Archimede's principle states that the weight of a floating object is equal to the weight of the water displaced by the object. For an object to be in equilibrium, the upward force of buoyancy must be equal the downward force of gravity (weight). Also, the center of gravity and the center of the underwater volume (center of buoyancy) must be vertically aligned.
The application of Archimede's principle to a surface vessel is straight-forward. The vessel sinks until the weight of water equal to the volume below the water is equal to the weight of the ship and the vessel will lean one way or another until the center of weight is above the center of buoyancy.
A simple experiment will illustrate this point. Obtain a lightweight, rigid container (preferably rectangular) and a much smaller object that weighs considerably more than the container. Weigh the container and the weight separately. Place the container in water with the open side up. It should float level and have a significant amount of freeboard (the distance from the water to the lip of the container). The volume under the water will be equal to the weight of the container divided by the density of the water (62.2 pounds per cubic foot for fresh water). The waterplane area will be equal to the length times the width of the container (assuming it is rectangular) and the draft (the distance from the top of the water to the bottom of the container) will be equal to the volume divided by the waterplane area.
Now add the weight near the center of the container. The draft will increase until the underwater volume times the density of water is equal to the weight of the container plus the added weight.
Now move the weight toward one edge of the container. Note that the shape of the underwater volume changes into order to move the center of buoyancy under the center of gravity.
All this changes when the container is submerged.
Water is virtually incompressible. As a result, the volume of a submerged body such as a submarine is constant (neglecting the compression of the hull due to pressure). Consequently, the buoyant force is a constant.
"Positive buoyancy" occurs when the weight of the submarine is less than the buoyant force and causes the submarine to rise to the surface. "Negative buoyancy" occurs when the weight of the submarine is greater than the buoyant force and causes the submarine to sink. "Neutral buoyancy" refers to the condition where the weight of the submarine exactly matches the buoyant force, so that it neither floats to the surface, nor sinks to the bottom. True "neutral buoyancy" is impossible to obtain. Consequently, a submarine at rest will rise to the surface or sink to the bottom.
It was a common misconception in the late 1800's, that a submarine could control its depth by adding or removing water from the ballast tanks. Typically, the submarine would come to a stop on the surface, close all hatches and open the ballast tank valves. As the tanks filled with water, the submarine would slowly disappear from sight. Once submerged, the valves would be closed, but the submarine was already negatively buoyant and momentum was taking it deeper. As the hull compressed, the buoyant force decreased and the submarine starting sinking faster. Water would be pumped from the tanks, until the submarine gained sufficient buoyancy to arrest it's descent. By this time, the submarine would be positively buoyant and it would begin to rise. As the submarine rose, the hull would expand, increasing the positive buoyancy and increasing the rate of ascent until the valves were opened and sufficient water was added to stop the ascent and start the cycle all over again. The only way to control depth was to keep the submarine moving and use "horizontal rudders" or dive planes.
Another important difference between surface ships and submarines is that since the volume is constant, the location of the center of buoyancy is fixed. Consequently, a small shift in the center of gravity will cause a large rotation of the submarine in order to align the center of buoyancy with the center of gravity.
It was the inability of early submarine inventors to control the center of gravity that lead to the myth that the only safe submarine was a level diving submarine. Submarines such as Reverend Garrett's Resurgam and those by Nordenfelt had a large amount of water in partially empty boilers and tanks. If the bow of one of these submarines were depressed, the water in the boilers would rush forward, shifting the center of gravity forward and depressing the bow still further. If the operator over corrected and the bow came up, the water would rush aft and the bow would rise further. Such wild oscillations often caused early submarines to strike the bottom or broach the surface.
John Holland understood the danger inherent of an uncontrolled center of gravity and insisted that the tanks in his submarines be either completely full or completely empty. In 1898, Frank Cable convinced John Holland that he could bend the rules a little and use water instead of pig iron as variable ballast as long as the tanks were small. During the overhaul in early 1899, two torpedo compensating tanks and two aft trim tanks were added to the Holland VI. As a result, the Holland VI became the first submarine to incorporate separate main ballast tanks, auxiliary compensating tanks and trim tanks.
The main ballast tanks of the Holland VI were located inside the pressure hull, outboard and below the batteries. When the tanks were completely empty, the submarine had sufficient freeboard (the distance between the deck and the surface of the water) to operate safely on the surface (in sheltered water). When the tanks were completely full, the freeboard was reduced to zero. This condition (the deck flush with the surface of the water) is known as “deck awash”. In the deck awash condition, about 18 inches of the Holland’s turret was visible above the water and the submarine had approximately 100 pounds positive buoyancy. This positive buoyancy was easily overcome by the action of the diving planes, yet was sufficient to cause the submarine to rise to the surface if propulsion power was lost.
Prior to 1860, submarines filled their ballast tanks by opening a valve and emptied their ballast tanks using pumps. In 1863, Captain Bourgeois and naval constructor Brun built Le Plongeur. Le Plongeur was the first submarine to use compressed air to force the water out of the ballast tanks. This worked so well that every submarine built since 1898 has relied on compressed air to “blow” the ballast tanks.
The main ballast tanks of the U.S.S. Holland provided about 10% reserve buoyancy. As the demand for better surface performance grew, the reserve buoyancy of later submarines increased to better than 30% and the main ballast tanks were relocated outside of the pressure hull. As the main ballast tanks got larger, a more efficient means of filling the tanks was required in order to submerge quickly. Large valves called "vent valves" were installed at the highest point in each tank, and large holes called "flood holes" were cut in the bottom of each tank. Using this system, opening the vent valves allows the air to escape quickly, and the large holes allow the water to rush in. Once the tanks are full of water, the vent valves are closed. With the vent valves closed, releasing a blast of high pressure air into the tank will quickly force the water back out through the flood holes in the bottom of the tanks.
During World War II, negative tanks were added in the forward portion of the submarine. When the main ballast tanks and the negative tank were flooded, the submarine was negatively bouyant and would assume a down angle. This helped get a submarine underwater in a hurry (very important when under attack). Once submerged, the negative tank would be emptied, restoring the submarine to neutral buoyancy and level trim.
With the advent of nuclear power, surface performance became less important and the main ballast tanks were reduced in size until they provided about 10% reserve buoyancy. The time required to submerged is no longer critical, so the negative tank has been abandoned. Nonetheless, vent valves and flood holes are still used to flood the ballast tanks quickly.
The weight of a submarine is rarely constant. As food, fuel and weapons are used, the submarine gets lighter and would float to the surface unless additional weight was added. The easiest way to do this is to take on additional water. Small auxiliary tanks are provided for this purpose. By keeping these tanks small and short, movement of the water in the auxiliary tanks has little effect of the center of gravity.
The density of seawater is not constant either. The cold water of the North Atlantic is denser than the warm water of the tropics and the fresh water flowing into the sea from rivers affects the density of the water near the coast. Auxiliary tanks allow the submarine to adjust its weight to compensate for changes in the density of water in addition to variable loads.
All successful submarines also include a forward trim tank and an aft trim tank. These tanks are used to move water (hence the center of gravity) forward or aft as necessary to level the submarine.
When the water in the auxiliary and trim tanks has been adjusted such that flooding the main ballast tanks will result in neutral buoyancy and a level keel, the submarine is said to be in “diving trim.”
ÓCopyright 1999,2000,2001,2002 Gary McCue