Touch Weight

James Ellis claviers@nxs.net
Tue, 23 Dec 2003 17:35:34 -0500


I got several questions this last time around, and I don't remember for
sure who asked what, so I'll just try to cover it in general, and hit the
"high spots".  

Inertia is a minifestation, a property, an effect, of acceleration and
deceleration.  It's proportional to the square of the change in speed, or
velocity.  Acceleration and deceleration are changes in velocity.  The
velocity, or speed, of a mass revolving about a central point is
proportional to the radius of the orbit of that mass.  Therefore, the
moment of inertia is proportional to the square of the radius, or the
square of the acceleration or decelaration.  If you are slinging a rock in
a sling at the rate of two RPS, its force on the sling will be four times
what it would be at one RPS.  In the case of the rock in the sling, we are
dealing with centripetal acceleration.  These are just different
manifestations of the same thing.  Inertia is simply the resistance a mass
has to being accelerated or decelarated, or forced to change direction.
You will find this discussed in a variety of textbooks.

If we release the rock from the sling, and measure how hard it hits, we
will find that it hits four times as hard when it is traveling twice as
fast.  This is kinetic energy.  Kinetic energy and inertia are first
cousins.  Inertia, as Don reminded us, is an effect, or property, and
kinetic energy is a measurable quantity.

If we are looking at one complete key system, from key front to hammer
head, we are, in effect, just looking at a compound lever.  The
acceleration and decelaration of the hammer head dominates the action
inertia, because that's where the velocity changes the most, and as we
said, that effect is not linear.  It's a square function.  If we just look
at the key all by itself, we will be kidding ourselves.

As for the effect the pianist feels on the key, the static weight is simply
multiplied by the total action ratio.  But since the moment of inertia
varies as the square of the radius, or the lever arm, the moment of inertia
of the hammer head must be its mass multiplied by the square of the total
action ratio to determine what its inertia will feel like to the pianist.
This still neglects the moments of inertia of the other action components.

I'm not sure exactly how I will do the experiment, but I have some ideas.
I'll have to see what gives me some measurable, definitive results.  No, I
don't have a suitable high-speed camera, but I can rig up some sensors that
can "look" at the hammer and the key, and that will tell me when something
starts to move, how fast it accelerates, and when it reaches a certain
position.  I can display the signals on a scope, or with a computer, and
time it to a fraction of a millisecond.  I won't post it unless I can come
up with something that's meaningful, but I believe I can.  What I want to
see is how long it takes the jack to get back under the knuckle, under the
following conditions:  1. Key weighted in the usual way,  2. Key weighted
near the center,  3. Key with no lead, but very strong wippen assist
spring.  Same key, same action parts, in each case.

It will probably be sometime in January 2004 before I'll have anything to
report.

Merry Christmas,

Jim Ellis



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