Where's the engineer? - was string seating - was bridge caps

[Brian Lawson]

Hi Roger, bur surely your fence differs in that it doesnt have 20 tones of
pressure bearing down on it?

Brian Lawson, RPT
Johannesburg, South Africa

TEXOMA CHAPTER
http://texoma.int.chapter.tripod.com

----- Original Message -----
From: "jolly roger" <baldyam@sk.sympatico.ca>
To: <pianotech@ptg.org>
Sent: Friday, April 13, 2001 9:20 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" i
f
> >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
> >
>