<!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>hello David.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>I was just thinking about the relative = errors inherent in every measure, multiplying or dividing themselves with = indirect math formulas.</FONT></DIV> <DIV><FONT face=Arial size=2>If you measure the height above the = agraffee hole of a carpet thread attached to the corresponding hitch pin on the plate, = and just touching the bridge, you will measure say 2mm (or equivalent in inches).  But depending on how you measure those 2mm, say with = a ruler, this effectively means the true value lays somewhere between 1.7 = mm and 2.3 mm, because your ruler shows only graduations every 1 mm, = because you can't eyeball so precisely the top of the hole in the agraffee, = because it's hard to ascertain exactly when the thread is not touching the bridge = anymore, because the thread is not 100% straight, etc.</FONT></DIV> <DIV><FONT face=Arial size=2>When doing maths with that value, those = 2mm, we should do the same maths with lowest limit (1.7 mm) and highest limit = (2.3 mm) and after the math is done, you get results in a sometimes much, much = larger fork.  Sometimes opposite.  </FONT></DIV> <DIV><FONT face=Arial size=2>My math knowledge hasn't been used for = such a long time that it is no more valid.  But when it comes to such critical = matter as evaluating string scaling, we all know that a caliper is just not = precise enough to give us useful information about string diameter : you really = need a micrometer to work at a 0.01 mm precision.  I greatly suspect the = same about downbearing measures.</FONT> <FONT face=Arial = size=2>Carpet thread method, and even more bubble gauge readings seem ok for me to tell if = there IS some downbearing, but far inadequate to tell exactly how much within = acceptable limits.</FONT></DIV> <DIV><FONT face=Arial size=2>Though, I didn't do the needed = experiments myself, and I was hoping some engineered minded fellow to have done it.  I = would be very interested.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>By the way, I appreciated you input = very much.  I feel so often discrepencies between what is commonly = accepted theory and what usually happens in the real world.</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=davidskolnik@optonline.net href="mailto:davidskolnik@optonline.net">David Skolnik</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> Friday, February 20, 2004 = 3:10 PM</DIV> <DIV style="FONT: 10pt arial"><B>Subject:</B> Re: what is = downbearing?</DIV> <DIV><BR></DIV>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 class=cite cite="" type="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 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><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 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><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 class=cite cite="" type="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>> = </DD></BLOCKQUOTE></DD></DL></BLOCKQUOTE></BLOCKQUOTE></BODY></HTML>