Downbearing

[Ron Nossaman]

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