Key Leads and Inertia

[Sarah Fox]

Hi Ric,

Sorry to have taken a while to get to this one.  I was away temporarily.

> Yes... thats sort of how I read the results, tho its going to take me a
bit to
> weed through the refered too maths that explain the moment of interia as
> described by this site. So let me see if I understand this correctly.
Ignoring
> the moment of inertia for the key, this is shows that for a given FW
> specification, more leads placed closer to the balance rail pin yeild a
lower
> moment of inertia, and yield greater degrees of acceleration then less
lead out
> towards the end of the key. Yes ?

Exactly

> This being the case... then loweing key inertia, and hence increasing key
> acceleration can be accomplished by concentrating more of whatever key
mass is
> used in the center.. yes again ?

Yes again

> If so... what happens to half the argumenation
> against the accelerated action ?

Personally, I'm not convinced that S&S's accelerated action really does
anything.  The shift in fulcrum would be miniscule, hardly enough to make
any sort of measurable difference in either the action ratio or the key's
moment of inertia.  There would *technically* be shifts in these values, of
course.  Technically, the mechanical advantage over the capstan end would
decrease as the key is depressed.  As for the moment of inertia?  Off hand,
I would guess that the moment of inertia would technically decrease as the
key is depressed and the fulcrum (technically) shifts, but I could easily be
wrong.  It really depends on the overall distribution of mass in the key,
which I'm sure varies from piano to piano.

Peace,
Sarah