Rules of thumb....
16-sided object: Width = Diameter ÷ 1.7
Width = Diameter ÷ 2.4
Width = Diameter ÷ 3.7
Width = Diameter ÷ 5.0
Where width is width of stave....
So - for 24" diameter, 6 sides - width of stave is 24/1.7 = 14"
Or - if you want a 3' diameter, 8 staves....36/2.4 = 15"....
<BRuce> wrote in message
A little late but I have I have a copy of a miter program that is small and
it calculates the angles, lengths, and slope of different thickness wood for
any given number of sides. I can e-mail a copy to you if you like.
<BRuce> wrote in message
A smart-ass answer would be "take the radius of the ring, and multiply by 2".
Seriously, assuming the sides are all the same length, and you know
a) the number of sides,
b) the length of a side
it's fairly straightforward.
"Imagine" a line from the end of each piece, to the center of the ring.
You now have a set of matching isosceles triangles, where each side of the
ring is the base of one of the triangles.
The 'vertex angle' of those triangles is (obviously) 360/n degrees, where n is
the number of sides.
In plane geometry, the sum of the inside angles of a triangle is 180 degrees.
And, for an isosceles triangle, the base angles are equal, so the base angle
will be (180-vertex_angle)/2.
Thus, the 'base angle' for each segment of an 'n-sided' ring will be:
(180-(360/n))/2) or (90-180/n)
This doesn't look meaningful, until you realize you can 'imagine' another line
from the midpoint of each side to the center. Which just happens to make a
right angle with the side.
Now, simple triginometry applies. we have the 'angle', and the length of
the 'adjacent side' (which is _half_ the total length of the side of the ring),
and want the length of the 'opposite side'. 'opposite'/'adjacent' is the
'tangent' function, so the length of the "opposite side" is:
This 'opposite side' is the radius of the largest circle that fits _inside_
the ring, so you double it to get the diameter.
If you want the circle that connects the 'points' of the ring, use
to determine the radius of _that_ circle, and, again, double the result for
Short-cut: if you use the total length of the side of the ring, rather than
the length from the end to the point where the vertical connects, you get the
Quickie table of tangents and cosines
sides base angle tan cos
4 45 1.000 .7071
5 54 1.376 .5877
6 60 1.732 .5000
8 67.5 2.414 .3826
10 72 3.077 .3090
12 75 3.732 .2588
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