The extra width is also needed for the curved boards since the lift forces on the curved boards decrease righting moment via the leward board.
Eh? The leeward board is pushing the hull up, thus increasing RM!!!
Yeah but since the board is also curved - some of that force directed upwards at the tip end of the board is going to result in a "torquing" of the hull, meaning that its effectively going to rotate the leward hull outboards.. increasing the amount of capsize moment.
You might be right though that the effect of the board lifting overall would equalize the effect of the boat spinning the leward hull outwards.
AFAIK, the issue here is the balance between transversal and longitudinal stability.
Suppose we start with a traditional 2/1 L/B ratio catamaran, that reaches both stability limits simultaneously at a given wind speed.
We can increase its righting moment by making it wider and then it will be able to carry more sail area. However, since its longitudinal stability remained the same, the extra sail area will make it pitchpole earlier then before, so it will not reach the full speed potential of the enlarged sailplan.
Lifting foils placed forward of the CG increase the longitudinal stability at speed, solving the problem - granted, at the expense of a fraction of the extra righting moment.
Conclusion: keeping hull shapes unchanged, curved foils allow a cat to be wider and to carry more sail area, so it becomes faster then before.
Check: the new AC cats have curved foils and their L/B is 1.5:1
Check: the tris with even smaller L/B (1:1) are where curved foils were developed, for they need them badly. Without those foils they reach their longitudinal stability limit a lot earlier than their capsize limit. You certainly remember how the first 1:1 tris were pitchpole prone.
Cheers,
