Cone Layout

CONES

The rules are simple.
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The layout radius is the length of the side of the cone. For truncated cones the lengths are to the theoretical point (c1 + c2).

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The FLAT layout angle is determined by the circumference of the finished cone divided by the circumference of the layout circle (from radius 1. above).
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Since PI cancels in the two circumferences above you divide the radius of the base (b2) by the length of the side (for truncated cones use the length to the theoretical point c1 + c2). This is the ratio or percentage of the layout circle. This is also the sine of half the angle of the top of the cone (angle B).

So, if you want a cone with a 90° point then the ratio is the sine of half the angle of the point (B above).

sine(45°) = .7071

Therefore the layout angle S = .7071 x 360° = 254.6°

You can use either method, the ratio or the sine of the angle. Both numbers are the same. sine is simply a word for ratio in geometry. If you have a starting angle it is easy to use a modern calculator to determine the sine.