(Harald Mueller enquired whether the Triola roll speed I quoted was
an initial or average speed).

Harald, yes, you are right.  I measured the overall length and the
playing time, which gives the average speed.  As you say, the initial
and final speeds can be calculated from the length, paper thickness,
and the corresponding diameters, but I find I have to allow an extra
0.001" as an "air gap" between the turns in order to get the
calculations to agree with reality.

 [ Richard Tonnesen also found that the effective paper thickness
 [ increases, in part because of a 'dish' effect created by punching
 [ holes the paper.  -- Robbie

So here are some further measurements that I hope will be of more use
to you.

At the start of the roll, the opening phrase takes 12.81 seconds,
and is 400 mm long.  Near the end of the roll, perhaps 5500 mm later,
I played the same phrase in 12.84 seconds, but the length was 600 mm.
So we have an initial speed of 31 mm/sec (6.0 feet/min), and a speed
after about 5500 mm of 47 mm/sec or 9.2 feet/min.  The total length
of 6300 mm required 58 turns on the take-up spool and increased the
diameter from 1.00" to 1.65", implying a paper thickness of 0.0056".
The paper measures 0.0045", hence the "air gap" of 0.0011".  The
half-way point is at turn 33.

(Sorry about the mixture of units.  Australia converted to metric
about 30 years ago, but most of my tools are stuck in imperial units).

As a matter of interest, the gear ratio is 8:60, so the crank makes 435
turns at 175 RPM.  The plucking fingers make 6 strikes per crank turn,
so the tremolo rate is 17.5 strikes per second.

John Wolff
Melbourne, Australia.