Moment of Inertia of grand action parts.

[Mark Davidson]

I think the key to making a usable system is going to lie in distilling the
results and automating the calculations.  For example, most rotating shapes
have a moment of inertia that looks like M*L^2/C where C is some constant
particular to that shape.  For a thin rod rotating around its center, C=12.
For a thin rod rotating around one end, C=3.  I believe that there is a
value for C that gives a good approximation for a piano key (less leads)
within a few percent.  Maybe you need different C's for black/white keys, or
different types of pianos.  Likewise, for a hammer and shank, I believe that
a formula for MOI based on SW, radius and total mass can be empirically
derived (based on taking lots of measurements of actual MOI) that will be
quite usable, and will not require the user of the formula to measure MOI
directly (these are not easy to measure, but it IS doable).

Using these types of estimates and some software to perform the
calculations, I believe reasonable estimates of total action MOI can be made
that will give a useful picture of whether an action feels light or heavy.
We may just end up learning that Stanwood's recommendations for combinations
of SW and SWR are right on target and perfectly adequate.  We may learn
additional useful things.  Who knows until someone tries?  I would say the
work already done suggests that small variations in SWR are probably of more
concern than small variations in key MOI.

Usability will require that someone do much work up front in order to make
and keep such a system usable for the rest.  This is not work that the
typical tech has the time or inclination to do, but that doesn't mean it's
not doable or that people will not use the results if they are made
accessible and offer the opporunity build a better piano.

-Mark


Richard Brekne Richard.Brekne@grieg.uib.no wrote:
>
> Hmm...
>
> I dont really see why some useful and easy to implement method should be
> too awfully difficult to work out John, tho to be sure it depends on
> just what you are trying to do. That said there have been quite a few
> points drawn out that allow themselves to be rather easily quantified or
> measured. When thats doable, arranging these same on a scale gives a
> reference from which purposeful planning can be drawn.
>
> That is essentially what Stanwoods system did. His so called equation of
> Balance is simply a set of measurable parameters that fit into an
> equation. Quantities such as Strike Weight and Front Weight have been
> scaled on graphical charts in reference to that same equation. It all
> adds up to a set of guidelines about static balance weight where a few
> cause/effect relationships are clearly shown. There is little or nothing
> in his formula per se that points to what SHOULD be. That depends
> largely on what one is after to begin with. It DOES show you how to get
> there once you've decided. Unfortunantly, it leaves out relevant
> information and guidlines as to the subject of action inertia,
> compliance, and other relavant overall ratios.
>
> In anycase, I would not be a bit suprised to see a <<next step>> system
> appear in the not to distant future.