A question people sometimes ask is how a big steel boat or ship can float on water. At first glance it’s almost as mysterious as how jumbo jets can fly.
The answer I always give is that it’s because of gravity. Boats float because of gravity. This has caused reactions from puzzlement to arguments about buoyancy and stories about Archimedes running about naked shouting Eureka.
For those not familiar with the story, Archimedes was having a nice deep bath when he noticed that the water rose as he submerged himself. His naked excitement was because he realised that the volume of the displaced water could be measured accurately, and would be exactly the same as the volume of the body that displaced it. Calculating the volume of a cube or a sphere is not too difficult but odd shapes like bodies are more difficult. You might wonder why this matters but, at the very least, it could stop you overfilling your bath.
The text book answer to floating objects refers to ‘buoyant force’, but why would water exert an upwards force, particularly when we see so many things sink to the bottom of it? The answer is, of course, gravity.
At first, a downwards force producing lift might seem counterintuitive. Here is a sketch of Jemima and me on a see saw:
If Jemima and I were the exactly the same weight, the see saw would remain balanced but, as is easy to imagine, she will go up and I will go down. How did she get up there?
Earth’s atmosphere is a relatively light gas but it exerts a pressure of about 14 pounds per square inch. That is like a stone of weight (6.5kg) pressing on each square inch of our skin. The air gets its pressure from all the air on top of it which crushes it under the force of gravity.
Water is much heavier than air, and the pressure increases with depth. The water towards the bottom has the force of the water on top of it. The force creating this pressure is, of course, gravity.
Pressure exerts itself in all directions. The bottom of a dam is always thicker than the top to withstand the increasing pressure towards the bottom.
Warm air rises, against the force of gravity, not because of some mystical buoyant force, but because the cooler, heavier air falls to replace it. In any fluid (air is fluid), there is a tendency for the light stuff to end up on top – but it was forced (or pushed) up there up by the heavier stuff falling to replace it. A bit like Jemima on the see saw.
But surely a steel boat is heavier than the water? It would be if it were solid steel. A cubic metre of steel weighs about eight tonnes; the same volume of water is only one tonne. I calculated the volume of Crystal Clear to be about 130 cubic metres. The same volume of water would then be 130 tonnes.
Ignoring the engine, water tank, fuel tank and furniture etc., Crystal Clear works out at about 16 tonnes based on 10mm thick steel. If she were made from 12mm steel she would weigh about 20 tonnes. It’s fair to say she weighs less than 30 tonnes.
If we submerged the boat entirely, 130 tonnes of water would be displaced. But we would need a 100 tonnes of extra downwards force to get her under the water (if we sealed all the windows and doors to prevent water getting in). Put simply, we cannot lift 130 tonnes of water with only 30 tonnes of boat. If I weighed four times less than Jemima, she would never enjoy the dizzy heights of see sawing. I would though.
So the boat floats. The volume of water, being heavier, exerts more pressure under gravity than the boat. That pressure builds up below her; she is pushed up because the water is more dense than the air filled vessel and displaces the boat upwards.
Crystal Clear is about 8ft tall. About 2ft (one quarter) is below the water’s surface. As she weighs about a quarter of the water she would displace if completely sunk, that makes some sense.
If you have a helium balloon, before emptying its contents into your lungs to do silly voices, take your balloon for a car ride. If you brake suddenly, the occupants and loose stuff will lurch forwards. The balloon, however, will go backwards in the opposite direction…