I just posted something about cargo ships and shipping. Last night I watched a special about Titanic. Leading to my pondering how much I don’t understand about why ships float or sink.

Cargo ships and aircraft carriers obviously weigh gazillions of tons. So why don’t they sink? Is it somehow the case that even though they weigh so much they still somehow manage to weigh less than the water they displace weighs, allowing them to float?

Can someone give me a very simple explanation of how this works?

Water’s fairly heavy stuff. A gallon weighs about eight pounds.

The other trick in boats is that the water is displaced not only by the volume of the structural material of the boat’s frame (heavy metal) but by the interior volume of the boat that is below the waterline (imagining the very simplest rowboat), which is mostly filled with very light air, or on a carrier, air and somewhat heavier people, etc.

Nitpick: assuming it’s just floating there, it’s displacing water equal to its weight - it’s capable of displacing more than its weight of water, which is why it can float with some freeboard (hull above the waterline)

Right, and one way to imagine this is putting a 25 pound concrete block in your rowboat. The boat will need to “find” an additional 25 pounds of water to displace and the way it does this is by the hull pushing down a bit further in the water to push more water aside till the force again equilibrates. Take 50 pounds of fishing gear off the boat and it stops displacing an incremental 50 pounds of water, so the hull moves up in the water till things, again, equilibrate.

Correct, if 1 gazillion is approximately equal to 100,000.

If we’re talking about an aircraft carrier of 100,000 tons, it needs to displace around 88,300 cubic meters of sea water. That’s the volume of a cube 44.5m on a side.

P.S. To get a sense of how buoyancy works, you can partially fill a sink with water, and float a glass in it. If you measure how far the water is from the top of the sink, and then put some coins into the glass, you’ll see the water level in the sink rise. The amount of rise times the area of the sink is the volume of water that is being displaced by the weight of the coins; if the sink was originally full (after you put the glass in, but before you added the coins), the weight of the water that spilled over the edge of the sink would equal the weight of the coins.

Here is how it works: Imagine two stacked cubes of water. The lower cube is holding up the upper cube. To keep the upper cube from falling or rising, the reaction force at the top of the lower cube must equal the weight of the upper cube. If you stack more cubes, the force on the bottom cube is the weight of all the cubes above it. Fluids are squishy, so instead of force, we talk about pressure, which is the force divided by the area of the side bearing the weight. If they are one-inch cubes, the pressure is stated in pounds per square inch. In the sea, we have more cubes stacked alongside each other. Each one experiences the same pressure as others at the same depth, because each one is holding up the same height of water above it. In general terms, pressure increases with depth.

Now if you put a box in the water, the water at the bottom of the box is pressed in by the adjacent water at the pressure appropriate to that depth, and, because water is incompressible, the water beneath the box pushes up on the box with that same pressure. If the force (pressure times area) on the bottom of the box is greater than the weight of the box, it pushes the box up until the forces just balance. But wait! At that depth, the volume of water displaced by the box is the same volume as if the box were not there! The result is the principle stated in the previous posts: A floating body displaces a volume of fluid equal in weight to the weight of the floating body. Cool!

As naval architect, I get this question often. It can often come up as the weirdness of steel vessels floating. I’ve actually switched to explaining it thru blimps. There is a light, but heavier than air skin. And we have heavier than water stuff, air, inside. I think the most common mental disconnect is that, unlike in zeppelins, the air can flow out. But it can only be replaced by air. If you have sufficient freeboard. And you always should.

A more mathematical way to look at it is density. To be exact, the density of the air and water displaced by the ship must be equal to the density of the ship. But the density of air is only one thousandth of the density of water, so you can ignore it. The density of a steel structure is only 10-15% of the density of water, so it is easy to make steel ships work.

Relative density is a convenient way to visualise it - and it works - an object whose overall density is one tenth that of water, will float with one tenth of its volume submerged.

it’s really only another way of saying that one tenth of the volume of the object is equivalent to a volume of water that equals the entire weight of the object - and we’re back to displacement. Some folks object quite vehemently to discussions that express this in any other terms than displacement and upthrust, but it’s the same thing, in practice.

Yes, they do, and I should have left that out. Having said that, I noticed that the other posts merely invoked Archimedes principle, without attempting to communicate any understanding. Don’t know if I helped.

Roughly, salt water weighs 64 lbs/cu. ft., as opposed to fresh water, which is about 62.2 lbs/cu. ft.
So a gallon of salt water weighs 8.556 lbs, a gallon of fresh water weighs 8.314 lbs.

Imagine a ‘box’ that is 12" x 12" x 12". How many gallons does it look like it would hold?