9 Lance Armstrong's Story a Case Study in Human Psychology

It is quite fascinating isn't it, that when we step away for a second from the intricacies of this epic doping saga connected to Lance Armstrong, you find larger underlying questions about behavioral psychology - the way we humans operate, why we behave in certain ways and why we choose to believe or not believe in things we come across especially when some form of philanthropy is involved. 

I was driven to this post because I was struck by the curious 30% increase in funds going to the Lance Armstrong foundation right after the news came out that USADA wiped his Tour de France wins from the books.

Bear with me for a few minutes here and I hope this will lead to some interesting discussion of a more psychological nature.


Ethical People Can Do Unethical Things

There is a fundamental assumption that unethical people do unethical things but that's not always true. Ethical people can do unethical things because they repeatedly fool themselves about the real implications of their transgressions. Slipping into this unethical state is driven by many many factors. In the early races of the 90's, Lance and his team probably knew there was no way to stay in competition and produce the numbers their sponsors were looking for other than to partake in doping. So they doped too.

The real transition came the instant when Lance decided to become the driver of the doping rather than just a participating rider. He allegedly became the self-appointed leader of the Omerta. What led to this behavior? You could say a self confidence he gained from winning races, the fact that he was an American in a long time to hold the Yellow Jersey, maybe the friends he made in the peloton who were also doping that he had to stay friends with. A lot of theories are out there. Forgive me for speculating.

Whats most interesting is the cognitive blind spot people as his fans have towards unethical behavior given that the same person has done a lot of good, both for the sport and for those suffering from cancer. For fans, LA is a symbol and they feel empathy so they want to help his cause out. I can't find any other way to explain why financial contributions to the LAF cancer fund have suddenly jumped 30% in the last few days.

It begs the question : are people actually worried about cancer patients suffering. Or are they worried about Lance Armstrong's financial troubles that come ahead? Are people running out, suddenly contributing to make a statement that they support their hero or are they really concerned where their money is going to and what for? Are the contributions a show of arrogance from his fans that his legitimacy is still valid? You'll never know. But it brings out a great opportunity to talk about psychology. 

Relational Dynamics of Philanthropy

It is quite popular now for a decently successful sports star to fall into the web of philanthropy. You win something big, make lots of money and then the next day, you come out in a press conference or through a PR ad showing you're contributing to rid the human race from their most excruciating plight. 

There's a reason why this works in today's world. When you're a sports star and you start something philanthropic that people can instantly relate with, either because you know what they want or you have gone through similar things as they have, you've a winning idea. You've now latched on to their minds and hearts very tightly. 

Lance Armstrong was made into the quintessential American hero that appealed to our tastes - a firm, strong minded and brash Texan taking on the storm of cancer, emerging from it victorious and then in a gutsy move, snatching seven Tour de France wins. A feat no one has ever accomplished. That's the celebrated version. The nuances of that journey that his closest allies, enemies and independent journalists knew about has little place in these accounts.

Between each year of his Tour de France victories, he was doing things at home that continued making him a larger than life figure. He grew in popularity. The few who accused him of doping was not a big concern but rather an inconvenient nuisance that he had to brush off every once in a while. The stories of a few smaller riders from the peloton who couldn't stand to make a successful living because of his harassment was swept under the rug because they were insignificant, they didn't "make" the news - hence discarded.

People around the world flocked to hear from him. They bought his books, attended his talk shows, bought the Livestrong bands. Through him, it gave everyone a deep sense of "doing good" too and a sense of identity. I suppose nothing is worse than being a mere ectoplasm in society and living your life being of no value to anyone else.

More so, for the many in the hospital beds who identified with him, it had everything to do with the disease that he called arms against. Cancer has been an all consuming presence in our lives. Some books out there say the first documented cases of cancer go back all the way to 1000 BC. Its a deadly disease that has managed to co inhabit with the human race. In spite of all human efforts to get rid of this disease, the interesting bit is that latest data show cancer deaths have budged little from the 1950's. 

If Lance had won just once or twice, the average Joe wouldn't shy away from calling it a random act of nature. There's nothing spectacular in "a" win. But seven times ? That packs a punch. Its not a cheesy story by any standard. There's nothing to say against that. Its powerful. People found credibility in that. Businessmen found a whole lot of marketability in that. They wanted Lance because you're a loser if you can't have the cash cow on your side.

Popular media has always concentrated on the benefactor of philanthropy. The people who receive aid, and care are documented proclaiming how they would done much worse weren't it for the the great Philanthropist's deeds. Some couldn't care less what a Texan was doing with his bicycle in a wind tunnel to perfect himself for a race in France. They were receiving indirect monetary benefits, without going through the embarrassment of begging for help because they were dying. 

Now if you have lots of money and a great PR team, you can make anything out of anything these days. Most importantly, if you can make a claim a patent on the idea of a "war against cancer", which I think is quite fascinating because "war against cancer" began to go mainstream when the "war against terror" was the buzzword in political circles. Hundreds of other non-profit cancer funds operate in this country, providing care to patients and support of research but that's hardly important to the media. Media wants glitz, glitter, flair, finesse, celebrity status. They didn't fight the "war against cancer" that Lance did.

On the other side of this dynamic is the Philanthropist. The theory is fascinating that the the Foundation must have given him just immense power over ordinary human beings. A feeling of invincibility. A confidence that you don't get just winning a bicycle race. Never mind all the shady stuff he was doing with his teammates on U.S Postal team. The masses were on his side and they can be his pawns in a public court. The anti-cancer movement was card he could play anytime, any day, anyway he wants. So far, almost every press conference Lance has initiated in response to doping allegations has had a non-trivial coverage given to cancer. 

Here's what I think. More than a few times, deep somewhere, Lance must have felt guilty of the things he had done to himself and his teammates. But when there are signs that a lot of people are happier with him back home with his anti-cancer propaganda, that good deed must have become greater than the bad deed in his own mind. Let the sleeping dogs lie, why worry about what you've done in the past when you're doing a whole lot of good now? Perhaps this served to clear his conscience so he could rest his inner demons and go to sleep in peace every night. We may never know...

Humans as Reductionists

It is fascinating that the idea of cancer and cycling has become so intertwined in Lance Armstrong's world that there appears to be no room for an alternative. How is this possible? Today, there is a such a strong mass following for Lance that going against the grain to challenge him on his legitimacy comes looking merely as a criticism against his anti-cancer evangelism.  

You reduce one idea -  the question of taking drugs, to another - anti-cancer movement. Since you now have more options to berate someone for going against the anti-cancer movement, instead of debating him on the drugs issue, then you've just found a channel, a strategy to defeat the other person's argument as a whole using the cancer card. This reduction can be compared to what they call "Straw man" information fallacy. Its a fallacious way to argue but its alarming that a lot of people don't think about this. Its too simplistic and irrational.

When Does A Good Deed Become Greater Than a Bad Deed?

For sake of discussion, say that in the future, if there comes out of this ugly world a truly great hypothetical philanthropist, an individual who lives purely for the masses, who supports fighting some of the biggest problems of our times but later was found to operate the biggest global scamming operation, when do you decide that the good committed is lesser than the bad committed?

It is quite interesting to me that with the right amount of external input to the human being, their minds can be so programmed that they do not understand when to separate one independent variable, in this case being the idea someone did wrong in another time and place, from another independent variable, that someone did good in a second time and place.

I suspect there will be remain a stark division in the sporting world on Lance Armstrong's rise to success. There will be the believers, there will be the heretics. Lance's anti-cancer movement and his statistically spectacular athletic talents will continue to seduce. Others will talk about data and court proceedings and witness testimonies and continue to hate him for who he was. Another group stand somewhere in the middle of this messy issue.

Perhaps this whole doping question will be deemed so significant that future presidential candidates would be asked what they believe in - whether Lance Armstrong was a liar and cheat, or won his competitions fairly. If you can extract a person's operation of thinking based on tough questions such as these, perhaps we'll be to tell something deep and subtle about them as a human being that would be hard to gain otherwise.

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0 Tour de France 2012 : Permitted Stage Finish Times

Hello everyone! Its that time again of the Tour de France, and I for one am quite thrilled by this year's route and the open field we have in 198 riders.

I've been quite curious lately as to how the Tour organizers calculate their "permitted" finish times for each stage. Obviously, if a racer finished outside of this time, they will unfortunately be eliminated from the entire Tour (unless special circumstances kick in, where the riders will be docked points or things like that). This brings to mind the famous incident last year at the Tour where our 'fastest man on wheels', boy Cavendish himself narrowly escaped elimination when he finished 35 minutes clear of the winner of Stage 18. 

Anyway, here's how the Tour organizers decide what the elimination cutoff will be : on each stage, the cutoff time will be the winner's time + % of the winner's time. The % of the winner's time is based on a co-efficient as follows : 

Where :

Today, Cancellara bested everyone in the 6.8K prologue in 7:13. That's an average speed of 34.33 mph!  If by some stroke of luck, you got to test yourself in the prologue against the best in the world. You better be in shape to finish this TT in around 9 minutes and change. Hence, you need an average speed of atleast 45.33 kmph or 28.16 mph to be considered for dead last. That puts a bit of perspective into this whole thing. 

More interesting things as the Tour rolls will come soon. Stay tuned.

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42 Modern Bicycles and Cycling Speeds : Any Measurable Relation?

Its not about the bike. Or is it?

Without a shadow of doubt, most of us will say that today's Grand Tours are faster than those of the past. True. For instance, since its inception in 1903 to the 1990's, the Tour de France had seen its winner's average speed increase some 50-55%  as this site will show.

But here's the big question - how much of that speed increase came from bicycle improvements alone? If you don't factor in the contributions from all other things- temperature, course, race tactics, improved training methods, nutrition and doping - what role does bicycle technology alone have to play in higher speeds? Is it significant to be appreciated?

This most entertaining problem is one that maybe analyzed with a technique called multiple regression. This method, a staple in any statistician's arsenal of tools, allows one to estimate the effects of many factors on a single dependent variable, in our case - cycling performance.

For starters, there are a number of independent variables that factor into a favorable cycling performance. I have shown these factors diagrammatically below.

In my opinion, these independent or explanatory variables can be broadly termed into 4 categories :

1. Human Performance Related - Physiology, training, nutrition, medicine and doping
2. Technology Related - Bicycles, fancy apparel etc. We'll disregard other things and consider just bicycles.
3. Race Specific - Course, weather, tactics employed, rules, etc.
4. Random Events (Noise) - Example - a freak crash 2 km from the finish line that injured many riders, a neutralized stage due to the death of an athlete, any day to day variation that cannot be predicted but is present. 

In 100 years of cycling history, innovations have come and gone. Some have stuck through to Grand Tour racing, the list of which is mandated by the final word of the UCI.

To consider the effect of just bicycle technology alone on cycling speeds, a multiple regression analysis has to be performed. You would require lots of data for many years and a handy computer to make some meaning out of it. Unless someone gives me serious money, I won't be diving into such an endeavor.

But recently, Ph.D's Jan Heine and Mark Vande Kamp who write for the magazine Bicycle Quarterly sought to answer this question in their article titled "Are Modern Bicycles Faster? An Analysis of Tour de France Speed". To me, the article appeared to be a logical investigation of why speeds increased in the Tour and whether they could be explained by the latest racing bikes. 


The article had ignited controversy in cycling circles about its apparently "flawed" analysis. I think it will be to everyone's benefit if the strategy of the article's investigations are clarified first and foremost. We'll then explore its conclusions.

Here's the strategy behind the article's investigation :

1. Fundamental assumption : The fundamental assumption that the authors imply, but which is not stated explicitly in the article, is that all modern bicycles and related technology are introduced into the market to strictly increase cycling speeds. With this assumption, they proceed to quantify how much that speed increase is.

2. Eliminate day to day performance variations : They selected the Tour de France as the main race of interest with this notion that multiple stages and over 150 riders will eliminate the influence of day-to-day variations in fitness, weather and other factors on individual performance.

3. Eliminate course specific variations : With the view that courses change "somewhat" in the Tour de France, they selected the Milan-San Remo as a supplement in the analysis as the race has been run on the same course for over a 100 years without change. The race's difficulty has also been consistent since smooth speed curves have been displayed for over a century.

4. Separate human performance improvements from bicycling technology improvements :  This one is tricky so pay attention. The authors wanted another race as a control to compare cycling with. They thought of a race from another branch of endurance sports that had little to do with technology or inconsistent conditions and where performance was mostly limited by the "human factor".

They selected medium distance running, specifically the 5 and 10 km running race from all events worldwide and studied trends in running speeds. The logic? If bicycles have truly become faster, the trend line for cycling speeds in the Tour would deviate from that of human speeds in running by showing step increases. If bicycles have not become faster, the trend lines should closely match each other due to the "human factor" common to both endurance sports.

5. Regression Analysis : Using the data of speeds, a regression analysis was performed on the Tour de France and running speeds for the last 100 years. The "athletic performance" regression lines would show the long term speed trends for both races. This was made into a "Chart 1". "Chart 2" was also made where the authors smoothed TdF and 10 Km running speeds for many years by taking a 5-year running average. These curves were compared to each other and to the long term "athletic performance" regression line in Chart 1.


Summary Of Results :

1.  Co-relation between actual TdF speeds and speeds predicted by the runner's trend line was 0.94. Strong.

2.  Co-relation between actual running speeds and the long term running speed trend line was 0.95. Also strong.

3.  88% of increases in TdF speeds over the last 100 years can be explained by improved athletic performance.

4.  For both running and cycling, there appears to be an unexplained 9-12% that are simply random occurrences seen when athletes compete.

5.  The regression curve (or line fit) for TdF speeds have a shallower slope than that of running indicating that cycling speeds increased at a slower rate. The authors propose that this is due to wind resistance factor in cycling as power demand increases by the cube of velocity. But the non-linearity of aerodynamic resistance is not much, it is instead minimized in the Tour de France and spread over a large group of riders.

6.  Over the last 20 years, TdF speed increase trends parallel that of runners' speeds. Technology has had minor roles to play in these achievements according to the logic in the analyses (no step increases were observed).

7.  There were steeper speed increases in the TdF in between 1926-1940 than running speeds during that time. The early 1920's saw periods of low performance and the authors propose that World War I had depleted the pool of cycling champions taking part.

The late 1920's, however, showed a marked speed increase was not observed in the Milan San Remo which got the authors to conclude that something particular to the TdF caused these increases. They propose the radical shortening of stage distances as a possible reason.

There were pronounced speed increases in the 1930's that corresponded well with the significant, revolutionary and long term changes introduced on racing bikes such as lightweight steel frames with thinwall tubing. The authors state that of all advances, lightweight steel frames had the most pronounced effect on Tour speeds. These speed increases were also observed in the Milan San Remo in the 30's as well, indicating that this was a sport-wide phenomena.

8.  Since 1947, speed increases in cycling, relative to runner's speeds, came during times when cycling technology did not even change. The late 1950's saw a jump in cycling speeds but nothing significant was invented or innovated in bicycles during that time, since the introduction of Compagnolo's rear derailleur in 1951. Since speed increase came at a time when technology was stagnant, the logical conclusion is that speed increase cannot be explained by technology. The authors state that other reasons, like the paving of roads, may have been primarily responsible.

9.  In the early 1980's, TdF speeds increased between 1981-1982 without a rational reason and then dipped down without an explainable reason as well. Between 1985-1990, time trial bikes, such as those used by Greg Lemond in his 1989 Time Trial did increase stage speeds but the time trial stages were too short to influence overall speed of the entire Tour. Moreover, the bikes used in mass-start races "evolved little" during this period, wrote the authors.

10.  From 1999-2009, lots of things in bicycles evolved - from index shifting, to rear cassettes, increased gearing, aerodynamic wheels and ceramic bearings. Sure, the speeds of the Tour de France saw an almost linear increase as well. But what the authors found was that the long term trend of running speeds tracked this increase in cycling speeds very closely indicating that almost all these improvements can be tracked to physiological factors common to both running and cycling.

Since 2005, speeds started to drop below the predicted trends, possibly indicating that strict doping controls are responsible for the lower speeds. Speeds decreased 3.5% from their peak, while running speeds decreased only 1.8%. This shows that something not common to both sports have influenced the speeds in cycling.

By now, you must be tired with all this information overload. So let's take the justifications provided by the authors for speed fluctuations and plot it on a chart for the last 100 years. I did it below for you :

Conclusions :

The authors wrote that there is no evidence that advances in cycling technology since WWII led to faster racing speeds. There is no systematic co-relation between the two.  Some speed increases came during times when athletic performance as a whole were increasing. Others came at times when bicycle technology and innovation were stagnant.  The only period where bicycling technology led to a pronounced speed increase was during the 1930's with the introduction of lightweight steel frames. Bottom-line of this whole affair is as follows, quoted from the article :

"It is tempting to look over the Tour de France speed curve and pick [technology] factors that appear to have caused increases or decreases in speeds. [...] However, when taken in the context of all the data, these specific examples don't add up to a compelling case that bicycle technology increased Tour de France speeds. Neither of them stand up to close scrutiny.  [...] Across the whole timeframe of the last 100 years, even radical changes like the introduction of the derailleurs did not alter the trend of Tour de France speeds. Clearly, the larger pattern suggests that bicycle technology has had little, if any, effect on racing speeds, especially in recent decades."

Critique & Suggestions :

1. Choice of control : Why was medium distance running chosen as a control and not ...say, the marathon? I don't know. The authors don't provide an explanation for this deliberation, although they suggest that the medium distance races do not see much "influence of technology". So does the marathon see influence of technology then? I don't know. You would think not. Long distance running, to me, is the purest form of endurance sports. It would be interesting to see if marathon running speeds closely followed all the trends of cycling speeds for the past 100 years.

2. Choice of race : One will agree that are simply too many variables in the Tour de France to make a valid relation between one aspect, such as cycling technology, and another aspect, cycling speeds. Why not extend the research to a solo performance such as the hour record where variability is reduced even further? Or a time trial? Or a sprint? In a past post, I revealed details of a study that found that between 1980 and 1990 before UCI regulations came about, 60% of cycling hour records in the discipline were solely due to engineering. The authors may want to catch up with that.

3. What to investigate : The authors start off the article by asking the question - how much faster are the lastest racing bikes compared to classic machines? But it seems that throughout the article, they tend to look at small innovations across years such as the rear derailleur, or increased gearing, or thin walled tubing to see if they made an effect on the "overall" speeds of each year's Tour. How could does a tiny component translate to anything appreciable in the overall speeds across successive years? Rear derailleurs or improved front brakes alone don't make any appreciable change to Tour de France speeds across successive years.

4. Details of each stage : The exact details of each stage were not investigated by the authors. It would be interesting to see how many flat stages and how many mountain stages each Tour so far consisted of and how gravity would play a role in changing outcomes. Data may be tricky to find. Now keep in mind that we do have data for the speeds, distances, number of entrants and number of finishers in each of the Tours. Perhaps blending all this information into one graph for different eras of cycling may lend some insight.

For illustration, lets take the Hinault Era (1978-1985). I plotted speed (kph), % of entrants who finished the race, and number of stages with respect to the years and the distances involved. Check this out :

You may be able to come to some kind of understanding about what was going on in those 7 years. For instance, during 1980-1982, speeds increased drastically. It is also interesting to see that between 1980-1981, the number of participants who finished the race had also risen and the distance in Km of the race had fallen, although the number of stages were increased from 22 to 24. It would be interesting to superimpose the percentage of km in uphill roads and downhill roads on this graph for those years. It would also be interesting to see how the "Badger's" temperamental tactics and pace control influenced the speeds in those years.

5. Successive yearly investigations vs leaping : Based on the initial question posed, it would be more meaningful to take a vintage racing bike and a modern racing bike and compare the two.  Hypothetically, a 1903 racer traveling across a period of 100 years into the future to ride the Tour de France on a 2010 race bike with a lighter frame and aerodynamic wheels should be faster. Similarly, a group of 1903 racers climbing a 2 hour long Alpine climb on 40 pound steel bikes would be slower than the same group of racers riding on flyweight machines of similar sizes in similar terrain. It is basic physics.

Investigating this issue year by year, where all riders would have access to the same bikes and the same technology won't show you clearly how cycling technology is improving overall Tour speeds, if they do at all. Besides, some modern equipment and technical wear don't always serve to increase speed solely. Some of them have intangible benefits as comfort and so on. That is an advantage when you stay seated in the saddle for 90 hours of racing.


Overall, I don't think this is as bad of a study as many people think. Besides, it was published in a popular magazine to open up a forum for discussion. It is not a rigorous scientific white paper.

I do agree with one thing that studies like this discover time and time again - that majority of racing performance is related to the human body.

Racing is never a level playing field, no matter what race it is or how much you want to complain - be it the Berlin Marathon, or the Tour de France, the 24 Hours of Le Mans or the Baja 1000. There's always those few individuals genetically gifted or blessed with the finances and talent needed to win.

Then there are those who cheat to win. They may have the talent, but they want to boost it with some extra energy from extraneous sources, illegal by all rules.

Kamp's and Heine's study corresponds with several people's observations that cycling speeds have been coming down since 2005 due to doping regulations. In July during Tour time, I had done my own analysis of this Stage 17 power to weight ratios and my approximate figure of 6 W/kg agreed with other people's observations, among them the Science of Sport bloggers (see their article).

In the end, we may never know exactly what portion of those early TdF speed increases were "fabricated" through cheating. How much came from Amphetamine use, or alcohol, or narcotics, steroids, growth hormones, EPO and blood transfusions or using mechanical devices? Food for thought?

What do you think? Come discuss this article and its implications!

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11 Tour TT Statistics & Contador's Climbing Abilities Reviewed

The 2010 Tour de France, the last one of this decade, draws to a close. Alberto Contador, the consummate cyclist of our times, has nearly clinched his third Tour de France title as he and his team roll into Paris today. This will be his 5th Grand Tour win in a row, and he has everything under the sun from the Giro d'Italia to the Vuelta a España. He is at the level of Lemond, Bobet and Thys. Meanwhile, Andy Schleck made slow but steady improvements in his time trialing to give El Pistolero a serious run for his money.

TT STATISTICS

I was hoping to shed a bit of interesting light across both last year's and this year's time trial stages at the Tour. See below. 

1. 2009 TdF Prologue.  Let's go back a year. This was the profile of the opening prologue if you'll recall :

This was how the resulting times played out.

A nearly normal distribution. I used a 0.2 minute bin width. 180 riders started, gave their best. Average time was 20"20' and the average of each rider's time variation from this mean was 0.63 min, or 37.6 seconds. More people tended to perform better than average than not. It was short. Legs were fresh so a violent effort. There were 2 or 3 out there in the land of under-performance.


2. 2009 TdF Final TT.  This was its profile :

This was how the results were distributed. 

By stage 18, just 158 riders remained to time trial compared to 180 who had started. 22 riders said "I'm done, thank you very much", that's 12% of the peloton who were missing. Contador surprisingly, beat Cancellara by some precise pacing strategies (a topic that was explored in depth by the SportsScientists). The fastest guys could do this 40K course (25 miles) in 48 and a half minutes. Andy Schleck performed better than 86% of the rest and he was 1 min 44 sec slower than Contador. Menchov posted just close to average times but he must have been toast from the long Giro season earlier (racing against a doped up Italian challenger is not so easy, as it goes). Towards the end, everyone must have been cooked 80% anyway. More riders tended to perform slower than the average times. 83 are slower than some 72 . The average spread is close to 2 min.

3. 2010 TdF Prologue. This was its profile. A much shorter route than last year.

This was how the results were distributed.

The fastest man covered 9K in 10 minutes. Contador, meanwhile, didn't give his best like last year. Taking it easy? A big field - 197 riders - raced, posting a mean time of a little over 11 min with a spread of just about half a minute. Schleck was embedded in the average. Menchov was slightly better than him. Overall, again, more riders tended to go fast with violent effort and perform better than the average than not. A few were cast way out in in the world of under-performance. What on earth were they thinking?
 
4. 2010 Final TT. This was the profile. Very flat but was this a welcome respite for the riders?

 Not really. This was how the race results played out.

The headwinds were brutal. But again, the same names were out there in the front, the best guns (Martin, Cancellara) could pedal a little over 30 miles in an hour. Stop to think about that. And the average time was 1 hour 8 min or so and the spread much bigger than last year - almost 2 and a half minutes. More riders tended to perform worse than the average. Over 85 riders were better than the rest. Contador appeared to be struggling. Schleck, who does better than 73% of the field, is even worse than Contador, but just by 31 sec!

Menchov, though, was the big surprise as he had a big leap in performance - what I'll call a 2x2! He raced faster than Contador, beating him by almost 2 mins. Furthermore, he had beaten Sanchez by exactly 2 mins to seal that 3rd place on the podium (the most un-talked news yesterday). Also note that out of 197 riders who began the Tour, 27 riders had quit, meaning 14% of the peloton were missing. Comparable to the 12% last year who had also quit by the final time trial.

From all this data, one can understand that the Tour has been even getting challenging for riders and the number of casualties are higher this year than 2009. Contador's placings in time trials have taken a toll over the last one year. He has not won a single stage at the Tour either. What is the matter, fans wonder? Illness again? Tiredness? Lack of ability? The champion who beat an ever consistent Cancellara last year looks vulnerable more than ever. GC contenders who want to beat him must tap into this 30 second time trial weakness.


CONTADOR'S CLIMBING PERFORMANCES

On the climbing front, Contador has posted consistent values in climbing performance over the past years. The following table was put together by me after reviewing a bunch of people's calculations. I took the averages of all their numbers and integrated them into the table with average VAM's. This will hopefully average out the error from each person's math, instead of sticking to just one inflated/underinflated number.

With these approximations on the climbs, we find Contador stands somewhere at 5.9-6.1 W/kg average in Grand Tours, not considering the 2008 Giro d'Italia. The big surges in performance were on the long climbs at Verbier and Angliru, which were massive efforts and on the short-steep Côte de la Croix Neuve, which was a little over 1 mile long and 10% average in average grade. That must have been one violent effort to cut 10 seconds into Andy's time. Readers can verify these numbers or put a reality check on it if they choose.

It will be interesting to see how Alberto Contador and Andy Schleck perform in future. Thanks to them for what will be great memories.

For your pleasure, here's the Col de la Croix Neuve attack from Contador to top this post off.

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20 Col du Tourmalet Climb Analysis From 2010 TdF Stage 17

Today's mountain top finish involved the climbing of 18.4 km of the western side of Tourmalet (see detailed 3D terrain here), from Luz-Saint-Sauvier onwards. The Tourmalet is the queen of all climbs in the Tour de France and the roads here are some of the highest in France. The Henri Degranges prime was won on the summit by none other than the lanky, steely looking Luxembourgian Andy Schleck, but he did not manage to gain any time advantage on the Spanish climber Contador as the latter finished an inch away from him. Andy promised a strong effort today to aim one last time for the yellow jersey before the final time trial. It didn't happen as planned.

How It Happened :

1. At 18.4 to go, the leaders were in one group of some 10 riders. The speed, as reported on Eurosport at 19K to go was some 25 kmph. But this was on a mild gradient before the Tourmalet officially began (we can assume their speed dropped by 2 Kmph when the gradient kicked in) . At this point, they had 3:59 seconds advantage over the chasing pack.

2. When the leaders had 18K to go, the chasing group with the favorites had just passed the 20K to go sign.

3.       Time Gap 

 = Time To Finish (Slower) - Time to Finish (Faster Leaders)

Knowing the time advantage of 3:59s (0.066 h), speed of leaders = 23 kmph, and distances left for each as stated above, speed of the chasing pack at 20K to go is then calculated by :

Speed = 20 / [0.066 + (18/23)] = 23.58 kmph ~ 14.7mph

This speed is high as the sections before the foot of the climb were only gradual.

4. When the leaders were at 10.1 K to go, Carlos Barredo from the chasing pack attacks. The time gap to the leaders drop steadily per kilometer.

5. Andy Schleck who is also in the pack chances upon the opportunity to make something happen. With 10K to go he accelerated and passed Barredo. Contador marked Schleck and took his wheel. Both go hand in hand up the climb, eating up into the time advantage of the leaders (by now, their group had also splintered due to several attacks within.

6. The time gap drops rapidly per kilometer after Schleck's attack (see graph below). How rapid is the Contador-Schleck surge? In a matter of 1.6 km, they completely destroyed the advantage of 1:21s enjoyed at the front by Katusha rider Alexandr Kolobnev. He was caught and passed at 8.4K to go in a matter of 28:30s from the start base of the climb.

7. From hereon, Contador and Schleck are the leaders. With 5K to go, they had a 1:15s advantage on the chasers.

8. Alberto tested Andy's legs by giving it a go at 3.8K to go. Andy responded and trivialized the effort but surprisingly, he did not counterattack. Perhaps both may have found that they were at their absolute limits and hence decided to ride to the summit without any further attacks. There was no sprint to the line but the finishing speed as reported on Eurosport was 14.4 kmph, with a margin of 1:30s over the chasing group. Andy gave a hug to Bert on the summit while the latter winked at Andy and patted his face. "You know, we really are the best around here..."

Data & Calculations :

1. Weather : 10 deg C, low visibility with bit of snow in the morning, overcast with a weak wind from the SW, according to Metro News France. Wind can be consequential to the race. Racers like Carlos Sastre know it.  However without a CFD analysis or something similarly sophisticated, the wind vectors are hard to predict given the number of switchbacks, trees, spectators & vehicles. A theoretical analysis of its effect on power to weight ratio was given here for perspectives sake.

2. Procedure : Climb profile divided into 18 sections was borrowed from Velopeloton. Grade was extracted for each individual kilometer. Using a mammoth Eurosport footage recorded using 18 GB of hard drive space (phew), the racers were timed on these 18 sections using my stopwatch with an error of +/- 2 sec. Time gaps/advantages and VAM's were also extracted/timed from the footage video. Power to weight ratio was then calculated with Ferrari's formula using VAM, taking into account the grade of each of the 18 sections. An analysis done this fashion, is a bit on the conservative side opposed to one assuming a constant grade and constant ground velocity. From the perspective of drafting, this analysis is a bit on the overestimating side. All in all, the VAM method is between those two. So for Watts/kg, it is good to represent a figure obtained from this method with an error tolerance of +/- 0.2 W/kg.

3. Change of time gap per kilometer : As shown below : 

4. Climb Time : Time taken by Contador & Schleck to complete climb was approx. 53 mins 25 seconds for 18.4 kms according to race footage. However, from Horner's power output file, it was determined the he took some 52 minutes 22 seconds to climb which puts the leaders at 50:37. This is the figure I will use (with some caution because this depends on how it was operated on). It is quite challenging to put this into perspective with previous editions of the Tour. Data is lacking and I have had to pour into past Cycling News reports to extract any sort of approx. information. I have put together what I could glean in the following table. Please do review it, correct me, or help me fill in the blanks if you can. 

5. Average speed for climb : Av. speed of the duo from calculations (after passing Kolobnev) = 12.62 mph for 8 km. From Eurosport live online, their finishing speed was recorded to be 9 mph. 

6. Average power to weight ratio : Prior to getting caught, Kolobnev and his group exhibited approximately 5.5 W/kg +/- 0.2 W/kg. Average for Contador-Schleck was 6.03 W/kg +/- 0.2 W/kg for 8km after passing Kolobnev. See speed and power to weight ratio below :

7. Climbing Rate (VAM/Ascention Speed) : Average VAM or climbing speed (see detailed explanation for climbing rate) after Schleck and Contador overtook Kolobnev was 1696.5 m/hr. The change of VAM with grade is exhibited below for the parties in the Kolobnev group before the catch and the Schleck-Contador breakaway after the leaders were caught.

Power Meter Data

Both Chris Sorensen and Chris Horner put forth hard efforts during the climb. Surprisingly, Horner made it with the group of chasers and he was the best placed Radioshack rider. As and when I see powermeter information about their efforts, it will be appended here for review/comparisons. The trend of releasing powermeter data is limited in that it monitors only a few riders for a limited amount of time/kilometers before they are expended. But it is should be the most objective indicator of performance, while heart rate is the best indicator of effort. 

UPDATE : Chris Horner's Power Output file from SRM is shown below. His average power output is 5.65 W/kg for the entire climb. Relates very well to my estimate envelope of 5.5 +/- 0.2 W/kg as stated above. Notice that SRM missed out on publishing this cyclist's HR value. It is absolutely important to know his effort intensity level. Viewing such information without HR is as good as no information.

Some Limited Footage

Found on Youtube for your pleasure : 

Part 1 :

Part 2 :

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35 The Quiet Goombah

"The former Soviet state of Kazakhstan is the size of Western Europe, and is not so much of its own country as its own planet, a vast sameness of boreal forests and grasslands, boiling in summer and frozen in winter, a land the Soviets found ideal for growing wheat and testing nuclear bombs - 470 tests between 1949 and 1989, most of them thoughtfully done on Sundays, so as not to disrupt the happy productivity of the proletariat. The ensuing years have only added to its charms : the rivers are so syrupy with toxins that they can't manage the trick of freezing; the rails of the trans-Siberian railroad are so elaborately twisted by frost that passenger trains cannot exceed thirteen mph. Kazakhstan, in short, is the perfect hothouse in which young cyclists may bloom."[1]

That's where the story of a stoic all-rounder began. He mumbled softly in press conferences, but spoke boldly with his legs. His enigmatic persona was only overwhelmed by his resilient desire to win. There are few who possessed his attacking style, fewer who could bring the theatrics that he gifted to any race.

A little Kazakh - Alexander Nikolaivich Vinokourov - was born on November 16, 1973 to his farming parents. At the age of 13, he applied for a position at the Spartan-like sports academy of Almaty with the burning desire of becoming a pro rider. From then on, he and his 13 colleagues were given extraordinary harsh training; up to three times a day they gave everything they had in their young bodies, in series of continuous labor. One hour at the crack of dawn, a three-hour trip right after the first meal of the day, and then another 2 times, 60 minutes going into the red right after the obligatory resting period: an education that can either break or make a person.

"Vino became known as one of the hardest of cycling’s hard breed: the Eastern Bloc goombahs; riders who had been selected as children, their growth plates and femurs carefully measured by state examiners, their biotype profiles matched against that of a “superior child,” and who were duly whisked away to the barracks of various sports schools throughout the Soviet empire. Once there, their life became an endless series of training exercises, the governing philosophy of which was summed up by a former coach: “You throw a carton of eggs against the wall, then keep the ones which do not break.” " [1]

When he was 16, the big day had come. The sports academy didn't have anything left to teach Vinokourov and his classmates. The West, where the beating heart of cycling lay, was calling. In the fall of 1996, Gilles Mas, assistant DS of the Casino pro team, received a letter from the Kazakhstani national coach. The offer: the 6 best young guns of the entire batch. The question:  Could he land a spot in the pro peloton for these guys?

Mas decided to take two of them, on probation. The Frenchman realized that fitting in Vinokourov and Mizourov - the two chosen ones - wouldn't be so easy, so he decided to install them at EC Saint-Etienne Loire, an amateur team, for a year. 

He showed up at the French amateur EC Saint Etienne Loire in 1997 with a rucksack on his shoulder and a coach's note in his pocket that sketched out the outline of his story. The wall had come down, and Vino had come to race bikes.

Vino quickly learned French and adapted well, but Mizourov became extremely homesick and was replaced with Andreï Kivilev, one of Vino’s classmates in Almaty. Together, they found shelter with their host family.

Vino was not taken seriously. From the beginning to others, he looked like he was nine - bright blond hair, pink ears - with an affection for shiny shorts and fat gold necklaces. Coy, of brief words, he resembled a cross between a mafioso and an elf. At first people assumed it was because he didn't know French, but was that really so?

"He knew it was fine. He just didn't talk. His background was, and remained, a blank slate. His parents were reported to have been chicken farmers in Petropavlovsk, but he would not speak of it. When he did speak, which was about once a week, it was in short, pointed sentences, so simple that it was like listening to Japanese poetry :

I will ride hard today.

The hill is not steep.

I will attack them. " [1]

Mas immediately understood that he made the right choice, especially since Vinokourov was tearing apart the amateur circuit. Soon it is clear that he was way too good for the éspoirs. One year later, the Kazakhstani made his first appearance in the pro peloton. The neo-pro immediately won the 4 Days of Dunkirk and the Circuit des Mines; later in the season he would add stage wins in the Tour of Poland and the Tour de L’Oise to that.

From there on, things only got better, and that’s almost an understatement - the Amstel Gold Race, the Dauphiné Liberé, the Tour of Valencia, the Tour of Germany, Tour of Switzerland, twice Paris-Nice, twice Liege-Bastogne- Liege, summer Olympics Road Race (2nd), the Vuelta a Espana and stage wins in just about every stage race of importance! The stats are remarkable. In his pro career since 1999 up until now, Vino has had 108 podium finishes :  forty eight 1st place wins, thirty 2nd places  and thirty 3rd places. 

Talent, power, character, money: Vinokourov has plenty of it all. A house in Monaco, a huge villa in the surroundings of Nice, some real estate here and there in Kazakhstan.

"But the man who raises his daughter Irina and his twin sons Nikolas and Kiril together with his spouse Svetlana also has a very big heart. The boy that grew up in miserable circumstances never forgot  where he came from. From his first public celebration in his country, he brought gifts with him for his colleagues, who had to work with a lot less than he. He donated 5 brand new Pinarello bikes to the Kazakhstani Cycling Union, and his club in Petrapavlovsk got 20 cycling kits, including shoes." [2]

Perhaps the biggest sadness in his life came when he lost his classmate, the same friend and companion he had raced with in his young years in the 80's - Andreï Kivilev. The 29 year old Kazakh climber crashed some 20 km from the finish during the second stage of the 2003 Paris-Nice and lay motionless on the ground, his skull crushed, his ribs shattered. Next morning, he died in a coma on his hospital bed. The dangerous sport of cycling had taken yet another victim. His shocking departure was the reason the UCI even enforced the compulsory wearing of helmets in all endorsed races.

"We were always there for each other," said a heart broken Vinokourov of Kivilev. "We raced for the first time together in 1986, and took the same road through the national team to the 1996 Olympics in Atlanta. We turned pro at the same time, Andrei with Festina, me with Casino. To lose one of my best friends is really bad. We were such a strong gang; the Kazakhs are a strong family."

In memory for his friend, Vino founded the Andreï Kivilev Foundation, a charity fund that provides for Andreï’s wife and children, as well as for his parents, brothers and sisters that he supported during his career.  “Being a famous cyclist opens many doors. It would be a shame if I wouldn’t put that in good use," he said. "I want to make some people’s lives a bit more bearable than they are now, in my own way.”

A year after his comeback, in the same characteristic style, Vino eluded the best sprinters of the world today, won the stage and added another brilliant feather to his cap. Meanwhile, Ned Boutling, a strong Vino critic wrote thus about him :

"For 4 or 5 years, and in an era dominated by the monotony of US Postal victories set against the fading star of his T-Mobile teammate Jan Ullrich, Vinokourov had been the thrill-seeker. He could be a one-man firework one day, and embark on the most suicidal of escapades. And the very next day he could disappear altogether, only to reemerge a few days down the line in true Lazarus fashion. He was loved. You could even say he was best thing about those Tours." 

Any doubt?

[1] Dan Coyle, "Lance Armstrong's War"
[2] www.Gva.be
Many thanks to translation from Daily Peloton, stats from CQ Ranking, interviews from Cycling News, photos from Graham Watson.

ADDITIONAL READING :


The Alberto Contador You Did Not Know

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24 Wind & Altitude : Effects On Power To Weight Ratio

The following, divided into 3 parts, is a simple physics exploration of wind and altitude's independent effects on power to weight ratio, a subject that has not been treated by any cycling book so far.  Independent effects are important to understand in order to get a feel for how they affect power to weight ratio when acting in combination. The climb chosen is the famous Col du Tourmalet which is featured in this year's Tour. Assumptions in the analysis, for simplicity, include constant speed, constant grade and a formula for frontal area developed by Bassett & Kyle. Validation is done against calculations done by Alex Simmons (see conclusions) for wind vs power to wt results. Power models from Tom Compton's "Analytic Cycling" site and data from prominent researchers are compared with for altitude vs power results.

Courtesy : New Scientist

We have explored VAM calculations  here and here, However, climbing rate by itself does not provide an understanding of the effect of transient wind and altitude on performance. The wind and altitude can make a big difference. On the other hand, one could also argue that the effect of switch-backs and spectators along the road may effectively cancel out the contributions from head and tail winds. I'm not sure how much that contributes but that can be a topic in the comments section.

 
The equation explored in a previous post to understand climbing rate explored only the power needed to increase a rider's potential energy. Lets call this A. If W is total weight of bike and rider in Newtons, Vg ground speed in m/sec :

A = W.V_g.sin[arctan(grade/100)]  Watts

While this is a big piece of the power pie for climbing, there are  couple of other elements to the power equation. One deals with rolling resistance at low speeds. Let's call that B. If Crr is the co-efficient of rolling resistance (typically 0.004 or so for a 100psi tire)

B = W.V_g.Crr.cos[arctan(grade/100)]  Watts

Both A and B are constant if grade and ground velocity are steady.

There's a third element that comes to play which is the effect of wind and density. We can call it C. This is composed of frontal area A and associated drag force. If Cd is the co-efficient of drag (0.9 typical for cyclist on hoods) and this multiplied with area gives drag area, then :

 C = 1/2.C_d.Area

Say very little change happens with the cyclists' drag area (Cd.A where Cd is coefficient of drag and A = area), velocity V and say, density altitude is fixed as p. Let's also assume speed to be steady and gradient of slope to be an average. If  Vw is the wind speed (negative for tailwind) and Vg the ground speed, then not accounting for the tiny drive-train losses in your super efficient bicycle, the power to climb will then be a function of relative velocity as follows :

Power to climb, P  = A + B + C.p.Vg.(Vg + Vw)²  Watts

Let's work with just the third term, calling it Term. Its interesting to see what happens when you normalize Term by the the cyclist's ground speed on the climb. Dividing and multiplying throughout by Vg to change its form but preserve its meaning, we get : 

Term  = C.p.Vg³(1+ Vw/Vg )²

  => K.p.(1+ Vw/Vg )²

where K is defined to be K = C.Vg ³

Vw/Vg is called velocity ratio. Now you can see that when there is no headwind, Vw/Vg =0 and power becomes a function of K and p only. 

PART 1 : Power Variation With Velocity Ratio While Keeping Density Constant

Let's look at how that wind term varies with a change in velocity ratio. The density of the air on Tourmalet is kept uniform for this exercise, at a value of 1.06 kg/m³

When a headwind picks up, the velocity ratio increases from its baseline of  0. The following geometric growth is seen in Term :

• -When headwind is 1/10th of cyclist's forward velocity, Term is an extra 21% compared to no wind condition. 
• -When headwind is 1/4th of cyclist's forward velocity, Term is an extra 56% from no wind condition.  
• -Similarly, when it is half of cyclist's forward velocity, Term is an extra 125% from no wind condition and you must supply 44% more power from case 3).  
• -At an extreme case (assuming you're traveling atleast faster than 5mph), (1+ Vw/Vg) could be highest when the headwind is same as your forward velocity. When that happens, 1+1 = 2 and 2 raised to itself = 4 meaning that all things kept constant, Term is more than 4 times its original value, a 300% increase.  

But this component of power, Term, is added to A and B to produce power, P. Hence, percentage increases shown above don't mean the sum power will also increase by same percentage. So for the last case above, P does not increase by 300%. When one does the math properly (unlike my poorly done first edition of this article), the increase in P from a no-wind condition is actually  :

300% x [ Kp/(A+B+Kp) ]  

Or generally, if all other things are kept the same, 

% increase in power, P%. = [(1+ Vw/Vg )²-1].[Kp/(A+B+Kp)] 

increase in absolute power = P%.(A+B+Kp)

 

We know how to calculate the first part.  The second term, Kp/(A+B+Kp) can be called the Correction Factor. Once this puzzle is solved, we can solve for the proper required increase in power.

Without going into too many details, here are graphs I produced. Maximum height and weight were extracted from the Navy Seals' website. These are some of the fittest people in the world and they were a good choice because it makes no sense to work with data of unhealthy, overweight people. (Note, their dimensions are not like Tour contending emaciated cyclists but it should be close). Frontal area was then calculated using Bassett and colleague's formula that was retweeted by Jonathan Vaughters.  The speed is kept constant at 10mph.  p is kept constant at the average of 1.06 kg/m3. The gradient was uniform at 7.5%, with no change. 

FIG 1 & 2 (above) : First and second plots show the wattage expended to sustain 10mph on the Tourmalet for men and women. The numbers are shown for potential energy and rolling resistance components. Sanity check is to note that wattage needed to counter rolling resistance, for a constant velocity but varying rider weight (shown in red line), is pretty small compared to the wattage needed to fight the grade which is true.

FIG 3 & 4 (above) : Frontal area across riders vary with height and weight. The above plot shows how C varies for men and women according to their dimensions. These dimensions are the maximum accepted in the Navy Seals, who are among the fittest people. Frontal area was calculated using a formula developed by scientist Bessett & Kyle. The area is an approximation ofcourse, and does not account for changing positions on the bike. 

 FIG 5 : The last plot is the power correction factor plot, the puzzle I was seeking to unravel before. Does it make sense? Below, I describe how to use this plot to calculate percentage increase in the total power requirement. 

Going back to the question we were asking earlier : How much increase in power is required to combat a 10 mph headwind (velocity ratio of 1) for a 70 kg male Navy Seal cycling at 10 mph (4.4704 m/sec)? 

Here's how to solve this question. Looking at the figures above, the corresponding numbers for his weight are:

A = 253 W (power due to grade)
B =  15 W (power due to rolling resistance)
C = 0.14 m²
Corresponding correction factor for his weight is ~0.047.
Kp = C.Vg ³p = 0.14(4.4704³).1.06 = 13.25 kg.m²s^-3

Solving using the equations shown earlier in the post,
   

 % increase in power= [(2)²-1].[0.047]~ 0.141 (14.1%)
 increase in absolute power= 0.141(253+15+13.25)~ 40W
 increase in power to weight ratio = 40/70 = 0.57 W/kg

Similarly, we can quantify how much extra boost one would need per kilogram of body weight for different velocity ratios. 

Here's a case scenario for a Tour de France contender on the Tourmalet :
Weight = 65 kg
Height = 1.78m
Power to weight 6 W/kg riding
Desired speed = 10mph.

The plots are shown below : 

 FIG 6 : The operating zone of a Tour contender can, for example, be 6.0 W/kg. This example is for a rider weighing 65 kg. Other parameters assumed are shown in red. In an ideal case, the rider traces a straight horizontal line on the 0 point (y-axis) when there's no wind. Any additional wind will force him to trace horizontal lines as he pushes his body harder. Horizontal trace will move vertically up on the plot with wind change.

The above plot perhaps proves why it pays to prepare the extra mile for July. If 6.4 Watts/kg is what a person needs to win the Tour, perhaps only 6.2 is really needed. The additional 0.2 W/kg is used as insurance, against attacks, accelerations and misfortune winds. Very rarely are riders gifted as such to keep doing this over the course of 3 weeks.

Note : You could also have a tailwind of similar proportions, except that now the (1+ Vw/Vg) term is modified to (1- Vw/Vg). A tailwind of the same proportion as your forward velocity means 1-1 = 0 which multiplied to K effectively cancels your need to combat any wind. It is free speed which you can devote to the terms A and B.  The funny part is that a tailwind never gives you back the "same amount" of speed as the headwind will take away from you. Its a law of nature.

PART 2 : Power Variation With Density Change As Velocity Ratio Remains Constant

Previously, we looked at change in power to weight ratio with change in wind speed. 

Fact of the matter is, air density does change appreciably with altitude as you ascend.  So this term varies with density as climbing progresses :

Term = K.p.(1+ Vw/Vg )²

where K is defined to be K = C.Vg ³ 

The Standard Atmosphere chart, which I pulled out of a book and approximated by a polynomial fit in Excel, tells me the following :

1) At an altitude of 500m (1640 ft), the density is 95% of what it is at sea level. That's a 5% decrease.
2) At an altitude of 1000m (3281 ft), density has decreased by 9.2%. 
3) At an altitude of 1500m (4921 ft), density has decreased by 13.5%. 
4) At an altitude of 2000m (6562ft) , density is now only 82% of its sea level value, a decrease of 18%.

Air density is gently geometrical for the first 1 or 2 miles of the earth's atmosphere. Here is how it behaves :

Like before, I derive the % decrease in power requirements due to altitude with zero headwind (Vw/Vg=0). Let L be the amount representing % of sea level density at any given altitude. If po is sea level density,

 % decrease in power =

[1- (L/100)] / [1+ (A+B)/(Kpo(1+Vw/Vg)² ]

The effect altitude and hence air density has on relieving a rider is very gently geometrical, and not linear. This is proven below. The linear trend-line as you can see doesn't fit 100%.

FIG 7: The number on the y-axis shows how much power to weight ratio one can potentially save while climbing at higher altitude. This is because the higher the altitude, the lesser is the pressure and density of air. This is also why World Hour Record attemps are often done in stadiums that are located high above sea level. Beyond 2500 m ofcourse, advantages in power savings are countered by the thinning of the air. 

FIG 8 :  This diagram simply shows to what degree headwinds and air density contribute to power requirements.

Part 3 : Conclusion & Validation

If wind conditions changed as climbing progresses, density decreases. Whereas wind exponentially increases the power requirements, the density moderately decreases it since you require lesser effort to propel in a less dense medium. But wind is the biggest power soaker.

Here is an interesting chart showing the effects of wind on power to weight ratio given finishing times for Alpe d'Huez. This legendary climb is much more shorter and steeper than Tourmalet but located at lower altitude. It was compiled by Alex Simmons, a cycling coach from Australia.  Perhaps my charts can supplement his or vice versa? It is really well made. 

Simmons' plot can be a sanity check in that power to weight ratio needed with wind on Alpe d'Huez closely correspond with mine for the Tourmalet. I must however add that I have not considered the losses due to drivetrain in my model. For example, a +2.5 mph headwind is a 0.25 velocity ratio. Corresponding additional power to weight ratio (Fig 6) is about 0.13 W/kg from the no wind condition. Assuming a bike is 95% efficient, 0.13/0.95 = 0.14 W/kg. This is my required increase.

Simmons' model for the steeper Alpe d'Huez, on the other hand, says that it should be +0.5 W/kg.  Is this +0.5 W/kg an overestimation, considering that a 2.5 mph wind is classified as just "Light Air" in the Beufort Wind Scale?

If 70 kg rider is producing 6W/kg, he is riding at 420 Watts. A +0.5 W/kg increase means he has to propel himself now at 455 Watts! Phew!

I'm not surprised it is higher than mine since the grade is steeper and my rider weight is 65 kg, although my choice for bike weight is same as his. Also, an important thing to note is that Alpe d'Huez is at lower altitude than the Tourmalet. Hence, it is more than likely that a rider has to put forth more watts on the Alpe than on the Tourmalet. Remember the mildly geometrical reduction effect of density decrease?

Another interesting bit to notice also from the plot above is that a cyclist climbing Alpe d'Huez doesn't get back the same relief from power to weight ratio with a tailwind as the extra amount he has to spend in a headwind. Its funny how that works. Its like climbing hills. You don't get back the time you spent going uphill by going fast downhill.

How about verification of the altitude's effect? First, Analytic Cycling's "Forces on Rider" model shows the following power requirements at the bottom, mid point, and top of Tourmalet. Speed was kept constant at 10 mph and all other parameters were made to match my choices before.

You can notice a 1 Watt power demand reduction just by riding from the bottom of the Tourmalet to approximately its midpoint (a 600m elevation change). Not much really in the overall scheme of things since that's a 1W/65kg = 0.003 W/kg decrease. My model (Fig 7) says 0.016 W/kg is the reduction so they're pretty close. From 1400 to 2200m, the reduction is again 1 W, or 0.003 W/kg for the Tom's model. My model says 0.02 W/kg.

Secondly, although data is severely lacking with regards to the effect of altitude on power to weight ratio, a couple of other researchers in the exercise physiology field looked at how aerobic power varied  for 4 groups of runners, not cyclists. They estimated that aerobic power as a percentage of that at sea level, signified by "y", drops off wrt to elevation by the following relationship :

Below, I have plotted those 3 estimations along with mine (65 kg rider producing 6W/kg) upto an altitude of 2200m (the max height of the Tourmalet).

What we see above is apples and oranges. Mine calculates the relief in effort to maintain the same speed due to decrease in altitude density while the others have calculated the decline in power output due to a decline in VO2 max output. They really don't co-relate, do they (advantage vs degradation) ? But is it fair to say that the net effect of both of these phenomena is a curve in-between them?


I must conclude by stating that Alex's theoretical calculations for the wind effect matches closely with mine but this is not the same case for the altitude effect (see above). However, it remains to be said that all our numbers remain to be validated from real powermeter data and CFD simulations for cycling. I'm curious to see how both wind, and high altitude, affect a cyclist in the real world and I'll bet the changes are highly non-linear in nature.  Discussions ongoing at Cycling Forums.

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