How do I find the X and Y intercepts for equadistant points along the perimeter of a circle.?

Question

That's the one part of my project I can't seem to figure out, but more generally, how would I figure out the measurements to construct an 8-foot-wide concave semi-globe using 24 flat, long, bendable panels that are 3/16" thick? I know that the panels will be 12.56 feet long, and I know they will be 0.523333 feet wide in the middle, but they taper off at a curve until they have zero width at the poles. I need to figure out the width of the panels at each increment, such as every 12 inches, or maybe at 10%, 20%, and so on. Any takers?

Answer 1

Observation: circumference (C) = pi * d

You have stated that d = 8'. Therefore C = 25.13'

With 24 panels, the 'middle' width should be 1/24 * C, or 1.047', NOT 0.523', as you stated!

The previous poster gave you a good formula for working your other widths. To convert from degrees to radians, use:

deg = rad * 180 / pi
rad = deg * pi / 180

Answer 2

That just takes a little geometry and trig.

Assuming you have each panel starting at 12.56' x 0.5233', mark dead center on the panel. Let's call the distance towards the top, or bottom, of the panel as S. Then for a given S, the width at that point will be

(12.56/24)*(1 - cos( S*(pi/12.56)))

Caution -- the argument of the cosine is in radians!!

This was a quick analysis. Contact me if you want some detail.

And of course, measure twice, cut once.