Hand-Powered Stone Saw [ background discussion ]

Design for Hand-Powered Stone Saw

Jonathan Sheetz, M.D.

It is still not clear how ancient Egyptian stone masons cut stone. It would seem that ancient Egyptian masons had at their disposal a tool that is not used by modern stone masons to cut stone, one that could be made from materials available to the ancient Egyptians.

A ‘new’ type of circular saw design, a “centrifugal saw” which generates sufficient cutting force for cutting stone on an industrial scale and could have been made of material available to ancient Egyptians may be an answer. The “centrifugal saw” presented here resembles a large scale garden-trimmer with rotating copper-tipped cords spun on a vertical axis by a central wooden cylinder axle. The cutting properties of a “centrifugal saw” are compatible with the work left by ancient Egyptian masons; including the industrial scale of precision stone cutting of hard rock.

(photographs: Francis)

The pyramids of Giza are the most famous example of the astounding skill of Egyptian stone masons five thousand years ago. There are some 2.5 million limestone blocks used to build the Great Pyramid of Gizah with an average size of 4’ x 4’ x 2.5’, equal to 40 cubic feet and an average weight of 5,000 lbs (2.5 tons). Stone for the Great Pyramid was cut on an industrial scale.  There persists debate over the tools and methods employed by the ancient Egyptians to cut stone. James states the mystery clearly “key industrial tools [of the ancient Egyptians] are unknown… these include a stonecutting tool” (James 2003). Moreover, in addition to the limestone blocks, the Great Pyramids contained several granite blocks, which are much more difficult to cut.

Ancient stone masons somehow produced large quantities of stone, cut to a high precision, with access neither to modern tools nor to modern power. Modern stone masonry tools are often powered by motors, while ancient Egyptian stone masons relied on human labour for power.

W.M.F. Petrie, noted that ancient Egyptian possessed a complete set of ‘modern’ masonry tools at their disposal : “They comprised bronze saws over eight feet long, set with jewels, tubular drills similarly set with jewels, and circular saws.” (Petrie 1883)

Archeologists have found evidence of nearly all the same tool designs used by modern stone masons to work stone. Modern stone masons can use a variety of tools to cut stone: chisels with hammers, drills, lathes, planers, circulating saws and reciprocating saws. However, ancient stone masons did not have the same materials from which modern stone masonry tools are made; modern stone masonry kit is made of advanced materials, such as tempered steel, metal alloys and diamond tips. Tools, made of material available to ancient Egyptians, cannot explain how they cut hard stone on an industrial scale. “The methods used [by ancient Egyptian stone masons] to quarry hard stone, particularly granite, are debated” (Novokshchenov 1996).

(photograph: Francis)

Francis noted the extraordinary precision with which ancient Egyptian masons cut stone.

You can see long saw cuts going through this hard rock very quickly. In most cases it can be seen that the cut is straight and clean with smooth, consistently parallel sides - even at the start of the cut. They show no trace of the 'walking' or wobble that might be expected of a long hand pulled blade as it starts into a hard material. (Francis )

Authors typically allude to this mystery, rather than explicitly state the fact, that no modern tool design in use by stone masons, made from material available to ancient Egyptians (copper, wood and stone), has the cutting properties necessary to cut hard stone to the precision with which stones were cut by ancient Egyptian masons. The mystery deepens when one considers how the ancient Egyptians might have generated an ‘industrial’ scale output of cut stone. The scale has been the subject of studies that have tried to characterize it and make “an assessment of the industrial nature of the enterprise” (Ashton 1994)

A “centrifugal saw” is a tool that could have been used by the ancient Egyptians to produce an industrial scale output of high-precision cut stone. The “centrifugal saw” is a design not used by modern stone masons.  Nevertheless, “back of the envelope” calculations suggest a ‘centrifugal saw’ generates cutting forces comparable to those generated by a modern ‘diamond-tipped’ disc saw used to cut granite stone. It is also a tool made of material available to ancient Egyptians: emery copper, cured leather (or intestine) and wood. Moreover, a “centrifugal saw” could cut stone on an industrial scale, with a speed approximating that of modern saws. Another feature of the “centrifugal saw”s design, the outward force on its cutting blades would naturally produce smooth, straight cuts orthogonal to the machine’s axle (simplifying the process of producing perfectly squared, right angle blocks).

As stated, all of the materials necessary to build a Hand-Powered “centrifugal saw” were available to the ancient Egyptians.

The machine uses a series of wooden cogs to transfer (and perhaps multiply) the force of human labor to a rotating wooden axle, the machine’s core. This central axle is made from a cylindrical shaft of wood. Wood was available to ancient Egyptians. The machine’s cutting heads are made of emery copper attached to the central axle by braided cords of cured leather (or intestine). Cured leather (or intestine) has sufficient tensile strength to withstand the centripetal force generated by swinging a 1 kilogram cutting head around a 30 meter circle once a second. Emery copper has the hardness necessary to cut through hard stone. Emery copper is made of smelted copper mixed with quartz grains (sand) producing a tool “almost as hard as modern diamond-set tools”(Novokshchenov 1996), a process originally suggested by the famous Egyptologist W.F. Petrie (Petrie 1883).

Calculations show that the cutting force generated by a “centrifugal saw” is comparable to the cutting force generated by a modern, diamond-tipped disc saw. The “back of the envelope” calculations are based on a “centrifugal saw” designed to swing 1 kilogram cutting heads around in a circle 10 meters in diameter, once every second.

The circle has a circumference of 31.4 meters. The velocity of the cutting heads are thus 31.4 m/s.

The proposed means of attaching the copper cutting heads, cured, braided leather (or intestines) would have adequate tensile strength to withstand the centrifugal forces involved. The maximum centrifugal Force (F_c) of such a “centrifugal saw” is equal to the mass of the cutting head times the square of the velocity, divided by the radius: that is 197 Newtons (ie. kg*m/s²).

The cutting Force of the centrifugal saw can be calculated from the formula F = m(Δv/Δt), which is; the Force is equal to the mass times the change in velocity divided by the change in time.

The saw has a 30 m circumference and completes 1 revolution per second. Assume that it is in contact with the stone for 1 m of that revolution (about 3 feet), a time of 0.03 seconds. Assume that over these 0.03 seconds, the cutting head slows from 30 m/s to 28 m/s during its cut. Then, the tangential (cutting) force, F_t, will be equal to 1 kg, times 2 m/s, divided by 0.03 s: that is a cutting force = 60 Newtons (ie. 60 kg*m/s²). Comparing these calculations to data measured for existing (modern) granite stone saws suggest that such a maximum tangential force is more than sufficient to cut granite.

Segade et al measured force, including the tangential force, involved in a modern disc saw cutting granite. The study showed that tangential forces of between 10 N and 50 N were adequate to cut granite, when the cutting heads were rotating “at a speed of 30 m/s.”(Segrade 2010)

Such figures for tangential force suggest the eminent potential of the “centrifugal saw” to cut granite, and other stone, on an industrial scale.

A prototype of the suggested design cut through cardboard with ease - at the predicted rpm.

Photos of the prototype cutting blades:

A video of the prototype 

The question remains, if the potential to cut stone with a “centrifugal saw” is so promising, ‘why have such saws not been suggested by the archeological evidence?’

It could be argued that the Egyptians simply neglected to picture the saw in their images (drawn in tombs and cut on monuments), and that nothing remains to be found of the saws themselves. The lack of remains could be explained by arguing that the Egyptians surely recycled the precious copper cutting heads and the wood and animal cords would have decomposed long ago.

Regardless, work needs  to be done to review the archeological record for possible evidence of a “centrifugal saw”.

It may be that no archeological evidence has been found suggesting a “centrifugal saw” because none was sought. The shape of the cutting heads is unknown. But, it may be that the ancient Egyptians could have used the predictable shape of a ‘half-moon’ cutting blade. Above this they could have had two ‘wings’ to ensure the blades swung true. And, at the top they could have had a hole to attach the cord to the cutting head. A cutting head in such a form, or a representative of such a shape may exist in the archeological record, and not have been identified as a stone cutting tool.

Likewise, it is possible that the ancient Egyptians did represent a “centrifugal saw” in images and that archeologists did not recognize such images as a tool for cutting stone.

The modern process of cutting with a rotating disc saw, and the associated forces, are described by Segrade:

Segment cutting can be considered as abrasion at multiple contact points (diamond grains) at different passing depths. Only a few grains of diamond form part of the abrasion process on each pass. The main parameters for diamond disc cutting are, cutting speed, v_s, is the tangential velocity of the [cutting head] at the moment of cutting; feed speed, v_w, is the velocity at which the disc’s axle is moved relative to the rock; and pass depth, a_p, is the depth at which the disc penetrates into the rock at each pass.(Segade 2010).

However encouraging such figures, the process of cutting stone is complex and the calculations cannot be definitive. It is recognized that there is clearly need for real-world testing of the “centrifugal saw”.

Other caviates require further investigation and further elucidation in detail. The attachment of the copper ‘head’s to the leather (or intestinal) cord needs to be done in a manner that makes it strong enough to withstand tremendous centrifugal forces. The copper ‘head’s must be balanced to equalize the centrifugal forces.

References:

1.     Ashton, B.G. (1994). Ancient Egyptian Stone Vessels: Material and Forms. Heidelberg Orientverlag.

2.     Fonte, G.C.A. (2007). Building the Great Pyramid in a Year. Algora, NY.

3.     James, F.E. (2003). Building the great pyramid: Probable construction methods employed at Giza. Technology and Culture, 44(2), 340-354. Retrieved from http://search.proquest.com/docview/198436758?accountid=33851

4.     Novokshchenov, V. (1996). Pyramid power. Civil Engineering, 66(11), 50-50. Retrieved from http://search.proquest.com/docview/228530926?accountid=33851

5.     Petrie, W.M.F (1883). The Pyramids and Temples of Gizeh. London: Field and Taer.

6.     Segade et al (2010). The rock processing sector: Part II: Study of cutting forces. Dyna, 77(161), 77-87.

7.     Stock, D. (2003). Experiments in Egyptian Archeology: Stoneworking Technology in Ancient Egypt. Routledge. NY.

8.     Francis, R. Stone Saws. The Global Education Project. Retrieved from http://www.theglobaleducationproject.org/egypt/articles/hrdfact2.php