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I need help with the geometry used to construct a segmented bowl. I am trying to produce a segmented bowl using 12 pie shaped wedges of 4/4 rough mesquite with a compond bevel on the jointing edges. As the slope of the bowl’s side decrease the pie shape widens and the edge angle changes but I can’t for the life of me find the math to understand this. I have looked at a barrel (vertical sides) and then tried to intuit the angle change as the sides are sloped down….but I have not succeeded. Any idea where to go to find help.
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An article that may have what you are looking for is FWW Issue 15 (Mar/Apr 1979), entitled "Staved Containers". I'll check tonight; there may be some other references as well.
*Got it. Try Issue 10 (Spring 1978) - this has the general mathematics.
*Hi David, Compound miters are non-intuitive-at least for me. I calculate them using these formulas, letting a spreadsheet program do the math:Blade tilt angle = arcsine(sine(A) * sine(B/2))Miter gauge angle= arctangent(cosine(A) * tangent(B/2))Where:A = the angle at which the sides tilt (if it were 0, the sides would lie flat; at 90 degrees the sides would be perpendicular).B = the angle at which the sides meet (for a four-sided object the sides meet at 90 degrees, for an eight-sided object they meet at 45 degrees, 12 sides at 30 degrees, and so forth).Contact me directly if you want a copy of the Excel spreadsheet.Best, Kim Carleton GravesCarleton Woodworking
*I just checked in to see if my note was up yet and lo-n-behold the answers are coming in. My thanks to all of you. We are going to help a small village in Northern Mexico transition from ironwood carving into a more sustainable project. We are going to see if they can turn bowls from the mesquite they are pulling up for pasture. I will wait until tomorrow for more info and then laminate something up Sunday. We are heading south Monday morning early..... my thanks again.
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