We all know the story. Fat greek man jumps into the bath, gets excited, runs naked down the road shouting something odd, but strangely catchy…. No, this isn’t a normal Tuesday night in Faliraki, it’s actually the story of one of the fundamental discoveries about the interaction between the solid and the liquid parts of our environment.

Who was Archimedes ?

Born in 287 BC, Archimedes of Syracuse had more up his sleeve than just a bar of soap. Aside from the whole ‘float or sink’ thing, he devised formulas for the area of a circle, the surface area and volume of a sphere and anticipated the discovery of calculus, which wasn't actually discovered until some 1600 years after his death. This is my cousin Alex. He’s pretty brainy as well.

As if all that wasn’t cool enough, Archimedes not only conceived of, but actually built a ‘death ray' worthy of darth vader, as well as a massive ‘claw’ which could apparently smash enemy ships to pieces. What a lad. Oh, and there’s the “Archimedes Screw” which, although it might sound like a sex move invented by Hugh Heffner for geriatric playboys, is actually a clever way of moving water up hill.

So… before we get too far off track, what on earth has all this got to do with freediving?!

Archimedes’ Principle and Freediving

Oh ok… one more story: Once upon a time, a very powerful King ordered a crown to be made as an offering to the local temple and supplied a particular goldsmith with an amount of pure gold for the purpose. When the crown was made, however, and presented to the King, the King became suspicious that the sneaky goldsmith had stolen some of the gold and replaced it with an equal weight of some lesser metal like silver, but had no way to prove it. Enter Archimedes. Being a brilliant mathematician, Archimedes quickly realised that gold is very dense, so a crown made of gold and other metals combined would be just a tiny bit larger than one of the same weight made of gold alone. Problem was, although he could accurately measure the weight of the crown, he had no way of determining its volume.

Pondering the problem in the bath one day, Archimedes suddenly realised that an object, like himself, immersed in water displaces an amount of water equal to its own volume. Using this vital piece of information, he was able to work out the volume of the crown, compare it to the volume of a sample of gold of the same weight, and prove that the goldsmith had been dishonest. God knows what happened to him. The rest, as they say, is history. Buoyed up (geddit?!) by his own success, Archimedes developed his theory, writing a treatise called “on floating bodies” (required reading for all Natalia Molchanova’s students no doubt) in which he concluded that “a body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces”. This is known, even today, as “Archimedes’ Principle”.

Floating and Sinking

So, for any object immersed in water, there are 2 forces acting on it: Its weight (equal to its mass multiplied by the ‘force of gravity’), and the buoyant force equal to the weight of the water it displaces:

(If you’re interested in knowing where the buoyant force comes from by the way, let us know in the comments box below.) Large objects that are not very heavy - an enormous rubber duck for example - have a small weight and a large buoyant force so they float. Small objects that are much heavier -like a pebble- will sink because their weight is greater than their buoyant force.

In the example above, the inflatable duck and the pebble weigh a (roughly) similar amount, but the duck has a much larger buoyant force because it displaces more water. Another way of saying this, is that the pebble is more dense than the inflated duck. The duck is less dense than the water around it, and the pebble is more dense. This is why one floats, and the other sinks.

Sinking in the Freefall

In most freediving disciplines, the weight of the diver is constant throughout the dive, but as you descend under the water on a single breath, your volume decreases in accordance with Boyle’s law, mostly because your lungs act like the balloons in the picture below.

As your volume decreases, your buoyant force decreases and eventually becomes less than your weight, allowing you to enter the freefall: And that’s Archimedes’ principle! Join us again next week for more physiology bootcamp, with the Mammalian Dive reflex coming up soon! How long do you think a pig can hold its breath?!

Dr Otter is the resident physiology whizz kid here at Freedive-Earth. If you’ve got a question for her, let us know!