In the article, Antoine Vayer calculates that given Contador’s power output on that climb (which he calculates as 490W for a 78kg “normalized” rider – more on that later), and with one or two assumptions to turn that power output into oxygen consumption, Contador would be riding at 5.55 L/min. The problem with this is that it implies that Contador’s VO2max is about 99.5ml/kg/min!

Not that VO2max is the be-all and end-all of exercise, mind you (though some still believe it’s the key variable), but that value is off the charts. Some would say preposterous. Most elite athletes have VO2max values between 70 and 80 ml/kg/min, with a few above this. For Contador to be approaching 100ml/kg/min clearly raises a flag.

And it did, with Greg Lemond calling for proof that Contador is capable of achieving these numbers without using performance enhanching products “assuming the validity of the calculations”.

## And herein lies the catch – are the calculations valid?

Well, first of all (and *thank you to Seb for pointing this out* – my French is hardly ‘parfait’, so I’m afraid I can’t do the original piece justice!), the **Cycling News article is actually incorrect when it quotes Vayer as calculating a power output of 490W**. In fact, what Vayer has done is to work out a power output and then normalize it for a rider of 70kg and a bike of 8kg, so that different riders can be compared. This **value of 490W actually corresponds to an ‘absolute’ power output of 440W for Contador**. This has implications for how one discusses Vayer’s subsequent calculations.

Just on this note, I still think that this calculated power output of 440W is a little on the high side. For example:

- Last week, we looked at Contador’s climbing rate (VAMs) and using Michele Ferrari’s formula, arrive at a power output of 6.78 W/kg, or
**420W****.** - Alex Simmons very kindly provided some calculations for the climb, given the speed and gradient, and he
**arrived at a value of 422 W**. He went on to show that**if you assume even a small following wind, this power output drops to 397W.** - Using the same principles, but making more “aggressive” assumptions,
**I have calculated the power output at around 440 W**– this is an upper end, call it the “worst case scenario”, because I think**Alex has pretty much arrived at the accurate figures**using his equations (which match the estimation of the Ferrari equations based on VAMs).

The only way I can arrive at this high a power output is to assume a headwind (which is very unlikely), or that the climb was steeper or longer (or that Contador was riding a bike weighing 13kg!). The length and gradient are contentious – we couldn’t find any agreement on how long it was or how high it climbed, so Vayer may well be right. In the end, the data from Trainingpeaks.com showed an 8.7km climb and 640m ascent, which seems the safest bet.

There are some other assumptions you have to make – the air density, surface area and so on. However, these have a much smaller impact on the power output than gradient, speed and mass – a lot of people wrote in about this, the effect of air density and road surface. They’re factors, don’t get me wrong, but they’re really very small in comparison with speed, mass and grade.

So that’s the first problem with the calculation. That said, **Antoine Vayer knows about power output **– he published the book I referred to in my previous analysis of Tour climbing power, and has a library of all the Tour climbs. He, more than anyone, knows how to look at a climb in context, and so his figures deserve more than out of hand dismissal.

## Converting power to oxygen – some assumptions required

Next, you have to convert that power output into oxygen consumption. This also requires some assumptions. I don’t know the specific ones made, but an interesting exercise is to go through what might be “reasonable” assumptions and see what happens. First, you** have to assume the level of efficiency**. The more efficient the rider, the lower the oxygen consumption at any power output. So, Vayer may have assumed efficiency to be lower than the reality for Contador – short of measuring it, you’ll never know.

Next, you **have to assume energy use per liter of oxygen**. This is tricky because depending on how hard you are riding, the value varies – if you are burning fat, it is lower than if you’re burning carbohydrates as a source of energy. For example, the oxidation of fat provides 4.69 kcal/L of oxygen, whereas carbohydrates provides 5.05 kcal/L. Because Contador was climbing at a high intensity, he’ll be on the carbohydrate end of the spectrum, so the assumption would probably be around 5 kcal/L.

If you do this, and **assume 23% efficiency** (which is in the normal range, and I’d assume would be where Vayer would go), then you **arrive at a VO2 of 88.6ml/kg/min on the climb**. Next, you assume that this is 90% of the VO2max, and you have the **estimated VO2max of Contador – 98.4 ml/kg/min**! *(note the small difference is because I don’t know what assumptions he’s made – if you assume even slightly more energy from fats, then the VO2max rises to 99.4 ml/kg/min, for example – I’m just using some assumptions for illustrative purposes for now)*

## The problem – the starting power output is calculated, not measured

The problem of course, is not necessarily these assumptions – they can be made to be conservative and work out a “worst case scenario” as I did for power output. Then they are actually very instructive, because if you are conservative and still get ‘unphysiological’ values, then you have a real problem! The problem is that** missing one assumption can create a misleading picture****.**

First, you have the power output of 440W. You must remember that this is a CALCULATED power output, and is therefore the result of performance. Any factor that improves performance (like a following wind) will cause an overestimation of the power output if it is not taken into account in the calculation.

In my analysis of the climb, looking at the VAMs (which are also contentious, but minimize the requirement for assumptions to calculate power output), I went to great lengths to explain all the factors that could have contributed to the record climbing speed** **of Contador. These included the **shorter length of the climb, the suspected following wind, the race situation **(and of course, the possibility of doping, which is now receiving the bulk of the headlines in this article). Given the shorter climb, the following wind and the relatively conservative riding up to that climb, perhaps the climbing performance was expected.

On the other side, one has to also acknowledge that **Contador’s VAM (and hence estimated power output) would have been even higher on a steeper climb**, as I tried to explain (unsuccessfully in many cases, it seemed!). Of course, this assumes you use VAMs, which is not the best for this kind of interpretation. However, on balance, it was clear that you can’t take this single climb and read too much into it.

## The impact of wind

For example, just to illustrate the impact of the following wind,** for every 3.6 km/h of following wind (and that is a very gentle breeze), the required power output drops by between 2 and 3%**. The result is that by the time the average following wind speed reaches 10km/h, the estimated power output has fallen from 422W to 387W (8%). By all accounts, the general wind direction on the Verbier was from behind or the side, so I think it’s fair to assume the wind helped the climb.

Therefore, Contador’s “real” power output may have been substantially lower than what Vayer has calculated. If his assumption is 440W, it is conceivable that the **following wind may reduce it to around 396 W** (with an average wind speed of 15km/h from behind). Suddenly, **the estimated VO2max drops to 89 ml/kg/min.**

Just out of interest’s sake,using the same assumptions for converting power output to oxygen use, and using Alex’s calculated power output of 387W with an average wind of 10km/hour, the estimated VO2 on the climb is 78 ml/kg/min, and the VO2max estimate is 87 ml/kg/min.

## What can be inferred from power output and oxygen use – physiological markers of doping?

They are still exceptionally high, but are more in the realms of “normality” (whatever that means). I **still have my doubts about these figures **– if Contador’s efficiency really is 23% (as I’ve assumed to work that out), then it’s highly unlikely his VO2max is that high. We know that VO2max comes DOWN as efficiency rises. So the combination of a high VO2max and high efficiency is unusual indeed.

Having said all this, then, I really do believe that Greg Lemond is onto a very important aspect of performance analysis. There are upper limits to what can be achieved physiologically, there are without doubt physiological “impossibilities”. Unfortunately, in this case, I think the calculation of the key parameters is too fraught with error to be truly meaningful.

## What is physiologically possible?

If this kind of analysis is to be useful, then **every single aspect must be factored into the calculation **– the wind speed throughout the climb, the mass of rider and bike, the length and gradient of the climb. Then one might be able to make a strong case for the position that what we are seeing is impossible physiologically.

There are people (experts in the sport) who believe that the upper limit of performance should lie around 5.6 to 5.8 W/kg on a longer climb. This is well below what is being calculated for the current Tour, particularly the Verbier. However, if the wind speed is not controlled, then the calculated power output may well fall below that “ceiling”. The point is, we just don’t know what the wind is doing and so the margins are currently too large. Therefore, **you cannot use isolated performances, lacking control over variables, to infer doping.**

What we should rather do, and I hope can be done after this Tour, is to look at the average of all the major climbs – Arcalis, Verbier, Col de Colombiere, Col de Ronne, and see how the power output goes on average. Why? Because doping’s biggest impact may not be on the single performance, but on repeat performances through its effect on recovery between rides. Analysing many riders over a longer period also helps to control the influence of these variables a little better. This analysis would still require accurate estimations of power output, however.

A fascinating subject, and one that’s sure to get a lot of air-time, but frustratingly, too many grey areas, and “ifs” and “buts” – I look at this type of analysis, and I can see that there is something there, but it’s just out of reach… For now!

Ross

This post is part of the following threads: Tour de France Analysis, Tour de France timeline – ongoing stories on this site. View the thread timelines for more context on this post.