Hi Alexander,
I hope you'll allow me to jump in here; David's clock radio probably reads 6A now. 2 things:
1.) There should be no confusion that the motion in which inertia is being calculated is rotational (moments of inertial and angular momentum).
2.) I'm not sure if ANYONE (Darrel Fandrich, Bruce Clark, etc.) is actually calculating inertia, outside of the R&D departments of the well-established factories. I do remember, maybe 15 years ago, that one of the people on this list (
Steve Birkett) set to work created a thorough mathematical model of a grand action, on a grant to uwaterloo.ca from Steinway&Sons. We never heard the results of course, because these were proprietary. But Steinway wouldn't have made this investment unless they were unhappy with their R&D dept.'s model on hand.
As you well know, the accuracy of an inertia calculation is only as accurate as the amount of data you can plug into the formula (the mass of every last little object in the system, plus that object's center of mass, plus the distance from that to the center of rotation). Most of us work by analogy.
I also use David Stanwood's metrology (and don't begrudge the fact that it's based on static measurements). But for me, FWs are a good analogy for the total mass in the system, from whence inertia comes.
1.) Reducing the 3-lever grand action to 1 (the keystick, with the weight of action parts on the backside and the counterbalancing leads in front), the FWs are an indication of the weight of parts (modulated by the AR) needing counterbalancing.
2.) David Stanwood's solution to arranging the front leads in a way that satisfies both the counterbalancing of the gravitational force, and a smoothness in their moment of inertia, is probably no different from most factories (Stwy included): pattern leading for the majority of any key's FW load, and the remainder set by a "free agent" lead. David favors smooth moment of inertia (over the gravitational force) by having the "free agent" leads run a straight line from the first note in any section of the pattern leading to its last note. (For good reason: gravitational resistance is fixed, but inertial resistance is variable, in often unpleasant ways.)
In that single lever reduction, gravitational resistance is the difference between the side, inertial, their sum.
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William Ballard RPT
WBPS
Saxtons River VT
802-869-9107
"Our lives contain a thousand springs
and dies if one be gone
Strange that a harp of a thousand strings
should keep in tune so long."
...........Dr. Watts, "The Continental Harmony,1774
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Original Message:
Sent: 06-13-2022 00:10
From: Alexander Brusilovsky
Subject: Change key dip?
David,
When you are dealing with what you call inertia - do you operate masses and forces( linear movements) or momentum of inertia and rotation moments( circular motion)?
Alexander Brusilovsky