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Scale Problems Again

That’s a very big stove.

To be more precise, that’s a wood replica of a stove, created by the Michigan Stove Company for the 1893 World’s Fair in Chicago and displayed after the fair ended at the company’s headquarters in Detroit. It supposedly weighed 15 tons and, amazingly, survived until 2011 when a lightning strike burned it down. The photo makes it look approximately the same height as three stories of the adjacent factor, or about thirty feet high. Paul Bunyan comes to mind. But there’s one obvious question: this was an ad for a company making cast-iron stoves, so why was it made of wood?

I’ve talked about the square-cube law before, both seriously and in the context of movie reviews. In short, there are structural problems when you take an object (or a creature) and increase its size without changing its proportions. In the case of this stove, there are a number of such problems. Here’s the first one that jumps out at me: the span from leg to leg. If the stove is 30 feet high, the long side is maybe 40 or 45 feet from leg to leg. Moment goes up by the square of the distance, so if the stove is, say, ten times the size of the real thing, the moment mid-span would be a hundred times bigger than in a real stove, except that the weight is also increasing more than linearly because the stove has got wider as well. If the stove is ten times bigger its weight has gone up by a thousand times and the sides won’t span properly any more. And the weight on the feet would be enough to punch through whatever it’s sitting on. And so on.

Building the replica out of wood reduced the weight and also meant that the big stove was not actually built like a stove. There could be wood trusses hidden in the sides, sheathed in wood plank made to look like the iron sides of a stove. The weight savings may have gone further than expected: if you look closely there are a bunch of guy wires connecting the underside of the stove to the ground. A big empty wood box this size would have a tendency to blow around a bit in the wind. In other words, a wood stove this size has scale problems from being too light, just as an iron stove this size would have scale problems form being too heavy. There’s a Goldilocks reference waiting to be made.

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