For multihulls, there are four important indicators of performance and stability: the Bruce Number; the Real Performance Index; the Stability Number; and the Stability Factor.
Bruce Number is another form of the sail area-displacement ratio (a power-to-weight ratio). It shows how much sail area relative to displacement (weight) a boat has, but tells nothing about a boat’s ability to stand up to that sail area. (Sail area is main plus 100% foretriangle. Add mizzen area for a ketch or yawl and foresail area on a schooner.)
RPI = Real Performance Index h = height from DWL to center of effort of sailplan, with 100% foretriangle, ft.
Real Performance Index (RPI) gives the Bruce Number (the power-to-weight ratio in Bruce Number form) that the boat can handle in mid force-7 winds (30.7 knots).
The Stability Number equals the RPI divided by Bruce.
If the Bruce Number for force-7 winds (the RPI) is greater than the boat’s actual Bruce Number, then the boat’s rig is suitably sized for safety at sea.
Stability numbers for all offshore multihulls intended for ordinary cruising or racing must be higher than 1.0.
Say you had a catamaran 44 feet LOA, 25.6 feet Beam overall, and with a rig (full main and 100% foretriangle) of 1,058 sq. ft. The center of effort of the sailplan is 29.1 ft. above the DWL and displacement is 13,200 pounds. The numbers work out as follows:
This boat has acceptable stability in regard to its rig. At the same time, the Bruce Number is reasonably high. This indicates a safe offshore cruiser, with a good turn of speed for a catamaran. If the hulls are long and slender at the waterline, this boat can achieve very high speeds safely.
Note that some unlimited offshore racing multihulls have Stability Numbers lower than 1.0. These craft can be exceptionally fast, but they are not safe offshore. This was clearly demonstrated in a recent Round Britain Race, where all but two of the Unlimited 60 trimarans competing either capsized or had catastrophic structural failures during the race.
Some Representative Bruce Numbers: Performance Monohulls J/24 = 1.16 Santa Cruz 27 = 1.18 Laser = 1.33
Multihulls Brown Searunner 34 cruising tri = 1.11 Newick Val Tri racer = 1.44 Kelsall 52-ft. racing tri = 1.62 Hobie 16 = 1.72
Since Bruce Number is a form of sail area-displacement ratio, you can convert from one to the other as follows:
Stability Factor indicates the approximate apparent-wind speed at which the multihull will have to begin reefing. The Stability Factor for all offshore work and all cruising boats should be 19 knots or higher.
For our example boat this works out as:
Since this is over 19 knots, the rig is acceptable for offshore and cruising use.
The above assumes low angles of heel, under 9 degrees, which applies quite well to essentially all catamarans that don't fly a hull and to most trimarans that don't fly a hull. A few trimarans may sail well in heavy air at over 9 degrees without or without flying the vaka out of the water. In this case, the "beam" in all the multihull stability formulas above should be replace with:
"Beam x cos heel angle," in expected sailing trim.
In most instances; however, the heel angle will be under 9 degrees and the difference is then 1% or less—too small to be worth calculating.