From Ron Nossaman <RNossaman@cox.net>
>Now we just need the velocity of the hammer.
Except it doesn't work that way in a real action. The peak velocity of a
hammer in a real action is limited by the compliance of the parts, not the
input impulse. That is primarily, but not entirely, key flex. So beyond a
certain level of input impulse, hammer velocity won't increase no matter
how hard the key bottoms out on the punching. Action saturation, and hence
maximum hammer velocity, depends on cumulative and interactive effects of
the mass, stiffness, moment arms, compressibility of felt and leather, of
every affected part for each hammer. Factors influencing saturation point
of any given position in the scale include the hammer mass, shank length,
mass and flexibility, knuckle placement and compressibility, hammer rail
stiffness, wippen mass, beam stiffness, capstan pad compressibility, angle
and positioning, wippen rail stiffness, key mass, stiffness, and moment
arms, balance rail punching compressibility, and balance rail stiffness.
Key bed flex is also present, but it's usually way down on the list. All
mass measurements include considering MOI, naturally, and I probably missed
some things, but the point is that this isn't something you are going to
casually calculate to any degree of accuracy beyond a very rough estimate.
This is the way I see it, for whatever that might be worth, with more than
a few decimal points lopped off. Once the basic geometry is established and
the friction is under control, the hammer weights are the priority. High
hammer weights need more key lead to get static weights in the ball park of
usability. The excess key leads are perceived as being the cause of the
inertia problem, when they are only there because the hammers are already
too heavy. Moving the leads back toward the center of the key and adding
more does change the inertial effects of the key leading. It also increases
the flexibility of the key making it somewhat easier to bottom the key
before the hammer moves significantly, giving the impression of playing
easier as the more flexible key lowers the saturation point and limits
hammer velocity. It isn't the Moonlight Sonata crowd that notices the
difference. It's the aggressive pianist.
Adding a wippen assist spring does a number of things. It provides static
balance compensation for excess hammer weight, which allows lead removal
from the keys, which lowers the overall inertia of the action. The spring
obviously has no direct affect on the inertia of anything in the action.
When we set repetition springs on the bench, we typically use hammer rise
as an indication of spring strength. In play, the hammer doesn't rise for
the jack to reset. The key does, lifted by that little rep spring. With no
wippen assist spring, there is somewhat of a correlation between hammer
weight and key weight as seen by the rep spring, but the addition of a
wippen assist spring changes that relationship considerably. So less key
mass means faster jack reset and higher repetition rates even if the
hammers ARE still too heavy. Less key mass will translate to slightly
higher key down velocities for a given input even though the hammers still
contribute most of the overall inertia. Fewer leads mean fewer holes,
therefor stiffer keys, making terminal hammer velocity more a function of
input, and less of action compliance. It raises the saturation point. In
some instances, this will mean that the pianist needn't pound the keys as
hard to get the high end, and should get better control over a wider range.
I don't know if the rep spring will lift a center weighted key easier and
quicker than an end weighted key, but I suspect so, even if it is only that
the key flex means that weights toward the ends of the keys travel
proportionately farther than weights placed toward the center, and so have
to be moved proportionally farther to reset the jack. Again, this is a real
concern only with high amplitude, quick repetition playing, but that's
where this stuff is noticed, so I think it's a factor.
As long as I'm already here and have some on me, I'd also like to comment
on the idea that key lead inertia doesn't happen until the downward
acceleration exceeds gravitational acceleration. I disagree. The system is
counterweighted. The key weights are not in free fall, so for mass being
pushed down, mass is being levered up. Gravity only counts in static
balance measurements.
No math, no minutia, just my attempt to step back for an overview of my
own. There are a whole lot of minute details being discussed here, all of
which are worth defining and clarifying to the degree that it's possible,
but the original questions of how these things fit together in an action
are of more general interest and use, and that still isn't being addressed.
The problems we deal with, and the confusion that remains is still how all
this stuff mechanically interacts in a piano action.
Ron N