Originally Posted by Wayfarer
I've always wondered about how initial stability is actually measured.
The most I've ever seen was less than 40 degrees, and that was plenty scary. I can't imagine 70 or 80. You'd be walking on the bulkheads.
Transverse stability is the righting action of any floating object. It's the result of the buoyancy force acting upwards and the displacement force acting downwards. The displacement force is equal to the weight of the vessel and operates through the center of gravity (CG)
of the boat. According to Archimedes, "An immersed body is buoyed up by a force equal to the weight of the fluid it displaces", this is the buoyancy force, acting through the center of buoyancy (CB)
As the boat heels the center of buoyancy moves to one side (the lowest one) while the center of gravity remains (hopefully pretty much) stationary. This sets up a rotational force to right the vessel. The horizontal distance between the downward displacement force (on the centerline) and the upward buoyancy force is the righting arm
. Multiplying the length of the righting arm by the buoyancy force (equal to displacement) gives you the righting moment
Rolling big boats around in real life is awkward and expensive. It's rarely done, except with some Pilot boats, Coast Guard, some ocean racing sailboats, and the occasional stunt as mentioned in the note above about the Elling. I'll come back to that....
Today we have cheap personal computers and inexpensive software that can do stability calculations all day long with no sweat. From the above we can see that, if you have an accurate hull model floating at the correct level, and an accurate center of gravity, and know the density of the fluid our ship floats in, we can accurately calculate her stability (righting force) at any heel angle.
So large angle stability is not usually measured, it is modeled in a computer program, very carefully. Taking into account things like tanks and their contents, downflooding points, and the flooding of deck spaces (cockpits, etc).
What is physically measured is small angle (up to 3 degrees heel) stability. By heeling the boat with a known weight a known distance from centerline, and measuring (very accurately) the heel angle, and using geometry, we can precisely locate the center of gravity of the boat. This is known as the Inclining Experiment
. The results of inclining experiments are often surprising, the center of gravity is always higher than anyone expects. And it's always higher than the NA calculated. Thus it's a vital part of any realistic stability study.
To return to rolling boats over over with cranes and watching them pop upright, it's spectacular but not really useful IMO. Some classification rules require this proof-positive of self-righting for certain vessels, almost always specialized commercial boats. A few years back a new 60'ish Pilot Boat was being tested like this in the PNW. During the inversion with a crane, a fire extinguisher fell out of it's mount and cracked a window. The boat started flooding, the water forming ballast inside the roof, the Pilot Boat failed the test and underwent expensive repairs. Just think about the 100's of pounds of stuff that would land on the roof should your average pleasure boat roll over. It makes these sort of "tests" seem pretty silly.