Get the Lead out

[Ron Nossaman]

Hi all,

As I see it, the moment of inertia figured from the balance rail has very
little to do with anything other than the total distance the weight travels
when the key is depressed, *unless* you also consider how far from the
balance rail pin the force is applied. You are not only dealing with an
inertial moment arm, you're dealing with a simple lever that is increasing,
or decreasing the inertial effect depending on where the force is being
applied. From the input side (key), the leverage against the inertial mass
of a keyweight is *worst* directly under the finger. At that point, it's a
1/1 correspondence of force input against inertia. That's as bad as it can
get for the downstroke. As the weight is moved back toward the pivot, the
effective inertial resistance at the point of input (finger) is a function
of the proportion of the distance between finger and balance pin, and weight
and balance pin. You get a mechanical advantage on the power stroke that
increases as the weight is moved back. On the back side of the key, the
capstan is the input for the key return stroke and the same proportional
inertial relationship exists there between capstan - pin, and pin -
weight... except for one thing. It's possible to have weight(s) farther from
the pin than the capstan is, which puts the capstan at a worse than 1/1
leverage ratio. Putting more weight anywhere in a key forward of the balance
pin will slow down repetition, but may lighten touch weight, up to the point
where there is too much weight and you have an inertia problem. I would
think the better option would be to lighten the hammers, optimize action
geometry, and keep the whole action from fingertip to hammer strike point as
light as is reasonably practical. 

Thrill me, I can use all the education I can get.

Ron
  

:
>Here's a question:
>
>	Recently, I published  an article on grand piano action  diagnosis, and
one of the conclusions I came to was re-balancing  keys with many 1/2" leads
per key. Basically I remove larger leads  near the balance rail and insert
smaller leads near the end of the  key. This seems to make the actions feel
inertially lighter, and  there is less 'thumping' from heavy keys on balance
rails. 
>
>	However, it was brought to my attention that (I quote here) 
>
>"When the key is moving the "moment" of inertia becomes much more
important. Unfortunately it is affected by the distance from the balance
rail by a factor of R squared. This means a lead weight 2 cm from the rail
might have a moment of inertia of 1, but that if the weight is 4 cm from the
rail the moment of inertia will be 4, 6 cm = 9 and 8 cm = 16!"
>
>This all makes sense.  However, when I played the piano with 5  1/2" leads
per key, it felt heavy to play, despite the 55 downweight  30 upweight
average. With lead removed from near the balance rail  and 3/8" lead
inserted farther away to balance the key to original  weigh-off, the action
wasn't as hard on my forearms to play for long  periods.
>
>Mathematically, it seems that the smaller leads further from the  balance
rail would result in the same inertia as the larger leads, but  my arms
don't get tired playing! 
>
>Any ideas?
>
>
>
>Rob Kiddell, 
>Registered Piano Technician, PTG
>atonal@telusplanet.net
>
>"Windows NT crash
>I am the blue screen of death
>no one hears you scream"
>
>-Windows haiku error message
>
>
 Ron