Segmented bowl workflow
Omni's bowl segment calculator focuses on one ring of a segmented bowl at a time. You choose the number of pieces in the ring, the desired radii, and any safety allowance or fudge factor, then solve the cut angle and segment dimensions.
Formulas from the fetched article
theta = 360 deg / n
alpha = 180 deg / n
L_o = 2 x tan(180 deg / n) x (R_o + a_o)
L_i = 2 x sin(180 deg / n) x (R_i - a_i)
R_i = R_o - T_r
T_s = (R_o + a_o) - cos(180 deg / n) x (R_i - a_i)
Useful simplification from Omni's FAQ
The source FAQ also highlights a quick rule for equal segments: the cutting angle is 180 degrees divided by the number of pieces. After that, a simplified outer-length estimate is L = D x tan(alpha).