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In article ,
says...
In article ,
Ned Simmons wrote:

In article ,
says...

Making the race heavier doesn't help, because while the cross sectional
area (and thus strength) increases, so does the weight (and thus outward
force). My recollection from discussions of energy-storage flywheels is
that these effects cancel more or less perfectly, so all that matters is
the strength-to-weight ratio of the material from which the outer race
is made. Only hoop stress matters, so storage flywheels are often made
of boron fiber.

Yes, the stress on a rotating thin cylinder is dependent only on density
and peripheral speed.

What alloy are bearing races made of? What's the tensile strength?

By far the most common material is AISI 52100, UTS is around 300,000
psi. I don't believe that centrifugal force alone is enough to burst the
bearing race. I figure a peripheral speed of around 1700 FPS would be
required to reach 300 ksi stress. That's close to 2x the speed of sound,
almost 20 miles/second, or about 250,000 RPM for a common 6203 (17x40mm)
bearing. (Those numbers may be a bit high, depending on how chunky the
bearing is, i.e., how far it deviates from a "thin cylinder.")

I doubt that the airstream from a hand blowoff nozzle is supersonic, so
twice this speed might be hard to attain.

Exactly.

My recollection is that in rocket engines, the flow "chokes" (speed
limited by the speed of sound) in the throat of the engine, and then
goes supersonic only while expanding in the bell.

Blowoff nozzles have a throat, but no expansion bell.

I suspect that lubrication failure leading to galling of the balls and
consequently jamming is the big culprit. Perhaps the race expands enough
from the centrifugal force to rattle around and hasten the failure, but
it seems unlikely to me that it's possible to get the bearing spinning
fast enough for this to be much of a factor. The strain in the
hypothetical 6203 race would be about 0.15% at 100 KRPM - in other words
the bearing might loosen up a thousandth or two at that speed.

This mechanism would have a hard time managing the very precisely
symmetric explosions we have heard reported, so uniform that the finger
isn't torn off.

I didn't see any claims that the explosions of the bearings were
symmetric; in fact, if they were perfectly symmetrical there would have
been no finger injuries at all, and Eric and Leon would have been
tempted to repeat their experiments g. I don't have any idea how much
energy is required to sever a finger, but I'm sure a bearing race
spinning at tens of thousands of RPMS is up to the job *if* the finger
is restrained and the bearing can't leave the finger. And while a broken
or severed finger doesn't seem an unreasonable outcome, it also seems
plausible that the impulse of the disintegrating bearing could slew your
whole arm around til your finger is in an orientation where the bearing
slips off. The velocities are vastly different, so it's not a great
analogy, but think of the difference between hitting your finger with a
hammer while it's on the workbench as opposed to while it's held out at
arm's length.

Ned Simmons