Key Leads and Inertia

[Bill Ballard]

At 6:00 AM -0400 6/13/03, Mark Davidson wrote:
>  > Don't forget, if the variation is on the front side of the key, it's
>>  included in the FW.
>
>Not sure I believe this (or I just don't understand what you're
>trying to say).  The FW is just the key's contribution to the BW.
>

I hope I can explain this clearly. I'm also always grateful to be corrected.

There are two forces (beyond friction) to be dealt with: inertia and 
gravity. You're right, when reckoning inertia, the entire key has to 
be counted as one player. FW however, reads only gravitational force 
on the key.

You know the picture. The key is mounted on a frictionless pivot, and 
if the front half of the key is heavier than the back half it will 
come to bear on a gram scale. Except for back-leaded keys in the top 
octave, it usually will. The amount we read is the gravitational 
force with which the front (heavier) half of the key bears on the 
measuring point set up on the gram scale. Unlike reckoning the force 
of inertia, the two halves or the key are treated as separate and 
applying a force at a different locations (visa vis, the fulcrum) and 
in different directions.

None of the complex modeling which we demand in inertial readings, 
mean anything here. Yes, this is still a system of rotating mass. 
There's the gravitational attraction on the back half of the key, and 
on the front half, and they're both still rotational. The important 
part is that one rotational force is greater than the other, and when 
you measure that surplus at a specified place, you get a specific 
measurement: the FW. We don't need to know gravitational force 
(rotating, as the key is) of either side of the key. All the FW tells 
us is the net force, how much heavier the front half is than the 
back. That's all we need to know.

BW is the same sort of net gravitational force in a 
(partially-)balanced beam. What it tells us is that when you load the 
top action parts onto the capstan, the back half of the key is now 
heavier than the front half, and by "x" grams, measured at the same 
place as DW, UW, FW, and the key ratio.

>So all the weight of the key matters, not just the front. (Proof: cut off
>the back of the key -- the FW changes!)

I hope I've explained it. Yes, when reading BW, the back half does 
matter. Yes, if you cut off the back half, the reading of the front 
half changes. Pop quiz: how does it change? <drum roll> It rises, 
because the back half is no longer counterbalancing it.

A further example, and a useful one. How would you measure a negative 
FW? You know, where the key hangs in mid-air above the scales. How 
about placing a 20g weight on the front, on top of the measuring 
point. The key now has FW greater than the back weight. But the FW 
will be less than 20g.... by an amount equal to the backleading.

At 10:22 PM -0400 6/11/03, Bill Ballard wrote:
>When we measure FW, what we are measuring is actually how much 
>heavier the front half of the key is than the back half. One thing 
>which we expect to find in the front half of the key is lead, but 
>the other things you mention (difference between the nats and 
>sharps, between a D and G key) are also in the front half of the 
>key. They may not be made of lead, but because they're in the front 
>half of the key, they're contributing to why the front half of the 
>key is heavier than the back.

BW is based on FW, and FW is based on some unknown figure for the 
weight on the back half of the key. Is it necessary to know that 
weight (to the same degree we can read it for the FW). If we were 
trying to read inertial forces, most definitely yes. But we're 
reading gravitational forces here, and the back half's actual 
quantity can stay unknown and not affect any of the static balancing.

As long, of course if there are no wild fluctuations in mass in the 
back side of the key. It's not a place that invites wild 
fluctuations. It's shorter, the shape of the key stick isn't varying 
the way the front half is, and those add-ons (capstan, backcheck, and 
key end felt) don't vary anywhere as much in weight and location the 
way the leads added on in front.

David Stanwood can speak to this. Ten years ago he was sawing through 
discarded key sticks to measure back-half sticks. The jist of it was, 
the back half is quite consistent across a keyboard.

Bill Ballard RPT
NH Chapter, P.T.G.

"No, Please wait, you're all individuals" Brain Cohen, exasperated
"Yes, we're all individuals"  the throng assembled in the street          
                 below his window, in unison
"I'm not..."  Lone dissenter.
     ...........Monty Python's "Life of Brian"
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