The ballast tanks on a submersible take in and expel seawater, changing a vessel's buoyancy and thereby enabling it to vary its depth. The ballast tanks of our submersible are placed in the lower portion of the vessel, just below the center line of the vessel. The capacity of each of these tanks is 0.5 m3, and the total amount of compressed air stored (per canister) is 10 m3. A smaller trim tank, with volume 0.1 m3, is located near the stern of the vessel.

Buoyancy
Buoyancy is typically described as a measure of an object's tendency to float in a given fluid. To quantify this, we will define the buoyant force (Fb) as the upward force exerted on a object when submerged in a fluid. This force is equal to the mass of the fluid displaced multiplied by the gravitational field, and the mass of the fluid displaced is equal to its density (r) multiplied by the displaced volume(V):

Fb = rVg

For an object to remain stable while submerged in a fluid, the weight of the displaced fluid must equal the weight of the object.

Our vessel has an approximate volume of 10 m3. This estimate can be easily reached by treating the shape of the vessel as the junction of a hemisphere, a cylinder, and a cone. Since the density of water is 1000 kg/m3, our vessel has a mass of approximately 10,000 kg so as to equalize the buoyant force of the water it displaces.

Two points within the volume of the vessel are important when considering buoyancy and placements of ballast tanks. The center of mass Xcm is defined by the given equation below, where mi is the mass at any given point, and xi is the vector locating this point.

Xcm = (m1x1 + m2x2 + ...)/(m1 + m2 + ...)

This equation can be extended into an integral form, where the mass element mi is the density at the point multiplied by the differential volume at the point. The center of mass tells us where a the mass of the vessel would be located were it concentrated at a single point.

The center of buoyancy locates the center of the bouyant force. This is also the center of mass of a mass of water in the shape of the volume displaced by the vessel. Similarly as above, the center of mass of this mass of water can be calculated to give the center of buoyancy.

There are two very important constraints on the centers of mass and buoyancy which a submersible vessel must obey:

1. The center of buoyancy and the center of gravity of the vessel must lie on a common vertical line. This is true because were these to lie on different vertical lines, this would produce a torque which would rotate the vessel.

2. The center of gravity of the vessel must be below the center of buoyancy. It is common knowledge that dense objects sink in fluids with lower densities, and this fact can be used to infer the previous requirement. If the center of gravity of the vessel is below its center of buoyancy, this means that the majority of the weight rests below the center of buoyancy. This implies that the volume of the vessel below this point is denser than the same volume of displaced water, and the volume above this level is less dense than the same volume of displaced water. Thus the lower portion of the vessel will tend to sink while the upper portion will tend to rise, preventing the vessel from rolling.

Ballast
To provide buoyancy for a submersible vessel, ballast tanks are typically used. These are tanks which are made to hold air to increase the vessel's buoyancy, and can selectively take in or expel seawater. Water is taken in through slits in the bottom of the tanks, while air is simultaneously released through flaps in the rear area of the top of the tanks. To expel sea water, compressed air at high pressure is released into the tanks.

When the ballast tanks take in water, the seawater they contain is of the same density as the surrounding water, so they can be treated as part of the sea water. This effectively changes the shape of the vessel. Thus the center of buoyancy of a vessel changes when the amount of water in the ballast tanks is varied.

Subsequently, the ballast tanks should be placed in such a manner so as to obey the second rule (listed above) both while empty and while containing water. Thus the ballast tanks should be placed below the center of buoyancy of the vessel when the ballast tanks are empty (initial center of buoyancy). This is so that the volume below that point will descrease as water is taken in, and the center of buoyancy will rise.

However, placement of the ballast tanks within the vessel affect the center of mass. The tanks are of very low mass when empty, and it is preferable to place high density objects lower in the vessel. Therefore, the ballast tanks should not be at the immediate bottom of the vessel, but should still be below the initial center of buoyancy.

The vessel's center of mass can shift location based on movements of items or people within the pressure hull. The center of buoyancy can be shifted accordingly by means of a trim tank. This is like a small ballast tank with a different posiiton than the main tanks so as to change the location of the vessel's center of buoyancy.