The primary concerns in the design of a catamaran are seaworthiness and performance. The former is a complex subject involving the hull shape under the water, reserve buoyancy and windage above the water, beam, weight, rig size and efficiency, and of course the strength and integrity of the structure. We will have to limit the discussion here to only one of the primary concerns - lateral stability.
Before we get into the math, the "friends" of performance are lots of Sail Area (SA in sq. ft.) and long Waterline Length (LWL in ft.). The principal "enemy" of performance is Weight (Wt in lbs.) with its effects on wetted surface area and shape required to provide the volume to support the boat in the water. For a catamaran, the "friends" of lateral stability are Weight and Beam (Bm = 1/2 hull centerline beam in ft.), with the "enemies" being Sail Area and Height of the Centre of Effort of the Sail above the water (HCE in ft. Since HCE is rarely quoted, a good approximation is 1/3 of the sail luff, or 40% of the mast length plus the height of the mast base above the water). As you can see, with a couple of exceptions, your friends for going fast are your enemies for stability in a blow, and vice versa. Each catamaran design is a "positioning" on these basics.
Two empirical formulas have been developed (by Kelsall, Shuttleworth and others) which allow you to calculate and compare the performance/stability positioning of any design. These formulae should be considered only as "Figures of Merit" for comparing designs, since they only consider static forces and do not include the dynamic effects of wind, waves, hull shape, etc. The performance formula gives as a result the boat speed, relative to wind speed, to be expected on a reach. (For example, a result of 0.8 means 8 knots boat speed in 10 knots of wind, etc.)
Performance = 0.5 sqrt(SA * LWL/Wt)
The stability formula gives a result which is the wind speed (in Knots) required to just lift the windward hull (the point at which, in a cruising boat, not a beach cat, you scream "Let go the sheets!", or better still "Let's put a reef in her").
Stability = 13.7 sqrt(Wt * 1/2Bm/SA * HCE)
Taking the TomCat 6.2 and 9.7 as examples, we get the following:
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