Importance of being round
On January 28, 1986 the shuttle Challenger exploded 72 seconds after the lift-off. All seven astronauts perished in the explosion. Who does not remember this horrible disaster? Next to this memory, I have stored the famous, broadly televised presentation of Richard Feynmann's experimental demonstration. It was so simple, one could not help but wonder why it took a Nobel Prize winner to point out a weak point in the shuttle design. A compressed piece of rubber, after being released, is expected to jump back to its original shape. Feynmann showed that, with falling temperature, rubber is liable to lose its elasticity. Until recently I believed this was the explanation for the Challenger disaster. A chapter (Space Shuttle Geometry by H. Moore) in a book edited by David F. Hayes and Tatiana Shubin showed the situation was more complex and mathematics is more relevant.
The cause of the accident was determined to be the failure of a seal on one of the boosters attached to the shuttle. The defective seal let the fuel leak which caused the explosion. Three factors were found to contribute to the seal failure: poor booster joint design, slow o-ring response, and out-of-roundness.
The shuttle is attached to two boosters and a fuel tank which drop off after the fuel is used up. The boosters are made up of several cylindrical metal pieces that are joined together. The place where the pieces fit together is called a joint. The joint bulges outwardly during the lift-off due to the large forces inside the booster.
The first factor - the booster joints - have been redesigned to minimize their tendency to bulge out.
The o-rings are thin rubber rings that serve as washers. They are usually compressed between metal parts. They are supposed to fill up gaps whenever those appear. Due to the freezing temperature at the site of the launch, the o-rings lost their elasticity and did not fill a gap fast enough which led to a fuel leak. This was what Feynmann's impressive demonstration was about. Since the Challenger disaster, shuttles no longer launch in freezing temperatures. But their was yet a third factor to consider.
After a launch, the boosters are fished out of the ocean, taken apart, and the pieces reconditioned. Each part is examined to ensure their roundness. NASA's test for roundness was to find three diameters of the cross section and verify that the three were equal.
It does not take a Nobel Prize to realize that NASA's test was absolutely unreliable. There are two meanings to the word diameter. First, the diameter of a plane figure is the longest distances between any pair of its points. Second, this is a line segment joining such a pair of points where the longest distance is achieved. A circle has infinitely many diameters, an equilateral triangle has three (each of its sides), a regular hexagon also has three diameters (the diagonals joining the opposite vertices), any other regular n-gon with
Actually, any figure of constant width passes NASA's test with flying colors. And they are many.
So NASA has changed its roundness' test. On the new test, a booster pieces is placed inside a circular tube, probably with some kind of alignment, and several measurements are taken of the distance between the tube and the border of the booster piece. These need all be equal for the piece to pass the test.
Far as I can see, NASA has to compare a huge number of measurements to ensure a reasonable approximation to roundness, because shapes of constant width formed with a reasonably large number of generating segments would easily pass the new test.
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