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I am looking to determine the lateral angle at which an underwater camera system will no longer right itself. When on the ocean floor it is $-24.30~\text{kg}$ buoyant with the difference between its center of gravity and buoyancy being $45.14~\text{cm}$. The two centers are almost directly underneath each other with the buoyancy on top.

I am struggling to determine its righting moment because it is fully submerged and most text seems to be aimed at floating vessels.

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  • $\begingroup$ Given the camera is meant to be submerged, I think it's pretty likely that the center of buoyancy will be quoted for totally submerged conditions. Work out the angle assuming this, and then test it in a tank. $\endgroup$ – WetSavannaAnimal Aug 16 '16 at 12:45
  • $\begingroup$ Please show your attempt to calculate an answer. $\endgroup$ – sammy gerbil Aug 16 '16 at 19:26
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Most surface vessels purposely engineer the center of gravity to be slightly above the center of buoyancy for maneuverability. Surface vessels that don't have that property are termed bottom heavy and are difficult to turn. The stability of a surface vessel is usually measured by its metacentric height and determined by the inclining experiment. The reason the ship is stable is that it picks up a restoring moment as the ship rolls one way or another and the water plane increases and so you'll have a roll frequency develop. Too high and the crew gets easily seasick.

Submarines are a different matter. There is no water plane when the sub is submerged and the metacenter merges with the center of buoyancy. Surfacing is a critical operation, and if not done carefully it can cause the submarine to roll over during the transition of metacenter.

Your camera problem is the submarine problem and you don't need to concern yourself with metacenter since it merges with the point of buoyancy. Your righting arm is strictly the difference between the c.g. and c.b. assuming your camera body is rigid.

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