leverage: was aftertouch

[Dan Squire]

At 09:46 AM 9/15/95 -0600, Mr.Johnson wrote:

>        That element of the total sensory impression of all this work,
>acceleration and inertia which cannot be accounted for with touch weight
>measurements, is a quantity which must somehow be added to the touch
>weight, however intuitively.

You're absolutely correct on this point.  Using the standard method of
weighing off a piano (at least the way I was taught a long time ago in
Cincinnati) the hammer will move at a constant velocity.  When the hammer is
moving at a constant velocity there is a force balance which means that the
force provided by the gram weights is equal to the force resisting the key's
motion.  And as we all know, when the velocity is constant there is no
acceleration.  When the piano is being played by a real person rather than
gram weights the hammer/key assembly can undergo an acceleration.
      Acceleration can play a significant role in the force needed to produce a
motion.  The force produced by the acceleration combined with the static
force increases the force that must be applied by the pianist's finger.
      In the case of a piano action the acceleration is not linear, it is angular
acceleration.  This angular acceleration causes an inertial torque.  The
value of this inertial torque is the product of the angular acceleration and
the mass moment of inertia.  Since the angular acceleration in a piano
action can have an infinite number of values, the orientation of the mass is
really the only thing can be adjusted to cause a change in the inertial
torque.  This orientation of mass is what is meant by the mass moment of
inertia.  The mass moment of inertia is the measure of how much is how far
away.  Therefore, as more mass is placed farther away from the axis the
resistance due to the inertial torque will be greater for a given acceleration.

Dan Squire

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        Long live this thread!
                                -Dennis Johnson
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