# Is there a shape that when submerged in a fluid is stable across all axis?

When placing a jar in a body of water an air bubble can be formed. If the air bubble is large enough forces are equal and the jar will be buoyant and float on the surface of the fluid (see fig. a).

If too much air is introduced into the jar when it is placed in the fluid it will be too buoyant, this will result in instability and the jar will flip, resulting in the air bubble escaping and the jar sinking (see fig. b).

My question: Is there a 3D shape that is inherently stable across most (all?) orientations? How can the stability of a geometry be measured?

Another way or wording the question: If I am to toss an container above a body of water with it than landing in the water in a random orientation. How can the likelihood that it'll reach a stable orientation and float be measured?

Constraints:

• The shape has a cavity that can contain air
• The shape is not enclosed (when submerged some orientation will result in the air escaping)
• If you make the lip of the jar arbitrarily heavy, it won't flip no matter how big the air bubble is. A real jar flips because the bottom weighs more than the open top. Commented Jan 18 at 21:53
• You need to look up some terms - heel, list, and loll. All are stable, it's just that the attitude changes depending on the exact center of buoyancy (this is loll). Are you looking for a shape that has constant loll no matter how much air gets trapped? A sphere does that. Also look up "free surface effect" Commented Jan 18 at 23:56
• There's an interesting question in here, but needs to be defined a little more clearly Commented Jan 19 at 0:36
• to wit - please define the two fluids, and provide us with their densities - it matters. Please provide us with the hull material, thickness, and density. This matters a lot. Is the container open at the bottom, or can it be sealed? What volume percentages of the lighter fluid do we have to consider? This calculation is required to be done on every ship and is summarized in the ship's stability book. It may get redone by ship's master or engineer if loaded in a way not covered by the book. In other words, this is done hundreds of times a day the world over. Commented Jan 20 at 0:09
• I figured IMO rule would have something about the stability of diving bells. "5.4.2 Diving bells whose emergency ascent is initiated by the release of ballast at its maximum service weight and with its trunk flooded, must exhibit a positive buoyancy equal to at least 3 per cent of its displacement at maximum operating depth. In these circumstances, the bell should have sufficient stability to maintain a substantially upright position after release of ballast." So when full of air and no ballast and 3% buoyant, it must be stable. Commented Jan 20 at 0:15