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
Open segmenting intentionally leaves space between adjacent segments. There are several ways to create that opening, ranging from fully calculated open-segment geometry to practical shop approximations.
Traditional Open Segmenting
A true angular-gap layout. The segment and gap are calculated directly, so the miters can become arbitrary angles that may not match the fixed presets used on closed-segment cutting sleds.
Shortened Standard Segments
Uses the normal closed-segment miter angle, then cuts each segment shorter. This is useful when parallel sides are wanted for contrast strips, spacers, or glue-up details.
Equivalent Segment Count Method
A hybrid method: cut with a higher closed-segment preset while assembling fewer segments in the ring. Both sides of each gap still point toward center, so the angular gap is closer than the shortened style while keeping preset-based setup quick and repeatable. This allows turners to explore open-segment designs using familiar preset counts without calculating custom segment angles.
Equivalent Segment Count Theory
Equivalent Segment Count Theory uses the geometry of one segment count while assembling another. For example, build a target 24-segment ring using a 36-segment Wedge-Pro setting: the target space is 15 degrees, the preset cut space is 10 degrees, leaving an approximate 5 degree gap.
Calculating Segment Length for the Equivalent Method
When using the Equivalent Segment Count Method, the actual ring count controls how many segment positions are placed around the ring. The equivalent setting controls the geometry of each segment.
This is an important distinction. The segment length should be calculated from the equivalent setting, not the actual ring count.
Example
- Target ring
- 24 segment positions
- Equivalent setting
- 36 segments
- Desired finished OD
- 10 inches
The ring layout is still based on 24 positions. However, the segment itself is built using 36-segment geometry.
That means: use the 36-segment miter angle and the 36-segment corrected segment length.
The 24-segment ring controls the placement positions. The 36-segment geometry controls the segment angle and segment length. The difference between those two geometries creates the open gap.
Equivalent Method Rule
Actual Ring Count = Placement Geometry
Equivalent Setting = Cutting Geometry
- Segment angle
- Segment length
- Ring layout
- Gap-angle calculations
This is the foundation of the Equivalent Segment Count Method.
Practical Takeaway
Traditional open segmenting gives the most direct angular-gap layout, but it may require custom miter angles outside common closed-segment sled presets.
Shortened standard segments are simple and useful when parallel sides, spacers, or contrast strips are part of the design.
The equivalent segment count method is a practical preset-based approach that keeps the gap sides pointed toward center while avoiding custom segment-angle setup.
For quick shop planning, the lookup table helps compare preset settings and see the approximate gap each setting creates.
Equivalent Open Gap Lookup
Choose the target segment count per ring, then compare higher Wedge-Pro settings.
| Wedge-Pro Setting | Cut Space | Approx. Gap |
|---|---|---|
| 24 | 15.000° | Closed |
| 30 | 12.000° | 3.000° |
| 32 | 11.250° | 3.750° |
| 36 | 10.000° | 5.000° |
| 40 | 9.000° | 6.000° |
| 48 | 7.500° | 7.500° |
| 60 | 6.000° | 9.000° |
| 64 | 5.625° | 9.375° |
| 72 | 5.000° | 10.000° |
Flagship design software
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