Archimedes' Principle of Buoyancy

How do Ships Float?

How could ships weighing thousands of pounds float on water when a small coin sinks right to the bottom? The key was a discovery by a Greek mathematician and inventor named Archimedes.

Archimedes' Solves a Problem

The Greek Mathematician and inventor Archimedes lived during the 3rd century BC. According to history he was in the bath one day when he discovered the principle of buoyancy which is the reason why huge Greek ships weighing thousands of pounds could float on water. He noticed that as he lowered himself into the bath, the water displaced by his body overflowed the sides and he realised that there was a relationship between his weight and the volume of water displaced. It is said that he ran naked into the street yelling "heurEka" which is where we get our word  "eureka!" (I found it), Greek heurEka I have found, from heuriskein to find.

Archimedes was not thinking about ships at the time, he was on a mission to solve a question that was asked of him by King Hieron II of Syracuse, the home of Archimedes which was a Greek city at the time. The question that the king had asked was about his crown. Was it pure gold or partly silver? Archimedes reasoned that if the crown had any silver in it, it would take up more space than a pure gold crown of the same weight because silver is not as dense as gold. He compared the crown's volume (measured by the amount of water displaced) with the volume of equal weights of gold and then silver, he found the answer. He had to inform his king that the crown was not pure gold.

The Buoyancy Principle
Archimedes continued to do more experiments and came up with a buoyancy principle, that a ship will float when the weight of the water it displaces equals the weight of the ship and anything will float if it is shaped to displace its own weight of water before it reaches the point where it will submerge.

This is kind of a technical way of looking at it. A ship that is launched sinks into the sea until the weight of the water it displaces is equal to its own weight. As the ship is loaded, it sinks deeper, displacing more water, and so the magnitude of the buoyant force continuously matches the weight of the ship and its cargo.

The Metacenter
Archimedes figured out that the metacenter had to be determined which is a point where an imaginary vertical line (through the center of buoyancy) intersects another imaginary vertical line (through a new centre of buoyancy) created after the ship is displaced, or tilted, in the water.

The center of buoyancy in a floating ship is the point in which all the body parts exactly balance each other and make each other float. In other words, the metacenter remains directly above the center of buoyancy regardless of the tilt of the floating ship. When a ship tilts, one side displaces more water than the other side, and the center of buoyancy moves and is no longer directly under the center of gravity; but regardless of the amount of the tilt, the center of buoyancy remains directly below the metacenter. If the metacenter is above the center of gravity, buoyancy restores stability when the ship tilts. If the metacenter is below the center of gravity, the boat is unstable and capsizes.