Monday, August 25, 2014

A Better Way to Build a Pyramid?

The Egyptian pyramids are some amazing works of engineering. The biggest, the Great Pyramid at Giza, held the record for nearly 3,800 years as the tallest man-made structure in the world. What's astounding is that each limestone and granite block weighing up to eighty tons had to be dragged from quarries miles away, then hoisted up to 400 feet before finally being laid in place. 

Two of the pyramids at Giza. Image: Ed Yourdon via WikimediaCommons

Doing that for one stone takes an immense amount of manpower; repeating that for hundreds of thousands of slabs boggles the mind. The archeological consensus holds that huge crews of workers dragged the immense stones on sleds.

Maybe they should have tried rolling the stones is what Joseph West of Indiana State University is proposing. He and his undergraduate students Gregory Gallagher and Kevin Waters posted an idea on the ArXiv the other week for a simple way to roll a rectangle.
The idea is pretty simple: Lash a dozen thick logs around the stone to turn its rectangular shape into a 12-sided, dodecagon shape.

"Rolling them by trying to change the square shape into a round shape makes it easier to move," West said.

It's a pretty simple and elegant way to reduce the work needed to transport these blocks by fundamentally changing the dynamics of what's going on. When sliding a stone (or a stone on top of a sled) you have to overcome the static friction that the ground exerts on the block in the opposite direction you're pulling. How much force is needed is determined in a large part by the frictional coefficient of the two surfaces rubbing against each other. The higher the coefficient, the more force is needed to overcome the resistance and slide the block along.

Once the block is moving a different frictional force sets in, kinetic friction. It's the force that slows down a moving object when its sliding over a surface. Applying a lubricant can reduce the friction, and it does looks like the Egyptians used water to make it easier to slide the stones.

A large team of workers pull an enormous stone statute while one appears to pour water on the ground in front of
the sledge in this drawing of an ancient tomb painting. 

When rolling an object, static friction is actually really helpful. It's how a wheel grips the ground and keeps it from slipping like a car spinning out. There is still a number of forces acting against the rotating wheel, collectively known as rolling resistance. It's roughly analogous to kinetic friction, in that it works to slow down a moving object, but it's a different collection of forces working together.

West thinks that overcoming the rolling resistance of the giant stone blocks would have been easier than overcoming the static and kinetic friction of the stones. He and his students carried out a couple of small scale tests on blocks about 20 cm per side.

The team's small test block. Image: Joseph West

They measured how much energy they had to put into moving the rig over how far it traveled. West and his team found that they were on average as efficient as the very best reported result of the team that tested stones over wet sand.

Unfortunately, there doesn't seem to be much evidence that the ancient Egyptians used a system like this. A few archeologists have pointed to "rockers" discovered in ancient tombs that hint at such a roller system, but it's not really widely accepted.

"It’s a way they should have considered if they did not," West said. "Maybe this way could have potentially have been easier."

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