Key acceleration

[rhohf@eagle.idcnet.com]

It was reassuring recently to read that there are other adult technicians who
spend time at their action models.  I am always finding excuses to tinker with
mine.  Some time ago, after  watching my model go through perhaps 100k
repetitions of  its cycles, it began to dawn upon me that,  when the key is
depressed, all movement in the action is up except for one part.  That part is
the front of the key and it goes down.

During the last month or so there has been a lot of discussion about physics,
but I have not seen gravity mentioned. Let us briefly review a few of the
things we know about gravity:
      a.  Gravity assists things going down
      b.  Gravity impedes going up
      c.  Gravity does both these things with a force of mass times
acceleration (F=ma)         where a is gravitational acceleration
(g),therefore F=mg
And:
      d.  Inertia (proportional to mass) impedes everything that tries to
accelerate

Applying these principles to the up and down movements of the piano action,
one begins to suspect that gravity has a curiously unbalanced effect.  When a
key is depressed, gravity and inertia impede all motion in the action exept
the motion of the front of the key which:
      1.  gravity assists more than inertia impedes at accelerations less
than g            2.  gravity assists less than inertia impedes at accelerations
greater than g          3.  the quantity of these effects increases as the
mass of the key increases
      4.  the quantity of these effects increases as the key acceleration
increases

Let us assume two things:
      e.  that the range of accelerations (the "acceleration envelope")
imposed upon          the key during playing includes g
                           f.  that the dynamic level of a note increases as
the acceleration of the key       increases

This means that a pianist will give the key less than g (>g) during pianissimo
playing and greater than g (<g) during fortissimo playing.

In order to help clarify what this means to the pianist,  we can consider the
effects of adding and removing a lead weight at the front of the key:

Adding a lead weight to a given key will do these two things:
      5.  it will >decrease< the force required to play pianissimo  (more
assist @ <g)
      6.  it will >increase< the force required to play fortissimo  (more
impede @ >g)
The acceleration envelope expands at both ends.

Removing a lead weight from the key will do these two things:
      7.  it will >increase< the force required to play pianissimo  (less
assist @ <g)
      8.  it will >decrease< the force required to play fortissimo  (less
impede @ >g)
The acceleration envelope shrinks at both ends.

Restating 5-8 in more general terms:
      9.  the more mass on the front of the key, the wider the acceleration
envelope
       10.  the less mass on the front of the key, the narrower the
acceleration          envelope.

For those who have conducted their own investigations along these lines, I
would like to clarify a couple of points:
      h.  this discussion is strictly qualitative, nothing has been
quantified
      i.  we are considering the effects of gravity and inertia on the
movement of the       key indepently of  other movements in the action;
we are treating the action        as nothing more than a constant mass that
the key must move.

The results are surprising and, as is often true, raise more questions than
they answer. Please excuse me for stopping short of drawing conclusions until
after comments.

Bob Hohf