Answer Geek: Why Do Boats Float?

-- Q U E S T I O N: I live on the Great Lakes and it has always astonished me how these gigantic freighters can stay afloat. Why is it that huge seafaring ships can stay afloat even though they may weigh hundreds of tons, but I can’t stay afloat in the bathtub?

— Shane

A N S W E R: Why is it that you sink while a gigantic seafaring ship made mostly of metal and carrying tons of heavy freight floats? Quite forward of you, Shane. Compared to the ship, you are very dense.

But, please, don’t take offense. We’re not talking about your mental acuity here. Density, in this case, is a function of weight divided by volume.

Every substance has density, including water. If the density of a given object is greater than the density of the water around it, it sinks. If it is less, it floats. Simple as that. That supertanker may be made of material that is denser than water, and it may outweigh you by a few thousand tons, but much of the area enclosed by the ship’s metal hull is just air. And the average density of the total combination of metal, air, and cargo is less than the density of the water it floats in.

‘Eureka’

There is a law of physics that covers this. I’ll give you a hint. It has something to do with a bathtub. And a Greek mathematician.

If you didn’t come up with the answer, your high school science teacher is very, very disappointed. Remember Archimedes’ Principle? According to the story, Archimedes lowered himself into the bathtub one day, watched the water spill over the edge, and realized that the amount of water he displaced was related to how much he weighed and how much space he occupied. Rumor has it he jumped out of the tub and ran out into the street naked shouting “eureka,” which is Greek for “I found it.”

Once all the excitement died down, Archimedes sat down and came up with a basic definition for why things float: “An object immersed in a fluid is buoyed up by a force equal to the weight of the fluid it displaces.” That force is sometimes called upthrust. What that means out on the high seas is that a boat that weighs, for example, 1,000 tons will sink until it displaces 1,000 tons of water. At that point, the upthrust from the water will equal the downward pressure of the ship. If it has been designed correctly, that will happen before the vessel is completely submerged.

One of the Greatest Answer Geeks EverWhile we’re on the subject, I’d like to use this opportunity to take a moment to honor Archimedes, who was one of the great Answer Geeks of all time.

Born in Sicily in 287 BC, this great mathematician not only came up with Archimedes’ Law, he also defined the principle of the lever, and invented the compound pulley, the hydraulic screw, and the catapult. His studies of the area and volume of shapes and solid figures anticipated integral calculus by a few centuries. He came up with a way to determine the density of irregular shapes, and he proved that the volume of a sphere is two-thirds the volume of a cylinder that circumscribes the sphere.

He also pulled a couple of crazy stunts in his day. There was the infamous naked bathtub episode, of course. Then there was his threat to move the earth to demonstrate that the laws of pulleys and levers that he had discovered really did work. He is also credited with helping to defend his hometown of Syracuse against the Romans during the Second Punic War by designing some very innovative war machines, including a catapult for hurling boulders over the city’s walls, and special lenses used to focus the sun’s light on the sails of Roman ships, thus setting them afire.

But there was also a fateful day during the siege. As the famous Romanwriter Plutarch tells it, a Roman soldier came upon Archimedes while he was drawing mathematical diagrams in the sand. Apparently Archimedes was so caught up in his work that he ordered the soldier not to disturb him. Enraged, the soldier killed him on the spot.

Being an Answer Geek, especially in war time, can be a hazardous occupation.

Todd Campbell is a writer and Internet consultant living in Seattle. The Answer Geek appears weekly, usually on Thursdays.