- posted on September 4, 2003, 6:57 pm

BRuce

- posted on September 4, 2003, 7:23 pm

Rules of thumb....

6-sided object: 8-sided object: 12-sided object: 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"....

Cheers,

Rob

- posted on September 4, 2003, 7:26 pm

- posted on September 4, 2003, 9:39 pm

thanks for all the input. this will be much easier now. well it is off
the garage to start the next project.

BRuce

BRuce wrote:

BRuce

BRuce wrote:

--

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BRuce

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BRuce

- posted on September 4, 2003, 11:15 pm

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 *

- posted on September 5, 2003, 4:45 am

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

tangent(90-180/n)*adjacent_side

This 'opposite side' is the radius of the largest circle that fits

If you want the circle that connects the 'points' of the ring, use

adjacent_side/cosine(90-180/n)

to determine the radius of

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 diameter directly.

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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