Roll acceleration is easy to do if you try to do it.  It's a linear
factor of the length of paper wound onto the spool; if the spool turns
at a fixed rate, the circumference of the spool increases by the amount
of paper built up.  The factor for a typical roll is about 0.01% per
linear foot.

Some parameters to set this are directly measurable; paper thickness
and [take-up] spool size.  Others are fuzzier; the buildup is a bit
more than paper thickness, but is easy to calibrate or estimate.

More variable is the wind motor response to varying load.  It's
affected by the state of the motor, its regulator setting, the spoolbox
brake and geometry and the condition of the paper.  Each player will
respond differently.  There's no one exact answer.  But the variation
is barely ever a topic of conversation around the player.  Good enough
is good enough.

All this, of course, only applies to hand-played rolls that were
recorded onto a take-up spool.  In other words, mostly classical
reproducing rolls -- only a small percentage of all the rolls made.
All other rolls are metrically constructed, which is easy to see as
they have a fixed number of steps per beat.  When played onto a spool
their music accelerates.  But most rolls are short and this is accepted
or more likely not spotted.  Fixed-tempo simulations are musically more
accurate for these rolls, excepting the small number that allowed for
acceleration in their construction (e.g. Frank Milne medleys).

But how many simulations really get this wrong?  Software from Wayne
Stahnke, Warren Trachtman, and mine, accelerate.  There are two
approaches: Warren re-times the notes and plays the file at a constant
MIDI tempo.  I do it differently by adding a constantly-increasing MIDI
tempo so I can retain the musical master-file structure.  Software will
always -- always -- be more accurate if run from a reconstructed master
with accurate simulation of all aspects of the playback device.
Because it uses the exact same data as the actual roll, not an
approximation of the roll.

The same effects apply in reverse when making new rolls from MIDI.
My software optionally allows for acceleration.  Like original rolls,
hand-played material is best compensated, but arranged material is
better cut retaining its musical structure without inbuilt
acceleration, allowing the pianolist to vary tempo to suit.

Julian Dyer