----- Original Message ----- From: Ron Nossaman <RNossaman@KSCABLE.com> To: <pianotech@ptg.org> Sent: Wednesday, April 11, 2001 10:28 PM Subject: Re: string seating - was bridge caps > >I have no doubt that the bridge is moving, what I questioned was whether > >this was > >the reason (or how much of the reason) for the string indentations. As I > >said, with > >positive down bearing it would seem to me the same indentations would come > >about > >anyways. Grin... > > The difference between static downbearing and bridge swelling bridge > grooving should be pretty dramatic. Downbearing at 1° and 160lb is a little > over 9 lbs. The resistance to the string being pushed up the bridge pins > has to (not should be, but HAS to) be considerably more. Where are all > those engineers that abandoned all that expensive training to take up piano > thumping? Someone please come up with the math for this one. I'd really > like to know how to compute this. > > > >I suppose you wouldnt mind explaining the significance of > >1470 psi > >here... > > Fiber stress proportional compression limit for hard maple... what else? > > >What would happen I wonder if you took oversized bridgepins, and notched them > >purposely to hold the string in place vertically....grin.. > > That might actually work very well. > > > Ron N Ron, I guess I'm one of those nerds turned thumpers that you're looking for. I kept my schedule free today so I could repaint the bedroom, but what the heck, I never could resist an engineering challenge. I tend to approach most engineering calculations just like tuning or regulation - first pass quick and approximate, evaluate the results in terms of which refinements will do the most to reduce the most significant inaccuracies, make another pass, etc. etc. The question we'll try to answer is: As the bridge swells with increasing moisture content, the top surface rises relative to the bridge pin. Will the resistance of the wire to slide up the bridge pin be enough to permanently indent the top of the bridge cap? First pass, let's simplify the problem by assuming the bridge pins are perpendicular to the surface of the bridge. We'll also assume we have brand new copper plated bridge pins with no wear or indentations where the string contacts them. #15 wire (0.035) at 160# tension. #8 pins (0.096), 3/4 inch between front and rear, pins centered on a straight line from agraffe to hitch pin so that the offset seen at the centerline of the string is the sum of the pin diameter plus the wire diameter, or .131. For small angles, the sideways force of the wire against the pin is approximately equal to the offset (.131) divided by the pin separation (.75) times the tension ( 160)., or 28#. For small angles like this (10 degrees) the error is only a couple of percent. The resistance of the wire to follow the rising bridge is, in this first pass, only due to static friction of the wire against the side of the pin (no angle, no wear or indentations in the pin). This force is equal to the force of the wire against the pin, times the coefficient of static friction of the two materials. For hardened steel wire against the copper plating on the pin, with no lubrication, the static coefficient of friction is .53. So, as the bridge swells and tries to push the wire up the pin, the wire resists with a 15# force. This force is generated at each pin, so the total indenting force of wire against bridge cap is 30# Ron has indicated that the elastic limit of maple is 1470 psi. Dividing 15# by 1470 psi will give us the maximum area of an indentation which could be created with 30# of force = 0.020 square inches. So, over the 3/4 " length of wire resting on the bridge cap, the indentation could be up to .027 wide. Going back to our approximations, and evaluation their effect on our accuracy: The pin is really inclined towards the string by about 20 degrees. This should increase the indenting force (sort of a wedging action). The surface of the pin will not be smooth, the string will press or wear an indentation in the copper plate. This will also increase the the indenting force. If the bridge pins are not copper plated, or if the string has worn through the plating, the coefficient of friction of steel on steel is 0.75, so the force goes up by 50%. Since the approximate first pass shows significant bridge indentation, and the more accurate calculations will show even more indentation, the smart (or lazy) engineer would not bother with further calculations, but he would ask some questions: We've been working with static friction. Once the materials are sliding, the friction is lower (.36 vs. .53). When is the string-to-pin friction dynamic? During tuning/string rendering? FFF hammer blows with sustain? Is any of this sufficient to let the string slide downward to follow the shrinking bridge during periods of reduced moisture content? What happens (tone quality, bridge indentation, strings "climbing pins" if the pins are put in at more or less than 20 degrees? (Wapin?) Has anyone experimented with pins made from, or plated with, a material which is harder and has a lower coefficient of friction? Nickel plated? Are there any lubricants which can safely be applied to strings and bridge pins which would help reduce the friction? Can the pins be installed so that they are anchored to the top of the bridge, rather than the bottom? Maybe by not driving the pointed end into the bottom of the hole, bonding the top with CA or Epoxy? This gets into the debate about how the sound is transmitted from pin to soundboard, energy leakage, etc. Anyway Ron, it's obvious from your comments that you don't need to have "all that expensive training" to have a good feel for what's happening in a piano. Regards, Mike
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