Displacement of Boats
Date: Spring 2013
In "twenty thousand leagues under the sea", Captain Nemo says that he makes ten percent of his sub stick out of the water by having the weight be ninety percent of the displacement. Is Jules Verne correct in saying this? If so, why does more than ten percent of an aircraft carrier stick out above the surface when its displacement is more than ninety percent of its weight?
He may have said it in an odd way, but Jules Vern is correct. Any body
floats in water by displacing its own weight of water, whether it is a
submarine or an aircraft carrier. It makes no difference that an aircraft
carrier LOOKS like it is sticking way out of the water. Like any other
boat, the weight of water displaced by its hull exactly equals the total
weight of the aircraft carrier. Remember that inside the aircraft carrier,
is mostly air, which weighs essentially nothing.
Thank you for your question.
You said that Captain Nemo makes ten percent of his sub stick out of the water by having the weight be ninety percent of the displacement. This is correct.
"Why does more than ten percent of an aircraft carrier stick out above the surface when its displacement is more than ninety percent of its weight?" This sounds misleading (but it is not wrong). Its displacement must exceed its full weight and in fact is much more than its full weight, so it certainly exceeds 90 percent of its weight, which is a smaller number. It is similar to saying that the aircraft carrier displacement is more than my weight which is certainly true.
I believe that the aircraft carrier statement was probably made in error because it is misleading but not completely wrong. I can restate it as:
"Why does more than ten percent of an aircraft carrier stick out above the surface when its weight is less than 111 percent of its displacement? (1/90% = 111%) If the weight is 110% of its displacement then it will sink. But if it weighs only 40 percent of its displacement (this seems more likely) then 60 percent will float above the water. In that case its displacement will be more than (100%/40% = 250%) of its weight which is more than 90% of its weight.
We are saying that the aircraft carrier weighs less relative to its displacement. A submarine in "neutral buoyancy" has its weight equal its displacement. The less the vessel weighs, the more of it will protrude above the water. For floatation, the displacement must be more than the weight. I think that your aircraft carrier statement was written incorrectly. Does this make sense now?
An object experiences a buoyant force equal to the weight of the volume of water displaced by the object. While this sounds a bit convoluted, what it means is the SHAPE of the object plays a very important part in whether or not the object floats or sinks. A piece of aluminum foil will float if it is flat with small walls, but the same piece of foil crumpled up sinks immediately. Captain Nemo has a very compact submarine so it tends to sink. You cannot tell how much water an aircraft carrier displaces by just observing what is floating on the surface of the water. It may be quite ?fat? beneath the surface of the water. Submarines float or sink depending upon how much ballast water the submarine takes on in its ballast tanks. The water is pumped in or pumped out depending upon the amount of water taken on or blown out.
Thanks for the question. Yes, Captain Nemo is correct and his statement can be verified by a quick calculation. The aircraft carrier has a hull and most of the volume of its superstructure is actually air and not steel. So judging by looks can be deceiving here.
I hope this helps. Please let me know if you have more questions.
Jules Verne is correct.
When Archemedes got into a bathtub that was filled to the rim, a volume (cubic feet) of water spilled over the side of the tub. Then Archemedes measured the weight of that water (in pounds) that spilled. So the principle is that a body that weighs less than the volume of water it displaces will float.
So, if a ship weighs 25 tons, but the water it displaced weighs 100 tons, the ship will float (exhibit positive buoyancy).
If a 25 ton submarine displaces 25 tons of water, it will remain in neutral buoyancy and neither rise nor fall in the water.
If a 25 ton ship only displaces 12.5 tons of water, it will sink (negative buoyancy).
The waterline of a ship is the point where the weight of the volume of that part of the ship that is in the water (in pounds) equals the weight of the water it displaces (in pounds), and in the case of the aircraft carrier, the weight of the part of the ship you see on top of the water represents the excess of the weight of the water the part of the ship that is underwater displaces.
Hope this helps. There are big and lots of career opportunities in Marine Engineering.
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Update: November 2011