Hmm. It's amazing how confused people get about this. Your analysis
is incorrect. The effect of water ballast is precisely the same as
the effect of any kind of ballast -- you get more weight below the
center of bouyancy, which increases the righting moment. In a
particular boat design it may increase the effective beam, but that
is basically incidental to the point.
Take a basketball, and cover it with fiberglass. You now have a
model "boat" that is completely tender -- it will turn turtle instantly,
because there really is no top or bottom. It has no righting moment
whatsoever, and the "beam" is constant -- it's just a ball floating
in the water, and you can spin it freely in any direction.
Now cut it in half, attach a small weight to the inside of one half,
and glue it back together. Now you have a boat with righting
moment -- it will *always* float with the heavy side down.
It doesn't matter what that weight is -- it could be a block of lead
or an ice cube with neutral bouyancy, or water in a small container,
or even a small block of wood that would otherwise float. The
density doesn't matter. It will float heavy side down.
While the mass of course has inertia, that has essentially nothing to
do with the effect. Likewise, the increase in beam may be a factor
in a particular boat, but that really is a totally separable effect,
as well.
-- Kent Crispin "Do good, and you'll be kent@songbird.com lonesome." -- Mark Twain