Figure 10.25. Striations on the stone at Abu Roash
Figure 10.26. Calculating the y axis radius.
Figure 10.27. Calculating the z axis radius
Three points were selected along the arcs in both figures 10.26 and 10.27 to create circles. Zooming in on the arc, it was determined that the radius in figure 10.27 (which defines where the cut ended) is accurate over approximately 93 percent of the arc. As seen in figures 10.26 and 10.27, using the dimensions of the chord (56.75 inches (1.441 meters) and the sagitta, or arc height—1.404 inches (0.035 meter)—in the y axis, and the dimensions of the chord and the arc height—1.42 inches (0.036 meter)—in the z axis. The radius of the arc is 23.95 feet (7.3 meters) in the y axis and is 23.684 feet (7.218 meters) in the z axis.
It should be noted that the sagitta of the y axis radius was taken on the end of the block nearest the camera and that the radius may not be the same where the surface meets the end of the cut where the stone is broken off. Taking all of this into account, the figures given here are the result of measurements taken under specific conditions. I make no assertion that they are perfect measurements and that they are not subject to change if the stone is examined under laboratory conditions. I recognize, also, that others may take their own photographs and achieve different results, or may achieve different results from my photographs.*2 The two and three decimal point callouts do not imply two and three decimal point precision. Yet I do assert that they both indicate, with close agreement, that the saw that cut this block had a very large diameter.
Our view of the calculated arcs along their theoretical axes does not reveal the saw’s true diameter. It assumes that the centers of these radii were located perpendicular to the camera’s axis, whereas the cut surface being studied had a concave radius cut along its length. These conditions suggest that the saw that cut both radii must have been on an angle or that the granite block was pushed into the saw at an angle. By knowing the dimensions of both radii, therefore, we can make a more accurate calculation of the saw diameter.
When viewed at right angles, the radius cut at an angle into the stones is seen as a segment of an ellipse. A useful trick in machining is to tilt a cutter on an angle to machine a larger radius into a work piece. The rules are that the block has to be much narrower than the cutter in order to avoid creating more of an elliptical shape. The formula, that is usually found secreted in a toolmaker’s toolbox under or inside a copy of Machinery’s Handbook, is given as the cutter diameter/diameter of desired radius = radian measure. The following table was created by adjusting the cutter diameter until the radius from the top view and the radius from the end view produced an angle that combined added to approximately 90 degrees. A difference of 0.6 degrees is noted and expected, considering the lack of a precise laboratory inspection of the block.
In calculating the diameter of the saw, I used an Excel spreadsheet and input the known radii, seen from the top and the end, then adjusted the diameter of the cutter until both angles equaled 90 degrees:
This was tested in a milling machine on a micarta plastic 1/61 scale model, the results of which were compared to the photograph of the granite (see plate 22). The process involved tilting a cutter on a 45-degree angle and cutting along the x axis (identified as the y axis in figure 10.11) until I had reached a point where I could break off the material at the cutting edge. The piece that broke away from the block had all the characteristics of a pyramid casing stone, but the angle was not consistent with Egyptologists’ speculation on the angle of the pyramid. Lehner, though unsure of the exact angle, proposes a range of 48 to 52 degrees.22 Considering the slope of the pavement, however (see figure 10.4), a block with a 45-degree angle would be tilted in the opposite direction of Lehner’s hypothetical angles, which means that we cannot use this block as evidence of the angle of the nearby pyramid. Whether this granite block is the piece of sarcophagus that Petrie had noted is also uncertain at this juncture.
It seems fairly certain that the block at Abu Roash was not cut with the saw tilted on an angle, but with the block rotated at 45 degrees and moved into the saw, perpendicular to the saw’s axis of rotation. To cut the block by pushing it at an angle against the face of the saw not only would apply significant lateral forces, but also it would be inefficient, because the volume of material to be removed would be increased tremendously. Without going back in time and witnessing how this block was cut, we can only speculate, but having thought long and hard about a possible method that would remove the least amount of material and provide the features evident on the block, it involves cutting the block in three operations as seen in figure 10.28.
The small step seen 4 inches away from the radial break on the granite indicates that the block may have been moved through the saw in three stages. If this was the case, then it is possible that two blocks with the same 45-degree angle were created, and then the angle was recut on each to the pyramid angle.
The operation seen in figure 10.28, stage A, created the compound arc and broke off what appears to be a block with the pyramid angle (shaded area). Stage B cut parallel to the bottom of the block and produced another triangular block, which may have also been used as a pyramid block. These blocks are nowhere in the vicinity at the site and must have been carried off with many other blocks. These cuts left a thinner block, which is the focus of our study. At this point, the block would have had a flat face with a step down to the radial break (see figure 10.28 B and E). Then again, for unknown reasons, it appears that the builders decided to make the surface even across the length and passed the piece across the saw, where at two points there was movement in the block, and steps in the surface were left (see figure 10.28 C and F).
Figure 10.28. Proposed stages of cutting the block
Figure 10.29. Machined model with step
This theory was tested on a piece of plastic, and a predictable step was created where the cutter was used perpendicular to the surface rather than at an angle and, therefore, cut a smaller radius. When the full width of the block was reached, the cutter was passed along the entire surface and then the step was measured to be 0.003 inch at its deepest part using an Interapid indicator (see figure 10.29). Across a block the size of the stone at Abu Roash, the step would have measured 0.183 inch deep. Without an exact measurement of the step in the Abu Roash block, I would estimate that it was no more than 0.25 inch. Figure 10.30 provides a close-up of the area showing the parallel striations.
It seems bordering on the impossible to imagine such an operation being performed by ancient Egyptians, but what other method would create each of the following?
A compound radius
Parallel striations that follow an uneven path across the stone
A step about 4 inches away from the break
Figure 10.30. Stone at Abu Roash with machined step
The wobble of the striations provides support for the proposed method, for it would be very likely that a saw blade that is approximately 37 feet in diameter would have some lateral movement, even with small inaccuracies in the bearing—unless there are stabilizing bearings that apply support on both sides toward the outer rim. The evidence in the stone shows clearly that a tool with fixed cutting points was passed across the surface with a reasonable degree of regularity, given the distance between the striations—but seen from one end to the other, there is lateral movement in the striations, which indicates a wobble in the tool.
Because the machines that cut the Chinese jade burial rings and the Egyptian granite blocks are no longer in existence, the evidence is considered circumstantial. Yet it provides us with a fairly accurate picture of at least their diameter, if not quite how they were driven or the materials used in manufacturing the saw.
As we consider the megasaw at Abu Roash, it might be useful to consider machines with similar dimensions that are in use today. Between 1987 and 1994, megamachines that were thought of as marvels of modern technology chewed through 31.6 miles (51 kilometers) of chalk marl beneath the Engli
sh Channel at a rate of 482 feet (150 meters) per week. Hardened steel and carbide bits at predetermined placements around the cutting face of a Tunnel Boring Machine (TBM) traveled around an 84-foot circumference, creating a tunnel that was 27 feet (8.2 meters) in diameter. These were monster machines designed for a mammoth project in which size truly mattered.
With the new evidence gained from Abu Roash, we now know that when the ancient Egyptians tackled mammoth projects, size also mattered. The evidence shows that when it came to designing equipment that was up to the job of pyramid building, nobody did it better than the ancient Egyptians. While the TBMs that bored through the English Channel were 27 feet (8.2 meters) in diameter, objective evidence shows that the ancient Egyptians used megasaws for cutting granite, limestone, and basalt that exceeded that diameter. We can calculate the size of these saws by the impression they left on the granite block seen in plate 21.
We should not be surprised that a culture able to conceive and build the largest and most impressive structures on the planet did not limit their efforts to just the constructions, but also to the tools they used to build them. The ancient Egyptians created an abundance of evidence from which methods of manufacture can be inferred.
As this evidence drove me to grapple with these concepts, I was stunned by their implications, and I tried to imagine what such a saw would look like, how it was installed on the Abu Roash Plateau, and how the stone to be cut was secured and moved through the blade. The radius on the stone indicated that it was cut slightly off the center line of the saw, which meant that the block was secured to a table that must have been 15–16 feet (4.57–4.87 meters) from the ground. It seems a bit extreme to have to haul blocks of stone 15 feet in the air to be able to cut them, but then it finally dawned on me that there are other features at Abu Roash and at Giza that may provide an answer to this mystery.
Close to where this stone is located and cut into the bedrock there is a deep trench that is 121.39 feet (37 meters) long and 31.5 feet (9.5 meters) deep (see figure 10.31). Similar trenches can be seen on the Giza Plateau on the east side of the Great Pyramid. These long trenches have been labeled boat pits by Egyptologists because of their shape, and they are considered to be the symbolic transport of the dead king into the afterlife. Considering the appearance of solar boats in Egyptian art, particularly the prolific reliefs inside the Temple of Denderah and the discovery of a boat in a rectangular pit south of the Great Pyramid, the association of the pits with boats is understandable. The trench at Abu Roash, however, is quite narrow and deep and does not accurately represent the shape of a boat’s hull. In addition, no remains of boats were found in these trenches—unlike the rectangular trench south of the Great Pyramid, where, in 1954, an ancient Egyptian boat was found in pieces. The boat was reconstructed, and it is now housed in a museum built specifically for its display. Within an engineering context, it would not be far-fetched to propose that the empty trench in the vicinity of Abu Roash was originally used to accommodate the lower part of the saw’s massive diameter (see figure 10.32). This, more than likely, will not be a popular suggestion among Egyptologists, but from an engineering perspective, it makes more sense—considering the work that was required to construct Abu Roash—than installing symbolic items for the use of the pharaoh’s soul in the afterlife.
The revolutions per minute of a saw that is 37 feet in diameter would be relatively low. If we consider that a 1-inch-diameter diamond-tipped drill rotates at 900 rpm, the surface speed calculates to 3.1415926 × 900/12 = 235.619 surface feet per minute. In one revolution, a saw that is 37 feet in diameter would travel 116.24 feet, so it would require just 2.03 rpm to achieve 235.619 feet per minute at the cutting edge. Of course, this is based on modern tools—the kind of materials embedded in the substrate of the segments of the outer rim of the saw (if they had reached the same logical idea expressed in the aforementioned patent) are a mystery.
Figure 10.31. Trench at Abu Roash
Figure 10.32. Abu Roash with a megasaw installed in its trench
After this enlightening visit to Abu Roash, I returned to the Giza Plateau where seven so-called boat pits located at various places around the pyramids have been uncovered. Two of the largest pits—or slots, as they really appear to be—are oriented north to south on the east side of the Great Pyramid (see plate 23 A and B). Others are located between the queen’s pyramids (plate 23 C and D). Another rather dilapidated pit with a fence that has fallen down (plate 23 E) is near Khafre’s pyramid to the north of the contoured stone discussed in chapter 6 (refer to figures 6.17–6.20). Note that the inset in plate 23 D shows a radial undercut on one end of the trench, which is indicative of a circular saw’s action.
When we look at the trenches on the Giza Plateau and consider the enormous task of cutting millions of blocks of stone not just for the Great Pyramid, but also for the other pyramids on the site, the use of megasaws that can cut efficiently through granite and limestone to exacting tolerances somehow gives the manufacture of pyramids a different perspective—a perspective that allows a sense of comportment with engineering on an appropriately massive scale, and one that takes into account methods and machines that were equal to the task at hand. The whole plateau would have been a hive of activity, with quarried stone being moved onto the plateau next to the saws, in line to be cut to shape for placement in the pyramids. At the same time, ancillary workshops would have manufactured cutting segments that were installed on the rims of the saws as others were worn through use.
It is well known that the biggest enemy of the life of a tool is heat. With a given segment of the saw working only for a fraction of the time it takes to rotate 360°, as it is in contact with the piece being cut, the heat generated during the cutting process would dissipate as the saw turned slowly around. It might also have been beneficial to fill the saw pits with water and have the saw pass through the water after cutting in order to cool it and wash away rock dust embedded in the edge. By the time a given segment of the saw had to cut again, it would have lost most of its water and dried off. A totally dry process, however, would be preferable for waste removal.
Figure 10.33. Installation of a saw in the trench shown in plates 23 C and D
The removal of waste is a concern. The pits are more than twice as long as their depth, most likely, to allow workers access to remove the waste. One trench on the Giza Plateau has steps descending from one end—an indication that frequent access was necessary.
A discussion of the materials and power available to the ancient Egyptians to manufacture and drive the saws must also consider materials and methods that have not yet been found in the archaeological record. This discussion must take into account not only this chapter, but all the previous chapters of this book.
How many other pits or features near the pyramids may be found lying under the sands of Egypt? As Zahi Hawass has said many times, 70 percent of Egypt’s treasures are waiting under the shifting sands for one fortuitous turn of the spade.
The tool marks on the stone at Abu Roash provide evidence for the movement of the tool that cut the granite. Since 1995, tool marks similar to these have been at the center of an ongoing Internet debate concerning a granite core that was taken from a drilled hole and thrown on a prehistoric trash heap at Giza. Sir William Flinders Petrie stumbled onto this piece of granite, took it back to London, and wrote about it in his book The Pyramids and Temples of Gizeh. The granite core now resides in the Petrie Museum at the University College, London, along with some other interesting pieces that will shed even more light on the manufacturing capabilities of the ancient Egyptians.
The tool marks left on ancient Egyptian granite tell a story. This story is one of remarkable capability. Resident in academic arguments regarding the efficiency of the ancient Egyptians is that time did not mean the same to the ancient Egyptian artisans as it does to twenty-first century artisans. All of their monuments, we are told, were crafted with simple tools and the time it would take using these simple tools to
manufacture all of their monuments and statues. The evidence in the Petrie Museum, however, strongly argues against this notion. The evidence shows that they were using processes that modern manufacturers may yet need to discover. Let’s look at that evidence.
11
Walking in the Shadow of William F. Petrie
Where is the other evidence of this culture? Show me a potsherd. Show me a tomb. Show me an inscription. Show me any other piece of sculpture that dates from this period.1
MARK LEHNER, EGYPTOLOGIST
Sir William Flinders Matthew Petrie was born in 1853 and died in 1942. In the course of his career, he wrote 102 books and articles appearing in forty-eight journals and six magazines, resulting in 1024 numbered items. His shadow was cast over all who came before him and has influenced those who came later. He is considered to be the father of British Egyptology.
In 1972, Eric P. Uphill created a comprehensive bibliography of Petrie’s work. He thanks Ms. Ann Petrie, Sir William’s daughter, for allowing him to search her home for rare articles to make his bibliography more complete. His introduction to the bibliography provides insight into how Petrie was viewed by his peers of that time:
Lost Technologies of Ancient Egypt: Advanced Engineering in the Temples of the Pharaohs Page 25