# Using a Square Wheel

Huge amounts of intellectual horsepower have gone into trying to figure out how the ancients built giant stone structures like the Pyramids or Stonehenge. Over the past 200 years archeologists, engineers and physicists have all chipped in to try to solve the problem.

They should’ve asked a retired construction contractor from Michigan.

I find the part where Wallington rolls a 300 lb block like a log especially interesting. He’s using a square wheel. Over the years, I’ve seen lots of discussions of square wheels as geometric oddities or sources of humor but it never occurred to me, or apparently anyone else, that you could use a square wheel to roll a heavy square block as if it were a cylinder.

I’m sure the ancients had a lot more work cutout for them than Wallington’s experiments show. For example, they would not always have had smooth and level hard surfaces to move things one. Yet, it’s easy to see how the basic ideas could be used in almost any environment with a little work, like laying down paving stones.

On a related note, have you ever wondered how you go about drilling a square hole?

### 7 thoughts on “Using a Square Wheel”

1. I had the privilege of meeting Arthur Bishop, the inventor of variable rack ratio steering, some years ago. He had a model of the steering system on display (see the link). It’s sort of a higher order square wheel.

2. …have you ever wondered how you go about drilling a square hole?

That triangle rotating in a square looks suspiciously like the action of a rotor in a Wankel engine…

3. Blacque Jacques Shellacque ,

That triangle rotating in a square looks suspiciously like the action of a rotor in a Wankel engine…

Yes, the rotor in a Wankel engine is a Reuleaux triangle.

4. The first reference in the wikipedia article discusses the problem of drilling a square hole….

http://upper.us.edu/faculty/smith/reuleaux.htm

You miss the corners, and need your point of rotation to move around quite a bit. I’m not that familiar with what it is practical to get tools to do, but I’m a bit skeptical about drilling square holes this way….

5. The bit itself has to oscillate around its own center to get a square hole. It’s not perfectly square of course, but it’s pretty damn close.

6. The tag line at the end is quite apt.

There is a special drill bit used by wood workers to make square holes. However, it does not make use of a Reuleaux triangle, clever though it may be. Rather, a conventional drill bit in combination with a hollow, square-shaped mortising chisel is used. In practice this sort of thing proves to be far more practical than the seeming elegance and simplicity of the Reuleaux triangle.

Wallington’s techniques are indeed clever as well, but there is no evidence that Stonehenge was built this way. Nor even that his techniques are the most practical. It may seem extraordinarily efficient to use a technique that allows a single person to move a giant stone piece, but this is deceiving. There is considerable inefficiency in the amount of time required for setup and movement using such complex techniques. If you have dozens of individuals available to help, you may be able to do the same work using less sophisticated techniques in much less time and with much less preparation. Indeed, the differential may be great enough such that the total man-hours used for the move may be less for the brute force method.

Given that it’s fully possible to erect a structure like Stonehenge in a very reasonable amount of time with a very reasonable amount of labor (as proved by NOVA, for example: http://www.pbs.org/wgbh/nova/stonehenge/), I have a hard time believing the builders of Stonehenge would have spent much time trying to figure out more complex techniques to finish a task that was already within their grasp let alone that they would have considered delaying completion of construction in order to save labor effort.

7. Robin Goodfellow

There is a special drill bit used by wood workers to make square holes.

A mortise chisel does not work in hard metals. Machinist use a drill bit based on a Reuleaux triangle.

There is considerable inefficiency in the amount of time required for setup and movement using such complex techniques

Not really. His method of raising the stone vertically is lot quicker than running dozens of strong ropes under a monolith and then marshaling several hundred people to pull on the ropes. This is doubly true when you consider the logistics of housing and feeding a large work crew under primitive conditions. It is also less likely to fail and kill people or break the stone.

Wallington can do the vertical lift of the monolith in just a day working alone. I don’t think that is very much slower than a rope method. If he had a team of a dozen people, he could go much faster.

I have a hard time believing the builders of Stonehenge would have spent much time trying to figure out more complex technique…

Well, they would have centuries of experience figuring out how to move stones, starting small and working their way up, before they tackled a large project. They would have these techniques as part of their stone working repertoire before they even took the project under consideration.

I don’t think we’ll ever know for sure how Stonehenge and other such structures were built unless we uncover a lot of new archeological evidence. But we can say that Westerners, because of our historical availability of large draft animals and steam engines, have a bias towards methods that use brute force to move things. Other cultures without these power advantages develop more subtle techniques to work around their lack of power.

Modern reconstructionist tend to view such problems through our power-centered model. We also tend to think that our knowledge base completely encompasses that of the ancients i.e. they didn’t know anything that we don’t know.
Wallington’s work shows that this is not true. There are techniques that we have never considered. Archeologist will have to factor his work into their models of how the ancients built.