<!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><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></BODY></HTML>