Breaking the Law of Averages, Part 1: Why it’s so difficult to “even out” your speed

Sometimes we math-and-physics folks forget that things we think are simple aren’t as easy for literary scholars and violin prodigies. Our focus on math and physics causes us to lose perspective on many other things.

This was proven twice in the same problem recently when I got into a discussion about cycling performances in the Tour de France with a friend of mine who teaches English. He was perplexed by an article on Bicycling magazine’s website about the relative physical abilities of average and professional cyclists. He thought the writer didn’t give amateur cyclists enough credit when he wrote that “average” cyclists would only ride about 9-10mph over hilly terrain, while a professional would clock in between 21-25mph.

“No way,” he said. “An average cyclist would average more than that, because he would still descend faster.”

It sounds like a very reasonable argument. What goes up typically comes down, and while many grand tour stages finish on climbs (thereby robbing climbers of their richly deserved descent), you would assume that on the whole things generally even out. Despite going less than 10mph up a hill, if your handling skills are up to snuff you can probably hit 40mph or more on a steep enough hill. If the climb and the descent are equal, that means we just take the average of 10 and 40. 10 + 40 = 50. 50 divided by 2 is 25. Our amateur hits an average of 25mph! He’s right up there with the pros… right?

Not quite. The math is right, but there’s an error in observation. Let’s try it again with a hypothetical situation.

Let’s assume we have a 10-mile climb up a reasonably steep hill. Once we get to the top, we turn around and come back. We have a skilled cyclist of average strength who pedals up at 10mph. He can then bomb down at 40mph. Let’s break it down in parts and see what happens.

He goes 10 miles at a speed of 10mph. The first half of the trip takes him 1 hour.

He goes downhill for 10 miles at 40mph. The second half of the trip takes him 15 minutes.

His total distance is 20 miles. His total time is 1 hour and 15 minutes, or 1.25 hours.

20 miles divided by 1.25 hours is the same as 16 miles in 1 hour, or 16mph.

If you have a copy of my new book FASTER, you can flip to the section of the bike chapter about weight and aerodynamics to see the influence of hill incline on your performance, or if you log your rides on a program that estimates your power (or, even better, if you have a power meter!) you can get an idea of what it would take to ride 10mph for 10 miles up a 5% grade.


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The point is that it’s very difficult for many of us average folks to go much faster than that for any real distance. The pros really aren’t “making up” for any lack of speed on the climbs by zooming down the hills. To achieve that average velocity, they really have to work to keep their speed high on the climbs.

This is an especially important principle to keep in mind when riding your bike during a triathlon. How many times have you heard someone talk about “riding hard” into a headwind on a course, and then “taking advantage of the tailwind” on the way back? Probably as many times as you’ve heard someone say the exact opposite.

What forces are actually at work here? As with all things in aerodynamics, it’s not as simple as you might think. We’ll advance this principle just a bit and tackle the subject of headwinds and tailwinds in part 2.

As a special note, I hate that I didn’t discuss this further in the book. It did not occur to me that this little “math trick” would escape so many people. My head was buried so deep in calculus and Ph.D. papers that I didn’t see this part of the bigger picture.

One of the greatest things about triathlon is that we as athletes love to share the experience, though. In this case, I think I learned more from my English teacher friend that he did from me, and now the information is here for everyone to benefit from.

If you’re interested in getting faster, you’ll be fascinated by FASTER: Demystifying the Science of Triathlon Speed. In Faster, astronautical engineer and triathlon journalist Jim Gourley explores the science of triathlon to see what truly makes you faster—and busts the myths and doublespeak that waste your money and slow down your racing. With this knowledge on your side, you can make simple changes that add up to free speed and faster racing.


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