> Hopefully you spent four years doing something more enjoyable and > ultimately more lucrative (oh, wait, you went into the piano business - > well, hopefully you spent four years doing something more enjoyable). Intermittently, though not necessarily work related. > Sheesh. Someone's actually gonna check my numbers? Now I'm in trouble. Nope, it's only math challenged me. You're safe. > I'm sure that Ptolemy won't be happy to hear that. I don't know what you > mean about the sin function getting less accurate as the angle increases. Something I thought I had figured out about downbearing angles a long time ago. I can't find an example of the code anymore, and I don't remember exactly what I did - except that it was likely wrong. > The square of the length of the hypotenuse is the sum of the > squares of the side lengths. Clear as mud? Sorry, I'm not a math teacher, > so I hope I haven't said something not strictly correct here. Caveat emptor. Got it. Yes, that does make sense. > If the string is firm against the cap then you're correct. The point of my > little exercise was to show that if the string was in fact above the cap > that it might not want to slide down. Ok, got it. > I don't understand why you have a different number for moving down the pin > and moving up the pin? Static friction is dependent on the normal force > between the string and bridge pin and the coefficient of friction. The > initial force to start an infinitesimal movement of the string should be > the same whether it moves up the pin or down. The difference is the downbearing and vector force from the pin tilt. Going down, the vector is in your favor. Going up, it is resistance. What I was originally looking for with this spreadsheet was an indication of the PSI load placed on the bridge cap by the expanding cap pushing the string up the pin. I wanted ammunition for my cyclic destruction scenario of cap damage. This seating thing was an afterthought. >> By my reckoning, the 2.6lb of downbearing and the 5.4lb down force from >>the pin slant and side bearing exceeds the static resistance, and the >>string will seat on the bridge automatically. > > > Perhaps you can give me a little more detail on how you arrived at your 6.7 > LB static resistance number. It's the static resistance less the down force vector. Hmmm. Going back to my spreadsheet and untangling and simplifying what I did to get there I find I was using the down vector from pin tilt twice. That figures. So I'd still have the 6.7lb resistance down with only the 2.6 lb downbearing force to overcome it, so in theory, it should be possible for a string to remain up on the pins. In practice, I don't see any evidence that this happens. I see strings in contact with bridge caps with crushed edges, so I'm assuming that string movement from play and the continual moisture and temperature induced dimensional changes of everything involved are partially overcoming the static friction and the down vector force seats the string on the bridge. Until reports of feeler gages going under strings on bridge caps start poring in, I won't believe it happens. The easily observable fact that the notch edges of old bridges, and not so old bridges, are crushed at an angle far exceeding any downbearing angle the bridge ever supported means that a string seated on the bridge top is quite likely not touching the notch edge, and can still be measurably forced down there. Thanks for the clarification on the calcs. Ron N
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