Would it be possible for me to build a simple mini-submarine in a home workshop?
There are a lot of things to consider in building a working submarine other than the strength of the hull. Here are some of the basic design considerations: (1). The volume of water ballast space which will enable you to submerge the submarine and bring it back to the surface when the ballast is removed, at all your possible loading condition. (2). Trim tanks which would ensure that your submarine does not trim excessively when submerged. (3). Depth control tanks (4). Propulsion system ( note that you can not use internal combustion engine when fully submerged as it would use up all your reserve air) (5). Safety which includes, hull circularity, weld joint efficiency, watertight integrity of entry hatch,material reliability, and emergency provisions. (6). Also there is such a thing as equilibrium polygon, which is a plot of your submarines capability to submerge and resurface at a given loading condition. (7). Stability of the submarine on the surface and when submerged at all possible