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I worked on the Hubble (my dad was systems manager for Perkin-Elmer's bid), on the ball bearings. They are literally the ones that were rejected from the spy sats.

The spy sats bought a bunch of ball bearings (these might be a foot in diameter and are speced to be extremely low noise at low turn rates). They tested them all (using a phono needle resting on the outside of the bearing while it was slowly turned). The ones that made the least noise went in the sat while the others were sealed in a plastic bag and put on a shelf in the clean room.

I was told that when Hubble came along, the US no longer had the capability to make those (I'm not sure if that was true). In any event the ones that went in Hubble were the least noisy of the ones that had sat on the shelf. My summer job was (largely) testing to see which was the best. A cool job.

In a product design class, the prof asked us to draw the distribution of resistors in a bag of, say, 5-ohm resistors, bought from a local electronics shop.

It turned out that a normal distribution centered at 5 ohms was not quite right. It was a normal distribution, but with a deep notch taken out right at 5 ohms. All the resistors that tested to very close tolerance had been bagged separately, and sold at a higher price.

(The context was why you might want to put, say, four 5-ohn resistors in series, rather than just use one nominal 20-ohm resistor.)

I hope your product design class covered error propagation, because one 1% 20 ohm resistor would still be cheaper and more precise than 4 5% 5 ohm resistors.

But four 5%-tolerance 5-ohm resistors could be chosen to add up to almost exactly 20 ohms, but a 20-ohm resistor would never be 20 ohms due to the notch.

In the old days, it might have been cheaper than the more accurate resistors. These days, high precision resistors are relatively inexpensive.

I think his point was that it would be better assuming you used the same "grade" resistor.

Apparently you can take an off the shelf resistor and 'tune it' by sanding the exterior, so to increase it slightly.

But of course it's better when the tolerance doesn't matter (or only of a few components)

That'd work for a bare piece of wire, but a resistor is covered with enamel.

Unless you sand enough to go through the enamel and reach the conductive surface

how heavy were the bearings?

I remember them as being between the weight of a pack of cards and that of a dinner plate. I don't believe they were titanium - I'd guess they were stainless. Again, perhaps 10-12 inches in diameter and nothing in the middle; they were just the two races and the balls in between. For the fine guidance sensor.

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