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Saturday, July 24, 2010

Power output on the Tourmalet - resolving discrepancies

Ferrari: "6.42 W/kg".  Everyone else: "Less than 6 W/kg".  Who is right?

Thanks everyone for the great discussion in response to the post yesterday looking at the climbing power output on the Col du Tourmalet.  As if often the case, your responses make the comments section to the post is better than the post, so if you have to time, you might consider reading it here!

However, a short post today, because something came across our twitter account yesterday and today mentioning that Dr Michele Ferrari has estimated the power output on the climb and his values contract those presented here yesterday.  I was going to post this in the comments section only, but I felt it worth putting out, since the disagreement is so large, and from such an 'infamous' source, that it demands attention.

From the site 53 x 12.com, Ferrari writes the following:
"Col du Tourmalet, in the last 9 km they climbed at 1780m/h, equal to 6.42 w/kg."
You'll recall that we said yesterday that:
"My overall estimation is that they took 49:08 to climb what I believe to be the final 17.6km at a gradient of 7.6%.  This gives a VAM of 1,633 m/hour, and a relative power output of 5.9 W/kg."
Even over the final 9.3km, after Andy Schleck attacked, we estimate a power output that is even lower than this.  We wrote:
Horner's power output over the final 4km will be very similar to that of Contador and Schleck, because of the constant time-gap between them.  There is some error thanks to drafting, wind and so forth, but we're talking small differences.  From the graph, Horner rode the final 4km at about 350W, and so Contador and Schleck finished the climb in this range of between 350W and 360W - 5.5W/kg to 5.7W/kg
So 6.4W/kg vs 5.9 W/kg?  Ferrari's numbers demand scrutiny, because they're so different.

Look at the SRM for the real values

And to find an answer, let's take the guesswork out of this and look at the SRM data - this way, we don't have to assume the length, the vertical gain in height, or the gradient of the climb.

So, for Chris Horner over the final 9.3 km (since this is what Ferrari claims is 6.42 W/kg (graph can be seen in yesterday's post):

Distance = 9.3 km
Gain in height = 736 m
Gradient = 7.91%
Time taken = 28:36
VAM = 1544 m/hour
Estimated power output = 5.53 W/kg

Of interest here is that the SRM gives Horner's power output over this interval as 348 W, or 5.4W/kg.  The VAM thus overestimates the power on this climb, and this is telling (bear in mind that if you have a following wind, you'll overestimate, whereas a headwind will produce an underestimate when using VAM - this is one of its 'flaws', and the reason why the SRM is the ultimate source of "truth", notwithstanding issues of calibration)

Now, let's look at Contador and Schleck over exactly the same 9.3km interval.  Remember that they all started this part of the climb together, with Schleck's attack creating the time gaps.

So, the stats are the same as above, with the exception of the time.  Horner concedes 1:46, and so therefore Schleck and Contador do the 9.3km in 26:50.

Now, VAM = 1646 m/hour
Climbing power output = 5.90 W/kg.

Not 6.42 W/kg.

The only way to explain this discrepancy is if the climb has been mapped differently, so that Ferrari's gradient and the vertical change in height over the final 9km are completely different.  Which is reality?  You have to believe the SRM.  Also, given that Horner is riding at 5.4W/kg, is it feasible that he "only" concedes 1:46 to guys supposedly riding a full 1 W/kg faster?  No, it's not, and so Contador and Schleck cannot have been at that power output.  And therefore, all Ferrari's assumptions and resultant calculations are doubtful.

The tactical battle - two ways to explain the racing

One final point about what Ferrari writes in that piece:
"the heat influenced the development of the TdF 2010, making the riding all the more demanding and hard, forcing the riders to measure out energies carefully, growing thinner and thinner every passing stage...None among the favorites dared to attack far from the finish, especially on the mountains, just as no team was really capable to make the race hard and selective in the first phases of the stages. "
Ferrari's observation can just as easily be explained by a reduction in the ability of riders to recover from one maximal effort to the next.  We know that doping improves this ability enormously - it improves the ability to sustain high power outputs and relative intensities for longer, and it enables repeat bouts at higher intensities.

Therefore, some of the hypotheses around a "cleaner" Tour would be that:
  • The same rider will not attack every day.  The "cost" of attack prevents this.
  • A single team with the identical cast of characters will not be able to dictate the tempo on the entire climb every day, and their ability to ride up more than 50% of the climb will be reduced (remember the days of three or four men from one team reaching halfway up a climb?)
  • When attacks are made, they have to be delayed, because the physiological/energy cost of attacking early and then sustaining 6 W/kg or higher for 40 minutes is excessive
  • The attacks themselves will be 'muted', at a lower power output.
I would argue that all three have happened, and not just in this Tour, but in the last two or three years, and in other 3-week races like this year's Giro.  It's not only the 5% to 10% reduction in power that is telling, it's the way races have evolved.  Look at Andy Schleck on the final climb - his hand was forced by the race situation - he had to attack early (9km to go is still later than some attacks back in the 90s and 2000s), and for his efforts, he and Contador paid so much that the chase group held them over the final 5km.  Their maximum effort was not sustainable.  And that's expected of physiology.  Doping, on the other hand, would allow it.

So the point is that Ferrari has blamed the heat, but there is another possibility, which must be acknowledged.  And sure, it's been hot.  I would argue that France in summer is always hot, and some basic thermophysiology is that heat is far less an issue on the bike than in running.  It's important, yes, but the thermal load produced by a temperature that is say 1 to 2 degrees higher than normal is not sufficient to produce these changes. 

I believe the more likely explanation is linked to what we (and NY Times, New Scientist and even Jonathan Vaughters) have pointed out, that performance suppression indicates a cleaner Tour.  Ferrari may have a different take, but then he did once suggest EPO was as dangerous as orange juice...

Enjoy the time-trial later!
Ross


 

52 Comments:

Anonymous said...

You've made a good number of posts that suggest that this year's tour is cleaner than some of those in the past, but the evidence presented seems to me to mainly suggest that there is less use specific, and clearly effective, doping techniques, EPO in particular, not that these riders are really clean. Watching the final time trial - with no scientific analysis whatsoever - my impression was certainly that things were not as they have been since at least before the time of Lemond - there did not seem to be so many out of the ordinary final day performances, particularly for riders for whom it mattered. Which is to say - I am buying that they are riding cleaner - but I am not buying that they are riding clean.

A question: is it plausible, physiologically, that Contador and Schleck are substantially better than everyone else on the difficult climbs? Is the difference really so significant?

The cynic in me is starting to think that all the great athletic champions of my lifetime, the singular performers a touch ahead of everyone else, were dopers (in some sense) ... going back at least to the 1970's.

Ross Tucker and Jonathan Dugas said...

Hi Anonymous

The cynic in you is not alone - the cynic in me feels similarly. However, I don't think it's the case that EVERY one is a doper. The one point I must make is that the margin between 1st and 2nd (or in the case of this Tour, 2nd and 3rd and 4th) is actually really very small. We're talking about 3 to 5% differences at very specific moments of the Tour. Even on the Tourmalet climb, Horner and the next best riders were beaten by 1:45 on a 50 minute climb - less than 4%, and most of that gap was established in a few kilometers of attack, after which the gap was held constant. And this is certainly physiologically plausible - 5% more power for literally 20 minutes on two or three days in the entire race. It's tiny, but the way the race is timed, seems larger than reality.

Where I think there are grounds for suspicion is exactly what you have pointed out - the out of the ordinary performances from the same people day after day, the riders who mattered. You've hit on a really key point there, and that's that the allocation of energy over 3 weeks is crucial, and is altered by doping. What we're seeing this year is a much tighter race. Think back for example to the mountain stages - the gaps you see on the GC were set up on two days - the Tourmalet and the Madeleine. Every other climb, Menchov, Sanchez and co were able to climb with Schleck and Contador. Even on the Port de Bales, Contador couldn't drop Menchov and Sanchez. He only succeeded on the Madeleine and Tourmalet.

So my impression is that while there are two great cyclists, the difference between them and the others is tighter than in the past, it's a dogged race, attritional, whereas days gone by have seen the same riders dominant day after day, all the way to the time-trial.

So to conclude, you're 100% correct. And I apologize if I've given the indication that the Tour is clean. I don't believe it is, because doping will of course always happen. But I think it's certainly cleaner, and the signs of change are there, and I think that is very positive!

Ross

Frans Rutten said...

I rather focus on time trialling versus climbing. At the pinnacle of the so-called doping era the final long time trial has always been very enlightening. However, the 2005 TT has a moderate climb. But the 2003 49km flat TT clearly fits to be compared with this year’s 52km flat TT.

Clearly this year’s TT was partly for some riders harder due to the wind. IMO, it should be about 2km/h loss, which is still quite a distance (say a mile).

Averages for 1st/10th/25th/50th/100th/148th (last rider in 2003).
2003: 54,36-53,96-52,04-51,22-49,92-46,06km/h
2010: 51,20-48,32-47,24-46,18-45,22-43,96km/h

Within 1st rider (%) for 1st/10th/25th/50th/100th/148th/170th (last rider).
2003: 0-2,58-4,28-5,78-8,18-15,27% (148th) of the 1st rider
2010: 0-5,63-7,75-9,82-11,69-14,14 (148th)-16,22% (170th) of the 1st rider

Riders within 1% of the 1st rider: 2003 vs 2010: 5 versus 2 riders
Riders within 5% of the 1st rider: 2003 vs. 2010: 36 versus 7 riders

Tricky, but 21 riders did both TT. Only one rider (Koos Moerenhout) did beter: 48,46km/h (10,85% off) vs. 48,76km/h (4,77% off). On average these 21 riders were 5,49km/h slower.
In comparison with the 1st riders: 5,10% off vs. 9,98% off.

This isn’t solid statistical work, since you cannot exactly pinpoint all the factors involved.

But one thing in these kinds of evaluations is always striking.

In the so-called doping era the broader top is in absolute sense always better, but still rather tight, before performances rapidly begin to decrease. Nowadays the broader top is all but tightening, but performances then don’t decrease so much. For me this is the flag, that in the past at least half of the peloton doped.

Sigmund1 said...

First off I must congratulate you on a fantastic site. I have been following it closely since I discovered it during last years TdF. I think the way you mix science and well founded (and articulated) opinion all the while making it accesible to us non - scientists out there is fantastic. That doesn't mean that I agree with you all the time, though, and I quite strongly disagree with your cycling performance limits.

First, from where does the number 6,2 w/kg come from? I have not seen any particularly convincing argument from you as to why this should be the limit and not something higher (or lower). I think, however, that A Coggan argued quite convincingly in the debate on Cyclingnews for why this, as a limit, is way to low.

Also, I think you yourself are a bit inconsistent when comparing this limit to other sports. Last year you posted that you think Usain Bolts performances are clean (and personally I agree) but if one were to identify some kind of performance limit for the 100 m surely this would be quite a bit slower than 9.58? I mean comparing to historical performances we know that just about every run below 9.90 done from the late 80's till app 2000 were done by athletes who have either admitted or been caught doping.

I think this is the biggest problem with the concept. That every time a unique specimen comes a long they will fall foul of previous limits, and as such have their performances groundlessly doubted. I think we must humbly admit that we do not yet know enough about human physiology to set such limits (I am not saying that cyling has been clean the last 15 - 20 years, quite obviously most hardly any of the great performers competed clean) .

I must also say that based on my own performances 6,2 w/kg sounds very low. I am an ambitious week end warrior competing as pack fodder at the highest level in Norway (nr 37 TT Norwegian Championsship). I am 36, have a full time, rather demanding job and have only trained seriously for 6 - 7 years, yet I can do app 5,5 w/kg for 20 min in top shape (my point is not that I am very good, there are plenty of weekend warriors much better than me). Given this, and that I am too tall and heavy (192 cm and 78 kg) for and optimum cycling body, I think 6,2 w/kg sounds pretty low for the best in the world.

I also think you make too big a point out of the fatigue issue. The GC team leaders are very well shielded from the wind and I'd venture that every stage except the mountain stages and the TTs are pretty much active recovery intensity for these guys. They spend 20 - 30 hours a week on the bike all year so that the TdF app. 90 hours in 3 weeks and app. 9 really hard stages aren't that much more than a regular training week. Personal experince also tells me that how the body reacts to big doses of high intensity training is very unpredictable. I have had some of my absolute best days on the bike at the end of very hard training periods (and some of my worst).

This became a very long comment, but summing up I agree with you in that the performances this year indicates that the peloton is racing pretty clean this year, but I think the performance limits at the very least needs a thourough re think.

On a different note I would love for you guys to tackle the issue of why doping is forbidden in the first place, or more specifically why the list of forbidden substances looks like it does.

As there are quite a few performance enhancing substances which are legal, and quite a few of the substances on the list are reular medicines there must be more to it than athlete safety and artificial performance enhancing per se. I would also love to know how bullet proof the tests really are. I mean, if they're 99% certain to not return a false positive this still means that there must be quite a few false positives out there.

You did a couple of posts last year where you touched on this issue and I think the topic merits much more attention.

Anonymous said...

Brilliant. Great analysis and a bit of a turn around I must say on the last few years of your comments, where you've used VAM and observations of the race to say that in your view nothing had changed, and imply everyone was cheating.

Glad the SRM data is finally giving us an unbiased point of view.

Ross Tucker and Jonathan Dugas said...

To Anonymous at 1:29PM

"Have you included the cobblestones that drained and injured many people in your calculations ?"

How exactly? And do you have any reason to think that the cobblestones were any more draining than a hilly road stage? Because I don't - I've seen the SRM power data, and what I will say is that the cobbles required a really high intensity, high power output for 5 to 8 minutes at a time, but when you're riding in a small pack like Schleck and Contador were, this has a negligible effect on the overall effort.

A typical day in the Pyrenees or Alps is much more difficult than this day. As for injury, yes absolutely - I didn't bother analysing Frank Schleck's performances. Any one else injured in the GC race?

"And as a new part of the Tour, have you calculated when Andy and Alberto allmost stood still in a tactical move ?"

Yes of course - I explained the importance of this in the post, and have widely acknowledged that their power output would be lower here. Menchov and Sanchez did not however get caught up in this, and they gained 1 minute. Given the narrow margins between Schleck, Contador and the other two, I would argue that their tactics affected their overall performance by a little less than you'd like to believe.

But, what you should really be asking is "Why did they need to play this kind of tactical game?" In days gone by, they'd have attacked at 8W/kg, settled to 6.4W/kg and just ridden everyone else off their wheel. That's no longer happening - 9km was the longest attack of the race.

And finally, this post was on the Tourmalet, and if you believe that tactics affected this particular stage, then you're watching a different race. The only tactics on this climb were to ride as hard as possible. This was a max effort, and still only it reached 6W/kg.

"Have you included that there are no real climbers in this years tour, the best we have is Alberto and Andy ?"

This is really reaching for it, sorry. Contador is one of the great climbers of the last decade. Schleck is now equal to him. So the race has two of the great climbers. And then Menchov, Sanchez have been only 2 to 3% off them. So to say there are "no real climbers"...which race have you been watching?

"Have you included that this years race have been run in 40 degrees for most of the stages ? "

Yes, indeed. Welcome to France in the summer. I'm afraid this is the Ferrari/Armstrong school of performance analysis. France is always hot. I was at the Tour is 2004, 2005 and 2006, and I can assure you, it was very rarely less than 40 degrees in the sun. If you have data to show that it's 4 to 5 degrees hotter, then produce it. But I believe it was hotter, but not crippling heat. Typical of a French summer. This can at most account for 1% of a decline, in my estimation.

On the whole, you're right in principle that there are a lot of factors. But you're grabbing at straws a little, when you name these specific factors. My position is based on the balance of the tour, where assumptions can be controlled for or at least quantified.

Ross

Ross Tucker and Jonathan Dugas said...

To continue from above:

I think it's important to note that not a single rider has produced 6.2W/kg (in fact, I can't find a 6.1W/kg) in this Tour on climbs longer than about 20 minutes. The short 10 min pull to Mende was at 6.6W/kg, but that's physiologically expected - you're at 100% for that short a duration.

So if this figure was 'way too low', as Coggan has suggested and argued, then we'd be seeing it. I don't put much stock in his argument, I'll be honest. According to that model of thinking, the marathon should be run in 1:58, and I don't think that is going to happen either.

On the Tourmalet, where Schleck had to go as hard as he could, only one other cyclist could go with the power, and it was less than 6W/kg...that's very telling to me. I'm pretty confident that they're on the limit, and so 'way too low' is ignoring the obvious - it doesn't happen.

Oh, and just to respond about Bolt. Studies have been done on the limit to 100m sprinting - mathematicians and statisticians are always working out modelling equations, and their figure is 9.48seconds. So Bolt is within the realm of 'plausibility'.

No-one has really modelled what should be possible in cycling, but I guess, in a sense, that's what this whole debate is intended to do! And my 'model' says that riding at anything much above 6 W/kg for around 40 minutes at the end of a 5 hour ride (call it 6.2W/kg like Sassi, or 6.4, whichever), starts to challenge every observed and known concept in physiology.

I know it's not definitive, and you're 100% right - no one can, or should, be found "guilty" based on performance. But I think what the last few weeks have shown, by way of comparison, is that something is different. Performance analysis has shown this - riders were regularly above 6.2W/kg, even up to 6.4W/kg, and now they are riding most climbs in the mid 5s, finishing climbs around 6W/kg. So that drop-off, and the physiology that I believe underpins it, is what leads me to suggest that a) the performances of the 90s and 2000s were not credible, and b) the performances this year are MORE credible, and 'cleaner' - not clean, that's impossible to say too, but I take heart from the change!

Lastly, your suggestion of a post or two on doping and ethics and whether it should be allowed is duly noted - that is something we must definitely discuss. We did do an interview with Bengt Kayser on this topic, I'm not sure whether you read that post:
http://www.sportsscientists.com/2009/07/very-different-view-to-anti-doping.html

Something to cover again in the future, for sure!

Thanks again for your balanced and well put views! Much appreciated!

Ross

Ross Tucker and Jonathan Dugas said...

To Sigmund

My apologies - it seems our gremlins have now affected my posting - the first part of my response has been lost in the ether somewhere...

So the post above is the second part, this is the first (sorry for doing this backwards)

Thanks for your comments, much appreciated and I appreciate the balanced approach.

I'll try to respond briefly...

First, the 6.2W/kg, I must take great pains to point out, is not a definitive line in the sand that divides dopers and non-dopers. I apologize if it came across that way. What I was trying to argue there is that there comes a point (or rather, an 'area') where performances begin to create physiological implausibilities. That point, based on my reading, the views of Aldo Sassi, and also athletes that we've worked with, lies AROUND 6.2W/kg.

It would be completely foolish to say that a rider who produces 6.25W/kg is doping, but a rider who does 6.15W/kg is not. And this is not meant to happen. Rather, the issue is that there is a power output, which I believe to be in the range of 6.2W/kg, where physiological implications become 'unrealistic'.

For example, if I take your 5.5W/kg - the 'cost' of that power output is about 64 to 66ml/kg/min, assuming a normal efficiency. Because you do it for 20 minutes, I'd assume that it represents 90 to 95% of your max, which means your max capacity is likely around 70 to 75 ml/kg/min. We test decent athletes at this level often. They're good, not dime-a-dozen, but they exist.

6.2W/kg on the other hand, creates a problem. The 'cost' is around 74 to 77 ml/kg/min. And if a rider can hold this for 40 minutes, then you have a real problem, because either their max capacity is HUGE, bigger than anything seen, or their ability to ride at 100% VO2max exists, and this too is just not seen.

And I know that Andrew Coggan has tried to make a case for 9W/kg. If I may offer another sport, a running biomechanist suggested last year that based on "theory", humans could run 100m in 6 seconds...right.

The problem is that if you apply this kind of 'extreme' principle theory, you get extreme possibilities, and all you have to do is look at actual performances to know that they don't exist. And therefore, as I've said above, to say that there's a strong case that 6.2W/kg is "too low" is ridiculous - the obvious observation of the Tour is that the very best in the world don't get up to 6W/kg for very long, never mind 6.2W/kg, and certainly not 9W/kg as theory suggests!

And finally, for this part, the fatigue issue is significant. Look again at Horner's data - even sheltered like the GC riders, he is producing 300W or more on three climbs leading up to the final climb. That effort is not free and so fatigue is the result. It may be less than for you or I (for me, much less), but it's there. So to produce 90% for 40 minutes at the end of a day where they've done that much work (average power output over 200W for 6 hours), not feasible. That's why I'd work with 85% and then you get these implausible figures.

The rest of my response is above...sorry about that!

Ross

Ross Tucker and Jonathan Dugas said...

To anonymous at 10:40pm

As am I. I think last year, when we first looked at this issue, we did lack the context the SRM provides, and so it's been a relief to have it, both the somewhat re-inforce the VAM method and to provide discussion without speculation.

I will say that last year, the initial discussion on VAM was to suggest that some of the accusations about, for example, Contador having a VO2max of 99ml/kg/min were flawed. And so we actually began trying to provide a more balanced view, to say "hold on, this method can't be too stringently applied, there are assumptions".

But then it soon evolved into comparison with previous Tours, and once you look back on the Tours of the 90s and early part of 2000s, before the biopassport and 'policing' (literally) of doping, you got these physiological implications that kind of demanded discussion.

And now, one year on, that same approach is suggesting a reduction in power, and this is great because of the SRM. So we're trying (and no doubt failing!) to report the whole story, with my obvious opinion and hypotheses, but it has been a good exercise, I believe, if only because of the awareness and discussion it's produced!

Ross

Anonymous said...

hello,

love the blog I've been reading for a while. I came across this article on VO2max
http://btc.montana.edu/olympics/physiology/pb02.html

and I thought the graph close to the end was interesting, it implies that cross country skiers maintained a pace at almost 100 percent of VO2max for half an hour and were close to 90 percent of VO2max after an hour. Theoretically (if the results are applicable to cycling) it seems a cyclist should be able to average a power output around 95 - 100 percent of their VO2max for a climb of one hour. (I averaged the percent VO2maxes) Of course this is not counting the effort spent up to that point in the course / previous days.

Would this change your estimation of 6.2 Watts / kg as the maximum physiologically possible for a ride of one hour? Does it possibly Explain Lance Armstrong's power output time trial on the Alpe Huez?

Anonymous said...

How much Hb mass does it take to produce 6.2 W/kg for 30-40 minutes and why?

David Barry said...

Am I being too cynical in thinking that Ferrari is throwing out numbers like 6.4 W/kg to make it sound like you guys (Tucker, Sassi, ...) don't know what you're doing when you give 6.2 W/kg as a pseudo-limit?

Anonymous said...

I dont know if this question has been raised before: what do you think of Indurain's stratospheric performances both in TT and climbs (these ones mainly in his last years), specially cnsidering most of his rivals has admitted being doped by those years. Is there any SRM/VAM/VO2max analysis available?

Great work,

Ross Tucker and Jonathan Dugas said...

Hi Anonymous at 1:50AM

Thanks for the link. To answer your qeustion: It doesn't change it - I've used a similar principle from running and cycling to estimate the relatively percentage of max that a cyclist could sustain. We know in running, for example, that a 10km race is done at between 85 and 90% of max. That lasts 30 minutes, roughly, which is where the 85 to 90% assumption for a cyclist came from.

The cross country skiier, incidentally, is the same as marathon running incidentally - a marathon runner is at around 80 to 85% for two hours as well. I've not seen such high relative intensities for shorter durations, though I would surmise that this has to do with the nature of the sport and involvement of a larger muscle mass. That's conjecture though.

But my assumption (and it is this) is that a cyclist will sustain 85% during the final hour of a five-hour ride. And I must confess, I think this is too high, I think it's an over-estimate, but it's to give the benefit of the doubt.

The reason I think this is because we know that a cyclist can't sustain what one might call their threshold power for longer than about 15 to 20 minutes. THe SRM data confirm this because Chris Anke Sorensen was riding 415W for maybe 10 to 12 minutes before peeling off, and his FTP is around 410W (their numbers). Now, that FTP is measured in different ways, making comparison difficult, but it's often around 90% of a max. So here you have a top level guy riding 90% of max for 10 minutes. Then he's done. So to ride 90% of max for 40 - that requires something else.

But you raise an interesting point (thank you), and it does highlight (again) why there can't be this dividing line in the sand. I fear that i may have made it appear that way, but this was never my intention. Rather, that 6.2W/kg is maybe the start of an area of 'doubt'. A guy at 6.1W/kg could just as easily be doping as a guy at 6.2W/kg is not! So you can never commit, precisely because there are these assumptions.

However, on the balance of ALL the climbs in this Tour, and the numbers from the 90s and 2000s, it's telling that not a single climb this year touched 6.2W/kg for more than 25 minutes. Even Ax-3-Domaines, which is short, didn't get there. So the 6.2W/kg was "out of reach" for this group of riders. Why not those of the 90s and 2000s?

And regarding Armstrong's time-trial, yes, it's possible. I've seen conflicting reports on the power he produced there, by the way. Some are saying 6.4W/kg (which is super high), but others are even higher - I was at a conference in 2004 where a phD student had modelled the entire climb, and wind directions, and worked out 6.9W/kg. So even the benefit of the doubt takes you to 6.4W/kg - that's massive, but again, not definitive proof of anything. It's part of a larger picture to me, the whole sport at that time.

Thanks!
Ross

Ross Tucker and Jonathan Dugas said...

To anonymous at 3:04AM

I don't know. I don't know that there is a figure - 48% maybe would be enough, if a rider is normally at 44%.

But I don't think hemoglobin holds the answer. I'd rather be looking at a study on the effects of EPO on performance, done a few years ago.

That study found that EPO improved sub-max performance FAR MORE than it did maximal performance. NOw this is really important, because one might expect that maximal performance (VO2max and peak sustainable poweroutput) would be affected most if you increased oxygen carrying capacity.

But it wasn't - the effect on the ability of the cyclist to ride at a high poweroutput for a long time was far more improved. So practically, this means that that doping (and possibly blood doping) would improve performance by allowing a rider to sustain a given power output for much longer before exhaustion. The application to climbing is obvious - when they hit the bottom of a climb and suddenly ride at 6W/kg, the race is all about who can hold it the longest, or who has to drop off.

In the past, guys have held 6.2W, 6.3, up to 6.5W/kg for 30 minutes or more. Now, we're back down to a lower sustainable power and this is just what the EPO research would have suggested would happen.

Ross

Ross Tucker and Jonathan Dugas said...

Hi David

The thought had crossed my mind! I don't know if Ferrari reads this. I'm sure he knows of Sassi's views, but whether he knows ours, I don't know...

To repeat what I've said before though, I think it's really telling that all the longer climbs at this year's Tour were done under 6W/kg. Never mind 6.2W/kg or 6.4W/kg, they're under 6W/kg.

Now I simply cannot believe that Schleck and Contador were NOT at the limit on the Tourmalet - that was as hard as it gets for that length of time, in a race that demanded it. I dare say the time-trial performances showed this two days later. And there, you had them riding maybe 6W/kg. So when one talks about a limit, the much-maligned 6.2W/kg (which was an indicator, not a dividing line) suddenly takes on some context...

So I don't know - all I know is that Ferrari's method, whether deliberate or accidental, disagrees with the SRM. So maybe the SRM for Horner is off. But I'm more inclined to think that maybe Ferrari makes a different calculation.

Ross

Frederic Portoleau said...

There is an error on Horner SRM graph.
The attack of Andy Schleck was not at 9.3 km but at 11 km to the summit.

So Horner did more than 5.9 watts/kg
and Contador/Schleck more than 6.0 watts/kg from the Schleck attack.

Drafting and tailwind explain for me the difference of power between Sorensen and Horner during the first part of the Tourmalet.

-Tailwind of 20 km/h from North before Luz Saint Sauveur.

-weak wind after Barèges

Frédéric Portoleau

Frederic Portoleau said...

correction of my message:

Drafting and tailwind explain for me the difference of power for Horner between the first part and the second part of Tourmalet

Ross Tucker and Jonathan Dugas said...

Hi Frederic

Thanks for pointing that out.

I am not sure that it means that Horner rode 5.9W/kg for more than just the attack. The SRM for the last 9.3km clearly show that he rides 5.4W/kg, and even the addition of those 1.7km at about 400W (on the graph in the previous post) does not increase the power output enough to say 5.9W/kg.

If anything, Horner rode at 400W (6.3W/kg) for only about 4 minutes, and then dropped right off that level. As did Contador and Schleck, since the time gaps remained more stable.

The issue for this particular post is that Ferrari has worked out 6.4W/kg for the final 9km - the fact that Schleck attacked sooner actually makes this even less plausible, because now, the section he has analysed doesn't even include the big attack. And so this doesn't really change the overall picture, in my estimation.

The total power output for Horner on the climb is still 5.6W/kg, and thus not more than 6W/kg for the leading riders, irrespective of where the attack took place.

Thanks again for the post!
Ross

fxg said...

I’m waiting to see the standardized calculations of Porteleau, but it does seem that the power output dropped significantly from last year. To me, this is an important red flag as we are comparing apples and apples. But are we? Allan Hunter on hometrainingpeak and the SRM website argued that many intermediate stages were ridden at a much higher intensity than expected for such stages, maybe combined with the heat it can explain part of the power drop. I also think that looking at the evolution of the number of riders above a given power output, as Porteleau does, is telling. However, pointing at an individual based on its power alone is very risky. Also, I don’t understand why having a tight race means a cleaner race. In every sport there is always an individual who, once upon the time, rise above everyone else for a long period (think of Gretzky, Jordan, Woods, Federer to name of few). Why should it be different with cycling??? Besides, you still have to reply to my previous comment on Santalla et al. studies. I do understand that you receive many comments and I am already quite impress at the number of replies you post, but this question is the keystone of your entire argument. Your inference of doping for riders above 6.2 W/kg rest on the crucial assumption that the efficiency does not vary much between top-level riders and does not improve with time. It was perfectly legitimate to do that before reading Santalla et al. 2009, but in one of your post written a while ago, you did mention having read it. So now you can’t simply continue the same arguments without first putting solid arguments against their study. To put things in context for readers not familiar with that study, they tested 12 world-class Spanish riders, including podium winners of big Tours, for a period of 5 years with the same protocol, machine and at the same time of the year. They documented an average increase in efficiency from 23.61% to 26.97%. Their Fig. 2 shows a graph of efficiency vs VO2max and what is impressive is the wide range for both of these values with efficiencies ranging from 21% to 32,5% and VO2max varying between 63 and 88%. Using your method of calculation, one finds power at 85% VO2max varying between 5.9 and 7.1 w/kg for the average weight of the riders. Many of these riders were most likely on a doping program, so this must have screwed the VO2max calculations, but would this affect the efficiency?

Finally, I have to mention that the improvement in climbing power of Armstrong that you posted on your website fits perfectly the improvement curve in efficiency published by Coyle if one assumes that his VO2max stayed at 85 ml/min/kg and that he was climbing at 80-90% VO2max. You convinced me of the poor methodology employed by Coyle, but in my eyes, Santalla et al. study lends credit to Coyle’s. Hence, the perfect fit is either an amazing coincidence or is telling that the extraordinary performances of this individual were within the realm of “plausibility” as you stated for Bolt. Here are the numbers:
TDF99 : 396-445W
TDF00 : 400-450W
TDF01 : 405-455W
TDF04 :419-471W
Now let’s compare these values with the range of calculated power presented on this website :
TDF99 : 387-436W
TDF00 : 406-457W
TDF01 : 411-452W (Plateau de Bonascre at 475W)
Alpe d’Huez04 : 465W
I’ m not negating that there was (and probably still is) a serious doping problem in cycling and I agree that there are many circumstantial evidence against Armstrong, but I am just not convinced of you scientific arguments.

smicyl said...

I suspect Dr Ferrari is normalizing the power outputs to 1000 meters. The Tourmalet is over 2000 meters and Ferrari mentions elsewhere that power output declines about 3% per 500 meters.

Ross Tucker and Jonathan Dugas said...

Hi fxg

I'm in the middle of student oral exams, so don't have a lot of time to respond.

However, I just want to emphasize the comments I've written above, and in the previous posts, to answer your questions. Note that I'm trying very, very hard to point out that 6.2W/kg is NOT a definitive line in the sand - it was never intended this way, and I have tried as hard as I can now to point out the approach. i apologize if it came across as a dogmatic "6.2W/kg is doping", because that would be risky, and wrong.

But I've said this maybe a dozen times in the last two weeks, and I've tried very, very hard to explain what I was (and am) getting at.

I think, to repeat myself again, that the fact that this Tour has not seen efforts of 6.2W/kg for more than 30 minutes is very telling. At the start of this Tour, I said that 6.2W/kg represented the start of a grey area, and that the 90s and 2000s lay in the 'black', to the right of this area, where I felt doping was likely based on performance. I did not put this forward as proof - rather, I did everything to say that it WASN'T proof.

But now that this Tour is over, we have data and we see that no days were done at above 6W/kg. Even the race's decisive day, with maximum motivation. I think the Tour's performances have validated the theory to some extent. So, coming to that efficiency, the Spanish efficiencies are highly debated - Lucia et al first found such high values, and Jeukendrup argued them in the literature. I don't know the ultimate resolution of that case, I must look into it again.

But, if we assume 27% efficiency, then yes, 6.2W/kg becomes more feasible. Strangely, however, no one is doing it. If these guys were riding at 27%, with VO2max values of 85ml/kg/min, then 10 guys would be riding at 6.5 W/kg. The obvious implication of the actual race performance thus 'validates' many of the assumptions I made (and ackowledged).

So to conclude, I'm 100% in agreement with you that this is not proof of anything. It's one of many arguments, and I think, now more than ever, that the current level of the Tour indicts the previous Tours, and vindicates the physiological theory.

And I've steered clear of singling out historical performances of individuals in this series on performance analysis, precisely because of this problem. However, when I look at this year's best guys, at their limit at 6W/kg, I have a tough time believing anyone at 6.4W/kg. That performance, incidentally, would beat Contador and Schleck by about 2 minutes...

So either Contador and Schleck were really poor (as was the class of 2010), or performance reveals a flaw. Again, not proof (sorry to be repeating myself...)

Thanks for the comment! Gotta dash!

Ross

Andrew R. Coggan, Ph.D. said...

"So if this figure was 'way too low', as Coggan has suggested and argued, then we'd be seeing it."

Please don't go putting words in my mouth. My *entire* point is and always has been *no one* knows *precisely* where to draw the line as to what is/is not physiologically plausible. That is why I have never responded to requests that I do so myself.

Andrew R. Coggan, Ph.D. said...

"And I know that Andrew Coggan has tried to make a case for 9W/kg."

And there you go again. Based on such comments, I can only assume that you have either missed my points entirely, or that you are being deliberately disingenuous.

To reiterate (for the 3rd or 4th time): 9.04 W/kg is the figure you derive for maximal sustainable power if you use an approach directly paralleling that employed by Mike Joyner in modeling marathon performance in his paper in J Appl Physiol. My point in mentioning this figure is not because I necessarily believe it (as I stated quite clearly at the time), but simply to illustrate the broad range of values that are at least theorectically possible depending upon your starting assumptions.

Ross Tucker and Jonathan Dugas said...

Andrew:

"Way too low" is quoted because Sigmund used the words and this response was to him, not you.

You did very much argue that 9W/kg was a theoretical limit, and so Sigmund has (quite rightly) pointed out that 6.2W/kg is too low. I fully understood you, and that it was based on "starting assumptions". Just like last year, someone put forward the theory that 100m would be run in 6 seconds, based on some assumptions...

I wasn't aware anyone had asked you to draw a line. It's a pity you didn't though because it's an opportunity to initiate valuable discussion about principles and make progress, and ultimately, there is some point at which the discussion bears fruit. A line in the sand? No. But sometimes taking a stand for the sake of a bigger picture contributes something.

Ross

Anonymous said...

Junk in, junk out. Garbage science.

Ross Tucker and Jonathan Dugas said...

To anonymous 6:05 PM,

Ok, fine, you disagree with our analyese and our science. You are most definitely entitled to that opinions, but to log on and post a critical comment in an anonymous fashion accomplishes absolutely nothing.

If you feel there are problems/errors/limitations that cause this to be "garbage," then please produce an argument to outline why you hold such an opinion.

Taking anonymous potshots from the gallery is pointless.

Kind Regards,
Jonathan

Anonymous said...

TO Anonymous:

You are obviously a vastly superior human being, with intellect that none of us can comprehend. So what a great pity you aren't more specific or actually constructive in your opinion, to the point where you, the "non-garbage" peddler, could actually help with the discussion. Instead, you simply dismiss it because presumably you haven't bothered to read the entire series, or because you've been drinking Lance's Koolaid for too long?

Ken

Andrew R. Coggan, Ph.D. said...

Ross,

My apologies - in skimming the numerous comments, I missed where he had previously introduced my name into the discussion.

Still, you seem to be missing the point re. the 9.04 W/kg figure: I arrived at that not just by making some assumptions, but by making assumptions for the same variables that we all agree/know are key (i.e., VO2max, % of VO2max sustained, gross efficiency) *and* by following a previous precedent in the scientific literature. IOW, I was most definitely not trying to make a case for that number as you claim, but to emphasize just how dependent the final figure is upon one's starting assumptions.

I do not recall in what context someone asked where I would "draw the line", but as I indicated, I did not respond because I do not think it is legitimately possible to do so.

G Skillet said...

Regarding the Orange Juice jab at the end of your article. Not to defend Ferrari or doping or EPO, but for the sake of accuracy, Ferrari was not saying that EPO was as safe as orange juice, but was using (an albeit silly analogy) for the "the dose makes the poison".

Anonymous said...

Can someone please help me, Im trying figure out Andys VAM after his chain feel off on Stage 15.. heres what info I have ...

21.9 km-16.4 km =

450 m attitude/height it says on climybike.....

http://www.climbbybike.com/climb.asp?qryMountainID=7057

Andy climbed time : 5:08 minutes

ohh if needed over the 4.5km the gradient is around 9% on average.........

Heres is the climb.....

http://www.youtube.com/watch?v=kId8VvKKwgo

I'm new to this but really find interesting, its great reading...

281

Anonymous said...

The time of 5:08 might be wrong, proably is... I got the time from a youtube video.. can anybody help me? (;

Kaz..

Ross Tucker and Jonathan Dugas said...

Hi Kaz

I think the distance is wrong - it can't be that he climbed 4.5km in 5:08.

The SRM data from Horner and SOrensen (see Post 1 of this series) show that the climb overall is 19.3km at a gradient of 5.7%. I would go with this as the most accurate.

And then maybe work backwards. Earlier in this thread,Pierre worked out that the climb was 155m and that he did it in 5:04, which gives a VAM of 1836 m/hour. That is in response to our latest post, by the way.

So I think your time is correct, but the distance and the gradient and vertical climb seem off to me...

Ross

Frederic Portoleau said...

Excuse me for my error. It was not "more than 5.9 watts/kg" for Horner but "more than 5.5 watts/kg".

Frédéric Portoleau

Christ said...

I had an even more cynical take on Ferrari's estimates: I think he posted his estimates in order to calibrate his overall estimations of power output higher than yours. That way, it can be argued that if your assumption of 6.2W/Kg is a nice theoretical non-doping limit for a typical Tour mountain stage, well, that is approximately the same as a Ferrari-esque estimation of 6.7W/Kg. So, you see, his Lance estimates were simply miscalibrated and really are in line with yours!

Mike said...

This is posted in the spirit that the only dumb question is the one you don't ask so please forgive my naiveté. I am not familiar with the SRM device but I presume that like most scientific instruments it requires calibration. Throughout your analysis you place great reliance on the SRM data so could you give an estimate of the tolerance of the power numbers. Thank you.

Ross Tucker and Jonathan Dugas said...

Hi MIke

That's a good question actually. You're quite right that it would require calibration. If not calibrated, then all bets are off, and so this is important. now obviously, one has to assume that they're calibrated, and it's not possible to get Bjarne Riis on the line to ask just how sure he is of their team's units!

However, there are a couple of things that re-assure me: One is that all the riders using them are producing similar values when riding together. So Sorensen and Horner, in the bunch, are riding at more or less the same power output, same speeds, same gradients - it is not as though one is reading different to another. Similarly, with the other riders, you can check and find reasonable agreement between different devices.

Second, the values they're producing match well with methods of estimation. This is a somewhat circular argument, but the estimations are based on real power output values, measured using SRM, so when you then have the SRM, and you're measuring values very similar to those calculated, then either the estimations were done with faulty devices too, or the SRM is calibrated the same, correctly.

In terms of variance, I'd be lying if I said I knew it was 2%, or 5% or 10%. So this is an important point. But the estimations are producing lower power outputs, as are the SRMs, so it's a start!

Ross

Anonymous said...

I look at the podium of the TdF in 1989 and see Greg Lemond in front of 1 self confessed doper, and another proven doper...yet Greg vanquished them riding clean...why does he whine so much? People might finally start to believe him if he admits to his own doping. Hopefully he can have the fortitude that Landis has to admit what is obvious to anyone that follows his own doctrines...that he himself was a doper.

Mike said...

Thanks for taking my enquiry seriously and also thanks for a great site and all the work you do. I just discovered it and have joined your mailing list.

As you acknowledge the importance of calibration, I persued this further and found two sources of information on the accuracy of the SRM's. Firstly, the SRM site (http://www.srm.de/index.php?option=com_virtuemart&Itemid=482&lang=us) gives the accuracy of the SRAM powermeter as +/- 2%. This is presumably as it leaves the factory and in their FAQ they emphasize the importance of checking the "zero offset" before each ride. So in the real world errors could be greater.

My second source (http://biketechreview.com/reviews/power-meters/61-power-meter-review) says "There are several fundamental sources of error that must be mentioned when using strain gages. These include temperature effects, strain field assumptions, and orientation of the gages/transverse sensitivity. Since the underlying structure will deform with a change in temperature, the strain gages will also sense these changes. Therefore, there may be a drift in the zero torque point depending on how warm or cool it is outside. Through clever design and increasing the total number of gages, it is possible to auto-correct these effects and minimize their impact on the final magnitude of the measured value. No system is perfect at accomplishing zero temperature sensitivity and this is perhaps one of the reasons why SRM recommends that the zero point be determined prior to every ride."

If we make the rather generous assumption that the zero offset was set in Pau to give +/- 2% tolerance, then it would be useful to know how lower temperatures as the climb progressed would affect the SRM accuracy. Presumably for the worse, as lower temperatures would increase the force necessary to bring about a given deformation of the strain guages. As this would affect similar devices equally, agreement between two SRM's doesn't confirm their absolute accuracy.

Since your calculation of Horner's W/kg and by extrapolation Contador's and Schlek's W/kg depend on the accuracy of the SRM power numbers and the weights of the riders, which is not known precisely, I think it would be appropriate to put some confidence intervals around the estimates. Whether or not they would amount to the 9% difference between your numbers and Ferrari's seems unlikely. So I think your main argument is valid:

* SRM data confirms ball-park accuracy of VAM
* VAM comparisons this year to previous years show decline in climbing performance
* decline in climbing performance is circumstantial evidence of a cleaner tour this year.

Thanks again for making this data and analysis available.

Mike said...
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Oops! The site said my post was too long but after several attempts I discovered it had been posted anyway. Hence the deletes.

Anonymous said...

"But I don't think hemoglobin holds the answer. I'd rather be looking at a study on the effects of EPO on performance, done a few years ago.

That study found that EPO improved sub-max performance FAR MORE than it did maximal performance. NOw this is really important, because one might expect that maximal performance (VO2max and peak sustainable poweroutput) would be affected most if you increased oxygen carrying capacity."

I don't get it. How does EPO being more effective at sub max efforts according to some study indicate that Hb doesn't hold the answer??? It's still about the hemoglobin! EPO is only performance enhancing because it causes the body to produce more Hb, or have I missed something?

Ross Tucker and Jonathan Dugas said...

Hi Anonymous

I guess it depends on the paradigm by which you want to explain the limitations in performance. The theory (not to create a straw man, but to explain it as I understand it) is that hemoglobin will improve performance because it improves the capacity of the blood to carry oxygen, thus delaying the onset of fatigue.

The problem is that EPO use doesn't improve maximal performance much at all. And if the hemoglobin is acting to improve maximal capacity, then this is where the improvement would happen. Rather, the biggest gains come from being able to ride at the same power output for longer. And this likely down to a combination of the increased ability of the body to defend homeostasis, but there must be another mechanism that works outside of hemoglobin. Otherwise, if a cyclist is riding at 90% VO2max, with almost full oxygen saturation, then how does increasing hemoglobin mass help them go further? Possibly because it enables the cyclist to maintain a given oxygen saturation for longer, in a signaling mechanism.

Also, EPO does not increase the hemoglobin levels by more than a few percent, yet the performance improvement in that study was enormous. So if a rider is going at 350W, or 90% of VO2max, then how does at 1 to 2 g/dL increase in hemoglobin produce a 37% improvement in time to exhaustion?

I don't know the answer to this, but the point I was making is that if you're looking for a one-to-one relationship between performance and hemoglobin, then you won't find it. And the initial poster to whom I was responding was saying that one should be able to just measure hemoglobin. It's part of it, yes, but not by itself the solution.

Otherwise, you could just issue bans on the hemoglobin levels.

Ross

Anonymous said...

1-2 g/dl is a 7-15% increase, not just a few percent. What does EPO do besides make the body produce more RBC's? A higher RBC count has to be the reason for the increase in performance. There is not some magical unobservable performance enhancing effect of rEPO just beacause you can't see a one-to-one relationship between Hb and performance. EPO and blood doping only works because it gives the athlete more RBC's. That is a fact. So if 6.2 W/kg for 30-40 minutes at 85% of VO2 max is indicative of hematological doping, then it must also be indicative of having an RBC count above the normal range, because otherwise it's not out of reach for clean athletes.

Anonymous said...

And there ARE bans on Hb levels as well as large variations in Hb levels.

Ross Tucker and Jonathan Dugas said...

To Anonymous

Semantics aside, your model cannot be entirely correct, and you're very quick to dismiss other possibilities. If the improvement in performance was solely due to increases in hemoglobin, then altitude training and iron supplementation, both which can increase hemoglobin levels by a similar relative amount (particularly when a person is iron-deficient to begin with) should produce a comparable increase. Yet it doesn't.

While I'm on this, let me ask you the following: If a cyclist is riding at 85% VO2max, then how does the increase in RBC actually improve performance? Given that the person is not at maximal aerobic capacity? I'd like to hear your thoughts, and not just "it is that way because it is that way" according to a book. I'm genuinely curious about this, because if performance is impaired by the limitation in oxygen delivery, then how does increasing RBC improve performance when delivery is not limiting at 85%VO2max?

As for Hb - the test is only part of the biological passport screen, as I'm sure you're aware. I'm not disagreeing with you that RBC is important, but I just think there's something else there that may be important. I'd be curious to see how changes in performance track changes in RBC mass.

Andrew R. Coggan, Ph.D. said...

"If the improvement in performance was solely due to increases in hemoglobin, then altitude training and iron supplementation, both which can increase hemoglobin levels by a similar relative amount (particularly when a person is iron-deficient to begin with) should produce a comparable increase. Yet it doesn't."

Iron supplementation does not increase hemoglobin/hematocrit/red cell mass in individuals who are not iron-deficient.

While exposure to altitude increases hemoglobin/hematocrit acutely, this is due to a reduction in plasma volume, not any increase in red cell mass. The latter takes time (and necessitates having sufficient iron stores), during which time an athlete may experience a detraining effect due to the reduction in absolute exercise intensity. However, if the latter can be maintained (e.g., by periodically traveling to lower elevations to perform higher intensity training, or by breathing a hyperoxic gas mixture while training), then VO2max and performance increase along with red cell mass.

Bottom line: I think you clearly are barking up the wrong tree in arguing that EPO influences performance by any mechanism other than inducing erythropoeisis.

(BTW, the reason I was lurking on your site was that I was searching for your email address. I was going to suggest that you might want to use Mike Joyner's new paper on the "2 h marathon: who and when?" as the basis of a blog entry.)

Andrew R. Coggan, Ph.D. said...

"There is not some magical unobservable performance enhancing effect of rEPO just beacause you can't see a one-to-one relationship between Hb and performance."

And in fact in studies using blood doping there is never a one-to-one relationship between the % change in hematocrit/hemoglobin concentration and the % change in VO2max. Thus, the fact that one does not exist when red cell mass is manipulated using EPO instead is not at all surprising, and cannot be used as evidence that there must be some other mechanism at play.

Andrew R. Coggan, Ph.D. said...

"If a cyclist is riding at 85% VO2max, then how does the increase in RBC actually improve performance? Given that the person is not at maximal aerobic capacity? I'd like to hear your thoughts, and not just "it is that way because it is that way" according to a book. I'm genuinely curious about this, because if performance is impaired by the limitation in oxygen delivery, then how does increasing RBC improve performance when delivery is not limiting at 85%VO2max?"

Well for starters, 85% of a higher VO2max is a higher absolute exercise intensity (pace or power output), and contrary to your prior assertions, EPO use clearly significantly increases VO2max.

That aside, however, there are numerous mechanisms by which variations in red cell mass could influence muscle metabolism and/or performance even when the metabolic rate is below the maximal rate of O2 consumption. For example, an increase in red cell mass would enable the demand for convective O2 transport to muscle be met via redirection of a lesser fraction of the overall cardiac output to muscle (cf. Saltin et al.'s classic studies using the knee extensor model, in which they examined the influence of variations in hematocrit/hemoglobin). In turn, this would require lesser activation of the sympathetic nervous system, which could reduce the rate of muscle glycogenolysis. As well, based on Wilson's model of the control of mitochondrial respiration (in which he distinguishs between O2-regulated and O2-limited respiration) it is possible that there would be a lesser disturbance to cellular energy homeostasis even when O2 availability is not, per se, rate-limiting (i.e., the subject is exercising at <100% of VO2max).