Inertia, was "Grand Touch"

[Dean May]

Mike wrote:
At the midpoint of a 1/2" hole in a 1" tall key, the
stiffness is reduced by approx. 12%.  Is this negligible, or can a
sensitive pianist feel the difference?  



You are technically correct. Actually, according to my quick and dirty
calculations, the rigidity of the keystick is reduced about 18%, assuming
the lead does nothing to add to the stiffness. But, as you say, that is at
the midpoint of the hole, a very narrow region of the key. The reduction of
stiffness on either side of the hole is reduced exponentially as one moves
to either side of the midpoint. 

So what are we talking about? Flexure of the keystick occurs as a sum total
of infinitesimal strains along the keystick, from the front to the back. But
it is certainly not uniform. At the front and back there is no flexure. The
maximum strain occurs at the balance rail hole where the maximum bending
stress occurs and it decreases linearly to the front and to the back of the
keystick. Integrate all of the micro strains along the keystick and you'll
get the total flex. 

The question, then, is how much will the total flexure change because of an
18% reduction in stiffness in 4 very narrow regions of the key where the
bending stress is 30-50% of it's maximum? I don't want to do the calculus
but I'll stand by my statement that it is very negligible. 

Ron N's fix of adding the hardwood shoe at the balance rail hole on the
other hand will make a huuuge difference. Why? Because he is increasing the
stiffness at the outer fibers where it does the most good: at the point of
the greatest weakness (balance rail hole goes through the outer web) where
the key is experiencing its greatest bending stress. My quick and dirty
calculations show the balance rail hole reduces the stiffness of the key at
that point of greatest strain by at least 40%.

The weakening effect of that balance rail hole on the keystick beam cannot
be overstated. It is the weak link in the system. The effect of any hole
drilled for leads pales in comparison. I suspect cracks between the holes
occur not because of bending stress per se, but because of the internal
stress placed on the wood by swedging the leads in holes too close together.


But I've been wrong before. :-)

Dean



-----Original Message-----
From: pianotech-bounces at ptg.org [mailto:pianotech-bounces at ptg.org] On Behalf
Of Michael Spalding
Sent: Friday, July 14, 2006 5:58 PM
To: Pianotech List
Subject: RE: Inertia, was "Grand Touch"

Dean,

Think for a moment about the assumptions behind your statement.  Do you
assume the key material is homogeneous and isotropic?  Ever see a key with
3 or 4 closely spaced 1/2 inch leads with cracks in the wood connecting
some or all of the lead holes?  Text book formulae are one thing, the real
world is  another.  At the midpoint of a 1/2" hole in a 1" tall key, the
stiffness is reduced by approx. 12%.  Is this negligible, or can a
sensitive pianist feel the difference?  What about 2 holes, or 3 or 4? 
Worth testing on actual components, I say.

Mike


> [Original Message]
> From: Dean May <deanmay at pianorebuilders.com>
> To: Pianotech List <pianotech at ptg.org>
> Date: 7/13/2006 9:53:51 AM
> Subject: RE: Inertia, was "Grand Touch"
>
> The stress is all carried by the upper and lower fibers of the wood. Holes
> in the middle have negligible effect. Think I-beam. All the stress is
> carried by the upper and lower webs. You don't want to drill holes in
them.
> You can, however, drill through the connecting center web with no loss of
> strength.
>
> Dean
>
> -----Original Message-----
> From: pianotech-bounces at ptg.org [mailto:pianotech-bounces at ptg.org] On
Behalf
> Of Michael Spalding
> Sent: Thursday, July 13, 2006 9:31 AM
> To: Pianotech List
> Subject: Re: Inertia, was "Grand Touch"
>
> Jude,
>
> I think it's great thatyou will be testing this experimentally.  One
factor
> you might want to look at is how the lead holes in the keystick affect its
> flexibility.  It seems to me that a keystick with several large led holes
> close to the balance pin would flex more on a hard blow than one with
fewer
> or smaller holes further away from the balance pin.  Looking forward to
> hearing and discussing y our results.
> \
> Mike
>
>
> > [Original Message]
> > From: Absolute Piano <absolutepiano at comcast.net>
> > To: Pianotech List <pianotech at ptg.org>
> > Date: 7/12/2006 9:02:37 PM
> > Subject: Re: Inertia, was "Grand Touch"
> >
> > Thanks Vladan and all for all the info.
> >
> > There is a lot to chew on. My interest is in the practical application.
> Why 
> > is it that two keys with the same balance weight and the same front
> weight 
> > but leads arranged differently seem to me to feel the same?
> >
> > I ask because I had a customer that asked me to place all the leads
> closer 
> > to the front and to use less leads after I had already set up the FW to
> my 
> > specification in a new keyboard using a tower pattern nice and close to
> the 
> > balance rail. I went through all the trouble but as far as I or anyone
> else 
> > could tell the action felt the same.
> >
> > I'm in the process of building several action models to test the science
> as 
> > I am slowly digesting it so you are all being quite helpful.
> Unfortunately 
> > with reality hanging over me it may take awhile to report back any
> results.
> >
> > Best,
> >
> > Jude Reveley, RPT
> > Absolute Piano Restoration, LLC
> > Boston, Massachusetts 
> >
>
>
>
>