I couldn't resist this one.

As a former cyclocross World champion, Boom was able to perform a 'cross-style bike change at the foot of the final climb; jumping from his time trial bike onto a normal road bike, held out by a team mechanic.

"I had a great feeling today,” said Boom afterwards. “Everything went well from start to finish. The wind was strong with crosswinds and some tailwinds. In the beginning I saw Marco Pinotti riding ahead of me and I could catch him at approximately ten kilometres from the finish. But mainly I made the difference with changing bikes. Climbing went a lot faster than on the time trial bike.

So, to summarize, Boom jumped off his aero bike with just over a mile to go in the approximately 15.5-mile time trial. The question everyone (well, everyone who's a nerd like me) is asking is whether it really made a difference.

Brace yourselves. Math is coming.

I did the scratch work and decided that the answer is possibly, but not noticeably. Here's what I came up with. First, let's take a look at the course. I mapped in Google Earth to get as good an approximation of the road grade as possible. After checking my work against the profile on the Tour de Mediterranean site, I think I'm close enough for blog work.



Now let's look at the course profile.



There are three distinct hills. The first two don't matter because they never exceed 2.5% grade and Boom rode the TT bike over them. The big concern is the final climb. The last climb is 0.87 miles with an average grade of 11.2% and an estimated maximum grade of 20.5%. That's pretty much steep enough to scare me to death. It will also slow you down substantially.

Unless you're Lars Boom. He completed the course in 32:25, giving him an average speed of 28.52mph, or 45.9kmh if you're a European, or 12.75m/s if you're an engineer. If you're a cyclist, he was just wicked fast. The question is whether changing bikes had anything to do with that.

The crux of this argument goes back to the age-old question among cyclists-- weight or aero? It's often a clear decision, but so frequently one way or the other that highly competitive cyclists feel like they need two bikes. Nowadays manufacturers are trying to split the baby with "aero road bikes." Boom needed the absolute superior aerodynamics of a dedicated TT position for 99% of this course and bet that jumping to a road bike for the last mile would give him the edge. He figured intuitively that, because wind resistance is proportional to the cube of velocity, the amount of wind resistance drops quickly as you slow down. Hills at 11% grade have a habit of making you slow down quite a bit, so Boom's whole strategy rested on the assumption that he would go so slow up the hill that wind resistance would matter less than weight. 

We're dealing with physics and I don't have actual numbers, so as always there are going to be some flaws in the approach. Let's identify those right up front. Here are all the things I had to assume because I don't know them. Hopefully the numbers are close enough and the fact that this is a comparative study negates some of the errors.

Assume the following:

Event took place at standard air pressure and temperature.
Head and crosswinds interact similarly with each bike.

Tires on both bikes were the same.
Boom lost 8 seconds or less in slowing down, changing bikes and accelerating.

The time trial bike had a mass of roughly 8500g.
The road bike had a mass of roughly 6500g.
Approximate weight difference = 2000g (4.4 lbs)

The drag area of TT bike and Lars was roughly 0.297*
The drag area of the road bike and Lars was roughly 0.481


Drag area is defined as the drag coefficient multiplied by the frontal surface area. I'm using values previously measured on other elite cyclists on top-end bikes, since I don't know what they specifically are for Boom. Drag coefficient doesn't get talked about enough in the cycling world. We're too hung up on grams of drag as measured in wind tunnels. That's a false idol if I've ever seen one. It doesn't really tell you anything except the object's drag at a particular speed. It's not even a good point of reference for other conditions. Drag coefficient is better, because it allows you to calculate drag at all speeds, which is what is necessary to solve this problem.

 Calculations:

Let's start with the big question. How much slower would Boom have had to go for his switch to have made a difference with regard to aerodynamics?

According to my research, the threshold where aerodynamics really start to matter is 18mph. So how fast would he have conceivably (since I couldn't find any reports about it from the race) gone up the hill?

According to Wikipedia (add "Wikipedia is accurate" to the assumptions), Boom is 170 pounds (75kg). Total mass of Boom and his bike is then 81.5kg. We also know from looking at his past results that he achieved an average speed of 31.7mph (14.17m/s) in an 8.8km time trial at the 2011 Tour of Britain and that his average speed at the French TT was 28.52mph (12.75m/s). Using the estimated drag area value for a TT position and the right equations, we deduce that his power output can get as high as 500w over a short distance and that his average output yesterday was in the 380w range. So let's say he pushed it as hard as he could on the flats while saving for that last mile, then hit a maximum of 400w on that climb. Using the spreadsheets I cooked up for my book, I get that it probably took him 5:45 to get up that hill, which amounts to about 10.5mph or so. That's far enough below the speed limit for aerodynamics to become involved. So he was right that the road bike would be faster. Now we split the hairs over how much faster.

I added the 2kg difference in the weight of the bikes and ran the calculations again maintaining the same power output. On a TT bike, Boom would have gone up the hill in 5:55. He saved approximately 10 seconds. Factor in the (assumed) 8 seconds he lost on the deceleration and acceleration during the change, and his total time savings is 2 seconds.

Which is a time savings that actually matters in bike racing, but just seems crazy to me. Then again, that's the opinion of a guy who just cranked through all the math on this.



* Values obtained from the paper "Reference values and improvement of aerodynamic drag in professional cyclists," published in The Journal of Sports Science, February 2008. Written by Juan Garcia-Lopez and others.