Re: [math-fun] Free surface effect
If CG means center of gravity, then I don't understand this. Otherwise, I don't understand it because I don't know what CG means. —Dan ----- Sure. Imagine a circular cylindrical tank. When partially full roll of the ship would leave the tankage CG unchanged while the CG of the rest of the ship (assuming it's stabilized by a keel) would move opposite the roll. So the overall CG would change. But you can't tell the stability of a floating object in general just by considering the CG location. You have to consider the center of buoyancy too and their relative motion. Think of a catamaran. The CG doesn't change when it rolls, but the center of bouyancy moves to provide a righting moment. -----
I did use CG to mean center-of-gravity. I'm sorry it wasn't clear. I was imagining a ship that was just a cylindrical tube, that it partly full of some fluid, say oil, and it has a heavy keel. If it rolls, say counter-clockwise looking forward, the oil will stay exactly where it was (neglecting boundary layer friction) while the ship keel will move to the right and upward. Hence the ship structure CG will move to the right, while the oil CG doesn't move. Did that help? Brent On 7/30/2018 12:52 PM, Dan Asimov wrote:
If CG means center of gravity, then I don't understand this.
Otherwise, I don't understand it because I don't know what CG means.
—Dan
----- Sure. Imagine a circular cylindrical tank. When partially full roll of the ship would leave the tankage CG unchanged while the CG of the rest of the ship (assuming it's stabilized by a keel) would move opposite the roll. So the overall CG would change.
But you can't tell the stability of a floating object in general just by considering the CG location. You have to consider the center of buoyancy too and their relative motion. Think of a catamaran. The CG doesn't change when it rolls, but the center of bouyancy moves to provide a righting moment. -----
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Brent Meeker -
Dan Asimov