- Really interesting as a means to add value to watching the sport, and
- Potentially interesting as a means to flag suspicious performances.

And rather than wait until the Tour begins, I thought I’d take advantage of a rest day in the FIFA World Cup to get some thoughts going, since I left yesterday hanging somewhat (deliberately, but still…)

And so here are some thoughts on the ability of performance to predict physiology.

## Estimation and assumption

Perhaps right up front, I have to talk briefly about estimation and assumption vs measurement. Of course, the ideal would be to get accurate SRM data on the power output on the climbs. Of course, it would be wonderful to know with precision what the power output was, but as I hope to illustrate, the errors in these kinds of calculations can both be minimized and controlled so that you end up with a ‘best case scenario”.

This is much the same situation you would find yourself in if, for example, you wanted to open a coffee shop and had to do prepare a business model. You don’t know how many cups of coffee you’ll sell, you don’t know how many biscuits to bake. But if you know your market, and its people (your future customers, you hope), then you can control your assumptions and go a long way to making a conclusion. That is, if you make “best-case” assumptions and still your coffee shop is running at a loss, then it clearly is not a viable business. If your “worst-case scenario” (few customers, few sales) still makes a profit, then the business works. Realistic and sensible assumptions are the key to ensuring that your conclusion is accurate, even in the absence of a crystal ball! Similarly, for these physiological calculations, you can make “best-case” assumptions and if the picture still doesn’t fit, then you have a good case for a problem.

So over the next few weeks, I think we must acknowledge right away that these are always estimations – of power output, of body mass, of bike mass, of wind speeds and directions – all these factors will affect the eventual physiological calculation, but for two reasons, their effect is not as large as you might think:

- We’re not proving anything here – only suggesting physiology for the purposes of increasing enjoyment and stimulating discussion, and
- The physiological implications are so large that even errors don’t affect the conclusion.

So let’s say it now, one last time – this is not proof, but an interesting exercise nonetheless, and I believe a compelling way to approach the problem. Ultimately, people will believe what they wish to, even when presented with a ‘creaking and ugly edifice’.

So let’s get cracking…

## An extreme case – the physiological implications of 8 W/kg for 40 minutes

Let’s take a rider who produces 8 W/kg. Assume his mass is 70kg, which means an absolute power output of 560W. Clearly, very high.

In order to work out the physiological implication, by which I mean the oxygen cost, there are two potential methods.

The first involves the use of a published paper called “Peak power output predicts maximal oxygen uptake and performance time in trained cyclists” ^{[1]}. This study looked at 100 trained cyclists and established the following relationship between oxygen consumption (VO2) and power output. The relationship is:

*VO2 (L/min) = (0.01141 x Power output) + 0.435*

Therefore, if you take the power output of 560W, and you apply this equation, you will calculate an oxygen consumption of 6.82 L/min. Relative to body mass, this is equal to 97.49 ml/kg/min.

The second method, just for comparison’s sake, requires that you do three things:

- You calculate the real energy cost of producing that power, by taking advantage of the fact that cyclists are not perfectly efficient. In fact, elite cyclists are only about 23% efficient. What this means is that a cyclist who is riding at 560W is in fact producing 2435 W. Clearly,
**we now have our first assumption – the efficiency**. Lance Armstrong’s efficiency was measured as 23.12%. Other studies find values that range between 21% and 27%, though values over 25% are hotly debated, and basically dismissed as an artefact of testing and equipment. This is a controversial issue, but most elite cyclists seem to be around this 23% value, and since Armstrong’s was measured there, I’ll use it for the remainder of this calculation. - The total energy can now be used to work out an oxygen consumption. This requires that you have knowledge of the contribution of various energy stores to the physiology. We know that every liter of oxygen used produces between 4.69 kCal and 5.05 kCal, depending on whether fat is being used, or carbohydrates. So,
**this is our next assumption**– which end of this spectrum do we use, the 4.69 or the 5.05kCal? The answer is the further right extreme, for two reasons. One is that it’s physiologically reasonable – a cyclist producing maximum effort is going to be near maximally using carbohydrates. Second, this is the “conservative” or “best-case” assumption, as explained earlier. So we’ll run with 5.05 kCal/L O2. - We can now work out the oxygen consumption for a given power output at a given efficiency.

In our example, 560 W produces an oxygen consumption of 6.91 L/min, or 98.71 ml/kg/min.

You’ll note that this is similar to the value of 97.91 ml/kg/min that we calculated using Method 1. This suggests that the above assumptions of efficiency 23% and energy use per liter of oxygen are correct. I must point out that we haven’t yet considered the contribution of non-oxygen dependent pathways (the so-called anaerobic contribution) to energy. This is of course important, but I would also point out that we are talking about a cyclist who is producing this power output for 40 minutes at the end of a 5-hour cycling day, and so the assumption on energy demand, given the length of exercise, is still valid (in my opinion).

Now, what do you make of that oxygen consumption of 97.9 ml/kg/min? If I measured it in the lab, I’d be checking my equipment…clearly, something is wrong. And if a cyclist were able to produce that power output (8 W/kg) for 40 minutes, with that physiological implication, then you’d be calling him out (or you’d be looking for the electric motor in his pedals).

If you assume, for example, that a cyclist can maintain 90% of their maximal level for 40 minutes, then this oxygen use of 97.9 ml/kg/min corresponds to a VO2max of 110 ml/kg/min. The red flag is clearly waving.

So when is it possible for a cyclist to ride at 8W/kg, assuming they have a VO2max of 80 ml/kg/min? Well, their cycling efficiency would have to be around 32% – many percent higher than anything ever measured before. 9 W/kg, which I throw out only because it was suggested is possible on a chat forum, would require that a cyclist with a VO2max of 80 ml/kg/min is 35% efficient. Either that, or a cyclist with an efficiency of 23% would have to have a VO2max of 123 ml/kg/min. It simply doesn’t happen, and therefore, neither do 8W or 9W/kg for 40 minutes.

Now, let’s look at a much more conservative assumption – the decent level cyclist…

## The “low end” – 4 W/kg for 40 minutes

Most trained cyclists would be able to produce this power output. In our lab, we test the range of beginners to elites, and this what you would expect of a decent level cyclist. And we know that a decent cyclist will produce a VO2max of around 60 ml/kg/min.

Using the same method as before, we can estimate that the **oxygen consumption associated with this performance of 280 W is equal to 51.9 ml/kg/min**. If you prefer method 2, using an efficiency of 23%, then you’ll calculate 49.4 ml/kg/min. The reason this is lower, incidentally, is because this person is unlikely to have an efficiency of 23%, but one that is lower than this. If we use 22%, for example, we calculate 51.6 ml/kg/min. Again, this shows that 23% is a pretty safe “best case” estimation.

Again, if you assume that a rider such as this is maintaining 90% of max, then the inferred VO2max would be equal to 57.6 ml/kg/min. That’s a perfectly reasonable value. If anything, it’s on the low side, which I again point out shows that the assumptions I’m making for all these calculations are “conservative”.

The key assumption in this regard is the 90% of maximum assumption. In reality, a good level cyclist will ride at 85% of maximum, which means our inferred VO2max suddenly rises to 61 ml/kg/min. I also maintain that a Tour rider, on the final climb of the day, will be closer to 85% than 90%, given that they’ve been riding for five hours. However, this assumption is debatable. My point is, if the physiology is still unrealistic with these safe assumptions, then you know you have a problem.

So now, we’ve looked at two extremes – the high, which simply doesn’t exist, and the low, which is safe and clear and maybe even a little conservative. There is a point in between, where elite Tour riders exist, where the really interesting questions begin. So let’s look at a Tour rider…

## Bjarne Riis – 6.8 W/kg for 35 min on Hautacam. Or Armstrong – 6.6 W/kg for 38 min on Alp d’Huez

Bjarne Riis is estimated to have produced 6.8W/kg (480W) on Hautacam when he won the Tour in 1996. Armstrong’s estimated power output on Alp d’Huez was 6.6 W/kg (465W). This is Vayer and Portoleau’s estimation, and I believe it to be accurate. I actually saw a PhD student from Texas present a similar analysis at the ACSM conference in 2005, and he had worked out 495W (7 W/kg), taking into account the gradient every 100m as well as wind speeds. If anything this is more accurate. But as I mentioned, we’ll be “conservative” in our calculations, so let’s take the lower option and see what it means, physiologically.

We again assume 23% efficiency (in Armstrong’s case, this is not an assumption – it was measured by Coyle), and we can calculate that the oxygen cost of producing 465 W is equal to 81.96 ml/kg/min. Using method 1, the equation from the published literature, we find oxygen use of 82.00 ml/kg/min, pretty much identical.

Now, is it possible to ride at 81.96 ml/kg/min for almost 40 minutes? If you are at 90% of maximum, then it means that the VO2max must be equal to 91.07 ml/kg/min. If you are at 85% of maximum, then the maximum must be 96.42 ml/kg/min. Given that by the time these performances happen, the cyclist has been in the saddle for five hours, not to mention about 2 weeks before, I feel pretty safe in saying that you’re projecting a VO2max that lies somewhere between 91 and 96 ml/kg/min, probably closer to 96 ml/kg/min.

Another example comes from Armstrong’s own words. In this interview, he says *“I also cranked out 495 watts for more than 30 minutes”.* 495 W is about 7W/kg, and applying the same equations as I’ve done throughout this post, you can **work out that it requires oxygen consumption of 87 ml/kg/min, and a VO2max of 97 ml/kg/min** (and that’s at 90% of maximum. If you go with 85%, you get 103 ml/kg/min…).

Is that realistic? I suspect that your answer to that question depends not on what you know, but rather on what you want to believe. I don’t believe that it is possible, because the combination of high efficiency (and 23% is high) and high VO2max doesn’t seem to exist. In fact, Lucia et al showed that there was an inverse relationship, so that those with the best efficiency had the lowest VO2max ^{[2]}. So the problem is that if you suggest that we increase the efficiency to make the predicted VO2max come down, you’re chasing the pot of gold at the end of the rainbow, because the possible VO2max is coming down anyway!

However, people will draw their own conclusions. I am of the opinion, like Prof Aldo Sassi, that a value above 6.2 W/kg is indicative of doping. And in the coming weeks, I will post more on this, including graphs that hopefully illustrate this point even more clearly. But, as always, there is likely to be debate.

## Next up – the Quarterfinals

That’s it for cycling for now – during the course of the Tour de France, we’ll return to this kind of approach and look at some of the performances, and compare them to historical numbers. As always, the discussion is welcome.

The cycling now gets put on hold for a few days while the Football World Cup Quarter Finals take place! I am sitting on piles and piles of data about how far players run at different altitudes, and even how goalscoring seems to be affected by the altitude. But perhaps for two days, I will be a fan, and then resume the analysis next week!

Oh, and there’s Wimbledon! And the start of the Tour! Enjoy it, and we’ll be back soon!

Ross

## References

- J.A. Hawley, and T.D. Noakes, “Peak power output predicts maximal oxygen uptake and performance time in trained cyclists.”,
*European journal of applied physiology and occupational physiology*, 1992. http://www.ncbi.nlm.nih.gov/pubmed/1505544