Source: http://www.jasonbaldridge.com/greatpyramid
Timestamp: 2019-04-23 21:57:45+00:00

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Located in Giza, Egypt, the Great Pyramid of Khufu (Cheops) is the oldest of the Seven Wonders of the Ancient World. It is also the only one still standing. For thousands of years, it has remained an enigma to the many people who have attempted to discern how it was made. Although many questions about the Great Pyramid itself have been sufficiently (though not conclusively) answered, the debate over the precise manner of its construction has never ceased. Scholars (and non-scholars) from various disciplines and backgrounds have made countless attempts to resolve the many different issues involved in the creation of the Great Pyramid (GP). This paper focuses on the methods of transporting and raising the blocks of which the GP is made.
The importance of knowing how the GP was built is readily apparent. The construction of such an imposing building must reveal a great deal about the labor forces, tools and machinery, technical knowledge, and people of Egypt 4600 years ago. The sheer size of the structure alone commands us to reflect upon its builders with a certain degree of awe. The GP is still the largest building in the world. It stands 450 feet high (originally 479) and weighs six million tons. Its orientation is within five arcminutes of true north and the level of its thirteen-acre base varies by only one inch. The casing stones are so finely jointed that a knife's edge cannot fit between them. The precision of the workmanship throughout the rest of the GP is remarkable as well.
Khufu's workers faced several problems while undertaking the task of building the GP. First, they had to quarry the limestone blocks which were used to build the GP. After quarrying the blocks, they had to transport them to the building site and raise them to their final positions. Raising the blocks to the various levels of the GP was not a simple task; the limestone blocks weigh up to 15 tons and the granite monoliths in the interior of the GP weigh up to 70 tons. Indeed, the questions most often asked about the construction regard the method of getting these blocks to their final positions in the GP. A wide range of theories and opinions have been advanced to explain how this was accomplished. I will dismiss as inconsequential those speculations which attribute the moving and raising of the blocks to the use of anti-gravity and supernatural power by the high priests of ancient Egypt. I also will not consider theories that astronauts from other planets built the GP. The proponents of these ideas incorrectly assume that ancient Egyptians living in 2600 BC did not have the ability to do it by themselves--using straightforward, physical methods and working with the same natural laws we encounter in the present day. Of course, many scientific theories have been advanced that are less fanciful and more workable. The various scientific contenders differ substantially with regards to practicality, engineering feasibility, and the archaeological record. The purpose of this paper is to lay out and select the most promising of these.
Before discussing the different ways of moving and raising the limestone blocks, a contention that the blocks were never even quarried must be challenged. Polymer chemist Joseph Davidovits advanced an unconventional theory that the pyramid builders actually made the blocks by pouring a mixture of disaggregated limestone and a geopolymeric binder into wooden molds. This mixture then hardened and became almost indistinguishable from natural limestone. This would have allowed the workers to have simply passed potfulls of the mixture up the side of the GP, with no need for ramps or machines. Davidovits says that samples of pyramid casing stones revealed that they contained as much as thirteen percent of the binder; however, Michael Tite says that his own analysis of pyramid stone did not produce the same features (Peterson 1984, p. 327). Geologist James Harrell, who has done extensive work on the provenance of pyramid stones, performed an analysis of the very sample that Davidovits used and concluded that it was natural limestone quarried in the Mokattam Formation (Harrell 1993). It is quite clear that blocks were quarried, not manufactured.
How the limestone blocks were transported to the GP is a topic about which engineers have developed many hypotheses. The generally accepted theory is that the ancient Egyptians dragged the blocks on sledges over causeways made of either slaked lime or tafla (a local clay). The remains of causeways constructed of tafla have been found all over the Giza plateau (Hadingham 1992, p.51). Also, actual sledges at pyramid sites, and reliefs and paintings in tombs and quarries depicting the use of sledges have been discovered (Leper 1990, p. 242). A team led by archaeologist Mark Lehner successfully used the sledge when they constructed a small, eighteen-foot tall pyramid (Hadingham 1992).
Engineer John Cunningham (1988) proposed that the Egyptians carried the blocks on flexible poles. According to Cunningham, these poles would have given an incredible mechanical advantage by combining the weight distributing principle of the suspension bridge with the energy storing characteristics of the bow. This may be effective for lifting, but I question whether horizontal progress could be easily made. To keep the blocks from bouncing erratically, movement would have to be very slow and cautious. Also, the average limestone block is a cube with sides three feet long. At best, three poles could fit under one of these, and the onus of lifting 5000 pounds would be on the six individuals who held the ends of the poles. Cunningham stated that a load of 2,600 pounds had been lifted using twelve oak poles (Cunningham 1988). Simple calculations, left to the reader, will clearly show that Cunningham's proposal could not have been employed by the builders of the GP.
Engineer John D. Bush (1978) suggested an alternative method that uses ancient wooden circle segments similar to those uncovered during excavations (Figure 1a). Egyptologists theorized that they were used as cradles or rockers. Bush proposed that the pyramid builders transformed the limestone blocks into cylinders by attaching a circle segment to each edge of the blocks' square cross sections (Figure 1b). The blocks could then be rolled and moved with ease. Bush has demonstrated this technique, successfully rolling a 5000-pound block up a ramp with the help of six other men. However, even though this method is feasible and workable, it is unlikely that the GP's builders used it. The segments used by Bush had holes drilled into them to accommodate ropes which held the segments onto the block, yet none of the ancient segments found have such holes in them.
How these alternative proposals fail is most clearly seen by considering the extreme case. Neither theory accounts for the movement of the fifty-ton granite slabs used in constructing the internal chambers of the GP. Considering the immense size of these monoliths, the flexible pole method would be rendered even more awkward. Forward motion would be extremely tedious--assuming that these monoliths could even be lifted by this method. Bush's idea would also be problematic. The dimensions of these slabs are not uniform, so each slab would have needed specialized circle segments. The largest monolith is about 27' x 4' x 8' at its ends. Even if larger circle segments were used to create a pseudo-cylinder, the weight distribution would not be even around the central axis and the size of the entire ensemble would be quite large and unwieldy (Figure 2a). Ramps and causeways over 27 feet wide would have been necessary because the slabs would have moved perpendicular to them instead of parallel. In order to make these circle segments, the builders would have needed trees with diameters of at least three feet (perhaps up to five). How easily the Egyptians could have obtained such trees would have to be checked. Also, some of the slabs are rough-cut on their tops, which increases their height by one to two feet in their midsections (Figure 2b). This would cause the midsection to project beyond the cylinder created by the segment circles (Figure 2a, top). Consequently, the rolling of one of these blocks would be inordinately difficult and most likely unmanageable. The most plausible explanation is the sledge method. It would accommodate even these massive granite slabs, and it is most consistent with the archaeological record .
The greatest controversy over the GP's construction regards the manner in which the builders raised the limestone blocks to the various levels (courses) of the GP. The traditional view of Egyptologists is that the builders used some sort of ramp to raise the blocks. Evidence for the use of ramps includes paintings of construction ramps, a ramp found at an unfinished temple, and the remains of ramps present at a couple of pyramid sites. Originally, it was thought that a single ramp extended from one face of the GP. This has been rejected in recent years because such a ramp would have had a volume up to three times that of the GP itself. Also, it would have been over a mile long--extending far beyond the limestone quarries 500 yards away.
Another ramp theory proposes that a series of switchback ramps zigzagged up one of the faces of the GP. Even more popular is the idea that a ramp wound around the entire GP. Lehner successfully used a wrap-around ramp when he constructed his small pyramid. This method is a strong contender for being the best of the ramp theories, and it may well have been the one the pyramid builders actually used. Even so, it has several weaknesses. There is nothing in the archaeological record that indicates the use of such ramps. The depictions of ramps generally show straight ones which lead up to a wall. Like the straight ramp, the wrap-around ramp would be nearly a mile long. Turning corners would have presented great difficulties, though Lehner's team was able to solve this problem by planting posts at each corner and pivoting the ropes on the posts as they pulled a sledge around the corner (Hadingham 1992, p. 51). Even though Lehner was able to use a wrap-around ramp, I question whether the method would work for the GP, which is 240 times the size of Lehner's pyramid. The straight ramp would have also worked well for a pyramid eighteen feet tall. Also, the wrap-around ramp itself would have been a remarkable feat of engineering. A large amount of material would have been necessary to keep it stable, and, according to Zahi Hawass (1990, p.41), the greatest problem would be that the unfinished faces of the pyramid would not have supported the weight of the ramp.
An alternative method of raising the blocks is suggested by a comment the Greek historian Herodotus made in the fifth-century BC. When Egyptian priests were showing him the GP, they told him that the stones had been lifted with levers made of short timbers. Some theorists feel that this clue may offer a better solution than the ramps. The largest and heaviest blocks lie on the first course, and the blocks become smaller on each higher course. J.P. Lepré (1990) says that a ramp would be feasible only up to the fifth course, and that a different method would be necessary for the next 196 courses. He proposes that a machine which uses levers and counterweights could have effectively lifted the blocks. A line of such machines would have extended up one of the faces of the GP, each machine passing the blocks up to the next. Though I agree that machines were possibly used by the builders, the particular machine which Lepré devised seems much more complex than the builders actually needed, and it would have been too large to fit on the stepped sides of the GP. I am also uncomfortable with Lepré's machine because his knowledge of physics seems questionable; he depicts a 1-ton block that is 15 feet from a fulcrum as being in balance with a 10-ton block that is 5 feet from the fulcrum (p. 256). The 1-ton block would actually need a lever arm of 50 feet to balance the 10-ton block at 5 feet.
Sculptor and pyramid researcher Martin Isler felt that a simple levering process was employed (Boxer 1987, p. 8). According to Isler, a block could be elevated by alternately lifting each side of the block with a lever and placing a board underneath it. However, when this method was attempted during the construction of Lehner's pyramid, it failed miserably. After getting a 3-ton block two feet high, the whole setup became very wobbly and tricky to manage. It was also very time consuming.
Some theorists suggest that a simple machine using levers and counterweights was used to elevate the blocks. Such a machine, called a shadoof, has existed in Egypt for millennia and is still used to elevate pots full of water from the Nile River to the irrigation canals. Though a shadoof itself could never lift a 2.5-ton block, engineer Olaf Tellefsen (1970) observed three men using a similar machine to lift very large stones while he was riding up the Nile. Even so, a few considerations must be met before one can propose a machine that could be used on the GP. First, it must fit and be capable of operation on the pyramid's stepped face. Second, it must be manageable and controllable so that damage would not be done to the blocks being lifted and so that workers would face a minimal risk of falling or being knocked off the edge. Third, it should be simple so as to align as closely as possible with the scant archaeological record that such machines can claim. Finally, it must be capable of lifting at least 5000-6000 pounds.
I suggest that such a machine system could have been successfully employed by the pyramid builders. Having raised the first five or six courses of the GP (where the heaviest stones lie) with a straight ramp, the builders would have added a one-block extension to a twenty foot section up the entire face of one side of the GP (see Figure 3). They also would have not installed certain blocks so as to allow room for levers to operate. Stone blocks with special grooves would be installed on the extension as fulcrums over which long wooden tree trunks would be placed. These timbers would have diameters of one-half to one foot and would be 20 to 25 feet in length. The short arm of a timber would be attached to a block, while the longer arm would have a net-basket attached to it. Weights would be incrementally added to this end, thus raising the block (Figure 4). For example, about 2100 pounds 14 feet from the fulcrum would raise a 5000-pound block that is 6 feet from the fulcrum. Including the weight of the timber, the weight required would actually be less than 2100 pounds.
Figure 3a. Isometric view of pyramid-face extension with fulcrums and levers in place.
Some blocks have not been installed so that the lever and basket may move unobstructed.
Figure 3b. Plan view. Shading denotes altitude. The blocks are approximately 3' x 3'.
Figure 4. Block lifted after weights have been added in increments.
Workers would use their weight to manipulate the machine once the two ends gained equilibrium.
Once the height of the next course was cleared, the operators would use their own weight to maneuver the block onto the next course (Figure 5). The weights would be removed and the pole would be positioned on the next highest fulcrum and the process would begin again (Figure 6). In this way, each block would traverse a linear path up to the course it finally rested upon. When the pyramid was nearly finished, the machine staircase would have been completed from the top down, with the blocks from the extension being used to fill in the omitted areas. The fulcrums would have been shattered and sent down the pyramid with the machine weights. Alternatively, depending on their original dimensions, they could have been cut and finished and used as construction blocks. More than one such fulcrum-and-lever staircase could have been used, as needed. A lot of fine tuning would be necessary to make such a system perfectly workable, but as such it is quite simple and feasible. It must be noted that whether this particular system was the precise one used is not the main issue. My primary interest is in demonstrating that pyramid blocks could have been raised without ramps.
Figure 5a. Block and lever rotated so that block rests on next level.
Figure 5b. Plan view. Note: the true length of the lever is given in these two figures.
Figure 6. The levers are shifted onto the next highest fulcrum and the process continues.
One issue that has been left unexplained by theorists was raised by F.M. Barber (in Tompkins 1971). He questioned that the monolithic granite slabs used in the construction of the internal chambers of the GP could have been lifted by wooden machines. Barber felt that steel cranes or derricks would have been necessary to elevate them. Because the pyramid builders did not have such machinery, Barber concluded that ramps were the only way for them to raise the monoliths, some of which weigh 50 to 70 tons. Actually, the wrap-around ramps would also be strained to accommodate the inordinate weight and dimensions of the granite slabs. However, I feel that it was entirely possible for the builders to raise these massive slabs without the use of huge ramps or machines. All they needed to do was store them on the top construction level of the GP as it grew course by course. Once a course was completed, work would begin on the next. After the new course was partially built, a small ramp would be constructed and the slabs would be pulled up to the new course. The builders would have continued this process until the slabs were placed in their final positions. Though there are a large number of these slabs in the building, the builders would not have been lacking space to store them, since the area of the base of the GP is about 13 acres. None of the slabs is located more than halfway up the GP, where there would still be over four acres to work with.
One common objection to machine theories is that the ancient Egyptians would not have had access to the wood necessary for them. The trees that grow in Egypt are either too valuable as sources of food or they are not long and straight enough, nor are they sufficiently strong. However, the hieroglyphic Palermo Stone text states that the Pharaoh Sneferu (Khufu's father) had sent 40 ships to Lebanon to bring back timbers of cedar (Meiggs 1982, p.63). Cedar trees are quite straight, and they commonly reach up to eighty feet in height (sometimes 120). Other kinds of wood sufficient for machine purposes were available in the Mediterranean area, and there were plenty of trading networks through which the ancient Egyptians could obtain timbers (Meiggs, pp. 54-66). Some of Sneferu's pyramids contained cedar beams and timbers. A ship made of cedar wood was found in a pit near the south side of Khufu's pyramid. Clearly, the pharaoh who was responsible for raising the largest building in the world could have acquired the timbers necessary for machines easily enough.
Machine theories are also criticized because machines are not found explicitly in the archaeological record. I do not find this surprising. Wood, though available, was not in abundance in Egypt, so once the machines had lost their usefulness, they were probably disassembled and used for building other things or, at the very least, burned as firewood. The long timbers used in my method could easily have been utilized for other purposes. Thus, these machines disappeared from the archaeological record. It should be noted that the record does show that the pyramid builders were well aware of the principles of the simple lever, though it does not explicitly reveal any particular machinery. Also, some researchers, such as Tellefsen, consider Herodotus' statements about machines to be a part of the archaeological record, despite the opinion of many scholars that Herodotus is not a credible source.
Ramps were not the only means available to the pyramid builders. Making them and removing them would have been an enormously laborious process. Also, dragging the blocks up a lengthy ramp would have taken far more effort than using levers to move them straight up the face of the GP. The levers are feasible--they can lift loads like the limestone blocks. And though there is currently no explicit, physical archaeological evidence of them, clues from Herodotus and the ancient use of the shadoof hint that they were not unlikely. Also, the GP itself is unusually void of hieroglyphics or decoration, suggesting that the builders may not have left such evidence.
The theory that the ancient Egyptians used some sort of simple machine in the construction of the GP is a strong contender. Of course, it is entirely possible that a combination of different methods, including ramps and machines, were used by the builders of the GP. However, as one commentator put it when discussing pyramid construction methods, the only certain thing we know is that the Great Pyramid most definitely was built.
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