the Betz law in only applicable for standing wind power plants, not for moving. Sail are not like wings, but as well not like wind turbines )
Read what I actually wrote. I said :
"Look up the Betz law to get an idea of what kind of limits are at play."
I didn't state the Betz law was fully applicable to the sails just that similar limits are at play. Even a sail can not milk 100% of the energy enclosed in the wind as that would mean completely stopping the flow and as we all know, stopping the flow is associated with all kinds of bad effects like stalling.
Other then that I think you quotes of mathematical formula (physics) is confusing, also to yourself. You say :
Boat speed v and apparent wind will depend on wind speed vapp^2=vwind^2+v^2.
But this equation is ONLY true when sailing on a beam reach. For upwind sailing and broad reaching you'll need to modify this Theorem of Pythagoras considerably.
I understand what you are trying to get at, but beware of modeling errors. Todays racing sees very little beam reaching and that course is of no significant importance for bouy racing. If the iCat was designed as an optimal reaching boat then it would have had a jib.
Hence more chord is less speed, which is something what you have in mind, I guess
What I was getting at was that sail area itself is only of secondary of tertairy importance in the larger picture. Luff length (as that is associated with swept area) and sail shape (large heads) are more significant factors for overall performance, especially in light winds. Therefore I claim that using the same mast length and luff length as the F16's the iCat larger mainsail will at the very best show only very small performance improvements in conditions other then medium winds. As a result, it is questionable if the larger sail will be a factor at all in comparison to the F16's. I truly believe that iCat to be about the same performance with a 15 sq. mtr. sail as with its current 16 sq. mtr. sail although the measurement based rating systems will assign a full hit for the extra 1sq. mtr. anyway.
If I punch in the numbers for the 1-ups + spi in the Texel rating calculator I find the following
Hobie iCat 97.65
Formula 16 100.67
I've used the same data for the iCat as the F16 except for the hull length and mainsail sail area. In answering Karls question. The minimal weight for a spinnaker setup+snuffer is 4.0 kg or more. Typically they are around 5kg therefor the ready to sail weight of the iCat was set at 104 kg = F16 min weight in 1-up mode.
I personally don't see the iCat with the given specs outperforms the F16's by 3 handicap points (108 sec = a shy 2 min. per hour racing). Not when the only differences are a 0.290 mtr longer hull and an added sq. mtr mainsail area behind the same luff.
Wouter
