovered from a canal after flooding. The site of the great pyramid appears to have been designed to contain water at the pyramid's base. It may be that this was [besides surveying purposes] to facilitate transportation of large foundation stones in watery mud around the perimeter.
The next step was to test and prove a practical method for transporting large stone blocks down a river. The use of barges or bales of papyrus has been suggested by many others - one tied to each side of the stone for floatation. However the practicalities of lifting such large stones off the barges and up onto jetties or the dry banks has not been explained. In fact the absence of a credible explanation indicates that it was not done that way. Trials with a small scale model suggest that rather than floating large stones down the river, they could be dragged along the bottom of the river and then pulled up ramps on rollers. To test this idea 20 dried twigs [having a total volume approximately twice the volume of a 2.4 Kg stone] were lashed together like a raft. The raft was hitched close up to the block by a string tied around the block. The raft in turn was hitched behind a small wooden boat that was also approximately twice the size of the stone. Three paddles were fixed either side of the boat. This system floated slowly down a shallow river pushed by the stream, dragging the stone behind like an anchor. Sliding over a bed of smooth small pebbles was no problem either. The use of rivers for transporting logs and rafts is probably very ancient and it would not have required a large stretch of the imagination to develop this technique one step further. In fact this combination transport system takes care of both wood and stone transportation in one mutually synergistic process. Wood fires were needed for cooking and to make gypsum that was used as cement between the stones.
Consider for example the tricky task of trying to divert flotsam of massive logs and prevent them from floating past the point of retrieval on a straight section of the river. Consider as well the tricky task of trying to prevent massive 11 ton stones lashed to equally massive barges from floating in the current past the point of retrieval or floundering at bends in the river. Trials with the scale models showed that a wooden raft or a much larger wooden boat carrying the 2.4Kg block afloat had a tendency to head for the banks at bends in the river where they struck aground in the shallows. In real life the inertia of the massive block and barge [about 20 tons] would also be too large to negotiate the bends and islands with human power and paddles. Note that rudders have little effect on a boat floating down a river. It also indicates that once stuck in the shallows the possibility of rowing a massive 20 ton load back into the stream would be extremely difficult. In contrast the stone dragging along the bottom [and the accompanying logs] naturally follow the main course of the stream all the way. This combination transport system provides a very effective way of controlling and directing the movement of these commodities. The train can be stopped at any time by lifting the paddles out of the water. Then the boatmen could disengage, paddle diagonally to the shore, letting out more rope as they go. Once ashore they drag the logs and stone to the bank at an oblique angle so that the stream still helps to push the load along.
Real life experiments and trials have now revealed how easily large stones can be transported with rather primitive technology. The Nile River and flood plane would provide just the right environment for building watery clay or mud ditches to serve as canals with stone ramps at the terminations as a transportation system. All this requires is a certain amount of experience with the available media and technology as well as a number of "tricks of the trade." The transportation of even larger stones such as an obelisk in the above manner would be quite effective. The streamlined shape of an obelisk is perfectly suited to this system of transportation.
A major challenge is presented in lifting large stones up out of a quarry and onto wooden rollers. The use of mud-filled canals for facilitating the lift onto rollers was described in an earlier chapter. Other tools are needed where large quantities of water are unavailable. Ramps could do the trick, but the limitation of working space in a quarry would be prohibitive and the perimeter of the quarry constantly changes as stones are cut and removed. As mentioned in a previous chapter, a variant of the shadoof lifting device with a counter-weight mounted on a strong wooden tower structure would lift 12 ton stones and set them on rollers in one smooth operation. About 100 men [with a combined weight that exceeds 6 tons] would be required for that task. But with the perimeter of the quarry constantly changing, the tower structure would need to be mobile. A more efficient technological solution for lifting with the help of a mobile levering tower is proposed below. The solution is quite feasible, not necessarily the only solution but still a feasible and practical one for that primitive age. Leverage devices were within the means and capabilities of the ancient Egyptians and would work more effectively in the situation of a constantly extending open cast quarry.
Build a lattice tower structure from wooden poles in a triangular pyramid shape with a height to width ratio of about 6 to 1. The base needs to be more than double the length of the stones to be lifted. Fasten several long ropes to the top and bottom of the wooden tower. A smaller lighter tower of similar design will be needed to hoist the apex of the larger structure high enough above the ground for teams of men to then pull the structure into the upright position. Then pivot-walk the tower on its base corners into the right position by co-ordinated tugging of guy wires as explained further below. Position the structure at the edge of the quarry overlooking another stone ready waiting immediately below.
The stone to be lifted is separated from the base rock first by drilling, chiselling, sawing and then by finally cracking loose with multiple pendulum rams of the type described in an earlier chapter. The impacting forces of the rams applied at the top edge of the block translate through the stone down to the solidly attached base where they magnify several times due to the bending moment and concentrate along a correctly aligned and prepared sharp groove at the base. Before battering, metal wedges are driven into the groove to add to the distress of the rock. Simultaneously the destructive acoustic energy produced by repeatedly ramming the stone [to break it loose] will slowly induce micro-cracking along the groove. Eventually accumulated micro cracks transform into a fault plane that propagates deeper [fatigue failure] and finally cracks and separates the stone from the base rock. This was also tested on a small scale. Fracture leaves 2 relatively flat surfaces that do not require much further chiselling to finish. Naturally occurring weak strata in the rock facilitate the operation.
Some authors have described the use of long wooden wedges driven into the hand made crevices around the stone and swollen with water to produce the massive force required to crack the stone loose. Instead of metal wedges, that technique could be applied together with battering rams adding to the destructive force. However that dual operation initiates the crack from behind and relies on luck to get the crack to initiate at the perfect location. To help that situation a groove would have to be prepared all round the relatively inaccessible bottom of the hand made crevices by a rather difficult drilling operation. A crack that propagates from a round, drilled groove will not be as straight as one from a correctly prepared sharp groove at the front and side. So a lot more work [drilling] is required in that case and a lot more chiselling afterwards to square up the shape of the stone.
In a scale model experiment, using a 220 gram wooden ram without the additional driving force of wedges, 1560 impacts were required to crack a sawn and grooved 5cmX5cmX5cm soft sandstone block from its bedrock. The scaling factor would not significantly alter the number of impacts to crack the block; but the activity would translate to about 30 impacts per minute in real life. That is still only 52 minutes of ramming or 18 minutes if 3 teams ram the block simultaneously to dislodge the block and produce 2 flat surfaces. A task like that to produce two flat surfaces would otherwise probably require several hours of drilling, sawing and chiselling.
On another prepared piece of stone, the simultaneous use of a metal wedge was tested. Ramming alternatively on the wedge and stone required 1293 impacts to crack. That is not a really significant difference from the previous trial, since the number of impacts required if the cracking process is repeated for different similar sized blocks would typically range as much as double those figures mentioned above. Harder stone would take longer to crack. How hard or soft the limestone was 4500 years ago is difficult to guess, since limestone hardens with age.
After quarrying the block, a four-rope noose arrangement will grip the stone around the sides in a self-tightening knot for hoisting up. Less experienced earlier generations may have tilted stones with wedges and levers around the edges to help insert ropes underneath [about 10 men are needed for 10 ton stones if they only lift one end at a time].
The wooden levering tower should be positioned so that one side of the base is parallel to the edge of the quarry and one corner of the base of the tower is overhanging above the top centre of the waiting stone where the ropes join together. Tie the ropes to a point on the overhanging corner of the wooden structure. Arrange teams of men holding the ropes to keep the tower approximately upright. When one team of 80 men pulls the top of the tower in the direction away from the waiting stone it will leverage the stone upwards and lift it to the height needed to swing it onto the higher ground. As the top of the tower leans over it could become unstable and topple right over if pulled too far. To provide better control, a counter-weight [half size stone] is attached to one of the ropes dangling from the top of the tower when it is just at the right inclining angle. This half size stone helps counter-balance the weight of the large stone in a neat balancing act, freeing most of the other men to take on other tasks. It also provides an indicator of the range and optimum angle for maintaining the tower safely in balance. Once the 2 stones are at the right height, the counter-balance effect means it becomes an almost effortless task for about 10 men to hold the weight of the stone against gravity and manipulate its movements. From there the stone's movements in several directions can be well controlled with the ropes. In particular, the tower with stones dangling can be made to walk either backwards or forwards by the co-ordinated tugging to the left or the right by the teams holding the top guy ropes thereby pivoting the base of the structure alternatively on either one or the other back corners. This creates the momentary single pivot point that allows the tower the freedom to rotate. Or the tower can be swivelled around stepwise to the left or the right in response to the controlled tugging of the lower ropes as the top ropes pivot the tower - again an almost effortless and controlled balancing act, requiring about 80 men for the whole operation. So the stone can be positioned and lowered down over the rollers waiting next to the base. A scale model that requires four people manipulating the strings to help co-ordinate the pivoting manoeuvres demonstrates these operations quite easily.
No lifting mystery at all, provided you have well-disciplined teams of men, experienced supervisors who conduct the operation and sufficient time for the trials and errors required to understand and refine the technology.
The tower can be moved to a new position for the next lift using the same pivoting manoeuvres produced by the men pulling on the guy wires. The ancient Egyptians may have used primitive technology but they would have been very intelligent in their use of it. Their structural designs and accomplishments bear testimony to their intelligence.
Note that by halving all the dimensions of the stones we increase the number of stones to build a given pyramid 8 fold. Then it becomes clear that the number of years required to build a pyramid with stones having half the dimensions would increase 8 fold due to the working space limitations of the building techniques [unless we employed miniature sized labourers and 8 times as many]. It is feasible that smaller stones could be packed on sledges or linked one behind the other in trains to speed the process. But the number of operations required to lift the stones out of the quarry onto rollers and sledges or ram them into position on the summit would also increase 8 fold. Likewise limitations due to the space needed for teams to quarry thousands of stones is prohibitive. There's no advantage in bulk loading the stones up the ramps when they can't be quarried, lifted out of the quarry or rammed into perfect formation just as fast.
Furthermore, the total extent of stone surface area required to be chiselled and finished and the number of drilling holes would double when the stone dimensions are halved. The logistics of all the working operations are intrinsically linked so if 20 years are needed to build a pyramid with man sized stones, then 160 years would be needed to build the same size pyramid with stones having half those dimensions.
The technology described in previous chapters would also neatly explain why the stones on large pyramids are typically the large sizes they are. The ledges are just sufficient size for two labourers to pass or walk shoulder to shoulder across the top of the stepped layers of the pyramid or down the sides without hindering other teams working on adjacent rows of stones and ramps. Consider the labourers pulling ropes down the side of the pyramid using the counter-balance principle. The situation with zigzag ramps on the 4 faces of the pyramid might provide something of a bottle-neck. There is a limit to the number of teams that could work in parallel pulling stones along different levels without getting in each other's way. The next stone can only move onto a ramp once the stone it is following reaches the top of the ramp and moves aside. Large steps provide the space for multiple teams of labourers to work in parallel without hindering one another. If the project built and relied on external ramps for access and traffic the size of the ledges would be of no real consequence.
Using the technology described above, the larger the stones, the quicker the pyramid will be completed. Given the human life expectancy of less than a hundred years it is hardly likely that Pharaohs, architects and master builders would plan a project, knowing that others will have the satisfaction of seeing it to completion. It's not within the normal capability of human nature to plan a project over 160 years if it can be completed equally well in only 20. It is also interesting to consider that the pyramid shape lends itself particularly well to the logistics of maintaining a constant work force as the project progresses. In the earlier stages of building the majority of the workforce is employed in quarrying and lifting out operations as well as levelling the rock foundation. Later, teams are required for building horizontal roller tracks and positioning the stones on the base layers. Still later a few teams are required to start building ramps and hoisting stones up ramps but no more levelling or building tracks. As the structure rises, more are employed on multiple levels in hoisting the stones up ramps and less in positioning them because the upper layers are smaller. Eventually no one is left doing quarrying and lifting operations, the majority of the workforce is employed hauling and hoisting stones with considerably fewer employed in positioning them on the uppermost layers. Those who chiselled at the quarry end up chiselling the protruding edges of the stones on the faces. For the most part, the logistics requires a constant work force maintained by constantly shifting the labour into different locations and types of work.
Accretion layer step-pyramid designs are good examples of stone structures that would make use of partially completed layers to form a spiral staircase around the perimeter as described in an earlier chapter. On close examination of the masonry it becomes clear that these accretion layers lend themselves particularly well to the spiral staircase design where each partially completed accretion layer adds another full revolution of the upward spiral. Djocer's step pyramid and Snefru's step pyramid show certain zones of stone colour and texture on the faces that suggest quite strikingly how partially completed lower layers might previously have formed layered sloping structures that were later completed with slightly different stones at a later time period. Each accretion layer is just wide enough for human traffic and the slight inward tilt on the top of the partially completed layers would also help prevent people or moving stones from falling off the ledge particularly when turning corners. These accretion layer pyramids were built with much smaller stones than the later designs. That is well suited to the formation of a gradually sloping ramp on partially completed masonry by overlaying the small stone steps with planks or split poles. A walkway for pedestrians could be formed alongside the ramp by building up the row of stones at the inner part of the ledge one course higher than the surrounding stones and leaving those stones uncovered. Each time a new course is built, sections of planks or poles would need to be lifted in turn and temporarily stored on the walkway while the subsequent course is being laid. Smaller stones are required so that they can be easily lifted up onto the summit that exists at that time when the innermost accretion layer is built. They are needed to form a strong new corner buttress on the summit for the hauling teams to pull around because the ramp section along one face of the innermost accretion layer is too small to pull along in a straight line. This system only works with much smaller stones therefore the building progress is slower but compensated by the fact that there is no need for the huge task of building a massive external ramp that has to be later dismantled. Successive accretion layers can be built up simultaneously although the start of each successive layer requires its forerunner to have been more than half way completed.
The technical and logistical problems associated with the task of building and dismantling the large external brick ramps shown in books and articles is not always appreciate by modern theoreticians. The ramp building and extending program halts the rest of the pyramid building program every time construction moves up a layer. This is fully appreciated when attempted in practice as the ancient Egyptians would have known through experience. The ramp dismantling program would take just as long as the ramp building program. So a building project requiring large brick ramps takes about three times as long to complete as one that doesn't use such ramps. No remains of large ramps have been found in the archaeological records - only small ramp remains have been found.
There is still the practical difficulty of finishing off each partially completed layer without building a massive external ramp reaching from ground level to the very top of the pyramid for completing the top layer. The steep slope of the sides would not support zigzag ramps nor the brickwork for a suitable spiral ramp design. Fortunately, the steep slope of the sides and the steps formed by this step-pyramid design allows the use of ropes for hauling up small stones to complete the partially completed steps, one step at a time. For short lifts a variant of the shadoof lifting device would work efficiently in tandem with the ramps, allowing about three quarters of each step to be completed that way. The last stones to be placed in each step would require longer lifts - the ropes would be thrown over the steep side and the team pulling on the ropes would walk along the summit [or for lower courses the completed steps] to haul up the stones. The ramps would be converted into horizontal steps in stages from the top step down so the labourers are always able to haul along a horizontal plane at each level. The top step is completed first since the lower ramps are still needed for transporting stones up to complete the innermost accretion layer first, then the next layer, and so forth until at last the outer layer [lowest step] is completed. This is possibly what Herodotus meant when he wrote that pyramids were built from the top down. Although the lowest step can technically be completed first, that would mean many more lifts using ropes and shadoof devices in series. Lifting by hauling with ropes is more dangerous than with ramps. The builders would have learned through experience that it's safer completing steps from the top down with maximum use of the ramps.
The neat transportation arrangement described above seems to be the reason for leaving the step-pyramid shape as the completed form for most accretion layer pyramids - the shape is necessary for this particular construction and transportation technique. If external ramps had been used there would have been no limit to the various shapes and design of pyramids. In reality, shapes and designs follow fairly strict patterns. The step-pyramid shape and transportation technique resembles the counter-weight and counter-ramp arrangement of the later pyramids with larger stones and suggests it was the forerunner of the more advanced transportation systems used to construct later pyramids.
One of the arguments in support of the systems proposed in this article is that these efficient transportation techniques for pyramid construction were already in use and prepared the way for the transportation and erection of 200 ton or 300 ton obelisks at the next stage in history. The Egyptian pyramids took on a change in shape and design as the construction techniques became more efficient through different stages of evolution. But there is generally one basic design for the Egyptian obelisks - one tall, massive stone in the ground. The obelisk stands out as the culmination of the evolutionary stages of ancient Egyptian stone construction. There are no signs of primitive multiple-stone obelisks or prototypes that might have served as trials in a succession of designs during which the transportation and erection techniques were discovered and improved by trial and error. For a project that involves the transportation and erection of a large single stone there is little room for trial and error as there would be in the construction of a pyramid. The loss of a few stone blocks in the river or down the side of the pyramid face during the construction of a pyramid is of much less consequence in comparison with the loss of the obelisk in the river!
As already pointed out in a previous chapter, the shape of an obelisk is perfectly suited to dragging down the muddy bottom of a river and along a muddy canal onto rollers for the rest of the journey. The problem associated with controlling a massive weight [such as an obelisk] floating on barges down a flowing river and steering the load around rocks and islands can only be fully appreciated when attempted in practice or using scale models. The task would require hundreds of paddlers and massive anchors, with all that extra weight [of paddlers and anchors] compounding the problem. Instead it is proposed that the technology already in use for the construction of the Great Pyramid provided the confidence and inspiration for the engineers to plan the project for erecting a large obelisk. One or two large barges and rafts would drag a massive obelisk along the bottom of the river in a well controlled operation.
A ramp that terminates with the high point well short of the obelisk's foundation socket [short by about one third of the length of the obelisk] would facilitate the first step of erection, as other authors have pointed out.
The first step is to haul the obelisk up the ramp until the base tilts down like a seesaw into the socket and the counter-balancing pointed end tilts up high. The tilt and height provides the opportunity for the next step, which is to pull the obelisk with ropes until it rotates into the upright position. Of course thousands of men pulling on dozens of ropes would be required to do the final trick - according to the scale model, approximately 2000 men for erecting a 300 ton obelisk. Although not essential, a leveraging tower would reduce the manpower requirement.
The obelisk needs to be hauled up to and past the top of the ramp [by at least a third of the length] for the first stage of the manoeuvre. The labourers would need to be either hauling on ropes attached to the rear of the obelisk and walk along tracks built along the ramp parallel to the obelisk; OR they would need to be hauling ahead of the obelisk on long ropes that descend down beyond the top of the ramp [the counter-weight and counter-ramp technique]. OR, use counter-ramps and divide the labour force into the fore, middle and aft positions. Accommodating even just 1000 men close enough to the rear end of a 30 meter obelisk so as to enable them to contribute effectively to the hauling operation becomes a logistical impossibility if a sledge and oiled track were to be employed. This requires 500 men to take up positions alongside less than 20 meters of the obelisk with sufficient room to grip and pull on parallel ropes. In contrast 175 labourers either side could reasonably do that and this would be sufficient if rollers and planks were used to facilitate transportation.
As pointed out in a previous chapter, long ropes for hauling a massive stone uphill cause the load to move in jumps and starts. This is nowhere near the degree of control of movement that is required to bring the obelisk slowly up to the poise position on the pinnacle of the ramp. There it will need to balance [perhaps on a mound of sand] as the final preparations are made until the moment of finesse when it tips over and slides down into its foundation socket. The roller and plank system with counter-ramps has all the requirements of engineering precision for the manoeuvre at hand. A similar technique with ropes could have been developed to erect and position the massive stones forming the gabled roof of the king's chamber.
Technical and logistical considerations indicate that the system of rollers and planks together with the counter-weight and counter-ramp technique was the necessary pre-existing system for erecting an obelisk. The other logical alternative is that the first few projects for erecting an obelisk failed and then roller ramps were designed as a modification. However it seems more likely that successful obelisk construction projects were the culmination of successful pyramid building feats.
There would be few if any serious technical objections [among engineers] to the ideas described in this article as a working model of pyramid construction. Dozens of other technically acceptable models have been published to explain part of the construction project but the practical limitations and logistical problems associated with those techniques are not well recognised. The ideas described in this article were worked out, tested and constantly modified with careful attention to all available details of the known archaeological and historical facts relating to pyramid construction. Whether there would be major objections on archaeological and historical grounds remains to be seen.
Much of the background information on Egyptian pyramids and the historical setting can now be considered common knowledge, having been published in numerous books and websites. Background information for this article was taken from several authors without crediting them by name in the text. These authors are - Larry Orcutt, Mark.Lehner, Ian Shaw, Miroslav Verner, Andrew Collins, Allen Dittmer, Roumen V. Mladjov, S.E. and Ian S. R. Mladjov, B.A.
Special credit is due to Larry Orcutt whose help was sought at different stages of testing and writing. His comments and critique were valuable in trying to ensure that the proposed transportation and lifting techniques are consistent with the known archaeological and historical facts. Some technically minded authors focus so closely on the technical and logistical aspects of pyramid building that they fail to align their techniques and solutions with the archaeological remains and historical records.
© Copyright 2006 by Mike Molyneaux.
Catchpenny Mysteries © copyright 2000 by Larry Orcutt
