Many kinds of wood float on water, ice floats on water, and cooking oil floats on top of water. A solid lump of clay or iron will sink in water. It is tempting to say that heavy things sink and light things float. But how big or how heavy something is does not decide whether it floats; yet clay that sinks as a lump floats once it is molded into the shape of a boat. A big ship floats thanks to all the air inside it. So what does decide? People worked on that question long ago, and we can ask how we know the answer.
Archimedes was an ancient Greek mathematician and inventor, and two stories are told about him and a question of floating. About 2,000 years ago the Roman architect Vitruvius told a story about King Hiero II of Syracuse, who had suspected that silver was mixed into a golden crown. In the story, Archimedes caught the goldsmith cheating. In a popular story, Archimedes made his buoyancy discovery in a bath and then ran through the streets shouting "Eureka!" That story was written down in the first century BC, long after he lived, and some scholars doubt the method it describes. It should be treated as a popular story and not as settled fact.
What Archimedes left in writing is clearer. He wrote On Floating Bodies, the first known work on hydrostatics. It is about how solids float in a fluid. He is recognized as the field's founder. He lived in Syracuse, Sicily, from about 287 to 212 BCE. Anything in water is pushed upward, and his principle gives that push a size. Put simply, the upward buoyant force on an object is as big as the weight of the fluid that the object pushes aside. If that force is greater than an object's weight it rises and floats; if it is less, the object sinks; if the two are equal, it hangs in place.
The modern explanation begins with pressure. Buoyancy means the tendency of an object to float or rise in a fluid. Either a liquid or a gas can be the fluid. It comes from pressure growing with depth: a submerged object is pushed up on its bottom harder than it is pushed down on its top, and the gap is the buoyant force. A floating object has a specific gravity equal to the fraction of it that lies under the surface, and an object with specific gravity exactly 1 hangs in the fluid, neither sinking nor floating. Even a thing that sinks gets pushed up by the water, and it seems to weigh less when it is under water.
The same idea works as a test of density. A coin's density can be found by weighing the coin in air and then again under water. The weight that seems to disappear is the weight of the displaced water, and that tells the coin's volume. Putting any object under water pushes aside water with the same volume as the object, which means water offers a way to measure the volume of a lumpy object. At a huge scale, a ship's hull must be big enough underneath that the water it displaces weighs as much as the whole loaded ship, so that it floats no deeper than its design waterline. Even heavy material can float as a hollow boat full of air, instead of as a solid lump.
Marking a safe waterline took time. On the side of a ship, a painted line called the Plimsoll line shows the lowest the ship may safely sit in the water. One early try at ship safety marks came in 1835 from Lloyd's Register, a classification society, though it applied only to ships that Lloyd's Register itself classed. Samuel Plimsoll, a British MP, started investigating ship safety in 1870. A law in 1876 made load lines compulsory. Worldwide, the Plimsoll mark is recognised: it is a circle crossed through its center by a horizontal line. The water may reach different parts of the line depending on its temperature, saltiness, season and place, because salty water is denser than fresh water.
Ice is a strange case among solids. Ice floats on water because it is less dense than liquid water, and ice is about 90 percent as dense as water, though this can vary because ice can contain air. Measured against liquid water, ice is about 9 percent less dense, and so most of a cube of it sits under the water line. Inside ice the molecules of water are spread out with a lot of space between them. One odd relative breaks the pattern: "heavy ice", which is made from heavy water (D2O), is roughly 10.6 percent denser than normal water and sinks in ordinary water.
Water is not the only place where floating happens. Most fish hang in the water with the help of a gas-filled swim bladder, but sharks have no swim bladder, and their large oily liver, lighter cartilage skeleton and the glider-like shape of their body and fins help them stay up. Buoyancy works in gases too. A helium balloon is held up by air in the way a floating cork is held up by water. In a volcano lava rises, and mountain ranges float on the denser crust and mantle under them. Back at the water's edge, two rules go with every swim: a grown-up must be watching, and you ask before you go in.
Words to know
- hydrostatics: fluid science
- displaces: pushes aside
- waterline: design depth
- scholars: expert thinkers
- recognised: known as
