# Physicist foresees Tour de France results

This Sunday the Tour de France will pass through the Arc de Triumph for the 102nd time in history. John Eric Goff sees it all coming.

The professor of physics at Lynchburg College takes Newtonian laws to the three week race to estimate the winning time for each stage. We speak with him about his eight-stage streak with an error less than 1.85 percent.

ResearchGate: What’s the model you use to predict the winning race times?

John Eric Goff: Every year in June, the Tour de France releases snap shot profiles of what each stage will look like geographically. It offers certain information, like distance, elevation and the names of towns the cyclists will be riding through, but not nearly enough for an accurate representation: The Alpe d'Huez and its famous 21 hairpin turns is just a steep mountain onscreen, for example. So we gather additional data about the course online. We also make use of published research on power output for elite cyclists and on bicycles. This includes factors like air drag on the cyclist and their bicycle, rolling resistance of tires on the road – essentially all the physical forces acting on the cyclist and their equipment.

We then use a simple introductory physics idea to create a sequence of inclined planes that represents our model of the complicated terrain. Each surface (or plane) shows whether the course is going up, down or flat, depending on the stage of the race and where the cyclist is. We then employ the laws of physics, add our data about the cyclists, and compute how fast each stage can be bicycled.

RG: Up until stage 15 you had a streak of eight consecutive stage predictions with an error 1.85% or less. That’s impressive! What factors make it particularly difficult to stay ahead of the game?

JEG: Thanks! The fact is it’s a very complicated event: You’ve got 3 weeks of complicated terrain, street configurations and obstacles. You’ve got fans on the side of the road and sometimes in the road. And sometimes the fans are dressed but occasionally they’re not. There are also crashes… but the most difficult factors to predict are team strategies and the weather.

Stage 15 is a perfect example of not knowing various team strategies. We predicted the finishing time for the peloton winner, Vincenzo Nibali (last year’s champion), almost exactly but we were slow on the actual stage winner’s time. That’s because the general classification leaders like Nibali just hung around in the peloton, content to concede the stage win. Rest days are also tough in terms of figuring out how a cyclist chooses to perform before a day’s rest: Maybe they’ll ride like crazy and wear themselves out because they know they can rest the next day – maybe they won’t.

In terms of the weather, the early northern stages are notorious for cross winds, head winds, and rain, that slow the race down. And so we’ve noticed over the years our predictions are always a little bit fast in these stages.

RG: You build your model in June yet release your predictions the day before each stage. What last minute factors do you incorporate, if not the weather?

JEG: When building our model we don’t know how the general classification is going to shake out. We don’t know if the leader after the 10th stage will be 1, 2, or 6 minutes ahead of the rest. So we do make slight modifications during the race if it looks like the cyclists are performing better or worse than what we’d thought the typical power output would be.

Also, I should say that while I don’t include the weather, I do include the fact the air density goes down with elevation. So when the cyclists move into the high mountains the air density drops and the air drag on the cyclists goes down.

RG: How do you adapt and improve the model each year?

JEG: Well, classical Newtonian physics will always be the workhorse of the model. But what we can refine is the cyclist’s power output model, and how that changes whether the rider is going up or downhill. We’ve also refined our model for the air drag over the years and, starting last year, we now account for allometric scaling. For example, if the cyclist has a bigger mass he can generally do better on flat stages, and if he has a smaller mass he’ll do better in the mountain stages. It’s obviously not always true but it’s a pretty good rule of thumb.

RG: I’m dying to ask: Who you think will win?

JEG: To be honest I’ve never tried to pick an actual cyclist to win. The model we set up and the science we’re pursuing are what we believe the prototypical athlete is going to do to win a certain stage. We’re trying to predict what the best of the best in the world could do on a sprint stage, or what the best climber could do on a mountain stage.

In saying that, I don’t know if I’d bet against Chris Froome right now! He has such a strong team behind him and he’s going to be tough to beat. There are four stages in the Alps coming up. That’s where you’ll see the likes of Nairo Quintana and Alberto Contador who are really good in the mountains challenge Froome, but whether it’ll be enough I don’t know.

RG: Have you ever used your predictions to place a bet?

JEG: I don’t bet. I am, however, keenly aware of all the attention my blog gets around the world. I’d be shocked if there isn’t at least one person using our predictions for betting.

RG: The Tour de France is notorious for drug scandals. Have you ever been suspicious of doping based on your results?

JEG: We’ve never had any issues about a specific rider. All I know is that in 2013, one stage after another we were seeing record-setting speeds. There were certain stages where cyclists were matching and even blowing away Lance Armstrong’s time on similar stages. It could very well be that in the past ten years the cyclists and their equipment moved beyond what we thought possible.

RG: How did you get into it and what keeps you interested?

JEG: It is a lot of work. There’s the science, which is the serious side to this, but it’s also a lot of fun. I started this with Ben Hannas, a student of mine in 2003, who’s very into cycling. At first I thought that if we could get under 10% then that’s good because it’s such a complicated event. But over the years we’ve gotten better at it and other students have made helpful contributions: Chad Hobson has been an integral part of research advancements during the past two summers. And so now, missing the mark by 5% or so has us analyzing what happened. We’re sticking our necks out a little bit with posting our predictions ahead of time, but seeing the students get excited when our predictions are so close makes it all worthwhile.

Thank you, Eric.

You can read more of John Eric Goff’s work on ResearchGate, in his blog, and in his book, Gold Medal Physics: The Science of Sports.

This story also appeared in the Washington Post.

Feature image courtesy of RayMorris1