Rib dimensions

[Don A. Gilmore]

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The two-straightedge method will indeed produce a true and exact =
circular arc and is an ingenious way to draw large curves.  And calculus =
is not involved; it is simple, high-school geometry. =20

If you view the system as an arc just from the left pin to the top pin =
and draw lines representing the straightedges, from these two pins to =
any pencil point on the curve, it is more clear what is going on.  =
Drawing lines from one end of a chord to a point on the curve and then =
back to the other end of the chord makes a triangle.  No matter what =
point on the curve you choose, the angle between the two lines is always =
the same for a circle.  This is a basic theorem of geometry.  It can be =
proven simply if you note that lines drawn from the center of the circle =
to each chord-end and to the pencil always creates two isosceles =
triangles.

Locating one straightedge parallel to the chord and one across the two =
pins is just a clever way to set them up for our circle.  The top =
straightedge is thus tangent to our circle at the top pin and the second =
straightedge is simply another line from a point along the circle to the =
pencil (now literally at the top pin).

Now the question is: does the curve need to be a true circular arc?  =
It's hard for me to believe that slight discrepancies in an arc of such =
large radius and short length could really cause any noticable =
difference in the performance of a soundboard. =20

Don A. Gilmore
Mechanical Engineer
  ----- Original Message -----=20
  From: Farrell=20
  To: Pianotech=20
  Sent: Thursday, December 11, 2003 6:00 AM
  Subject: Re: Rib dimensions


  Lots of good methods for calculating the radius of an arc have been =
provided. But there is also the question of whether the curve is a true =
arc or some other shape (this assumes you have a specific shape as a =
target). Most of the provided methods do not address that concern - in =
fact you could have an obtuse angle with two straight sides rather than =
an arc. That's why I suggested making a number of measurements along the =
curve - offsets from a straight line.

  Terry Farrell
    ----- Original Message -----=20
    From: Absolute Piano=20
    To: pianotech@ptg.org=20
    Sent: Wednesday, December 10, 2003 4:40 PM
    Subject: Rib dimensions


    Hello,

    I'm trying to apply some science to my soundboard rib making and I =
am
    looking for "tables of static values for  the Resisting Moment (W) =
and the
    Moment of Inertia (I) for all the possible cross sections of =
sugarpine and
    spruce (DIN 1052 Class I will suffice).

    What is the formula for converting pounds/inch squared to kg/cm =
squared?

    Given a right angle connected to the outside of an arc of a circle, =
how do
    you prove the circle is 60'? (I made a jig for crowning ribs that is
    adjustable and I want to calibrate it.

    Thanks,

    Jude Reveley, RPT

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