CE for four-sided sails - an easier method
Your recent cover shot from David Nichol's article prompts me to submit what I believe is an easier method for locating the center of sail area/center of effort for the very special case of four-sided sails.
We know that if you divide a four-sided sail into two triangles (say, Peak-to-Tack) and determine the locations of the CEs each of the two triangles, the CE for the four-sided sail will fall on the line between the two CEs for the triangles, just as is shown in the common method used in David Nichol's article. See Sketch A (below).
But, if you divide the sail into two triangles the other way (Throat-to-Clew) and locate the CEs for these two triangles, the CE for the four-sided sail also falls on the line connecting the CEs for the two new triangles. See Sketch B (below).
So, by superimposing Sketches A & B, you will note that the lines connecting the CEs for the two pairs of triangles will intersect at a single point - the four-sided sail's CE. Simple, and no math!