Last Look at 2020 Tour de France

I noted in my last blog post that a lot of work on this past Tour de France remains to be done.  I leave interested readers with a few tidbits in this space that have come from recent calculations.

Ever wonder how many Calories elite cyclists burn on a Tour de France stage?  I can show you a great estimate.  I adjusted my model's power outputs so that my model would "predict" the time that exactly matched all 21 stage-winning times.  Energy burn in the body is a complex phenomenon, but a reasonable estimate is to assume a 20% efficiency in the body's conversion of consumed energy into useful output for cycling.  Some muscle groups are more efficient; other muscle groups are less efficient.  Check out the graph below.

Click on the graph so you can see it better.  I plot an estimate of each stage winner's Calorie burn.  You can see which stages are flat, medium mountain, mountain, and individual time trial, plus I include the distance for each stage to add some context.  It's not uncommon to burn 6000 Calories on single stage!  That's why cyclists need to eat while biking.

The combined total energy burn for the winners of the 21 stages came to 120,649 Calories, or an average of 5745 Calories per stage.  To put that number in perspective, consider the following, tasty, but not-so-healthy food:

According to the McDonald's website, a Big Mac contains 550 Calories.  That means that the average energy burn on a single Tour de France stage is over 10 Big Macs!  Do NOT try to prepare for a Tour de France stage by consuming 10 Big Macs prior to the stage's start.

Figuring out weight loss with the number of Calories burned isn't trivial because fats, carbohydrates, fiber, and proteins (among others) have different energy densities.  But, again, keeping things simple, one quasi-decent rule of thumb is that 3500 Calories have to be burned to get rid of a pound of fat (or consume 3500 Calories to gain a pound of fat).  A Tour de France cyclist can burn nearly two pounds of fat per stage.  Using the figure above for the sum of the winners' energy burn, a total of about 34.5 pounds of fat could be burned during the three-week race.  Those guys have to eat while biking!

Though we predict a stage-winner's time, and we never go after a particular cyclist's time, it's interesting to see how the general classification winner's time compares to the sum of stage-winning times.  Check out the table below.

You can see the time that Tadej Pogačar won the general classification with.  The actual sum of stage-winning times is obviously smaller than the winner's time.  The sum of my model's predictions is also shown.  We were only about 6.5 minutes faster than the actual sum.  Though the error looks great, a lot of individual errors were canceled.  In other words, some of our stages were too fast, whereas other stages saw our predication come in too slow.  But my model does a good job predicting the sum of stage-winning times, if ever anyone is interested in that number.  Tadej Pogačar was only a bit more than three-quarters of an hour slower than the sum of stage-winning times.  To put that into perspective, note that 146 riders finished the 2020 Tour de France.  The last rider came in over 6 hours behind Pogačar!  A time of about 45 minutes slower than Pogačar's time sits between the riders that finished in 15th and 16th places.  In other words, even though he won just three stages, which is great, Tadej Pogačar competed extremely well against the winners of all the stages.  He had one helluva great Tour de France!

Tadej Pogačar Wins Tour de France!

Tadej Pogačar will turn 22 years old tomorrow.  What a way to end his 22nd year!  He and his team rode well today and Pogačar was able to finish in the final bunch.  What an amazing Tour de France for Pogačar!  He won each of the mountain stages before rest days, giving his competition something to think about on days off from racing, and then road a time trial for the ages yesterday.  Pogačar was the best climber and the best young rider, meaning he leaves the Tour de France with the yellow, polka dot, and white jerseys.  The Tour de France concludes by having Pogačar on the center of the final podium with second-place finisher and fellow Slovenian Primož Roglič on Pogačar's right and third-place finisher Richie Porte on Pogačar's left.

The final stage is such a celebration of Paris.  It's hard for me to watch the final eight circuits and not want to return to France to visit Paris!  Check out cyclists on the roundabout at the Arc de Triomphe.

What a lovely sight!

The final sprint to the finish line was thrilling.  Sam Bennett sealed the deal on the green jersey earlier in the stage, but that didn't stop him from an explosive effort in the final 100 m.

We finished the Tour de France this year with a good prediction.

• Stage 21:  2h 53' 32" (actual), 2h 57' 44" (prediction), 04' 12" slow (2.42% error)

We usually do well on the last stage.  Until the riders get to Paris, cycling is slow, but then those vying for the stage win kick it up and fly through the streets of Paris.  I'm happy to finish under 3% error!  Check out Bennett's average speed below.

• Stage 21:  11.72 m/s (42.18 kph or 26.21 mph)

That's actually pretty high for the final stage, but not unreasonably so.  It was great seeing fast racing on the final couple of circuits.  Bennett donned his green jersey with Pogačar and his three jerseys for a final trip to the podium.

No sports fan, or anyone for that matter, will see 2020 as a great year.  But at least we had a wonderful Tour de France to watch, despite the delayed start.  The 2021 Tour de France begins 9 months and 6 days from today.  Let's hope 2021 is a better year, the race begins on time, and life is closer to normal.

There is much to learn on the scientific front from this year's Tour de France.  And that's what is so great about being a scientist -- there is always more to learn.  Advancing technologies continue to make riders fitter, healthier, stronger, more efficient with their power output, more aerodynamic with better clothes and bikes, and better equipped with strategies for riding all the stages.

Modeling the Tour de France each year is a part of my scientific research.  Using the laws of physics and terrain information to predict the winning time for each stage, and then posting a stage prediction the day before each stage takes place is merely a little fun on top of all the research.  My physics research students at the University of Lynchburg make my work all that much more rewarding.  We certainly love watching the Tour de France for three weeks and we root for our predictions.  But the real joy comes from discovering more about how the natural world works and learning how science and technology continue to push the envelope of what's possible in the world of sport.  I thank Noah Baumgartner for once again working with me on the Tour de France.  We both had to work on the race while our fall semester was in full swing.  It's a lot easier working on the Tour de France in July when neither one of us is involved with classes!  There is still work ahead to dissect what happened over the past three weeks.  We had 10 great stage picks with errors under 3%, four were merely okay with errors in the 3 % - 6% range, six had errors 6% - 9%, a range I thought was okay when I started this work, but not now, and one really bad prediction with an error over 9%.  Team strategies reeked havoc on our predictions early in the Tour de France with some stages painfully slow and lacking attacks, and then a few other stages with all-out effort that stunned race organizers, commentators, and us.  Investigating and studying the vast complexity contained in a three-week bike race, one that concluded with 146 riders crossing the finish line, is a small part of what makes my job so much fun!

Pogačar Performs Slovenian Swap in Historic Ride!

I've modeled the Tour de France for 17 years, but I've never seen anything so exciting as today's Stage 20.  The split screen with Primož Roglič in yellow on the left and Tadej Pogačar on the right made for incredible drama.

Pogačar rode a time trial for the ages.  He kept obliterating the times at checkpoints, and he continued to shave time off the lead Roglič had on him.  The top two general classification competitors were about 1 km apart heading to the finish.  Roglič entered the day with a 57" lead on Pogačar, but Pogačar finished today's action with a 59" lead on Roglič.  The two Slovenians will be on the podium in Paris tomorrow, but Pogačar's glorious ride today made sure that he would be on top.

Our prediction was a bit fast today.  The final climb took a little longer than we expected.  But after watching Pogačar blow the field away on that climb, I know that we have more work to do to better understand that climb.

• Stage 20:  55' 55" (actual), 52' 47" (prediction), 03' 08" fast (-5.60% error)

Look at Pogačar crossing the finish line.  That is what winning the Tour de France looks like!

Pogačar's average speed is given below.

• Stage 20:  10.79 m/s (38.84 kph or 24.14 mph)

Pogačar sealed up both the polka dot jersey as the best climber and the white jersey for the best young rider.  Richie Porte's great ride today moved him up to third in the general classification, so he'll be on the podium tomorrow.  The only suspense in tomorrow's final stage will be the race for the green jersey.  Peter Sagan will go all out to catch Sam Bennett, which will be very difficult to do.

Tomorrow's 122-km (75.8-mi) Stage 21 will begin in Mantes-la-Jolie and head southeast to Paris.  There won't be much racing on the way to Paris.  The stage is mostly ceremonial.  Pogačar may be seen sipping champagne with his teammates while they are on their bikes.  Real racing will pick up close to Paris as cyclists get close to the Champs-Élysées and the sprinters compete for the stage win.  Our prediction is given below.

• Stage 21:  2h 57' 44" (prediction)

Tomorrow will be a coronation for Tadej Pogačar, and one he deserves after a ride today that cycling fans will be talking about for many years to come.

Søren Kragh Andersen Repeats Stage-14 Strategy!

Søren Kragh Andersen executed the exact move today that won him Stage 14.  With 16 km (9.9 mi) left in today' Stage 19, Andersen broke away from the leaders and entered into time-trial mode.  A few cyclists tried to catch him, but Andersen increased his lead most of the way to the finish line, winning by 53" over those chasing cyclists.  I grabbed the screen capture below when his speed hit 76 kph (47 mph).

Andersen was down in his bike, fully into time-trial mode.  Check him out crossing the finish line.

It was jaw-dropping watching Andersen treat those last 16 km like a time trial.  He simply powered his way to the finish line, only holding back in the last 100 m or so.  As I predicted yesterday, our prediction came in a bit slow.

• Stage 19:  3h 36' 33" (actual), 3h 50' 00" (prediction), 13' 27" slow (6.21% error)

The yellow jersey group with all the general-classification contenders came in 07' 38" later, meaning my model did well with them, but when considering next year's Tour de France model, I'll have to think about the power outputs cyclists like Andersen are capable of.  Check out his average speed.

• Stage 19:  12.81 m/s (46.13 kph or 28.67 mph)

Even race organizers weren't anticipating an average speed above 45 kph.  Well done, Mr Andersen!

Tomorrow's Stage 20 is a mountain time trial.  Starting in the small commune of Lure, riders will travel 36.2 km (22.5 mi) to the northeast.  They'll finish in La Planche des Belles Filles, but only after contending with a 5.9-km (3.7-mi) category-1 climb to the finish line.  The average gradient is 8.5%, but the final hill to the finish line is an insane 20%.  When the cyclists will be at their most tired, they'll need a little extra in the tank for the push to the finish line.  Our prediction is given below.

• Stage 20:  52' 47" (prediction)

It will be interesting to see how the general-classification contenders fare on the final climb.  Can the Slovenian duo hold on to the top two spots?

Ineos Grenadiers Pair Ride to Victory!

I love the competition in sport.  Grit teeth, sweat, blood, determination, and hard work all show on the bodies of elite athletes performing at the pinnacle of their métier.  But every now and then it's great seeing cooperation and teamwork for which the winner isn't important to the participants.  Michał Kwiatkowski and Richard Carapaz, both of Ineos Grenadiers, dominated today's Stage 18.  They helped each other, and when they had amassed a nearly two-minute lead on third place, they decided to cross the finish line together.  The screen capture I grabbed below was when they knew they had won, and when they knew how they would finish at the line.

Kwiatkowski is on the left, and he would get the stage win, but only by a fraction of a tire's width.  Kwiatkowski has been so helpful to Ineos Grenadiers in this Tour de France, a consummate teammate.  It was nice that he happened to finish first.  Carapaz is 13th in the general classification rankings; Kwiatkowski is 29th.  Below is the screen capture I grabbed a minute later.

They could have hit the 1-km-left red flag and raced each other, but I think what they did was wonderful.  They celebrated the teamwork that went into both of them getting to the finish line before any other cyclist.  A bit more racing at the end would have helped our already great prediction.

• Stage 18:  4h 47' 33" (actual), 4h 42' 38" (prediction), 04' 55" fast (-1.71% error)

That's what I like to see!  Check out the above pair's average speed.

• Stage 18:  10.14 m/s (36.52 kph or 22.69 mph)

Finishing a tough stage like today's in under five hours is quite good.

Tomorrow's 166.5-km (103.5-mi) Stage 19 is listed as flat, but there are several ups and downs that riders will navigate.  Starting in the commune of Bourg-en-Bresse, riders will make their way northeast to Champagnole.  They'll finish in a commune that looks to be about 25 km (16 mi) from the French border with Switzerland.  Our prediction is given below.

• Stage 19:  3h 50' 00" (prediction)

I think the general classification contenders will opt for a safe ride to the finish line tomorrow.  They'll want to be in the best shape possible for the Saturday time trial.  I don't want a repeat of Stage 5!  I want to see several cyclists go for the stage win with lots of attacking.  If a few cyclists go all-out tomorrow, our prediction could be a bit on the slow side.

Superman Conquers Col de la Loze!

Miguel Ángel López picked one helluva stage to win during his first Tour de France.  The brutal climb up Col de la Loze cracked many cyclists who were part of a string of riders crossing the finish line for more than half an hour after López finished.  Check out an elated López approaching the finish line after gritting his teeth on the last 300 m, which saw gradients of 16% - 18% (YIKES!).

My physical model did quite well today.  With today's two brutal climbs, it's impossible for my model to know who will crack and when, who will break away from the lead group, and whether or not there will be riders helping each other toward the finish line.  Coming in under 3% error is always good, especially today.

• Stage 17:  4h 49' 08" (actual), 4h 40' 46" (predication), 08' 22" fast (-2.89% error)

Some of the riders eclipsed 90 kph (56 mph) on the steep descents.  It is unimaginable for me that a human being could be moving at interstate speeds on a bicycle.  Couple that with a final climb that took roughly an hour to complete, and an error under 3% looks pretty good.  Check out López's average speed.

• Stage 17:  9.80 m/s (35.28 kph or 21.92 mph)

Only a tiny number of human beings on the planet right now could achieve an average speed on today's stage that is anywhere close to the above.

López's win moved him from fourth overall to third, a huge deal for anyone looking to stand on the final podium in Paris this Sunday.  Primož Roglič finished second today, adding 17" to his general classification lead over today's third-place finisher, Tadej Pogačar, who just couldn't stay with Roglič as the pair neared the finish line.  He may not have won the Tour de France today, but Roglič heads into tomorrow's stage with a 57" lead, and barring crashes and other disasters, that could be enough to get him to Sunday in yellow.

Tomorrow's 175-km (109-mi) Stage 18 has a little something for everyone.  Beginning at the ski resort in Méribel, riders will get near the French border with Italy before heading north to the finish line in the commune of La Roche-sur-Foron.  The first quarter of the stage is mostly uphill, culminating in a category-1 climb to the peak of Cormet de Roselend.  Climbs of category-3, category-2, and category-1 follow, so the downhill specialists will have opportunities to trim time off what they will lose on the climbs.  A 6-km (4-mi) hors catégorie climb up Montée du plateau des Glières will be the last major climb.  The final 10 km (6 mi) will see a mostly downhill sprint to the finish.  The intermediate sprint is early, so the sprinters won't be scattered by the climbs.  Climbing, fast descents, and a sprint finish will make for an exciting stage.  Our prediction is given below.

• Stage 18:  4h 42' 38" (prediction)

I hope my model will see us under 3% error again!

PERFECT Attack Sends Lennard Kämna to Stage Win!

German cyclist Lennard Kämna, just six days after turning 24, executed the perfect attack and dominated Stage 16.  Richard Carapaz attacked with 2 km left in the final big climb.  That attack left Julian Alaphilippe, who attempted to stay with Carapaz, utterly cracked.  Carapaz earned the most aggressive rider, but Kämna flew past Carapaz as they were nearing the final peak.

I actually grabbed the above screen capture because I knew if Kämna, on the left, could hold off Carapaz on the descent, Kämna would have the stage.  And that's what happened.  Kämna finished 01' 27" ahead of Carapaz.  Our prediction was again too slow, but not terrible.

• Stage 16:  4h 12' 52" (actual), 4h 22' 15" (prediction), 09' 23" slow (3.71% error)

Kämna's average speed is given below.

• Stage 16:  10.81 m/s (38.91 kph or 24.18 mph)

My model was again about 1 kph too slow.  But the model did well for the majority of the stage.  A total of 154 riders finished today's stage, and the model's predicted time came after the 16th rider crossed the finish line.  About 10.4% of the cyclists beat our predicted time.  Several of today's breakaway cyclists finished in that top 16.  Had the peloton managed to chase down the attackers, our time would have been better.  Lots of interesting things to learn from today's stage -- and that's what makes the science of the race so fascinating!

Check out a happy Kämna crossing the finish line.

Tomorrow's 170-km (106-mi) Stage 17 looks brutal.  Riders start in Grenoble and head northeast.  The first half of the stage is mostly flat, but then cyclists will contend with the hors catégorie 17.1-km (10.6-mi) climb up Col de la Madeleine.  That will lead to blisteringly fast speeds on the descent, followed by the 21.5-km (13.4-mi) hors catégorie climb to the finish line at the 2304-m (7559-ft) peak of Col de la Loze.  The view of the French Alps at the finish line will be breathtaking.  Our prediction is given below.

• Stage 17:  4h 40' 46" (prediction)

Many riders will crack on the climbs.  The general classification could be shaken up.  Stage 15 ate up Egan Bernal.  Will one of tomorrow's two brutal climbs eat up another GC contender???

Stage 16 Prediction

The Tour de France picks up tomorrow in the commune of La Tour-du-Pin.  Cyclists will travel 164 km southeast to Villard-de-Lans.  Instead of showing the map, I'll show the stage profile.

(Image Credit:  https://www.letour.fr/en/stage-16)

Stage 16 is clearly a mountain stage with a couple of good category-2 climbs in the middle of the stage.  The category-1 climb near the end will surely see a rider or two crack.  Our predication is given below.

• Stage 16:  4h 22' 15" (prediction)

Riders better save a little for Wednesday's stage.  They'll need their legs for a brutal Stage 17!

Col du Grand Colombier Gobbles Bernal as Pogačar Wins His Second Stage!

I wrote yesterday that the 2020 Tour de France could be won or lost today.  I don't know if the race was won today, but last year's winner, Egan Bernal, lost his chance to defend his title.  The flat first half of the race saw a torrid pace as the peloton reached the first climb with an average speed of about 50 kph (31 mph).  Michael Gogl broke away early and kept the peloton pace high.  Pierre Rolland, today's most aggressive rider, joined Gogl, and I wondered if the two of them could keep up their pace and vie for the stage win.  But Team Jumbo-Visma and its powerful riders finally took over the race on the Col du Grand Colombier.  The team kept Primož Roglič, who finished second today, safely in the yellow jersey.  But it was fellow Slovenian Tadej Pogačar who won the final uphill sprint to take the stage win.

Climbs were fast, but our prediction wasn't too bad.

• Stage 15:  4h 34' 13" (actual), 4h 41' 32" (prediction), 07' 19" slow (2.67%)

I'm happy being back under 3% error.  To put our error in perspective, Egan Bernal finished in 25th place, 07' 20" behind the winner.  In other words, my model exactly nailed Bernal's time.  Given that he won last year, that's pretty good!  But Team Jumbo-Visma just dominated today, especially with the work done by Wout van Aert and Tom Dumoulin on the final climb.

• Stage 15:  10.61 m/s (38.18 kph or 23.72 mph)

My model had the winning average speed about 1 kph slower.  Great racing today!

Tomorrow is the second rest day of this year's Tour de France.  Riders will be in Isère tomorrow, preparing for three consecutive brutal mountain stages in the Alps.  I'll post our Stage 16 prediction tomorrow.

PERFECT Attack Sends Søren Kragh Andersen to Stage Win!

Danish cyclist Søren Kragh Andersen and his Team Sunweb mates set up the finish of today's Stage 14 as well as could be done.  Andersen was in perfect position in what was a blisteringly fast peloton today with about 3.2 km (2.0 mi) to go.  He attacked and kicked up his speed as if his legs were fresh and ready for a time trial.  Nobody could catch Andersen and he finished 15 s ahead of the pack.

That was an impressive performance!  Just as impressive was the fast-moving peloton.  It seemed from the very beginning that this was going to be a fast stage.  The peloton itself appeared to be on the attack.  Our prediction was a bit slow today.

• Stage 14:  4h 28' 10" (actual), 4h 44' 25" (prediction), 16' 15" slow (6.06% error)

The racing was a lot of fun to watch, but as the cyclists flew up the category-2 climb, I was thinking they might blow away the stage organizer's top average speed guess.

• Stage 14:  12.06 m/s (43.41 kph or 26.97 mph)

Given that the power output in my model is roughly where elite cyclists perform, I was blown away.  Race organizers weren't expecting more than 42 kph for today's average speed.  Perfect weather for racing and peloton dynamics surely played a role in today's high average speed.

Tomorrow's 174.5-km (108.4-mi) stage picks up in Lyon and sends riders east toward the Jura Mountains.  Just over half the stage is flat before a couple of category-1 climbs will break up the peloton.  Waiting for cyclists at the end of the stage is the hors catégorie climb up to the 1501-m (4925-ft) peak of Col du Grand Colombier.  The 2020 Tour de France could be won or lost on that climb!  Our prediction is given below.

• Stage 15:  4h 41' 32" (prediction)

Will the peloton be slow during the flat first half of the race so that cyclists save their legs?  Who will crack on the climb to the finish?  I can't wait to watch tomorrow's action!

Daniel Martínez Wins BRUTAL Stage 13!

What a fantastic day of racing at the Tour de France!  Breakaways and attacks, brutal climbs, and general classification shakeup were all part of today's Stage 13.  Daniel Martínez and Lennard Kämna battled each other up the final climb, with Martínez prevailing in the final push to the finish line.  Check out Martínez crossing the line with Kämna just 4 s behind.

Last year's winner, Egan Bernal, cracked on the final climb and lost his second-place general classification standing to Tadej Pogačar, who now sits 44 s behind fellow Slovenian Primož Roglič.

We had a pretty good prediction today.

• Stage 13:  5h 01' 47" (actual), 4h 53' 59" (prediction), 07' 48" fast (-2.58% error)

I'll definitely take under 3% on today's stage!  It was brutal, but incredibly fun to watch.  Check out the average speed for Martínez today.

• Stage 13:  10.58 m/s (38.07 kph or 23.66 mph)

My model had the stage about 1 kph faster.  Not too bad!  The last group to finish the stage today was more than 34 minutes slower than Martínez.

Tomorrow's 194-km (121-mi) Stage 14 will commence in Clermont-Ferrand and take riders east to Lyon.  Climbers will dominate early with the category-2 climb up Col du Béal.  The finish should be pretty fast with a mostly downhill ride into Lyon.  Our prediction is given below.

• Stage 14:  4h 44' 25" (prediction)

I hope we're under 3% error again tomorrow!

Great First Pro Win for Marc Hirschi!

What a great ride for 22-year-old Swiss cyclist Marc Hirschi!  On an exciting stage with lots of attacking, nobody could catch Hirschi down the stretch.  He road to the finish line with an exuberance that had to be motivated by the fact that he was about to earn his first professional stage win.  Check out Hirschi crossing the finish line in the screen capture I got.

I complained yesterday about a lack of aggression from the peloton.  Not so today!  It was a blast watching elite cyclists do their thing.  Check out how our prediction fared.

• Stage 12:  5h 08' 49" (actual), 5h 21' 56" (prediction), 13' 07" slow (4.25% error)

I always want to be under 3%, but I'm not disappointed with that prediction.  The longest stage with several climbs and great racing all provide me with ample information for refining my physical model of the race.  Lots to learn from today's stage!  Check out Hirschi's average speed.

• Stage 12:  11.77 m/s (42.36 kph or 26.32 mph)

Tomorrow's Stage 13 represents the last of the medium mountain or hilly variety.  Beginning in central France in the commune of Châtel-Guyon, cyclists will travel 191.5 km (119.0 mi) south to the category-1 climb to Puy Mary.  They won't reach the 1783-m (5850-ft) summit, but they'll finish at an elevation of 1589 m (5213 ft).  Our prediction is given below.

• Stage 13:  4h 53' 59" (prediction)

The final climb will be wonderful to behold.  Cyclists will travel about 30 km (19 mi) while raising their elevation more than 1 km (0.6 mi)!

Caleb Ewan Gets Second Stage Win!

Caleb Ewan won his second Tour de France stage today after an exciting and controversial final sprint to a photo-finish.  The screen capture I obtained below is the best I could get from today's finish.

Ewan has the red helmet on in the middle of the image.  Yesterday's stage winner and wearer of the green jersey, Sam Bennett, is just to Ewan's right.  Wout van Aert is in yellow to Bennett's right.  He was vying for his third stage win of this year's Tour de France, but had to settle for third in today's stage.  And that's where controversy comes into the story.  Just three seconds from the finish line, Peter Sagan had barriers on his right and van Aert on his left.  Sagan elbowed and shouldered van Aert in an effort to get by van Aert.  The screen capture below is the best I could get when I watched the replay.

Sagan is on the far left in the image, shouldering van Aert.  Race officials relegated Sagan to the last rider with the peloton's time.  That will definitely hurt his chances to break his own record and finish the Tour de France with his eighth green jersey.  He would probably already have eight in a row if not for his actions that led to Mark Cavendish crashing at the end of Stage 4 in 2017, actions that resulted in Sagan being disqualified.

For all the high speed and drama of the stage's finish, the rest of the stage was quite slow and uneventful.  Below is how our predication fared.

• Stage 11:  4h 00' 01" (actual), 3h 39' 48" (prediction), 20' 13" fast (-8.42% error)

Another terrible prediction!  This has been a Tour de France unlike any I've modeled before.  There have always been two or three stages that we've missed wildly.  My model works on the idea that an elite cyclist will win the stage while performing at an elite level.  But this year, Stages 3, 5, 8, and 11 have more resembled fun rides through the French countryside than what I've seen in past years, which was cyclists breaking away from the peloton, having to be chased down, and keeping the peloton's speed high.  Stage 5 was nearly unwatchable because there were zero breakaways.  Zero.  I don't know if the global pandemic and the postponed start to the race have influenced this year's edition of the Tour de France.  Stage 7 was an example of cyclists going ballistic and outperforming my model, so the cyclists clearly have it in them to output more power.  That always happens once or twice a year.  I've simply not seen so many slow stages, and we're only halfway through the entire race!  Ewan's average speed is given below.

• Stage 11:  11.63 m/s (41.87 kph or 26.02 mph)

That's not terribly slow, though it is slower than what race organizers estimated as the slowest possible average speed.  I expected another 3 kph or 4 kph tacked onto that average speed.

Tomorrow's 218-km (135-mi) hilly Stage 12 is this year's longest stage.  Beginning in Chauvigny, riders will travel southeast to the tiny commune of Sarran with a population less than 300.  There will be well over 300 people there tomorrow!  Our prediction is given below.

• Stage 12:  5h 21' 56" (prediction)

Two category-4 climbs, one category-3 climb, and a category-2 climb toward the end of the stage will greet riders.  None of those climbs is longer than 4.8 km (3.0 mi), so "hilly" is about right for the stage.  I want to see action during the first couple of hours.  If the winning time is close to six hours, my model's power output will have to be downgraded from "elite" to account for less aggressive team strategies.

Bennett Wins Stage 10 and Takes Green Jersey!

Sam Bennett just edged out his competition to claim the Stage 10 win.  On a gorgeous day in western France that saw the peloton set a scorching pace, Bennett barely nudged past Caleb Ewan, who was denied a second stage win in this year's Tour de France.

That was the best screen capture I could get.  Bennett is the one surging ahead in white while Ewan is doing all he can to shove his bike forward on the right.  Peter Sagan, on the left coming in third, will have to pass his green jersey to Bennett, a sight that all of Ireland will enjoy tomorrow.

It was great watching the peloton move through towns and around roundabouts at high speeds.  Look at the onscreen speedometer during the intermediate sprint.

As a recreational rider, I can't fathom going 65 kph (40 mph) on a bicycle.  I'm glad the cyclists didn't go too crazy with speeds because we had a good prediction today.

• Stage 10:  3h 35' 22" (actual), 3h 41' 08" (prediction), 05' 46" slow (2.68% error)

Bennett's average speed, which was essentially the average speed of 65 other riders who got the same stage time, is shown below.

• Stage 10:  13.04 m/s (46.94 kph or 29.17 mph)

That's pretty fast!  Elite cyclists are amazing athletes for sure.

Tomorrow's 167.5-km (104.1-mi) flat Stage 11 takes riders northeast from the west coast of France.  They begin near the beach in Châtelaillon-Plage and reach the finish line in Poitiers.  I hope that the cyclists enjoy great weather tomorrow and that the racing remains fast.  Our prediction is given below.

• Stage 11:  3h 39' 48" (prediction)

Barring crashes and other such disasters, tomorrow's middle stage of this year's Tour de France shouldn't see changes to the top rankings for the general classification.  Which sprinter will win the day?  I'm rooting for Peter Sagan to break through with a stage win tomorrow.

Stage 10 Prediction

Tour de France cyclists are resting today.  Tomorrow they will do some island hopping for Stage 10.  Beginning on the island of Île d'Oléron off the western coast of France, riders will loop to the south and then move north to the finish line on the island of Île de Ré.  See my crop of the map below from the Tour de France website.

I don't believe that the Tour de France has done such island hopping before.  Cyclists will enjoy wonderful weather with gorgeous views of the Atlantic along much of the stage.  There can't possibly be a flatter stage.  Minimum and maximum elevations are 1 m and 16 m, respectively.  Our prediction for the 168.5-km (104.7-mi) stage is given below.

• Stage 10:  3h 41' 08" (prediction)

Will we be much too fast as cyclists opt for a boring, no-breakaway effort as in Stage 5?  Will we be much too slow as cyclists go bananas like they did on Stage 7?  The fun is watching the race to see how well our model predicts reality.  I can't wait!

Roglič Wrests Yellow Jersey from Yates!

Postponing this year's Tour de France from July to late August and much of September because of the global pandemic has surely influence cycling this year.  On a much smaller scale, the postponement has influenced my ability to watch and study the race.  Classes at my university commenced on 12 August, which has meant that I've been unable to watch some stages live.  I've had to watch them on replay.

Besides altering my academic and research work, this year's Tour de France overlapped with my transition from quadragenarian to quinquagenarian, which happened during yesterday's Stage 8.  Today I've managed to watch replays of the last few kilometres of Stages 8 and 9 so that I could see the winners, get the winning times, and grab screen shots.  I'll have to watch longer stretches of those first two mountain stages tonight so that I might better understand what happened.

Stage 8 saw Nans Peters finishing alone and thrilling his home country of France.  He looks happy!

General classification battles were taking place behind Peters.  We were a bit fast on this stage.  Our prediction's comparison with reality and Peters's average speed are given below.

• Stage 08:  4h 02' 12" (actual), 3h 44' 26" (prediction), 17' 46" fast (-7.34% error)
• Stage 08:  9.70 m/s (34.93 kph or 21.70 mph)

Were cyclists holding back a little in anticipation of Stage 9?  Even the race organizers didn't think the average speed would be below 36 kph.  I'll have to watch the replay to see how slow the peloton looked early in the stage.

Stage 9 saw serious shakeup in the general classification as Primož Roglič of Slovenia took the yellow jersey from England's Adam Yates, who now sits in 8th place, 62 seconds behind Roglič.  Today was a red letter day for Slovenia because Tadej Pogačar, who won't be 22 years old until the 21st of this month, won the sprint to take Stage 9.  Check out Pogačar on the left just as he crossed the finish line today.

Racing speeds must have been up to something more normal today.  We did much better on today's stage compared to yesterday's stage.

• Stage 09:  3h 55' 17" (actual), 3h 51' 01" (prediction), 04' 16" fast (-1.81% error)
• Stage 09:  10.84 m/s (39.02 kph or 24.24 mph)

Tomorrow's rest day could have been on riders' minds as they pushed harder today than yesterday.  I like our Stage 9 prediction!  Look out for last year's winner, Egan Bernal, who now sits in second place in the general classification, just 21 seconds behind Roglič.

I will take advantage of tomorrow's rest day by watching replays of Stages 8 and 9 tonight, and then posting our Stage 10 prediction sometime tomorrow.

Van Aert Wins a BLISTERINGLY Fast Stage!

Wout van Aert won his second stage of this year's Tour de France today.  He may have finished just ahead of the sprinters today, but almost all of the cyclists set a torrid pace through the stage.  Crosswinds blew up the peloton with about a quarter of the stage left to ride.  The lead group continued the fast pace, but the second group lagged a bit.  As the sprinters approached the finish line, speeds of 64 kph (40 mph) were reached.  Check out the close finish.

Van Aert is in yellow, and he knew he had won about a metre before the finish line.  We had our worst prediction today.  Check it out.

• Stage 07:  3h 32" 03" (actual), 3h 57' 13" (prediction), 25' 10" slow (11.87% error)

Ouch!  Not even when Ben Hannas and I first began this area of research in 2003 would an error that large have been acceptable.  Look at va Aert's average speed.

• Stage 07:  13.20 m/s (47.54 kph or 29.54 mph)

I simply can't believe that average speed.  Even the Tour de France organizers put their upper limit at 45 kph on their time schedule.  I hope nobody was late getting to a spot to watch the race.  Cyclists would have been long gone if someone cut it too close.  As always, I'll have to look at this stage in much greater detail once the race is over.  Next year's model, like every year's model, will need some adjustment.

I will not be able to watch the next two stages as they happen.  I'll have to watch them on replay, hopefully Sunday night.  I'm anxious to watch Stages 8 and 9, both mountain stages in the Pyrenees.  But I'll be busy with other goodies this weekend.  I'm even pressed for time getting this blog post written and posted.  I regret that I'll have to skip my usual stage descriptions and just offer our predictions for the next two stages.

• Stage 08:  3h 44' 26" (prediction)
• Stage 09:  3h 51' 01" (prediction)

Speeds will obviously come down in the mountains, but if cyclists perform like they did yesterday and today, we'll be too slow.  I'm rooting for how we did on Stage 4!

Lutsenko DOMINATES Climb to Mont Aigoual!

I complained about yesterday's stage being boring.  No such complaint today!  Breakaways and attacks, riders cracking on climbs, and an inspirational ride by a cyclist from Kazakhstan all made for a thrilling sixth stage of this year's Tour de France.  Alexey Lutsenko was a joy to watch during the massive climb to end the stage.  He broke free from the breakaway group on the climb, and he never looked back.  Spaniard Jesús Herrada made a gallant effort to catch Lutsenko, but finished with a very respectable second place.  Check out Lutsenko crossing the finish line.

Lutsenko finished nearly a minute ahead of Herrada.  Early on, I could tell that our model would be slow today.  The breakaway group kept the peloton's speed up.  Cyclists were positively flying at times, and climbers like Lutsenko, Herrada, the young and bold Neilson Powless, and Greg Van Avermaet were setting a torrid pace on the final climb.  Julian Alaphilippe, surely smarting from yesterday's food gaffe that cost him the yellow jersey, kicked hard in the final half kilometre to finish in fifth place.  Check out how our prediction did.

• Stage 06:  4h 32' 34" (actual), 4h 51' 26" (prediction), 18' 52" slow (6.92% error)

Our error was a little worse than yesterday's error, but I'm not nearly as bothered as I was yesterday.  Yesterday's stage looked like a lot of riders simply trying to make it to the end without injury or shuffling of the general classification.  Today's stage look like the best of the best in the saddle racing their butts off.  Our model needed about 15% more power to match today's time.  Check out Lutsenko's average speed.

• Stage 06:  11.68 m/s (42.04 kph or 26.13 mph)

For a stage like today's, that's a fast speed!  Well done, Alexey Lutsenko!

A couple of category-3 climbs appear in tomorrow's 168-km (104-mi) Stage 7, although the stage is classified as flat.  The last half of the stage is mostly downhill.  Cyclists will start in the French commune of Millau and then head southwest to the commune of Lavaur.  Our prediction is given below.

• Stage 07:  3h 57' 13" (prediction)

Will the cyclists hold back like yesterday or let it loose like today?  I would rather miss being too slow than too fast because at least I'll get to watch some great racing!

Van Aert Takes Stage 5!

Belgian Wout van Aert dominated the final sprint to win today's fifth stage of the Tour de France.  Look at the great timing I had in grabbing a screen capture of the finish.

That's Dutchman Cees Bol just a couple of centimetres behind van Aert.  What a finish!  Cyclists were reaching speeds of 60 kph (37 mph) in the final hundred metres.  For all that late speed, the rest of the race was slow.  Check out how our prediction fared.

• Stage 05:  4h 21' 22" (actual), 4h 05' 44" (prediction), 15' 38" fast (-5.98% error)

Van Aert's average speed is given below.

• Stage 05:  11.67 m/s (42.01 kph or 26.10 mph)

Our prediction wasn't as bad as the one we offered for Stage 3, but I want our predictions to be as good as what we offered for yesterday's stage.  I want to be under 1% error!  This desire allows me to make a brief aside.  Science doesn't care at all what I desire, believe, think, or yearn for.  If I create a scientific model of something in the natural world, like a cycling race, I want the best data and most accurate application of the laws of physics.  For something as complicated as the Tour de France, my students and I can't possibly have enough information to offer a perfect prediction for every stage.  Team strategies, weather, fan disruptions, crashes, call-of-nature breaks, eating, and other such factors are all unknown to us.  And that makes for part of the fun.  If a stage has lots of rain and cycling is slow, I don't mind if our model's prediction is too fast.  I also want to know if we have something modeled poorly, like cyclist power output or aerodynamic drag.

Having written all that, I have ask the following question.  Were Stages 3 and 5 not absolutely BORING until the final sprint?  I don't ask that question as an indirect way of offering an excuse for a prediction with nearly 6% error.  I ask it because the entire stage, which was mostly downhill, lacked attacking cyclists.  Where were the daring riders who dashed ahead in a breakaway, only to cause angst in other teams, who would then feel compelled to chase the attackers?  On the best athletic day of my life I couldn't do what those elite cyclists do.  But as a fan, I want to see more action and fewer slow-moving pelotons.

Tomorrow's 191-km (119-mi) Stage 6 takes riders southwest from Le Teil nearly to the peak of Mont Aigoual.  The first 155 km of the stage is flat as can be.  The final 36 km (22 mi) of the stage, however, will see the cyclists increase their elevation by 1336 m (4383 ft).  That will be some brutal climbing!  Our prediction is given below.

• Stage 06:  4h 51' 26" (prediction)

What I definitely don't want to see tomorrow is a slow-moving peloton on the flat part and then the climbers taking over at the end.  I want to see more action on the flat part.  Let's see some breakaways!

Roglič Puts Us Under 1%!

Primož Roglič simply owned the final 200 m of today's fourth stage of the Tour de France.  He put himself in great position for the final sprint after great pacing in the stage.  The image below shows Roglič just after he crossed the finish line.

What a gorgeous day for cycling!  Our model was back on track today after cyclists opted for a leisurely bike ride yesterday.  Check out how we did.

• Stage 04:  4h 07' 47" (actual), 4h 09' 28" (prediction), 01' 41" slow (0.68% error)

Now that's more like it!  From the initial pace of the peloton to the final category-1 climb, our model matched today's cycling quite well.  I always root for fast racing, but a tiny part of me wanted the cyclists to slow a bit in the final kilometre.  I was yearning for perfection!

Roglič's average speed is given below.

• Stage 04:  10.80 m/s (38.86 kph or 24.15 mph)

That wasn't too shabby on a mostly uphill stage.  Roglič leaped all the way up to third in the general classification, just 7 s behind Julian Alaphilippe.

Riders begin tomorrow's 183-km (114-mi) flat stage in the commune of Gap.  They head west to the finish line in the commune of Privas.  In contrast to today's stage, tomorrow's stage is mostly downhill.  There are a couple of short category-4 climbs in the latter half of the stage, but racing has a chance to be fast tomorrow.  Our prediction is given below.

• Stage 05:  4h 05' 44" (prediction)

Can we get under 1% error again?  I hope so!