Dr. Clarence Hickman published some Ampico hammer velocity data in
the first issue of the Journal of the Acoustical Society of America,
Vol.  1, No. 1, October 1929, pp. 138-146, under the title

  "A Spark Chronograph Developed for Measuring Intensity of
   Percussion Instrument Tones", By C. N. Hickman, Research Laboratory,
   American Piano Company

Hickman wrote:

  "Curve #2 shows the steps of intensity of the Ampico plotted against
the logarithm of the square of the hammer velocity.  Here it is seen
that the slopes of the curves for the two hammers are almost identical.
The increase in energy can be determined directly from the logarithms
and shows that in each hammer there is an increase in loudness
corresponding to 18.2 decibells."

The data given in curve #2 is

code step   Pres Vbass  Vtreb   Vmean   "S.U."

 -   000    4.25   38.    45.    41.35   30.0
 -    00    4.65   45.    53.    48.84   31.5
sub    0    5.25   55.    64.    59.33   33.0
canc   1    6.0    66.    78.    71.75   34.6
  2    2    6.8    78.    92.    84.71   36.1
  4    3    7.8    92.5  109.   100.41   37.6
  6    4    9.4   110.   130.   119.58   39.1
 26    5   11.6   132.   155.   143.04   40.6
 46    6   15.1   158.   186.   171.43   42.1
246    7   19.5   187.   220.   202.83   43.7
       8   26.0   222.   262.   241.17   45.2
       9   34.9   266.   312.   288.08   46.7
      10   46.25  315.   370.   341.39   48.2

where

  code - expression code on Ampico roll
  step - Steps 000 & 00 weren't implemented in the Ampico B.
         Step 7 is max suction without the crescendo active.
         Steps 8, 9 and 10 are suctions with crescendo active.
  Pres - suction, inches water column
  Vbass - velocity of bass hammer, centimeters per second
  Vtreb - velocity of treble hammer, cm/sec
  Vmean - geometric average of bass & treble hammer velocity
  "S.U." - Sound Units, decibels

A close approximation for Vmean (hammer velocity in the middle
of the keyboard) is given by this simple equation:

  P(v)  = Po + (v/c)^2, where Po = 4.0, c = 51.52

where

  P(v) = suction needed for a given velocity v
  Po = constant = the suction needed to overcome gravity acting on
       the hammer and damper of a grand piano, or the force of the
       hammer and damper springs of a vertical piano.
   v = hammer velocity (dependent variable)
   c = constant

This equation plots as a straight line on log graph paper.

Po is the effective stack suction needed to overcome friction and
the dead weight of the hammer at rest.  Altering Po causes the line
to curve one way or the other.

According to Hickman's data above, the Ampico B piano could achieve
a hammer velocity ratio of 8.25, resulting in 18.2 decibels audio
dynamic range, assuming that the pump and crescendo mechanism were
adjusted for 46.25 inches suction at maximum crescendo.

I asked Wayne Stahnke about the dynamic range of the Boesendorfer
solenoid piano that was used to record the Rachmaninoff Ampico rolls
(Telarc CD-80489 and CD-80491).  He said that the softest notes were
at velocity 32 cm/sec and the loudest at hammer velocity 640 cm/sec,
or 20:1 ratio of soft to loud, or 26 decibels dynamic range.

To estimate the suction needed in an Ampico stack to get 640 cm/sec
hammer velocity, the data of Dr. Hickman's curves can be extrapolated
or the formula above can be used:

  P(v)  = Po + (v/c)^2, where Po = 4.0, c = 51.52

        = 4.0 + (640/51.52)^2
        = 4.0 + (12.4)^2 = 4.0 + 154 = 158 inches w.c. suction

That's a lot!

Robbie Rhodes