Hi, Gary,
I never in a million years would have thought of such a carefully controlled methodical experiment to measure performance to windward. You're doing great empirical work to help us understand our boats; thank you, for instance, for publishing a benchmark for tacking. 100 deg on a boarded boat. Now I don't have to scratch my head wondering if 105-110 on a boardless is good or if I should be looking for serious impovement. And the observation about wave vector explaining differrential tack performance - I guess out on the water I've made allowance for a heading sea vs a beaming one, sure, but to see it in B&W like that really makes me think.
I have some reservations about the CE moving much as a direct consequence of changing to a square top. I agree, the main's total contribution to the combined CE goes up some (5%? 10%?? 2%?), but since that combined CE is so heavily influenced by the main already, further incremental increases in the *power* expressed at the main's CE doesn't seem (to my intuition) likely to move the combined CE terribly much. (I'm too lazy to do the math, so I'll cheerfully accept correction (and 40 lashes) if you care to run a sample ratio and comparison - say 4:1 vs 4.2:1, how much does the combined CE move on a 5% increase in main's effort, if 5% is proper allowance for the squaretop, etc etc. yikes, all the guestimating...)
Small changes in the *Location* of the main's CE should provide relatively larger changes in the combined CE. However, the CE of the main doesn't seam likely to move especially aft on the change; particularly in the case of the "same sail area" squaretop, where I believe the foot is typically shortened to match the extra material up top, right behind the mast. Even the squaretops with more sail area have that extra area added right behind the mast, pretty much on top of the pinhead's CE. Heck, maybe a sailmaker will opine on whether the main's CE moves at all? I'm guessing not very much, or even "not even a little" in light of your post about chord thickness and effort center.
Finally, Marc added a spi too. Shouldn't that balance any impact of the Square top? Of course, only when it's actually up the pole! So my main question for the real experts out there is, "Do you still use the same process of raking to produce optimum lift off the rudders with a spinaker on the boat, or is there a different strategy? For instance, is the offwind performance of the rudders more significant, with a spin, and in which direction does that modify the larger process? Do you want more headway or more leeway, as a specificic strategic goal consequent on using the spi?"
