Reading a dial gauge

[Sarah Fox]

Hi David,

That's a great question for a math nerd.  ;-)

What angle are you trying to measure?  Backscale segment to speaking 
segment?  Backscale to bridge and speaking to bridge?  I assume you're 
putting the plunger at the center of the bridge.  Yes??

The sine of 1 deg is roughly .018.  That reading would correspond to the 
angle from "horizontal."  Then double the angle to go the other way.  In 
other words, the total angle between speaking and backscale would be 2 deg. 
A 1 deg angle would give you a reading of .009.  This of course assumes that 
your bridge has no width to it, like a violin's.  That's a very bad 
assumption, of course.

The distance between the front and read bridge pins is an important factor. 
If you measure across the bridge, with the plunger at the center of the 
bridge (which is how you do it??), then you would estimate the total 
downbearing angle (between speaking and backscale segments as...

A=2 Arcsin(d/(1-b/2)),

where

A=downbearing angle
d=deflection (gauge reading)
b=bridge width from front pin to back pin

Downbearing pressure would be estimated as...

P=2Td/(1-b/2),

where

P=downbearing pressure
T=string tension

Of course these formulas assume an angle near zero and are only 
approximately correct, but they work very well for the first several 
degrees.  They also assume a sharp angle in the wire, with no arching across 
the bridge.

Peace,
Sarah


----- Original Message ----- 
From: "David Love" <davidlovepianos@comcast.net>
To: "'Pianotech'" <pianotech@ptg.org>
Sent: Tuesday, July 05, 2005 6:03 PM
Subject: Reading a dial gauge



So I picked up this dial gauge from Schaff and I'm not really sure how it
works.  The center prong is the plunger and the two outer prongs are 1" from
the center.  The smallest increments that can be read are .001".  So if I
put the plunger on the center of the bridge with the two outer prongs
resting on the front and back segments respectively, does a reading of .018"
equal 1 degree?  Or would that be 1/2 a degree since the total reading must
be split between the two prongs at a total of 2" apart?

Yeah, I shoulda paid more attention in trig class.

David Love
davidlovepianos@comcast.net



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