Wout van Aert Wins Sprint for Second Stage Win!

Wout van Aert outsprinted Michael Matthews and Tadej Pogačar for his second stage win in this year's Tour de France.  Another beautiful day of racing with a great finish!

My photo cropped van Aert's head on the finish.  Oh well, I might have been more interested in the sprint!  I was also interested in the time.

• Stage 8:  4h 13' 06" (actual), 4h 11' 22" (prediction), 01' 44" fast (-0.68% error)

After the past three stages, I'll definitely take that prediction error!  Check out van Aert's average speed.

• Stage 8:  12.27 m/s (44.16 kph or 27.44 mph)

Will anyone be able to get the green jersey off van Aert?  Will anyone be able to take down Pogačar?

Tomorrow's 192.9-km (119.4-mi) mountain stage begins in the Swiss town of Aigle and takes riders in a big loop through southwest Switzerland before finishing just across the border in the French commune of Châtel.  A couple of great category-1 climbs in the Alps await the cyclists.  Our prediction is given below.

• Stage 9:  4h 38' 03" (prediction)

Monday is a rest day, so teams may go all-out.  It will be interesting to watch the strategies unfold.

Can Anyone Beat Tadej Pogačar?

For the third straight stage, speeds were through the roof, though not as unbelievable as in yesterday's stage.  But today's final kilometer on the gravel was breathtaking. Lennard Kämna was biking for stage-win glory.  Nope, he cracked inside 100 m and finished fourth.  Jonas Vingegaard blasted his way past Tadej Pogačar and Kämna.  Nope, he couldn't hold off the explosion from Pogačar in the final 5 m on the 24% grade and finished second.  Tadej Pogačar is simply better than his competition.

Elite riders came in under four hours today, which is incredibly fast.  Our prediction was once again too slow.

• Stage 7:  3h 58' 40" (actual), 4h 11' 24" (prediction), 12' 44" slow (5.34% error)

Though much better than yesterday's prediction, I still don't like having over 3% error.  Pogačar and his fellow cyclists are simply outperforming what I've seen in recent years.  It's amazing to see what human beings are capable of on a bicycle!  Check out Pogačar's winning average speed.

• Stage 7:  12.31 m/s (44.32 kph or 27.54 mph)

He was more than 2 kph faster than my model cyclist.  For a kid who's not yet turned 24 years of age, the rest of the field has to wonder how long Pogačar will dominate cycling.

Tomorrow's 186.3-km (115.8-mi) medium-mountain Stage 8 commences in the French commune of Dole and finishes to the southeast in the Swiss city of Lausanne, which sits on the north side of Lake Geneva.  Our prediction is given below.

• Stage 8:  4h 11' 22" (prediction)

More grueling stages follow tomorrow's stage.  Will cyclists hold back a little or will speeds continue to be sky high?  It will be fun to see what happens!

Pogačar Back in Yellow and Disastrous Modeling!

Tadej Pogačar showed why he is the man to beat in this year's Tour de France.  He dominated the final sprint, showing an explosive ability that had my jaw on the floor.  He was pretty excited to win today's stage and grab the yellow jersey!

My jaw was on the floor for more than just the final sprint.  For this year's longest stage, I couldn't believe the speeds the cyclists were able to maintain.  I thought yesterday's stage was the ultra-fast stage that I miss every year.  But today's stage gave me, if not my worst prediction, nearly my worst prediction (I have to check).

• Stage 6:  4h 27' 13" (actual), 5h 06' 53" (prediction), 39' 40" slow (14.84% error)

Yeesh!  Check out Pogačar's average speed for today's 219.9-km (136.6-mi) stage.

• Stage 6:  13.72 m/s (49.38 kph or 30.68 mph)

With super-fast stages, I want to learn something about what elite athletes can do.  I will need a lot more time to digest what I witnessed today.  Stage 1's 13.2-km (8.2-mi) individual time trial, during which cyclists were going all out, saw the winner with an average speed of 51.78 kph (32.17 mph).  Cyclists were going at that rate during much of today's stage -- and they already had five stages under their belts!  A quick calculation shows that I needed nearly 40% more cyclist power output (or peloton power output) on much of today's stage.  I'm as flummoxed as I've ever been in nearly two decades modeling the Tour de France.

Wout van Aert and his yellow jersey were attacked mercilessly today, and he earned the most combative rider with an admirable effort to hold onto the lead.  But he fell to 103rd place, 7' 28" behind Pogačar.  The last rider to finish today was nearly 16 minutes off the winning time, still much faster than our prediction.  The yellow jersey attacks pushed speeds to heights I'd not seen before.  Can these ridiculous speeds continue???

Tomorrow's 176.3-km (109.5-mi) Stage 7 is nearly a repeat of Stage 7 in the Tour de France ten years ago, though this year's version is a bit shorter.  Both Stage 7s have the same endpoints.  Beginning in the French commune of Tomblaine, riders will head south to La Planche des Belles Filles in the Vosges Mountains.  This year's first mountain stage will have a great category-1 climb to the finish.  Our prediction is given below.

• Stage 7:  4h 11' 24" (prediction)

After yesterday and today, I won't be surprised if we are slow again!

Simon Clarke Wins Photo Finish!

Cobblestone racing, crashes, and a photo finish made for an exciting day in the Tour de France, though Team Jumbo-Visma may not agree.  Wout van Aert crashed but then rode with gritty determination to hold on to the yellow jersey.  Simon Clarke won an amazing sprint against Taco van her Hoorn to take the stage.  Check out the photo I took.

What also made today's stage exciting was the blistering pace set by the riders.  They were practically flying, even on some of the cobblestone sections.  This is the stage I wrote about yesterday when wondering when the ultra-fast stage would be.

• Stage 5:  3h 13' 55" (actual), 3h 31' 36" (prediction), 18' 01" slow (9.31% error)

After four wonderful predictions to start this year's Tour de France, we have our first terrible prediction.  Check out Clarke's average speed.

• Stage 5:  13.52 m/s (48.66 kph or 30.24 mph)

How fast is that average speed?  It's 1.66 kph (1.03 mph) faster than the Tour de France website's estimated top time schedule speed, and it's just 3.12 kph (1.94 mph) slower than Stage 1's individual time trial, which was only 8.4% the length of today's stage.  It seems that every summer there is a Tour de France stage that blows me away with high speeds, and that stage this year is Stage 5.

Tomorrow's Stage 6 begins in the Belgian city of Binche, just across the border from France.  At 219.9 km (136.6 mi), the hilly stage is this year's longest.  Cyclists will ride southeast to the French commune of Longwy, not too far from where Belgium, France, and Luxemburg meet.  Our prediction is given below.

• Stage 6:  5h 06' 53" (prediction)

I hope we can get back on track tomorrow.  I don't think we can do any worse than we did today!

Second No More -- Van Aert BLASTS to Victory!

After three consecutive second place stage finishes, Wout van Aert blasted his way to victory in today's Stage 4.  He and his Team Jumbo Visma mates went for it with about 12 km (7.5 mi) left in the stage.  They powered their way up the final climb and van Aert took over the final 10 km (6.2 mi).

Van Aert was 8 s ahead of the peloton.  He was very happy!  I am happy, too, after watching a stage raced on what looked to be a beautiful day in northeastern France.  I got even happier when I saw how our prediction fared.

• Stage 4:  4h 01' 36" (actual), 3h 59' 04" (prediction), 02' 32" fast (-1.05% error)

I thought we could be a bit slow today, but we did well.  Check out van Aert's average speed.

• Stage 4:  11.83 m/s (42.59 kph or 26.46 mph)

Not too shabby!

Tomorrow's 157-km (97.6-mi) hilly Stage 5 begins in Lille and ends to the southeast in Trouée d'Arenberg.  Our prediction is given below.

• Stage 5:  3h 31' 36" (prediction)

Wout van Aert has been the dominant rider for the first four stages.  Will he have the yellow jersey after tomorrow?  I cannot model team strategies because I do not have access to those strategies -- obviously.  With tomorrow's stage being relatively short in length, our prediction could be too slow.  We've had four great predictions, but I keep waiting for the blisteringly-fast stage that happens every year.

Groenewegen Wins Brilliant Sprint!

The three Danish stages are in the books, and Wout van Aert earned bridesmaid distinction.  The great Belgian cyclist was second on all three stages.  In today's third stage, Dylan Groenewegen just edged van Aert in a spectacular sprint to the finish line.

Groenewegen is just right of center in my photo, in light blue.  He was across the line just a couple of centimeters ahead of van Aert, who at least retains the yellow jersey.

We had another great prediction.

• Stage 3:  4h 11' 33" (actual), 4' 08' 46" (prediction), 02' 47" fast (-1.11% error)

I though we would be a tad slow today, but it wasn't until the last 10 km that speeds went through the roof.  I loved seeing in the final few km a speed limit sign for 70 kph (43.5 mph), which the peloton was just breaking.  Check out Groenewegen's average speed.

• Stage 3:  12.06 m/s (43.41 kph or 26.97 mph)

That's quite a clip!

The Tour de France transfers to France tomorrow, giving cyclists a break from the saddle.  I'll put our prediction up today instead of waiting until tomorrow.

Tuesday's 171.5-km (106.6-mi) hilly (six tiny category-4 climbs) Stage 4 begins in Dunkirk and ends in Calais.  The route in northeastern France, not too far from Belgium, will take cyclists through a lot of French history, especially WWII history.  It will be fun to watch.  Our prediction is given below.

• Stage 4:  3h 59' 04" (prediction)

I'm still waiting for the first ultra-fast stage, and Stage 4 could be it after a day of rest.  I hope we aren't too slow!

I'll enjoy Independence Day tomorrow and get back to the Tour de France on Tuesday morning.

Jakobsen Wins Fantastic Sprint!

If you love watching cycling with crosswinds and headwinds and gorgeous bridges, today's second Tour de France stage was made for you.  How great was it watching the peloton move across the Great Belt Bridge?  Too many crashes in today's stage, though, including on the bridge and within a few kilometers of the finish line.  Fabio Jakobsen timed his sprint in great position to just edge Wout van Aert by half the width of a wheel.  Two stages, and two second-place finishes for van Aert, but he'll wear the yellow jersey tomorrow.  I once again took a photo of the finish.

We had a great prediction today.

• Stage 2:  4h 34' 35" (actual), 4h 32' 29" (prediction), 02' 06" fast (-0.76% error)

I'll take the first two stages predicted to better than 1%!  Check out Jakobsen's winning average speed.

• Stage 2:  12.27 m/s (44.18 kph or 27.45 mph)

Tomorrow's Stage 3, the final Denmark stage, commences in Vejle and ends in Sønderborg.  The 182-km (113-mi) flat stage should have another great sprint finish.  Our prediction is given below.

• Stage 3:  4h 08' 46" (prediction)

We could be a tad slow if headwinds aren't a problem.  Hard to predict weather effects!  I can't wait to see more of Denmark and more great racing!

Lampaert Wins Time Trial!

Belgian Yves Lampaert won today's first Tour de France stage, an individual time trial in Copenhagen.  My prediction was nearly perfect with fellow Belgian Wout van Aert sitting in first place, just one second off what I had predicted.  It seems there is a big push by media companies to prevent screen shots, so I had to use my lousy cell phone camera to get Lampaert crossing the finish line.

I'm a dinosaur with social media and cell phone usage.  Maybe I'll find a better way to grab an image.  Seems like the media outlet wouldn't mind me doing free advertising for it!

We started this year's Tour de France off with a great prediction.

• Stage 1:  15' 17.76" (actual), 15' 21" (prediction), 3.24" slow (0.33% error)

Not a bad way to begin!  Lampaert was really cooking on his bike, despite lots of rain and 18-kph (11-mph) winds.  Check out his average speed.

• Stage 1:  14.38 m/s (51.78 kph or 32.17 mph)

Lampaert will be in yellow tomorrow, but he and 174 other riders were put on notice when Tadej Pogačar finished third, just 7 s behind the yellow jersey.  He's still the man to beat!

Tomorrow's flat second stage begins in Roskilde and ends after 202.2 km (125.6 mi) of cycling, in Nyborg.  It will be fun seeing more of Denmark.  I'm not sure we can hit tomorrow's winning time as well as today's, but we'll try.

• Stage 2:  4h 32' 29" (prediction)

Early on in each Tour de France, I wonder if predictions will be too fast, too slow, or about right.  It seems there are usually a quarter to a third of the stages that we can't predict to better than 3% error.  We'll learn a lot during tomorrow's long stage!

Time for the 109th Tour de France!

For the first time, the Tour de France will begin in Denmark.  Stage 1 will be an individual time trial of just 13.2 km (8.2 mi) in Copenhagen.  I will once again be modeling the world's most famous bicycle race.  My research student this summer is Michael Charecky, a rising junior physics major here at the University of Lynchburg.  We are excited for the start of the race!

Our prediction for Stage 1 is given below.

• Stage 1:  15' 21" (prediction)

Whoever wins the short time trial will get to don the famed yellow jersey for Saturday's second stage.  The man to beat this year is the winner of the past two Tours de France, Tadej Pogačar.  Who can knock PoGo off his pedestal?!?

When Empathy is Impossible

The slaughter continues.

My wonderful wife, Sally, stopped me dead in my tracks yesterday when she informed me that elementary school children were killed in Texas.  Robb Elementary School in Uvalde, Texas is now likely known to most Americans.  That is where 19 children and two adults were murdered.  I've tried to explain reasons for mass shootings to my overseas colleagues who are just as perplexed as I am for why killings continue with little to no action taken to prevent future killings.  I wrote a blog piece after Sandy Hook in late 2012.  I wrote another blog piece in early 2018 after Stoneman Douglas.  I doubt the words I write in this blog piece will add much to what I've already written, but I'll attempt a slightly different angle.

Webster's second definition for "empathy" is:  the action of understanding, being aware of, being sensitive to, and vicariously experiencing the feelings, thoughts, and experience of another of either the past or present without having the feelings, thoughts, and experience fully communicated in an objectively explicit manner.  As a parent of two incredible daughters, it takes no effort for me to empathize with the parents who lost their children yesterday.  It also takes zero effort for me to empathize with those who regret that yesterday's perpetrator had been killed, only so that something worse -- more painful -- could happen to that evil individual.  But I predict that it is impossible for me to empathize with yesterday's shooter, even though I know next to nothing about him.  I am not wired for "vicariously experiencing the feelings, thoughts, ..." of someone who enters a school and opens fire.

I suspect that nothing in my previous paragraph is especially disagreeable.  Let me change that.  I struggle mightily to empathize with those who love guns.  I've held various opinions on that topic during more than half a century of life.  The empathy I feel for a parent whose child was murdered is effortless for me to experience.  Most of the time, though, empathy is hard.  Empathy requires effort and, sometimes, a lot of work.

I own a .30-06 Savage rifle that sits in a gun cabinet about 200 miles (as the crow flies) from my home.  I hunted with my family for a few years, mostly in an effort to understand hunting culture.  I enjoyed it.  My family loved deer meat, and I felt better about eating deer I killed than I did eating meat that came from factory farms.  I've been a vegetarian for over five years, but the reason for that choice has nothing to do with guns.  I've no interest in hunting because of my diet choice.  But I also have no interest in the rifle I own.  And here is where empathy is hard for me.  Regardless of conversations with hundreds of gun enthusiasts over several decades, much study on the history of guns in America, and my own experience of owning a gun, I've been incapable of empathizing with those who adore guns.  Facebook friends have recently posted the need to arm teachers, and despite my best efforts, I cannot get my mind in a place where I could ever imagine the efficaciousness of such a strategy.  I wouldn't bat an eye if I had to give up my gun as part of a national effort to eliminate gun use.  I understand that there are those who will read that previous sentence and be unable to empathize with me.

Far from being the first to point this out, people are tribal.  Social media, with it's headlines-only approach to disseminating news, is but part of the reason why diametric sides of an issue are on opposite sides of a vast chasm that used to be filled with nuance.  Like empathy, nuance requires a lot of work.  Reading long articles and books, talking to people from all walks of life, and spending serious time cogitating in a sans-cell-phone environment are just some of the ways people begin to develop nuanced views.

Consider the following 10 questions.

1. Do you believe in a god?
2. Should abortion be legal?
3. Should capital punishment be legal?
4. Should research be performed on stem cells?
5. Do you think animals should be killed for food if non-animal food options are readily available?
6. Do you support Donald Trump?
7. Should torture ever be used during an interrogation?
8. Should private citizens of adult age be allowed to own guns?
9. Should marijuana use by private citizens of adult age be legal?
10. Do you support government-funded, universal healthcare?

Perhaps my biases have been partially revealed by the way I asked each question even though I tried to pose questions that did not suggest a preferred answer.  Does asking "Should abortion be legal?" imply something different about me compared to asking "Should abortion be illegal?"  I've no idea.  Each of the above questions is meant to evoke an immediate "yes" or "no" answer.  But I can imagine objections to insisting on binary responses.  Those objections would be founded in desires for nuance.  Any one of my questions could occupy classroom discussions during a semester-long course, and entire books could be, and have been, devoted to addressing my questions.  If you had to answer "yes" or "no" to my questions, could you do so?  My guess is that most people could, even though they would be yearning to offer slews of caveats.

Now for a simple math question.  What is the number 2 raised to the 10th power?  It won't be hard to come up with 1024.  Because each of my 10 questions sought only a "yes" or "no" answer, there are 1024 distinct ways of answering those questions.  That means if you and a thousand people answer my questions, there is a chance, albeit vanishingly small, that each one of you could have a unique set of answers.  And if you feel passionate about each of your 10 responses, you could look upon the answers given by the other thousand people -- and want nothing to do with each and every one of those people.

Yesterday was 24 May 2022, the 144th day of the year.  The massacre in Texas was the 27th school shooting this year.  That's one school shooting per 5 days and 8 hours.  How does this problem get solved when tribalism reigns supreme, nuance is all but gone, and empathy is hard to come by?  I know people who would have nothing to do with me if they were aware that my answer to a particular question on my list differs from theirs.  How does someone in the pro-gun culture talk to a person who wants to eliminate guns?  Sure, they likely agree that shooting children is evil, but neither might be able to empathize with the other on what to do with guns.  The traditional political spectrum has been replaced with a Möbius strip; left and right meet at a twisted point behind the part of the spectrum where nuance used to sit.

While people shout at each other, try to cancel each other, and refuse to do the hard work of empathizing with each other, the slaughter continues.

Skating History!

Russian figure skater Kamila Valieva is the first woman to land a quad jump at the Winter Olympics.  After seeing Valieva's performance, I knew I had to analyze her history-making jump, which was the first jump of her routine.  Check out Valieva as she initiates her quad.

Valieva's right leg is bent with lots of stored energy while her left leg and right arm are extended so that she can pull them in fast, doing work to get herself spinning.  In the next image, Valieva leaves the ice.

She's already spun half a turn.  Her arms and legs are moving inward so as to reduce her moment of inertia and increase her spin rate.  The image below shows Valieva after her first turn.

Isn't that wonderful!  Valieva has moved her arms and legs as close to her spin axis as she can, minimizing her rotational inertia.  Her skirt hasn't been thrown outward; it's horizonal so that tension in the fabric can provide the inward force necessary to keep the skirt moving in a circle.  A great look at Valieva near maximum height is in the image below.

The image below shows the completed third turn.

Now it's time to return to the ice with a completed fourth turn, as the image below shows.

The guy on the left has a great look at history being made!

From the first image above to the last image, Valieva needed just 0.93 seconds.  I estimate about a sixth of a second for Valieva's third turn, which leads to a rotational rate of about 360 rpm.  That rotational rate is about 80% of the rotational rate for helicopter rotor blades!  She jumped from the ice with a speed of about 7 mph and reached nearly 20 inches in height off the ice.  That's a great jump!

Wout van Aert Sprints for Hat Trick and Tadej Pogačar Repeats!

Wout van Aert won his third stage of this year's Tour de France.  After winning a mountain stage and a time trial, he showed what an all-around talented cyclist he is by winning a sprint stage.  He held off Mark Cavendish's attempt to set the record for stage wins.

Racing was very slow at the start, making me worry that our prediction would be too fast.  Serious racing did not begin until the last three or four laps of the seven famous laps in Paris.  Had the race ended with six laps, we would have been nearly perfect.  But the extra lap gave us a fast prediction.

• Stage 21:  2h 39' 37" (actual), 2h 33' 04" (prediction), 06' 33" fast (-4.10% error)

I do not like seeing another stage prediction off by more than 3%, but I am bothered less on the final stage because I never know how much ceremony will play a role in the first half of the stage.  We have usually hit the last stage quite well, but this year's prediction was a bit fast.  The beauty of being wrong is learning something!  We will have a lot to dissect with this year's Tour de France.  Check out van Aert's average speed.

• Stage 21:  11.32 m/s (40.75 kph or 25.32 mph)

That is definitely a slow average speed for the final stage.

Cycling a safe and sound Stage 21 meant that Tadej Pogačar would secure his second straight Tour de France win, and that is just what he did today.  Pogačar not only won the yellow jersey, he won the polka dot and white jerseys, just as he did last year.  Who can beat this guy over the next few years?

Pogačar will face a serious challenge from this year's runner-up, Jonas Vingegaard, shown on the left above.  Vingegaard gave Pogačar his most worrisome moment this year.  Coming in third is Richard Carapaz, the first Ecuadoran to earn a podium finish.  It was wonderful seeing the cyclists' kids on the stage, too!

I have noted in this space before that the science is what motivates me to model the Tour de France.  Learning how elite cyclists do what they do fascinates me.  Posting stage-winning time predictions on my blog interjects some additional fun into my research.  My students always get a kick out of seeing how close we get.  Noah Baumgartner worked with me again this year.  We will have a lot to do with post-race analysis.  We hit 13 stages to less than 3% error.  For the other eight stages, some were close to 3% error, some were not.  Weather and team strategies played role, as did a lone cyclist going ballistic on a couple of stages.  All 21 stages will provide fertile ground for learning.

Wout van Aert Takes Time Trial!

Belgian Wout van Aert won his second stage in this year's Tour de France with an impressive individual time trial.  Just seven other cyclists could get within a minute of van Aert.

At least our prediction was within a minute of his great ride!

• Stage 20:  35' 53" (actual), 36' 40" (prediction), 00' 47" slow (2.18% error)

I am happy with that prediction.  What made me even happier was watching van Aert really crank up the speed.

• Stage 20:  14.31 m/s (51.50 kph or 32.00 mph)

I certainly know what that speed is like in a car, but not on a bicycle, especially as an average speed for more than half an hour.

One of the seven riders who came within a minute of van Aert was this year's Tour de France winner, Tadej Pogačar.  He will ride into Paris tomorrow, cross the finish line as the winner for the second straight year, and also collect the white and polka dot jerseys.  He still has two months to go before turning 23!

Tomorrow's mostly ceremonial stage begins in Chatou.  Riders will travel 108.4 km (67.36 mi), first going west, and then making a counterclockwise circle back east to Paris.  Our prediction is given below.

• Stage 21:  2h 33' 04" (prediction)

It will be hard to not root for Mark Cavendish to break the record!

Matej Mohorič Wins Another BLISTERINGLY FAST Stage!

Matej Mohorič did in today's Stage 19 what he did in Stage 7.  He blew away his competition -- and our model! -- with a stunningly fast stage.  He rode the final 25 km (16 mi) as if he were riding a time trial.  He stayed in his biggest gear and grinded out those final 25 km in the blink of an eye.

Check out Mohorič's obliteration of our model.

• Stage 19:  4h 19' 17" (actual), 4h 37' 30" (prediction), 18' 13" slow (7.03% error)

Yeesh, that is not a good error.  But look at Mohorič's average speed.

• Stage 19:  13.31 m/s (47.90 kph or 29.76 mph)

I cannot believe he averaged nearly 48 kph (30 mph) on a 207-km (129-mi) long stage!  The Tour de France organizers estimated 45 kph (28 mph) as the top average speed on their time schedule.  Mohorič also blew away the Stage 7 time schedule.  When he decides to go for a stage win, he goes all out!

The peloton and the yellow jersey came in nearly 21' after Mohorič crossed the line.  As with Stage 7, we did a great job modeling the peloton!  We will have to think about power outputs on stages where lone cyclists are likely to go bananas!

Tomorrow's Stage 20 is a 30.8-km (19.1-mi) individual time trial.  Picking up in Libourne, cyclists will head around a clockwise loop to the east and finish in Saint-Émilion.  Our prediction is given below.

• Stage 20:  36' 40" (prediction)

I doubt much will change in the GC classification after tomorrow's stage, but it will be exciting to watch nonetheless!

Déjà Vu on Stage 18!

Tadej Pogačar continues to dazzle cycling fans.  I thought I was watching yesterday's stage when today's Stage 18 nearly had its winner.  Inside of half a kilometer, Pogačar simply accelerated past his competition.  He makes cycling up a tough climb look easy!

Our prediction was a bit slow today, but not too bad at just outside the 3% error I want to be under.

• Stage 18:  3h 33' 45" (actual), 3h 40' 36" (prediction), 06' 51" slow (3.20% error)

Speed was fast and the elite climbers set a torrid pace up the final climb.  Check out Pogačar's average speed.

• Stage 18:  10.11 m/s (36.41 kph or 22.62 mph)

Pogačar is on a different level.  He has nearly a six-minute lead in the GC classification.  Winning back-to-back brutal mountain stages is amazing!

Tomorrow's Stage 19 is a long, flat stage to get cyclists to the final individual time trial.  Beginning in the commune of Mourenx, riders will travel 207 km (129 mi) north to Libourne.  Our prediction is given below.

• Stage 19:  4h 37' 30" (prediction)

Will Mark Cavendish break the record tomorrow?

Is the Tour de France Over?!?

What an unbelievable battle on the climb to the summit of Col de Portet!  Watching Tadej Pogačar, Jonas Vingegaard, and Richard Carapaz attack and battle on that climb is something I will never forget.  Carapaz made a late surge for the stage win, which left Vingegaard behind for a bit, but Vingegaard caught up.  Pogačar got inside of half a kilometer and just blasted forward for the stage win, which he got.

Can anyone take that yellow jersey from Pogačar?  I do not see it happening.  The Tour de France looks to be over.  We had another great prediction today.

• Stage 17:  5h 03' 31" (actual), 4h 58' 23" (prediction), 05' 08" fast (-1.69% error)

I love that error with such a difficult final climb!  Check out Pogačar's incredible average speed.

• Stage 17:  9.80 m/s (35.27 kph or 21.91 mph)

Tomorrow's 129.7-km (80.59-mi) mountain Stage 18 begins in the commune of Pau and takes riders southeast to the ski resort at Luz Ardiden.  Cyclists will face two hors catégorie climbs, including the stage's end.  Our prediction is given below.

• Stage 18:  3h 40' 36" (prediction)

I cannot see Pogačar finishing tomorrow's stage with less than a five-minute lead in the GC classification.

Patrick Konrad Outduels Pursuers to Take Stage 16!

With just over 36 km (22 mi) left in today's stage, Patrick Konrad broke away from the lead group and went for the stage win.  He took care of the last couple of climbs, navigated wet roads, which slowed descents, and took his first Tour de France stage win.

Our model was back on track today.  The wet roads made me think we would be a tad fast.

• Stage 16:  4h 01' 59" (actual), 3h 56' 52" (prediction), 05' 07" fast (-2.11% error)

Konrad had an impressive average speed.

• Stage 16:  11.64 m/s (41.90 kph or 26.04 mph)

Tomorrow's Stage 17 is not for fainthearted cyclists.  The 178.4-km (110.9-mi) mountain stage begins in the commune of Muret and takes cyclists southwest to Saint-Lary-Soulan.  The first two-thirds of the stage is fairly flat.  But two category-1 climbs will then greet riders.  The stage ends with an hors catégorie climb to the summit of Col de Portet.  How will riders' legs be when they begin climbing?  If there is ever a time to challenge the yellow jersey, tomorrow is the day!  Our prediction is given below.

• Stage 17:  4h 58' 23" (prediction)

The final climb will be exciting to watch!

Stage 16 Prediction

Tomorrow's 169-km (105-mi) medium mountain Stage 16 begins in the east Andorra town of El Pas de la Casa.  Cyclists will ride northwest until they reach Saint-Gaudens back in France.  Racing will be fast at first, but then two category-2 climbs and one category-1 climb in the Pyrenees will allow fans to watch the climbers shine.  Two brutal mountain stages follow Stage 16.  Will the yellow jersey be challenged tomorrow, or will GC challengers wait for the two stages to follow?  Our prediction is given below.

• Stage 16:  3h 56' 52" (prediction)

We have hit two thirds of the stages to this point.  The ones we missed have either been won by a crazy-fast time or stages in which the GC contenders did not fight too hard.  Strategies are always fun to guess!

Sepp Kuss Wins a Stage for the USA!

Racing was a bit slower than I expected because there were no serious attacks on the yellow jersey.  But how our prediction would do was out the window when I had the chance to root for fellow countryman Sepp Kuss.  He was pursued by Alejandro Valverde, but Valverde could not catch up.

I was standing in my office while Kuss crossed the finish line.  That was exciting!  Our prediction was too fast.

• Stage 15:  5h 12' 06" (actual), 4h 55' 58" (prediction), 16' 08" fast (-5.17% error)

I wanted to see more attacking on the yellow jersey.  With tomorrow's rest day, I thought GC contenders would push a bit more today.  But check out Kuss's average speed.

• Stage 15:  10.22 m/s (36.78 kph or 22.85 mph)

That's a great average speed!  As a middle-aged physicist watching the Tour de France in my office, it is very easy for me to root for faster speeds!

Tomorrow is the second and final rest day of the Tour de France.  Cyclists will relax where they finished today, in Andorra la Vella.  Teams will discuss their strategies for the next three stages in the Pyrenees.  I will post our Stage 16 prediction tomorrow.

Mollema Rides Away with Stage 14 Win!

With about 40 km (25 mi) left in today's stage, Bauke Mollema simply made up his mind to go for the stage win.  And before long, nobody could get closer than about a minute to Mollema.  He crossed the finish line with no one in sight.  What a great ride!

Our prediction did well today, though we were closer to the peloton, which crossed the line nearly seven minutes after Mollema.

• Stage 14:  4h 16' 16" (actual), 4h 23' 19" (prediction), 07' 03" slow (2.75% error)

That makes 10 stages we have hit to better than 3%.  I like the four we got under 1%, but I will definitely take today's result after Mollema went all out and beat our prediction.  Check out his average speed.

• Stage 14:  11.95 m/s (43.01 kph or 26.73 mph)

Tomorrow's 191.3-km (118.9-mi) mountain stage begins in Céret and takes riders west into Andorra la Vella, the capital of Andorra.  Three big climbs and a fast downhill finish will make for an exciting day of racing in the Pyrenees!  Our prediction is given below.

• Stage 15:  4h 55' 58" (prediction)

Michael Woods grabbed the polka dot jersey from Nairo Quintana today.  Will Woods hold onto that jersey tomorrow?  Guillaume Martin jumped from 9th to 2nd in the GC classification today, and also shaved more than a minute off Tadej Pogačar's overall lead.  Will the yellow jersey be seriously threatened before Monday's rest day?  It will be fun to watch!

Cavendish Ties Merckx!!!

Mark Cavendish was set up beautifully by his Deceunick--Quick-Step mates in the final kilometers.  And then the Manx Missile did what he does best -- blast past his competition.  He's now tied with Eddy Merckx for the most Tour de France stage wins with 34.  What an amazing sprint to make history!

That's the look of a man with his 4th stage win in this year's Tour de France and his 34th overall.  Our model was back on track with today's stage.

• Stage 13:  5h 04' 29" (actual), 4' 59' 08" (prediction), 05' 21" fast (-1.76% error)

Cavendish had a great average speed, given that temperatures exceeded 30 C (86 F) and cross winds surpassed 18 kph (11 mph).

• Stage 13:  12.04 m/s (43.33 kph or 26.93 mph)

Tomorrow's Stage 14 is a medium mountain stage that picks up in Carcassonne and takes riders south to Quillan.  There are five category climbs in the 183.7-km (114.1-mi) stage.  Our prediction is given below.

• Stage 14:  4h 23' 19" (prediction)

It's now time for the climbers and GC contenders to make some noise!

Nils Politt Blows Away Competition!

Nils Politt was all about winning today's stage.  We were headed for a great prediction today until Politt made a solo attack and simply barreled his way to the finish line.  As I wrote and feared yesterday, we were too slow with our prediction.

We had our second-worst prediction in this year's Tour de France.

• Stage 12:  3h 22' 12" (actual), 3h 39' 30" (prediction), 17'18" slow (8.56% error)

Check out Politt's average speed.

• Stage 12:  13.14 m/s (47.30 kph or 29.39 mph)

The time schedule on the Tour de France web page estimated 45 kph as the top average speed.  Suffice to note, Politt's average speed was amazing!  I love the image below.

That's Mark Cavendish in the green jersey, leading the peloton across the finish line.  Cavendish officially finished 14th today with a time of 3h 38' 05".  The next 126 riders received the same time.  Our model actually nailed the peloton!  But our goal is to hit the winner's time.  I hope we do better tomorrow!

Stage 13, at 219.9 km (136.6 mi), is a long, flat stage, which commences where Stage 12 ended, in Nîmes, and takes riders southwest to Carcassonne.  The route is not too far from the coast, so winds could play a role.  Our prediction is given below.

• Stage 13:  4h 59' 08" (prediction)

Tomorrow's stage is a mostly flat travel toward the Pyrenees.  Five medium mountain and mountain stages follow tomorrow's stage!

We Nearly Nail Wout van Aert's Great Ride!

Wout van Aert showed today why he's such a dominating young force in cycling.  He left his competition behind on the final climb and won today's Stage 11 of the Tour de France by more than a minute.  For all the attacking that took place, Wout van Aert withstood all challengers to set up an emotional ride across the finish line.

I was actually hoping he would push a tad harder to the finish line so that we could have a shot at a perfect prediction.  That's a silly thing to root for!

• Stage 11:  5h 17' 43" (actual), 5h 16' 02" (prediction), 01' 41" fast (-0.53% error)

We really nailed that stage-winning time!  Check out Wout van Aert's average speed.

• Stage 11:  10.43 m/s (37.56 kph or 23.34 mph)

That's a terrific average speed for such a grueling mountain stage!

Tomorrow's Stage 12 is flat and relatively short at 159.4 km (99.05 mi).  It begins in the commune of Saint-Paul-Trois-Châteaux and takes riders southwest to Nîmes.  Our prediction is given below.

• Stage 12:  3h 39' 30" (prediction)

It's always hard to read a stage like this one.  It's flat and fairly short, so the GC contenders are likely to stay together in the peloton.  There could be some attacking and a few riders going all out to win the stage.  I don't think we'll be fast, but we could be slow.

Hat Trick for Cavendish!

Today's Stage 10 of the Tour de France was a bit sluggish for most of the race.  The peloton moved through some beautiful parts of France, but speeds were fairly slow.  Only in the final 30 km (19 mi) or so did frantic racing begin.  Speeds shot up, cross winds helped break up the peloton, and sprinters jockeyed for position in the final kilometers.  And once again, the Manx Missile shot past his competition to earn his 33rd Tour de France stage win, just one behind the great Eddy Merckx.  Check out Mark Cavendish just after he crossed the finish line.

Cavendish now has three stage wins in this year's Tour de France.  We were a tad fast because of the slow pace for most of the stage.

• Stage 10:  4h 14' 07" (actual), 4h 07' 59" (prediction), 06' 08" fast (-2.41% error)

I'm just happy to be under 3% error!  The fast pace during the final part of the race brought up the average speed to a pretty good clip.

• Stage 10:  12.51 m/s (45.03 kph or 27.98 mph)

Cavendish will have a few more shots to tie Merckx.

Tomorrow's mountain Stage 11 begins in Sorgues and ends to the northeast in Malaucène.  The final part of the 198.9-km (123.6-mi) stage will be a joy to watch.  There will be two climbs to the 1910-m (6266-ft) summit of Mont Ventoux.  The first climb will be category 1; the second will be Hors Catégorie.  The second descent off Mont Ventoux will make for a blisteringly fast finish.  Our prediction is given below.

• Stage 11:  5h 16' 02" (prediction)

Will the yellow jersey face serious attack?  It will be fun to see!

Stage 10 Prediction

Beginning in Albertville, the home of the 1992 Winter Olympics, tomorrow's flat Stage 10 takes riders 190.7 km (118.5 mi) southwest to the commune of Valence.  I've no idea what the weather will be like, and I certainly don't know if the yellow jersey will be attacked.  I suspect the yellow jersey will cross the finish line with the peloton, just prior to some of the top sprinters going for the win.  But the fun of the Tour de France is not knowing all the strategies ahead of time!  Below is our prediction for Stage 10.

• Stage 10:  4h 07' 59" (prediction)

Barring a major crash, Tadej Pogačar should retain the yellow jersey after tomorrow's stage.

Ben O'Connor Dominates Stage 9 -- and Nearly Grabs Yellow!

Ben O'Connor made Australia proud today with a dominating ride that showed what an incredible climber he is.  After yesterday's seemingly super-human performance by Tadej Pogačar, the yellow jersey looked safe on Pogačar.  But O'Connor had the ride of his life today and vaulted up to the overall lead for several kilometers during today's stage before Pogačar exploded at the end of the final climb to maintain the yellow jersey.  O'Connor is now second in the general classification, 2' 01" behind Pogačar.  Instead of putting an image of O'Connor at the line, I'll opt instead for a shot of O'Connor on the podium.  He won the stage by more than five minutes!

As O'Connor said after the race, today's conditions were "atrocious."  It didn't take long after the stage began for me to realize that our prediction was going to be much too fast.  It was pouring the rain for much of the stage.  And it was cold; temperatures dipped below 9 C (48 F).  With such treacherous conditions, all I can do is note that we can't know the weather on each stage prior to the start of the Tour de France.

• Stage 9:  4h 26' 43" (actual), 4h 07' 31" (prediction), 19' 12" fast (-7.20% error)

Cyclists were changing jerseys, getting waterlogged, fumbling with gloves to keep their hands warm, and constantly eating gels to maintain energy balance.  With stages like today's that are riddled with horrible weather, we simply have to eat a fast prediction.  Check out O'Connor's average speed.

• Stage 9:  9.05 m/s (32.60 kph or 20.25 mph)

All is not lost today with modeling because I get to learn a lot more about cycling in poor weather.  We hit two thirds of the first nine stages quite well.  Two other stages saw faster-than-expected speeds, and today's stage had weather issues.

Tomorrow is the first of two rest days in the Tour de France.  Cyclists will remain in Tignes for their much-deserved day of rest.  I'll celebrate 4th of July here for the rest of today, and tomorrow I'll post our prediction for Tuesday's Stage 10.

Dylan Teuns Takes Stage 8!

Lots of rain today made me think our prediction would be too fast.  But I underestimated just good elite cyclists can navigate fast descents on wet roads.  Speeds reached around 80 kph (50 mph) on the descents.  I was in awe of how lead riders flew downhill, narrowly missing gravel and walls.  Dylan Teuns was amazing in winning the stage, but fans will remember Tadej Pogačar defend his Tour de France win with an incredible attack near the summit of Col de Romme.  And then Pogačar ate up his competition as he took on Col de la Colombière and secured the yellow jersey with nearly a two-minute lead when today's stage finished.  Check out Teuns crossing the finish line, thinking of his recently departed grandfather.

Our modeling got back on track today.

• Stage 8:  3h 54' 41" (actual), 3h 58' 34" (prediction), 03' 53" slow (1.65% error)

Speeds were again fast, but not well beyond what we predicted, as happened on the previous two stages.

• Stage 8:  10.71 m/s (38.55 kph or 23.96 mph)

There were moments when my jaw was agape while watching Pogačar fly up the mountains.  Just like the most elite of great athletes, he almost made riding up those 10% and greater climbs look easy.

Tomorrow's 144.9-km (90.04-mi) Stage 9 begins in the eastern French commune of Cluses and takes riders mostly south to Tignes, high in the Rhône-Alpes.  Lots of great climbing, including an uphill finish, await riders tomorrow!  Our prediction is given below.

• Stage 9:  4h 07' 31" (prediction)

We are looking for another fast stage tomorrow.  If Tadej Pogačar does tomorrow what he did today, he'll head to Monday's rest day with the Tour de France all but locked up.  He is his only competitor now!