May I respectfully suggest that a defined diameter of take-up spool be
settled upon. The fact of the matter is that take-up spools are not
all of the same dimensions.
The larger the take-up spool is in diameter, the less acceleration
there should be from the beginning to the end of a roll being played.
Of course, the use of a smaller diameter take-up spool would mean
greater acceleration over the length of the roll.
A roll that might play without acceleration or deceleration on one
player might not do so on another.
[ True, the take-up spool diameter for player pianos is not defined
[ by any standard, and there is no standard published by the industry
[ relating to acceleration.
[ The best standard I know of is the standard implied by the Ampico B,
[ which features extremely good regulation of the take-up axle speed.
[ The Ampico B service manual states that, when the Tempo lever is set
[ to 87-1/2, "the take-up spool should then make exactly twelve
[ revolutions per minute."
[ To meet this definition the diameter of the take-up spool must be
[ 2.784 inches. The smaller take-up spool in the Ampico A would mean
[ more acceleration than desired, but the air-motor slows down due to
[ the increased load as the paper transfers from the supply spool to
[ the take-up spool. -- Robbie