Angular Acceleration in a Piano Key

[Michael Wathen 556-9565]

Ah Hah!!!  Now were talking.  I always feel a particular sense of
pride when something I posts gets the ball rolling (angular
acceleration).

First, a few clarifications about the terminology.  "Speed" is
nothing more than the ratio of change in position with respect to
time, like 50 miles/hour.  "Acceleration" is the ratio of change
of Speed with respect to time, like 0 to 60 miles/hour in 7
seconds.  If the speed does not change then there is no
acceleration.  In terms of a piano key we might wish to know the
acceleration of the key as it moves through its travel.  Every
car can start a course at zero and get up to 60 miles/hour but
the question is how long did it take.  After the gram weights
begin to move the key how long does it take to reach the bottom
of its travel?  Answering this question is not really the same as
finding the acceleration but it is rather finding the average
speed.  So how do we find the acceleration?  That will take some
doing.

Another point of clarification; Finding the Weight by the methods
previously elaborated is really finding the Torque of the Action
parts.  Torque is defined as a force applied times the distance
of that force from a fulcrum point.  This is very important.
Every position of every component of the action plays a part.
There is the torque of the components on either side of the
balance rail. In this case everything can be thought to act at
the point where the capstan is located.  There is the torque of
the center of gravity of the whippen.  There is the torque of the
action parts pushing at the knuckle.  There is the torque of the
center of gravity of the hammershank and hammer assembly. So
where do we start.

Now I will think outloud...My current thinking is pushing in the
direction of asking what is the proper strike point distance of
the Hammer along the shank in relation to the center pin (one
fulcrum).  In other words, if the strike point along the shank is
too close to the center you would expect that the Weight of the
action would decrease and if the Hammer were placed on the shank
too far away the Weight would feel two heavy.  So where is or
what is the theoretically correct way to locate.  Keep in mind
that I don't give a damn about what the manufacturer claims.  I
want to know for myself how to determine its optimal location.
The same applies to all the other torque points in the action.
If you did not see my post regarding knuckle configurations you
may Email me and I will send you a copy.

Now the question that we were originally trying to answer.  How
hard must I work the finger to get the hammer up to all the
different speeds that correspond to the loudness spectrum.  As a
pianist I'm probably more concerned about this question.  If I
step on the gas pedal and the car jerks off to a breakneck speed
and if I can't regulate my foot pressure to get a nice slow speed
then I will probably ask the salesman for something else.
Likewise, if I step on the pedal and the car does seem to want to
get up to speed fast enough then I will complain the car isn't
reliably safe.  I might get stuck out in the middle of an
intersection!  As a pianist I will want something similar since
there is this direct correlation between the speed of the hammer
upon impact and the loudness of the tone.

Finally, since we are dealing with torque (movement around a f-
ulcrum) then we must consider that everything moves in an arc.
That is  everything moves through an angle.  This is why we will
need to call it angular acceleration.

One more point, how do you think reproducing players work?  They
must at least measure the angular speed of the shank as it moves
through a fixed point.


Michael Wathen
College-Conservatory of Music
University of Cincinnati
WATHENMJ@UC.EDU