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by Dr Paul Behrens, International and Policy Officer at the Royal Society of New Zealand and former research fellow at the University of Auckland

Last week has seen the final vestiges of Lance Armstrong’s fig leaf of innocence disappear; knowing Lance he probably smoked it.

Notwithstanding the fact there is a lot of evidence against Lance from teammates and doctors, is there a way we can look at the physics behind his performances to provide more indications?

Disgraced cycling star Lance Armstrong

There are quite a number of ways you could use physics to provide some indication if a cyclist is doping or not, but one suspicious indication might be a very high Watts per Kg value (w/Kg). The BBC’s More or Less programme talked to a sports scientist who measured the W/Kg in this year’s tour and compared them to previous races. What he found was that the winning riders this year had a W/Kg value of 6, which is about 10% lower than during Armstrong’s dope-dominated years. But what does W/Kg actually mean and why is it important?

## Drug pedalling

To get a feel for the overall difficulty in completing a stage in a bike race, we need to look at is how much energy is required to ride through a stage like this one at the Tour de France and more importantly how quickly a rider can convert the stored chemical energy in muscles into kinetic and potential energy on the bike.

The unit of energy is the Joule and the rate of energy conversion is called power and is given in Watts (this is number of Joules per second converted). The Watt is a unit commonly used when analyzing Tour de France riders.

Lance Armstrong, in his heyday could average about 470 W climbing all out on the last hill of a stage. To put this in perspective, the average social rider can average between maybe 150-200 W all out over the same time (a common way to compare power in the media is with incandescent lightbulbs – I think we should be more modern and talk about LED lightbulbs – it sounds a lot better when you can go from powering 2 to 60 lightbulbs for no extra effort).

Now both potential energy and kinetic energy are directly proportional to the mass of the rider and bike, so a heavier rider will need to use more energy to both maintain a forward speed but to also lift his/her weight up a hill. Being good on hills is important because races like the Tour de France can be won or lost in the mountains. But we have to remember that a heavier rider is also likely to be musclier and be able to store more energy in the form of chemical energy (glycogen in your muscles). So by looking at the power output alone it looks like we are not going to be able to evaluate a rider’s performance.

Let’s put this into numbers: Lance, was 71 Kg at the time he won a tour, and could develop an average of 470 W on a hill, Michael Rasmussen was only 60 Kg at the time. So Lance, when climbing a mountain, would have to output 18% more power than Rasmussen because he is 18% heavier (to a very rough first order). Rasmussen has to output over 400 W and he’s got Lance beaten (470 W/1.18 = 398 W).

This is why analysis of riders often involves calculating how many Watts per Kg a rider can output. So Lance Armstrong, 71 Kg and outputting 470 W would have a Watts per Kg figure of 6.6 W/Kg (470 W/71 Kg= 6.6 W/Kg).

## Implications of suspicion

As the sports scientist on the More or Less program pointed out, the average output per Kg in this year’s Tour de France was 6 W/Kg, 10% down on the Armstrong years. This is definitely not conclusive evidence, but it could be seen as another indication of suspicion (although 11 team mates, coaches and family members calling him out as a cheat is probably enough). It might also indicate that there is no doping in modern Tours (or at the very least, less doping).

Since so many of Lance’s contemporaries have also been found guilty of doping, it looks like the international cycling body is not even going to bother awarding the titles to anyone else. This means that Lance will have won exactly the same number of Tours as most of the rest of us.