The following boats have similar LOA, Beam, Ballast / Disp ratio, and Draft. The "Racer" design has 50% less displacement, 50% longer righting arm (due to a flatter bottom and lower center of gravity), and a 66% lighter weight rig. Both boats are subjected to a constant 30,000 ft.lb. overturning moment, which is less than their maximum static righting moment. The simulation begins with an under damped condition which allows the overturning force to capsize the boat. The damping is then increased until the boat oscillates rather than capsizes, eventually damping out to a constant heel angle. The first case gives us the time to capsize, the second lets us measure the period of oscillation. Under static conditions, damping is largely determined by the rate that water is swept away by the keel as the boat rolls. The lateral area of the underbody normally controls damping (deep keels and centerboards help), however in a storm the keel may be in breaking water (froth) and the damping forces drop dramatically, allowing the boat to heel more.

                                                RACER CRUISER

Disp., lb                                   16000         24000

Hull, lb                                     9300         13900

Ballast, lb                                 6400          9600

Mast and Rig, lb                          300          500

Roll Period, sec                           4.6            5.7

Static Stability

Righting Arm, ft                                2.4             1.6

Max. Righting Moment, ft.lb            38347          38399

Heel at Max. Moment, deg.              62              64.5

Dynamic Stability

Moment of Inertia, lb.ft.sec^2         17304          26522

Time to heel 30 degrees, sec              .9             1.1

Time to heel 60 degrees, sec             1.4             1.7

Time to heel 90 degrees,sec              2.0              2.5

Time to Capsize, sec                        2.8              3.6

    The first thing we notice is that the light weight racer has a much shorter roll period than the cruiser. Its tempting to claim that this indicates more static stability, however this is not completely accurate. Static stability does reduce the roll period, but so do other factors such as the roll moment of inertia. When we look at the actual values for static stability, both boats are about the same. Even though the racer ends up with a longer righting arm, the cruiser’s heavy displacement compensates for it since static stability is a function of both.

    The big difference is in dynamic stability. The Cruiser has a 53% bigger roll moment of inertia, which greatly slows down its response to the overturning moment, resulting in the increased roll period. At 90 degrees heel, the cruiser lags the racer by 1/2 a second. At the point of capsize, this time difference has increased to .8 seconds. In a sever storm this could be the difference between an unpleasant knockdown and a life threatening capsize.