<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META http-equiv=Content-Type content="text/html; = charset=iso-8859-1"> <META content="MSHTML 6.00.2800.1400" name=GENERATOR> <STYLE></STYLE> </HEAD> <BODY bgColor=#ffffff> <DIV><FONT face=Arial size=2>Hi Don.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><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></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Best regards,</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Stéphane Collin</FONT></DIV> <BLOCKQUOTE dir=ltr style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; = BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px"> <DIV style="FONT: 10pt arial">----- Original Message ----- </DIV> <DIV style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: = black"><B>From:</B> <A title=dgilmore@kcmpi.net href="mailto:dgilmore@kcmpi.net">Don = Gilmore</A> </DIV> <DIV style="FONT: 10pt arial"><B>To:</B> <A = title=pianotech@ptg.org href="mailto:pianotech@ptg.org">Pianotech</A> </DIV> <DIV style="FONT: 10pt arial"><B>Sent:</B> Thursday, February 19, = 2004 11:13 PM</DIV> <DIV style="FONT: 10pt arial"><B>Subject:</B> Re: what is = downbearing?</DIV> <DIV><BR></DIV> <DIV><FONT face=arial><FONT size=2>Hi Julia:</FONT></FONT></DIV> <DIV><FONT face=arial><FONT size=2></FONT></FONT> </DIV> <DIV><FONT face=arial><FONT 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></FONT></DIV> <DIV><FONT face=arial><FONT size=2></FONT></FONT> </DIV> <DIV><FONT face=arial><FONT size=2>Ideally, downbearing is = proportional to the 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></FONT></DIV> <DIV><FONT face=arial><FONT size=2></FONT></FONT> </DIV> <DIV><FONT face=arial><FONT size=2>F = T * sin = A</FONT></FONT></DIV> <DIV><FONT face=arial><FONT size=2></FONT></FONT> </DIV> <DIV><FONT face=arial><FONT 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></FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><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></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>F = T * h / b</FONT></DIV> <DIV><FONT face=arial><FONT size=2></FONT></FONT> </DIV> <DIV><FONT face=arial><FONT 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></FONT></DIV> <DIV><FONT face=arial><FONT size=2></FONT></FONT> </DIV> <DIV><FONT face=arial><FONT size=2>T = 0.0023 * = (fLd)^2</FONT></FONT></DIV> <DIV><FONT face=arial><FONT size=2></FONT></FONT> </DIV> <DIV><FONT face=arial><FONT size=2>Where f is the frequency in = Hertz, L is the 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></FONT></DIV> <DIV><FONT face=arial><FONT size=2></FONT></FONT> </DIV> <DIV><FONT face=arial><FONT size=2>Hope this = helps.</FONT></FONT></DIV> <DIV><FONT face=arial><FONT size=2></FONT></FONT> </DIV> <DIV><FONT face=arial><FONT size=2>Don A. Gilmore<BR>Mechanical Engineer<BR>Kansas City</FONT></DIV> <BLOCKQUOTE dir=ltr style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; = BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px"> <BLOCKQUOTE class=cite cite="" type="cite"> <DL> <DD>At 11:11 AM 2/19/2004 EST, you wrote:<BR> <DD>>Greetings,<BR> <DD>> <BR> = <DD>>           What exactly is downbearing? Does it affect the sound of the<BR> <DD>>piano or is it a mechanical/ physics measurement for the = playability of the<BR> <DD>>piano? Why is it important to measure it? Can it be = calculated by a<BR> <DD>>formula(e)? What does it mean?<BR> <DD>> </FONT><BR></DD></DL></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE></BODY></HTML= >