Force=Mass*Acceleration

Yardbird47@aol.com Yardbird47@aol.com
Sun, 08 Jan 1995 14:28:29 -0500


I can't let such a tidal wave of a discussion go by without grabbing my
surfboard and trying to touch some of the high points. Please forgive and
bear with me as I do this in one post rather than a series of replies (whose
"re:Re:re:Re"'s quickly lose the ability to specify their subject).

Dennis Johnson rote (Re: Bechstein Action_Hamm Weight 1/4/95):
<<However, wouldn't you agree that in the end a scale cannot tell you exactly
how to solve an actions weight problems.   This comes from a throughly
intuitive understanding of the entire action, its mechanics and geometry.....
but I do insist that my end result would be same- with or without a scale.>>
I agree, if all that you're going to do with the weights is to look at their
numbers. Simply weighing and looking isn't going to change the end result.
However once you know the hammer weights, you're one step away from getting
the hammer weight where you want it. Where should that be, you ask? This, in
David's process, is a function of the action's overall ratio, and whether the
action will be spring or lead balanced.

Ken Sloane rote (Hammer Weight. etc. Date:  95-01-05):
<<There is a definite correlation between deviations from the "ideal" or
theoretical 2 to 1 ratio designed into most (all??) contemporary pianos and
the touch resistance conditions those deviations produce. I have some
interesting conclusions, along with some interesting conclusions about hammer
weight and knuckle position. >>
Right on the mark, Ken., with this discussion of key and shank leverage.
Action ratio is half the battle (hammer weight being the  other half). But if
we lose this half of the battle, then the whole banana goes down the tubes.
As you've documented, Steinway has frequently lost this half of the battle
and, in the case of teflon and pre-'84 parts, did so categorically.
<<this "black art" of regulating touch resistance.>>
Consider this "tuning up mass and leverage". a necessary aspect of action
assembly.

Michael Wathen rote (Angular Acceleration in a Piano Key Date:  95-01-05):
<<you have to consider a variable kinetic friction force and a changing
weight component as the hammer-shank assembly moves through it stroke>>
I'm interested as to why the mass of parts changes as the assembly moves
through its stroke.With this acceleration are we approaching anything near
the speed of light?  ;-)  But I do aggree that the friction will vary through
the stroke. Mainly at the outset and only at the knuckle, when the it is at
its lowest inclination with respect to the hammer center. As the knuckle's
angular motion proceeds, the distribution of vector motion changes from the
horizontal (sliding) to the vertical (lifting). It's this phenomenon which I
believe is behind the friction gradient. You've seen that the hammer shank's
rise with minimal dead weight at the key will require a couple of bumps on
the bench. The same happens when running an up weight: the friction gradient
will cause the hammer to lodge 1/4" above rest. The NH Chapter has started
into an ongoing project, called "Junior Science Project", with a stroboscopic
videography exploration of fast/deep repetition as its first subject. I also
intend we should find the contours of this friction gradient.
<<I typically find that the speed of the shank is the fastest at about half
way through its travel.  I originally had thought that the acceleration would
be constant.>>
Maybe this is Bill Spurlock's "flexing of levers".

Ken Sloane rote (Re: Angular Acceleration in a Piano Key Date:  95-01-06 02):
<<The ability to accelerate a key rapidly is important to a pianist, and what
hinders that ability is the presence of too much friction and/or inertia in
an action.>>
Agreed. In fact this is the crucial transaction between pianist and action.
(No, I'm not overlooking another one between hammer texture/soundboard and
pianist's ear.)
But please let's, look at mass and friction as separate matters. They affect
the feel differently and they're dealt with  separately. The pianist pours
their energy into the action, and this is absorbed by each of these two.
Friction is like an operating expense: you're working against constantly,
coming or going. Mass is like start-up capital. After you've invested the
energy do get mass rolling, the subsequent momentum of the parts is a form of
equity: it'll do some of your work for you. The disadvantage of an action
with such a high "up-front capital investment", is that it complicates any
change of finger pressure/key velocity the pianist may want to make partway
through the stroke. A change to the increase will require yet another
investment. A change to the negative will be unheeded by the momentum of
parts.The only thing help in this case is the constant brake of friction.
<<but         inertia. No one has come up with a good way of measuring it or
even begun to figure out how much is appropriate.>>
In fact David Stanwood did in early '92. The process has already been granted
its initial patent.

Bill Spurlock rote (Re: Angular Acceleration in a Piano KeyDate:  95-01-06
01)
<<Consider two keys on the same action: A13 with a 9 gm hammer and 4 key
leads, and A73 with a 4gm hammer and no leads. The difference in inertia
between these two keys is tremendous, much greater than the change in inertia
we might make when customizing an action, yet both keys are capable of nearly
equal repetition speed. >>
I don't believe that repetition is where inertia will make itself felt,
though anything involving reversal of motion would be an obvious place to
look. Keep in mind the speed with which the hammer comes flying off the
string. In the closed loop cycle that is fast repetition, this rebound should
certainly override any inertial "tax" incurred in such a reversal.. Inertial
resistance is certainly felt with increasingly harder attacks by the
pianist's finger. The finger hits the keys (and action) at a dead rest, if
not heading in the opposite direction. When the key's ability to accelerates
fails to respond to and match the finger's impact velocity, the finger may
seem to be pushing on a dead weight. It's this temporary mismatch in
velocities, as the key and action pick up speed, which can be so tiring to a
pianist. (Like dancing  with a partner on thorazine.)
<<So it is action mass, geometry, voicing, power of the piano structure, and
of course regulation that combine to give an action a certain feel. I doubt a
single formula for ideal hammer mass would apply to all actions given all the
other variables. In general, I feel the biggest and easiest gains in piano
performance come not from hours of work on special modifications, but rather
on getting the basics right: choose appropriate hammers, shape them properly,
attend to all pinning and alignments, bed the key frame and everything else
as solidly as possible, and regulate well. Then, nit-pick the regulation and
voicing some more. Not that there aren't pianos that came out of the factory
needing modification, but very often it's the dull stuff that really pays
off, and often gets overlooked in the rush for the magic formula.>>
The point is well-taken, and is fine advice for someone who might dream that
some miracle "GL-70" additive can obviate all the basics, "the dull stuff".
However here, you're among people for whom the latter is a premise. Ken
Sloane wouldn't be complaining to us about "some pretty unwieldy pianos", if
he knew the answer he was missing lay somewhere in the  basics. That goes for
a whole bunch of us who are fastidious on the basics. We may charge good
money for it or lose the same on these "basics", but we do them. With all due
respect, Bill, what we're talking about does lie beyond this tedious realm.

Michael Wathen rote (Re: Angular Acceleration in a Piano KeyDate:  95-01-06
01):
<<After the gram weights begin to move the key how long does it take to reach
the bottom of its travel?  Answering this question is not really the same as
finding the acceleration but it is rather finding the average speed.  So how
do we find the acceleration?>>
Is not acceleration simply a matter of leverage ratio (taking into account
the distortions induced by Bill Spurlock's flexing of levers and softness of
bearings)? I wouldn't try to determine acceleration from observations of
shanks speed as driven by a dead weight at the key front. To do so adds
friction to the already complicated product of how the mass of the parts
throughout the lever train is translated by overall action ratio into the
balance weight at the key front which opposes the driving dead weight.
<<So where do we start?>>
You start with a simple requirement that as many of these force measurements
will  be taken at a standard point in the leverage. Why not the front end of
the key where we now do our down and up weights?
<< In other words, if the strike point along the shank is too close to the
center you would expect that the Weight of the action would decrease and if
the Hammer were placed on the shank too far away the Weight would feel two
heavy.  So where is or what is the theoretically correct way to locate?>>
To paraphrase Beavis and Whats's'name, Sound Rules! If you check it out,
you'll find that the shank length isn't nearly as sensitive to 1/8" as some
other junctures in the lever train which Ken Sloan has already mentioned. I
don't see this bearing much on leverage.
<<One more point, how do you think reproducing players work?  They must at
least measure the angular speed of the shank as it moves through a fixed
point.>>
The digital ones surely must. The original pneumatic renditions of shank
acceleration must have chopped the curves into steps, given the state of
technology back then. I should warn you that I speak as someone who knows not
a stitch of player actions, old or new.

Sorry about the 1700 words, gang. Heck, it's Sunday. Stick this right in with
the sports section. I repeat my offer to fax out illustrative charts.

Bill Ballard RPT   "I'll play it, 'n tell you what it is later"
NH Chapter                                 Miles Davis..........


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