Kittel Bookends 100th Tour de France Won by Froome

German Marcel Kittel just edged fellow countryman André Greipel and my pick, Mark Cavendish, to win the final stage of this year's Tour de France.  Kittel took the first stage this year, as well as Stages 10 and 12.  Darkness was falling upon Paris as Kittle crossed the finish line, but the good times were just getting underway as the city will surely celebrate its 100th Tour de France well into the night.  Below is how Kittel's time compares to our prediction.

• Stage 21:  3h 06' 14" (actual), 3h 15' 47" (prediction), 09' 33" slow (5.13% error)

I am surprised that this final stage was as fast as it was, though I shouldn't be, given how the second week went.  Below is Kittel's average speed.

• Stage 21:  11.95 m/s (43.0 kph or 26.73 mph)

At least there was some exciting sprinting to close out this year's race!  Congratulations to Christopher Froome of Team Sky for winning this historic Tour de France.

It was a fun three weeks following the Tour de France and posting predictions.  I thank my student, Brian Ramsey, for all the work he put into this year's model.  I also thank colleagues, friends, and the many people I don't know around the world who checked out my blog.  If a little physics you found here increased your enjoyment of the Tour de France by just the tinniest amount, that's good enough for me.  I'll probably have more to write about the Tour de France in the not-too-distant future.

Huge Day for Quintana!

Colombian Nairo Quintana and his Movistar Team had a monster mountain win today.  The 23-year-old climber not only dominated Mont Semnoz to reach the finish line first, he secured both the white and polka-dot jerseys AND now sits second overall, 05' 03" behind Chris Froome.  Nairo Quintana will be a major force to be reckoned with in future Tours de France!  Below is Quintana's time and the comparison with our prediction.

• Stage 20:  3h 39' 04" (actual), 3h 45' 04" (prediction), 06' 00" slow (2.74% error)

We were worried that our time was going to be much too slow, but we had no need to worry.  We'll take another prediction under 3%!  Below is Quintana's average speed for the stage.

• Stage 20:  9.510 m/s (34.24 kph or 21.27 mph)

Of the 170 cyclists who crossed the finish line, 25 (about 14.7%) beat our predicted time.  All the athletes should sleep well tonight after the past three days in the Alps.

The 100th Tour de France comes to an end tomorrow as Stage 21 takes riders between two famous cities.  Beginning in Versailles, cyclists loop south for a couple of short category-4 climbs before heading northeast to Paris.  The flat stage has a length of 133.5 km (82.95 mi).  The ride along the famed Avenue des Champs-Élysées toward the Arc de Triomphe will be a day to remember as the 100th edition of the world's most famous bicycle race reaches its climax.  Chris Froome should close the deal and give Team Sky two wins in a row.

The final stage is difficult to predict because so much of it is ceremonial.  There are some good sprints, and Mark Cavendish usually dazzles, but predicting how competitive the stage will be is tough.  Nonetheless, we offer our final prediction for this year's Tour de France below.

• Stage 21:  3h 15' 47" (prediction)

That time might be a bit fast, but we are hoping to see some great racing in addition to all the pomp and circumstance.  Enjoy the final stage!

Costa Takes Stage 19 in the Rain!

Rui Costa of Portugal won his second mountain stage today.  There was a lot of rain in the latter part of the route.  We were denied a great downhill sprint to finish the stage.  Cyclists were cautious on the final descent, including having to dodge some nutty fans who were out in the road with their umbrellas.  Below is Costa's winning time and the comparison with our prediction.

• Stage 19:  5h 59' 01" (actual), 5h 48' 01" (prediction), 11' 00" fast (-3.06% fast)

We like our small error and, as I wrote yesterday, we were a faster than today's top cyclist.  Below is Costa's average speed.

• Stage 19:  9.494 m/s (34.18 kph or 21.24 mph)

I mentioned yesterday that I thought the winning time should be over six hours.  When I saw all the rain on the final descent and watched Costa cruise to victory with no real sprint at the end, I was even more surprised that the top two cyclists sneaked in under six hours.  The reason is that today's stage is almost an exact replica of Stage 17 in the 2004 Tour de France.  Click here and scroll down to Stage 17's profile.  When you compare that profile with today's profile (click here, scroll down, and click on "Stage profile"), you'll see the same 204.5-km distance, the same two early climbs to Col du Glandon and Col de la Madeleine, and then a category-2 climb followed by two category-1 climbs.  The second category-1 climb was indeed a different mountain in 2004 compared to today's stage, and there are some more differences in the middle of each stage, including the location of the sprint.  I am neither claiming that the two stages are exact nor that cycling Stage 17 in 2004 is exactly the same as cycling Stage 19 in 2013.  But, the stages are about as similar as two stages of the Tour de France can be:  same beginning and ending communes (sightly different elevations), same distance, and almost the same climbs.  Lance Armstrong won 2004's Stage 17 with a time of 6h 11' 52", which is why we thought our prediction was going to be much too fast today.  We are impressed to see 46 of 170 (about 27%) cyclists finish today's rainy stage in a time less than 6h 11' 52".

Given that they finished today's stage in the same group, Froome maintained his 05' 11" lead on Contador.  It is clearly Christopher Froome's Tour de France to lose.

Tomorrow's final mountain stage is short at just 125 km (77.7 mi).  Beginning in the commune of Annecy, Stage 20 has cyclists tackle a category-2 climb early on, followed by three category-3 climbs by the time they reach the two-fifths point of the route.  They then have a category-1 climb to the 1463-m (4800-ft) peak of Mont Revard.  The Alps bids cyclists adieu with an hors catégorie stage-ending climb to the 1655-m (5430-ft) peak at Mont Semnoz.  As much as we thought today's stage prediction would be too fast, we think that the way this year's Tour de France has played out, we'll return to being too slow tomorrow.  Below is our Stage 20 prediction.

• Stage 20:  3h 45' 04" (prediction)

If I were betting, this year's Tour de France makes me think 3h 15' 00" will be more likely tomorrow.  But, if the past two, grueling mountain stages have worn the cyclists down a little, we might be have a shot.  Let's hope there is no rain tomorrow!

A Great Day for France!

What a phenomenal stage today!  My student, Brian Ramsey, and I sat in my office and watched the second half of today's stage with its historic double pass on Alpe-d'Huez.  Right at the 2-km (1.2-mi) mark, France's very own Christophe Riblon found a reserve of energy and kicked it into high gear.  Riblon blew past Tejay van Garderen of the US and then savored the final few hundred meters of the stage as throngs of French cheered him on.  Below is how our prediction fared against Riblon's great day.

• Stage 18:  4h 51' 32" (actual), 4h 59' 50" (prediction), 08' 18" slow (2.85% error)

We are extremely pleased to hit such an unpredictable and challenging stage to better than 3%!  Of the 175 cyclists who finished today's stage, 32 (about 18%) beat our predicted time today.  Riblon's average speed is given below.

• Stage 18:  9.862 m/s (35.50 kph or 22.06 mph)

What an impressive ride for Riblon!  I hope cyclists are able to get plenty of rest tonight.  Tomorrow's 204.5-km (127.1-mi) mountain stage will require lots of energy expenditure, perhaps as much as 9000 Calories.  Beginning in the commune of Le Bourg-d'Oisans, cyclists will be immediately hit with an hors catégorie climb to reach the 1924-m (6312-ft) peak of Col du Glandon.  A lightening-fast downhill leads to another hors catégorie climb to Col de la Madeleine's peak at an even 2000 m (6562 ft) elevation.  A category-2 and two category-1 climbs must be traversed before reaching the stage's end north of the starting point at the commune of Le Grand-Bornand.  Below is our prediction.

• Stage 19:  5h 48' 01" (prediction)

Of all this year's Tour de France stages, this is the one we thought our model would get too fast.  I'll explain in tomorrow's post why I think this stage should be won in a time that goes over six hours.  If tomorrow's winner sneaks in under six hours, I'll be writing about top speeds again.

Froome gained nearly a minute of time today over Contador for the overall classification lead.  Will anyone catch Froome tomorrow???

Froome Edges Contador in Rainy Time Trial!

Chris Froome was the last rider in, and just eclipsed Alberto Contador's time by nine seconds to win today's individual time trial.  Contador is now second overall at 04' 34" behind Froome.  Below is how Froome did against our prediction.

• Stage 17:  51' 33" (actual), 44' 49" (prediction), 06' 44" fast (-13.06% error)

Our prediction for this time trial now represents our worst prediction of the race.  After the way this Tour de France has gone, we would have been shocked that we were so fast with our prediction had we not observed the competition.  But today was not an ordinary race day.  There were thunderstorms, swirling winds, and even hail at times.  Riders slowed through some very dangerous spots, especially on the two major downhills.  Instead of seeing possible through-the-roof speeds, Mother Nature slowed everyone down.  Even the Tour de France's time-schedule conservative estimate of 47' was well off the winning time.  Just when we thought we had a predicted time that could compete with this year's speedy cyclists, the weather put a stop to that!  Froome's average speed is below.

• Stage 17:  10.35 m/s (37.25 kph or 23.14 mph)

Probably the most anticipated stage of this year's Tour de France is tomorrow's Stage 18.  The 172.5-km (107.2-mi) long mountain stage begins where Stage 16 left off, in the southeastern French commune of Gap.  The stage ends north of Gap at the famous ski resort Alpe-d'Huez, which sits at an elevation of 1850 m (6070 ft).  Alpe-d'Huez has appeared in several Tours de France, always challenging riders with its renowned 21 hairpin turns (click here for a great Wikipedia image).  What makes this year's Stage 18 so special is that for the first time in the 100-year history of the Tour de France, the ascent to Alpe-d'Huez will be made twice.  Cyclists will reach Le Bourg-d'Oisans after being on their bikes for 108 km (67.1 mi) and having already navigated a category-3 climb and two category-2 climbs.  They will then begin their first climb toward Alpe-d'Huez, an hors catégorie climb for sure.  Reaching the peak won't be their high-elevation mark for the day because they then have a category-2 climb to the top of Col de Sarenne, which sits at 1999 m (6558 ft) above sea level.  A sure-to-be fantastic downhill sets 
up the final hors catégorie return to Alpe-d'Huez.

When we developed our model for this year's Tour de France, we were especially interested in what our model had to say about Stage 18.  Below is our prediction.

• Stage 18:  4h 59' 50" (prediction)

So many unpredictable complications take place on mountain stages.  The weather is unpredictable, elevation changes wreak havoc on cyclists, and strategies may change on the fly.  Regardless of how our prediction comes out, tomorrow's stage is bound to be memorable!

Costa Takes Stage 16!

Portuguese cyclist Rui Costa won today's Stage 16.  He cruised to the finish line with a 42-second lead over the next rider in.  Below is Costa's time compared to our prediction.

• Stage 16:  3h 52' 45" (actual), 4h 12' 20" (prediction), 19' 35" slow (8.41% error)

As advertised yesterday, we once again came in too slow.  My "throw my hands in the air" guess of 3h 45' 00" would have made for a fine prediction today.  Today's race began with a temperature around 32 C (89.6 F) and a 10 kph (6.2 mph) tailwind.  I knew our prediction was in trouble when I saw the tailwind.  Winds then swirled for much of the second half of the stage.  Below is Costa's average speed.

• Stage 16:  12.03 m/s (43.3 kph or 26.91 mph)

We don't find that average speed to be especially anomalous.  With early tailwinds and higher-than-expected overall speeds this year, our prediction is about where we thought it would be.  Of the 179 riders who competed today, 93 (about 52%) beat our predicted time.  In 2003, getting a prediction under 10% was the expectation.  A decade later, we expect to do much better.

To give you a feeling of where things stand after 16 stages, we note that Chris Froome, who retains the yellow jersey after today's stage and now has a 04' 14" lead over Bauke Mollema of the Netherlands, currently has an overall average speed of 41.92 kph (26.05 mph).  After 16 stages (i.e. Stages 0-15) in last year's Tour de France, Bradley Wiggins was the overall leader with an average speed of 40.27 kph (25.02 mph).  If the 2012 version of Bradley Wiggins were competing right now with that same average speed, he would currently sit in 165th place with just 15 cyclists behind him.  Clearly, the first 16 stages of this year's Tour de France are different from the first 16 stages of last year's race.  What is written in this paragraph is not meant to be a rigorous comparison between the race after 16 stages this year and the first 16 stages from last year.  I offer the average speed comparison merely to point out that speeds are up this year.  I'll make the same comparison once this year's Tour de France ends.

Tomorrow's Stage 17 is an individual time trial of length 32 km (20 mi).  Beginning in the southeastern French commune of Embrun, the stage heads due west to the commune of Chorges.  The time trial contains two category-2 climbs.  Below is our prediction.

• Stage 17:  44' 49" (prediction)

The way the second half of this Tour de France is going, we fully expect to see jaw-dropping speeds tomorrow.

Stage 16 Prediction

The Tour de France picks up tomorrow in the southeastern French commune of Vaison-la-Romaine.  The medium mountain stage takes riders 168 km (104 mi) east and slightly north to the commune of Gap.   Riders meet a category-3 climb early, followed quickly by a category-2 climb.  A second category-2 climb in the Alps awaits riders near the stage's end as they'll ascend the 1268-m (4160-ft) peak of Col de Manse.  The stage should end with a great downhill sprint.  Cyclists will meet Col de Manse again on Thursday in this year's much-anticipated Stage 18.  Below is our Stage 16 prediction.

• Stage 16:  4h 12' 20" (prediction)

I fully expect our prediction to be slow once again.  The temptation to tweak our model in the middle of the race is strong, but I resist that because such a tweak at this point is not scientific.  We need more time to explore motivations for needed changes.  If I were betting on tomorrow's stage, I might go with a time of 3h 45' 00", given how fast the cyclists were in the past week.  As I've already noted, our model that worked well in 2012 worked well during the first week of this year's race, but did not work well last week.  There is much to learn this week!

Froome is King of the Mountain!

Chris Froome gave Team Sky a huge win today after beating Nairo Quintana of Columbia to the top of Mont Ventoux.  Our prediction was just terrible.

• Stage 15:  5h 48' 45" (actual), 6h 30' 17" (prediction), 41' 32" slow (11.91% error)

This stage is, by far, our worst predicted stage of this year's Tour de France.  Below is Froome's unbelievable average speed for today's win.

• Stage 15:  11.60 m/s (41.72 kph or 25.92 mph)

To give you some idea of why we are stunned by what has been happening in the past week, consider a few more details about today's stage.

1. As I wrote yesterday, today's monster climb began after 221 km (137 mi) of cycling.  When the lead cyclists reached that point today, they were averaging just a hair under 47 kph (29 mph).
2. Knowing that climbing Mont Ventoux was ahead of them, cyclists had biked 30 km (19 mi) longer than yesterday's Stage 14, and the leaders had an average speed 2 kph (1.2 mph) greater than yesterday's winners.  Granted, yesterday's stage had more climbs than the first 221 km of today's stage.  Still, that is quite a pace for a distance that exceeds all but two stage lengths this year.
3. My estimate is that Froome finished at 4:33 pm local time.  The Tour de France's website created three time schedules based on three average speed estimates.  Those estimates were, from high to low, 39 kph, 37 kph, and 35 kph.  The time schedule has the finish time for the fast average speed estimate at 4:58 pm local time, 6h 23' after the race started, and 5:41 pm for the slow average speed estimate, 7h 06' after the race started.  As I've noted in my last couple of posts, I hope those looking for live action in France are getting to various points along the route well in advance of the time schedule estimates.
4. When Juan Manuel Gárate of Spain won Stage 20 in the 2009 Tour de France, which was a 167-km (104-mi) long stage that ended atop Mont Ventoux, his average speed was 35.87 kph (22.29 mph).
5. When Richard Virenque of France won Stage 14 in the 2002 Tour de France, which was a 221-km (137-mi) long stage that ended atop Mont Ventoux, his average speed was 38.61 kph (23.99 mph).  Froome biked 21.5 km (13.4 mi) farther today, and it took him just five minutes longer than the time Virenque needed in 2002.
6. When Marco Pantani of Italy won Stage 12 of the 2000 Tour de France, which was just 149 km (92.6 mi) long and also ended atop Mont Ventoux, his average speed was 35.03 kph (21.77 mph).

I joked with a few colleagues yesterday that if today's winner had an average speed over 40 kph, I should jump out my office window and see if I, too, can fly.  To see nearly 42 kph as the winner's average speed for this stage boggles my mind.  180 cyclists beat our time today; one did not.  Froome clearly retains the yellow jersey as well as the polka-dot jersey.

What has happened in the Tour de France this past week has been unprecedented.  Not only do the cyclists need a day off tomorrow, I need a day off to get my head to stop spinning.

Our sure-to-be-slow prediction for Stage 16 will be posted tomorrow.

Trentin Wins Stage 14!

Matteo Trentin ended Italy's three-year absence from the winner's podium by taking today's Stage 14.  No shock how our prediction fared against this year's fast cyclists.

• Stage 14:  4h 15' 11" (actual), 4h 35' 15", 20' 04" slow (7.86% error)

As with Stage 13, my "if they're still flying more than in 2012" prediction of 4h 20' 00" was still five minutes too slow.  Also as in Stage 13, all 181 cyclists beat our time.  We went from great predictions early on to rather slow predictions for the past four stages.  Trentin's average speed is given below.

• Stage 14:  12.47 m/s (44.91 kph or 27.91 mph)

Today's stage was 191 km long.  How fast is the above speed?  Stages 2 (156 km) and 3 (145.5 km) from this year's race were both classified medium mountain.  The averages speeds for the winners in those two stages were 41.94 kph and 39.43 kph.  The Tour de France's website had 43 kph as its maximum estimate for today's Stage 14 (I hope those of you in France got out earlier than what was on the time schedule!).  Today's last place finisher (181st place) had an average speed of 43.02 kph.  How about a comparison to last year's four medium-mountain stages' winners' average speeds?  Check out the table below (2012 Tour de France medium-mountain stages).

Stage	Length (km)	vave (kph)
3	197.0	41.77
7	199.0	39.99
8	157.5	40.01
12	226.0	39.56

Medium-mountain and mountain stages are probably harder to compare from year to year than flat stages because weather, strategy, and all the random things that happen during a stage can make comparisons in different mountains moot (i.e. simply looking at length and average speed is not good enough for a scientific comparison).  With much study ahead of us, all I can do now is a superficial comparison.  Today's last-place finisher's average speed beat the winners of this year's Stages 2 and 3 and all of last year's medium-mountain stage winners.  To say that we are perplexed by what is happening in the middle of this year's Tour de France is an understatement.

Tomorrow's Stage 15 is a 242.5-km (150.7-mi) mountain stage.  When the stages were released for this year's Tour de France, I thought Stage 15 looked incredible.  Imagine what it takes to cycle 221 km (137 mi), enduring three category-4 climbs and one category-3 climb along the way.  Think you would be tired?  That 221-km distance is longer than all but two of this year's 21 stages.  So, imagine beginning in eastern France in the commune of Givors and then biking for 221 km all the way to the commune of Bédoin, which sits in southeastern France.  You would have biked a distance that would have had you finished in 19 of 21 stages this year.  But you wouldn't be finished yet!  Another 21.5 km (13.4 mi) remains in the stage.  You reach Bédoin at an elevation of 330 m (1083 ft) knowing you won't be finished until you ascend Mount Ventoux and reach an elevation of 1912 m (6273 ft or 1.188 mi).  How do you fancy that?!?  The hors catégorie climb is a 7.5% grade on average and will surely separate contenders from pretenders.

Given how the middle of this race has gone, the prediction below is offered with tepid confidence.

• Stage 15:  6h 30' 17" (prediction)

There is a reason that Monday is a rest day.  Enjoy the magnificent scenery and the grueling 1582-m (5190-ft) climb up the "Beast of Provence" in the final 21.5 km (13.4 mi) of tomorrow's stage!

The Manx Missile Blasts Off Again!

Mark Cavendish won his second stage of this year's Tour de France.  Chris Froome maintains his hold on the yellow jersey.  As I expected, we were once again too slow.  Below is Cavendish's time compared to our prediction.

• Stage 13:  3h 40' 08" (actual), 4h 01' 57" (prediction), 21' 49" slow (9.91% error)

Despite 15 kph (9.3 mph) crosswinds with headwind components, Cavendish was able to achieve the average speed you see below.

• Stage 13:  13.10 m/s (47.15 kph or 29.30 mph)

Check out my post from yesterday.  Granted, only Stage 15 from last year's race was shorter than today's 173-km (107-mi) stage.  Still, no average speed from last year's flat stages comes close to what was seen today.  Last year's Stage 15 was 14.5 km (9.01 mi) shorter than today's stage, yet the winner's average speed in that stage was 43.18 kph (26.83 mph).  Even my super-low estimate of 3h 45' 00" at the end of yesterday's post would have been five minutes too slow.

All 181 cyclists beat our prediction today.  The last rider's time was 3h 53' 44", which gives an average speed of 44.41 kph (27.59 mph).  That would have been the third fastest average speed for last year's flat stages.  Put another way, today's last-place finisher had an average speed that would have won six of last year's flat stages.

To say we are flummoxed by the speeds we've seen in recent stages would be an understatement!  For those of you in France who are watching the race live, be sure to get out earlier than what the Tour de France website suggests on its time schedule.  Today's time schedule had 46.0 kph (28.6 mph) for its maximum estimated average speed.

Tomorrow's Stage 14 is of the medium-mountain variety.  The 191-km (119-mi) stage begins in the commune of Saint-Pourçain-sur-Sioule and ends to the southeast in the city of Lyon.  Along the way, cyclists will meet five category-4 climbs and two category-3 climbs.  Our prediction is given below.

• Stage 14:  4h 35' 15" (prediction)

If this were 2012, I would be quite confident with the above prediction.  Given how this year is going, I won't be surprised to see something close to 4h 20' 00".  I am not trying to play two predictions.  We are sticking with what is written above because we want to be fair to the model we created when this race started.  It is clear, however, that the jump in athletic performance and technology from last year to his year is greater than we anticipated.

Kittel wins his third stage!

German Marcel Kittel won his third stage of this year's Tour de France (recall he won Stages 1 and 10) by just barely beating out Mark Cavendish at the finish line.  Chris Froome still holds the yellow jersey.  Below is how Kittel's time compared to our prediction.

• Stage 12:  4h 49' 49" (actual), 5h 02' 54" (prediction), 13' 05" slow (4.51% error)

There is a clear theme with our modeling this year.  We simply do not have quite enough power output to match the winning times we are seeing.  All 182 cyclists beat our prediction today, and that was despite 20 kph (12 mph) crosswinds with predominately headwind components.  Check out the average speed below for Kittel's win.

• Stage 12:  12.54 m/s (45.13 kph or 28.04 mph)

You see the average speed above for today's 218-km (135-mi) flat stage.  Below is a table of last year's (2012 Tour de France) flat stages and the average speeds for the winners of those stages.

Stage	Length (km)	vave (kph)
1	198.0	39.82
2	207.5	41.92
4	214.5	40.40
5	196.5	41.88
6	207.5	44.95
13	217.0	43.69
15	158.5	43.18
18	222.5	45.38

I left out the ceremonial last stage.  Only Mark Cavendish's phenomenal ride in last year's Stage 18, a stage on which we were 7.10% slow, has an average speed in excess of today's average speed.  What is all the more remarkable about Cavendish's win in last year's Stage 18 is that that stage was 4.5 km (2.8 mi) longer than today's Stage 12.  Whether last year's flat stages were longer or shorter than today's stage, only last year's Stage 18 exceeds today's speed.

It should be obvious from the above table why we have been surprised by this year's race.  The technology that goes into the bikes and apparel, the teams' strategies, and the athletes' performances must have improved considerably since last year's race.  Every Tour de France is different and every stage is different.  Still, we are impressed with this year's speeds.

Tomorrow's Stage 13 is also flat.  It picks up where today's left off, in Tours, and sends riders 173 km (107 mi) southeast to the commune of Saint-Amand-Montrond, which is located right in the center of France.  Below is our prediction.

• Stage 13:  4h 01' 57" (prediction)

Will riders save a little for the daunting mountain stages in the Alps?  Or will they go all out to secure the best time position before the climbing begins?  There is a short category-4 climb in tomorrow's stage, but the route is mostly flat.  Given how fast cyclists have been this year, I won't be surprised to see a winning time closer to 3h 45' 00", but I'll stick with the prediction above.

Tony Martin Blows Away Time Trial!

We continue to be stunned by speeds at this year's Tour de France.  German Tony Martin won today's Stage 11, an individual time trial.  He was 12" faster than second-place finisher Chris Froome of Great Britain (Froome retains the yellow jersey) and 01' 01" faster than third-place finisher Thomas De Gendt of Belgium.  That is quite a gap between first place and third place!  Below is Martin's winning time compared to our prediction.

• Stage 11:  36' 29" (actual), 39' 23" (prediction), 02' 54" slow (7.95% error)

Below is Martin's average speed.

• Stage 11:  15.08 m/s (54.27 kph or 33.72 mph)

Let's try to put that average speed into perspective.  Today's time trial took place over 33.0 km (20.5 mi).  Last year's Stage 9 was an individual time trial over 41.5 km (25.8 mi).  Bradley Wiggins won that stage with an average speed of 13.46 m/s (48.44 kph or 30.10 mph).  When today's winner, Tony Martin, won Stage 20 in 2011, an individual time trial over 42.5 km (26.4 mi), his average speed was 12.75 m/s (45.90 kph or 28.52 mph).  Granted, those two time trials were over distances more than 25% longer than today's time trial, so we fully expect today's average speed to be greater than the two aforementioned time trials.

Well, what about Stage 4 in 2008, an individual time trial over 29.5 km (18.3 mi), about 89% the length of today's stage?  Stefan Schumacher won that stage with an average speed of 13.76 m/s (49.53 kph or 30.78 mph).  That stage was run in the French commune of Cholet, which sits at an elevation not much different from today's stage.  Winds with tailwind components switched to headwind components as today's action moved along.  Even with a tailwind, we are immensely impressed with Martin's ride!

Our predicted time was beaten by 37 cyclists; 145 came in slower than our prediction.  We thus predicted a time that about 20% of the cyclists beat.  Martin not only beat our prediction, he crushed it.  He and Froome also crushed the other 180 riders today.

Tomorrow's Stage 12 is about as flat as flat can be.  Starting in the northwest French commune of Fougères, the 218-km (135-mi) stage takes riders southeast to the city of Tours.  Below is our prediction.

• Stage 12:  5h 02' 54" (prediction)

The way stages have turned out so far, we certainly won't be surprised to see a cyclist cross the finish line in under five hours!

Headwinds Dominate Stage 10!

German Marcel Kittel just edged fellow countryman André Greipel at the finish line of a very windy Stage 10.  Below is a comparison between Kittel's time and our prediction.

• Stage 10:  4h 53' 25" (actual), 4h 34' 42" (prediction), 18' 43" fast (-6.38% error)

Had we not been following today's action and seen only the winning time, we would have been quite disappointed.  What we noticed while following the race is some wild wind.  There were crosswinds of 30 kph (19 mph) with headwind components dominating the entire stage.  We simply knew our prediction was going to be too fast if cyclists had to battle headwinds all day!

Below is a table showing what a small horizontal headwind can do to our prediction for Stage 10.

vhead (kph)	Prediction
1	4h 41' 17"
2	4h 48' 13"
3	4h 55' 30"
4	5h 03' 11"
5	5h 11' 16"

Note that what is assumed in making the above table is that riders feel a constant headwind of a given magnitude for the entire race, which is a gross oversimplification of reality.  What we noticed today were gusts of winds that reached 30 kph with directions mostly perpendicular to the riders' motion (i.e. crosswinds) with headwind components.  That means that cyclists felt only a small piece of the wind as a headwind on average.  There were times when the headwind was strong, and there were a few times late in the stage when the wind actually gave a tailwind component.  What the above table shows us is that the effect of today's wind was equivalent to riders feeling a constant headwind of about 3 kph.

Below is Kittel's average speed.

• Stage 10:  11.19 m/s (40.28 kph or 25.03 mph)

Stage 11 is an individual time trial.  Beginning in the northwest French commune of Avranches, the 33.0-km (20.5-mi) time trail ends on the tidal island of Mont Saint-Michel in the English Channel.  Riders should go all out with a flat stage to follow on the next day.  Below is our prediction.

• Stage 11:  39' 23" (prediction)

Look for top speeds tomorrow!

Stage 10 Prediction

The Tour de France is at rest today.  Tomorrow's action picks up with a flat Stage 10, which begins in the western French commune of Saint-Gildad-des-Bois and then heads due north for 197 km (122 mi) to the city of Saint-Malo on the English Channel.  There is one category-4 climb nearly three quarters of the way in, but it's a short climb and certainly nothing like what riders experienced in the Pyrenees.  Below is our prediction.

• Stage 10:  4h 34' 42" (prediction)

Six more stages greet cyclists before the next rest day.  Will cyclists use today's rest to gear up for tomorrow?  Or will they hold back a little for the next day's individual time trial?  We shall see!

Martin Takes a Grueling Stage 9!

Irishman Dan Martin made a late move to win today's five-climb mountain stage.  Below is Martin's time and a comparison with our prediction.

• Stage 9:  4h 43' 03" (actual), 4h 56' 40" (prediction), 13' 37" slow (4.81% error)

Though we did better than yesterday's bad prediction, and we are glad to be back under 5% off, we will have to examine our model's power outputs for the mountains stages.  The power outputs we use are based on physiological research and power outputs needed in previous races.  The athletes are simply doing a bit better than we thought.  We always hope for small errors, but the past two stages have given us an opportunity to learn something.  That's what makes doing science fun!

Below is Martin's average speed for his big win today.

• Stage 9:  9.922 m/s (35.72 kph or 22.19 mph)

That is a phenomenal average speed for such a grueling mountain stage!  A total of 57 riders beat our time with the bottom 16 of that group coming in only about two minutes under our time.  There were 125 riders who came in over our time, which means our prediction was beaten by about 31% of the riders.

Chris Froome retains the yellow jersey.  He now has a 01' 25" lead over second-place rider Alejandro Valverde, the Green Bullet from Spain.  Cyclists will have to fly due north for the next stage, which takes place in northwest France.  A day off tomorrow will get them ready for a flat stage on Tuesday.  Check back tomorrow to find out what we will predict for Stage 10.

Great stage for Froome ... bad stage for us ...

Chris Froome of the Sky Procycling Team, one of the world's best climbers in the mountains, won today's Stage 8.  He also took hold of the yellow jersey; he holds a 51" lead over Sky teammate Richie Porte of Australia.  Below is Froome's time and the comparison with our prediction.

• Stage 8:  5h 03' 18" (actual), 5h 30' 55" (prediction), 27' 37" slow (9.11% error)

When I began modeling the Tour de France in 2003 with Ben Hannas, we were happy that the majority of our predictions came in under 10%.  That's not true today.  Our prediction for this stage was just BAD -- no other way around it.  We'll have to look carefully at this stage and determine where the flaw in our model for this stage is lurking.  We note that 94 cyclists, which represent half the field, finished in a time greater than our prediction.  What our prediction pegged was the average Tour de France cyclist, not the day's best.

Froome's average speed is given below.

• Stage 8:  10.72 m/s (38.58 kph or 23.97 mph)

That's a great average considering the two big climbs cyclists traversed today.  Well done, Froomey!

Tomorrow's Stage 9 is a full-fledged mountain stage in the Pyrenees.  The commune of Saint-Girons is the starting point of the 168.5-km (104.7-mi) stage, which ends to the west in Bagnères-de-Bigorre.  Riders contend with a category-2 climb early on, and then face four category-1 climbs before the 30-km (19-mi) descent to the finish line.  A stage like this requires incredible athletes and well-planned strategy.  Below is our prediction.

• Stage 9:  4h 56' 40" (prediction)

We've been just a bit slow on each stage, until today when were much too slow.  We love our predictions for the first seven stages; we hope to take a mulligan on today.  Monday, 8 July is a rest day.  After tomorrow's stage, riders will need a day off!

The Terminator Takes Stage 7!

The Terminator, as 23-year-old Peter Sagan from Slovakia is known, won today's Stage 7 after a great downhill sprint to the finish.  Below is how our prediction fared against today's result.

• Stage 7:  4h 54' 12" (actual) 5h 00' 15" (prediction), 06' 03" slow (2.06% error)

We are thrilled to be just 2% off today's stage-winning time.  We are especially happy with our modeling given that cyclists enjoyed a tailwind of roughly 15 kph (9.3 mph) during most of their final 30-km (19-mi) descent toward the finish line.  Without that tailwind, we would have been much closer!  As I've noted all along, though easy to include if known, we can't predict local weather effects.

Below is Sagan's average speed for today.

• Stage 7:  11.64 m/s (41.91 kph or 26.04 mph)

South Africa's Daryl Impey retains the yellow jersey with a three-second lead over Edvaold Boasson Hagen of Norway.

The Tour de France hits the Pyrenees in tomorrow's Stage 8.  Beginning in the southern French commune of Castres, the 195-km (121-mi) stage has a category-4 climb early on and heads south from there.  The end of the stage features a brutal category-1 climb to the resort Ax 3 Domaines, which is at an elevation of 1375 m (4511 ft).  Before thinking that the end climb is what will challenge riders most, consider the climb to the 2001-m (6565-ft) peak of Col de Pailhères, which riders reach 29 km (18 mi) before the resort finish.  The climb to that peak is classified HC or hors catégorie, which means "beyond categorization."  You wouldn't know Stage 8 is a mountain stage two-thirds of the way in.  After that, the Pyrenees Mountains take over!  Below is our prediction.

• Stage 8:  5h 30' 55" (prediction)

If you can only watch part of tomorrow's stage, tune in to the final third.  Two monster climbs sandwiched between a sensational downhill will make for exciting viewing.

Gorilla and a Windy Stage 6

As I wrote yesterday was possible, weather played a role in today's stage win for German André Greipel, aka Gorilla.  Wind speeds were in the 30-50 kph (19-31 mph) range, often hitting cyclists from the side.  There were also portions of the race where headwinds were prevalent; other portions had tailwinds.  It had to be a lot of fun to be on a bicycle in southern France today!

Below is how our prediction fared against Greipel's winning time.

• Stage 6:  3h 59' 02" (actual), 4h 05' 47" (prediction), 06' 45" slow (2.82% error)

We'll definitely take an error under 3%!  I am happy to see riders sneak in under four hours.  With strong, changing winds and a crash not too far from the finish, the best of the best still finished a grueling stage in a few ticks less than four hours.  Below is Greipel's average speed.

• Stage 6:  12.31 m/s (44.30 kph or 27.53 mph)

History was made today as Daryl Impey now leads the overall time classification.  Impey took the yellow jersey from fellow Orica-GreenEDGE teammate Simon Gerrans, who now sits third in the standings.  Impey is not only the first South African to lead the Tour de France, he will be the first African to don the famed yellow jersey.

Tomorrow's Stage 7 is a 205.5-km (127.7-mi) medium-mountain stage that commences in Montepellier and finishes in the commune of Albi.  Riders continue west on their approach to the Pyrenees.  The stage features a category-4 climb near the end, a couple of category-3 climbs, and a category-2 climb near the halfway point.  Below is our prediction.

• Stage 7:  5h 00' 15" (prediction)

Save a little energy for Stage 8 when the race hits some monster climbs in the Pyrenees!

The Manx Missile and 11 Measly Seconds

Mark Cavendish, aka the Manx Missile, had a great sprint to the finish line in today's flat stage.  I yelped a bit at the finish when I saw today's winning time.  Below is the comparison between Cavendish's winning time and our prediction.

• Stage 5:  5h 31' 51" (actual), 5h 32' 02" (prediction), 0' 11" slow (0.06% error)

I am very pleased with our prediction!  We slightly underestimated power output and technological advances in yesterday's team time trial.  Today, we had a great feeling for how the long, flat stage would go.  Below is Cavendish's average speed.

• Stage 5:  11.48 m/s (41.31 kph or 25.67 mph)

That is an impressive average for such a long time on a bicycle.  Those Tour de France athletes are something special!

Tomorrow's Stage 6 is another flat stage.  It starts in Aix-en-Provence and takes riders due west nearly along the southern coast of France to Montpellier.  Shorter than today's stage, Stage 6 is 176.5 km (109.7 mi) long with one category-4 climb just over one third of the way in. Our prediction is given below.

• Stage 6:  4h 05' 47" (prediction)

Will weather play a role as riders are going to be close to the coast?  Will riders be thinking ahead to Stage 7 and its four category-ranked climbs? Or will someone have the best day of his life and come in under four hours?  Team Orica-GreenEDGE should be safe after tomorrow.  Simon Gerrans maintains the yellow jersey today, and will probably have it after tomorrow's stage.

Top speeds in Nice today!

The Australian Orica-GreenEDGE team dominated today's team time trial.  In time trials, cyclists wear special helmets and use modified bikes so as to reduce drag.  They further reduce air resistance in team time trials by employing the strategy of drafting, which is also used by race cars.  Tucking oneself right behind another cyclist reduces air drag.  The team time trials are fun to watch because of the tight linear formations used by the various teams.  It really is a coordinated thing of beauty as the cyclists take turns leading their teammates.

Below is how our prediction came out against today's result.

• Stage 4:  25' 56" (actual), 27' 33" (prediction), 01' 37" slow (6.23% error)

After nailing last year's two individual time trials to better than 1%, we had high hopes for this year's time trials.  The athletes once again surprised us!  We now know that our drag coefficient reduction and power increase were not quite enough.  We will never cease being amazed by the quality of the athletes and the technological advancements in equipment made by scientists and engineers.  Well done!

Team Orica-GreenEDGE's average speed is given below.

• Stage 4:  16.07 m/s (57.84 kph or 35.94 mph)

Wow, that's fast!  I've certainly never been on a bike moving anywhere close to that speed.  Again, kudos to the athletes and their teams for a phenomenal stage.

The Orica-GreenEDGE team put itself in great position today with team member Simon Gerrans now in possession of the yellow jersey.  Two Orica-GreenEDGE members are right behind Gerrans.  With sprinters looking to dominate the next two flat stages, Orica-GreenEDGE and its team of sprinters should keep the yellow jersey for another couple of stages.

Tomorrow's Stage 5 starts cyclists just southwest of Nice in the commune of Cagnes-sur-Mer.  Though designated a flat stage, riders will open the stage with a category-3 climb, and then meet three category-4 climbs throughout the rest of the 228.5-km (142.0-mi) stage.  The stage ends in the southern French city of Marseille.  Below is our prediction.

• Stage 5:  5h 32' 02" (prediction)

Look for an exciting downhill sprint to finish the stage.

Gerrans just edges Sagan!

A thrilling finish to today's Tour de France action saw Australia's Simon Gerrans sprint across the finish line a split second before Peter Sagan of Slovakia.  The decision to begin the 100th Tour de France with three stages in Corsica was phenomenal!  The first three stages were thrilling, to say the least.  Below is how our prediction fared against today's result.

• Stage 3:  3h 41' 24" (actual), 3h 44' 26" (prediction), 03' 02" slow (1.37% error)

We are pleased with our prediction!  As I wrote yesterday, "I won't be surprised if tomorrow's winner edges our time once again."  The athletes are impressing us this year!  Seeing the Tour de France unfold gives us the opportunity to appreciate how months of training and new technologies employed in equipment pay off.

Below is Gerrans's average speed for today.

• Stage 3:  10.95 m/s (39.43 kph or 24.50 mph)

Despite his 19th place finish today, Jan Bakelants retains the coveted yellow jersey with a one-second lead over Julien Simon of France.  Gerrans's big win today gets him classified third overall.

The Tour de France leaves beautiful Corsica and heads to France tomorrow.  Stage 4 is a team time trial in the southeastern city of Nice.  At just 25 km (15.5 mi) in length, expect riders to go all out!  The trip through Nice is almost entirely flat.  Below is our prediction.

• Stage 4:  0h 27' 33" (prediction)

Don't turn away from tomorrow's action -- it's going to be FAST!