Mr.Penguin - those are good questions. Ask away, it's how I learn where my mistakes are
1) 1/4 chord pt. validity: I don't know the math for locating dynamic CE (or CLR) there. The 1/4 chord location shows up a lot on aerodynamics books and internet sites, I did not invent it. I suspect it was initially just something derived from experiment - where does the wing balance (equal lift fore and aft of a fulcrum)? This would be pretty easy to figure out just by noticing if the wing tips up or tips down around a fulcrum when it's put in the windtunnel. Move the fulcrum until the wing does neither, and you have dynamic CE ta da! CEdyn moves some with angle of attack. But sailboats use the same AoA for beating and reaching - it's set by what is the minimum AoA you need to keep a flexible membrane (of cloth) filled with wind? Answer, about 3 points off boom parallel with the wind. So we don't really have to worry about changes in CE with changes in sheeting. Sloops beat at 4 points off the wind: 3pts to fill the sail, plus 1pt to get the boom off the hull centerline so that some lift moves boat forward.
In real planes with a single spar, the spar is located at the 1/4 chord point, or there-abouts, not at the middle (1/2 chord). That way, the strongest part of the wing is at the strongest part of the lift. As for real reasons for offset-from-center lift, if you look at the distribution of pressure over a wing, you notice it's not symmetric, but weighted towards the leading edge. Pressure is a proxy for lift. Thus, the summation of the lift results in being farther forward than the center of the wing.
I've seen estimates of CE as far aft as 1/3 chord, but most sources I've read seem to use 1/4 chord. I'd think the airfoil shape would affect the CE location, but have not actually seen this in books. But I don't know it all, by any means.
2) Relative area of jib fore&aft of dynamic CE, and relative area of triangular mainsail (or quadralateral mainsail) fore&aft of dymanic CE does not really matter. The mathematical center of lift, the CE, is what it is. Which way the right triangle points (Jib vs mainsail) affects the location of individual CE. They do all cancel out at some point along the hull. The method of moments allows you find that point.
3) This is another topic, but lift is not Why you (probably) think it is
. Good old Bernoulli has almost nothing to do with it :-0. Prior to the end of WW2, aerodynamicists used Newton, not Benoulli, to explain lift. After WW2, for some reason US guys (and maybe others) adopted Bernoulli. The big B can't explain a lot that is true of flight: eg. flight upside down, flight using a symmetrical airfoil. If you ever get a chance to look at the airfoil at the wingtip of a business jet, you may be amazed to see that it's upside down - the curved part is on the bottom, and the straight part is on the top! Holy Non-Flying Cow, BernoulliMan!
So why did they use Bernoulli post WW2? Possibly because it's easy to measure the negative pressure distribution above a wing (using little manometers connected to holes in the upper surface). Since Big B is related to lift, you can use it as a thermometer of lift. Somewhere along the line, though, the thermometer got confused with the furnace. FAA backed the wrong horse, equating Bernoulli with lift, and US pilots have been mislead ever since. Fortunately, you don't need to know Why lift exists to fly a plane or sail a boat
Recently, physicists at U of Washington and Fermi Lab recalculated lift for a Cessna 172 (they are both pilots). They found that Benoulli can't account for more than 1-2% of the lift needed to fly that plane. But, Newton calculations can
. The wing throws air downwards, and the "Equal and Opposite Reaction" law of Newton explains that the air, in turn, throws the wing upwards. You can read all about their work here, which they call the "Physical Description of Lift" :
http://home.comcast.net/~clipper-108/lift.htmAnyone who stands behind an airplane propeller has felt the air being thrown. The Wrights, in one of their important insights, realized that a prop is just a rotating wing. Well, if the prop is throwing air, then the wing must be too, is one way of looking at it. The plane is not sucked forward when the prop spins, but is thrown forward in reaction to the air being thrown aft. There is suction, but it's miniscule compared to the force generated by all that mass of air thrown aft.
All the same happens with the sails and the keel. The difference is that the sail pulls to leeward (pulls perpendicular to the boom, actually), and the keel pulls to windward (perpendicular to the hull). W/o the keel's lift to windward, we'd never be able to sail to windward
. The hull and keel each form symmetrical airfoils (which Benoulli hates). Due to the leeway of a boat, the hull & keel have a positive angle of attack, which lets them generate lift. We don't pull the boom to the hull centerline when we want to go to windward because if we did, all the lift would be directly perpendicular to the hull, and we'd only go sideways. But letting out the boom a bit, we get some of the lift to point forward, sending us on our way. The keel's lift combats the leeward part of the sail's lift, otherwise we'd go forward (pointing upwind), but drift to leeward faster than the movement upwind since the majority of the sail's lift is pulling us leeward.
Just fun stuff I like, not much to do with balanceing sails and keel.
Hope I answered some of your questions.
