What would I experience if I was trapped in an air bubble on a sinking battleship?

If it were to sink deep enough, provided the air bubble were large enough to sustain life, eventually oxygen toxicity would kill you. See the MOD table here.

Oxygen toxicity occurs at about 1.4 atmospheres, or about 187 feet of depth. Nitrogen narcosis is highly variable between individuals, but- at 80% atmospheric concentration- getting "narked" is common at depths over 100 feet, and "usually incapacitating" (ibid) at 300'.

Also note that as depth increases and the partial pressure of oxygen increases, things become more flammable. It is generally thought that there were some survivors on the submarine Kursk that died hours or even days later when an oxygen generator came into contact with water, causing a flash fire with a film of oil and fuel that covered the surface of the water, causing pretty much everything that was combustible in the enclosed chamber to burn. Anyone who survived THAT would probably die soon after from carbon monoxide poisoning. FWIW, the bow of the Kursk was at a depth of 108 meters. The chamber in which the survivors were caught was slowly filling with water, making it impossible to escape after a relatively short period of time, due to the likelihood of death from decompression sickness due to the saturation of nitrogen under pressure.

It also seems likely they didn't try the escape hatch as the method to escape relies upon allowing water (at nearly freezing temperatures) into a tightly confined space until the pressures equalize, and then hoping the hatch isn't jammed from the initial explosion or the collision with the ocean floor, and then swimming upwards nearly a hundred meters without bursting your lungs. And THEN you have to hope a ship will notice you before you freeze to death in the ocean. So perhaps they can be forgiven not trying to escape.

/r/askscience Thread