The Universe of Discourse

Sat, 11 Mar 2006

On the manufacture of spherical objects
In an earlier post, I mentioned shot towers, which were used up into the 19th century for the manufacture of lead shot. The shot must be made spherical, or else it won't work properly when it's fired from a musket barrel; it will get stuck, or the expanding gases will blow past it and leave it in the barrel, or something of the sort. (Rifle bullets, in contrast, are very much not spherical. I would like to write an article about this someday, but at present that one statement has nearly exhausted my store of information on this fascinating subject.)

The manufacture of spherical objects is a nontrivial matter; hence the invention of shot towers. Molten lead is poured through a copper sieve at the top of the tower, and the resulting droplets are allowed to plummet to the bottom of the tower. (Incidentally, "plummet" is the most correct possible word here. It is derived from the Latin plumbum = "lead", and means "to fall like lead".) At the bottom, the droplets land in a tub of water. The congealed droplets are recovered from the tub and sorted for size; they are also sorted for roundness by being rolled down a large table. Insufficiently round shot are melted and dropped again.

This method is obviously only suited to the mass production of bullets; it makes lots of bullets of different sizes at the same time, and requires a giant tower. In one of the Laura Ingalls Wilder books, the author describes her father, Charles Ingalls, making bullets one at a time by the hearth. He would melt pieces of lead broken off a big chunk, and pour the melted lead into a spherical bullet mold. When the lead had cooled the bullet was turned out of the mold, and the sprue and flash trimmed off with a knife. I don't know for sure, but I imagine from the description that the mold looked something like the picture at the right. (All pictures in this article get bigger if you click them.)

Round bullets could also be manufactured by stamping. The picture to the left shows a Civil-war era bullet mold, shaped like a scissors. A cold lead wire was put into the end of the mold and the handles were closed. This cut the end off the wire and pressed it into a spherical shape.

[ Addendum 20070307: the bullet mold at right is probably used for casting bullets, not for stamping them. See this addendum for more details. ]

Simon Cozens inspired this article by writing to inform me that shot towers were also used to manufacture ball bearings. (But what were the bearings made of? I don't know. I imagine that lead ball bearings would deform too easily to be useful. ) Modern ball bearings are manufactured by a casting process, followed by machine polishing to remove the flash and any imperfections.

When I was in college, my professor brought to my attention the famous stone spheres of Costa Rica. These spheres range in size up to seven feet in diameter. He asked me to think about how the spheres might have been made. It is not clear, by the way, how close to spherical they actually are. Supposing that they really are nearly spherical, I have an educated guess, but I'm going to work around to it. In the meantime, you might like to puzzle about this yourself. The spheres were probably made sometime between 800 and 2200 years ago, so you are not allowed to use a CAD system.

When you make a submarine, it's very important that the hull be as exactly circular (in cross-section) as possible, so as to distribute the water pressure evenly. How do you make sure that your submarine hull is not deviating from the ideal of circularity? The first thing that was tried was to measure the distance across the hull in all directions, to make sure that all the diameters had the same length. Shapes with this property are said to have constant width. The first submarines the Germans made using this technique buckled and collapsed when they were subjected to high pressures. Why? Because they weren't circular! Circles do have constant width, but there are many other shapes that also have constant width; the shape to the left, known as a Reuleaux triangle, is an example. Constant width is no guarantee of circularity.

The Germans eventually solved the problem by making giant wooden forms and comparing the submarine's hull to the wooden form as construction progressed. It's easy to make a two-dimensional wooden form: take a big piece of wood, drive in a nail, tie a string to the nail, and draw a circle around the nail. Then cut out the circle and throw it away, and cut the remaining piece in half; you now have two semicircular forms, as large as you want. If you try to fit the form around the outside of the submarine, you will immediately see whether the hull deviates from circularity. I believe this technique is still used for submarine hulls.

I suspect that the Costa Rica spheres were made similarly. You start with a big lump of rock, a chisel, and a semicircular form of the appropriate size. Then you start chiseling at the rock, checking it for circularity by fitting the form to it, and cutting away the parts that don't match. The only difference from the submarine is that you need to check for circularity in multiple planes. You can do this by rotating the form around the point you are working on. The Costa Ricans can't make their forms out of sheets of plywood, of course, but they should be able to make them out of something.

Baseballs are made spherical by a completely different process. The outside of a baseball is a leather cover, most of a baseball is made of yarn, which is wound around a cork until the baseball is the correct size. The tension in the yarn makes the yarn want to move inward, toward the center of the ball. If part of the ball of yarn is too narrow, then that part is closer to the center and the subsequent yarn will tend to to move there, evening it out. Rubber-band-balls are spherical for similar reasons.

Billiard balls were originally made either from wood or were cut whole from elephants' tusks. I don't know how they were made spherical, although the wooden-form technique seems likely to work. Modern billiard balls are cast in molds and then polished.

[ I discussed some other round objects, including gumballs, marbles, and pellets of taconite ore, in a followup article. ]

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