Hi Richard & all, The problem with the nickel/dime/quarter thing is it just represents the different relative proportions of bearing needed according to where you are on the board. It's a rough proportional approximation of how the board will deflect under load. Other than that, it doesn't mean much of anything unless you can factor in the amount of crown in the board, plate height relative to the soundboard rim, and the size of the piano involved. It has to be reducible to angles to mean anything. Even if you have a way to measure the height at the bridge relative to the agraff and aliquot, you have to figure each angle, in degrees, taking the sin of the result of dividing the segment length by the offset height, combine the angles into one representing the slope difference between the segments, and working the chart from there. It's a whole lot easier just taking the readings from the strings with the Lowell gage. Again, I was looking for a way to get *adequately* accurate information with a minimum time and cash expenditure. I had already purchased the Lowell creature as a result of rebuilding a Baldwin grand with Accujust hitch pins, so I geared the process toward the tools I had at hand. Here's the program that generates the chart. TPascal's trig functions work in radians, hence the "radcon" constant for conversion to degrees after the calculation. If you do this by hand with a calculator, you will probably get degrees back without the conversion. const radcon=0.017453292; {radian/degree conversion} var bearing,angles:array[0..99]of real; {ten degrees ought to be enough} outfile:text; Function Formatbearing(r:Real):String; Var s:String; begin str(r:8:8,s); {convert from engineering to human format} While s[ord(s[0])]='0' do Delete(s, ord(s[0]), 1); While (s[1]=' ') do Delete(s, 1, 1); s:=copy(s+' ',1,16); Formatbearing:=s; end; function formatdegrees(r:real):string; var s:string; begin str(r:2:1,s); formatdegrees:=s; end; procedure compute; var i:integer; angle,straight,temp:real; begin straight:=180; angle:=0.0; angles[0]:=0; bearing[0]:=0; for i:=1 to 99 do begin {set up in easy steps for clarity} angle:=angle+0.1; angles[i]:=angle; temp:=(straight-angle)/2; {angle represents two string segments} temp:=cos(temp*radcon); {compute one segment} bearing[i]:=temp*2; {double it for total bearing force} end; end; procedure printem; var i:integer; s,s2:string; begin writeln(outfile); writeln(outfile,'Measure angle difference between string segments on either side of the bridge.'); writeln(outfile,'Multiply times tension for downbearing weight.'); writeln(outfile,'Ron Nossaman June, 1997'); writeln(outfile); writeln(outfile,'Angle Bearing Angle Bearing Angle Bearing'); for i:=1 to 33 do begin s:=formatdegrees(i/10); while length(s)<5 do s:=' '+s; s:=s+' '+formatbearing(bearing[i]); s2:=formatdegrees((i+33)/10); while length(s2)<5 do s2:=' '+s2; s:=s+s2+' '+formatbearing(bearing[i+33]); s2:=formatdegrees((i+66)/10); while length(s2)<5 do s2:=' '+s2; s:=s+s2+' '+formatbearing(bearing[i+66]); writeln(outfile,s); end; end; begin assign(outfile,'bearing2.txt'); rewrite(outfile); compute; printem; close(outfile); end. At 03:26 AM 6/22/97 -0500, you wrote: > ~~~~~~~~~~~~~~~~ > The problem I would like to solve is similar to; " a piano string at >a tenion of 180 pounds is pushed up 1/8 " by the bridge. What is the >pressure of the wire on the bridge.? " > ~~~~~~~~~~~~~~~~ > On reflection, I am wondering if it might not be easier to measure >angle. ~~~~~~~~~~~~~~~~ > In the meantime it would be intersting to convert >Travis's rule of thumb for bearing (unloaded) of a dime, nickle and >quarter through the sections, to down pressure. But I think the >measurements of distance of deflection must be taken after tension is >applied. > So after spending all of this time rambling here, I wonder if Ron >can come up with a chart that shows the down pressure for distance >the string is deflected? Some one of us will have to put in the >time, I guess it is my turn,,but sometimes I am slower than an >elephant. > > Thanks for the calcualtions and tables Ron. I don't have turbo >pascal installed, but do have 3 hours credit from a >university...(four years ago, so figure out what is left from not >using it for that long) However if the equations can be posted, I >might could convert them to a spread sheet style that could be cut >and pasted into most brands, especially MS Works for Windows, Quatro >Pro and and 1 2 3. > >Richard Ihavenotyetbeguntoramble. > ~~~~~~~~~~~~~ >> Hi all (that's left), > >Is that left brained, left handed, left of center, or left here? >Takes a left brained person to ask that>? > No, no, so what, yes, oh? Ron Nossaman
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