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Posted: **Sun Dec 06, 2009 4:19 pm**

I am trying to solve the volume of gasoline needed to keep a submarine stagnant in saltwater. I was given the weight of the sub in air, and then I solved for the weight in water. My question is this: to get the mass of the sub, (to plug in the equation p=m/V to find the volume of gasoline) would I divide the weight of the sub in air by 9.8, or the weight of the sub in water by 9.8. My mind is telling me to divide weight in air by 9.8, but it's confusing me for some reason.

Posted: **Sun Dec 06, 2009 4:33 pm**

I think you are right, as you multiply by g to get acceleration in air, you can divide to get rid of that, the way it would be the case in water.

Posted: **Sun Dec 06, 2009 4:49 pm**

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Posted: **Sun Dec 06, 2009 5:16 pm**

That's what I thought, but since the entire problem was under water, it was confusing me.

Posted: **Sun Dec 06, 2009 6:36 pm**

The volume of the submarine when it has the same weight as the water it displaces will then have neutral buoyancy. Find the weight of the seawater the sub displaces. Find the weight of the sub while empty. Add as much weight of gasoline as needed to make the sub and gas equal the weight of the water it displaces.

When the sub has the same average weight density of seawater, it will have neutral buoyancy under water.

Posted: **Sun Dec 06, 2009 8:06 pm**

So are we going to take variable water density due to thermoclines and compression of the sub hull into account?

Posted: **Sun Dec 06, 2009 8:26 pm**

I just finished reading the book Das Boot not long ago and it does not sound fun balancing a submarine in water during WW2. There's so much to take in to account, apparently the amount of salt in the water changes with temperature and the places you go or something like that anyway which affects buoyancy.

Posted: **Sun Dec 06, 2009 9:11 pm**

MrCrowley wrote:I just finished reading the book Das Boot not long ago and it does not sound fun balancing a submarine in water during WW2. There's so much to take in to account, apparently the amount of salt in the water changes with temperature and the places you go or something like that anyway which affects buoyancy.

Much like maintaining freeway speed in wind and with hills, the throttle needs constant adjustment.

Balast tanks are adjusted as needed to maintain the required mass. Small amounts of miss alignment can be ignored as with forward momentum, the sub with sails perform like an airplane underwater. It can be steered. Only at rest is the critical balance important.

Posted: **Sun Dec 06, 2009 9:30 pm**

Here's the bit from the book that talks about it:

At the desired depth, the weight of the boat must exactly equal that of the water it's displacing, so that the boat hovers perfectly, ready to react precisely to the smallest push from the propellers and be easily maneuvered up or down, right or left, by the hydro¬planes or the rudder. It mustn't have any tendency to sink or to rise. Unfortunately the boat's weight changes every day, through the consumption of provisions— water and fuel, for example. The crazy thing, however, is that not even the weight of the water displaced by the boat remains constant. So everything is always changing.

The thing that gives us the most trouble is the chang¬ing specific gravity of water. If we were diving in fresh water everything would be simpler. Then all we'd have to do every day would be to add the same Weight of water to the trim cells as we used up in food, oil, and water, and that would be that. But in salt water it's very tricky. There's no getting away from it. In this pond, water is not just water. Our buoyancy changes from day to day—even from hour to hour.

The specific gravity of salt water is influenced by every imaginable factor. Depth, temperature, the time of year, the various currents. Even the sea life—plank¬ton, for example—affects it appreciably. A little more plankton in the water and we have to pump. And it depends on the sun as well. The sun causes evaporation, which increases salt content. Greater salt content in the water and the specific gravity goes up.

A difference in the specific gravity of the water—well, let's take a really minimal one, of one one-thousandth— that means that the weight of the boat, to maintain its balance, must also be changed by one one-thousandth. Now assume that the boat weighs eight hundred and eighty tons. So: a change of one one-thousandth gives us a bit over sixteen hundred pounds. That much of a difference would make for a serious mistake in calculating the content of the trim cells. To keep the boat adequately poised, we have to weight it out with the help of the trim tanks to within eleven pounds. I say adequately because in practice it's impossible to weigh out the boat so accurately that it remains poised without the help of propellers and hydroplanes. Even a pint—as a matter of fact, even a thimbleful—too much of water in the tanks would make it rise.

Sorry it doesn't have much to do with the question at hand, but since it's been answered and this is somewhat related and quite interesting I thought i'd share it.

Posted: **Mon Dec 07, 2009 10:37 am**

Interesting but partly wrong. Although the difference in density of fresh water varies less, it still does. For example water can have high contents of CaCO<sub>3</sub> and thus have a different dense when it meets a tributary and water with a low concentration of CaCO<sub>3</sub> comes in but with a higher temperature as it comes from a lake, this would change density again.

It would also be important to not that it takes a whole lot more energy to warm up sea water for it to have an effect while fresh water quickly cools, or warms, due to the fact there is less water at a time to be heated or cooled...

All in all it seems very Interesting how they calculated and maintained an equilibrium at all times.

Posted: **Mon Dec 07, 2009 3:16 pm**

I would think that balancing a sub is, and always has been, a classic feedback problem. Submariners don't calculate what they need to do, they just do it until they get the desired behavior. (OK, they might do a rough calculation to determine about how much they need to blow but that's just to tell'm how fast they can change things without going way out of equilibrium) Feedback is often much more usable than is calculation, especially when speed isn't a big issue.

Sub's are indeed much like aircraft. Submariners have a saying, "you drive your way out of trouble". Full speed and maximum up angle and most subs will rise even without changing their buoyancy.

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