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I went to Colonial Williamsburg a couple years ago and asked the cooper how the hell they get all the angles correct on the staves to get a water tight barrel, and the woman said that you just do it. It's muscle memory and done by eye. It's astounding to me because they had to make these barrels to very precise tolerances because they were legal measurements in commerce. Being off by 5% in volume when making the thing meant that either a buyer or seller was getting screwed during a transaction. I'm still not satisfied with her answer.
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