A big reason many start into segmented projects is to reduce the cost and the amount of lathe time that is required to get to the final shape. It just stands to reason that precutting to something that approximates the final shape will reduce the amount of wasted wood or other material you plan to use. So it makes sense that your method for developing the cutting instructions does a good job of sizing the segments for each of your rings.

Since my background is telling computers how to do their thing, I’ve put together a program to do the translation into cutting instructions that helps me visualize the design, determines the size information for each segment, and also tells me how much wood I need to buy. Using the Segmented Project Planner and a quad pad or a standard, and relatively inexpensive, drafting program such as TurboCAD, I can quickly turn a rough idea into all the details needed to make the project come to be.

For those of you with a mathematical bent, here are the formulae you will need to make the basic computations needed for a ring:

MiterAngle = 360 / (Sides * 2)
DtoR = 3.1415926536/180
SinOfAngle = Sin(MiterAngle * DtoR)
CosOfAngle = Cos(MiterAngle * DtoR)
EndRadius = (OuterDiameter / 2) * (1 + ((1 - CosOfAngle) / CosOfAngle))
SegmentEdgeLength = 2 * EndRadius * SinOfAngle
SegmentWidth = CosOfAngle * (EndRadius - ((OuterDiameter / 2) - WallThickness)))