Does the inner dimension of an iron doughnut increase or [Editor: "of" in the original] decrease when the...

[ Editor: It increases: the hole expands along with the metal. ]

With all of the discussion and all the theories and all the guesses,
hasn't anyone actually gone out and tried it, or is that cheating?

In high school physics we had a small sphere on a rod and a ring also
on a rod.  The ring could just pass over the sphere.  One experiment
that the teacher did was to heat [Editor: "head" in the original] the sphere and sure enough the ring
could no longer pass over the sphere.  A second experiment that he did
(on a different day, and no, the sphere was not still hot) was to take
a different ring, this one so small that [Editor: "it" added] could not pass over the
sphere.  He heated the ring and, sure enough, the heated ring could
easily pass over the sphere.

If anyone has ever watched a cooper, the way they get the iron barrel
hoops tight is to heat them, pound them in place and then let them
cool.  They tighten up as they cool.

-- Bert Sheldon <berts@empros.com>

[continuing discussion on iron hoops, coopers, and repairing wagon
wheels]

The comment on repairing wagon wheels, where an iron hoop is heated,
then placed around the wooden wheel, then let to cool and shrink
reminds me of the method followed in replacing automobile engine 'ring
gears' around the flywheel.

To quote my Haynes manual ...

   To fit a new ring gear, heat it gently and evenly with an
   oxyacetylene flame until a temperature [Editor: "tempurature" in the
   original] of approximately 350C (662F)
   is reached.  This is indicated by a light metallic blue surface
   colour.  With the ring gear at this temperature, fit it to the
   flywheel [snip].  The ring gear should be either pressed or [Editor: "of" in the original] lightly
   tapped onto its register and left to cool naturally, when the
   contraction of the metal on cooling will ensure that it is a secure
   and permanent fit. ...

Now, why didn't I remember this before?

-- Michael Bayrock <mbrock@gov.nt.ca>

I believe that the hole gets bigger.  The way I think about it is this:
suppose you have a disk that fits perfectly inside the ring.  When you
heat the system, the inside disk expands, but if we think about the
system as one connected disk there should not be any stresses between
the ring and the disk.  So we should be able to slip out the expanded
disk, and we have the ring, heated, with a larger aperture.

-- David Savitt <dsavitt@unixg.ubc.ca>