Outside segment
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Shop estimate. Measure your stock and cut a test on scrap.
How to use it
- Enter the finished outside diameter and the number of segments. Four is a square frame. Six is a hexagon. Eight is an octagon. Twelve and up is a typical bowl ring.
- Enter the wall thickness, from the finished outside to the finished inside.
- Enter the kerf if the segments come off one strip.
- Cut the outer edge long enough for the construction chord. The miter is the same number the flat-frame page would give.
The formula
Outer edge = outside diameter × tan(180° ÷ segments). Miter from square = 180° ÷ segments.
- tan. The construction chord. A raw chord of diameter × sin(180° ÷ segments) lands short of the finished circle at the corners.
- Wall. Finished outside radius minus finished inside radius. It is the width of the segment before you add a turning allowance.
- Stock. All the outer edges in a row, plus a kerf between segments.
Worked example
A 10 inch finished outside diameter in 12 segments wants a miter of 15° from square and an outside edge of 2.679 inches. That is the construction chord, 10 × tan(15°), about 2.679 inches. The raw chord of the circle is a little shorter, 2.588 inches.
A ½ inch finished wall makes the inside diameter 9 inches. With no kerf, the strip is 32.154 inches of those outside edges in a row.
What it will not decide
- A regular polygon only. Stave ovals and feature rings are not this.
- Add your own allowance if you want extra wood to turn. The wall you type is the finished wall.
- The saw still needs a test ring. A small angle error closes up on the last segment.
Questions
Why is the segment longer than the circumference divided by the count?
The circumference is the curve. The segment is a straight side of a polygon that has to reach that curve at the corners. For a 10 inch, 12-segment ring the construction edge is about 2.68 inches. The arc of the circle is a little shorter.
Is the miter the same as a picture frame?
For a square, yes, 45°. For a hexagon, 30°. For an octagon, 22.5°. The frame page only does rectangles. This page does any count from 4 to 64 and gives the segment length.
Which diameter do I type?
The finished outside diameter. If you type a construction diameter that already includes waste, the segments come out long. Decide which circle you mean before you cut the strip.