Moment of Inertia of grand action parts.

[John Hartman]

Mark Davidson wrote:

> 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.]

Mark, let's leave out the dampers for now, this is going to be hard enough.


> 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).

exactly! Sarah made the observation that the kinetic energy in the key 
would not go into the final product but be wasted. It was suggested that 
we could improve the action's efficiency by reducing the MOI of the key. 
Yes that does work but we now see that the improvement to efficiency is 
very little even if remove all the lead from the key.

> 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.

With a little more work (getting the equation for velocity right for 
one) we can do just that.

John Hartman RPT

John Hartman Pianos
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Rebuilding Steinway and Mason & Hamlin
Grand Pianos Since 1979

Piano Technicians Journal
Journal Illustrator/Contributing Editor
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