Adjusting wippen assist springs

[Sarah Fox]

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Hi Mark,

I agree with your napkin sketch, but this brings into question the =
psychophysical concept of a "just noticeable difference" (JND) -- the =
magnitude of difference that can just be detected by a human observer.  =
I am not very well versed in somatosensory (touch) characteristics =
(being an auditory person), but JNDs are typically on the order of 1/256 =
of the stimulus magnitude -- not *exactly* 256, of course.  However, the =
8-bit word worked out well for encoding things such as brightness, as =
1/256 is about a JND for brightness.

This leads to your napkintop example.  Would a 1 percentish change in =
inertia be noticeable?  Probably, yes.  Would it be very significant?  =
Probably not. =20

Would a 3% change (15 g off of BW, from 30 g of leading at a halfway =
point) be noticeable?  Yes.  Would it matter?  Yes, it would likely give =
the pianist some edge.  There are certainly pianists who like the spring =
assist for *some* reason.  At the very least, they notice the difference =
in the way the piano plays.

Now many pianos that are balanced in the traditional manner.  Some key =
leading is located way out on the front end of the keystick.  Now the =
key lead inertia becomes even more significant -- 6% of total inertia to =
achieve 15 g off of balance weight.  More of an edge.

But using the halfway-point leading, consider the leading consequence of =
adding a gram to the hammer and 12 g of leading to the halfway point on =
the keystick to compensate for the additional BW.  NOW we're talking =
about a 10% ratio of additional key inertia to additional hammer =
inertia, which is becoming more significant still.

Does 10% matter?  Does 5% matter?  Well, does a pianist notice BW =
inconsistencies of 2 or 4 or 5 g between keys during soft playing?  =
That's roughly the same degree of difference.  It would probably take a =
more advanced pianist to care, granted.

Even so, your napkintop sketch is very illuminating.  I frankly hadn't =
expected the ratio to be that high!

Peace,
Sarah

 =20
  ----- Original Message -----=20
  From: Mark Davidson=20
  To: Pianotech=20
  Sent: Friday, December 12, 2003 8:49 PM
  Subject: Adjusting wippen assist springs


  Jeez Ric. You go out on a limb=20
  and end up riding a freight train.

  I have to agree with Sarah's physics.=20
  Same force, less mass, more acceleration.
  That assumes a constant force, though.
  Basically if you speed it up, you push on
  it.  If you slow it down, it pushes on you.
  So if things are decelerating, then you can
  get force out of the key lead.  If
  somehow you could get it all moving and
  then stop pushing on the key with your=20
  finger, then there could be enough
  energy in the key to continue to drive the
  hammer home.  Not really how we typically
  play the piano though, unless you consider
  "striking" the key vs. other types of motions.

  But here's the real rub.  She's got you=20
  riding a train when you should be=20
  riding a bicycle. =20

  Let's do a little energy napkin sketch. =20

  Energy of mass m moving at velocity v=20
  is (m*v^2)/2.

  So if the key front is moving at speed=20
  1, then a key lead halfway out is=20
  moving at .5, while the hammer=20
  moves at approximately 6.

  If the hammer mass is 10g and the=20
  lead mass is 10g, then the lead=20
  energy is=20

  (10*.5*.5)/2 =3D 1.25

  while the hammer energy is=20

  (10*6*6)/2 =3D 180!

  That's a ratio of 1:144.
  So yes, any energy=20
  remaining in the key when it=20
  bottoms out is wasted, but by far
  most of the energy is in the hammer.
  And it would appear that adding=20
  a key lead makes less than a 1% change in
  the TOTAL inertia (hammer inertia=20
  is effectively much larger because=20
  of the leverage involved).

  Oversimplified - should all be
  rotational - and neglects
  the inertia of the unleaded key,
  but I think it makes the point
  that the SW and SWR are far and
  away the most important components
  of the overall inertia.

  For better repetition though, you=20
  still want low key inertia.  That would
  appear - at least based on this example -=20
  to be the chief benefit of assist springs.


  -Mark Davidson






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