Randolph Herr and Claus Kucher found these interesting research papers:

(1)
  Are computer-controlled pianos a reliable tool in music
  performance research?  Recording and reproduction precision of a
  Yamaha Disklavier grand piano, by Werner Goebl and Roberto Bresin,
  presented at MOSART IHP Network Workshop on Current Research
  Directions in Computer Music, Audiovisual Institute, Pompeu Fabra
  University, Barcelona, Nov. 15-17, 2001.

The paper can be downloaded for viewing at
http://www.ai.univie.ac.at/cgi-bin/tr-online?number+2001-27

The authors are

  Gerhard Widmer, Department of Medical Cybernetics and Artificial
Intelligence, University of Vienna, and Austrian Research Institute
for Artificial Intelligence (OeFAI), Vienna

  Roberto Bresin, Department of Speech, Music, and Hearing (TMH),
Royal Institute of Technology (KTH), Stockholm

From the PDF document:

  4.3 Relation of hammer velocity to MIDI velocity

  The relation between hammer velocity in meters per second and
  MIDI velocity is well matched by a logarithmic curve (see Figure
  3).  This figure shows also at what MIDI velocity the solenoids do
  not increase their drive force anymore.  For the lower keys it is
  already at around 85, the middle keys (G2 - C5) saturate at around
  90, only the G6 increases its hammer velocity up to a MIDI velocity
  value of 100.  However, in an informal recording of expressive
  music performances by the authors (over 26000 notes) the majority
  of MIDI velocity values were between 40 and 80, the highest value
  was 99, the lowest 6.  That means that, although in extreme cases
  (ff and pp) the piano clearly does not reproduce properly, the
  middle range seems to be quite accurate.

  Figure 3 Relationship of hammer-velocity to MIDI velocity of
  the original performance measured by the Disklavier and its
  reproduction.  A logarithmic curve is fit onto the original data
  (see formula).

The authors note that later models of the Disklavier may show different
characteristics.

(2)
  Measurement and reproduction accuracy of computer-controlled
  grand pianos, by Werner Goebl and Roberto Bresin, published in
  the Proceedings of the Stockholm Music Acoustics Conference,
  August 6-9, 2003 (SMAC03), Stockholm, Sweden.

The paper can be downloaded for viewing at
http://www.ai.univie.ac.at/cgi-bin/tr-online?number+2003-04

The abstract posted at http://www.speech.kth.se/smac03/abs03_link.html
says

  The recording and reproducing capabilities of a Yamaha Disklavier
  grand piano and a Boesendorfer SE290 computer controlled grand piano
  were tested, with the goal of examining their usefulness for
  performance research.  An experimental setup consisting of
  accelerometers and a calibrated microphone is used to capture key
  and hammer movements, as well as the acoustic signal.  Five selected
  keys are played by pianists with two types of touch ('staccato -
  legato').  Timing and dynamic differences between the original
  performance, the corresponding MIDI file recorded by the
  computer-controlled pianos, and its reproduction are analyzed.

  The two devices performed quite differently with respect to timing
  and dynamic accuracy.  The Disklavier's onset capturing is slightly
  more precise (+/-10 ms) than its reproduction (-20 to +30 ms), the
  Boesendorfer performs generally better, but its timing accuracy is
  slightly less precise for recording (-10 to 3 ms) than for
  reproduction (+/-2 ms).  Both devices exhibit a systematic (linear)
  error in recording over time.  In the dynamic dimension, the
  Boesendorfer shows higher consistency over the whole dynamic range,
  while the Disklavier performs well only in a wide middle range.
  Neither device is able to capture or reproduce different types
  of touch.

Note: The links at http://www.ai.univie.ac.at/cgi-bin/tr-online?
are faulty.  The downloaded file will be named *.html -- it must
then be renamed *.pdf for viewing with Adobe Acrobat reader.
Macintosh users must change the file type from HTML to whatever
a PDF type is at the Mac.

Robbie Rhodes
Etiwanda, Calif.