what is downbearing?

[Stéphane Collin]

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hello David.

I was just thinking about the relative errors inherent in every measure, =
multiplying or dividing themselves with indirect math formulas.
If you measure the height above the agraffee hole of a carpet thread =
attached to the corresponding hitch pin on the plate, and just touching =
the bridge, you will measure say 2mm (or equivalent in inches).  But =
depending on how you measure those 2mm, say with a ruler, this =
effectively means the true value lays somewhere between 1.7 mm and 2.3 =
mm, because your ruler shows only graduations every 1 mm, because you =
can't eyeball so precisely the top of the hole in the agraffee, because =
it's hard to ascertain exactly when the thread is not touching the =
bridge anymore, because the thread is not 100% straight, etc.
When doing maths with that value, those 2mm, we should do the same maths =
with lowest limit (1.7 mm) and highest limit (2.3 mm) and after the math =
is done, you get results in a sometimes much, much larger fork.  =
Sometimes opposite. =20
My math knowledge hasn't been used for such a long time that it is no =
more valid.  But when it comes to such critical matter as evaluating =
string scaling, we all know that a caliper is just not precise enough to =
give us useful information about string diameter : you really need a =
micrometer to work at a 0.01 mm precision.  I greatly suspect the same =
about downbearing measures. Carpet thread method, and even more bubble =
gauge readings seem ok for me to tell if there IS some downbearing, but =
far inadequate to tell exactly how much within acceptable limits.
Though, I didn't do the needed experiments myself, and I was hoping some =
engineered minded fellow to have done it.  I would be very interested.

By the way, I appreciated you input very much.  I feel so often =
discrepencies between what is commonly accepted theory and what usually =
happens in the real world.

Best regards,

St=E9phane Collin
  ----- Original Message -----=20
  From: David Skolnik=20
  To: Pianotech=20
  Sent: Friday, February 20, 2004 3:10 PM
  Subject: Re: what is downbearing?


  Stephane-

  What sort of errors do you suspect?

  David Skolnik



  At 01:02 PM 2/20/2004 +0100, you wrote:

    Hi Don.
    =20
    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 ?
    =20
    Best regards,
    =20
    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:=20
        >Greetings,=20
        >=20
        >           What exactly is downbearing? Does it affect the =
sound of the=20
        >piano or is it a mechanical/ physics measurement for the =
playability of the=20
        >piano? Why is it important to measure it? Can it be calculated =
by a=20
        >formula(e)? What does it mean?=20
        > 
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