[Psml] Stability with Deck Flooding

[jeff at usps-atlanta.org]

In studying for my Masters, I ran across the following equation for
"reduction in metacentric height" due to deck flooding.  Obviously it is not
an equation for reduction in GM, but rather an equation for GM which
includes deck flooding, ignoring factors of downflooding angle, dynamic
acceleration in the listing moment (sloshing), clearing time, and other free
surface effects.

 

GM ? (L x B^3) / [420*(D+W)] 

where L=wetted deck length(ft), B=Beam(ft), D=displacement(tons), W=weight
of the deck water(tons)

 

What I'm trying to find is the derivation or a discussion of the equation.
I've checked the MSM-Volume IV, and a few other sources, but haven't found
the exact equation.  It's obviously close to other B^3 equations, and I'd be
willing to accept D+W term, but I'd still like to see a
discussion/derivation.  Does anyone know where it comes from?

 

Thanks,

Jeff, 

D-17

 

PS, I wonder if the judge who ruled that the EPA couldn't exempt
recreational boats from deckwater runoff regulations considered that his
ruling will kill people by increasing free-surface water on decks and in
bilges. ;-)

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