Roger, Interesting leap, and not off the wall at all. I wasn't thinking about pins working up out of the bridge when I wrote that. Does it really happen? Or do they just get loose without moving up? I wonder if any of the many different bridge constructions does a better job of holding onto the pins: One piece, vertical laminated with quarter-sawn cap, or whatever? Mike ----- Original Message ----- From: jolly roger <baldyam@sk.sympatico.ca> To: <pianotech@ptg.org> Sent: Friday, April 13, 2001 2:20 PM Subject: Re: Where's the engineer? - was string seating - was bridge caps > Hi Mike, > Great post, but now another wrinkle. > Now this I thought was off the wall. I need to replace my garden fence, > and noting the loose fence post, I started to think in parallel of bridge > pins. And also find how deep I really needed to bore the new holes, to get > longer term stability. > Called a friend of mine at the University who put me in touch with a soil > Hydrologist. Who does a lot of consulting work for power companies with > regards to power lines and adverse soil conditions. > To cut a long story short, where there is moisture changes with an inbedded > post, a pumping action takes place that gradually forces the post out of > the ground. This is also the reason that rocks come to the surface in > farmers fields. > I switched the conversation to the bridge pin problem, his gut reaction was > this is a similar senerio. > With his power line post, they bore down to anchor into a stable substrate, > hoping to get enough stability to stop the post moving. Or bore four > angled anchor holes to to control the direction of forces, and movement. > His gut feeling again, since the whole bridge is being effected by moisture > changes, it will be inevitable the pin will eventually be pumped upwards. > The direction of movement, is always the line of least resistance, makes > sense, the pin is bottomed, so up she goes. The second area of movement, > is flag polling. Same for power lines caused by wind pressure, we have side > bearing. The quality of material and other factors, will help determine how > much of this will take place. > Our parallel, quality of quater saw, growth rings, seasoning, and bore > quality. > Of the wall, or food for thought. > Roger > > > > >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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