Sabbatical Journal

The 2015-16 academic year represents my second sabbatical year.  As I did during my first sabbatical year (2008-09), I will work with Matt Carré at the University of Sheffield in England.  Our first collaborative year yielded research results pertaining to the aerodynamics of soccer balls.  For this upcoming collaboration, I will join Matt's research group's investigations into friction in sport.  I've always been fascinated by the topic of friction, partly because the simple Coulomb model I learned as an introductory physics student is far from the complete story, despite the rather confident way in which Coulomb's model is usually presented.

I plan to use this blog space as my sabbatical journal.  My primary reason for doing so is that I am interested in keeping a record of what I will do over the coming year.  I think it will be fun to look back on some day.  Several colleagues, friends, and family members have told me that they are interested in knowing what my family and I are up to while we're away from the US, and that keeping a sabbatical journal is a good idea.  It always humbles me to think that anyone cares what I write in this space, so I'm flattered by the encouragement I've received to post regularly during my sabbatical.

Webster tells me that "sabbatical" may be used as an adjective with the meaning of "having the character of a recurring period of rest or renewal."  I'm not sure about "rest," as my first official sabbatical month, this July, has been anything but restful.  The Tour de France occupied my research time and kept me busy blogging predictions and stage results.  Media attention on my work further took my time as July came to a close.  I detailed some of that attention in my last post.  Even our local news ran a story on my Tour de France work last Monday (click here for that short television piece).  As flattering as the media attention has been, it only added to an already hectic week of preparing to move my family across the Atlantic.  I am fortunate, though, to have an extremely talented wife who makes international travel look much easier than it is.  Our two daughters, who were quite young during our first year abroad, have also helped in our moving preparations in more ways than they realize.

The second word in Webster's "sabbatical" definition that strikes me is "renewal."  That is a perfect word for a "sabbatical."  I joke with colleagues that my number-one rule for a sabbatical is "to put an ocean between me and my college."  Don't get me wrong.  I love teaching and researching at Lynchburg College.  Our physics students make teaching and researching thoroughly enjoyable for me.  One of my favorite former students, Crystal Moorman, will in fact be my sabbatical replacement, so my courses will be in good hands.  Despite my love for my job, being away for an extended period of time is vitally important.  A sabbatical gives me a chance to explore new research areas, meet and interact with new colleagues, and see more of the world.  That last item is important because seeing new places helps remind me that my little world in Virginia isn't the center of the universe.  There is much to learn from other cultures.  Just as my colleagues give me fresh ways to view the world scientifically, experiencing other cultures provides me with different perspectives on life.

We are near Washington, DC right now.  Our flight across the pond is quickly approaching.  Getting there will only be a small part of the fun that awaits us!

Fun Chatting Tour de France Science

As the Tour de France was coming to a close, I had the opportunity to chat with some media outlets about the modeling research I was doing in connection with the world's most famous bike race.  ResearchGate interviewed me and posted its story on Friday, 24 July.  Click here for that interview.  The Washington Post followed that up with a story the next day, which may be obtained here.  After the race ended on Sunday, 26 July, CNN International had me on live for a short post-race discussion about the Tour de France research I do.  That interview may be viewed here.

Media attention is flattering, but it's never the goal of the research.  Doing the science well is my goal.  There were a lot of things my student and I had right with this year's Tour de France.  There were also a few things we had wrong.  Investigating what needs improvement is what really makes the work fun because I gain a better understanding of the natural world.  The Tour de France is immensely complicated.  There are scientists and engineers across the globe who have made enormous strides in equipment design.  Athletic trainers have helped athletes push themselves to the very limits of what human beings can do on a bicycle.  All of us are constrained by the laws of physics.  Watching the best of the best push those constraints to their extremes is pure joy for me.  Kudos to the all the cyclists, trainers, scientists, and engineers who gave the world three weeks of awesome fun!

Greipel Sprints to #4 on Froome's Big Day!

We've done so well in the past when it comes to predicting the last stage.  It's mostly ceremonial, but there is usually a great sprint for the win.  Today was no different on that front, but rain really dropped speeds.  I've not seen rain in Paris like this on the final stage.  Check out Chris Froome and his Team Sky mates (click on the image for a larger view).

That was not long after the stage began.  Look at those wet streets!  I knew we would be too fast today.  Froome was offered some champagne to toast his victory (click on the image for a larger view).

The poor people running the cameras could barely keep their lenses dry!  Despite the rain, who could possibly complain about weather while riding through Paris (click on the image for a larger view)?

Now I can't wait to get back there!  Because the streets were so slick, race organizers called for all cyclists to get the same time with 68.5 km (42.6 mi) to go.  The screen capture I grabbed below shows the moment when Froome actually won the Tour de France (click on the image for a larger view).

Even though rain really slowed riders, we still got to enjoy a great sprint at the very end.  Who else but André Greipel was going to show the world who the best sprinter is?  He had himself perfectly situated for the final surge and powered his way past France's Bryan Coquard (click on the image for a larger view).

It was close, but the Gorilla always seems to be in first!  He now has four stage wins this year and ten overall.  He's the best sprinter in the world!  Below is a comparison between reality and our prediction.

• Stage 21:  2h 49' 41" (actual), 2h 35' 06" (prediction), 14' 35" fast (-8.59% error)

More than being annoyed with the weather and how it affected our prediction, I was hoping to see faster racing on the ten loops in Paris.  It was still a wonderful sprint, though.  Greipel's average speed is given below.

• Stage 21:  10.76 m/s (38.72 kph or 24.06 mph)

That is really slow for the final stage.  Thanks a lot, rain!  The weather didn't dampen the celebration as Chris Froome won his second Tour de France (click on the image for a larger view).

Froome completed the 3360.3-km (2088.0-mi) race in 84h 46' 14", which gives an average speed of 11.01 m/s (39.64 kph or 24.63 mph).  One has to go back to 2010 for an average speed that slow, and this year's race was the shortest since 2002.  Those mountain stages were truly brutal!  Froome was just 72 seconds faster than Nairo Quintana (left in the above image) and 05' 25" faster than Alejandro Valverde (right in the above image).  I loved seeing the kids on the podium!

This has been an incredibly fun Tour de France to watch.  My research student, Chad Hobson, made the science we pursued intellectually stimulating.  Just 342 days until the 2016 Tour de France begins!

Pinot Tames Alpe d'Huez and Makes France Proud!

What an incredible finish to today's stage!  And what a great day for France!  Alexandre Geniez of France was the first to reach the summit of Col de la Croix de Fer (click on the image for a larger view).

Geniez had a great ride, but finished 25th today.  I love the scene below, which shows riders in the valley approaching Alpe d'Huez (click on the image for a larger view).

The climbers were preparing for their assault on the famous ascent.  Not long after beginning the climb, Vincenzo Nibali had a flat tire.  That was too bad, as it would have been fun watching him compete for the stage win; Nibali finished 15th today.  Frenchman Thibaut Pinot was the star on the climb, and won the stage by 18 seconds (click on the image for a larger view).

We did quite well today!  Below shows Pinot versus our prediction.

• Stage 20:  3h 17' 21" (actual), 3h 15" 50" (prediction), 01' 31" fast (-0.77% error)

To be under 1% with an Alpe d'Huez finish makes us very happy!  But that happiness really doesn't compare to the joy I felt watching the best cyclists in the world compete on France's most famous climb.  Pinot's ride was inspiring, but I was probably more thrilled watching Nairo Quintana of Colombia.  That man can absolutely climb with the best of the best.  He did everything he could to overtake Chris Froome, and it was electrifying watching him tackle Alpe d'Huez with everything he had.  Quintana will take second this year, but at just 25 years old, he will be a rider to be reckoned with in future Tours de France.

Below is Pinot's average speed.

• Stage 20:  9.332 m/s (33.60 kph or 20.88 mph)

In my wildest dreams I can't imagine riding today's stage at that speed.  Kudos to all those cyclists who could even finish such a challenging ride.

Chris Froome and his powerful Team Sky mates did what they had to do today to keep Froome in yellow.  Quintana offered a marvelous challenge, but Froome fought to 5th place today and kept his overall lead on Quintana to more than a minute.  We'll see Chris Froome win his second Tour de France tomorrow.

Tomorrow's 109.5-km (68.04-mi) flat stage begins in the commune of Sèvres, just southwest of Paris.  The mostly ceremonial final stage will take riders through many Parisian streets and end on the most famous of them all, the Avenue des Champs-Élysées.  The final stage is always a challenge for modeling because the general classification leaders enjoy the final ride, while the sprinters will vie for the stage win once the streets of Paris are in view.  Below is our prediction.

• Stage 21:  2h 35' 06" (prediction)

It's hard to believe the 102nd Tour de France comes to a close tomorrow.  It's been a fun ride!

The Shark Jumps to 4th!

I felt like I was watching 2014 Tour de France today.  Italy's Vincenzo Nibali, who was such a joy to watch last year, showed that if he isn't going to repeat as champion, he will be a serious challenge for a podium spot in Paris on Sunday.

The penultimate Alpine stage took place on yet another beautiful day.  Cyclists have been lucky with mountain weather!  The hors catégorie climb to the 2067-m (1.284-mi) peak of Col de la Croix de Fer was more challenging than I initially thought.  The mountain not only tamed the Tour de France cyclists but our model!  But as tough as the ascent turned out to be, the scenery was still lovely (click on the image for a larger view).

France's Pierre Rolland was amazing today.  He led the charge up the monster climb and took the most points at the summit (click on the image for a larger view).

Nibali caught Rolland soon afterwards and appeared to get Rolland to work with him on the descent.  The two alternated drafting positions and fared well on the tricky turns.  I thought Nibali might even concede the stage win as long as Rolland would help him move up in the overall standings.  Rolland tried to stay with Nibabli, but with 16 km (9.9 mi) left, Rolland cracked on the climb toward Le Corbier, and the Shark took off alone.  Nibali was thrilled to win the stage (click on the image for a larger view).

Nibali looked like the Nibali of last year's Tour de France on the final climb.  As I noted in yesterday's post, our prediction was a bit bold.  The Alps were simply tougher than we thought.  Reality and our prediction are compared below.

• Stage 19:  4h 22' 53" (actual), 4h 03' 33" (prediction), 19' 20" fast (-7.35% error)

That is our worst prediction since early in the race when the riders were near the English Channel.  To give you an idea of just how bloody tough modeling is, we need only have brought our cyclist power output down to 98% of its current value to match today's winning time.  The times on the steep climbs are very sensitive to cyclist power output.  You can easily see that while watching the race.  When a cyclist cracks on a climb, he'll likely lose a couple of minutes or more.  Below is Nibali's average speed.

• Stage 19:  8.749 m/s (31.50 kph or 19.57 mph)

Tomorrow's final Alpine stage begins in the commune of Modane.  Cyclists will begin the 110.5-km (68.66-mi) mountain stage with a nice downhill as they head west for another rendezvous with the 2067-m (1.284-mi) peak of Col de la Croix de Fer.  But that will be only the first hors catégorie climb of the day.  The second one will close the stage and the riders' Alpine experience when they traverse the famous 21 hairpin turns up to the 1850-m (1.15-mi) peak of Alpe d'Huez.  Our prediction is below.

• Stage 20:  3h 15' 50" (prediction)

I've been waiting all month for the Alpe d'Huez climb.  Tomorrow should be fun!

Bardet Makes France Proud in the Alps!

Romain Bardet of France pushed my challenge from yesterday to the very edge.  The prediction I posted for today's stage was ambitious, and I admitted as much when I posted it.  I wanted to see a rider come in under five hours, and Bardet almost did it.

With temperatures around 32 C (90 F) at the base of the mountains and roughly 25 C (77 F) near the peaks, riders enjoyed a wonderful summer day in the saddle.  Alpine scenery was of course on full display.  The brutal climb up Col du Glandon separated the best from the very best, but all enjoyed views as good as it gets (click on the image for a larger view).

The screen capture I grabbed below shows the peloton with about 50 km (31 mi) left (click on the image for a larger view).

It is easy to see why that mountain is tough to climb on a bicycle!  Chris Froome got some help from a Team Sky mate on the way up (click on the image for a larger view).

I think that is Coca Cola!  It must have helped because Froome retains the yellow jersey with the same lead he began the day with.  The first cyclist to reach the peak of Col du Glandon was Romain Bardet (click on the image for a larger view).

Bardet is on the right and Winner Anacona (what a great name!) of Colombia is on the left.  Bardet would never relinquish the lead.  Look below as he makes France proud today (click on the image for a larger view).

As I noted above, Bardet wasn't able to sneak in under five hours.  Below is a comparison between his time and our prediction.

• Stage 18:  5h 03' 40" (actual), 4h 50' 12" (prediction), 13' 28" fast (-4.43% error)

I was hoping for a special performance today, and that's what I saw!  Getting through today's grueling stage in just over five hours is quite an achievement.  There were cyclists finishing more than half an hour later after Bardet crossed the finish line.  I'm happy we're under 5% on such a difficult stage.  Below is Bardet's average speed.

• Stage 18:  10.24 m/s (36.85 kph or 22.90 mph)

Tomorrow's Stage 19 is a deceptively short 138 km (85.7 mi), but a LOT of tough cycling will be shoved into those 138 km.  Picking up where today's stage finished in Saint-Jean-de-Maurienne, cyclists will have to contend with a category-1 climb right at the start.  After heading north, they will turn back toward the south where they'll face the hors catégorie climb to the 2067-m (1.284-mi) peak of Col de la Croix de Fer.  As if that's not enough, a category-2 climb will whet their cycling appetites before the category-1 climb to 1705 m (1.059 mi) elevation at the finish at La Toussuire.  Below is our prediction.

• Stage 19:  4h 03' 33" (prediction)

I suspect we'll be a tad fast again, however, the best effort from the best cyclist in the world can certainly make that time.  I am not rooting for any particular cyclist, but I would love to see Chris Froome get challenged today so that racing will be fast and the action will be intense.  A great stage awaits us tomorrow!

Geschke Prevails in First Alpine Stage!

Cyclists enjoyed wonderful scenery in today's first Alpine stage.  Unfortunately for Tejay van Garderen, who entered today's action in third place in the general classification, he got sick on the first climb and had to abandon the Tour de France.  High elevations and tough climbing would make all but the best cyclists in the world a bit woozy.  But check out my screen capture below as the peloton made its way up Col d'Allos (click on the image for a larger view).

A nice perk for those who can compete in the Tour de France!  Lovely, isn't it?  Temperatures got to about 30 C (86 F) on the climb, so many riders were content to have their jerseys open.  Simon Geschke of Germany was the first to reach the highest point (2250 m or 1.40 mi) in this year's Tour de France (click on the image for a larger view).

He looks happy to be finally going downhill!  Geschke skillfully maneuvered the treacherous descent with speeds reaching a reported 85 kph (53 mph).  He held on to win the first Alpine stage (click on the image for a larger view).

Germany now has five stage wins.  Herzlichen glückwunsch!  Below is a comparison between reality and our prediction.

• Stage 17:  4h 12' 17" (actual), 4h 21' 10" (prediction), 08' 53" slow (3.52% error)

I'm definitely happy with that error after such a tough stage!  A total of 26 out of 163 cyclists beat our predicted time.  For a stage like today's in the Alps, getting our prediction at about 16% of the cyclists is fine by me.  Below is Geschke's average speed.

• Stage 17:  10.64 m/s (38.29 kph or 23. 79 mph)

Tomorrow's Stage 18 begins back in Gap.  The 186.5-km (115.9-mi) mountain stage will take cyclists north to the commune of Saint-Jean-de-Maurienne.  There are a total of three category-3 climbs and three category-2 climbs, but tomorrow's star will be the hors catégorie climb to the 1924-m (1.20-mi) peak of Col du Glandon.  Riders will have to contend with 21.7 km (13.5 mi) of that climb!  Our prediction is given below.

• Stage 18:  4h 50' 12" (prediction)

I feel like our time is a challenge to the world's best cyclists.  How many will come in under five hours tomorrow?

Prediction for Stage 17

Tomorrow's Stage 17 promises great scenery as the Tour de France will be fully in the Alps.  Picking up in the commune of Digne-les-Bains, the 161-km (100-mi) mountain stage takes riders southeast for about 40 km (25 mi) before turning them northward toward the stage's category-2 climbing end at the ski resort of Pra Loup.  Alpine mountains will be on full display, particularly the category-1 climb to the 2250-m (1.40-mi) peak of Col d'Allos.

Will tomorrow be the day that teams challenge Chris Froome?  Or will teams wait for a later stage?  As with yesterday's stage, we never know what strategies will be like, but it's a lot of fun watching and finding out.  Our prediction is given below.

• Stage 17:  4h 21' 10" (prediction)

A well-rested cyclist with nothing to lose could surely beat that time.  We'll see if racing is as fast tomorrow as it's been in the past two stages.

Plaza Leads Breakaway to Stage Win!

There were two races in today's Stage 16.  The breakaway set a blistering pace and won the stage.  The peloton, which had all the general classification leaders, was content to concede the stage and jostle for position during the final descent.  It turned out that we were nearly perfect on the peloton, but, alas, we were too slow on the winner.

After 80 minutes of uphill racing, the average speed was a whopping 52.7 kph (32.7 mph).  A 15 kph (9.5 mph) tailwind played a big part in the early pace.  The weather was nearly perfect with warm temperatures (31 C or 88 F) and blue skies.

Peter Sagan was pure joy to behold today.  He is incredibly skillful on a bike and he got yet another second place today after catching all but one challenger in the various breakaway attacks.  And Sagan did it all without any team help!  The screen capture I grabbed below is Sagan getting 20 points for winning the intermediate sprint (click on the image for a larger view).

The first in the breakaway group to crest Col de Cabre was Belgian Serge Pauwels (click on the image for a larger view).

Sagan was in that breakaway group, and then he showed his skill on the subsequent descent (click on the image for a larger view).

As the main part of the Alps came into view, helicopters got some amazing scenery shots (click on the image for a larger view).

Who wouldn't want to visit the Alps?!?  The first rider to reach the top of Col de Manse was Spaniard Rubén Plaza (click on the image for a larger view).

Plaza made a great attack on the climb and left Sagan too far behind.  What was great about the breakaway reaching the peak of the final climb is that they were roughly 20 minutes ahead of the peloton!  Sagan fought hard during the final lightening-quick descent, but Plaza took the stage by half a minute over Sagan (click on the image for a larger view).

Below is a comparison between Plaza's time and our prediction.

• Stage 16:  4h 30' 10" (actual), 4h 47' 26" (prediction), 17' 16" slow (6.39% error)

We were slow by about the same percentage we were slow yesterday.  Now comes the interesting part.  The last breakaway rider came in 23rd, nearly nine minutes after Plaza.  Last year's winner, Vincenzo Nibali, executed a nice attack on the final climb and was the first of the peloton to cross the finish line.  His time?  Nibali finished in 4h 47' 54", less than half a minute off our prediction!  That is why I noted at the beginning of this post that we were almost perfect on the peloton; but that's not what we're after with each stage.  Below is Plaza's breakneck average speed.

• Stage 16:  12.40 m/s (44.64 kph or 27.74 mph)

Let that speed sink in for a moment.  That is for a 201-km (125-mi) medium-mountain stage!  Those riders in the breakaway went for the stage win, and they got it!

Chris Froome fought well on the final descent and made sure he would hold on to his prized yellow jersey.  His Team Sky mate, Thomas Geraint, suffered what looked like a devastating crash on the treacherous final descent, but Geraint admirably got back on his bike and proceeded to hold on to his 6th overall place in the general classification.

Cyclists will stay in Gap for a rest day tomorrow.  They will need all the rest they can get as four daunting mountain stages in the Alps await them.  I will get our Stage 17 prediction posted tomorrow.

The Gorilla Gets #3!

As the old saying goes, all good things must come to an end.  Our streak of eight consecutive stage predictions with error 1.85% or less came to an end today.  I watched in awe as the world's best cyclists set a blistering pace on another hot day (temperatures reached about 33 C or 91 F).  They were averaging about 48 kph (30 mph) after half the distance had been covered.  When the nine breakaway riders reached the category-2 peak of Col de l'Escrinet (click on the image below for a larger view), they were averaging 44.3 kph (27.5 mph), much faster than we predicted.

Once over that peak, the cyclists tore through the rest of the stage, at times reaching speeds around 80 kph (50 mph).  I was amazed by the skill with which they maneuvered around turns, avoided spectators, and dodged road obstacles.

The Tour de France organizers certainly knew what they were doing because fans were treated to a fantastic sprint for the stage win.  André Greipel once again proved he is as good as it gets when he eclipsed his competitors and took his third stage win of this year's Tour de France (click on the image for a larger view).

Greipel is on the far right of the screen capture, coming in just ahead of fellow German John Degenkolb.  Russian Alexander Kristoff is in third, and Peter Sagan in fourth is yet again just out of reach of the finish line.  Below is Greipel's time and a comparison with our prediction.

• Stage 15:  3h 56' 35" (actual), 4h 12' 01" (prediction), 15' 26" slow (6.52% error)

If our streak had to end, I'm glad it ended while I was watching the best of the best showcase what they are capable of on a bicycle.  Check out Greipel's average speed below.

• Stage 15:  12.89 m/s (46.10 kph or 28.84 mph)

That is an incredibly fast speed, and it's well outside the organizer's estimate for top speed.  I am definitely impressed!

Tomorrow's medium-mountain stage is the last before the second and final rest day.  Stage 16 is 201 km (125 mi) long and commences in the commune of Bourg-de-Péage.  Cyclists will head southeast toward the Alps.  A couple of category-2 climbs highlight the mostly uphill first 189 km (117 mi) of the stage before cyclists finish with 12 km (7.5 mi) of what is sure to be torrid downhill racing as they reach the commune of Gap.  Below is our prediction.

• Stage 16:  4h 47' 26" (prediction)

If riders tear out of the start tomorrow like they did today, we could be a tad slow again.  I can't wait to see the scenery as they get to the end of the stage.

Steve Cummings Sprints Us Under 1% Again!

I am always nervous watching the Tour de France.  My students and I stick our necks out the day before each stage is run when I post our winning-time predictions.  Science drives my interest, but posting predictions on my blog jacks the fun level up considerably.  Today's stage had me pacing in my office!

The French summer weather was once again hot today (33 C or 91 F), and there were no shortages of breathtaking scenery.  Just before the halfway point in the stage, cyclists passed under the Millau Viaduct.  I had to grab a screen capture of that (click on the image for a larger view).

I felt a bit of vertigo as the helicopter cameras provided images from so many views of the bridge.  What a structure and what a feat of modern engineering!  As if that wasn't amazing enough, the stage took riders through the Gorges du Tarn.  I grabbed the image below with about 73 km (45 mi) left in the stage (click on the image for a larger view).

My family will have to visit that place when we are next in France!

All the wonderful scenery was a pleasant distraction because I thought we were going to be too slow on this stage.  The pace on the very first climb was torrid.  After about half the distance was covered, the average speed was around 45 kph (28 mph).  Team Sky then really pushed the peloton on the first category-2 climb.  That is one powerful team that Chris Froome has backing him!  But in the end, the final climb did what we thought it would do; it slowed cyclists enough that we were actually a wee bit fast.  England's Steve Cummings out-sprinted French cyclists Thibaut Pinot and Romain Bardet to win the stage (click on the image for a larger view).

Below is a comparison between reality and our prediction.

• Stage 14:  4h 23' 43" (actual), 4h 21' 59" (prediction), 01' 44" fast (-0.66% error).

When I saw the final hill do what we thought it would do, I knew we had a shot at keeping our streak alive.  We now have eight consecutive stages with an error of 1.85% or less, and on five of those eight, we were under 1%.  Below is the winner's average speed.

• Stage 14:  11.28 m/s (40.61 kph or 25.25 mph)

Chris Froome really pushed himself on the final climb and widened his overall lead.  Nairo Quintana of Colombia managed to jump over Tejay van Garderen of the US for second overall.

Tomorrow's 183-km (114-mi) Stage 15 is more accurately described as "hilly," rather than medium-mountain.  It begins in the commune of Mende, which is where today's stage finished.  Cyclists will contend with a category-3 climb at the start, a couple of category-4 climbs about a third of the way into the stage, and a category-2 climb about two-thirds into the stage.  The stage is flat into the commune of Valence.  Below is our prediction.

• Stage 15:  4h 12' 01" (prediction)

If they don't crack on the early climbs, sprinters should compete for this stage!

Van Avermaet Catches Breakaway in Thrilling Sprint!

What a hot day for racing!  Temperatures reached 36 C (97 F) and cyclists were battling the heat all day.  I grabbed a screen capture of Pierre-Luc Périchon of France as he was putting ice down his jersey (click on the image for a larger view).

It must be nice having someone in a car hand you ice (and food and water) when you need it!  Though not quite the mountain vistas of the past three stages, riders still enjoyed great scenery, as evinced by what I grabbed with about 41 km (25 mi) left (click on the image for a larger view).

Last year's runner-up, Jean-Christophe Péraud crashed about 20 km (12 mi) before the above scene.  He rolled on the road a couple of times and was badly injured.  Despite all the blood, torn jersey, and obvious pain, he still managed to finish the stage less than six minutes behind the winner.  What a gritty performance!

I was rooting for the three-man breakaway to hold on at the very end, but the peloton caught them with about 200 m (656 ft) left in the stage.  Belgian Greg Van Avermaet just beat Peter Sagan of Slovakia across the finish line (click on the image for a larger view).

Sagan has a real knack for coming in second!  Below is a comparison between today's stage reality and our prediction.

• Stage 13:  4h 43' 41" (actual), 4h 46' 07" (prediction), 02' 26" slow (0.86% error)

We're happy to be under 1% yet again!  Below is Van Avermaet's average speed.

• Stage 13:  11.66 m/s (41.98 kph or 26.09 mph)

Tomorrow's 178.5-km (110.9-mi) medium-mountain stage picks up where today's left off, in the commune of Rodez.  Cyclists will head southeast for about half the stage and then northeast for the other half, ending in the commune of Mende.  Riders will have to contend with a couple of category-4 climbs and a couple of category-2 climbs.  Elevations will be a bit higher tomorrow compared to those in today's stage.  I'm sure cyclists will be rooting for cooler weather!  Below is our prediction.

• Stage 14:  4h 21' 59" (prediction)

We've hit seven consecutive stages to better than 1.85%, and four of those were under 1%.  Will our streak end tomorrow?  It all depends on the strategies of the various teams.  The stage has a climb at the start and a climb at the end, which make for interesting challenges.

Rodríguez Conquers Plateau de Beille!

Stage 12 of this year's Tour de France began with great summer weather.  Temperatures reached 35 C (95 F).  But then rain started on the first category-1 climb and temperatures dropped to around 26 C (79 F).  At that point, 22 riders were in the breakaway.  Kristijan Đurasek of Croatia was first atop Col de la Core (click on the image for a larger view).

Hairpin turns are the norm in the mountains and wet roads slow racing down just a bit.  Scenery was still spectacular (click on the image for a larger view).

Michał Kwiatkowski of Poland was the first to cross the line at the summit of Port de Lers (click on the image for a larger view). 

You can see Kwiatkowski getting much-needed calories after completing the category-1 climb.  Kwiatkowski had a quality stage, coming in 27th.  But the man of the day was Joaquim Rodríguez of Spain.  He dominated the final climb and was 72 s faster than the second-place finisher.   Does he look happy after crossing the finish line (click on the image for a larger view)?

Below is a comparison between reality and our prediction.

• Stage 12:  5h 40' 14" (actual), 5h 38' 04" (prediction), 02' 10" fast (-0.64% error)

We're back under 1%!  Given the rain and the fact that Rodríguez was celebrating in the final couple hundred meters, I'd say we did rather well.  Below is the winner's average speed.

• Stage 12:  9.552 m/s (34.39 kph or 21.37 mph)

That speed is impressive after nearly six hours in the saddle and a brutal climb to finish.

Cyclists get a more subdued medium-mountain stage tomorrow with only a couple of category-4 climbs and a category-3 climb.  Beginning in the commune of Muret, Stage 13 takes riders 198.5 km (123.3 mi) northeast to the commune of Rodez.  Below is our prediction.

• Stage 13:  4h 46' 07" (prediction)

Tomorrow's stage is a tough one to predict.  Chris Froome maintained his 02' 52" lead over Tejay van Garderen after today's stage.  Will BMC Racing Team challenge Team Sky tomorrow and make us slow?  Will sprinters try to speed up the pace?  Will the past three grueling stages in the Pyrenees cause riders to take it easy and make us fast?  It will be fascinating to watch tomorrow's action unfold!

Majka Dominates Stage 11!

The second Pyrenees stage was raced on yet another gorgeous French summer day.  Riders were challenged by warm temperatures (33 C or 91 F) during their climbs.  Below is a screen grab of the peloton during the climb up Col d'Aspin (click on the image for a larger view).

The Tour de France is a grueling athletic event, but look at that view for those who can do it!  Dan Martin was the first to reach the peak of Col d'Aspin (click on the image below for a larger view).

Martin had a great day.  He was aggressive and climbed with an enormous amount of grit.  But Martin was a minute slower than today's winner, Polish cyclist Rafał Majka, who made his move on the 17.1-km (10.6-mi) ascent up Col du Tourmalet.  When he crossed the peak, he had a 5.5-minute lead on his competition (click on the image for a larger view).

Majka was positively flying down Col du Tourmalet, expertly navigating hairpin turns and avoiding fans.  His downhill technique definitely minimized air drag (click on the image for a larger view).

Imagine sitting on a bike like that while zooming downhill at 80 kph (50 mph)!  My favorite moment on the Col du Tourmalet descent was when some cows decided to join the race (click on the image for a larger view).

That is French cyclist Warren Barguil who's the object of bovine curiosity.  Luckily, no cyclist was injured.

Cows aside, the day belonged to Rafał Majka (click on the image for a larger view).

Below is his winning time and a comparison with our prediction.

• Stage 11:  5h 02' 01" (actual), 4h 58" 09" (prediction), 03' 52" fast (-1.28% error)

Given how far ahead Majka was at the end, there was no sprint for first.  Had there been, we would have been even closer.  I was hoping for a big sprint to get the winner under five hours.  But we'll definitely take that error!  Below is Majka's average speed.

• Stage 11:  10.37 m/s (37.35 kph or 23.21 mph)

Stage 12 is sure to be the toughest Pyrenees stage.  Commencing in the commune of Lannemezan, the 195-km (121-mi) stage takes riders southeast to the ski resort at Plateau de Beille.  Sprinters will be thrown a bone after only about 20 km (12 mi) before the real stage gets underway.  A category-2 climb will get riders to 1069 m (3507 ft) on Col de Portet d'Aspet, and that's just the warm-up.  Two category-1 climbs, the first to the 1395-m (4577-ft) peak of Col de la Core and the second to the 1517-m (4977-m) peak of Port de Lers, occupy the middle of the stage.  If that's not enough mountain brutality, cyclists will have to finish the stage with a 15.8-km (9.82-mi) hors catégorie climb to the 1780-m (1.106-mi) ski resort.  I believe I counted six riders who abandoned the race today.  How many will tomorrow's stage claim?  Below is our prediction.

• Stage 12:  5h 38' 04" (prediction)

Because of the difficulty, length, and timing of the stage, we've backed off our model's power ever so slightly.  Will cyclists hold back and save themselves for the Alps or will some try to cut into Chris Froome's lead?  It will be fun watching the best cyclists in the world tackle tomorrow's challenging stage.

Froome DESTROYS Competition!

It was a beautifully clear day for cycling during the first of three days in the Pyrenees.  Temperatures were around 27 C (81 F) and the pace was fast at the start.  The peloton was averaging approximately 44 kph (27 mph) after about half the distance was covered.  Was that too fast?  I ask because of all the riders who cracked on the final, brutal climb.  Before they reached the climb, cyclists enjoyed some amazing scenery (click on the image for a larger view).

I grabbed that screen capture with about 45 km (28 mi) left in the stage.  Riders could definitely see what was lurking in their future!  Helicopters shot amazing vistas of the gloriously green Pyrenees (click on the image for a larger view).

France was breathtaking to behold on Bastille Day!

André Greipel took third place in the sprint (there were two breakaway riders at that point), and has the green jersey (click on the image for a larger view).

Today's stage came down to the final 15.3 km (9.51 mi) and the monster climb up Col de la Pierre St Martin.  I grabbed the screen capture below as the peloton passed the indication that the REAL mountain stage had begun (click on the image below for a larger view).

The climb destroyed many of the cyclists.  All the sprinters were obviously eaten, but so were some famous mountain climbers.  Last year's winner, Vincenzo Nibali, cracked with about 11 km (6.8 mi) left.  Two-time winner Alberto Contador cracked with roughly 6.8 km (4.2 mi) left.  It was painful watching the cyclists huff and puff as they slowly made their way up the mountain.

Cyclists had even more pain as they learned just how far behind Chris Froome they now sit.  Team Sky was brilliant today.  Richie Porte of Australia did yeoman's work up the mountain as he helped Froome.  Porte demonstrated his mettle as he came in second and was the only cyclist within a minute of Froome.  Does Froome look happy (click on the image for a larger view)?

You'd be happy, too, if you were halfway through the Tour de France with a commanding 02' 52" lead over second place!  Below is how we compared to Froome.

• Stage 10:  4h 22' 07" (actual), 4h 24' 38" (prediction), 02' 31" slow (0.96% error)

We are inside 1% again!  The fast pace at the start had me a little worried, but the mountain tamed the peloton.  Froome's average speed is below.

• Stage 10:  10.62 m/s (38.23 kph or 23.75 mph)

Day two in the Pyrenees begins in the commune of Pau.  The 188-km (117-mi) stage winds around southeast of Pau.  A category-4 and a couple of category-3 climbs will warm riders up for the category-1 climb to the 1490-m (4888 ft) peak of Col d'Aspin.  After they zoom down from there, they face the hors catégorie climb to the 2115-m (1.314-mi) peak of Col du Tourmalet.  An exhilarating 31-km (19-mi) descent will have cyclists flying before they reach the category-3 climb that finishes the stage in the ski resort commune of Cauterets.  Below is our prediction.

• Stage 11:  4h 58' 09" (prediction)

If the mountains eat up cyclists like today's final climb did, we could be too fast.  I want to see cyclists come in under five hours!