<!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 Stephane:</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>I guess it depends on how accurate your = downbearing figure needs to be.  Remember that it will be small in = comparison to the string tension.  A dip angle of as much as 5 degrees will = result in a downbearing force of T * sin 5.  Sin 5 is about .0872, so the downbearing force would only be about 9% of the string tension.  = For a string tension of 150 lbs this would only amount to about thirteen = pounds.  I guess it just depends on how accurate the downbearing figure needs to be.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Even how "in-tune" the piano is will = affect this force.  For example, changing A-440 from 440 Hz to 441 Hz would increase the string tension by about 1/2%.  The = downbearing would also change by this percent.  A string with a tension of 150 = lbs would increase by about .75 lbs.  If we use the 5-degree case = above, this would change the downbearing force by about .07 lbs, or about an ounce = (30 g).  Is this a lot?  Is this negligible?  I'll let you = guys argue that.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>If you have a good way to measure the = angle, this method should be pretty damned accurate.  I used it extensively to calculate the upward force on the agraffes for the self-tuning piano = (which has fiberglass agraffes) and got good results.  However, the angle is = greater in this case so the force is much larger.  The force increases to = as much as half the string tension at an angle of </FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>arcsin (1/2) = 30 = degrees.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>I was also only concerned with tensile = and fatigue strength, so I probably didn't need as accurate a figure as you are = looking for at the bridge.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>There are certainly more accurate = methods for measuring the string tension, if necessary.  Using a strain gauge = would be one of the most common.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial 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"> <DIV style="FONT: 10pt arial">----- Original Message ----- </DIV> <DIV style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: = black"><B>From:</B> <A title=collin.s@skynet.be = href="mailto:collin.s@skynet.be">Stéphane Collin</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 = 8:54 AM</DIV> <DIV style="FONT: 10pt arial"><B>Subject:</B> Re: what is = downbearing?</DIV> <DIV><BR></DIV> <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></BLOCKQUOTE></BODY= ></HTML>