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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