what is downbearing?

[Stéphane Collin]

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Hi Don.

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 ?

Best regards,

St=E9phane Collin
  ----- Original Message -----=20
  From: Don Gilmore=20
  To: Pianotech=20
  Sent: Thursday, February 19, 2004 11:13 PM
  Subject: Re: what is downbearing?


  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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