Ron & list:
I'm on my way out of town for two weeks, but this was an interesting thread,
and I
wanted to at least give a swag, in case the thread has died by the time I
get back.
Frictional force is equal to the normal force times the coefficient of
friction (Ff=Fn x u). I'm not a piano technician, so I will assume some
values for discussion purposes, but I think the logic will hold. The
downbearing force is a function of
the angle across the bridge versus the string tension. The side force
against the bridge pin is a function of the side angle against the pin and
the string tension.
The string tension being a constant for a particular string the forces
involved (down
force versus side force against the bridge pin) are a ratio of the angles
down and sideways on the pin. I looked at my piano and it looks like
typical ratios would be:
down force .1 inch down over a 30 inch length or a tangent of 1/300 versus a
side angle force of .1 inch sideways over a .75 inch length or a tangent of
1/7.5 (depending of course on what note you are looking at). Please
note that I am just wildly estimating, but the differences are so great that
the argument will hold with a large estimation error. Anyway..... the
sideward force on
the bridge pin relative to the down force will be a ratio of the above numbers.
In our hypothetical example above, down force would only be 7.5/300 of the
side force on the pin. With a friction coefficient of approximately .1 to
..15 for lubricated copper alloy versus steel, it looks like the bridge pins
could definitely hold a displaced string off of the bridge, even with the
negative angle the bridge pins have. If this thread is still going when I
get back I'll take some measurements, and can calculate the angle a bridge
pin would have to be at to prevent this from happening. Of course a
microscopic burr or imperfection on the pin will also lead towards causing
the string to stay up off of the bridge when displaced.
As to this causing false beats, I don't pretend to know the answer; but will
ask a
naive question (I don't have any acoustic background knowledge): When the
string is seated against the bridge it has one degree of freedom (it can
move up and down, it seems sideways would be rapidly damped). If it is held
off the bridge up on the pin it can vibrate in a more 360 degree mode -
could this cause false beats?)
Well, I've got to run - please forgive me for the above "off the top of my
head"
comments; I like to think things through more thoroughly, but wanted to
answer before I left!
Regards, Mike
At 05:46 PM 4/12/97 +0000, you wrote:
>Hi John,
>
>Ambrose Beirce defined apology as "laying the groundwork for a future
offense". With this in mind, and looking toward the future, I'm reluctant to
accept apologies where there was no offense. This being the case, I'm
returning your apology (unused) so you may save it for a more worthy cause.
>
>Doggone you John, I was hoping to get cheap answers without having to do my
own R&D. Now I'm going to have to go out in the shop and try your experiment
for myself. <G> I can see where the "stagger" and resulting side bearing
would have some bearing (sorry) on the phenomenon as it would vector the net
bearing more toward the horizontal. With little to no side bearing, the net
bearing vector would be vertical, straight down on the bridge. Maybe there's
still hope of clarification. Mike Imbler posted on another topic stating
that he was a mechanical engineer. Mike help, please! Is the coefficient of
friction between music wire and copper plated mild steel high enough to
account for this phenomenon with the forces and angles involved here in
pianos? In other words, does the math fit the model? What is the high limit
of angle at a given tension before the string slides on the pin?
>
>While Mike is deciding whether or not to play, I have more questions.
>
>A hard hammer blow (from below) will cause a string to slide up a bridge
pin. We seem to have a consensus on this one, yes? Since the hammer blow
isn't delivered anywhere near the bridge, isn't it the wave in the string
caused by the blow that propagates down to the bridge that does the deed?
Isn't the excursion of a string above the rest position balanced by an equal
(average-diminishing) excursion below? Why, then, doesn't the excursion
below the plane pull the string back down, especially with all the help it's
getting from down and side bearing????
>
>Lastly, how would a string stuck up on a bridge pin cause a false beat in
the first place? If it's hanging in there good enough to withstand all the
above mentioned forces to the contrary, the string termination is as solid
as one could hope for! If it's because the bridge pin is loose, we are back
to my original premise that most of the false beats found in pianos are the
result of loose bridge pins and aren't curable by seating strings to
bridges. I don't mean this to look like I'm trying to lead the discussion
with a bull whip, but this is where the logic process brought me. All
enlightenment, clarification, pertinent random musings, empirical
observations and universal truths cheerfully entertained.
>
>
>Expectantly,
> Ron Nossaman
>
>
>
>
>
><******* History beyond this point *********>
>
>
>
>At 09:17 PM 4/11/97 -0600, you wrote:
>>Hi Ron,
>>
>>My apologies for misinterpreting your question. I understand now what
your asking, and I have tried a very un-scientific, but possibly
enlightening experiment this evening.
>>
>>I am currently doing some work on my personal piano in my shop. I rebuilt
this piano (a Bradbury 5'6" reproducer grand) about six years ago, and it
happened to be my first bridge recapping job. Because of this some of the
bridge pin placement is, well, pretty embarasingly wacky. A few pins are
placed in such a way that there is very little, if any side bearing. The
rest of the job is fine: good downbearing, nice tight well angled bridge
pins etc. I took some strings off and checked bridge pins and found no
*visible* notching in them.
>>
>>I got to thinking that this would be a great situation to test if side
bearing played a major role keeping the strings off the bridge.
>>
>>Here's what I did: With the piano up to pitch, I simply pulled up on the
speaking lenght side of a couple of strings until they lifted off the
bridge, then let go and watched what happened. The strings that had no side
bearing went right back down to the bridge. The strings that had decent
side bearing stayed up! I did several in the sixth octave of the piano (this
is where the misplaced pins are) and the strings rode up above the bridge
anywhere from 10 to 15 thousandths according to my feeler gauge.
>>
>>This little test, while not very controlled, would seem to point to side
bearing, and its attendant friction as one of the major contributing factors
in keeping those suckers up in the air.
>>
>>Comments anyone?
>>
>>John McKone, RPT
>>St. Louis Park, Minnesota
>>(612) 280-8375
>>
>>-----------------------------------------------
>>>From : Ron Nossaman <nossaman@southwind.net>
>>Sent : 04/11/97
>>To : pianotech@byu.edu
>>Subject: Re: bridges/seating
>>
>>At 08:58 PM 4/10/97 -0600, you wrote:
>>>Ron,
>>>
>>>If you're asking why the string can creep up against the pressure of
downbearing and friction, you need look no further than the impact of the
hammer (on a grand anyway) Especially on a hard use piano.
>>>
>>>John McKone, RPT
>>>St. Louis Park, Minnesota
>>>(612) 280-8375
>>>
>>
>>
>>Nope, nope, not at all. It's quite obvious that a string can be knocked up
hill against tension, friction, or anything else you care to name. You can
here it happening if you work at it. It's quite clear to me how a string
GETS up a bridge pin. I'm saying that it's not possible for it to STAY up
off the bridge, AT REST, against tension and side/down bearing and pin
angle, unless there is something physically wrong with the bridge pin. What
else would hold it up there magically???? David Copperfield plating? There
has to be a real reason for an observable physical phenomenon. I get enough
mysticism and "have faith, trust me" metaphysics from Government.
Demonstrations can illustrate that it's possible (I'm still working on that
one), but I don't think anyone can realistically champion a fix without a
clear understanding of what's broke. Let's talk "mechanism". I'm willing to
accept the notion that this happens only in the context of a rational
explanation as to WHY it is possible. Wouldn't you like to know too?
>>
>>
>> Ron Nossaman
>>
>>
>> Ron Nossaman
>
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