bridges/seating

[Ron Nossaman]

Mike & all,

Duh, (forehead smack) of course the side bearing is considerably more than=
 downbearing. Even I should have figured that out. That's why we ask these=
 questions, to have someone point out what we should have observed on our=
 own and didn't. Makes sense. OK, it's real. Something else occurred to me.=
 Initial hammer strike starts a local wave in the string that would rush=
 down-string and strike the bridge like a Tsunami, whipping the string up on=
 the pin. Like flipping another loop of rope over your kid brother at the=
 noose end of the calf roping game. The reflection wouldn't be as violent as=
 the initial wave because the whole string would be involved and the effect=
 would be less concentrated in any one place. Also, the reflection of the=
 same wave off the agraff, from the other direction would partially cancel=
 out the wave reflection from the bridge. This is probably why the string=
 doesn't go back down by itself. Sound plausible? I think this is starting=
 to make sense. Now I'm really curious as to how close the critical vectors=
 are in the stagger/pin tilt/tension combination that makes this possible,=
 to what we see in pianos. Hurry back, Mike.




At 03:39 AM 4/13/97 +0000, you wrote:
>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=3DFn 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=20
>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=20
>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"=20
>comments;  I like to think things through more thoroughly, but wanted to
>answer before I left!
>
>                                                   Regards,  Mike =20

<***** history deleted *****> Ron Nossaman