Moment of Inertia of grand action parts.

[Mark Davidson]

> Oops.  I just realized a major flaw in my reasoning.  Other components of
> the action are also moving right before the key bottoms out.  They would
add
> to the total momentum of the system as well.  So much for simple.
>
> Let me give this more than two seconds of thought and I'll see what I can
> come up with.  Sorry for the false alarm.
>
> Don A. Gilmore

Yup.  Key, wippen and hammer all move.  And all have different m.o.i.  And
all have different angular accelerations  that depend on the lengths of the
various lever arms.

[Also, the jack trips out from under the knuckle just before the key hits
bottom  :).  Oh yeah, there are dampers too, but they don't start moving
until the key is halfway down.]

I think the goal here is to develop a model for predicting when an action
when feel light, medium, heavy, etc.  The presumption is that the moment of
inertia is a big part of this model.  But it needs to be the total moment of
inertia of key, wippen and hammer, as felt at the key, and not just the
key's m.o.i..  Also useful is knowing which of the various components is
most significant, allowing one to focus on the areas that will give the most
bang for the buck (i.e. how much time should one spend finding the perfect
keylead position).

Once you know the total reflected m.o.i. and front key radius it is possible
to figure the speed the key will accelerate for a given force which I would
expect goes a long way toward the goal.

...none of which takes into account "compliance" issues - flexing of wood,
compression of felt/leather, etc.

If you want to figure hammer velocity, it's probably more useful to do it in
terms of force on key and key dip, rather than keystroke time.  Key dip is
easily measured to .01", whereas keystroke time is considerably more
difficult.

-Mark