Segmented rings and polygon columns
Any number of sides, flat or flared or standing straight up: the miter, the blade tilt, how long each segment is for the diameter you want, and how much stock the whole stack takes.
Miter is 180 ÷ 12
0 lies flat, 90 stands up
Across the flats, after turning
= 1.5"
= 0.125"
12 segments, 0° wall
Miter
15.0°
Blade straight up
Blade tilt
0.0°
None — this one is flat
Outer edge of each
2 11/16"
Inner edge
1 7/8"
Cuts to get right
96
Flat on the table
Every piece lies flat with the blade upright, and the only setting is 15.0° on the miter scale. Cut every segment without moving that setting — swing the head the other way for alternate cuts rather than resetting the angle, because a setting you never touch is a setting that cannot drift.
Stock for 4 courses
- Strip widthOutside face to inside face of the ring
- 1 1/2"
- Strip length per course12 segments at 2 11/16", plus 1/8" of kerf each and a little to hold
- 2 ft 11 5/8 in
- All courses48 segments in total
- 11 ft 10 5/8 in
- Blank across the cornersTurns down to 10" at the flats
- 10 3/8"
- Joint angle in planEach segment turns 30.0° of the 360
- 150.0°
Before you cut
- Miter inside the 50° most saws reach — passes15.00° on the miter scale.
- Segments do not meet in the middle — passes7.00" of opening left inside the ring.
- Segments big enough to cut safely — passes2.68" on the long edge of each segment.
Every error lands in the same gap
There are 24 cuts in one course and no way for an error in one to cancel an error in another. A tenth of a degree out on every cut, all the same way, leaves the ring 3/16" from closed at this diameter. A tenth of a degree is inside the width of the line on a miter scale.
So do not trust the number on the saw. Cut the segments for one ring, dry-assemble them in two halves, and check each half against a straightedge: if the two halves close flat against each other the angle is right, and if they do not, the gap you see is twice the error. Adjust and cut a second test ring. That is how segmented work is actually done, and no calculator replaces it.
Why the diameter is measured across the flats
A ring of segments is a polygon, and a polygon has two diameters: across the flats and across the corners. Turn it round and you can only reach the flats, so the flat diameter is the biggest circle inside the ring and the one worth designing to. The corner diameter is what the glued-up blank measures before it goes on the lathe.
The difference grows fast as the segment count falls. Twelve segments lose about 3% of the diameter between corner and flat; six segments lose more than 13%.
About segmented work
- What angle do I cut for a segmented ring?
- 180 divided by the number of segments, on the miter scale, with the blade upright for a flat ring. Twelve segments is 15°, sixteen is 11.25°, eight is 22.5°. Every joint is two of those cuts, so the ring closes only if 2N of them add up to 360° — which is why the count matters more than the angle.
- How long is each segment?
- The finished diameter times the tangent of half the segment angle. A twelve-segment ring that turns down to 10" needs segments 2 11/16" on their outer edge; an eight-segment ring the same size needs 4 1/8". Measure the diameter across the flats, not across the corners — the corners are the wood you turn away.
- Why won't my ring close?
- Because every cut's error lands in the same gap. A twelve-segment ring takes twenty-four cuts, so being a tenth of a degree out on each of them — less than the width of the line on a miter scale — leaves the ring 2.4° short, which is a visible wedge at the last joint. Cut a test ring, close it in two halves against a straightedge, and adjust: the gap you see between the halves is twice the error in your setting.
- What is the difference between a segmented ring and a staved column?
- The orientation of the wood, and it swaps the two saw settings. A flat ring is mitered across the pieces with the blade upright; a staved column with vertical sides has no miter at all and is bevel-ripped down the edges of each board at the same 180/N. Anything in between — a flared planter, a tapered vessel — needs both settings at once, which is the same compound cut crown molding needs.
- How many segments should I use?
- Twelve is the usual answer for bowls: the miter is a round 15°, the segments are big enough to handle safely, and the ring only loses about 3% of its diameter between the corners and the flats. Fewer segments means bigger flats and more waste turning it round — six segments lose over 13% of the diameter between corners and flats. More segments means a thinner ring for the same stock and twice as many chances to be a tenth of a degree out.
You might also need
- Dovetail and box joint templatesSet out the joint, print it at true 1:1 scale, and glue the paper straight onto the board.
- Crown molding anglesThe miter and bevel for any corner and any spring angle, plus the single setting for cutting it nested.
- Circle and arc layoutA trammel arm's length for a full circle, or the radius of a shallow arc from its chord and rise.