Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne Submarine Density
Name: Gary M.
Status: educator
Age: 50s
Location: N/A 
Country: N/A
Date: 10/2/2004

Several of us got into a heated discussion about how and why a submarine submerges and surfaces. We all agree that it is doing so because the density of the submarine is being changed.However, some argue that it is because the water allowed into the ballast tanks to make the sub sink increases the sub's mass and therefore the density increases and the sub sinks. Others argue that allowing water into the ballast tanks decrease the sub's volume and therefore the volume of the water being displaced by the submarine. As the volume decreases, the density increases and the sub sinks.

In other words, the first argument is that the mass of the sub increases while the volume - and therefore the total volume of displaced water - remains constant. Density increases because mass increases and the sub submerges with the opposite being true to surface again.

The second argument is that the volume of the sub - and therefore the total volume of displaced water - decreases while the mass stays the same. Density increases because volume decreases and the sub submerges with the opposite being true to surface again.

So - what is the correct answer?

The volume of the submarine does not change. It does not change overall shape or dimensions as the ballast tanks are emptied or filled. The ballast tanks are part of the volume of the submarine whether they contain water or air. An analogy would be a balloon: Blow up the balloon to a diameter of 10 cm. First, fill the balloon with helium (it will rise in air). Second, fill the balloon with air (it will bounce around). Third, fill the balloon with water (it will fall to the floor immediately). In all cases the volume of the balloon is the same:

Volume = 4/3*pi* R^3 but the weight changes.

Vince Calder

Gary -

Not being a marine engineer and never having been on a submarine, I am out of my field, but have a few thoughts for you. My understanding is that the ballast tanks are filled as the air from those tanks is compressed and stored for later when the tank might need to be "blown." The ballast tanks are filled simply to replace the air that is compressed (thereby increasing the overall density of the submarine. The water is simply filling a void. The density is really adjusted by the compression of the air.

However dealing with your question of why the ship submerges, it is my understanding that the ship only achieves neutral buoyancy. By doing this, the ship can be maneuvered up and down by the bow control surfaces in the same way an airplane uses its elevator.

In an emergency, the ballast tanks are "blown" increasing the volume of the compressed air and causing the average density of the submarine to decrease and the ship to become buoyant. This technique is only used when the ship needs to reach the surface faster than the bow controls would allow.

Try that in your conversation and see if it floats. (pun intended)

Larry Krengel

Both ways of looking at the problem are correct. When you speak of density, you also need to specify exactly what the object is that you are calculating the density of. In the former interpretation, you are calculating the density of the overall submarine. When the density exceeds that of the local density of water, it will sink. In the latter interpretation, you are calculating the density of the submarine excluding the ballast tanks. Again, when the density exceeds that of the local density of water, it will sink.

Bob Erck


Your probably going to hate this answer, but both groups are right, depending on how you define mass and volume and which one you consider constant.

If the volume of the submarine is considered to be the outer hull dimensions, then this displacement never changes (ignoring deep dives). Bringing water into the ballast tanks increases the boats mass verses the volume displaced.

If we consider the mass of the boat to be all of the metal, equipment and sailors, then the mass will not appreciably change. The minimum volume would be those areas that never get wet. When the ballast tanks are empty, the boat has a greater volume then when full vs. its mass.

The same can be said for a sinking ship.

Anchors away!

Bob Hartwell

The submarine's mass changes. A submarine's volume is fixed by its hull, which is rigid.

You could make the argument that the water-filled fraction of the ballast tank becomes part of the ocean -- and not part of the sub -- when the valve connecting the tank to the ocean is open, and *after* all the water that is going to come in has come in. But once you close the valve, the tank would again become part of the sub, and now you have to go back to the mass-change viewpoint. Might as well just stick with the mass-change viewpoint, since it always works.

Tim Mooney


I think you could argue either way, but to me, defining the volume of a submarine to include the ballast tanks when they are filled with air, but not when they are filled with water seems rather artificial.

I would certainly prefer to say that replacing the air in the ballast tanks by water increases the mass of the submarine while keeping the volume constant, which then increases the average density of the submarine, and so causes the submarine to sink.

Best, Dick Plano...

I do not think it is worth arguing about. Both ways of thinking agree with both the structure and the behavior, and I do not think our logic is set up enough to clearly distinguish between the two. This "compare the density" concept is a rule of thumb, not a law of physics. A higher law of physics here is: which nearby (in space and time) submarine depth minimizes the total energy of the system? Or: that a unitized body will sink if the sum of all forces on it is downwards. You know that the inner hull of the sub, all its contents, and the outer hull which enclosed the ballast tanks, are part of your solid object. The air and/or water in the ballast tanks may be included or not, your free choice. The set of components of the calculation differs depending on your choice, but the net balance of forces does not.

My bias, since the water in the tanks usually travels up and down with the sub and the air always must travel with the sub, is to consider the contents of the tanks as part of the sub. But when flooded, the tanks could easily have openings at top and bottom, and then one could argue that the water part of the contents is not stuck with the sub.

Are you mutually willing to define a measurement of the inertia of the sub to velocity changes? Such derivatives sometimes determine your answer in tricky cases. Perhaps you would accept that as an arbitrator of whether the water is part of the sub. Irrelevant, anyway...

Happy Debating-

Jim Swenson

Click here to return to the Engineering Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (, or at Argonne's Educational Programs

Educational Programs
Building 360
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: June 2012
Weclome To Newton

Argonne National Laboratory