Theory

All the theory behind designing the submarine.

How a Submarine works

A submarine works by making itself neutrally buoyant, that is it weighs exactly the same as the amount of water it displaces, so it neither floats or sinks (i.e. it's density is that same as the waters).  The is achieved by having large ballast tanks that can be flooded with water to sink or pumped full of high pressure air to rise.  Once submerged, the submarine can move to any depth by propelling itself through the water and maneuvering it's elevators, much like an airplane moves through the air.  The depth is only limited by the structural strength of the submarines hull.


Water Pressure

Water pressure increases linearly with depth at a rate of approximately 14.7 PSI every 10 meters.  In comparison the standard air pressure at sea level is 14.7 PSI (1 atmosphere of pressure), so at 10 meters down you'll experience twice the pressure than at sea level; 20 meters would be three times, 30 meters four times, etc.


Ballast Tanks

The displacement of the empty ballast tanks had to be enough to lift the sub high enough above the surface of the water so that it could be easily retrieved onto a trailer, and so that it was stable and looked cool.  The are four main ballast tanks which are 0.16m in diameter and 2.7m long.  They are made from high pressure PVC pipe, although they won't be under much pressure at all since they will be completely filled with water in the dive.

The total volume of the tanks is;

quantity x (radius² x Pi x length)
4 x ((0.16m ÷ 2)² x 3.14159265 x 2.7m) = 0.2171m³

0.2171m³ is equal to 217100.0cm³, and given that the density of fresh water is 1g / cm³ (salt water is slightly higher, approx 1.03g / cm³), the weight that the ballast tanks will support before sinking will be, 217100g or 217.1kg.

Seeing as how neutral buoyancy is that the density of the submerged object is equal that of the medium (water), I know that with the main ballast tanks completely full of air I can't hold up above the surface of the water, more than 217.1kg.  Which is the same as 217.1 litres or 0.2171m³.


Circuit Operation of the main ballast tanks are shown below.

Fig.1

In (Fig.1) the ballast tanks are kept closed off from the outside water.

Fig.2

In (Fig.2), once the dive switch has been selected to dive, the control circuit will test both tank pressure and sea water pressure via the transducers for equality.  If tank pressure is less than that of the waters, the water valve will open first to equalise pressure, then the air valve will open to expel air back to the tank via the compressor.

If the tank pressure is greater than that of the waters, the air valve will open first and will be compressed back into the tank before opening the water valve.  If this isn't done then the higher pressure in the tank will force the water out before it comes in, thus putting air locks in the water valve system.

If both pressures are equal, both valves will open together to flood the pipes.

The float switches are to stop over filling or over evacuating of the tanks.  If the top float switch is off, more water can enter, otherwise the air system can become flooded.  If the bottom switch is off, more air can enter, otherwise it can force out too much water and create air locks in the water system or worse, waste air into the sea.

Trim Tanks

There are four groups of trim tanks which consist of two PVC pipes each. They are arranged so that I have precise control over buoyancy at all four corners of the sub.  The reason for these tanks is because the main ballast tanks need to be either completely full or completely empty to provide enough buoyancy, so they can't be adjusted to compensate for the varying weight of the pilot and the extra little bits and pieces external to the sub that provide buoyancy where it is too hard to accurately calculate their volume.  So, I needed smaller tanks that could do the job of fine tuning the buoyancy.

Another reason why I decided not to use the main ballast tanks as the trim tanks as well, was because of flow measurement.  The larger volume tanks would have more room for error than the smaller ones because they would have to be open for longer and the flow sensors are less accurate over a longer time.

In order to get neutral buoyancy I have to know how much too heavy or too light the sub is and control the trim tanks accordingly.  For that I will graph the flow rate into and out of the tanks at different water pressures (I'm thinking it'll be linear with pressure, fingers crossed) so that the onboard circuitry can use the external water pressure; the onboard air pressure and the known flow rate, to open and close the appropriate valves at the correct times to change the overall buoyancy.  That, as well as the circuit measuring the external water pressures rate of change, and thus the descent / ascent rate, should provide enough information to get the sub neutrally buoyant automatically.  How long it will take I won't know until I test it, but the more accurate I can measure the subs volume the better.

The trim tanks will also aid in controlling the level of the sub underwater.

Each set of trim tanks provide about 20 kg (total 80 kg) of buoyancy.  The plan is to have neutral buoyancy when the tanks are half full, that way there is an overall adjustment range of ±40 kg.