>That would depend on the point of departure being below the level of Sin >0.5 * d >where d is the distance of the point from center bridge... Otherwise the >bridge at >that point will still be higher or as high as the bearing angle... agreed ? Of course. I was assuming some bearing. >No no no no no... you cant use the linear sin expression to make that >comparison. >You need an exponential equation for that. I used the Sin function just to >get to a >low point for the edge relative to the bearing angle. I know that. I was just using your example, which doesn't work either (and for the same reason), to make a point. > As for how the string indents over the whole width of the >bridge...well..one would expect the indentation as one approaches the middle >of the >bridge to be farther away from such a straight line... the string is going >to want >to try and curve its way over the bridge, not cut a linear straight line. Correct, since the string stiffness is supplying a lot of the pressure between the clamp points at the bridge pins, where the pressure is considerably higher when the bridge swells. >As for your particular example...it would be nice to know what the real bearing >angle was for the points you sampled... what did you measure with by the >way....... >hard to be all that accurate with measuring such small distances without >some nice >tools. I'd like to check this out a bit closer myself so if you have a neat >trick >for exact measurements please share it. That's a big part of my point here. It's not the bearing angle that's doing the damage. It's the pin hanging on to the string as the bridge top rises, pressing the string into the cap. The corrected measurements I posted were taken with a dial indicator from the bridge top, zeroed to the surface, then measured with a wire smaller than the one originally on the bridge at that point. >I certainly see the sense in this... if the pins hold the string firmly enough >down, then the same "curving around the bridge surface" indentation would be >created. I have, as I said before no doubt that this is at the very least a >contributing factor. My only point is that string seating does not become >superfluous until the indentation at the bridge edge is below the bearing angle >line... thats where I brought in the Sin function.. as it can be used to >find that >exact depth any given point on the bridge. It's considerably more than a contributing factor. When you compare the force necessary to push a string up a canted bridge pin, against the friction of side bearing and tension, and against downbearing, it is considerably more than just downbearing forces alone. Mike Spalding posted some information to get me started, giving a simplified version illustrating the basic likelihood of my assumptions and offering that the smart (or lazy) engineer wouldn't bother with more calculations. Being neither smart, nor lazy, I spent most of yesterday digging through my piles of reference material until I put together what I wanted. Here's what my routines produce by way of numbers, using Mike's friction coefficient figure of 0.53. String TensionStagger AngleFriction CoefficientPin AngleResistance DownResistance Up StSaFcPaRdRu 160100.5228-0.041926.0454 160100.52251.6038125.0876 160100.52204.3347323.3399 160100.52157.0326621.4146 160100.52109.6770619.3262 160100.52512.247817.0908 160100.52014.725414.7254 These were pasted straight out of the spreadsheet. I hope they're visible. This is static friction. The string vibrating during play will lower these numbers, so if there is any bearing at all, strings will tend to seat themselves, even with vertical pins. The numbers in the far right column are the evidence I was looking for. Though I didn't include it into the spreadsheet (yet), string downbearing is added to the up values, and subtracted from the down values. Ron N
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