Physics and depth control of a small spherical submarine Recently, me and my dad were discussing the theoretical design of a small homemade submarine. Lets assume that it is a hollow acrylic sphere with a radius of around 25cm. The radius would likely need to be adjusted to meet certain requirements, like a certain depth at which the submarine should float, but that is mainly what this question is about... Inside, there would be electronic components like a camera and some type of system for relaying the information generated, so that it could be observed.
Assuming that the depth of the submarine is controlled by relative density of the submarine itself, compared to the surrounding water, how would the submarine need to be designed to reach a certain target depth? That would probably be dependent on the weight of the submarine and the volume of air inside the hollow area, right?
What would be the most effective system for bringing the submarine back to the surface? I read that real submarines use compressed air to achieve this. Would that be the best way to do it in such a small system like this one or would there be a simpler more energy efficient way, like a propulsion system?
Thanks!
 A: The submarine would sink to the depth at which it weighs the same as the surrounding water (see Greek guy plus bath minus clothes).
However since water isn't very compressible there isn't a lot of change in density of water with depth due to pressure. So if the submarine sinks at the surface it is likely to keep sinking. This is different from air which varies in density fairly linearly with height and so you can make balloons float stably at one height.
In practice the changes in density of seawater is mostly due to temperature and salinity differences, and these are small and variable.
ps the easiest way to make it rise is to weight it with a some scrap iron held by an electromagnet. Battery (or a timer) runs down, magnet turns off, weight drops, submarine rises = relatively fool proof
A: Since you are going to have communication with the submarine, you can make the depth an active control with a relatively simple mechanism to take on water and push it out again.

Here is a simple submarine with a piston that has outside water on one side, and the interior air on the other. The motor moves the piston in and out to control how much water is let into the piston housing. The submarine should be weighted so that it has neutral buoyancy in this position. There needs to be a seal between the piston and the walls of the housing to prevent water from leaking through. A bellows system would work, too.
When you want to dive deeper, pull the piston in to let more water into the interior.

Since the submarine has taken on water, it is heavier and will sink. Similarly, pushing the piston out will make the submarine rise.

As Martin Beckett noted, water density is constant with depth, so the position of the piston controls how fast you sink or rise, rather than the depth you stay at. This helps you save energy because the piston doesn't have to move that far, since any adjustment away from neutral buoyancy will cause constant speed motion up or down.
As a fail-safe, you could put a spring that's strong enough to push the piston all the way out should the motor fail, causing the submarine to rapidly rise back to the surface.
