Angular Acceleration in a Piano Key

[Michael Wathen 556-9565]

Below is a copy of an E-Mail which I sent to Bill
Spurlock some time ago answering a question he had about
a device that would measure the angular accleration.  Its
one thing to be concerned about touchweight but equally
if not of greater importance is this question of angular
acceleration.  We can not practically measure this
quantity in a piano action but we can deduce a something
similar with a technique which I describe below.

I have discovered a device that is commonly used in
Physics labs.  It consists of a infrared photogate that
can measure the speed of the shank at several places in
the arc of its travel.

What I have found is that you must look for an equivalent
measure for angular acceleration, i.e., you have to
consider a variable kinetic friction force and a changing
weight component as the hammer-shank assembly moves
through it stroke, and call this your angular
acceleration.  You can take about five samples with a
reasonable gram mass at the front of key and determine
Shank speed as a function of key travel.  I use as a
standard measuring point a point on the shank 100 mm from
the center of the center pin and this is the point I
consistently measure.  Letoff must be out of the way and
drop should be in the correct place.  First, I'll start
with some front rail punchings measure with a micrometer,
and say, take my first setting with 0.1 " of punching
placed on the front rail.  The weight is set on front of
the key to get the key to rest and the hammer to position
itself at the location that corresponds to this 0.225 "
key travel.  Next, set the photogate to measure the speed
at this point in the travel of the shank by removing the
punchings and taking an average of, say, ten readings.  I
typically find that the speed of the shank is the fastest
at about half way through its travel.  I originally had
thought that the acceleration would be constant.

What needs to happen now is that the procedure,
standardization, and statistical analysis need to be
developed before one tries to market it has a device for
technicians.

Michael Wathen
College-Conservatory of Music
Univeristy of Cincinnati