# How do center of gravity varies in submarine between surface and submerged?

I'm interesting in static* roll stability of submarines. I'm always tempted to compare submerged submarine to blimps and other bigger airships. For airships, roll stability is assured by a pendulum effect, the heavier components being located low into the structure **. I have no idea of how the masses are spread inside a submarine, but I imagine they are located such that the center of gravity is as low as possible to improve stability.

When submerged, I imagine the center of gravity varies as ballasts can contain a significant quantity of water. Cutaways I found show ballast tank extend over a significant height of the submarine. Filling them may thus bring the center of gravity closer to the geometrical center of the submarine. This is only an assumption I fail to confirm.

How does the location of the center of gravity change when filling the ballast?

The consequences of this variation on roll stability is out of the scope of this question as the geometry of the immersed part of the hull also change.

* i.e. when the submarine is not moving
** cutaway found on this website give a good overview of where payload was located.

• Does changing the fluid outside the control volume change the C of G? Or the roll centre? – Solar Mike May 9 '20 at 14:44
• @SolarMike what is the control volume? – Manu H May 9 '20 at 15:17

From the picture that I found from this book, the answer seems to be yes.

In regards with stability of submarines, there are two main terms involved; center of gravity and center of buoyancy. Center of gravity is the point on the body where gravitational force is acting and, Center of buoyancy is center of gravity of the volume of water the submarine displaces. As quoted from this MIT page on Submersible Ballast.

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

To understand more about the different submersion methods of a submarine, check this link.

Basically, there are two ways to submerge a boat: dynamic diving and staticdiving. Many model submarines use the dynamic method while static diving is used by all military submarines. Dynamic diving boats are submarines that inherently float that is, they always have a positive buoyancy. This type of boat is made to dive by using the speed of the boat in combination with the dive planes to force the boat under water. This is very similar to the way airplanes fly. Static diving submarines dive by changing the buoyancy of the boat itself by letting water into ballast tanks. The buoyancy is thereby changed from positive to negative and the boats starts sinking. These boats do not require speed to dive hence this method is called static diving.

Modern military submarines dive use a combination of dynamic and static diving. The boat submerges by filling the main ballast tanks with water. After that, the buoyancy is accurately adjusted with the trim tanks. Once underwater, the depth of the boat is controlled with the hydroplanes.

And this link has great details on the different ballast tanks used in a submarine.

And to understand more about the stability of a submarine and the working of a ballast tank, check out this link.

• those diagrams are incorrect for a modern US nuclear submarine. The round hull of a submarine does not allow the center of buoyancy to more significantly laterally to produce a righting moment. This is in contrast to a square-hulled surface ship, in which a roll puts more buoyancy volume towards the roll and thus moves the center of buoyancy towards the roll producing a righting moment. US nuclear submarines have the center of gravity always below the center of buoyancy, by placing heavy equipment lower in the boat (batteries and diesel generator). – Tiger Guy May 15 '20 at 8:31
• i.imgur.com/rW9uZLD.png The center of buoyancy seems to be below of the center of gravity at some point during the transition from submerged to surfaced. maritime.org/doc/fleetsub/chap5.htm @TigerGuy – Manu G May 15 '20 at 17:04

Main Ballast Tanks on US nuclear submarines are basically tori (donuts) surrounding the pressure hull. If you could get your hands on actual drawings, I suppose you could calculate the small difference in center of buoyancy, but in practice there is no change. When submerged, main ballast tanks are completely full of water. The act of submerging is accomplished by venting the main ballast tanks of air until only water remains.

You are correct that the center of buoyancy on a submarine is above the center of gravity. (If it weren't, the sub would capsize until it were.) What this means is that a submarine is always self righting- there is no limit of positive stability. But it also means that the righting moment is low. Submarines roll terribly in almost any sea state, either on the surface or even towards the surface when submerged. Square-bottom ships are aided in righting moment by the center of buoyancy moving laterally towards a roll, which makes the ship more stable. Submarines do not have this. Seasickness is a real problem on or near the surface.