Keylead inertia and leverage (was Re: Ideal leading pattern:)

[Mike and Jane Spalding]

Richard,

Interesting challenge.  So I did your little experiment.  Max weight was
about 6oz of lead plus a plastic pony clamp at about 3" from the balance
rail.  Min weight was the pony clamp horizontally at the end of the key
hanging out beyond the key for maximum lever length.  Roughly a 4:1 ratio of
weights and lever lengths.   Unlike your experience, I found the measurement
process to behave exactly the same in both cases.  With not quite enough
downweight, the key would start down, then gently stop with the hammer about
3/8 above the rest felt.  With steady gentle tapping on the base of the
action model, the hammer would continue its rise to (not through) letoff.
With small addition of weight, it would rise smoothly to letoff without
tapping.  (My model takes extra force to get through letoff because it was
put together from assorted previously owned parts, including hard flat
knuckles).

It could be that the mongrel character of the parts is also the reason it
doesn't behave like yours.  On the other hand, it probably represents the
real world of working pianos better than a model constructed of virgin
Renner parts.  If anyone else has too much time on their hands, try this and
let Richard and me know what happens.

Mike Spalding


----- Original Message -----
From: Richard Brekne <Richard.Brekne@grieg.uib.no>
To: <pianotech@ptg.org>
Sent: Sunday, April 01, 2001 3:33 PM
Subject: Re: Keylead inertia and leverage (was Re: Ideal leading pattern:)


> Nice explanation, leaving all friction issues aside for the moment I'd
like to
> continue on this and raise this little head scratcher I have been
wondering
> about that doesnt seem to add up.
>
> Take an action model of a grand and remove all the weights from the key.
> Otherwise set the model up with standard regulation, and Strikeweights.
Now do
> the following. First figure out what front weight you need to get a ball
park
> Balance Weight figure. Then find the two extremes for placement of this
weight
> along the length of the key. By that I mean find out how much weight you
need as
> close in to the balance rail as possible to get that FW, and then how much
you
> need out towards the end of the key.
>
> When you have that figured out then do the standard old fashioned dw /uw
> measurements with the weights in each configuration. Now the only thing I
want
> you to look at is how the actuall "measurement process" behaves. I have
found
> that with the weight placed out at then end of the key the measurements
> typically stop up half way through the key stroke, but with the weights in
close
> to  the center the measurment typically goes smoothly all the way down to
> letoff, or all the way up to hammer rest.
>
> Since the only difference is placement of key leads this doesnt seem like
a
> friction issue from the top action, rather an inertia /momentum issue. But
> intuitively at least it would seem like the "smooth" reaction to the
measurment
> should happen under circumstances of greatest inertial, yet the opposite
seems
> to be the case if we take the inertia formula...
>
> So how do you explain this ?
>
> I am not sure how much it matters as everything else also points to leads
being
> best placed towards the center...unless there is more to the factor of
inertia
> relating to the basic weight of the lever then the formular discussed
accounts
> for.... In anycase it seems curious to me and I wouldnt mind an
explaination
> that makes sense.
>
>
> Mike and Jane Spalding wrote:
>
> >
> > Let's take the key weight example, and we'll round off the numbers to
make
> > it easier, if not necessarily correct for your specific piano:  (You may
> > find it makes more sense if you sketch this as you read through)
> >
> > The key measures 8" from front rail pin to balance rail pin.  You want
to
> > increase the keyweight by 4 grams, and are considering putting the
weight at
> > 4" (4 grams times 8" divided by 4" = 8 grams required) or at 2" (4 grams
> > times 8" divided by 2" = 16 grams required).
> >
> > Let's let A equal the acceleration of the key, at the front rail pin,
for a
> > mezzo-forte blow.  The acceleration at 2" would be A times 2" divided by
8",
> > or A/4.  The force at 2" would be M * A/4, or 16*A/4, or 4*A.
> >
> > The acceleration at 4" would be A times 4" divided by 8", or A/2.  The
force
> > at 4" would be M * A/2, or 8*A/2, or 4*A.
> >
> > So, in both cases, the force AT THE WEIGHT is equal to 4*A.  But the
force
> > felt by the pianist, AT THE FRONT RAIL, is reduced by the leverage:  For
the
> > weight at 4", the force is reduced by 4" divided by 8", so the pianist
feels
> > 2*A.  For the weight at 2", the force is reduced by 2" divided by 8", so
the
> > pianist feels A.  Bottom line, the closer the weight can be placed to
the
> > balance rail, the less inertial resistance the pianist will feel.
> >
> > Mike
>
> --
> Richard Brekne
> RPT, N.P.T.F.
> Bergen, Norway
> mailto:Richard.Brekne@grieg.uib.no
>
>
>