My New Book and Intuitive Physics

My new book, The Physics of Krav Maga, came out on 19 November 2019.  My publisher, Johns Hopkins University Press, invited me to write a blog post to coincide with my book's release.  I decided to write on the topic of "intuitive physics" that I used as a basis for beginning my book's physics discussions.  There are no equations in my book.  I opted for conceptual descriptions and plenty of photos, figures, and graphs.  There are links in the book to movies of the various moves I discuss.  Click here to read my blog post, or just click on the image of my book's cover below.

In the interest of shameless book promotion, what could be a better stocking stuffer than a stocking stuffer with attitude?!?

Sumo Glory in 5.5 Seconds!

Ever since I began researching Chapter 9 of my first book, I have been fascinated by the sport of sumo.  I discussed the great Taihō Kōki in that chapter while discussing lovely physics topics like linear momentum.  Though Taihō died three years after my book was published, I still check in on sumo when I can.  I'm glad I watched the final match of the Autumn Grand Sumo Tournament that took place in Tokyo on 22 September (click here for an article in English).  Several top-ranked rikishi, including two yokozuna, were absent from the final of the top division.  But that didn't stop Mitakeumi Hisashi from attaining sumo glory after defeating Takakeishō Mitsunobu in just 5.5 seconds.

Check out the start of the match (click on image for a larger view).

The ring (dohyō) has a diameter of 4.55 m (14.9 ft).  The rikishi are behind the starting lines (shikiri-sen), which are 70 cm (2.3 ft) apart.  The referee (gyōji) is ready for the start of the action, which happens only by mutual consent of the rikishi.  Mitakeumi with a mass of 177 kg (a weight of 390 lb) is on the left and Takakeishō with a mass of 169 kg (a weight of 373 lb) is on the right.  The two rikishi combined for a mass of 346 kg (a weight of 763 lb), which is the weight of a good-sized grand piano or over a quarter of the weight of my Honda Civic.  A lot of mass was about to collide!

The initial charge (tachi-ai) saw Takakeishō opting to stay low and Mitakeumi looking to defend high (click on image for a larger view).

You can see Mitakeumi's hands are out, preparing to keep Takakeishō from getting too low.  Check out the initial collision (click on image for a larger view).

Even though rikishi seldom are able to get to a speed of more than 2 m/s (4.5 mph) or so due to the short distance they travel prior to collision, the combined kinetic energy can be large.  I calculated a combined kinetic energy at the collision to be about 850 J.  If that amount of energy could be turned into work, I could be lifted about a meter off the ground!  A baseball would have to be moving 108 m/s (242 mph) to have that much kinetic energy!  But the only work that kinetic energy was turned into was the work needed to depress and move fat around.  If ever there was an inelastic collision, it's what you see in the above image.  Most of that kinetic energy was gone after the collision.  Before you think of 850 J as being a huge amount of energy, and nobody wants to be hit by a baseball moving over 100 m/s, consider that 850 J is the same amount of energy as 0.2 Calories.  That's only 10% of a Tic Tac!  The next time you pop a single Tic Tac in your mouth, think about how much chemical energy is stored in food.

Okay, back to the action.  Mitakeumi's opening strategy worked; he kept Takakeishō from staying low (click on image for a larger view).

Note that the center of mass of the two rikishi hasn't moved much from the initial collision.  Because both rikishi were pushing back on the floor with roughly the same force, the floor pushed back on them with the same force (Newton's Third Law).  With those external forces nearly canceling, the system of the two rikishi felt no net, external force.  That meant that the system's linear momentum was conserved during the collision.  That's why the center of mass didn't move much after the initial collision.  But now we come to the key point in the action where Mitakeumi took advantage of physics and made sure the system of the two rikishi had a net, external force (click on image for a larger view).

You can see Mitakeumi on the left driving forward while Takakeishō got caught standing still.  The above image is just 1.3 s after the initial charge.  Because Mitakeumi has a little speed to the right, the system linear momentum isn't zero as it was during the initial hit.  The system linear momentum is to the right, which means the two rikishi will likely move to the right after the next big collision.  A split second later and Takakeishō is still stuck (click on image for a larger view).

Takakeishō is essentially at rest in the above instant, and Mitakeumi is heading toward victory.  Check out the next collision (click on image for a larger view).

The system linear momentum is to the right!  Mitakeumi is charging and you can see that Takakeishō is reeling by the fact that his left foot has come off the ground.  Mitakeumi's next big step with his left leg drove Takakeishō right where Mitakeumi wanted him (click on image for a larger view).

Takakeishō doesn't have much room to back up, which was Mitakeumi's intended goal.  Mitakeumi then opted for stability and went low (click on image for a larger view).

By keeping low, Mitakeumi avoided Takakeishō getting the advantage by pushing off the raised ring and offsetting Mitakeumi's balance.  In the image below, you see Mitakeumi low and ready to deliver the winning punishment (click on image for a larger view).

When Mitakeumi next drove into Takakeishō, Mitakeumi had his center of mass dropped and his right leg back for added stability (click on image for a larger view).

You can see that Takakeishō had his feet against the raised ring.  That was his last effort to keep from being pushed out of the ring.  Takakeishō tried to sneak out to his right, but the position Mitakeumi had achieved in the above image prevented that from happening (click on image for a larger view).

All that remained of the match was great technique, strength, and using physics in the way it's supposed to be used.  Mitakeumi next helped with leverage by grabbing Takakeishō's mawashi (click on image for a larger view).

You can just spot Mitakeumi's right hand under Takakeishō's mawashi.  And look at the wonderful stance Mitakeumi had!  His wide base with left foot slightly back prevented Takakeishō from driving off the raised ring.  Now comes the lift (click on image for a larger view).

Mitakeumi had Takakeishō's mawashi fulled gripped with both hands, and Mitakeumi was prepared to lift and push (click on image for a larger view).

Mitakeumi had raised himself and Takakeishō up and driven Takakeishō almost out of the ring.  A lot of chanko-nabe has to be consumed to get that massive and strong!  Takakeishō was done for at this point.  A look from behind shows the precarious situation Takakeishō was in (click on image for a larger view).

Takakeishō was out a split second later (click on image for a larger view).

You can see on Takakeishō's face what second place looks like.  The above image is just 5.5 s after the initial charge began.  That's all the time Mitakeumi needed to take full advantage of the laws of physics and secure a tournament win.  He got a pretty nice trophy, too (click on image for a larger view).

He can put a lot of Asahi Super Dry in that thing!

Albert Pujols and Lifetime 0.300 Hitter

With the Astros win over the Rays last night, the two American League heavyweights will be squaring off against each other for the pennant.  Game 1 of the Astros/Yankees series begins on Saturday.  Both of the National League heavyweights, the Braves and Dodgers, were ousted from the playoffs by the Cardinals and Nationals, respectively.  The Cardinals host the Nationals this evening in the first game for the National League pennant.  The silliness of partially deciding the champion a 162-game Major League Baseball season with a single game in the wild-card round and a best-of-five in the division-series round will have to be discussed in a future blog post.  The topic of this blog post is Albert Pujols.

(image credit:  https://www.flickr.com/photos/dherholz/246301261/)

Pujols hasn't played for the Cards since helping them win the 2011 World Series.  His Los Angeles Angles finished this past season 35 games behind the Astros.  But his old team being in the hunt for this year's World Series title got me thinking about Pujols.  His 11 seasons in St. Louis were not only some of the best seasons any player has had to open a career, they punched his ticket to the Hall of Fame.  He finished top-5 in MVP voting in 10 of those 11 seasons (and 9th in his "off" year!), winning the award three times.  Two of his second-place MVP finishes were to Barry Bonds (make of that what you will).  His career numbers after those 11 seasons in St. Louis already had him ranked among the game's best.  He had over 2000 hits, nearly 1300 runs, nearly 450 home runs, nearly 1000 walks, over 1300 RBI, an OBP of 0.420, a SLG of 0.617, and a batting average of 0.328.

We've known for many years now that batting average isn't nearly as valuable a statistic as, say, on-base percentage or slugging percentage.  But batting average still resonates with many baseball fans, even scientists like me (who should know better!).  I'm 49 years old and I have vivid memories of collecting baseball cards when I was very young.  The stats on the backs of those cards became numbers that my brain couldn't shake.  Batting titles, 200 hits in a season, getting over 0.300 batting average, and sluggers who could top 100 RBI became the baseball benchmarks of my youth.  Finishing one's time in baseball as a "lifetime 0.300 hitter" had the cachet of a great career.  When Pujols left the Cards after the 2011 season with his 0.328 lifetime batting average, that number caused names to pop up in my head at the time.  I was lucky enough to have watched Rod Carew and Wade Boggs on television during their prime years.  Those two names represent a combined 12 American League batting titles, two players who each topped 3000 career hits, and two players who have lifetime 0.328 batting averages.  You know who else hit 0.328 for his career?  Honus Wagner.  Setting aside disputes over 9 hits and 10 at-bats in his career, Wagner's name is known to any baseball fan, and certainly to anyone who collects baseball cards.  He was in the inaugural Hall of Fame class and regarded by many as the greatest shortstop, though comparing dead-ball-era players to the athletes of today is next to impossible.  The point I'm making here is that when Pujols left the Cards after their championship season in 2011, he had the career average of great hitters like Carew, Boggs, and Wagner.  But his power numbers blew those greats away.  Those of us who watched Pujols in his prime were privileged to see one of baseball's elites.

Despite finishing 5th in the 2011 MVP race, Pujols had his worst year with the Cards.  Though he had a year that essentially every baseball player would love to have, it wasn't the elite year that Pujols was used to in his first decade in the league.  It was the first year that he didn't top 100 RBI (he had 99) or hit over 0.300 (he finished at 0.299).  His OBP and SLG were down, and he continued his penchant for grounding into double plays, leading the majors with 29.  He was nearly 32 years old and, if he was like most players throughout baseball's history, was getting ready to enter the decline phase of his career.  Maybe the Cardinals could see all that, though they did offer him a lot of money to come back.  Pujols was traded to the Angels prior to the start of the 2012 season.  The Angels signed Pujols to a 10-year deal worth approximately $254 million, which was about $44 million more than what the Cards were willing to pay.  Much has been written about how financially crazy that was for the Angels, though hindsight does aid in the complaining about the contract.

The Angels surely thought they could get four or five seasons of Pujols nearly at the level of his best seasons with the Cards.  He walloped 50 doubles and 30 home runs in his first season with the Angels.  But the 0.285 batting average he had that first year with the Angels was, by far, his best batting average season with the Angels.  He made just one All-Star team in the past 8 seasons as an Angel, and that was in 2015 when he finished the year with 40 home runs.  But as impressive as that was, he hit just 0.244 with a paltry 0.307 OBP.  Over the past 3 seasons, Pujols collectively hit less than 0.245, had an OBP under 0.300, and had a -1.0 WAR.  That last number is almost hard to believe for a player like Albert Pujols.

Though he's hit over 200 home runs in his 8 seasons with the Angels, no one can argue that Albert Pujols has been anything close to the player he was for the Cardinals.  He did finish the 2019 season, his 19th in the big leagues, with a career batting average of 0.300, which means his years with the Angels knocked 0.028 off his career batting average.  But though the record books have Pujols as a 0.300 hitter, that's rounded.  He actually has a 0.2996 career batting average.  If he retired today, Pujols would indeed be able to wear the "lifetime 0.300 hitter" moniker.  But there is a trace of Ted Williams in me that wants to see Pujols come back for his 20th season and get his lifetime average over the exact 0.300 number.  Albert Pujols has come to the plate 12231 times in his career.  He needed just five outs he made in his career to have been hits for his lifetime average to be over the 0.300 line.  Five outs.  In 19 years.  Fans of Pujols can surely recall a couple of great defensive plays made against him, or a couple of blown umpire calls that cost him hits.

What would you do?  If you were Pujols and about to turn 40, would you retire and have the magic 0.300 in the record books?  Would you bust your tail over the off-season, get in the best shape of your life, and come back with a mission to get over .300?  Pujols hasn't reached 500 at bats in the previous two seasons, but let's give him exactly 500 at bats for the 2020 season.  Pujols would need 155 hits in those 500 at bats to have a lifetime average of 0.30008 (154 hits would have him at 0.299991).  Getting 155 hits in 500 at bats means Pujols would have to hit 0.310 next year, something he's not done since 2010, i.e. half his career ago.  So that seems very unlikely.  But what if Pujols got hot to start the season?  He could go 6 for 6 and sneak over the 0.300 line (0.300009 to be closer to exact).  Now that would be almost like Ted Williams going 6 for 8 in the double header to end the 1941 season and finish comfortably over 0.400.  Starting the season 6 for 6 is unlikely for Pujols, but not nearly as improbable as hitting 0.310 over the course of a full season.

So, again, what would you do?  The elephant in the room, of course, is what Pujols will earn next year.  Pujols has already made over $285 million in his baseball career (not including endorsements!).  He's set to earn $29 million next season, and then $30 million the following season.  He'll make over $179k per game next season, which is nearly $20k per inning (assuming each game has 9 innings, which won't be true).  He could be the DH and only play four or five innings per game.  Just a select few people can even comprehend the money that Pujols could make next year.  If Pujols comes back and plays one game, he'll earn more from that one game than I will in all of 2020.  So I would do what I suspect most everyone else would do, and that's come back and earn an incredible salary doing something that I love to do.  Even if he plays the next two seasons, and he plays well below his former self, he'll still finish his career with a first-ballot Hall of Fame ticket.  He'll also give fans like me, who have never seen Pujols play in person, the chance to cross off one item on our bucket lists.  I'm rooting for Albert Pujols to come back strong next season -- and hit at least 0.310!

Ewan Wins Stage and Bernal Makes History!

Caleb Ewan won his third stage in this year's Tour de France.  The loops around Paris are so much fun to watch at the end of the final stage.  Ewan just burst through at the end to win the stage (click on image for a larger view).

You can see Ewan on the far left in red and white.  You can also see Egan Bernal with the yellow jersey in the center of the screen capture.  He's about to come in 29th in the stage, but, more importantly, he's about to make history as the first Colombian to win the general classification at the Tour de France.  Before getting to Bernal, check out how our prediction fared today.

• Stage 21:  3h 04' 08", 3h 06' 05" (prediction), 01' 57" slow (1.06% error)

We've done well on the last stage in the past, and I'm thrilled with today's result.  Ewan's average speed is given below.

• Stage 21:  11.59 m/s (41.71 kph or 25.92 mph)

The ceremonial aspects of the stage make it a challenge to model.  Just after the stage commenced, Egan Bernal had a wonderful moment with Julian Alaphilippe (click on image for a larger view).

And it wasn't long afterwards that Bernal partook of the tradition of drinking champagne (click on image for a larger view).

Bernal won the Tour de France with a time of 82h 57' 00".  Given the two shortened stages in the Alps, the total distance came to 3365.8 km (2091.4 mi).  I'd have to bike from my office at the University of Lynchburg to Yellowstone National Park to match that distance.  What I couldn't possibly do is bike that distance in a three-week period while averaging 40.58 kph (25.21 mph) in the saddle!

The post-race ceremony was moving to say the least.  Julian Alaphilippe most definitely deserved the most combative prize.  It was a joy to watch Alaphilippe over the past three weeks.  He made France very proud.  Peter Sagan won his record seventh green jersey.  Romain Bardet recovered from a rocky start to win the polka dot jersey.  Besides the yellow jersey, Bernal won the white jersey -- and he's eligible to win it for three more years.  Check out the jersey winners (click on image for a larger view).

Bernal's muli-language speech on the podium was beautiful.  He stood with teammate Geraint Thomas, who came in second, and Steven Kruijswijk, who came in third (click on image for a larger view).

Can Bernal win another Tour de France?  At just 22 years old, he certainly appears to have a bright future!

Posting predictions on my blog has always added to the fun of watching the Tour de France for me.  I thank two of my research students, Carl Pilat and Noah Baumgartner, who both did excellent work this summer.  The real work always comes after the Tour de France ends when post-race analysis begins.  Stage 7 was our one really bad prediction.  Of the 20 stages we could predict, we hit 14 of them to better than 6%, including eight of them to better than 3%.  I'm on holiday beginning tomorrow.  I'll likely write one more Tour de France blog post after my return.

The Shark Takes Shortened Stage 20!

Vincenzo Nibali rode with gusto up to Val Thorens and held off his competitors in the final kilometer to win the penultimate stage of this year's Tour de France.  Check out Nibali after crossing the finish line (click on image for a larger view).

It was great watching the world's best on the final climb of this year's race.  The last two stages in the Alps got blasted by the weather, but there was still a lot of drama.  I wish I had a prediction to compare to today's result, but I simply didn't get a chance last night to analyze the new stage route.  Below is Nibali's winning time.

• Stage 20:  1h 51' 53" (actual)

His average speed is given below.

• Stage 20:  8.86 m/s (31.91 kph or 19.83 mph)

That average speed happens to be about 2 kph greater than the maximum estimated by the race organizers.  Cyclists were definitely outputting more power this year than the ones we've modeled in the past.

This will be an historic Tour de France as Egan Bernal will become Colombia's first general classification winner.  Oh, by the way, Bernal is just 22 years old.  This kid could dominate cycling for many years to come.  Last year's winner, Geraint Thomas, will finish second this year.  That gives Team Ineos (formerly Team Sky) the top two spots on the podium tomorrow.  Not only did the team do well without Chris Froome, they will have seven of the last eight Tour de France winners, including the last five in a row.  That's domination!  Dutch cyclist Steven Kruijswijk will finish third overall tomorrow.  Julian Alaphilippe, who stole the hearts of French cycling fans, will finish fifth.  What he did on Stage 3 and on the individual time trial in Stage 13 will never be forgotten.

Tomorrow's final Tour de France stage is mostly ceremonial, but the sprinters will go for the stage win as they near Paris.  The 128-km (79.5-mi) flat stage commences in Rambouillet and then takes riders northeast to the Champs-Élysées in Paris.  Our prediction is given below.

• Stage 21:  3h 06' 05" (prediction)

I can't wait to see history get made tomorrow!

Stage 19 Winner is ... ICE and MUD???

Each year's Tour de France brings me something new and exciting.  I'm not a lifelong viewer of the Tour de France, but in the 15 or so years that I've followed the world's most famous bike race with the interest of a physicist who modeled the event, I've never seen anything like what happened today.  As I wrote yesterday, and as any fan of the race probably suspected, the yellow jersey was attacked on the climb to the summit of Col de l'Iseran.  Julian Alaphilippe was giving it his all, but Colombian Egan Bernal simply dominated the climb to highest point (2270 m or 9088 ft) in this year's Tour de France.  I had no idea when I grabbed the screen capture of Bernal reaching the summit first that the summit would end up being the finish line for today's stage (click on image for a larger view).

Bernal began the descent as the virtual race leader.  Alaphilippe was hoping to make up time on the descent because he is an incredibly skilled downhill racer.  As the screen capture shows, he was a little more than two minutes behind Bernal (click on image for a larger view).

Alaphilippe then began flying on the descent, hoping to shave seconds off Bernal's lead (click on image for a larger view).

But then the stage was stopped!  Just passed one of the tunnels near Val d'Isère, a huge amount of ice, water, and mud had flowed onto the road (click on image for a larger view).

That didn't look as bad until the helicopters moved down the road (click on image for a larger view).

Race officials absolutely did the right thing.  Cyclists were approximately 10 km from what you see above, and there is no way the road would have cleared in just a few minutes.  Water and mud were still streaming down the hillside.  The plow was engaged in a seemingly futile attempt to clear water.

Alaphilippe was visibly angered by what happened.  He may have shaved several seconds off Bernal's lead during the descent, but would he have been able to do the same on the final climb?  Alaphilippe could have lost even more time instead of being 48 seconds behind Bernal going into the final mountain stage.

As for a model comparison, the best I can offer is the time our model predicted to the summit of Col de l'Iseran.  Entering today's stage, Egan Bernal had an accumulated time of 75h 20' 19".  He is now listed as leading the general classification at 78h 00' 42", but he earned an 8" time bonus today.  That gives Bernal a time of 2h 40' 31" to the point where the race stopped.  My model prediction to that point is compared to Bernal's time below.

• Stage 19:  2h 40' 31" (actual), 2h 49' 12" (prediction), 08' 41" slow (5.41% error)

That's the best I can do for today.  Would our model have caught up to cyclists on the final climb?  I've no idea, and I won't speculate.  I'll have to stick with what you see above.  Bernal's average speed to the stoppage point is given below.

• Stage 19:  9.26 m/s (33.32 kph or 20.71 mph)

Tomorrow's Stage 20 begins in the Olympic town of Albertville.  Cyclists will then travel 130 km (80.8 mi), first east, then south to the ski resort of Val Thorens.  After an early sprint, riders will have a category-1 climb to the 1968-m (6457-ft) peak of Cormet de Roselend.  The big finale will be the 33.4-km (20.8-mi) Hors catégorie climb to an elevation of 2365 m (7759 ft) at the finish line in Val Thorens.  Our prediction is given below.

• Stage 20:  3h 39' 46" (prediction)

How today's events will affect tomorrow's stage is anybody's guess.  Our model certainly can't predict that!  It will be exciting to see if Colombia will get its first Tour de France winner.  It's too bad that Thibaut Pinot had to abandon the race today with a torn quadriceps muscle while fifth overall in the general classification standings.  The hopes of everyone in France now sit squarely on Julian Alaphilippe.

Quintana Attacked Col du Galibier and Won Stage 18!

I've been rooting for Nairo Quintana for years.  The Colombian is a great climber, and he showed what he can do today.  He crossed the finish line in the rain and with blood on his jersey, possibly from a nosebleed while at high altitude (click on image for a larger view).

He attacked on the Col du Galibier with about 26.3 km (16.3 mi) left in the stage, and nobody could keep up him.  The riders he left seemed almost stunned at how Quintana burst forward.  Check out where Quintana made his move (click on image for a larger view).

You can see Quintana in his blue Movistar Team jersey.  He owned the final 7.5 km (4.7 mi) of the climb and easily crossed the peak first (click on image for a larger view).

I was not only thrilled for Quintana, I was thrilled for our model.

• Stage 18:  5h 34' 15" (actual), 5h 38' 19" (prediction), 04' 04" slow (1.22% error)

We nailed the first stage in the Alps!  Quintana's great climb led to a top-notch average speed.

• Stage 18:  10.37 m/s (37.34 kph or 23.20 mph)

It was a joy to watch Quintana on that final climb.  He vaulted from #12 to #7 in the general classification, now 03' 54" behind Julian Alaphilippe.  The race leader passed his first big test today, only sacrificing five seconds on his lead.  Expect attacking tomorrow on a relatively short 126.5-km (78.6-mi) mountain stage.  Riders will not want to leave everything to the final mountain stage.

Stage 19 begins in the commune of Saint-Jean-de-Maurienne.  Cyclists will head mostly east and mostly uphill for the first 70% of the stage.  That major uphill effort will culminate in the Hors catégorie climb to the 2770-m (9088-ft) peak of Col de l'Iseran.  The stage finishes with a category-1 climb into Tignes.  Our prediction is given below.

• Stage 19:  3h 32' 37" (prediction)

If a few riders are able to maintain a lot of pressure on the yellow jersey, we could be a tad slow.  I'm anxious to see more Alps climbing tomorrow!

Trentin Blasts his way to Stage Win!

Matteo Trentin broke off the lead group before the final climb and powered his way to the stage win.  The leaders raced at a scorching pace today.  I knew the general classification leaders would hold back today, but we ended up modeling the peloton's pace, not the winner's pace.  I'm simply amazed by the power output from today's elite cyclists.  Before getting to our prediction, check out Trentin crossing the finish line all alone (click on image for a larger view).

Okay, now for the comparison.

• Stage 17:  4h 21' 36" (actual), 4h 42' 42" (prediction), 21' 06' slow (8.07% error)

What's bizarre about what our model did today is that it nearly predicted the peloton's arrival to zero error.  The peloton came in 20' 10" after Trentin.  In other words, our model missed the peloton's time by just 54".  But we want to be able to model the winner, not the peloton!

Despite our model being slow today, it was great watching Trentin's ride.  Below is the moment when today's stage was won (click on image for a larger view).

I got that screen capture when Trentin broke off from the lead group and took a peek back to see if anyone was chasing him.  He accelerated past 60 kph (37 mph) to get in front.  The race was over at that point.  Check out Trentin's average speed.

• Stage 17:  12.74 m/s (45.87 kph or 28.50 mph)

The winning cyclist was once again about 2 kph faster than what the Tour de France organizers estimated for the top speed of the day.

The Tour de France will be decided over the next three stages in the Alps.  Tomorrow's Stage 18 will be something to watch!  Commencing in the commune of Embrun, cyclists will ride 208 km (129 mi) mostly north to Volloire, which is almost to the border with Italy.  Riders will climb to the 2109-m (6919-ft) peak of Col de Vars before two facing two Hors catégorie climbs.  The first is to the 2360-m (7743-ft) peak of Col d'Izoard; the second is to the 2642-m (8668-ft) peak of Col du Galibier.  The descents off each mountain will lead to some blistering speeds.  I hope there are several riders coming off the final climb because that would make for a spectacular downhill sprint to the finish line.  Our prediction is given below.

• Stage 18:  5h 38' 19" (prediction)

The Tour de France has befuddled me a bit this year, sometimes in exciting ways.  Regardless of how our model performs tomorrow, I'm anxious to see the monster climbs in the Alps!

Caleb Ewan Sprints to Second Stage Win!

Caleb Ewan's burst of acceleration inside 100 m left in today's stage put him in front of several of the world's best sprinters.  In fact, 48 of 162 cyclists (about 30%) who finished today's stage earned the same time Ewan achieved.  But Ewan got all the glory after coming in first (click on image for a larger view).

Ewan is in red and white, about to cross the finish line at a blistering 66 kph (41 mph).  Our model did wonderfully today.

• Stage 16:  3h 57' 08" (actual), 3h 53' 10" (prediction), 03 58" fast (-1.67% error)

That's what I like to see!  Check out Ewan's average speed.

• Stage 16:  12.44 m/s (44.78 kph or 27.83 mph)

Tomorrow's Stage 17 is hilly and 200 km (124 mi) long.  Riders begin at Pont du Gard and travel northeast to Gap, where the Alps will be waiting for them.  Much of the first half of the stage is uphill.  Our prediction is given below.

• Stage 17:  4h 42' 42" (prediction)

Even if the leaders in the general classification lay back a bit in preparation for the Alps, I hope to see the sprinters flying downhill at the end.

Stage 16 Prediction

Stage 16 is an interesting flat stage because it begins and ends in the same city.  The Tour de France cyclists are resting in Nîmes today, which is the city where tomorrow's Stage 16 begins and ends.  The 177-km (110-mi) stage loops counterclockwise to the north.  Our prediction is given below.

• Stage 16:  3h 53' 10" (prediction)

Will the general classification contenders ride safely tomorrow, staying in a leisurely-moving peloton, all looking to get the same time?  It wouldn't be the worst strategy, given the later stages in the Alps.  It will be interesting, though, to see if any of the teams try to push Julian Alaphilippe.

Brilliant Ride Wins Stage 15 for Simon Yates!

This year's elite climbers are definitely outperforming our model.  They are outputting more power than they did last year.  Simon Yates rode with great form and rode with aggression on the final climb.  I'll start with the screen capture I got when Yates crossed the finish line (click on image for a larger view).

But that's not when I jumped out of my office chair.  Yates and Simon Geschke were leading the race up the final climb when, with about 8.7 km left in the stage, Yates attacked with passion (click on image for a larger view).

You can see Yates near the motorcycle and Geschke, who finished 25th today, permanently dropped.  There was so much attacking and cracking on the final climb that Yates kept up a torrid pace.  Julian Alaphilippe, who climbed without help from teammates and came in 11th today, lost time on his yellow-Jersey lead.  Thibaut Pinot came in second today and jumped up to fourth in the general classification, just 01' 50" behind Alaphilippe.

Descent racing was spectacular.  Speeds were high, despite mist making visibility tough for the cyclists (click on image for a larger view).

Pace was fast today and I knew we'd be slow with our prediction.  We needed more than 4% more power on our model cyclist; 42 riders (out of 164, or 25.6%) beat our predicted time today.

• Stage 15:  4h 47' 04" (actual), 5h 03' 05" (prediction), 16' 01" slow (5.58% error)

I hope we can cut that error in half when the riders get to the Alps.  Yates's average speed on his second stage win in the year's Tour de France is given below.

• Stage 15:  10.74 m/s (38.67 kph or 24.03 mph)

That is truly an impressive average speed on a stage like today's stage.  That maximum anticipated average speed by the Tour de France organizers was 37 kph.  The athletes are clearly outperforming exceptions on many fronts.  It's impressive to watch!

Tomorrow is the second and last rest day.  Cyclists will rest in Nîmes, which is nearly on the southern coast with the Mediterranean Sea.  They'll need to rest because after tomorrow, they'll have a flat stage and then a hilly stage before three brutal mountain stages in the Alps.  Those three stages have four Hors catégorie climbs in them, compared to just one they endured in the Pyrenees.  The race will surely be won in the Alps.  I'll be back tomorrow with our Stage 16 prediction.

Pinot Dominates Col du Tourmalet!

Thibaut Pinot pulled ahead of fellow Frenchman Julian Alaphilippe in the final 250 m to win today's Stage 14 of the Tour de France.  Alaphilippe extended his general classification lead over Geraint Thomas to 02' 02".  Pinot moved from seventh to sixth overall, now 03' 12" behind Alaphilippe.  The French have to be thrilled with what's happening in this year's Tour de France.  Does Pinot look happy winning today's stage? (click on image for a larger view)

I always wonder how much of the scenery the cyclists take in.  They concentrate and focus on their riding, and they've ridden these routes before, but for someone like me, the top of Col du Tourmalet looks so amazing that I'd have trouble concentrating and focusing! (click on image for a larger view)

It was the 83rd time the Tour de France came to Col du Tourmalet.  I was watching in my office as some of the world's best cracked on the final climb.  The mountain split up the peloton and only the truly elite riders powered up for the top of stage standings.  Check out how our prediction fared.

• Stage 14:  3h 10' 20" (actual), 3h 19' 37" (prediction), 09' 17" slow (4.88% error)

I was hoping we could do just a tad bit better, but I'll take that error.  Twenty-six cyclists beat our predicted time today.  Climb strategies and cyclists' legs are unpredictable.  Check out Tim Wellens collecting 10 more points for his polka-dot jersey as he was the first atop Col du Soulor (click on image for a larger view).

Wellens did a great job pinning 2014 winner Vincenzo Nibali against the fans just before reaching the top.  I love watching the Shark on the descents.  Nibali kept the pace fast before reaching Col du Tourmalet, but fell back on the climb and finished 74th today.

At the end of the stage, fans were going crazy, crowding the riders (click on image for a larger view).

Pinot's average speed is given below.

• Stage 14:  10.29 m/s (37.04 kph or 23.02 mph)

That's impressive!

Tomorrow's Stage 15 begins in the commune of Limoux.  The 185-km (115-mi) mountain stage takes riders west into the Pyrenees. Top elevation will be the category-1 climb to the 1517-m (4977-ft) peak of Port de Lers.  That will be followed by a category-1 climb up Mur de Péguère.  The stage ends with a category-1 climb up Foix Prat d'Albis.  Tomorrow's stage is longer than today's, and it has more climbing.  Our prediction is given below.

• Stage 15:  5h 03' 05" (prediction)

It will be hard to beat today's action.  I hope tomorrow's stage delivers the goods!