Wouldn't the dodecagon solution put even more stress on the roads than the curved blocks? There's the same weight on the roads, but spread over a small end-of-two-poles, rather than a large surface-of-curved-block, so much greater pressure and therefore much more road damage. Andy On Wed, Aug 27, 2014 at 10:02 AM, Henry Baker <hbaker1@pipeline.com> wrote:
FYI --
https://medium.com/the-physics-arxiv-blog/how-they-should-have-built-the-pyr...
The Physics arXiv Blog on Aug 26
How The Ancient Egyptians (Should Have) Built The Pyramids
Modifying square blocks to form dodecagons would have made them easy to roll, say physicists
The Great Pyramid of Giza in Egypt is the only one of the seven wonders of the ancient world to survive largely intact. Almost 4000 years old, it is a vast structure constructed from 2.4 million limestone blocks, most about 2.5 tonnes but some weighing in at up to 80 tonnes. These were largely sourced from local limestone quarries.
That raises a famous question. How did the Egyptians move these huge blocks into place? One theory is that the blocks were dragged along the sand which offers reduced friction when lubricated with water. But although the Great Pyramid is close to the Nile, many pyramids are not and this would have made the transport of water as big an engineering task as the movement of the blocks.
Another theory is that the Egyptians attached quarter circle rockers to the flat surfaces of the blocks effectively turning them into cylinders and allowing them to be rolled. Experiments have shown that this method allows the blocks to be moved relatively quickly with just a few men.
But this method also has a disadvantage— these cylinders would exert huge pressure on the ground causing considerable damage to roads. Modern estimates of the rate at which the pyramid was built suggest that workers put in place some 40 blocks per day. In that case, even well-engineered roads would have required considerable maintenance.
Today, Joseph West at Indiana State University and a couple of pals suggest an alternative method for moving giant stone blocks. Their approach considerably reduces the ground pressure but at the same time allows the blocks to be moved with significantly less effort than dragging. They have even tested the idea to measure the amount of force workers would have had to use to move the blocks.
Their idea is remarkably simple. They strap wooden rods to a block, turning its profile from a square into a dodecagon, which can then be moved more easily by rolling.
West and co have tested their idea on a scale model consisting of a concrete block the shape of the square prism. This block was 20 cm square, 40 cm long and weighed almost 30 kilograms. They attached a set of three wooden dowel rods to each face of the block transforming its cross-section from a square to dodecagon.
Finally, they attached a rope to the top of the block and measured the force required to set the block rolling. Their measurements indicates that the block experiences a coefficient of dynamic friction equal to 0.3, for a steady rolling motion. This would require the crew to apply force of only 0.15 times the weight of the stone to pull a rope wrapped around the block.
They go on to calculate that a work crew of around 50 fit men would be required to move a block with a mass of 2.5 tonnes at the speed of 0.5 metres per second. “For full scale pyramid blocks, the wooden “rods” would need to be posts of order 30 cm in diameter, similar in size to those used as masts on ships in the Nile,” say West and co.
Of course, these researchers do not address the question of whether there is any evidence that the pyramids were constructed in this way, only that this would certainly seem a good option, not least because of the reduced wear and tear on the thoroughfares to and from the pyramid. Indeed, they say the mechanism would work without a formal, engineered road.
That’s an interesting, simple idea that might pique the interest of Egyptologists. Indeed, West and co say this idea, or something like it, needs to be studied in more detail. “It would seem that some variation of rolling the blocks should now be considered to be among the “best” and most likely method used to move the stones for the great pyramids,” they conclude.
A project for an Egyptologist with a little spare time.
Ref: arxiv.org/abs/1408.3603 : How They (Should Have) Built The Pyramids
http://arxiv.org/abs/1408.3603
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