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
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