What matters most?

[David Love]

>From a static point of view, Stanwood is correct (though there will be
differences in friction).  Whether this is true from a dynamic perspective
remains to be seen.  

The issue is really one of the "moment of inertia" which is a measure of
the resistance of an object to changes in its rotational motion, or torque.
It is not quite the same as Newton's second law f=ma.  

If I recall my basic physics (and there's no guarantee of that), you are
calculating the torque as a function of the angular acceleration, the
distance from the axis of rotation and the mass.  In the key, the axis of
rotation is clearly at the balance rail.  In the hammer shank assembly, I
don't recall whether you calculate the axis of rotation from the flange
center pin, or from the knuckle mounting, but I believe it is from the
knuckle mounting since that is where the force is being applied in the
second class lever.  Similarly the wippen lever must be taken into account.
The formula goes something like  t = m*r^2*a.  Torque equals mass x
distance from the axis of rotation x angular acceleration.  But I'm not
sure about this.  The torque in a system of compound levers, I believe, is
a simple sum.  The question would be, then, how  coordinated changes in the
set of levers such that the overall action ratio remains equal effect the
moment of inertia in each system.  In more practical language: what happens
to the torque when the knuckle is at 16mm and the key ratio is at .48
versus when the knuckle is at 17mm and the key ratio is at .52; all other
things being equal.  The issue become complex because each lever has mass,
distance from the axis of rotation and acceleration which are distintly
different from the other (the key's angular acceleration is much different
from that of the hammer shank).  What will be changing in this experiment
is only the r (or does the angular acceleration of each component change,
though the relationship between them remains the same???  Not sure.) 
Anyway, since the input "r" is squared, it's hard to imagine that changes
in three unequal levers that keep the overall action ratio the same will
not yield differences in the moment of inertia when all components are
added together.  

I'll take my answer on the air--and good luck.  


David Love
davidlovepianos@earthlink.net


> [Original Message]
> From: Richard Brekne <Richard.Brekne@grieg.uib.no>
> To: <davidlovepianos@earthlink.net>; Pianotech <pianotech@ptg.org>
> Date: 8/25/2003 3:54:36 AM
> Subject: Re: What matters most?
>
>
>
> David Love wrote:
>
> > Just to clarify, I think that different component ratio combinations
that
> > achieve similar overall ratios will, and do, feel differently.
> >
>
> I agree. Yet again.. Stanwood claims differently, tho I have seen no real
> justification for his claim. Some subjective experience related stuff...
but
> nothing more.
>
> As to the other direction this has all taken, which you get into below. It
> shouldnt really be too difficult to make some general ball park
calculations. A
> reasonable limit for key leading  is available for us. If the maximum
amount of
> FW for any given key yeilds a equal or greater amount of inertia then the
> minumum corresponding SW, then there can be some degree of achieving same
> overall inertia for different combinations of key / hammer inertia. If on
the
> other hand maximum key inertia is always less then minimum hammer
inertia...
> then that cant happen and the whole issue of similar over all inertia for
> different combinations of component inertia is moot.
>
> Mark just sent me a spreadsheet that may have something to do with this.
I'll
> get time to look closer at it perhaps tonite.
>
>
> >
> > On the other subject, something to remember here, since inertia relates
to
> > acceleration and since the key lever and the shank lever accelerate at
> > different rates (i.e. the shank moves 5-6 times faster than the key),
> > changes in mass on one or the other are likely to create a different
curves
> > when plotting inertia against acceleration for each component.  That
might
> > suggest that comparable inertia with mixed setups cannot be achieved. 
The
> > sum of the parts may not tell enough of the story.   Maybe someone more
> > formally schooled in engineering or physics can chime in here.
> >
> > David Love
> > davidlovepianos@earthlink.net
> >
>
> Cheers
> RicB
>
> --
> Richard Brekne
> RPT, N.P.T.F.
> UiB, Bergen, Norway
> mailto:rbrekne@broadpark.no
> http://home.broadpark.no/~rbrekne/ricmain.html
> http://www.hf.uib.no/grieg/personer/cv_RB.html
>