FROM NICK GRAVAGNE
Original Message:
Sent: 10-12-2013 17:43
From: David Love
Subject: Creating a Touch to Die For
... One problem becomes pretty obvious. There is no "the" AR. "The" AR is changing through the stroke. The distance ratio is simply an average of the AR through the entire stroke.
The distance ratio is uncompromisingly pegged to one and only one combo of some key dip (say, 4 mm) to its one and only partnership to hammer rise (say about 22 or 23 mm of rise). The DAR at this one and only point (per the example numbers) would then be 5.50 to 5.75, a seemingly dramatic difference, but based solely on the accuracy of measuring the 4 mm dip and the 22 or 23 mm of rise. An average AR for distance, say at half-blow (a bit vague in itself), is an idea we get from Dr. Pfeiffer and then repackaged via the Renner classes (Baldassin and Robinson) of many years ago now.
But in any case, Dr. Pfeiffer's model for this was the Langer action which depicts convergence not only at the capstan and whippen but also at the knuckle and jack top. When half-blow occurs at the knuckle and jack top, a "second magic line" forms between the whip center and hammer flange center. Thus, the whippen output arm and the shank input arm fall on the same line, and segmenting this line is straight forward.
Our actions do not come close to convergence at the knuckle and jack top; but as this sub-system closes in on convergence as far as it can the following takes place: the ratio of key input angular displacement to hammer shank output angular displacement slows down; the hammer rise to key dip ratio decreases, the overall speed ratio (same as what we call the action ratio) decreases, inertia values decrease, the mechanical advantage (MA) increases a bit (meaning that the overall leverages are able to "see" a heavier hammer later in the stroke). There is more, but that should suffice. See attachment, which has factored in a hammer / shank inertia value but irrespective of whippen and key (with leads) inertia.
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The only logical explanation to me is that the issue is confounded by the dynamics of the system.
Yes, if we accept the phrase loosely.
When we see, for example, a graph of the changing AR and the accompanying changing inertia curve we are using a static model, or so it seems. The AR is calculated at each point in the key stroke and then the accompanying inertia is assigned based on the changing AR at each point.
But to see the "changing AR and the accompanying changing inertia curve" we are
not using a static model; this
is the view of the dynamic model (again, a bit loosely stated). That is to say, we have for all practical purposes differentiated the problem so as to find a specific point in the graph for some meaning, same as we would when viewing any acceleration curve for a vehicle, etc. What is not seen in the graph is the formula for each curve or its differentiation. These formulas will accept any input value and yield a one and only output.
However, what doesn't seem to be accounted for in this is the fact that it is the initiation of the key stroke which will require the most force to overcome inertia, when the bodies to be moved are at rest. Once they start moving, then the calculations need to be based on keeping the various masses (hammer mostly) moving, not initiating movement. Like pushing the piano across the stage, the force to get it moving is the greatest, once it starts rolling the force required diminishes. The piano mass has not changed.
By this do you mean that the changing force vectors are desirable? From static to moving and to slowing? These can be worked out and also graphed and differentiated. I wonder how helpful they would be though. Accelerations would require a time factor in seconds.
In this respect, I would contend that the most important part of the key stroke with respect to inertia is the very beginning of the key stroke. The inertia at the end of the stroke is virtually of no consequence and the the importance of the inertia in terms of feel is diminishing rapidly through the entire stroke.
All data needs to be interpreted. This is your interpretation, and I think a good one. If you then choose to customize your hammer masses and AR setups to accommodate, then I think you are on solid ground. But an average could also be justified and supported. Though I don't wish to argue the case for that.
If I'm mixing terms then I apologize but my point stands and hopefully the engineers can read through to my meaning. Action ratios are most meaningful at the beginning of the stroke. Whether the AR at the beginning of the stroke is always the same as the AR at the end of the stroke, depending on which configuration you use (capstan move or knuckle move), or whether the shape of the curve is the same (i.e.the rate of change especially at the beginning of the stroke) needs to be more carefully examined.
Yes, "rate of change" is exactly the idea. Action ratios may be more meaningful at the beginning of the stroke, but in the larger world of machinery we would be intent to know the ratio at the end (should it change) if we needed a brake or clutch at the output end. The rate of change of hammer rise and inertia slows down as the hammer approaches the string, i.e. as the upper whip-out arm and the shank_in arm approach a straight line (never to realized in most of our modern actions). We should use this fact accordingly in our analysis.
The average AR, which will determine the actual regulation specs because it is this average that determines the overall relationship between key travel and hammer travel through the entire stroke, may not reflect what is happening at either end of the key stroke, in particular the beginning. This is something I'm still hoping to see graphed, but it is beyond my modeling at this point.
You wish to see a graph depicting the moment to moment change in dip to hammer rise?
Again, the "average" idea makes most sense per half-stoke and per Pfeiffer and a Langer type action but not so much for us working on Steinways. For distance AR (DAR for me) I prefer to know the theoretical dip required at the
end of the stroke, i.e. at let-off (say 45 mm). This guides me in knowing the impact on dip that any AR changes would require. This end-of-dip value will vary some depending on the AR (which BTW
is the action ratio). Hammers moving per higher ARs reach the point of let-off sooner than hammers moving per lower ARs. Our AR can be referred to in at least a few ways; as a transmission ratio, as a distance ratio, as a speed ratio, and although these relate to the masses being flung around in circles, the masses chosen to accelerate the system are completely independent of the radial geometry. Which is why I have also wanted know what the theoretical maximum hammer mass should be that would balance, say, a 50 gram mass at the key end and irrespective of friction and the actual mass of all the components.
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