Scooby_Simon, been a while since high school physics so please excuse the cloudy brain whilst i remember, but are you considering the calc as a 2nd class or 3rd class lever? If 2nd class, then you are correct, but I always thought as 3rd class. The crew is the lead weight lump at the end of the wing/lever pushing down. The force from the sails/wind/mast is on the middle of the lever pushing up. If you can move this force point closer to the point, the more effective the force pushing down.
Am i missing something?
All forces balance on the leeward hull. All mass is at a distance from the pivot (leeward hull).
If you JUST have a boat; you can assume the mass (in pivot terms is spread accross the boat. The windward hull is "beam" away from the pivot; the boat is symetric and so 1/2 mass of the boat is acting at the beam. If the boat-beam is reduced (because you have wings to make it back up to the same overall beam), you have less RM from the boat (1/2 mass * beam(remember smaller + (some RM from the wing). Crew provides the same mount of RM as they are the same distance from the pivot.
IF you have wings on the boat, the mast is not in the middle of the boat (+wings) and so the mass of the mast provies less RM. Also; as the boat heels; the mast moves to the otjer side of the pivot more quickly and so reduced RM again.
Heeling moment (from the sails) is balanced at the leeward hull. The heeling moment we are "balancing" is at 90 degrees to the RM and we balance at the leeward hull.
