Hi. The LCF is obtained most easily by cutting out a pattern of the waterplane (the area enclosed by the load waterline in plan view) and balancing it on a knife edge. This is point around which the boat pivots when pitching or diving at small angles. LCB is where the whole boat balances when floating. Depending on the underwater shape, the two may or may not be at the same place.
A good source of info for this stuff for people who can handle the math is:
Rod - Among my many experiments in another development class I mounted a monosail with a stern mounted mast on one of my 36/600s. Contrary to your belief that there would be very little stress on the aft mounted mast I experienced all sorts of control problems. The most vexing was that the spar would twist to leeward and then start to pump as the carbon mast would try to spring back. We mostly load our masts in line with the greatest stress, as a sort of post that the sail pivots around, or in the case of a swing rig the whole rig weathercocks in line with the wind. The masts tend to deflect in one direction, to leeward, not in a spiral twist.
There is also very little you can do to control sail shape of a large jib, particularly when the aft mounted mast twists. It was not practical on my 36 physically as well as weight-wise to add a spar along the luff to gain some mastery over camber and sail twist. A luff spar/boom combination would be more practical in Footy scale where the weight and stresses that carbon tubes can manage is more than adequate. Adding a luff spar doesn’t really change things that much from a McRig though.
As to the aerodynamics of my set up, I never got far enough to make a judgment pro or con. The rig just sucked from the outset.
Were I to try a large mono-jib on a Footy I think that I would go with a modified “pyramid rig”. I would use two light mast spars mounted athartships in the gunwales just aft of the point where the jib would pivot. There would be a cross-spar connecting the tops of these two mini masts and the halyard for the mono-jib would be attached in the middle. This arrangement gets the mast spars away from the sail so as not to disturb flow. One could even mount these spars on “wings” that could extend outboard of the box to really separate the masts from flow over the sail. The main advantage (in Footies) to this system over an aft mounted mast is that it doesn’t restrict the foot length of the mono-jib to the aft mast location.
Another variation on the theme is the “ladder rig”. Here you would use the same double mast arrangement with a forward jib and a “mainsail” that was also a jib. Perhaps 50/50 in area. The difference is that there would be two cross-spars, the lower being longer than the top one, thus pre-loading the mast spars and making them stiffer, possibly reducing any twisting stresses.
I don’t know if either of these suggestions is aerodynamically sound and would be an improvement over current technology. The ideas come from cruising boats where easy single handed sail management is an ongoing struggle. I haven’t seen them used on racing boats. I think that getting the whole setup light enough and strong enough (even in Footies) may be a fruitless challenge, but good luck to you if you take it up.
Dunno whether anything’s proven, but Moonshadow’s in in the Euro GP certainly suggests that a design path that started ut with Mariner is’t the wrong way to go.