Closed Segmenting Basics
In closed segmenting, each segment touches the next segment end-to-end to form a complete ring. Those rings are stacked to create bowls, vessels, platters, and other segmented projects.
Example: a 24-segment ring has a 15 degree full segment space and a 7.5 degree miter angle per side.
Understanding Segment Length
One of the most common questions in segmented turning is: what segment length should I actually cut? Three values are often discussed. They are close at higher segment counts, but they are not the same.
Arc Length
Distance along the curved circumference of the finished circle.
Easy to calculate, but a wood segment is straight rather than curved, so this is an approximation.
Arc length remains popular because it is easy to calculate and naturally produces a slightly larger value than raw chord length. In many traditional shop workflows, that small amount of extra material is simply removed during turning, which is one reason arc length often works acceptably in practice.
This is one reason arc-length-based methods have remained popular in segmented turning for decades despite being an approximation.
Raw Chord Length
Straight-line distance between two points on the finished circle.
Raw chord length correctly describes a straight chord on the finished circle. However, a segmented ring is constructed as a polygon and later turned to its finished shape. If the chord is calculated directly from the desired finished outside diameter, it does not include the extra construction material needed for turning.
Sagitta-Corrected Chord
For construction methods based on a desired finished outside diameter, sagitta-corrected chord length accounts for the material that projects beyond the finished circle and is later turned away.
A useful construction value when the diameter represents the desired finished outside diameter.
Why the Difference Gets Smaller
As segment counts increase, the difference between arc length, raw chord length, and sagitta-corrected chord length becomes very small.
This is one reason many segmented turning methods produce similar results at higher segment counts.
At lower segment counts such as 6, 8, 10, and 12 segments, the differences become more noticeable and geometric assumptions have a greater impact on the finished ring.
At higher segment counts, the three values begin to converge and the practical differences become much smaller.
Practical Takeaway
Arc length is simple, familiar, and often close enough for many projects.
Raw chord length describes the actual straight chord, but does not include construction allowance if calculated directly from the desired finished OD.
Sagitta-corrected chord length is useful when you want the segment length to account for the polygon shape and the finished outside diameter.
If you use Wedge-Planner, these calculations are handled automatically so you can focus on the design while Wedge-Planner manages the underlying geometry.
Closed Segmenting Reference
Example values use a 10 inch desired finished outside diameter.
| Segments | Full Angle | Miter Per Side | Arc Length | Raw Chord | Corrected Chord |
|---|---|---|---|---|---|
| 6 | 60.000° | 30.000° | 5.236" | 5.000" | 5.774" |
| 8 | 45.000° | 22.500° | 3.927" | 3.827" | 4.142" |
| 10 | 36.000° | 18.000° | 3.142" | 3.090" | 3.249" |
| 12 | 30.000° | 15.000° | 2.618" | 2.588" | 2.679" |
| 16 | 22.500° | 11.250° | 1.963" | 1.951" | 1.989" |
| 18 | 20.000° | 10.000° | 1.745" | 1.736" | 1.763" |
| 20 | 18.000° | 9.000° | 1.571" | 1.564" | 1.584" |
| 24 | 15.000° | 7.500° | 1.309" | 1.305" | 1.317" |
| 30 | 12.000° | 6.000° | 1.047" | 1.045" | 1.051" |
| 32 | 11.250° | 5.625° | 0.982" | 0.980" | 0.985" |
| 36 | 10.000° | 5.000° | 0.873" | 0.872" | 0.875" |
| 40 | 9.000° | 4.500° | 0.785" | 0.785" | 0.787" |
| 48 | 7.500° | 3.750° | 0.654" | 0.654" | 0.655" |
| 60 | 6.000° | 3.000° | 0.524" | 0.523" | 0.524" |
| 64 | 5.625° | 2.813° | 0.491" | 0.491" | 0.491" |
| 72 | 5.000° | 2.500° | 0.436" | 0.436" | 0.437" |
Reading the Table
- Arc Length:
- Simple and commonly referenced.
- Raw Chord:
- The straight chord on the finished circle.
- Corrected Chord:
- A construction value that accounts for the polygon shape when working from a desired finished outside diameter.
Open Segmenting Starts With Assembly
Open segmenting intentionally leaves space between adjacent segments. The most important shop decision is how you want to assemble the ring. That choice usually points you toward either angular gaps or dimensional spacers.
Angular Gap / Traditional Method
Use this when the desired opening is an angular gap and the assembly system uses angular wedgies, glue plates, or open-segment jigs.
- Angular gap is the design input
- Custom cut angle and segment length
- Gap sides point toward center
Best for: purist or traditional open segmenting with angular assembly references.
Dimensional Gap / Spacer Method
Use this when the desired opening is a physical gap width and the assembly system uses spacers, strips, or inserts.
- Dimensional gap is the design input
- Preset cut angle remains unchanged
- Segment length is shortened
Best for: simple repeatable glue-up with standard preset angles and physical spacers.
Angular Gap / Traditional Open Segmenting
Angular open segmenting treats the open space as an angle. The sides of the gap point toward the center of the ring, and the cut values are calculated around that angular opening.
This is the most geometrically pure open-segment approach, but it may require custom miter angles, custom segment lengths, and an angular assembly reference such as wedgies, glue plates, or a purpose-built open-segment jig.
Dimensional Gap / Spacer-Based Open Segmenting
Spacer-based open segmenting treats the open space as a physical width. The target preset angle stays the same, the segment length is shortened, and the gap is controlled during glue-up by a spacer, strip, or insert.
This is the simpler preset-friendly workflow. It is especially useful when the project benefits from parallel gap sides, contrast strips, repeatable spacers, or standard Wedge-Pro setup positions.
Practical Takeaway
Neither open-segmenting method is wrong. They solve different assembly problems.
Angular gap segmenting is the most geometrically pure method when the opening is designed as an angle and assembled with angular references.
Dimensional spacer segmenting is simpler and more accessible when the opening is controlled by a physical spacer, strip, or insert.
Choose the method based on how you want to glue the ring together.
Quick Comparison
| Question | Angular Gap Method | Dimensional Spacer Method |
|---|---|---|
| User input | Angular gap | Physical gap/spacer width |
| Cut angle | Custom | Preset/standard |
| Segment length | Calculated from angular gap | Shortened from closed length |
| Gap sides | Point toward center | Parallel |
| Glue-up | Angular wedgies/plates | Physical spacers/strips |
| Wedge-Pro friendly | Limited | Yes |
| Best for | Purist angular open segmenting | Simple repeatable shop setup |
Flagship design software
Design It In Wedge-Planner
Wedge-Planner.com is our flagship segmented design software. It supports closed rings plus both angular and dimensional open segmenting. Choose the assembly method you want to use, and Wedge-Planner manages the underlying geometry.
Q1WP Shop
Q1WP builds Wedge-Pro segmented cutting sleds for closed segmenting and dimensional spacer open segmenting. Preset angles support repeatable cutting, and the Wedge-Pro Material Stop helps dial in the shortened lengths that spacer-based open segmenting depends on.