Alpe d'Huez: TDF Fastest Ascent Times 1982-2015

Update of the Alpe d'Huez climbing times and speed chart previously posted here and here. Read those previous posts for discussion of context.

Edit (28 July 2015): since posting this two days ago, I was alerted to some updates made to the 1991 ascent times. Two sources did work with archive video to better verify these times, the net result being an addition of 41 seconds to each of the 1991 ascent times.

Thanks to https://twitter.com/ammattipyoraily for the posting the data.

This chart shows the average speed of the five fastest ascents up the Alpe d'Huez climb for each year the Tour de France included this climb, with the exception being the times from the 1980s which are the average speeds for fewer riders (as data on five fastest ascents in those years is not available to me).

As a reminder, I chose to average the 5 fastest ascent times for a couple of reasons:

- it reduces the individual noise in the data for year by year comparisons

- the 5 fastest were most likely to have been giving it close to maximal effort and would be representative of the quality at pointy end of the field

- the available historical data I have on ascent times doesn't permit increasing that sample size all that much in any case.

 Here's the data in table format, along with some extra context information. I've also ranked the average ascent speeds of the 5 fastest for each of the 13 occasions during 1991-2015 that Alpe d'Huez was climbed. I left out ranking 1980s ascents as I don't have times for all 5 fastest riders for those years (IOW the actual average speed of 5 fastest would be lower).

As we can see, 2015 ranks as the 8th fastest TdF ascent over that period, when based on the 5 fastest ascents each year.

Here's the same table but with weather conditions for the airport nearest to Boug d'Oisans listed from 3pm to 5pm on the day of the race. I was only able to source data back to 1997. If anyone knows of an online almanac of weather data for near Bourg d'Oisans for years prior to 1996, please let me know.

Weather data source: http://www.wunderground.com/

Note the variability in temperature from year to year, and importantly the prevailing wind direction and speed. 

Now how such prevailing wind actually plays out on the slopes of the Alpe is hard to say, but we should expect some differences from year to year in the speed riders can attain given their power on the day.

Or put another way, any power estimates from ascension rates comparing year to year will have some error depending on how the localised wind plays out. The climb obvious has many changes of direction, and wind at rider level is different to the prevailing conditions (normally measured at 10m above ground level and as a rough estimate it's about half that at rider level). Of course localised wind will be shaped by the Alpe itself as well as boundary layer features such as trees, road cuttings, vehicles and so on.

Map: http://www.alpedhueznet.com/

The prevailing wind was from the North East in 1997, 1999, 2008, 2011 and 2015; from the North West in 2003 and 2013; from the South West in 2001 and 2006 and from the West in 2004.

Course profile shows the climb is not a constant gradient:

Source: http://bike-oisans.com/wp-content/uploads/2013/02/profil-montee-alpe-d-huez.png

Fastest five ascents up Alpe d'Huez from this year's stage were:

and here are the fastest 5 riders by year (click to see larger version), with lines marking the time of the 50th and 100th fastest ascents of all time:

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Climbing power estimates: Windbags II

No specific comment, I just wanted to create a public link to the following 2014 study investigating the accuracy of climbing power estimates and to include a graphic and quote the study's conclusion.

My earlier comments on this topic of estimation accuracy can be found in this post from two years ago:
http://alex-cycle.blogspot.com.au/2013/07/windbags.html

The study is:
Accuracy of Indirect Estimation of Power Output From Uphill Performance in Cycling 
Grégoire P. Millet, Cyrille Tronche, and Frédéric Grappe
International Journal of Sports Physiology and Performance, 2014, 9, 777-782 http://dx.doi.org/10.1123/IJSPP.2013-0320 © 2014 Human Kinetics, Inc.

Link:
http://www.fredericgrappe.com/wp-content/uploads/2015/01/Millet.pdf

Study Conclusions:

Aerodynamic drag (affected by wind velocity and orientation, frontal area, drafting, and speed) is the most confounding factor. The mean estimated values are close to the power-output values measured by power meters, but the random error is between ±6% and ±10%. Moreover, at the power outputs (>400 W) produced by professional riders, this error is likely to be higher. This observation calls into question the validity of releasing individual values without reporting the range of random errors.

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Alpe d'Huez: TDF Fastest Ascent Times 1982-2013

In this June 2013 post I outlined the average speed of the five fastest times up Alpe d'Huez each year during the Tour de France since 1982.

The data was sourced from the posts by Ammatti Pyoraily on this Finnish forum. Thanks to him we have lots of data on times to compare over many years.

At the time of writing I hadn't the data for the 2013 ascent (since TDF is in July each year), so here is an updated chart for reference:

Here are the top 5 from 2013:

The Tour visits Alpe d'Huez again in 2015.

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All Things in Moderation. Except Science.

This is my eighth year of blogging. It's a personal thing for me. I enjoy writing about training and racing with power. It's just stuff. Pub chat fodder for those four sad guys that talk about power meters in pubs. You know who you are. It's OK to come out and admit it, there's nothing wrong with it.

Occasionally I post an item that seems to be actually helpful to people, such as items on performance testing or indoor training. By posting I learn things and that's enjoyable. Hopefully others learn too. And I make mistakes. It happens.

I think I've held pretty well to the purpose as stated in my very first post.

I also used the blog to help me through difficult times, as longer term followers would be aware through sharing some of my experiences of getting back to racing after my 2007 accident and amputation. Where possible I tied the two themes together.

It's not a commercial blog and the subject matter is reasonably esoteric, and the following is modest with views numbering in the hundreds of thousands, not millions.

Moderation

I also know that public online interaction forums require moderation. Again it's mostly to keep spammers at bay, but occasionally some stretch the bounds of reasonableness and need to be reeled in or reminded of some basic netiquette. Troll watch duties as well. Sometimes you forget to check the moderation queue for comment that require moderation and they get posted a bit late.

I am a forum moderator myself, at the wattage forum on Google Groups which grew from modest beginnings in 2001 and was originally hosted on Topica. Want to pull apart anything to do with power and cycling? That's the place to do it. The archives are a gold mine of information, and the early days had a high signal to noise ratio. Only very rarely does moderation occur there, it's mostly self policed and the 10,000+ crowd are generally technically or scientifically oriented, so bullshit generally gets called out early and dealt with.

or Censorship?

But what I've never understood is why some forums or blogs dedicated to performance and/or training and racing would want to prevent actual relevant science or scientific discussion from being published/referred to.

I first encountered this a few years ago when I was banned by a triathlon forum owner from posting to the Slowtwitch forum. My crime? I wanted to know why they were persistently censoring the publication of a link to new published scientific research related to pedalling a bike. They didn't like the subject matter, nor my criticism of such censorship, so I was shown the electronic door and all evidence of the matter wiped. I was not offensive, I did not abuse, swear or curse at others, I did not break published forum rules. OK, it's their privately owned business, they can do what they like and they are large so what does it matter?

But it made me think. If you censor science, or discussion of science, is it really a place worth visiting? Well obviously lots think so, because such things are but minor ripples in the ocean of posts about saddle height, cadence, new bike frames, paleo diets, and the inevitable sarcastic pseudonymous responses.

So hooray for science. Perhaps.

Fast forward to a blog followed by many who, like me, enjoy their science in accessible form - the guys at The Science of Sport blog. I've followed it for a number of years, pretty much since it began in 2007. They dissect performance matters from a range of sports, in particular running, and introduce various topics for discussion. All good stuff and I think they do a good job of it.

Eventually they started writing about cycling performance like this one talking about the 2008 TdF and the all pervasive issue of doping. As they began to inform themselves on such issues in the cycling world, they also joined the bandwagon of estimating power from climbing speeds / VAM, and what we can learn from such information. They also began to suggest what is and is not physiologically plausible sans doping.

In the early days of such posts, I helpfully explained to them via the blog comments one of the difficulties in using climbing speed to estimate power, i.e. the large unknown factor of wind, and they got that message loud and clear. They even referenced my comments in subsequent posts. And they have usually referenced the issue of wind confounding such estimates whenever this topic comes up.

In general they have also tried to steer people away from the folly of using individual data points on climbing speed (or power estimations from them) as some means to infer doping status, but rather to consider the longer term trends. All good stuff.

Wham bam, thank you pVAM

Lately though they have been publishing a lot of information derived by the pVAM methodologies, which I am less enamoured with for a couple of reasons.

Firstly, whether intentional or not, it encourages the invalid use of such information as a "dopeometer" and secondly, I'm unconvinced they have sufficiently critically assessed the validity of the pVAM and dpVAM model. I think this is bordering on a desire for publicity than on good science. Not nearly to the extent that Antoine Vayer's occasionally dodgy maths does, but are they pushing the "Publish" button a little too quickly at times?

I get that their blog is designed to provoke discussion about sports science matters, make things accessible and to make people think more critically about stuff, and that's a good thing - but when you represent yourselves as "The Science of Sport" and present methodologies or models under that masthead that have not been peer reviewed or are based on known/published science, or without having done critical assessment against existing models, well I just think more caution is warranted before lending an overweighted amount of credibility to such things. Perhaps greater emphasis is needed on making it clear what is opinion and what is actually science.

I could of course be completely wrong and talking out of my arse. Happy to stand corrected. Most of us out here is the interwebs are not well versed in understanding the credibility differential of such material published by scientists under a heading of "The Science of ...".

It's difficult for me to strongly criticise since I'm not a scientist and not well versed in such peer review, so I just occasionally chip in with my amateur 20 cents worth and hopefully it generates some thoughts, at least in a pub chat kinda way. At the least I have a personal sense of contributing in some way, however insignificant that contribution may actually be. Which is what I did four days ago when I pointed out an error in a statement they made about the pVAM method.

This is what was written on their post:
"The error in the wind component is much larger, which has implications for the assumptions of cdA (drag co-efficients). In the model, however, the relative contribution of the wind during climbing is small, and so the total error is actually not too bad."

I then pointed out the obvious (to me anyway) physics mistake by posting this to the comments:

"The error in CdA isn't the issue, but the wind velocity most definitely is. Ignore that and you may as well throw darts at a W/kg board. That interpretation suggesting the error introduced by wind is, frankly, nonsense.

Even modestly different wind conditions for the same VAM can see estimates of power over a 1W/kg error range. The wind for the Armstrong/Pantani ascent was quite different to this year's ascent."

Perhaps my tone wasn't ideal, but nonsense is nonsense, right? And scientists generally have pretty thick skin.

For anyone wondering what I'm on about, when estimating power from steep climbing speed, if your assumption of the rider's coefficient of drag is (CdA) is wrong, well it doesn't generate a really big error in the estimate of power. It's not "sensitive" to that particular assumption. But it is most definitely sensitive to the wind velocity assumption. Get that wrong and the numbers can easily be wrong, and by a large margin.

Comment MIA

Then yesterday another SoS post about Alpe D'Heuz climbs and the pVAM and dpVAM methods appeared, so I thought I would post a comment with a link to djconnel's cool blog post which introduces a critical appraisal of the pVAM model, from both a physics and physiological basis, by comparing it with actual published and well established science models. I also provided links to a couple of charts about ADH climbing times that were easier to read than the ones they posted up.

As scientists, you think they might be interested in discussing the limitations of a model they are presenting as highly credible, or consider how it might be improved or under what circumstances we need to be very careful in using it.

Well for starters, I suggest using actual physics when estimating power from climbing speed, and also checking how the model stacks up with established physiological models.

Except my comments to them are now being moderated and have not appeared.

As Robert Chung would say, Hmmm.

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The Elusive Dopeometer

Readers of this blog no doubt have seen a number of examples I give about the (in)accuracy of estimating power from climbing speed, and in particular the confounding impact of wind on such estimates. Any climb with wind is going to be subject to error, and it doesn't take much wind at all to introduce quite a sizeable error.

There was my 2010 post about Alpe D'Huez ascent times, timely given the dual ascent this year, and my item yesterday about the significant error introduced by that great unknown, the wind.

I consider such W/kg estimates to be fine for a bit of pub chat fodder, but as a serious means to detect doping, really? I'll get back to this in a bit.

What has been more amusing than climb power estimates was more twitter/blogger/forum sphere musings on the power differential estimates from the Stage 11 individual time trial. Seriously. People are actually thinking they can reliably estimate the difference in power output of riders based solely on their time or speed in an individual time trial.

What complete and utter nonsense.

Aside from that affront to physics by Gazzetta dello Sport's Claudio Ghisalberti, there was also a post by the somewhat infamous Dr Ferrari about speed differentials from the same ITT and what that meant for power differences. Now Ferrari did say that this assumes all riders have the same "aerodynamic efficiency" as he calls it, which he then points out they don't.

So, given that they don't, why would you then proceed to produce and publish numbers as if they were all the same? More nonsense.

All this does is misinform the debate and feed Internet trolls.

OK, so people get the concept of comparing climbing performances (or attempting to) using power to body mass ratios, the now ubiquitous W/kg numbers. But can you do something similar with time trials over flatter terrain?

If you want to normalise flatter terrain ITT data, then you can make a reasonable stab at the differential of each rider's power to aerodynamic drag ratios i.e. the rider's time trial wattage output divided by the rider's coefficient of drag area (CdA), measured in units W/m^2. Of course this assumes the same wind conditions apply for the riders being compared which can be problematic in itself when the riders being compared are on course several hours apart (as was the case for instance with Tony Martin and Chris Froome).

On flatter ground, the higher your W/m^2, the faster you will go. This neat chart courtesy of Robert Chung shows the close relationship between flat road speed and power to aero drag ratio:

Hence we can reasonably say that the faster rider on the day has a higher W/m^2 (putting wind differences to one side of course). This is the flat land equivalent of the hill climber's W/kg.

What we can't say however is how much of that speed difference is due to higher power output and how much is due to a lower CdA. Indeed, it's possible for a rider to produce less power than another yet go faster if their aerodynamics is superior.

I’ve dealt with many riders of similar morphology who have significantly different CdA. I have a former team mate who was same height and weight as me (actually he was a bit heavier) and we have similar power output as well (mine was a bit better), yet his CdA is ~ 20% less than mine on our respective pursuit bikes. Our equipment was very similar. His natural body shape on the bike means he is just far more aerodynamically gifted. That’s why he medals at worlds and I don’t even make state finals.

Unless you know each individual rider’s CdA, attempting to derive power differentials from ITT speed is just pissing in the wind.

In this 2011 post I provided a short snapshot into this, with data provided by Andy Coggan who devised a draft variation to his Power Profiling tables, this time creating an Aero Profiling table:

The top of that list is a good indicator of what's required to set/break Boardman's hour record of 56.375 km (35.030 miles), now classified by the UCI as "best human effort".

Now if people think getting pro riders or their team management to release their power data is proving difficult, try getting their wind tunnel or aerodynamic field test data.

The Dopeometer

OK, so let's get back to obtaining riders' power meter data and using it as a dopeometer.

This seems to be a popular request. Greg Lemond wants the data released, as do the Bike Pure people. All over the net on forums and blogs and twitter and so on people are calling for the data to be released. The point being such transparency is a good thing, and I have no argument with that. But will it actually help? Or will it just be a public relations exercise and not really provide any additional insight into the issue?

Let us for a moment imagine that tomorrow morning we all wake up to find Froome and his professional riding colleagues and competitors release their power meter data.

Then what?

Will having more certainty over the accuracy of power data help us confirm or deny doping status?
A: No. All it will do is re-emphasise confirmation bias for those with an opinion one way or another.

What power output will confirm doping and what won't?
A: Nobody actually knows. All we have is differing opinions on the subject of what constitutes possibly suspicious performances. Yet people already have their suspicions. An SRM file isn't going to change that.

Just where is the doping power plausibility line? Can we really assign such a line? Is 6.2W/kg for an hour proof? 6.3? 6.4? 6.41?
A: In reality we simply can't put a clean line in the sand. The line for each rider may be different, and the line may vary depending on context. How long was the effort? When did it occur? What were the environmental conditions? How steep was the climb? Was it solo or with others? Was it a consistent effort or variable? Who responds better to doping?

Will it change which riders should be placed under scrutiny?
A: No, we already know who they are. They ride bikes professionally and at the elite level, win races and/or go up hills faster than the rest of us mere mortals.

Will it make doping detection easier?
A: Hardly, since proof of doping requires a positive test, a confession or reliable testimony and evidence, and we already know who should be scrutinised.

Will it prove riders aren't doping?
A: Of course not. Since it assumes there is an arbitrary upper power limit for doping to be confirmed, it does nothing to pick up any doping by riders who are below whatever that arbitrary limit is. No green jersey contender for instance is going to out ride the GC contenders on major cols. Hence such data only serves to tell us what we already know, i.e. a handful of riders finished ahead of their competition on the mountain top finishes.

Can power data be manipulated?
A: Yes, of course it can. Accidentally, inadvertently or deliberately. So then we'll have those on the conspiracy trail of a new doping detection avoidance technique of "data doping". Since we already know the amount of slop in power estimates from other methods, then fiddling with the numbers means no-one can really know if numbers are fiddled or not. There are of course forensic data analysis techniques that can identify some examples of that, but only if crude data manipulation methods are used. If riders and their support people are clever enough to manipulate blood to avoid detection, I'm pretty sure they'll be able to work out how to manipulate data to avoid detection.

Has "data doping" happened before? 
A: Sadly, yes as this example shows when a rider attempted to use doctored power data to prove a performance benefit from using a particular type of cycling equipment. Fortunately in this case the fraud was detected - but it took a Professor from Berkeley to point it out.

What would it cost to run such data collection in an independent manner, and free from possible manipulation?
A: Millions of dollars. Think about the number of bikes in the ProTour, the need to carefully calibrate say 1,000 SRMs, to have non-tamperable data loggers, to ensure all riders correctly perform zero-offset checks before and during races. The data collection process. Staff to manage this. Millions of dollars that perhaps would be better directed at improving doping control processes, technology, reducing testing costs, and simply performing more tests and more frequently testing in and out of competition.


I get that people want to see the data, and hope it's a short cut way to provide certainty around establishing whether a particular rider is doping. I get that release of such data may appear to increase transparency. But at the end of the day we'll just be back to where we started before all this data becomes available: i.e. none the wiser about riders' doping status.

SRM make a fine power meter, but it's not a dopeometer.

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Windbags

There seem to be a lot of windbags lately.

Once again people in the twitter/forum sphere are ignoring just how much wind affects speed for the same power output, even on steep climbs where overcoming gravity is the major energy demand factor.

Let me give you a basic example.

Let's take a rider with Pro Tour level power to body mass capability as follows:

400W Functional Threshold Power
69kg body mass
and allow 8kg for bike + kit

So that's a rider with an FTP of 5.80W/kg

A few assumptions about a point along a typical climb:
Gradient: 8%
Air Density: 1.065kg/m^3 (e.g. 1010hPa, 20C, 50% humidity @ 1000m altitude)
Rolling resistance: 0.0045
CdA: 0.350m^2
Wind: none

At that point on the climb, at 400W their speed would be 20.6km/h. But that of course assumes there is zero wind.

Conversely, if we have a rider climbing an 8% gradient at 20.6km/h with those air density, mass and rolling resistance values, then they will be required to output 5.80W/kg.

Pretty straightforward so far.

So what happens to our estimated power based on speed and gradient etc if there is some wind but we don't account for it? In other words we measure their speed as 20.6km/h, but we do not know the actual wind conditions?

Well let's assume we know precisely the mass (body and the bike + kit), rolling resistance, air density and rider's coefficient of aero drag (CdA). I'll get to errors in those later.

If there was an overall tailwind, then for the same power output the rider will climb faster. But if we don't account for that tailwind when estimating power output for that faster speed, then we will over estimate the rider's power output. And conversely, if we don't account for any headwind, we will under estimate the rider's power output.

So just how wrong can we get power estimates if we rely on climbing speed alone and do not account for the wind? Well to save you the trouble, I've plotted the W/kg actually required to climb at 20.6km/h with wind speeds ranging from a tailwind of 5m/s to a headwind of 5m/s.

Just so it's clear, this chart shows the power to body mass required to ride at 20.6km/h on that 8% gradient and with the other assumptions earlier listed. We can see just how much the wind conditions impacts the power required to maintain a given speed.

Hence, if you do not know the wind speed, then you have quite a sizeable potential error in any estimate of power from the rider's speed.

I've colour coded the Beaufort Wind Scale ratings on the chart. Of those shown on chart for instance, a Gentle Breeze is when light flags are extended. Even riding into a light breeze of 2.5m/s (that's not enough to extend light flags) means an error in calculating W/kg of over 9%! If the wind were a gentle head breeze of 4.2m/s, then the error in power estimated from speed increases to over 17%!!

Let's put that into perspective. A 10% power variation about the variation in power output for a trained rider from out of form / off-season to their peak fitness levels. That's the level of potential error in power estimates from a light breeze we can just start to feel on our skin.

Of course the actual wind speed and direction relative to a rider changes during a climb, some climbs have more shelter than others, the amount of shelter varies (trees, vans, people, other vehicles in race convoy etc), the wind does change direction due to the shape of the mountain itself, and of course the road itself changes its direction relative to the prevailing wind. Then there is the impact of drafting other riders, which is more of a factor with increasing headwinds.

So no doubt there are some swings and roundabouts, but who can really tell what the actual wind is? Answer: No-one.

If you can see flags flapping, then forget about making sensible estimations of riders' power to mass values. And if you can't see them flapping, then at least include some error bars in the estimate, unless you know exactly what the wind was doing.

What about the other assumptions, such as CdA, Crr, mass of bike + kit?

OK, well let's examine the impact of getting each one of those assumptions wrong by say adding 10% to each. What does that do to the power required to ride at that same speed?

CdA @ 0.385m^2
Power for same speed = 404W (+0.9% error)

Crr @ 0.00495
Power for same speed = 402W (+0.5% error)

Bike+kit mass @ 8.8kg
Power for same speed = 406W (+1.4% error)

We can see that error in estimates of power from climbing speed are less sensitive to errors in CdA, Crr and bike/kit mass*, and are dwarfed by the error introduced by wind, and wind is rarely, if ever, measured with any accuracy on these mountain ascents.

* even so, it helps to get them as correct as we can

Wind matters a lot when determining cycling power from speed, no matter the gradient.

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l'Alpe d'Huez. Again. Top 200

Some charts for fun. Pub chat, no more, no less.

Published on this Finnish forum are the top 200 ascent times for the Alpe d'Huez climb, often used in the Tour de France. I haven't been able to clarify how the times were established, nor if the same start and finish timing points were used. Official timing of the ascent started sometime in the 1990s but different timing points were used from 2001 onwards, so I cannot say with any confidence if we are comparing apples with apples. There are plenty on forums that definitely dispute Pantani's quoted climbing times (and that they should be somewhat slower than shown here, although still fast).

It's possible they reviewed footage to normalise these things, but in any case, nice work on collating the data, I'd say thanks personally but I don't speak or read/write Finnish. If any reader does, perhaps they can pass on my thanks.

Indeed racing context is also needed, e.g. Was it a long stage? Many previous cols? Attacking for the win or defending the maillot jaune? Conditions/weather/wind? Of course in 2004 the ascent was used for an individual time trial, not as the final climb of an alpine road race stage.

And yes, it's full of dopers and naturally covers the glory days when EPO, blood transfusions and other supporting cocktails were, sadly, the norm. Not that these things still don't happen, just seemingly not with the same outrageous impact on raw performance as before, at least not for the top of Pro Tour, but who knows about lower level riders trying to make the grade? Doping is still prevalent, and while the outrageous performance days may be suspended for now, the consequences are still just as insidious - shady characters and corruption, legitimate riders missing out on contracts and racing opportunities, people losing jobs, sponsors leaving, races and race results skewed and screwed, disillusioned fans. Long term health impacts. The list goes on.

As for conversion of ascent times to power to weight ratios, something that's been gaining in popularity lately with talk of mutants and the like as well as regular guesstimates published in online forums, well I cover that in this July 2010 post.

For reference though, using the methodology outlined in that post, the fastest time quoted in this list (whether or not accurate), would equate to a power to weight ratio of ~6.5W/kg +/- 0.4W/kg. Certainly not the nonsense level 7.2+ W/kg (or even 8W/kg) quoted by some.

In summary, just plot the ascent times and map the trends for individual climbs. Converting to a W/kg guesstimate may provide a way to make comparisons between climbs, but such estimates should be plotted with error bars, because there are too many unknowns in key assumptions and estimations are subject to methodological error. Converting actual performances to plot a wattage for a standard rider of 70kg makes even less sense, since W/kg is already normalising such estimates.

So here are two charts I whipped up from that Finnish forum data.

The first plots the fastest five riders each year. Click on it to see a larger version:

The next is a frequency distribution of the top 200 times for the years l'Alpe was raced.

What this means is that of the fastest 200 times recorded, 16 of them were in 1994, and so on. Quite clearly something changed between 1989 and 1991. One could speculate about other changes since then. Use of EPO, introduction of tests and of course doping detection avoidance measures, better tests, move back to blood transfusions as dominant in competition doping method and so on.

And a new chart, this one plotting the combined average speed of the top 5 riders (except for the first three years of data where there were fewer than 5 riders in the list for each of those years).

So, there you have it. enjoy the pub chat. And if you want to know how you compare, perhaps this other post about mere mortals might give you some beer for thought.

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l'Alpe d'Huez - one for the mortals

About this time last year I posted this item about ascent times of leading professional riders up l'Alpe d'Huez and what power to body mass ratio would be required to do that.

There's a chart which shows the relationship between ascent time and power to body mass ratio (watts per kg - W/kg). It also provides an indication the impact of wind can have on climbing speeds.

Times for leading riders since 2001 are shown on the chart.

The guys over at the Science of Sport blog referenced it in a post here, after seeing it on a cycling chat forum I posted to recently.

Well for a bit of fun (and considering the Tour de France is heading up the Alpe in a few days), I thought I'd post a follow up chart which covers the power to body mass ratio for the rest of us mere mortals.

Here it is (click to embiggen):


It's not a hard chart to read.

Want to ride up l'Alpe d'Huez in 1 hour dead? Then you'll need to be able to sustain around 3.75 W/kg, give or take depending on the wind. If you are 70kg, then that's around 260-265 watts.

If you know your sustainable power is 3.4W/kg, then you can expect to get up the Alpe in around 66 minutes.

In calculating these values, I've made a few assumptions (listed on the chart), although the relationship between speed and W/kg on steep climbs is not particularly sensitive to those assumptions.

After power and mass, wind has the biggest impact on speeds when climbing. Hence the two extra lines for head and tailwinds.

At my best form*, I would expect to climb it in around 56 minutes.

How fast have you been up l'Alpe?


* My power to body mass ratio for 1-hour at best is ~ 4.2W/kg (based on my racing power at the UCI World Cup this year), but I have to allow a bit of extra mass for my prosthetic leg. I'll get to do it one day.

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Ascension Rates and Power to Body Mass Ratios

As many of you know, the cycling speed attained when ascending steep climbs is primarily a function of a rider's sustainable power to weight ratio. More power and/or less weight means a rider can climb faster. Pretty simple really.

But it's not the only factor to consider. For instance, wind can still play a sizable role in speed attained. And of course when climbing in a race, race tactics will play a role, with attacks, surges and pacing by team mates (or motorbikes!) all serving to alter ascension rates for a given power output.

Recently there has been some (typically annual) discussion on a few cycling forums about ascension rates of pro riders, estimated power to weight ratios and whether or not such performances are plausible sans-doping, even suggesting that some ascension rates cross over some level of "sans-doping plausibility" and should be a red flag to anti-doping authorities.

Well I'm not going to delve into all aspects of this issue other than to say that, in essence, there are so many variables that such an approach is really a pretty futile exercise.

In the end, all the pro riders that demonstrate such tremendous physical acts will already be under the eyes of anti-doping authorities, so I really don't see how such an idea really adds any value to the issue of doping in cycling.

Many issues of a physiological nature have been batted about, and there are a couple of excellent summaries of some of the science demonstrating the massive variations in such estimations in these two items by Dr Andy Coggan:
Superhuman Performance? Part I
Superhuman Performance? Part II

Nevertheless, I thought I would look at the challenge of estimating power to body mass ratios from ascent times up one of the most famous climbs in Tour de France history - Alpe d'Huez. Below is a chart summarising (click on the picture to see a larger version):


In modelling of cycling power and speed, I used the mathematical model as per the 1998 Martin et al paper:
Validation of a Mathematical Model for Road Cycling Power.

The equation in question is shown below:


For the purposes of this exercise, I have simplified the equation a little. The main assumption being that of reasonably steady state cycling and no change in kinetic energy from start to finish (which is reasonable assumption given that the difference in speed from start to finish would be negligible and over ~40-minutes is a tiny proportion of overall energy demand). If there are a lot of surges or changes of pace along the way then a little more of the overall energy demand may go into changes in kinetic energy.

Then there is the climb itself. I have used a course elevation profile which, as far as I can tell, corresponds to the timing points which have been used to time the ascension up Alpe d'Huez since 1999. Before then different measuring points were used. My data indicates a climb of 13.93km with 1085m of vertical ascent (there are a few metres of marginally negative gradient right at the top).

I divided the climb into 56 segments of 250 metres (final segment a balance), with each segment having a gradient and wind vector assigned. The modeling then applied the maths to the segmented climb.

The following additional assumptions were used for the modeling:
- Rider mass: 70kg
- Bike + gear mass: 8kg
- A coefficient of rolling resistance (Crr): 0.0045
- A coefficient of drag x effective frontal area (CdA): 0.300m^2
- Air density: 1.046kg/m^2

Importantly, I have also assumed an even application of power for the duration of the climb. Of course no rider applies power perfectly evenly up a climb, although climbs with relatively consistent gradients generally produce consistent power outputs (if you inspect power meter files, you can usually pick the climbs as the power line is smoother and speed is low).

Then what I did was to calculate the ascension times up the Alpe d'Huez course profile for various power to body mass ratios, with a 2.5 m/s tailwind (9km/h), with no wind and with a 2.5 m/s headwind.

One can then see the quite sizable role that wind can play in estimating W/kg from ascent times.

To read the chart, for instance, take a time of 40-minutes flat (40:00) on the vertical axis and see where that time intersects the diagonal lines marking the tail-, no- and head-winds. The horizontal axis then marks the corresponding W/kg required for that time.

So, for 40:00, depending on wind conditions and assuming even pacing (and other assumptions as listed in the chart), then the power to body mass ratio required would range from 5.6W/kg for a tailwind to 6.35W/kg for a headwind.

Alternatively, if you are a 5.9W/kg rider then you could attain a time anywhere from 38:10 with a 2.5 m/s tailwind through to 40:00 with no wind and 43:00 with 2.5m/s headwind (off the chart).

I then added lines to mark the ascent times for various riders I selected from this Alpe d'Huez Wikipedia reference. Note that the times from 2004 were an individual time trial, the rest are final ascents during a TdF stage race. As we can see, the estimated power to body mass ratio for Armstrong’s super quick ascent time in the 2004 Individual Time Trial falls in the 6.00-6.85W/kg range, depending on overall wind direction.

Times for other riders in earlier tours such as Pantani were not taken using the same timing points, hence I have excluded them.

Of course the course winds its way up the ascent in various directions due to the famous switchbacks, and any wind vector would naturally vary accordingly, so by putting an indicator of reasonably modest but noticeable winds, at least one can see that any given ascent time will still end up with quite a wide range of possible power to body mass ratios.

All I can say is, given that some believe there is a performance level that is beyond plausibility sans-doping (some have suggested 6.2W/kg, some less, some more) then all the climb times listed in the chart straddle such "plausibility levels" with such a large range of uncertainty that it is simply not possible to draw any firm conclusions on power to mass ratios from ascent times alone.

Keep in mind that the highest ever 1-hour power to body mass ratio known and recorded is 6.4W/kg by, as far as is understood, a non-doped rider.

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