Figure 10.15. Collection of photographs from the basalt pavement near the Great Pyramid
Figure 10.16. Three images of the same basalt pavement block east of the Great Pyramid
Notwithstanding the appearance of a radial cut, the use of circular saws when cutting these basalt blocks is dismissed by Robert G. Moores Jr. In an article titled “Evidence for Use of a Stone-Cutting Drag Saw by the Fourth Dynasty Egyptians,” Moores writes, “The cut grooves could not have been produced by a rotating blade such as found on a circular saw. A rotating blade does not make scratches of variable radius. Even if the blade was four meters in diameter we would expect to see a pattern of circular scratches across the cut face of two meters radius, but this is not the case.”9
Moores describes the striations on blocks of basalt as having “. . . essentially-parallel grooves up to a half millimeter [.02 inch] deep, spaced about one to two millimeters [0.039–0.078 inch] apart. In cross section the grooved face would approximate a sine curve, with the valleys being slightly narrower than the lands between.”10
There are numerous examples of plunge cuts, where a saw left a slot in the basalt. Figure 10.16 and figure 10.20 show these types of cuts. The example Moores gives in his article shows the same cut but on a different block. On a block he identifies as block A, he measured the width of the cut where the saw ended and reported it to be 0.118 inch (3 millimeters; see figure 10.21). He notes: “In cross section, the kerf, i.e., narrow slot that the blade makes while cutting, has, by eye, a perfectly radiused bottom, about three millimeters wide, that tapers outward with an included angle of about eight degrees, (fig. 6.) [see figure 10.21]. The kerf sides are very smooth—not striated.”11 Moores’s observations regarding the perfect radius and smooth sides are important to remember as we discuss his proposed methods of manufacture.
Figure 10.17. Striated block of basalt on the Giza Plateau
Figure 10.18. The sine curve addressed by Moores
Without going back in time and talking to the pyramid builder, it is impossible to explain every anomalous action that created the complex variety of evidence on the basalt pavement. Considering that the now-exposed blocks that reveal these saw cuts were originally covered by adjacent blocks, it is not unreasonable to speculate that the sawed parts of the blocks were given a quick shave in order to remove irregularities that were inherent in the quarrying process and were holding one block apart from its neighbor. If we consider the overall roughness of the blocks, this quick shave was more than likely given by the only tools available on the site, and they were the tools used for finishing and cutting to size all of the blocks that went into building the pyramid. It is well known that these blocks are extremely precise in their cutting, especially those that make up the walls of the inner chambers and also the casing blocks—assuming they were all of the same exactness as the few that survive. It could be argued, therefore, that the roughing tools were not on the plateau, but were applied elsewhere.
Figure 10.19. Slots sawed into basalt blocks
Figure 10.20. Sawed basalt (identified as block A by Moores)
Figure 10.21. Cross section of slot. Drawing by C. Dunn after Moores’s figure 6.12
The quick shave proposed by Moores involved the use of a drag saw. The device, Moores admits, “. . . [i]s somewhat more advanced than general views of the pyramid builders’ technology level now held.”13 In this respect, Moores pushed the envelope of Egyptological thinking. But did he go far enough? Figure 10.22 shows Moores’s concept of how the marks on the basalt were made.
Moores proposes a blade made of copper with a notched leading edge. The blade was 157 inches (4 meters) long and 23.6 inches (60 centimeters) broad and was wedge-shaped from 0.393 inch (1 centimeter) at the top to 0.118 inch (3 millimeters) at the cutting edge. Moores estimates the weight of the blade was 308 pounds (140 kilograms). Quartz sand was used in the process as an abrasive. It was rubbed against the basalt both as a loose medium and also, by quartz sand that was embedded into the copper. This process, with fresh sand being added to the cut as used sand and sawed rock was flushed away, impressed the shape of the blade into the basalt.
Figure 10.22. Moores’s concept of the pyramid builders’ drag saw. Drawing by C. Dunn after Moores’s figure 11.14
As we see in figure 10.22, a team of workers dragged a blade across a block that was fixed inside a trench filled with water. The blade was suspended on ropes that were controlled by workers, who, according to Moores, managed the blade’s incremental descent into the basalt.
Using the cadence of a 78.7-inch (2-meter) pendulum, Moores calculates that the blade swung from one side to the other in approximately 2.84 seconds. Using the distance between the striations of 0.039 inch (1 millimeter), Moores then calculates that in one cycle, (two strokes, one in each direction) the saw plowed into the basalt 0.078 inch (2 millimeters). Using the physics of the pendulum, he then calculates that in one minute, the saw could have cut through 1.653 inches (42 millimeters) of basalt.15
These are extremely positive outcomes and do not seem to satisfy all questions that could be raised about the practicality of Moores’s solution. It is hard to imagine the successful employment of the physics of a pendulum on a swinging 308-pound object that ultimately is met with a hard, solid surface covered in sand. It is also hard to imagine a 308-pound blade slicing through basalt at a rate of 1.653 inches (42 millimeters) per minute. If we take into consideration the fact that the blade is wedge-shaped, which would mean its increasing width would impede its progress into the slot, the impossibility of the operation becomes more evident.
Fortunately, information has been published on experiments using saw blades made of copper plus quartz sand to cut granite. These experiments were carried out by Denys Stocks in March 1999 at a quarry in Aswan using a 32-pound (14.5-kilogram) copper saw blade that was 5.9 feet (1.8 meters) long, 5.9 inches (15 centimeters) deep, and 0.236 inch (6 millimeters) thick. The blade was weighted down with four stones on each end, for approximately 99.2 pounds (45 kilograms). Stocks provides sawing rates that are significantly less than those calculated by Moores. Using wet sand, Stocks was able to cut a 2.46-foot (75-centimeter) slot in granite to a depth of 3.149 inches (8 centimeters) in 30 hours. This calculates to 0.105 inch (0.267 centimeters) per hour cutting rate and a volume of stone removal that is 360 cubic centimeters (a rate of 12 cubic centimeters per hour). Stocks experimented using dry sand, and he cut a 3.117-foot (95-centimeter) slot to a depth of 1.181 inches (3 centimeters) in 14 hours, which calculates to 0.084 inch (0.214 centimeter) per hour, and a stone removal weight of 170 cubic centimeters or 12 cubic centimeters per hour.16 He reports the total weight of copper used to achieve these results as 459 grams in 14 hours, which would be 33 grams in one hour.
Stocks’s experiments show that a hand-powered saw advanced into the granite more slowly over a long cut than a short cut, but the rate of material removal was almost the same. If we apply Stocks’s data to determine how long it would take to saw the six sides of the granite box in Khafre’s pyramid, it would take approximately 6,270 hours17 (see box on next page). The total hours given are conservative estimates and do not take into account additional widening of the saw-cut, which Stocks measured to be 2.5 centimeters at the top and 6 millimeters at the bottom (emphasis added by author for clarity).18
It is impossible to reconcile Stocks’s experimental results with Moores’s hypothetical results using a drag saw. In pondering the results of Moores’s proposed sawing rate of 1.653 inches (42 millimeters) per minute (2,520 millimeters per hour) compared to Stocks’s experimental sawing rate of 2.14 millimeters per hour, we should take into account how modern saws perform when cutting granite. United States Patent 7082939, filed in 2003, describes an improved frame saw using carbon alloy steel blades with replaceable segments that are impregnated with diamonds. The patent cites a down-feed rate in granite of 30 millimeters per hour.19
These modern rates are 14 times greater than those achieved by Stocks, whi
ch is not surprising, but 84 times less than Moores’s proposed rates. Considering the operating conditions, Stocks’s rates make sense, while Moores’s hypothetical sawing rates once again seem impossible using the equipment he proposes. However, Moores does point out that his results are the maximum achievable using the cadence of a pendulum and recognizes that the hardness of the rock and friction could slow the process down. The capabilities of modern saws prove that Moores is correct in this one statement, which occupies the space of only one sentence in his article.20
COMPUTATION OF APPROXIMATE HOURS TO SAW GRANITE BOX IN KHAFRE’S PYRAMID
Basic Measurements
Stocks’s length of saw-cut 95
Stocks’s depth of saw-cut 3
Square centimeters 285
Hours worked 14
Square centimeters per hour* 20.36
*Added by author
Granite Box in Khafre’s Pyramid*
Top + Bottom East + West North + South
Box length, 263.35 Box length, 263.35 Box width, 106.4
Box width, 106.4 Box height, 96.82 Box height, 96.82
Square centimeters, Square centimeters, Square centimeters,
28,020.44 25,498.81 10,302.16
Total, 56,040.88 Total, 50,997.62 Total, 20,604.32
*Dimensions given by Petrie converted to centimeters by author.
Totals
Total square centimeters of Khafre’s box 127,642.8
Stocks’s square centimeters 20.36
Total hours for box 6,270.22
Before we return to Abu Roash, we must resolve the difference between Petrie’s observations and Moores’s with respect to the use of circular saws. The evidence Moores was looking at would certainly point to the use of straight saws. Yet there are other blocks on the pavement that pose a problem to the notion of the exclusive use of straight saws.
As we survey the area of the pavement, we see the marks of ancient tools that will appear to change geometry as our point of view changes. To understand what is happening, we can look at figure 10.23, which gives three examples of saw cuts on two different types of surfaces. Block A has a straight cut on a flat surface. This kind of cut will always look straight, regardless of any variation in the viewing angle. Block B has a curved cut on a flat surface. The radius of the curve will appear to shorten as the block is rotated down, or lengthen if the block is rotated up. Block C has a straight cut on a curved surface. We see that the straight cut of C-1 is curved in the z axis, looking perpendicular from the top (y axis), but a radius of varying size is seen depending on the viewing angle, see C-2 and C-3. Views from the side will also exhibit varying sizes of radii. If we use the radius of C and create a full circle, then the views seen in C-2 and C-3 are actually sections of an ellipse. An ellipse in a unique manufacturing process will be discussed further when we return to the granite stone at Abu Roash.
While the apparent curvature of the block seen in figure 10.16 is too ambiguous to provide a solid conclusion, another block lies a short distance away from the pavement and would go unnoticed by the casual traveler unless he or she stumbled over it. That block can’t be explained by the use of straight saws, because the surface is curved in a way that would eliminate the random arching of a blade or any amount of uncontrolled meandering by a shaky operator.
Figure 10.23. The geometry of a flat and radial saw cut on a flat or radial surface
Figure 10.24 contains three views of this basalt block that when viewed from the side at an angle, the saw cut seen in figure 10.24 A ends with a radius. Without examining the block further, it could be argued that a hand-operated straight saw created the cut, and that the operators of the saw did not keep the saw straight as it moved through the cut, but instead allowed it to drift up and down. This is a common occurrence and, in fact, achieving a perfectly straight cut with a hand-powered saw is almost impossible. Fully impossible is the achievement of a concave radius for the obvious reason that it is physically impossible to create a saw cut where the entrance and exit points are higher than the middle with a flat-edged straight saw. Some may argue that the saw could bend and create this condition, and indeed they are more than welcome to prove their claim. Stocks did not observe this condition during his experiments and neither have I during my experience working with handsaws that were thinner than Stocks’s.
If we look at figure 10.24 B, which is a view of the front of the cut surface, the striations are clear, but the radius where the cut ends is larger from this angle. The reason for this is explained in figure 10.24 C, in which we are looking at the surface from the top. It is clear from this angle that the entire surface is curved. It is possible, therefore, that the geometry of this block is the same as the example shown in figure 10.23 C-1, C-2, and C-3, in which a surface was cut on a radius and the tool that cut the radius left a step that was straight when viewed straight on, though it appeared curved if viewed on an angle, such as when viewed from two angles, to the side and from above, such as the view in figure 10.24 A. The radius appears smaller than B and C, which indicates that the cut surface is curved and not flat. Along with Petrie’s testimony to the use of circular saws at Giza, what we can gain from this block is further evidence that efficient circular tools were used on the Giza Plateau, though we are still left to wonder about what they looked like, how they were driven, and from what material they were made.
Figure 10.24. Evidence of circular cutting tools on the Giza Plateau
As discussed earlier, Moores’s observation of the root of one of the saw cuts he examined (see figures 10.19, 10.20, and 10.21 on pages 268 and 269) describes the bottom of the saw cut as being a perfect and smooth radius. Of his experiment in sawing granite at Aswan, however, Stocks notes that, “[a]s before, similar parallel striations were visible on the sides and the bottom of the slot.”21 This seems to be in conflict with the evidence noted by Moores on the Giza Plateau. Unfortunately, we have nothing to compare how similar Stocks’s striations are with ancient saw cuts because in his article, Stocks does not provide a thorough comparative analysis with photographic proofs.
The Giza Plateau provides further evidence for the use of circular saws, but first the stone at Abu Roash demands more attention: though the marks on the basalt blocks at Giza indicate the use of circular saws, the striations left on them are different from those on the granite block at Abu Roash. Though the ones at Giza appear to follow straight or curved lines, the striations on the stone at Abu Roash drift from side to side from similar theoretical lines. As seen in figure 10.25, the striations wander slightly from a true straight or curved path, but, inexplicably, each of the striations wanders in the same direction as its neighbor and follows a parallel path. This does not support the view that abrasive slurry was at work to create these marks. It seems to be powerful evidence that fixed cutting points that are set into a rotating cutting tool were acting on the surface. Why, then, were the lines wandering from a true path? A possible explanation for these striations is that there was some wobble in the saw as it moved across the granite. Yet other characteristics of the piece seem to pose more questions.
The radius where the cut surface terminates is puzzling when we consider different ways in which the block may have been made. Often in the dark early hours of the morning, I came up with numerous methods for cutting this piece, but each of them failed to provide a practical solution. One suggestion made to me was that the blade that cut the piece was a straight saw but that it was warped and cut the curve on the stone face. If that were possible, it would explain one radius on the block, but whether you view the block from above, or along its length, you see a radius. When considering this and pondering on how this inexplicable geometry was cut into the granite, the straight saw has to be eliminated, because it would be impossible for it to cut a concave radius along its face and along its edge. Another suggestion given to me was that the stone was cut by a stone ball swinging from a pivot point. Yet the evidence suggests a far greater amount of control and certainty than that
of a swinging ball—regardless of the skill put into the swing.
I tried to imagine a process in which the piece would be cut in one single sawing operation, but I could not come up with a method that did not demand more out of the tool than was possible due to an increase in surface area being cut. In other words, assuming a larger block was being cut along the striated surface with the saw on an angle, depending on the thickness of the entire block, the thin block, which is the one we are studying, would break apart from the thicker one. But passing the stone across the saw on an angle would result in an increase in the surface area being cut. In pursuing an answer to the puzzle, while providing an answer to Petrie’s question about the size of the saw, it was necessary to calculate the radius of the saw and the granite block at Abu Roash, provided the attributes to calculate the radius, with, perhaps, a tolerance of 5 percent of the diameter. To achieve this, it was necessary to use both radii swung around the y and z axes referenced in figure 10.11 (see figures 10.26 and 10.27).
Lost Technologies of Ancient Egypt: Advanced Engineering in the Temples of the Pharaohs Page 24
