Robert Marshall
05-31-2015, 7:46 PM
FWIW, here's a PDF of a form I developed for designing segmented bowls.
Here's the process:
Sketch the profile (cross-section) of the left side of the bowl, using the grid section of the form. The 0/0 point (bottom right of the grid) is the center-bottom of the bowl; as you move left, you are moving to the outside of the bowl. The wall of the bowl should be drawn with two lines, representing the inside and outside of the wall, at the intended final thickness. Remember, you are drawing the final intended profile of the bowl; not what you start with. The grid is intended to represent inches (large blocks) and quarter inches (smaller blocks inside the inch blocks).
Now, working from bottom to top, sketch the cross section of the segments that will allow you the finished profile you have drawn. Allow for rounding the polygons. Also, allow for error (misalignments in assembling, stacking and gluing the rings, going too far when turning, etc.) Don't draw a segment which perfectly fits the finished profile, unless you are the perfect turner.
Enter the dimensions and other criteria for the rings, numbered from 1 (I usually start numbering at the bottom, but you can do it either way). Use the upper right of the form for this. Included information is species, # of segments, thickness of the ring (from top to bottom of a segment), width of a segment (more on this, soon), inradius of the ring (again, more coming), and length of the outside of each segment (more, below).
Inradius is the radius of the largest circle which will fit fully within the polygon you are creating with your segments. Perfectly cut, assembled and turned, you could theoretically round the polygon to a circle of this radius. Realistically, the inradius should allow you a margin of error, so make it bigger (on the outside of the segments) than the intended radius of the bowl at that point. So, if the widest part of the design profile for the bowl at the level of a ring is 4 inches, make the inradius 4.25 inches, more or less, depending on how perfect you are.
The length of the outer side of a segment is related to the type of polygon (number of sides), and the inradius. At the bottom right of the form, I provide the percentage relationship of this length, to the inradius, for polygons of 8, 12, 16, 24 and 32 sides. So, for example, if you are creating a 12-gon (or, dodecagon) ring, the length of each segment outside will be 53.6% of the inradius. I also provide the miter saw angle setting, for the same polygons.
The width of the segments is determined by the difference between the inradius of the outside of the segment (allowing a margin or error), and the inradius of the inside of the segment (allowing a margin of error in the other direction). The width of the segments is another way of saying "the width of the strips from which you cut the segments."
Once you have this information filled in for each ring, you are ready to start cutting, sanding, assembling, gluing, etc., to create your rings, and then your stacked-and-ready-to-turn bowl.
Note that I've not discussed the bottom of the bowl. This can be segmented (triangles, with the point of the triangle segment being at point 0/0), or it can be a disk of solid wood (usually easier to do). If it is a disk, it can be applied to the bottom of the bottom ring, or can be inset into a mortise in that ring.
Here's the process:
Sketch the profile (cross-section) of the left side of the bowl, using the grid section of the form. The 0/0 point (bottom right of the grid) is the center-bottom of the bowl; as you move left, you are moving to the outside of the bowl. The wall of the bowl should be drawn with two lines, representing the inside and outside of the wall, at the intended final thickness. Remember, you are drawing the final intended profile of the bowl; not what you start with. The grid is intended to represent inches (large blocks) and quarter inches (smaller blocks inside the inch blocks).
Now, working from bottom to top, sketch the cross section of the segments that will allow you the finished profile you have drawn. Allow for rounding the polygons. Also, allow for error (misalignments in assembling, stacking and gluing the rings, going too far when turning, etc.) Don't draw a segment which perfectly fits the finished profile, unless you are the perfect turner.
Enter the dimensions and other criteria for the rings, numbered from 1 (I usually start numbering at the bottom, but you can do it either way). Use the upper right of the form for this. Included information is species, # of segments, thickness of the ring (from top to bottom of a segment), width of a segment (more on this, soon), inradius of the ring (again, more coming), and length of the outside of each segment (more, below).
Inradius is the radius of the largest circle which will fit fully within the polygon you are creating with your segments. Perfectly cut, assembled and turned, you could theoretically round the polygon to a circle of this radius. Realistically, the inradius should allow you a margin of error, so make it bigger (on the outside of the segments) than the intended radius of the bowl at that point. So, if the widest part of the design profile for the bowl at the level of a ring is 4 inches, make the inradius 4.25 inches, more or less, depending on how perfect you are.
The length of the outer side of a segment is related to the type of polygon (number of sides), and the inradius. At the bottom right of the form, I provide the percentage relationship of this length, to the inradius, for polygons of 8, 12, 16, 24 and 32 sides. So, for example, if you are creating a 12-gon (or, dodecagon) ring, the length of each segment outside will be 53.6% of the inradius. I also provide the miter saw angle setting, for the same polygons.
The width of the segments is determined by the difference between the inradius of the outside of the segment (allowing a margin or error), and the inradius of the inside of the segment (allowing a margin of error in the other direction). The width of the segments is another way of saying "the width of the strips from which you cut the segments."
Once you have this information filled in for each ring, you are ready to start cutting, sanding, assembling, gluing, etc., to create your rings, and then your stacked-and-ready-to-turn bowl.
Note that I've not discussed the bottom of the bowl. This can be segmented (triangles, with the point of the triangle segment being at point 0/0), or it can be a disk of solid wood (usually easier to do). If it is a disk, it can be applied to the bottom of the bottom ring, or can be inset into a mortise in that ring.