Key Leads and Inertia

[Sarah Fox]

Hi John, Ric, et al.,

Action acceleration is actually a means of reducing jerk, which is the
derivative of acceleration.  Oddly enough, it's a way of smoothly shifting
relative impedance to achieve an efficient transfer of kinetic energy from
one side of the lever to the other.

Think of circus acrobats propelling each other off of springboards.  The
most efficient fulcrum is curved.  When the falling acrobat first lands on
the board, he has a large mechanical advantage over the movement of the
acrobat on the other end of the board.  That softens his impact with the
board and likewise softens the initial acceleration of the other acrobat.
As the springboard rocks over the fulcrum, the mechanical advantage shifts
the other way.  Thus, the falling acrobat moves smoothly from a low rate of
deceleration to a higher rate of deceleration, and the rising acrobat moves
from a low rate of acceleration to a higher rate of acceleration.  Maximum
acceleration/deceleration occurs when the mechanical advantage is 1:1 (i.e.
when the board is level).  It is at this point that the "impedance" is
matched between the two sides.  As the board continues to rock, the falling
acrobat's rate of deceleration declines, as does the rising acrobat's rate
of acceleration.  If the entirety of the board rests on the fulcrum and is
massless, then the initial mechanical advantage is 0 and progresses to
infinity (or vice versa, depending on which acrobat one is talking about).

This dynamic is far preferable to the "bang" on both ends of the board that
would occur with a conventional fulcrum.  The smooth transition of kinetic
energy with a round fulcrum results in less lost energy and therefore more
altitude, not to mention reduced wear and tear on the acrobats' legs.  With
a "banging" springboard, the compliance of the system is limited to the
elasticity of the springboard and of the acrobats' legs, which are the
elements taking the brunt of the impact.  To the extent that any of these
elements are inelastic (or exhibit hysteresis in their response), energy
will be lost.

The implications for a key action are rather obvious.  It's a nice
innovation by S&S.  My question is this: How much is the balance rail
rounded, and over what distance?  (I'd be interested to try to duplicate it
in my Wissner.)

Peace,
Sarah


----- Original Message -----
[link redacted at request of site owner - Jul 25, 2015]
To: "Pianotech" <pianotech@ptg.org>
Sent: Thursday, May 01, 2003 4:33 PM
Subject: Re: Key Leads and Inertia


> Richard Brekne wrote:
>
> >
> > Much has been made of the idea that more mass requires more effort to
> > move, yet at the same time it is ignored that once that mass is moving
> > it takes less effort to keep it moving. In reality these are flip sides
> > of the same coin and to some degree whats good about the one side is bad
> > about the other.
>
> Well not exactly. Acceleration (change in speed) not velocity (constant
> speed)is what you need to look at in the action. Acceleration is the
> change of velocity and it always requires force. While it's true that in
> strict physics it takes no force to maintain velocity (as long as there
> is no opposing force like friction or the pull of gravity) this is not
> much of a factor in regard to the pianos action. In order to play a note
> the key is accelerated from  0 velocity to some  greater velocity during
> a short period of time. There is really no time for the player to
> benefit from any momentum (mass time speed) that may happen in the
> action. While playing the action bits and pieces are accelerating or
> decelerating. I can't think of any time when a part is moving with
> constant speed except when the note is not being played at all.
>
> Of coarse there is the escapement. But even a hammer flying free from
> the rest of the action feels restraint. It is being held back by
> friction and the pull of gravity. It is decelerating. This is why the
> let off is kept close to the string - the less of it the better. Any
> momentum the hammer has as it impacts the string was bought and paid for
> by the force applied to the key.
>
> > In answer to your querry, it is my guess that the reasoning for the
> > acellerated action has more to do with key motion after the finger gets
> > it moving, and after it rebounds of the keyfront cushion, as this is
> > where more inertia is more an aid then a hinder.
>
> No. More inertia does not help the key to rebound. When you play a note
> the key is accelerated till it stops (decelerates) on the front cushion.
> It must accelerate again to come back up.
>
> Reducing the inertia (the resistance to acceleration) helps with both
> accelerating the key while playing and the acceleration of the key
> coming back up. It makes the action easier to play and faster as well.
>
> John Hartman RPT
>
> John Hartman Pianos
[link redacted at request of site owner - Jul 25, 2015]
> Rebuilding Steinway and Mason & Hamlin
> Grand Pianos Since 1979
>
> Piano Technicians Journal
> Journal Illustrator/Contributing Editor
[link redacted at request of site owner - Jul 25, 2015]
>
>
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