what is downbearing?

[Don Gilmore]

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Hi Julia:

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.

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

F =3D T * sin A

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.

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). =20

F =3D T * h / b

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

T =3D 0.0023 * (fLd)^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.

Hope this helps.

Don A. Gilmore
Mechanical Engineer
Kansas City
      At 11:11 AM 2/19/2004 EST, you wrote:

      >Greetings,

      >=20

      >           What exactly is downbearing? Does it affect the sound =
of the

      >piano or is it a mechanical/ physics measurement for the =
playability of the

      >piano? Why is it important to measure it? Can it be calculated by =
a

      >formula(e)? What does it mean?

      >=20

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