“Like A Rolling Stone”
The Success of Failure /VITRUVIUS/ Petroski, Henry "The Success of Failure"
Rolling a 50 tonne stone up a 1 in 4 slope would require about 200 men, or some 50 men on each rope if four cradle runners were used. It is likely that up to eight cradle runners could have been fitted to reduce the number of men per rope and to give better rolling properties. The real possibility that the King’s Chamber beams were raised by rolling (and certainly no more feasible method has yet been proposed) leads to the intriguing question whether other ancient societies also knew of and used this technique. The reference by Vitruvius to the attempt by Paconius to roll a 40 tonne plinth clearly suggests this possibility. It is very tempting, too, to believe that the huge sarsens at Stonehenge could have been brought the 20 miles from Marlborough Downs by rolling. Ancient Achievements in Masonry Construction One of the great achievements common to a number of ancient civilisations was their ability to quarry, transport, raise into position and place every large stone blocks for the construction of structures such as tombs, temples and defensive walls. They also had the ability to transport huge statues and obelisks. Given enough human or animal power, strong enough ropes and sufficient time and motivation, stones of up to several hundred tonnes could undoubtedly be moved; and, indeed, there are famous Egyptian and Assyrian illustrations showing huge statues mounted on sleds being dragged along by large numbers of men. While conceding that brute force was frequently used to move and raise large stones it is also likely that some ancient civilisations developed more subtle and high-tech method of accomplishing these tasks. Although chronologically one of the more recent of the "ancient civilisations" the achievements of the Incas in moving and raising heavy stones are still breathtaking. Masonry walls of perfectly matched polygonal blocks characterised Inca masonry, and substantial remains of such walls can still be seen at the stronghold of Sacshuaman overlooking Cuzco, built in the 15th C. The largest blocks have main dimensions exceeding 5m and weigh well over 100 tonnes. While some of the masonry blocks came from nearby limestone and diorite quarries, blocks of land site came from quarries separated from the site by 20 km of rough terrain with steep slopes. According to Garcilaso, the son of an Inca princess and a Spanish conquistador, writing in the second half of the 16th C, it required 20,000 men hauling on large cables to move the larger blocks. As Garcilaso left Peru for Spain while still a youth, his account must be treated with some caution, as should his statement that on one occasion a block broke loose and rolled back down the hill killing 3000 people. The stonework in the walls and tombs built by the Mycenaens around 1500 BC led the Greeks to believe that the enormous blocks of stone had been raised by one-eyed giants, the Cyclopes, making this name synonymous with this type of construction. One stone, forming an inner lintel in the Treasury of Atreus, is estimated to weigh 120 t. Unlike the Inca walls the huge cyclopean blocks were at best only partly dressed and often not dressed at all, with small stones or clay filling the gaps. Where appropriate, however, such as in the surrounds of the Lion Gate entrance to the citadel to give it added dignity, they used large symmetrical blocks carefully dressed by hammer and cut by saw. Transporting and Raising Pyramid Stones – Sleds and Other Unlikely Methods The seven major Egyptian stone pyramids differ in one very important way from other ancient megalithic structures, namely the huge number of stones making up the structures. Each pyramid was constructed in a relatively short period of time. The Great Pyramid of Cheops, the fifth in the sequence of major stone pyramids, contains some 2.3 million limestone blocks weighing on average 2.5 tonnes each and up to 7.5 tonnes, which are believed to have been placed in a period of about 20 years. This means that the stones had to be placed at an average rate of one every two minutes during all the daylight hours over the construction period. This required not labour intensive brute force, but a high-tech solution. Many methods have been proposed for raising the stones, including the use of levers and the use of rockers as proposed by Petrie, the "Father of Egyptology". These methods would have been much too slow, extremely hazardous and provide no answer to the equally exacting task of transporting the stones from the quarries to the site, in some cases having to cross the Nile. They also could not have been used to lift the massive granite blocks of the King’s Chamber. Most writers on the pyramids assume sleds were used to transport and raise the stones to their final position, but sleds are highly inefficient and likely to have been used only for "one-off’ operations to move large, often awkward shaped objects, where speed was immaterial. The large mass of humanity pulling the sled would simply have emphasised the importance of the person whose statue, obelisk or sarcophagus was being moved. It would not have been practicable to have used rollers or lubricated tracks under the sled runners to transport pyramid stones as a large number of stones had to be on the move at any one time, originating from different locations in the quarries and ending at different positions in the pyramid. Quite simply, sleds could not have met the demanding logistics of pyramid construction. Even the most ardent sled apologists recognise that ramp slopes greater than one in ten could not have been used for sleds, and it is impossible to design a ramp system with this slope which does not dwarf, or even engulf, the pyramid itself. The Mechanics of Sliding and Rolling An efficient way to move a heavy object is to roll it (Cotterell and Damminga 1990), but this requires it to be cylindrical in shape or able to be fitted with circular runners. In theory, a centrally balanced cylinder on a perfectly elastic level surface can be rolled by applying any horizontal force, no matter how small, at its top, in a direction normal to its axis. Sliding the same object, sled mounted or otherwise, requires a sufficient force to overcome friction between it and the underlying surface. For example, for a realistic coefficient of friction of 0.25, a 2.5 tonne stone would require a pulling force of 0.625 tonnes to slide it, which would require about 25 men assuming each could pull with a sustained force of 0.25 kN. The same stone, on circular runners can readily be rolled by two or three men. If a block of weight W is pulled up a slope with angleß to the horizontal the forces acting on the block parallel to the slope are as shown in Figure 1. Fs and Fr are the frictional forces. If the coefficient of friction is µ, the forces the Ps and Pr required, respectively, to slide and roll the block up the slope are given by: Sliding Ps = W (sinß + µcosß) Rolling Pr = 0.5 W sinß If µ = 0.25, the force required to roll a cylinder up a slope is 1 of 4 (ß = 14°) is only one-quarter that required to slide a block of the same weight. it is of interest to note in Figure 1 that in contrast to the sled the frictional force on the rolling cylinder acts up the slope and assists in raising it. Cradle Runners Structures as remarkable as the pyramids could only have been built by people of high intelligence. They would surely have hit on the almost intuitive fact that rolling provided the most efficient solution to transporting and raising megalithic blocks. Writing 2000 years after the construction of the great pyramid Herodotus mentions the use of "contrivances made up of short pieces of timber" for raising the stones, a description which fits very well the cradle-like device shown in A large number of these were found last century by Petrie in New Kingdom temple foundation deposits. This example in the MMA, New York, is 235 mm long and is clearly a model of a prototype device used in the construction of the temple, as it was found with small models of other construction tools. Although dating from 1000 years after the construction of the Great Pyramid, Petrie believed that prototypes could have been used in pyramid construction, but it is unlikely to have been used to "rock up" the stones as suggested by Petrie. The curved edges of the side pieces form quarter circles and four of these attached to a square section block create a circular runner. Two such runners allow the block to be rolled, either by pushing from behind to propel it along a level surface or by pulling on ropes coiled around the dowels connecting the side pieces to negotiate a ramp. Model and Full Scale Tests Model tests performed by the writer, see Figure 3, have shown that a small concrete block, 107 mm square by 2 1 0 mm long and weighing 50 N (5.1 kgf) fitted with cradle runners could be pulled up a 1 in 4 slope by two thin strands of cotton. The same block on a wooden sled could not be pulled along a smooth wooden level surface by two strands of the same cotton. The efficacy of the technique has also been shown by full scale tests with concrete blocks 0.8 m square by 1.6 m long and weighing 2.5 tonnes. These tests were carried out by the Obayashi Corporation at a site near Tokyo, rolling a block along a level road surface and up ramps with slopes of 1 in 1 0 and 1 in 4. It was found that two or three men could easily roll a block fitted with cradle runners along a level compacted stone surface by pushing from behind, while sixteen men could haul the block up a 1 in 4 ramp by pulling on ropes coiled around the cradle dowels, taking about one minute to negotiate the 15 m length of ramp. Figure 4 shows the latter operation, in this case employing 18 men. The model tests and full-scale tests confirm that rolling the stones in this way could have been the method used, both to transport the stones from the quarries to the pyramid building sites, and for raising them up ramps with slopes as steep as 1 in 4 to their final positions. Certainly no other method would have been as economical in the use of manpower. Rolling Irregular Shaped and Larger Stones It is pertinent to ask if the method could have been used for rolling stones not having a square cross section, and for stones of much larger size than the average 2.5 tonne stones making up the Great Pyramid. Stones with a regular rectangular cross section present no problem, as equal size filler pieces could be used at each end of the cradles on the longer faces, and full scale tests of this type were carried out in Tokyo. Less regular shapes could be fitted with cradles by using variable size filler pieces, but extremely irregular shapes would be difficult to accommodate. Many ancient civilisations proved themselves capable of transporting huge megaliths commonly up to 40 or 50 tonnes, and there are stones of this size at Stonehenge, Mycenae, various Inca structures such as those at Sacshuaman and Ollantaytambo and in many Egyptian structures, not least in the roofing over the King’s Chamber in the Great Pyramid. Although speed of transport would not have been a factor in moving these megaliths it would still have been advantageous to have moved them by rolling if possible. A 17th C Jesuit priest recorded having seen blocks rolled up earthen ramps used in the construction of Cuzco cathedral, built using traditional Inca methods. Vitruvius describes the efforts of one Paconius to do just this in attempting to transport a 40 tonne plinth for a statue of Apollo. According to Vitruvius, Paconius encapsulated the ends of the stone block in wooden "wheels" 15 feet in diameter, then linked these with 2 inch crossbars at intervals around the rims to form a slatted cylinder. He then coiled a rope around the bars and, as anticipated, when pulled by oxen the rope uncoiled and moved the stone, but it proved unmanageable and swerved from side to side. This probably occurred because he used only a single rope and, worse, it was probably the rope and not the crossbars which contacted the road surface. This problem did not occur in the Tokyo tests. It is possible that this method of transporting large stones was common in the ancient world and Paconius had heard of it, but simply failed to apply it successfully. A method known as parbuckling has traditionally been used, perhaps for hundreds of years, to lower beer barrels down ramps into beer cellars, and it has been suggested that this method could have been used to raise heavy stones up ramps. It was proposed, for example, by Thomson 1954 as the method by which the lintels at Stonehenge could have been drawn up earthen ramps to rest on the uprights, In order to raise a stone by this method, two haul ropes fixed at the top would be run down the ramp, looped around the stone, and the stone rolled up the slope by hauling on the free ends, Raising the Granite Beams over the King’s Chamber By using dedicated ramps (Parry 1995) it is conceivable that the large granite beams over the King’s Chamber, situated at mid-height of the Great Pyramid, could have been raised by rolling. The largest beam has dimensions 1.3 m by 1.8 m by 8 m and weighs about 50 tons. The limiting factors on the use of cradle runners would have been possible crushing of the wooden rims of the cradles on very hard surfaces, or traction problems on softer haul tracts due to the cradle rims sinking into the surface. Tests of these two factors, particularly the latter, were included in the Tokyo programme, by running the 2.5 tonne blocks on three surfaces: lightly compacted crushed stone (California Bearing Ratio = 12), more heavily compacted crushed stone (CBR = 57) and steel decking. Elastic equations are available in the literature to calculate stresses and displacements of a loaded disc resting on a plane rigid or elastic surface. A very approximate estimate can also be made relating elastic modulus of a road surface to CBR. The total width of the four rims on the two cradle runners on the Tokyo blocks was 0.3 m and assuming typical softwood properties for the cedar wood used for the cradles, calculations indicated that on the compacted stone surfaces elastic stresses in the wood would not be exceeded and deflections of the road surface would be very small – about 2 mm for the lightly compacted surface and much less for the more heavily compacted surface. Although hysteresis in "elastic" behaviour can give rise to small traction forces, it was felt unlikely that such small deflections would have any measurable influence on the rolling of the stone. This proved to be the case and it was not possible to distinguish between the effort required to roll the blocks on the two different compacted surfaces. Similar calculations indicate that a 50 tonne stone could be rolled over a moderately compacted crushed stone surface, using four cradle runners each with rim widths of 1 00 mm. Rolling a 50 tonne stone up a 1 in 4 slope would require about 200 men, or some 50 men on each rope if four cradle runners were used. It is likely that up to eight cradle runners could have been fitted to reduce the number of men per rope and to give better rolling properties. The real possibility that the King’s Chamber beams were raised by rolling (and certainly no more feasible method has yet been proposed) leads to the intriguing question whether other ancient societies also knew of and used this technique. The reference by Vitruvius to the attempt by Paconius to roll a 40 tonne plinth clearly suggests this possibility. It is very tempting, too, to believe that the huge sarsens at Stonehenge could have been brought the 20 miles from Marlborough Downs by rolling.