# Phelps vs. Lochte: Who Could Better Power your House?

Thursday, August 2nd, the world watched as Michael Phelps and Ryan Lochte swam against each other for the last time. In just under two minutes, the 200 meter individual medley was over, Phelps hit the wall at 1:54.27, Lochte finishing a mere 0.63 seconds later. The world record for this event at 1:54.00 was set by Lochte last year during the World Championships in Shanghai, China, the first world record broken after the 2009 ban on full-body swimsuits.

So, why do swimsuits matter? Take a look at this graph from the Washington Post before you answer. Basically, suits reduce a swimmer’s drag, which is possibly their number one foe. Calculating the effects of drag on a swimmer is actually a lot more complicated than most people think, especially since first we have to ask what effect does the swimmer have on drag?

Body shape, stroke, and speed are just a few of the variables in this sport, and researchers within the past couple years have started becoming interested in finding out quantitatively what happens to the drag force when a human swims.

If we look at Phelps’ times, we can calculate the approximate drag force that he encounters.

By calculating the amount of power from drag, we can see the amount of energy it takes to fight it. In Mathcad Prime 2.0, we can choose whichever units we want, so let’s use kWh for now (you’ll see why in a moment).

Although that doesn’t seem like a lot, remember that this is only one part of the forces acting against a swimmer’s movements, and that this is only one type of drag force! In order to better understand this number, let’s compare this to the amount of energy consumed by the average American household. Over the course of a month, Americans use 958 kWh of energy, according to the US Energy Information Administration.

Now, if we establish “Phelps” as a unit of measurement, we can do this:

So it takes the equivalent of 98,980 Phelps swimming 200 meters at 1:54.27 to generate enough electricity for a family of Americans for a month. Wow. How does Lochte compare?

Instead of rewriting all my calculations, I just need to change the initial time parameter in my Mathcad worksheet, and voila!

Although it may look like they have the same energy, that is an illusion created by the fact that I rounded the answer to three decimal points (why? To heighten the dramatic reveal, of course). When we do the same conversions, we discover the following:

It takes 100,100 Lochte’s to power an American home for a month, while it only takes 98,980 Phelps’s. Either way, poor guys. Moral of the story: don’t use Olympic swimmers to power your house – it’s not nice and if they got tired, you wouldn’t have power… or the ability to do fun equations in Mathcad Prime 2.0.

## About Paige Grody

Paige Grody is an engineering student at MIT and a PTC intern. Grody has served as CEO of her city's FIRST robotics team, the Ligerbots, and is generally way too enthusiastic about anything and everything to do with science and technology.
This entry was posted in Mathcad and tagged , , , , , . Bookmark the permalink.