Mathematical Formulas

The calculations for segmented bowl dimensions are based on geometric principles. Here are the key formulas used in our calculator:

1. Segment Length (Chord Length)

The length of each segment is calculated using the formula:

$\text{Segment Length} = 2 \times \text{Radius} \times \sin\left(\frac{\pi}{\text{Number of Segments}}\right)$

Where:

• Radius = Bowl Diameter ÷ 2
• π = 3.14159...
• Number of Segments = Number of segments in each ring

This formula calculates the chord length of a regular polygon with the specified number of sides.

2. Segment Width

The width (or height) of each segment is typically determined by the desired height of the bowl:

$\text{Segment Width} = \text{Bowl Height}$

For more complex designs with multiple rings of different heights, the total bowl height would be divided by the number of rings.

3. Segment Angle (Miter Angle)

The angle at which each segment must be cut is calculated as:

$\text{Segment Angle} = \frac{360°}{\text{Number of Segments}}$

This represents the external angle of the regular polygon. For miter saw settings, you would use half of this angle (the complementary angle) on each end of the segment.

How to Use the Calculator

Our Segmented Bowl Dimension Calculator makes it easy to determine the exact measurements needed for your project. Follow these simple steps:

1. Enter Bowl Diameter: Input the desired final diameter of your bowl in millimeters.
2. Enter Bowl Height: Specify the total height of your bowl in millimeters.
3. Enter Number of Segments per Ring: Choose how many segments you want in each ring (minimum 3).
4. View Results: The calculator will instantly display:
   • Segment Length (mm)
   • Segment Width (mm)
   • Segment Angle (degrees)
5. Optional: Use the "Copy Results" button to copy all dimensions to your clipboard for reference in your workshop.

The calculator also provides a visual representation of your bowl design, showing both a top view of the complete segmented ring and a detailed view of an individual segment with dimensions.

Tips for Accurate Measurements

• Account for Kerf: Remember that the saw blade removes material (kerf) when cutting. You may need to add a small amount to your segment length to compensate.
• Consider Sanding: Allow extra material for sanding and finishing.
• Test Cuts: Always make a test cut and dry-fit your segments before cutting all pieces.
• Consistent Angles: Ensure your miter saw or jig is set to the exact angle calculated.

Use Cases

Beginner Projects

For those new to segmented woodturning, starting with a simple bowl using fewer segments is recommended:

• Fruit Bowl: A medium-sized bowl (200-250mm diameter) with 8-12 segments per ring is an excellent starter project.
• Pen Holder: A small cylindrical design with 6-8 segments per ring offers good practice with simpler geometry.

Intermediate Projects

As your skills develop, you can attempt more complex designs:

• Decorative Bowl: Create a bowl with contrasting wood species using 12-16 segments per ring for more intricate patterns.
• Lidded Container: Design a container with a matching lid, using the calculator to ensure both components have consistent dimensions.

Advanced Projects

Experienced woodturners can tackle challenging projects:

• Feature Ring Bowl: Incorporate a feature ring with a different number of segments than the rest of the bowl, using the calculator to determine different dimensions for that specific ring.
• Open Segmented Bowl: Create designs with spaces between segments, requiring precise calculations for segment placement.

Alternative Approaches

While our calculator provides dimensions for standard segmented bowls with regular polygons, there are alternative approaches to segmented woodturning:

1. Stave Construction: Uses vertical staves similar to barrel construction, requiring different angle calculations.
2. Compound Angle Segments: Creates more complex shapes by incorporating both horizontal and vertical angle cuts.
3. Open Segmented Technique: Leaves spaces between segments for decorative effects.
4. Ring-less Segmentation: Assembles segments directly onto the previous layer without forming complete rings first.

Each of these techniques requires different calculation methods, but the basic principles of geometry still apply.

History of Segmented Woodturning

Segmented woodturning has evolved significantly over the centuries. While turned wooden vessels date back thousands of years, the specific art of segmented turning gained prominence in the 20th century.

The technique was pioneered by modern woodturners seeking to create larger and more complex designs while using smaller pieces of wood. This approach allowed for the use of exotic and expensive wood species in smaller quantities, as well as the creation of intricate patterns impossible with solid wood turning.

Key milestones in the development of segmented woodturning include:

• 1970s: Publication of early articles on "polychromatic" woodturning techniques
• 1980s: Development of more precise methods for calculating segment dimensions
• 1990s: Formation of specialized groups and guilds focused on segmented turning
• 2000s: Introduction of computer software to assist with segment calculations
• Present: Online calculators and digital tools making segmented turning more accessible to hobbyists

Notable contributors to the field include Ray Allen, Malcolm Tibbetts, and Curt Theobald, who have all published books and instructional materials on segmented woodturning techniques.

FAQ

What is the minimum number of segments I should use per ring?

A: While technically you could create a ring with as few as 3 segments, most segmented bowls use at least 8-12 segments per ring for stability and aesthetics. More segments create smoother curves and more opportunities for decorative patterns.

How do I account for the saw blade kerf when cutting segments?

A: The kerf is the width of material removed by your saw blade. To account for this, you should add the kerf width to your segment length calculations. Typically, a standard table saw blade has a kerf of approximately 1/8" (3.2mm). For precise work, measure your specific blade's kerf and adjust accordingly.

Can I use different numbers of segments in different rings?

A: Yes, you can create feature rings with different numbers of segments. However, this requires careful planning to ensure proper alignment. You'll need to calculate each ring separately and consider how they will stack together.

What wood species work best for segmented bowls?

A: Almost any stable hardwood can be used for segmented bowls. Popular choices include maple, cherry, walnut, oak, and exotic species like purpleheart or padauk for contrast. The key is to use well-dried wood with consistent moisture content to prevent warping or joint separation.

How thick should each segment be?

A: Segment thickness (width) depends on your design, but typically ranges from 10mm to 25mm. Thicker segments provide more material for shaping the bowl's profile but require more wood. Consider the final wall thickness of your bowl when determining segment width.

Do I need to account for glue line thickness in my calculations?

A: Modern wood glues create very thin glue lines that typically don't significantly affect dimensions. However, for extremely precise work with many segments, you might add 0.1-0.2mm per glue joint to your overall circumference calculations.

What's the best way to ensure accurate angle cuts?

A: Use a digital angle gauge to set up your miter saw or table saw sled. Make test cuts and check the angles with a protractor or by dry-fitting segments to form a complete ring. For consistent results, create a dedicated jig for cutting segments.

How do I calculate dimensions for an oval or elliptical segmented bowl?

A: Oval segmented bowls are more complex and typically require specialized software or advanced mathematical calculations. Our calculator is designed for circular bowls. For oval designs, consider using a specialized woodturning design program.

Can this calculator be used for other segmented projects like vases or urns?

A: Yes, the basic principles and calculations apply to any circular segmented turning project. Simply enter the appropriate diameter and height for your specific project.

How do I adjust for wood movement and seasonal changes?

A: Use properly dried wood (6-8% moisture content) and align grain direction consistently in all segments. Apply a complete finish to all surfaces of the completed bowl to minimize moisture exchange. Even with these precautions, some minor movement may occur with seasonal humidity changes.

References

1. Tibbetts, Malcolm. "The Art of Segmented Woodturning: A Step-by-Step Guide." Linden Publishing, 2005.

2. Theobald, Curt. "Segmented Woodturning." Fox Chapel Publishing, 2012.

3. American Association of Woodturners. "Segmented Woodturning Resources." https://www.woodturner.org/

4. Smith, William. "Segmented Turning: A Complete Guide." Taunton Press, 2009.

5. "Geometry in Woodturning." Fine Woodworking Magazine, Issue 237, pp. 52-57.

6. Nish, Dale. "Woodturning with Ray Allen." Fox Chapel Publishing, 2004.

7. "Understanding Wood: A Craftsman's Guide to Wood Technology." Bruce Hoadley, Taunton Press, 2000.

Conclusion

The Segmented Bowl Dimension Calculator simplifies the complex mathematics involved in planning and creating beautiful segmented bowls. By providing accurate measurements for segment length, width, and angle, this tool helps woodturners of all skill levels achieve professional results with less waste and fewer errors.

Remember that woodturning is both a science and an art. While precise calculations are essential for successful segmented projects, don't be afraid to experiment and develop your own unique style. Use this calculator as a starting point, and let your creativity guide the final design of your segmented masterpiece.

Ready to start your segmented bowl project? Enter your desired dimensions in the calculator above and begin crafting your next woodturning creation with confidence!