what is downbearing?

[Don Gilmore]

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Hi Stephane:

I guess it depends on how accurate your downbearing figure needs to be.  =
Remember that it will be small in comparison to the string tension.  A =
dip angle of as much as 5 degrees will result in a downbearing force of =
T * sin 5.  Sin 5 is about .0872, so the downbearing force would only be =
about 9% of the string tension.  For a string tension of 150 lbs this =
would only amount to about thirteen pounds.  I guess it just depends on =
how accurate the downbearing figure needs to be.

Even how "in-tune" the piano is will affect this force.  For example, =
changing A-440 from 440 Hz to 441 Hz would increase the string tension =
by about 1/2%.  The downbearing would also change by this percent.  A =
string with a tension of 150 lbs would increase by about .75 lbs.  If we =
use the 5-degree case above, this would change the downbearing force by =
about .07 lbs, or about an ounce (30 g).  Is this a lot?  Is this =
negligible?  I'll let you guys argue that.

If you have a good way to measure the angle, this method should be =
pretty damned accurate.  I used it extensively to calculate the upward =
force on the agraffes for the self-tuning piano (which has fiberglass =
agraffes) and got good results.  However, the angle is greater in this =
case so the force is much larger.  The force increases to as much as =
half the string tension at an angle of=20

arcsin (1/2) =3D 30 degrees.

I was also only concerned with tensile and fatigue strength, so I =
probably didn't need as accurate a figure as you are looking for at the =
bridge.

There are certainly more accurate methods for measuring the string =
tension, if necessary.  Using a strain gauge would be one of the most =
common.

Don A. Gilmore
Mechanical Engineer
Kansas City
  ----- Original Message -----=20
  From: St=E9phane Collin=20
  To: Pianotech=20
  Sent: Friday, February 20, 2004 8:54 AM
  Subject: Re: what is downbearing?


  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:


         =20
        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.


         =20
        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


         =20
        F =3D T * sin A


         =20
        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.


         =20
        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


         =20
        F =3D T * h / b


         =20
        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


         =20
        T =3D 0.0023 * (fLd)^2


         =20
        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.


         =20
        Hope this helps.


         =20
        Don A. Gilmore

        Mechanical Engineer

        Kansas City=20
          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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