Earlier today, I wrote that if you ignored the increasing mass of paper on
the take-up spool, a piano roll that started at a tempo of 70 would be
traveling at a speed of 85 after 25 feet.  After arriving home, I checked my
notes.  The actual value I calculated was a tempo of 82.6.  Here is my
derivation:

I measured an empty take-up spool to have a circumference of 5.25".  After 41
rotations of QRS transparent white paper (circa 1970's), the circumference
had grown to 6".  The radius of the take-up spool was increasing by 0.00289"
with each rotation.

I then calculated that after 52 rotations, 24.8 feet of roll is wound on to
the take-up spool.  The circumference of the spool is now 6.2".  If we could
assume the take-up spool is still turning at 16 RPM, the roll would be
traveling over the tracker bar at a tempo of 82.6.  It seems that you would
be able to notice this change.  I can not.  Therefore, a significant amount
of this increase must be offset by the increasing mass of paper on the
take-up spool.

--Bill Jelen