Pardon me for dozing in the back row through most of this excellent
class and suddenly waking and not understanding what I have missed,
but......
On Fri, 13 Apr 2001,"Mike and Jane Spalding" <mjbkspal@execpc.com> wrote:
>The question we'll try to answer is: As the bridge swells with increasing
>moisture content, the top surface rises relative to the bridge pin. Will
>the resistance of the wire to slide up the bridge pin be enough to
>permanently indent the top of the bridge cap?
>
>For small angles, the sideways force of the wire against the pin is
>approximately equal to the offset (.131) divided by the pin separation (.75)
>times the tension ( 160)., or 28#. For small angles like this (10 degrees)
>the error is only a couple of percent.
Wouldn't the calculation of the sideways force need to include the
speaking length? IWO, if you took a straight sting segment and
applied a deflecting force 3/4" from the far end of the segment,
wouldn't the deflecting force also be a function of how short a
segment the front portion would be. Bear in mind I've got barely
enough math to balance my checkbook, but when you deflect that
original segment, don't you create two right triangles, sharing
opposite sides, the sum of whose adjacent sides equals the original
segment length, and the sum of whose hypotenuses equals the current
length of the now deflected segment? And wouldn't the force required
for the deflection be equivalent to the force required to overcome
the elastic forces of the strings, in producing the equivalent
elongation along the axis of that segment (instead of perpendicular
to it)? And wouldn't the elongation have to include as an ingredient,
not just the distance from the far end of the segment to the point of
deflection (3/4"), but the distance to the near end, in our piano,
the distance between bridge pins and the speaking length distance,
respectively.
It seems to me much easier to make a .131" deflection in the middle
of a segment than 3/4" from one end, and that ease increasing as the
overall distance from aggraphe/capo to rear bridgepin grows.
If there's going to be a quiz on this, I'd like to know the right answer. <g>
Also, correct me again if I've fallen asleep at a critical moment,
but isn't the calculation of the force of static friction between the
bridgepin and string simply to tell us what force would be holding
the two together should the bridgepin "heave" and the string have no
compelling reason to do anything other than "stick with it" and
follow it upwards? But at the very moment when the string follows the
pin upwards, and a gap opens up underneath the string, wouldn't the
string, experiencing the increasing elastic forces (of an increasing
horizontal deflection, and the arrival of a vertical deflection) much
prefer to reduce the increasing elastic forces of its own elongation,
by simply sliding down the pin back onto the bridge cap?. Assuming as
we have in this case a perfectly cylindrical bridgepin.
I agree with PR-J that bridgepins creep up out of their holes and
need to be tapped down, and I agree with his experience that tapping
drivepins is cures a far larger portion of false beats than tapping
strings. Its has a;so been my experience that strings wander much
more laterally, away from the pin than climbing upwards on the pin. I
even went so far as to set up a dial indicator on individual strings
of a heavily used rehearsal piano to look for downward motions of the
strings. Didn't see any. Maybe somebody else should try this.
Bill Ballard RPT
NH Chapter, P.T.G.
"Garth, Take me!"
"Where? I'm low on gas and you need a jacket"
...........Kim Bassinger and Dana Carvey in "Wayne's World 2"
+++++++++++++++++++++
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