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Stephane-<br><br>
What sort of errors do you suspect?<br><br>
David Skolnik<br><br>
<br><br>
At 01:02 PM 2/20/2004 +0100, you wrote:<br>
<blockquote type=cite class=cite cite><font face="arial" size=2>Hi
Don.</font><br>
<br>
<font face="arial" size=2>I would be interested in the maths calculating
the relative errors we do when we measure downbearing with the carpet
thread method and with the Lowell buble gauge method. I have the
feeling that these errors might be enormous. Right ?</font><br>
<br>
<font face="arial" size=2>Best regards,</font><br>
<br>
<font face="arial" size=2>Stéphane Collin</font><br>
<dl>
<dd>----- Original Message ----- <br>
<dd>From:</b> <a href="mailto:dgilmore@kcmpi.net">Don Gilmore</a> <br>
<dd>To:</b> <a href="mailto:pianotech@ptg.org">Pianotech</a> <br>
<dd>Sent:</b> Thursday, February 19, 2004 11:13 PM<br>
<dd>Subject:</b> Re: what is downbearing?<br><br>
<dd><font face="arial" size=2>Hi Julia:</font><br>
<dd> <br>
<dd><font face="arial" size=2>I won't purport to be an expert on the
subjective qualities of downbearing, but purely from an engineering
standpoint, calculating the force of downbearing is fairly simple.
I haven't been following the other downbearing threads, so forgive me if
this information is redundant.</font><br>
<dd> <br>
<dd><font face="arial" size=2>Ideally, downbearing is proportional to th=
e
angle that the string bends downward (toward the harp) after passing over
the bridge. If you can measure this angle, the downbearing force is
simply</font><br>
<dd> <br>
<dd><font face="arial" size=2>F = T * sin A</font><br>
<dd> <br>
<dd><font face="arial" size=2>Where F is the downbearing force, T is the
string tension and A is the angle that the string dips downward.
You can see that more tension means more downbearing as does a greater
angle. Note also that a negative angle (upward) means a negative
downbearing.</font><br>
<dd> <br>
<dd><font face="arial" size=2>If you don't have an accurate way to
measure the angle A, you can also calculate it by measuring the length of
string between the bridge and the next contact point (b) and how far the
string has dipped down at that point (h). </font><br>
<dd> <br>
<dd><font face="arial" size=2>F = T * h / b</font><br>
<dd> <br>
<dd><font face="arial" size=2>Obviously, everything is fine until you
realize that you need to know the string tension...but how? Well,
believe it or not, you can calculate the string tension theoretically if
you know the size of the string and its musical pitch. If I did my
math right, the formula should be</font><br>
<dd> <br>
<dd><font face="arial" size=2>T = 0.0023 * (fLd)^2</font><br>
<dd> <br>
<dd><font face="arial" size=2>Where f is the frequency in Hertz, L is th=
e
vibrating length (agraffe to bridge) of the string, in inches, and d is
the diameter of the string, also in inches. The answer will be in
pounds and the string must be steel. The tension should come out to
around 100 to 200 lbs or so. Then you can use the other equation to
determine the downbearing.</font><br>
<dd> <br>
<dd><font face="arial" size=2>Hope this helps.</font><br>
<dd> <br>
<dd><font face="arial" size=2>Don A. Gilmore<br>
<dd>Mechanical Engineer<br>
<dd>Kansas
City</font><font face="arial"></font><blockquote type=cite class=cite=
cite>
<dd>At 11:11 AM 2/19/2004 EST, you wrote:
<dd>>Greetings,
<dd>>
<dd>> What
exactly is downbearing? Does it affect the sound of the
<dd>>piano or is it a mechanical/ physics measurement for the
playability of the
<dd>>piano? Why is it important to measure it? Can it be calculated by
a
<dd>>formula(e)? What does it mean?
<dd>> </blockquote>
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