Key Inertia

[Mark Davidson]

Sarah Fox wrote:

>As for the center of percussion of the keystick?  New concept to me.
>The concept makes sense, but I don't really know how to work with it.
>(Alas, Freshling Physics was the extent of my education in mechanics.)
>I would think the effective center of percussion of a loaded keystick
>(i.e. loaded with the top action) would be very close to the capstan
>anyway.  I doubt it would be possible to impart that much energy to the
>top action by a mere "bonk" on the keystick, absent of any other forces.
> Put another way if the action were floating in microgravity, and if the
>key were not mounted in the keyframe, I doubt there would be much "play"
>from "bonking" the key into rotation against the wippen.  I'm sure it
>requires a deliberate stroke, corresponding to a prolonged upwards force
>of the balance rail on the underside of the keystick.  Thus the center
>of percussion of the keystick might be a moot point.  Dunno...  I'm
>curious to hear what our engineering friends think.

I guess my gut feel (as we know, gut feelings are often wrong in physics) is that you want the center of percussion to be at the
balance rail.  If that is where the key naturally wants to rotate, then you have several benefits.  1st less stress on key/action
compliance, etc. 2nd more of the impact translated at capstan (if COP is at capstan then you rely completely on the balance rail
force/leverage to push the back of the key up), 3rd quicker response - key begins to rotate upon impact without have to build up
pressure at balance rail first, 4th less work for pianist.

What I'm thinking is that this could be part of the reason that pianists prefer actions with assist springs, even though most of the
inertia may be in the top action.  Removing key leads moves the COP close to the balance rail giving the above benefits.

Okay someone - what is formula for C.O.P.?

-Mark