16 August 2018

Belated Tour de France Finish

I thought I would have this post out a few days ago, but my basement suffered a lot of damage from a storm that took place in my town on 1 August.  My girls and I returned from holiday to a big mess!  But on to happier topics:  the Tour de France.  The 2018 edition of the world's most famous bicycle race ended on Sunday, 29 July while I was on holiday.  I managed to snag a few glances of the race while I was away, but had to wait until I returned to watch the final four stages.  I'm sure all of Wales was going nuts when Geraint Thomas secured the win in Paris.  I grabbed a screen shot of Thomas on the podium with runner-up, Dutchman Tom Dumoulin on Thomas's right and Chris Froome, who came in third, on Thomas's left (click on image for a larger view).
Froome's second-place finish in the Stage 20 individual time trial secured his third-place finish in the general classification.

Our model did reasonably well during the final four stages.
  • Stage 18:  3h 46' 50" (actual), 4h 02' 11" (prediction), 15' 21" slow (6.77% error)
  • Stage 19:  5h 28' 17" (actual), 5h 17' 38" (prediction), 10' 39" fast (-3.24% error)
  • Stage 20:  0h 40' 52" (actual), 0h 39' 11" (prediction), 01' 41" fast (-4.12% error)
  • Stage 21:  2h 46' 36" (actual), 2h 45' 13" (prediction), 01' 23" fast (-0.83% error)
In my last post, I mistakenly typed 4h 02' 35" for the Stage 18 prediction.  Sorry about the typo!  I suppose the 24" reduction helped us a teeny bit, but Stage 18 will be one we need to analyze more closely in the future.  I'm glad we finished so well with Stage 21's prediction coming in under 1%.

One piece of silliness each year is to compare the sum of the actual winning times with the sum of our predictions.  Here is the result:
  • Total:  82h 32' 17" (actual), 81h 50' 50" (prediction), 41' 27" fast (-0.84% error)
Note that the above "actual" time is not Geraint Thomas's winning time of 83h 17' 13", but the sum of all the stage-winning times.  We do not model an individual cyclist.  Missing by less than 1% of the actual total time may seem impressive, but keep in mind that we missed some stages because we were too fast, and we missed others on which we were too slow.  We have a good feeling for how the entire race will be run, so errors tends to cancel when forming the sum.

Our model cyclist expended about 116,435 Calories (487.5 MJ or 135.4 kW⋅hr).  That amounts to over 5500 Calories burned per stage.  A McDonald's Big Mac contains 550 Calories, meaning a Tour de France cyclist burns an average of 10 Big Macs each stage.  Don't ever try fueling up for a grueling bike ride with 10 Big Macs!

Modeling the Tour de France was once again a delight.  Kudos to my research student, Carl Pilat, for his efforts.  More research work lies ahead as we dissect this year's race to determine what worked well with our model and what didn't work well.  We learn when we are ignorant of something and when we are wrong about something.  Continual learning is what makes being a scientist so much fun!

25 July 2018

Quintana Dominates Col de Portet!

Nairo Quintana won his second Tour de France stage with an inspiring climb to the summit of Col de Portet.  Does he look happy at the finish line? (click on image for a larger view)
The downhills were just a tad slower than my model predicted.  Below is the comparison between Quintana and my model.
  • Stage 17:  2h 21' 27" (actual), 2h 12' 27" (prediction), 09' 03" fast (-6.36% error)
To match the actual time, I need to drop my model cyclist's power output by only 1%.  See how tough it is to nail the winning time!  Chris Froome cracked a bit in the final kilometers and couldn't keep up with Tom Dumoulin, who jumped over Froome for second place in the general classification.  Geraint Thomas came in third day and made it clear that he is the man to beat for the yellow jersey, not Froome.  Quintana averaged 27.57 kph (17.13 mph).

Okay, now for something different.  I am going on a much-needed holiday.  I've only had three days off in 2018 and I need a break!  I'll do my best to keep up with the Tour de France over the next few days, but I'm not likely to write blog posts.  My model's predictions for the next four stages are given below.
  • Stage 18:  4h 02' 35" (prediction)
  • Stage 19:  5h 17' 38" (prediction)
  • Stage 20:  0h 39' 11" (prediction)
  • Stage 21:  2h 45' 13" (prediction)
When I return from holiday, I'll write a blog post that summaries how my model fared over the above four stages.  Can anyone catch Geraint Thomas???  Will Peter Sagan be able to dominate the remaining points after his crash today???  Lots of drama remains!

24 July 2018

Alaphilippe OBLITERATES Our Model!

There are stages like today's Stage 16 that I watch and think, "Wow, those guys are flying!  We're not going to have a good prediction today."  We had a terrible prediction today.  I'll start with the good news before showing the comparison.  Julian Alaphilippe was absolutely ecstatic as he crossed the finish line (click on image for a larger view).
French fans were cheering for the French cyclist.  His main competitor for the stage win was Brit Adam Yates.  Yates looked like he had a shot at the win as he was flying down the final descent, but he crashed (click on image for a larger view).
You can tell that he was about to get a very sore left arm and shoulder.  I was hoping to see a thrilling two- or three-man race for the finish line.  Yates was able to finish third.  He was not the only one to crash.  I cringed when I saw Belgian cyclist Philippe Gilbert fly over a short wall (click on image for a larger view).
Give the guy credit.  He got back up, finished the race in 142nd place, and easily won the combativity prize (I love the red award with the white 1).  The image below was inspiring to see (click on image for a larger view).
This stage of the Tour de France not only had crashes, it had a protest from farmers.  The race had to be paused early on (click on image for a larger view).
Some cyclists got sprayed with what looked like a fire extinguisher.  During the pause, they had to flush out their eyes.  Check out the Italian cyclist Oliviero Troia (click on image for a larger view).
The pause really threw me for a loop.  I thought the clock was stopped, but it kept ticking.  When Alaphilippe was approaching the finish line, I thought we were going to be slow, but inside 10 minutes off.  When the actual time came up on the screen, I couldn't believe it.  Check out our prediction.
  • Stage 16:  5h 13' 22" (actual), 5h 44' 15" (prediction), 30' 53" slow (9.86% error)
When I first started modeling the Tour de France in 2003, an error under 10% seemed okay.  But not any longer.  We've gotten a lot better, but that didn't show today.  I'd have to give my model cyclist a 15% power boost to make that winning time.  Of the 147 riders who finished today's stage, 141 beat our time prediction.  We actually did a great job modeling Philippe Gilbert's time, but we don't have crashes in our model!

Our string of great picks is over with this stage.  But as I told my research student, Carl Pilat, this morning, this is a learning opportunity.  When the race is over and we look at this stage again, we'll see where the model let us down.  I am stunned that all cyclists finished in less than six hours.  They are getting better every year and our model needs to keep up!  Alaphilippe averaged 41.74 kph (25.94 mph).  That's high, but not insanely so.

Everyone has been waiting for tomorrow's Stage 17.  Picking back up in Bagnères-de-Luchon, the stage is just 65 km (40 mi) long.  Right out of the gate, cyclists will face a category-1 climb to the peak of Col de Peyresourde.  A fast downhill will be followed by a sprint section before cyclists have the category-1 climb to the summit of Col de Val Louron-Azet.  The fast downhill will end abruptly.  This year's Tour de France winner might be settled on the highly-anticipated Hors catégorie stage-finishing climb to the peak of Col du Portet in Saint-Lary-Soulan.  Our prediction is given below.
  • Stage 17:  2h 12' 27" (prediction)
After today, I'm really nervous about tomorrow.  Putting physics aside, I can't wait to watch the stage!

22 July 2018

Magnus Cort Nielsen Gets Us Under 1%!

It was another great stage today with a trio sprinting for the win.  Rafał Majka of Poland, who is a great mountain climber, was out front for a good bit of the race, but a group of seven riders caught him.  Check out the screen capture I got as Majka was about to be caught (click on image for a larger view).
It's really tough for a lone rider to outpace a group of seven.  Those guys in pursuit are constantly swapping out the lead cyclist, thus saving energy for the following cyclists.  Drafting is a huge advantage the group had that Majka didn't have.

Majka ended up finishing eighth, meaning all seven pursuing riders finished ahead of him.  The trio of Magnus Cort NielsenIon Izagirre Insausti, and Bauke Mollema broke away from the group of eight and sprinted for the stage win.  It was the Dane who took the stage.  Does Nielsen look happy as he crossed the finish line? (click on image for a larger view)
Izagirre was second and Mollema was third.  Check out how our prediction fared.
  • Stage 15:  4h 25' 52" (actual), 4h 28' 09" (prediction), 02' 17" slow (0.86% error)
Oh, I love being under 1%!  Nielsen averaged 40.96 kph (25.45 mph) today.  But you see in the above image that the final sprint had the cyclists at 51 kph (32 mph) as they reached the finish line.

Riders will stay in Carcassonne for tomorrow's rest day.  Tuesday's 218-km (135-mi) Stage 16 takes riders from Carcassone into the Pyrenees.  The mountain stage will dip into Spain for a bit near the end before finishing in Bagnères-de-Luchon.  A couple of massive category-1 climbs are in the second half of the stage, and a huge downhill sprint will finish the stage.  Our prediction is given below.
  • Stage 16:  5h 44' 15" (prediction)
Many riders will surely take more than six hours to finish the stage.  That's a long time in the saddle!  It'll be a race to the summit of Col du Portillon to see who's in position for the big downhill sprint.

21 July 2018

Fraile's Timing was Perfect!

Omar Fraile timed his attack perfectly on the final, brutal climb in Mende.  He looked positively elated when he crossed the finish line (click on image for a larger view).
Behind Fraile is Julian Alaphilippe on the right, who came in second, and Jasper Stuyven, who came in third.  Peter Sagan is behind them and came in fourth.  I have to put a few words down for Jasper Stuyven.  He was part of a group of three who lead a good chunk of the race.  He broke away and looked determine to win the stage (click on image for a larger view).
There he is in the lead with less than 30 km (19 mi) to go.  He biked his tail off trying to get a large enough time gap to give him a chance when he hit the final climb.  It just wasn't enough.  Fraile and Alaphilippe benefited from drafting before they attacked.  They had more gas in the tank.  It just goes to show how critical strategy is.  If a rider goes for glory and sets out alone, he better be sure he's got enough energy to make it to the end without getting caught.  But Stuyven honored his home country of Belgium on Belgian National Day and most definitely earned the red jersey.

The general classification leaders were well behind the stage winner.  They came in a bit more than 18 minutes after Fraile.  Below is a comparison between Fraile's winning time and our prediction.
  • Stage 14:  4h 41' 57" (actual), 4h 38' 11" (prediction), 03' 46" fast (-1.34% error)
I love that error!  My model is performing well this year.  Fraile averaged 40.01 kph (24.86 mph) today.  I'm glad he got over 40 kph.  The pace seemed slow at the start and I worried that our prediction might be too fast.

Tomorrow's 181.5-km (112.8-mi) Stage 15 is another medium mountain stage.  Beginning in Millau, the stage ends in Carcassonne and get riders to the second of two rest days in this year's Tour de France.  The Pyrenees will be so close!  Riders will face a tough category-2 climb before they reach the halfway point.  They will contend with a category-1 climb that will take them nearly to the top of Pic de Nore.  After that climb, cyclists will have a thrilling downhill and fly to the finish line.  Our prediction is given below.
  • Stage 15:  4h 28' 09" (prediction)
Will a lone rider go for the stage win?  How will the general classification leaders ride with a rest day coming up and the Pyrenees to follow?

20 July 2018

Sagan Stretches for the Win!

Michael Schär left the peloton early today and rode courageously alone until the peloton caught him inside of 7 km (4 mi) left in the race.  I was hoping he could hold on because I was inspired by his efforts.  But when the cyclists got into Valence, the elite sprinters took over.  Peter Sagan timed his sprint perfectly and stretched as only he can at the finish line (click on image for a larger view).
The Slovakian finished just ahead of Alexander Kristoff of Norway and France's own Arnaud Démare.  It was a fantastic finish!  Oh, and check out how our prediction fared in today's stage.
  • Stage 13:  3h 45' 55" (actual), 3h 42' 28" (prediction), 03' 27" fast (-1.53% error)
I'd say I'm happy with that!  Sagan averaged 45.02 kph (27.97 mph) today.  Not too bad!  But I can't leave with Sagan.  I have to show an image of Michael Schär (click on image for a larger view).
He really pushed the peloton and made me root for him today.  He definitely earned the red jersey today!

Tomorrow's Stage 14 is classified as medium mountain, but it has some good climbs, including a category-2 climb near the finish in Mende.  The 188-km (117-mi) stage begins in Saint-Paul-Trois-Châteaux and heads west.  Our prediction is given below.
  • Stage 14:  4h 38' 11" (prediction)
How will the climbs during the second half of the stage shake up the general classification?

19 July 2018

Thomas Goes Back-to-Back After INCREDIBLE Finish!

I'm not rooting hard for any particular cyclist, but it was difficult not to root for Steven Kruijswijk today.  The Dutchman took a chance and broke off early.  He lead after that and tried so hard for the stage win.  With about 3.4 km (2.1 mi) left, Chris Froome caught Kruijswijk.  I was so inspired by Kruijswijk's effort that I was rooting for him to hold on, but he didn't have a strong team supporting him.  Team Sky is just too powerful.  Froome, who heard boos throughout the route, was part of a group of cyclists who battled Alpe d'Huez to the very top.  Froome was passed by home-country favorite Romain Bardet, Dutchman Tom Dumoulin, and stage-winner Geraint Thomas of Wales.  Does Thomas look happy going back-to-back and taming Alpe d'Huez? (click on image for a larger view)
I'd say that looks like happiness!  Check out how our predication fared.
  • Stage 12:  5h 18' 37" (actual), 5h 27' 15" (prediction), 08' 38' slow (2.71% error)
I'll definitely take an error under 3% with Alpe d'Huez!  I would need to up my model cyclist's power output by less than 1% to match today's winning time.  That's why slow cycling up steep climbs is hard to predict.  Check out Alpe d'Huez (click on image for a larger view).
Is that the most famous stretch of road in cycling?  I believe today's finish was the 30th Tour de France stage finish for the famous climb.  There is one problem with slow cycling up such steep climbs.  Fans -- not all, but some.  A few fans had flares ignited.  Look at Kruijswijk trying to get through the smoke (click on image for a larger view).
Check out the screen capture I got of some asshole punching Chris Froome (click on image for a larger view).

It doesn't matter what you think of Froome.  Punching a guy on a bike is a coward's move.  And of course we live in a world in which too many people are addicted to their damn cell phones.  Check out this idiot getting a selfie with Kruijswijk (click on image for a larger view).
He had been cycling for nearly five hours at that point and was trying to win the stage.  He didn't need that loser in his face.

Thomas won one of the most thrilling stages I've seen.  He averaged 33.05 kph (20.54 mph) and hit a top downhill speed of 97 kph (60 mph).  Whether it's that top speed or the ability to climb Alpe d'Huez after 4.5 hours in the saddle, I am in awe of elite cyclists.

Thomas maintains the yellow jersey with Froome 01' 39" behind.  Dumoulin sits in third at 01' 50" back.  Tour de France champ in 2014 Vincenzo Nibali is in fourth at 02' 37" back.  I wonder how much closer Nibali would be if a motorcycle hadn't bumped into him (click on image for a larger view).
Nibali was amazing afterwards.  He got up and managed to come in seventh, just 13" back.

Tomorrow's Stage 13 begins in the French commune of Le Bourg-d'Oisans and ends 169.5 km (105.3 mi) farther in Valence.  The stage is in the southeastern part of France, but racing is to the west as cyclists make their way toward the Pyrenees.  The flat stage has one category-3 climb early and then a short category-4 climb just past the halfway point.  Our prediction is given below.
  • Stage 13:  3h 42' 28" (prediction)
I keeping wondering if Thomas wants to support Froome.  That yellow jersey must be tough to get rid of!

18 July 2018

Thomas Dominates Alps and Takes Yellow Jersey!

Tom Dumoulin was inspirational on the final climb, but Geraint Thomas caught him and took the stage.  The three monster climbs ate up many riders.  The elite climbers created big time gaps.  Thomas now has the yellow jersey and his Team Sky mate Chris Froome is in second.  Tom Dumoulin sits in third overall.  Does Thomas look happy crossing the finish line? (click on image for a larger view)

We missed by roughly 10 minutes for the second straight stage.  And for the second straight stage, cutting power by just 2% would have allowed us to hit the winning time.
  • Stage 11:  3h 29' 36" (actual), 3h 19' 02" (prediction), 10' 34" fast (-5.04% error)
I want to do better than 5%!  We were spot on until the final 17-km (11-mi) climb.  Thomas averaged 31.06 kph (19.30 mph).  Top downhill speed went to Tom Dumoulin who was clocked at 93.5 kph (58.1 mph).  I can't even imagine going that fast on a bike!  Many people have been waiting for tomorrow's Stage 12.  The third Alps stage is 175.5 km (109.1 mi) long and begins in Bourg-Saint-Maurice.  There are three monster Hors catégorie climbs, culminating in another uphill finish via the famous Alpe d'Huez.  Our prediction is given below.
  • Stage 12:  5h 27' 15" (prediction)
I hope we won't have to cut 2% off our power to match the actual time.  We usually do better in the mountains, but teams' strategies have played a role in our errors.  Not as much shakeup yesterday, but massive shakeup today.  Will Froome help Thomas tomorrow or will Thomas go back to his role of helping Froome?  I'm anxious to see how it unfolds on that final, famous climb!

17 July 2018

Alaphilippe Makes France Proud!

France's own Julian Alaphilippe won his first Tour de France stage today with an outstanding ride that also earned him the polka-dot jersey.  He looked very happy crossing the finish line (click on image for a larger view).
You can see his winning time and average speed.  I was hoping he would cross the line one second sooner so that we'd miss by less than 10 minutes.  But Alaphilippe had no competition at the finish as he was 01' 34" faster than Ion Izagirre Insausti, who came in second.  Check out how we did with our model.
  • Stage 10:  4h 25' 27" (actual), 4h 15' 27" (prediction), 10' 00" fast (-3.77% error)
Want to know how challenging it is to model the mountain stages?  Tiny changes in our model cyclist's power output can lead to large changes in the final time.  The reason is that if power is reduced too much, our model cyclist will struggle to even make it up some of the steepest climbs.  To match today's time exactly, we need only reduce our model cyclist's power output by about 1.5%.  So I'll take an error under 4%!

Alaphilippe averaged 35.83 kph (22.26 mph).  He could have done a little better had there been someone challenging him all the way to the finish line.  Still, that's a great average speed for the Alps!  Check out Alaphilippe reaching the summit of Montée du plateau des Glières, an Hors catégorie ascent (click on image for a larger view).
Tomorrow's Stage 11 is a brutal 108.5-km (67.42-mi) tour through the Alps.  Beginning at the home of the 1992 Winter Olympics, Albertville, cyclists will have to tackle two Hors catégorie climbs and then a category-1 climb to the finish at La Rosière.  Our prediction is given below.
  • Stage 11:  3h 19' 02" (prediction)
Will a lone cyclist cross the finish line first or will there be real drama heading into the finish?  I can't wait to see how it unfolds tomorrow!

15 July 2018

Our Model is BACK as Degenkolb Takes Stage 9!

After two stages of inexplicably slow cycling, during which our model came up short, we got back on track today.  Germany's John Degenkolb out-sprinted two Belgian cyclists, yellow-jersey wearer Greg Van Avermaet and Yves Lampaert.  Check out the finish below (click on image for a larger view).
Van Avermaet obviously keeps the yellow jersey through tomorrow's rest day.  I'm thrilled that our model did what it was supposed to do, especially with 15 cobblestone sections in today's stage.  An example of a cobblestone section is shown below (click on image for a larger view).
It's a good thing it wasn't raining.  Cobblestones can be dangerous, especially when wet.  Check out how our model performed today.
  • Stage 09:  3h 24' 26" (actual), 3h 27' 37" (prediction), 03' 11" slow (1.56% error)
I just LOVE it when predictions come in under 2%!

Tomorrow, Monday, 16 July, is the first of two rest days for the Tour de France cyclists.  They will rest in Annecy, which is in southeastern France, near the Swiss border.  The Alps await them!  Stage 10 begins on Tuesday in Annecy.  This first mountain stage ends in Le Grang-Bornand after 158.5 km (98.49 mi) of cycling.  Climbers will shine and the general classification will shake up.  There are three grueling category-1 climbs and one Hors catégorie climb.  The finish has a slight uphill, but that follows what is sure to be a fast downhill as cyclists descend from the top of Col de la Colombière.  Our prediction is given below.
  • Stage 10:  4h 15' 27" (prediction)
I can't wait to see the scenery and watch elite cyclists do their thing in the Alps!

14 July 2018

Groenewegen (Good!) and Our Model (Bad!) Go Back-to-Back

Dylan Groenewegen won his second straight Tour de France stage today.  And for the second straight day, I was watching the race and wondering when the pace was going to pick up.  Yesterday, a cyclist would leave the peloton, but nobody would follow.  The peloton looked just as sluggish again today.  The only exciting part of the stage was the final sprint.  Check out the screen capture I got (click on the image for a larger view).
André Greipel is in red and Fernando Gaviria is in blue in the back.  Peter Sagan is on the left in green.  Both Greipel and Gaviria got relegated by the judges after some head-butting.  Sagan ended up with yet another second place.

Our model should be relegated after today's stage!  We did worse than yesterday.
  • Stage 08:  4h 23' 36" (actual), 3h 59' 44" (prediction), 23' 52" fast (-9.05% error)
Groenewegen averaged a rather pedestrian 41.20 kph (25.60 mph).  The time schedule on the Tour de France's website had 44 kph as its slowest projection.  I'm sure there were fans along the route who were wondering when the bloody peloton was going to reach them!  Other than teams' strategies, I don't have a good explanation for the slow speeds over the past two stages.  When I watched yesterday, I'd see someone leave the peloton, but nobody would go after him.  Teams seemed content to go with the flow of the peloton.  We'd have to cut approximately 20% off our power to match the times of Stages 7 and 8.  There is no way we can know that at the start of the Tour de France!

I hope there is faster racing for tomorrow's Stage 9.  Taking place in the north of France, the 156.5-km (97.2-mi) flat stage begins in Arras Citadelle and ends in Roubaix near the Belgian border.  The stage is short compared to the last two and a rest day follows.  Surely teams will push more with the rest day coming.  Our model's prediction is given below.
  • Stage 09:  3h 27' 37" (prediction)
More than seeing my model come through, I want to see some fast cycling, despite the 15 sections of cobblestones!

13 July 2018

Groenewegen Wins Our Worst Stage

Dutch cyclist Dylan Groenewegen won today's long flat stage.   Despite crosswinds slowing riders down, I thought the stage would have been completed a lot faster.  I kept watching the race live, thinking, "Come on!  You're only averaging 38 kph!"  As if I could do any better, right?!?  I did get a screen capture when Groenewegen finally crossed the finish line, out-sprinting his competitors (click on image for a larger view).
Our worst prediction so far is revealed below.
  • Stage 07:  5h 43' 42" (actual), 5h 16' 33" (prediction), 27' 09" fast (-7.90% error)
There was time when I used to think if we got below 10%, our model was doing pretty well.  I no longer think that way.  I want to do better than 5%.  Groenewegen won with an average speed of 40.33 kph (25.06 mph).  Even the time schedule on the Tour de France website didn't think the average speed would be less than 42 kph.  Racing just looked slow today.  The peloton coasted much of the time, even when it got split.  Was the length of the stage a factor?  Were cyclists saving energy for the next couple flat stages?  I don't know.  Our model doesn't know about teams' strategies.  We've got to study this stage after the race ends!

Tomorrow's Stage 8 is another flat stage.  It begins in north-central France in the commune of Dreux.  Cyclists will ride 181 km (112 mi) mostly northeast to Amiens.  Our prediction is given below.
  • Stage 08:  3h 59' 44" (prediction)
Time to pick up the pace!  I want to see cyclists under four hours tomorrow.  I hope our model does a better job!

12 July 2018

Martin OWNS the Last KM!

Irishman Dan Martin simply owned his competition on the final kilometer of today's Tour de France stage.  He stayed in front of home-country favorite Pierre Latour during the final sprint.  I grabbed the screen capture below as Martin came upon the finish line (click on image for a larger view).
Some of the downhill racing hit speeds around 74 kph (46 mph).  There were strong headwinds and crosswinds near the finish.  Strategies and winds had me thinking our prediction might be a bit fast.  Below is how we did.
  • Stage 06:  4h 13' 43" (actual), 4h 06' 24" (prediction), 07' 19" fast (-2.88% error)
I'll take another stage error under 3%!  Martin's average speed was 42.80 kph (26.59 mph).

Our terrain model is pretty good.  After the Tour de France is completed, we'll do as we always do each year and look over the entire race and see if our model can be tweaked for various stage types.  We nailed yesterday's medium-mountain stage, and we weren't too far off today.

At 231 km (144 mi), tomorrow's Stage 7 is the longest stage in this year's Tour de France.  The flat stage commences in the northwest French commune of Fougères and takes cyclists due eat to Chartres.  Below is our model's prediction.
  • Stage 07:  5h 16' 33" (prediction)
With such a long stage, will the peloton keep the pace slow?  Or will a rider decide that he wants the podium at the end of the day and attack early?  I can't wait to see how it unfolds!

11 July 2018

Sagan Gets #2 and We're Nearly Perfect!

Peter Sagan out-sprinted Italian Sonny Colbrelli to earn his second stage win in the Tour de France.  Check out the screen capture I got (click on image for a larger view).
I was again watching the race from home and I was yelping on my couch when cyclists were a few km away from the finish.  We had another shot at perfection.  Check out our prediction for today.
  • Stage 05:  4h 48' 06" (actual), 4h 46' 53" (prediction), 01' 13" fast (-0.42% error)
For the second time in five stages, our error is 0.4%!  I'm thrilled with how our model has performed over the first quarter of the Tour de France.  Sagan averaged 42.59 kph (26.46 mph) during the nearly five hours he spent in the saddle.

Tomorrow's Stage 6 is another medium-mountain (or hilly) stage.  The 181-km (112-mi) stage begins in Brest, which is about as far west as one can get in France.  The commune of Mûr-de-Bretagne is where the stage ends.  Cyclists will have one category-4 climb and three category-3 climbs.  Our prediction is below.
  • Stage 06:  4h 06' 24" (prediction)
Will Sagan win another stage or settle for second place?  Or will someone else rise up tomorrow?  I can't wait to watch it!

10 July 2018

A Thrilling Sprint to End Stage 4!

Wow -- just wow!  I watched today's stage from home instead of my office.  I was on the edge of my seat when that final sprint started.  Those cyclists have me in awe.  As I've written before, I never tire of seeing elite athletes performing at the pinnacle of their métier Peter Sagan planned his push perfectly, but just couldn't catch Fernando Gaviria, who won his second stage in this year's Tour de France.  Another second place for Sagan!  André Greipel was pedaling his tail off and came in third.  Check out the screen capture below (click on image for a larger view).
Sagan is on the far left, Greipel is in red in the middle, and Gaviria is the one crossing the finish line first.  Want to see that from the side?  Check out the screen capture I got from a replay (click on image for a larger view).
Pretty close, huh?  Below is a comparison of Gaviria's winning time and our prediction.
  • Stage 04:  4h 25' 01" (actual), 4h 17' 52" (prediction), 07' 09" fast (-2.70% error)
When I kept hearing the announcers talk about a "massive head wind," I knew our prediction would likely be a bit fast.  But I'm thrilled to be under 3%!  Gaviria's average speed was 44.15 kph (27.43 mph).  Greg Van Avermaet maintains the yellow jersey and Tejay van Garderen is right there with him.

Tomorrow's Stage 5 gives us the first medium-mountain (or hilly) stage.  Beginning on the west coast of France in Lorient, the 204.5-km (127.1-mi) stage ends to the northwest in Quimper.  There are a couple of category-4 climbs and three category-3 climbs.  Our prediction is given below.
  • Stage 05:  4h 46' 53" (prediction)
I hope tomorrow's finish is as exciting as today's!

09 July 2018

BMC Takes Today's Team Time Trial!

BMC Racing Team was focused, determined, and flat-out great in today's team time trial.  Check out that grit (click on image for a larger view).
Every year, we need to tweak our power output and air drag.  Cyclists get more powerful, bikes get more aerodynamic, and team strategies get more efficient.  Science plays a major role in these advancements.  I got a screen capture of BMC crossing the finish line with their winning time (click on image for a larger view).
Below is a comparison between their winning time and our prediction.
  • Stage 03:  38' 46" (actual), 39' 59" (prediction), 01' 13" slow (3.14% error)
We've been slow on recent time trials.  I continue to marvel at how great these cyclists are and how much improvement there is from year to year.  BMC averaged 54.94 kph (34.14 mph), an average speed that boggles my mind.  And the reason it boggles my mind is because I can't imagine being good enough to cycle that fast for as long as they did, even if I could draft the entire time!

Belgian Greg Van Avermaet takes over the yellow jersey and Tejay van Garderen from my country sits in second place.  It's been an exciting start to this year's Tour de France with a new yellow jersey wearer after each of the first three stages.

Tomorrow's Stage 4 gets underway in La Baule on the west coast of France.  The 195-km (121-mi) flat stage finishes a little ways up the coast in Sarzeau.  Below is our prediction.
  • Stage 04:  4h 17' 52" (prediction)
Will the yellow jersey be waiting for someone new after tomorrow's stage?

08 July 2018

Sagan Wins and We're Nearly Perfect!

No second place for Slovakian Peter Sagan today as he won a thrilling sprint to take Stage 2.  Check out the finish in the screen capture I got (click on image for a larger view).
Sagan stretches forward, narrowly ahead of Sonny Colbrelli of Italy.  France's own Arnaud Démare is right behind in third place.  What a great finish!  Sagan now has the yellow jersey.  Racing was again fast, but when I saw the winning time come up, I nearly hopped out of my chair.  Check out how our prediction fared today.
  • Stage 02:  4h 06' 37" (actual), 4h 07' 38" (prediction), 01' 01" slow (0.41% error)
I'll definitely take that error!  Sagan averaged 44.40 kph (27.60 mph), a bit slower than yesterday's winner, but an elite average speed nonetheless.

Tomorrow's Stage 3 is a team time trial.  Still in western France, the 35.5-km (22.1-mi) race will be held in the commune of Cholet.  Can Team Sky get Chris Froome closer to the lead?  We shall see.  Our prediction is given below.
  • Stage 03:  39' 59" (prediction)
With drafting and good strategy on swapping out the lead cyclist, team racing can be very fast.  I look forward to seeing how it unfolds tomorrow!

07 July 2018

Gaviria Makes Colombia Proud!

Fernando Gaviria of Colombia out-sprinted Peter Sagan (another second-place stage finish for Sagan!) to take this year's first Tour de France stage.  Racing was fast and some late crashes tossed Chris Froome 51 seconds behind the leader.  Vincenzo Nibali, who came in 11th today with the winner's time group, has to be smiling now that he's got a lead on Froome.  Team Sky may have the edge in Monday's team time trial over Bahrain-Merida, but Nibali has a lead on Froome that he'll try not to lose before the first mountain stage.  A favorite of mine, Nairo Quintana, came in 112th today at 01' 15" back.

It was a great sprint at the end as speeds shown on the live feed I had reached 61 kph (38 mph).  I cropped this image from the replay of Gaviria crossing the finish line with Sagan right behind him and powerful Marcel Kittel coming in third (click on image for a larger view).
Now let's see how our first prediction turned out.
  • Stage 01:  4h 23' 32" (actual), 4h 36' 43" (prediction), 13' 11" slow (5.00% error)
That's a good, but not great, start.  Racing was definitely fast today.  Gaviria's average speed was 45.76 kph (28.44 mph).  Not too shabby for nearly four-and-a-half hours in the saddle!

Tomorrow's 182.5-km (113.4-mi) Stage 2 commences in the western French commune of Mouilleron-Saint-Germain.  The flat stage ends to the west in La Roche-sur-Yon.  Our prediction is given below.
  • Stage 02:  4h 07' 38" (prediction)
We were 5% slow today.  Will we do better tomorrow???

06 July 2018

Time for the 2018 Tour de France!

The World Cup has kept me so busy that the start of the Tour de France sneaked up on me.  My research student, Carl Pilat, and I have this year's model ready to go.  I'm always nervous with the first prediction!

Stage 1 begins in Noirmoutier-en-l'Île on the west coast of France and ends in Fontenay-le-Comte after 201 km (125 mi) of cycling.  The flat stage looks to be in a beautiful part of western France.  Without further ado, here is our prediction:
  • Stage 01:  4h 36' 43" (prediction)
Will we be fast?  Slow?  It's always fun watching the race and seeing how our model performs.  We can't know detailed weather information, teams' strategies, what crazy fans will do, and if crashes occur.  There are a lot of unknowns in predicting such a complicated phenomenon.  But that's part of the excitement!

24 June 2018

Toni Kroos' Amazing Bend Beats Sweden!

With just a few seconds left in extended time, Germany got the goal it needed to move past Sweden, 2-0, in yesterday's World Cup action.  The win put Germany in a great position to move on to the knockout stage.  Toni Kroos kicked the game-winner and it was a thing of beauty.  The image below shows Kroos just before he kicked the Telstar 18 (click on the image for a larger view).
The view from behind the goal shows what the Swedish goalkeeper had in mind (click on the image for a larger view).
He is protecting the part of the goal to his right, perhaps thinking the Swedish two-player wall and other defenders would be enough to keep the Kroos kick out of the part of the goal to his left.  One of the defenders in the Swedish wall actually flinched away from Kroos' kick!  Check that out below (click on the image for a larger view).
See the blur of the ball on the back of the Swedish defender at the bottom of the image?  Hey, I'd flinch, too, with a fast-moving ball coming right at me, but I bet they guy wishes his back had at least let the ball graze him.

Now it's time to look at the beautiful trajectory.  The Magnus force helped Germany win the match because Kroos put a lot of counterclockwise (as seen from above) spin on the ball by kicking the ball right of center with his right boot.   That led to a Magnus force pushing the ball to Kroos' left, which meant the goalkeeper might have thought the ball would be wide of the goal.  Check out the trajectory that I've labeled with circles below (click on the image for a larger view).
Look at the lovely bend!  That's a banana kick with whipped air!  As the ball spins counterclockwise, the boundary layer of air is being whipped off the back right part of the ball.  If the ball whips the air that way, Newton's third law says the air has to push the ball to the left.  And did it ever!  Check out the view of the bend from a lower angle (click on the image for a larger view).
Air resistance worked to slow down the ball and Earth's gravity pulled the ball downward, but that gorgeous bend is due to the Magnus effect.  Want to see how close the Swedish goalkeeper came to deflecting the ball?  Check it out (click on the image for a larger view).
See the ball just barely off his outstretched right hand?  Want another view?  Sorry, Sweden, but I've got to show it (click on the image for a larger view).
The image will surely give Swedish fans heartache, but sometimes the beautiful game comes down to mere inches.

Okay, let's get quantitative.  I know the aerodynamic properties of Telstar 18 (click here for my research paper).  Modifying the result in my paper with what we've learned about spinning balls, I modeled Kroos' kick.  Check out the trajectory plot below, which shows the trajectory in red (dashed red line is the shadow on the pitch) and what the trajectory would have looked like without the Magnus force in blue (dashed blue line is the shadow on the pitch).  The goal plane is also shown (click on the image for a larger view).

The perspective I have on my 3D plot isn't quite the same on the actual views I showed above, which is why the red trajectory doesn't look quite as curved as the trajectories I put on the actual images.  Television images are also a bit skewed.  But you can see how much the Magnus effect altered the trajectory from the no-spin case.

The ball was kicked at 67 mph at about 13.6 degrees above the horizontal.  The ball was travelling a bit more than 51 mph when it reached the goal plane, having been slowed by air resistance and converting some kinetic energy into gravitational potential energy.

I'll now show you the sizes of the drag force and the Magnus force on Kroos' kicked ball while in flight.  I scale the forces by the ball's weight.  The ball took almost a second to reach the goal plane (click on the image for a larger view).
Look how close to the ball's weight the two forces are at the moment the ball was kicked!  You can see why the ball slowed so much and curved so much on its way to the goal plane.  Had there been no air resistance, the ball would only have slowed 1 mph or so at the height it reached in the goal plane.

I loved watching the kick and I loved analyzing the kick.  Physics makes the beautiful game all the more beautiful!