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 October 16, 2007

Archimedes, the Titanic and the science of water displacement

In the early hours of April 15, 1912, the world's largest passenger ship sank off the coast of North America with the loss of approximately 1,500 lives. The White Star liner, RMS Titanic, was on her maiden voyage from Southampton, England, to New York. It made it to within 1,000 miles off the US coast before disaster struck.

The disaster was made even more shocking by the fact that the Titanic was supposed to be unsinkable! In fact, the ship's builders, Harland and Wolff of Belfast, Ireland, had only claimed she was "practically unsinkable." However, many people may well wonder how such a huge metallic object - weighing over 46,000 tons - was able to float in the first place.

 'Titanic' tells the story of the men who built the most famous ship in the world.

Why do things float?

We all know that a stone sinks to the bottom when dropped into water, while a piece of wood floats on the surface. Also, a helium balloon rises into the air when released, rather than falling like an apple to the ground. But why do these things happen?

A simple explanation can be found by comparing the density of the object with the density of the surrounding fluid (liquid or gas). Density refers to the quantity and compactness of something per unit measure. The stone is denser than water, so it sinks to the bottom; while the wood is less dense than water, so it floats on the surface. The helium balloon is less dense than the surrounding air, so it rises.

This leads to the question: How can a boat made out of steel, which is approximately eight times denser than water, possibly stay afloat?

Eureka! The puzzle is solved

Archimedes (circa 287-212 BC) was a Greek mathematician who lived in Syracuse, now a part of Italy. He is famous for inventing war machines to help defend his city from the invading Romans and for calculating an accurate value of Pi (p), the ratio of a circle's circumference to its diameter, amongst other things.

Archimedes' wisdom was put to task when the King of Syracuse asked him to solve a riddle. The king had a gold crown made that he suspected was impure and mixed with less expensive silver. He asked Archimedes to test the crown to see if the goldsmith had cheated him.

Archimedes had to solve the problem without damaging or melting down the crown. While Archimedes was taking a bath, and thinking about this dilemma, he noticed how the water level rose once he climbed in. This observation helped him arrive at a solution. He was so excited that he jumped out of his bath shouting "Eureka" ("I've found it") and ran home naked so that he could write it down before forgetting.

Though the crown looked like it had been made of solid gold, Archimedes realized that its density would be different if an impurity of metals was mixed in. To test the crown, he put it into water and measured how much the water level rose. Then he put a lump of pure gold into the water that weighed the same as the crown. If the water did not rise to the same level, then Archimedes could prove the crown was not made of solid gold. Sure enough, the crown was found to be impure with less expensive metals added. The goldsmith was punished and Archimedes' fame spread.

Water displacement

 The Titanic is one of several exotic destinations marketed by Space Adventure and its affiliates.

The Archimedes Principle states that a body totally or partially immersed in fluid experiences an upward force, an upthrust, equal to the weight of the displaced fluid. Scientists now call this rising of water, "displacement."

If the upthrust, is less than the weight of an object it sinks like a stone. If the upthrust equals the weight of the object it will float like wood. And if the upthrust is greater than the weight it will rise like a helium-filled balloon.

According to one legend, the Archimedes principle was once demonstrated in Thailand during the reign of King Narai (1656-16881). A Greek adventurer known as Constatine Phaulkon, who had risen to high rank in Narai's administration, was asked by King Narai to weigh a heavy cannon.

Phaulkon placed the cannon on a boat and marked the water line caused by displacement. He then removed the cannon and replaced it with small stones until the same level of water was reached. The small stones could then be weighed with little difficultly to determine the actual weight of the cannon.

Building the 'unsinkable' ship

A ship's weight is usually called its displacement after the amount of water it must displace in order to float. The Titanic had a double hull made of thick steel and in order for it to float all it had to do was displace an amount of water that was equal to its weight. This was achieved by making the ship hollow and watertight.

Any steel ship can be made to float in the same way. However, if it fills with water it will sink because the weight of the water adds to the weight of the ship until it is no longer buoyant.

The Titanic was supposed to be "practically unsinkable" because it was designed with 16 separate water tight compartments, so that if it got punctured only the compartment with the hole would fill with water. This would increase the displacement of the ship making it sit lower in the water, but that alone would not be enough to sink the ship.

Disaster strikes

On the late evening of April 14, 1912, the Titanic was running at almost full speed through the North Atlantic, despite radio warnings from other ships that there were icebergs in the area. The over confidence in the Titanic's unsinkable design was about to cost lives.

The Titanic was too big and moving too fast to avoid the huge iceberg that was spotted at 11:40PM. Due to the speed and the angle of collision the iceberg made several holes along the side of the hull. That caused five of the watertight compartments to fill with water simultaneously. Nobody had ever thought that this many compartments would have holes all at once.

As the compartments filled up, and the Titanic sank lower in the water, more serious damage began. The compartments were not sealed at the top, so water overflowed into the adjacent compartments. This continued until the front of the boat (the bow) was so heavy that it began so sink.

Eventually, the back end of the boat (the stern) was lifted out of the water altogether until the deck was almost vertical. People and loose objects begin sliding down the deck. The boat snapped in two under its own weight and disappeared beneath the waves.

The Titanic came to rest at the bottom of the ocean, lying undiscovered until 1985 when Robert Ballard and a team from Woods Hole Oceanographic Institute discovered the site. They were using an underwater vehicle equipped with a TV camera, which they maneuvered by remote control back and forth across the ocean floor, a process which they called "mowing the lawn." They saw the first images of Titanic's giant boiler and some debris from the wreck on a TV screen.

A year later Ballard and his team returned, this time with a deep water mini submarine called Alvin and made a more detailed survey of the wreck. They also placed a memorial plaque at the site in memory of those who lost their lives.

Next time: We look inside gasoline (petrol) engines.

Corrin Funnell is a laser physicist with a specialty in laser spectroscopy. He has taught in the UK, Egypt, at Thailand's own Harrow International School, where he became head of the physics department. Currently, he is head of Physics at Island School, Hong Kong.

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