Physics and the Track, Part 2

Welcome to the second installment of why track cycling physics is awesome.

Since the summer is here and we're getting much hotter and more humid, I thought I'd point out some interesting things regarding air density and timed events. Many people are probably aware that moving through less dense substances generates less drag, and so for a given power output, one goes faster in less dense stuff than more dense stuff (think running in air vs running in water).

What's interesting is that hot air is less dense than cool air. So, if you have a given power output and you ride at noon, you will get a faster time than if you ride at 8pm. What's even more interesting is that humid air is LESS dense than dry air! (If you assume the number of molecules in a volume is the same, when you take out some O2 and N2, aka air, and replace it with H2O, water, the density goes down because H2O is lighter than both O2 and N2).

This is all lovely in a lab setting where other variables are under tight control, but what about outside? The atmospheric pressure will also play a role -- lower pressure air is less dense than high pressure air at the same conditions.

So all of this means that your times will be faster on a hot, humid day after a low pressure zone rolls through than on a cool, dry ones. But how much faster?

Using the data from the DLV weather station (link on the left hand side) for June 4th, here's what I found out:

Assume I rode a 200m TT at 7:30pm in 13.00 seconds. If I had delayed my run until 8:30, when it cooled down some (just over 1 degree), my time would be 13.02 seconds. Who cares, right?

Let's assume now instead of doing a 200, I did a 4000m TT in 5 minutes. If I had delayed my TT an hour, I would be half a second slower. Half a second is a big difference in a pursuit tournament.

Now, let's look at something with a bigger difference.

If I did my 200m TT at 2:30pm instead of 7:30pm, it would have been much hotter (88.5 degrees instead of 75.4 degrees). But, my time would have been a 12.83. A change in 0.2 seconds in a sprint is a big deal!

If I did my 4000m TT at 2:30pm, I would get a 4:56! That's 4 seconds faster, just by going earlier in the day! (On an hour time trial, I would save a full minute -- that's enough to win or lose a grand tour!)

So, in reality, it's not as clear cut as all this. To do the calculations, I had to assume that the rider power output is just as good at all conditions for all times. This may be true for a well-warmed up sprinter, but a pursuiter may overheat and lose power in a 5 minute effort in weather that's 20 degrees warmer. But, the difference for pursuiters is still significant with small changes in temperature, so it's still an okay assumption.

The moral of the story? Instead of being afraid to be the first to go for a timed event at our evening races, you should jump for the opportunity! Assuming you warmed up correctly, you will go faster (even if just a little) by going earlier when it's warmer. If you are at any other timed event, try to get a spot at the hottest part of the day (assuming you are physically capable of the effort in those temperatures of course).

And, for those who want to play with the numbers, I've attached the spread sheet to do the calculations. You can find all weather data from the DLV weather station. The units you need to enter are the same as reported, so no conversion is needed. There's two sheets -- one lets you enter average speed and distance, the other lets you enter time and distance. Both will tell you the speed and time for the second condition.

Have fun!

Tim