Crown radius = how much arch in a segment ?

[Richard Moody]

The next question is "how long is the arc?"
Which Clark answers below.
With a radius of 72 inches and  segment (chord length) of 36 inches
the arc
        is  37.7 inches.   (height of arc is 2.86 inches)
hmm a 1.7 inch compression of a 36.7 inch board arches it to a height
of 2.86 inches in the middle.  I know that "real materials" might come
out different but I wonder how different.  I suppose one could figure
from the angle what portion of the circumference the arc is and see if
that matches.
Shouldn't the angle be 72*2*pi / 37.7 divided into (under) 360? (which
is exactly 30?)

 For the spread sheet........

  Arc Length = A7*ASIN(B7/A7) = 37.7

A7= radius (72)
B7 = chord, or segment length. (36)

 ---ric
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----- Original Message -----
From: Clark <caccola@net1plus.com>
To: <pianotech@ptg.org>
Sent: Tuesday, March 13, 2001 2:43 PM
Subject: Re: Crown radius = how much arch in a segment ?


For arc length - in this case the width of the curved panel where it
is
attached to a crowned rib with a chord length [n]:

l_a=r*asin(n/r)

Of course, none of this applies to real materials. ;)

Clark
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