# Swimming pool physics

It’s summer, and for me that means the university’s 50 metre outdoor swimming pool is open. Lots of lunchtime lengths, dodging the morons who can’t cope with the concept that lanes are for lane swimming, rather than playing ball games. There’s a lot of physics that goes in with swimming. Hydrodynamics, the study of how water flows over something, is big business, and people have written seriously sophisticated computer programmes to work out just how water flows past something.

These computer programmes, collectively called ‘computational fluid dynamics’, are conventinally used to study problems such as the engineering of coolant systems, or design of ship hulls, but also have been used to study the shape and manouverability of penguins and design of those ridiculous looking new swimming outfits warn by Michael Phelps and co.

The reason why computers are needed to get that little bit of extra speed (not that Phelps needs any of that) is that water flow is what we call  ‘non-linear’. What do I mean by ‘non-linear’?  Well, linear behaviours are nice and easy to work with. Basically, if you double the input and get double the output, you are likely to have a linear system. Also, if you carry out two actions simultaneously, and the result is the sum of the results that you would have got if you’d carried out each action on its own, you have linearity. There are lots of examples of linear systems in physics and elsewhere. Many electrical components are linear. If you put double the voltage across a resistor (e.g. the heating element in your electric jug), double the current will flow – this is why you don’t plug 110 volt American appliances into the New Zealand supply – you’ll fry them.  If you put double the money into your bank account, you’ll double the amount of interest you get paid (OK – banks have tiered interest rates, so its not quite linear, but hopefully you see the idea). Movement of electromagnetic waves (e.g. radio waves, light), is pretty much linear. You don’t need computers to tell you how they will behave.

However, flow of water is not linear, and that makes it really really nasty to work out the effect that something has. Small changes to something can have effects that are not small at all. Any semi-keen swimmer knows that small details of your arm-pulls really matter when it comes to speed, and sometimes it is not at all obvious why.  I doubt that even the best yacht designer, for example, would have a hope of building a competitive racing yacht without aid of a computer.