Great Day for Team Sky!

Brit Chris Froome dominated the final climb today to win Stage 7 of the Tour de France.  He bettered last year's winner, Cadel Evens of Australia, on the last, grueling uphill toward the finish line.  Below is the comparison with our prediction.

• Stage 7:  4h 58' 35" (actual), 5h 13' 07" (prediction), 14' 32" slow (4.87% error)

Our error is lower than yesterday's, but I still remain amazed by how well cyclists have done over the past two days.  Their power outputs have exceeded what we've used in our model.  Don't let it slip your mind as you watch these cyclists that you are watching the best of the best.  There is no way I could have looked respectable on my bike on Stage 7's final climb!

Froome's average speed is given below.

• Stage 7:  11.11 m/s (39.99 km/hr or 24.85 mph)

Bradley Wiggins, Froom'e Team Sky teammate and fellow Brit, now has the yellow jersey.

Tomorrow's medium-mountain Stage 8 begins in the city of Belfort and takes cyclists 157.5 km (97.87 miles) southeast to the Swiss town of Porrentruy.  There are lots of great climbs in the Jura Mountains in this stage (click here to see the profile on the Tour de France website).  The stage ends on rather flat terrain, so look for a great sprint to finish things off.  Below is our prediction.

• Stage 8:  3h 57' 04" (prediction)

Based on how cyclists have done so far, I think the winner can cross the finish line in under four hours.  Will Team Sky keep the yellow jersey?

Sagan Wins Stage 6!

Peter Sagan of Slovakia won his third stage of this year's Tour de France with a performance faster than we predicted. Below are the results.

• Stage 6:  4h 37' 00" (actual), 4h 57' 12" (prediction), 20' 12" slow (7.29% error)

I usually don't mind having errors under 8%, but I was surprised how fast this stage turned out to be.  Check out Sagan's average speed below.

• Stage 6:  12.49 m/s (44.95 km/hr or 27.93 mph)

Excluding the average speed of the individual time trial that was the Prologue, the above average speed for the winner of Stage 6 is the greatest so far.  Sagan's average speed was 7.2% greater than what Mark Cavendish had in winning Stage 2, a stage that was the same length as today's Stage 6.  Those cyclists are amazing athletes!

Tomorrow's Stage 7 is the first of two straight medium-mountain stages before Stage 9's individual time trial.  After that time trial, riders will enjoy their first of two rest days on Tuesday, 10 July.  Stage 7 begins in the commune of Tomblaine and takes riders 199.0 km (123.7 miles) southeast to the ski station at La Planche des Belles Filles in the Vosges Mountains.  Besides having a great climb during the middle of Stage 7, the stage ends with the climb to the ski station, which is at an elevation of 1035 m (3396 feet) above sea level.  Below is our prediction.

• Stage 7:  5h 13' 07" (prediction)

Cyclists surprised us a little with today's speed.  Will they be able to surprise us tomorrow with a fast final climb?

Two in a row for Greipel!

André Greipel won his second straight stage of this year's Tour de France with a great sprint at the end.  Another big crash just a few kilometers from the finish line played a role.  Peter Sagan, winner of Stages 1 and 3, was among those involved in the crash.  Below is the comparison of how our prediction matched the reality of Stage 5.

• Stage 5:  4h 41' 30" (actual), 4h 35' 16" (prediction), 6' 14" fast (-2.21% error)

I'll certainly take that error!  Greipel's average speed is given below.

• Stage 5:  11.63 m/s (41.88 km/hr or 26.02 mph)

Tomorrow's stage is mostly flat and stretches east 207.5 km (128.9 miles) from the northern French commune of Épernay to the city of Metz, which is not far from where France meets Luxembourg and Germany.  Our prediction for tomorrow's Stage 6 is given below.

• Stage 6:  4h 57' 12" (prediction)

A couple of medium-mountain stages follow tomorrow's stage.  Fabian Cancellara still possesses the yellow jersey.  Let's hope there are no more big crashes tomorrow!

Greipel Wins Stage 4!

German André Greipel just won Stage 4 of this year's Tour de France with a great sprint.  A huge crash happened a few kilometers from the finish line.  Below is a comparison of Greipel's winning time with our prediction.

• Stage 4:  5h 18' 32" (actual), 5h 10' 00" (prediction), 8' 32" fast (-2.68% error)

Another prediction under 3% makes us happy!  Below is Greipel's average speed during his Stage 4 win.

• Stage 4:  11.22 m/s (40.40 km/hr or 25.11 mph)

Tomorrow's flat Stage 5 picks up in Rouen and takes riders 196.5 km (122.1 miles) east to Saint-Quentin.  Below is our prediction.

• Stage 5:  4h 35' 16" (prediction)

Fabian Cancellara, who escaped today's crash, maintains the yellow jersey.  Let's hope today's crash doesn't take anyone out of the race.  Mark Cavendish was involved in the crash, and tomorrow's Stage 5 is the kind of stage that Cavendish can win.

Sagan Takes Stage 3!

Peter Sagan of Slovakia just won his second stage of this year's Tour de France.  Sagan sprinted away from his competition as he ascended the last Category 4 climb at the stage's end in Boulogne-sur-Mer.  A big crash near the end of Stage 3 did not involve Sagan.  Below is the actual result compared to our prediction.

• Stage 3:  4h 42' 58" (actual), 4h 47' 16" (prediction), 4' 18" slow (1.52% error)

I can't complain about a 1.52% error!  Sagan's average speed is given below.

• Stage 3:  11.60 m/s (41.77 km/hr or 25.96 mph)

Tomorrow's Stage 4 is a 214.5-km (133.3-mile) long flat stage, which begins in the commune of Abbeville and ends in the capital of Upper Normandy, Rouen.  Much like Stage 3, my student, Brian Ramsey, and I had to fill in some geographic data not seen on the Tour de France website's stage profile.  The model I describe in Chapter 4 of my book requires geographic data to create inclined planes of the terrain.  Some of the stage profiles for this year's race were in dire need of additional geographic information.  Our prediction for Stage 4 appears below.

• Stage 4:  5h 10' 00" (prediction)

Will Fabian Cancellara hold the yellow jersey after tomorrow?  We shall see!

Tour de France Update and Stage 3 Prediction

I thank my brother-in-law, Bob Calano, for putting my Tour de France predictions on my blog for me.  Below is a summary of how our predictions fared against the actual results.

• Prologue:  7' 13" (actual), 7' 35" (prediction), 22" slow (5.08% error)
• Stage 1:  4h 58' 19" (actual), 4h 49' 18" (prediction), 9' 01" fast (-3.02% error)
• Stage 2:  4h 56' 59" (actual), 4h 48' 45" (prediction), 8' 14" fast (-2.77% error)

Fabian Cancellara of Switzerland won the Prologue; Peter Sagan of Slovakia won Stage 1; Mark Cavendish of Manx won Stage 2.  Below are their average speeds.

• Prologue:  14.78 m/s (53.21 km/hr or 33.06 mph)
• Stage 1:  11.06 m/s (39.82 km/hr or 24.75 mph)
• Stage 2:  11.64 m/s (41.92 km/hr or 26.05 mph)

Part of the reason my student, Brian Ramsey, and I may have been a tad fast on the first couple of stages is that no cyclist really broke free of the peloton.  Several riders were awarded the same time in each of the past two stages.  We were hoping for some late breakaways!

I am pleased with how our predictions came out for the Prologue and first two stages.  Anytime the error is around 3% for a stage that takes nearly five hours to complete, I'm happy.

Tomorrow's Stage 3 is mostly flat for the first half of the stage.  Some lovely rolling hills make up the second half of the stage.  Classified as a "medium-mountain stage," the riders start from the French commune Orchies and end 197 km (122 miles) later in the city of Boulogne-sur-Mer, nearly at the English Channel.  Below is our prediction for tomorrow's Stage 3.

• Stage 3:  4h 47' 16" (prediction)

Our predicted times for Stages 1, 2, and 3 are all quite similar.  Will we be a tad fast tomorrow?

Out of the Dark Ages!

At about 1:20 pm (Eastern Standard Time) today, electricity came back on in my home.  We spent nearly three days without electricity due to a major storm that hit the US this past Friday evening.  Daytime temperature last Friday hit 38.9 C (102 F) in my area, which made conditions ripe for huge pressure differences that gave rise to strong winds.  Click here for more details of the derecho.  My college (Lynchburg College) may not have electricity until the end of the week.  After checking it out today, I can see why -- lots and lot of trees were knocked down.


I know I sound like a whiny American for complaining about not having electricity for three days while many, many people around the world don't have air conditioning and quality refrigeration.  I get it that life can be a lot worse.  It's just a matter of what one is used to after so many years.


Because of lack of electricity, I missed Spain's dominating win over Italy in Euro 2012.  I've also missed the first part of the Tour de France.  My next post will update results from the Prologue and first two stages.

Stage 2 Prediction

Eric is still without electricity. His Stage 2 prediction is


4h 48' 45" (prediction)

Stage 1 Prediction

Eric is without power; this is his brother-in-law typing.  He has just phoned me with his stage 1 prediction.  


4h 49'18"  (prediction)

It's Tour de France time!

One of my favorite times of the year is at this very moment.  We are but a single day away from the start of the Tour de France.  This year's race begins with a Prologue stage in the Belgian city of Liège.  The 6.4-km (4.0-mile) individual time trail will whet our appetites for the 3496.9 km (2172.9 miles) that will be completed by the time cyclists hit the Champs-Élysées on Sunday, 22 July.


I wrote a guest post for The Johns Hopkins University Press blog that concerns my Tour de France modeling.  Click here for the direct link to the post.  As I state there, I plan to stick my neck out again this year and offer predictions for each stage's winning time.  My student, Brian Ramsey, and I incorporate real stage data into a model that employs the unalterable laws of physics and published human-performance research to come up with our predictions (see chapter 4 of my book).  We never know in advance, of course, if there will be poor weather, crashes, or some other impediment to great racing.  We do the best science we can, and have a lot of fun in the process.  So, without further ado, below is our prediction for this year's Prologue.

• Prologue:  7' 35" (prediction)

My best guess is that a cyclist will beat our time, but that's what makes this so enjoyable!

Balotelli Sends Italy to the Euro 2012 Final!

Mario Balotelli was sensational for Italy as The Blues knocked out a German team that I thought would make the final of Euro 2012.  The people in Warsaw's National Stadium got to see one of the world's best on display as Balotelli scored both of Italy's goals in the 2-1 win.


Click here for ESPN's GameCast of the match.  Balotelli's first goal came in the 20th minute as he received a perfect cross from Antonio Cassano.  Watch the replay of the goal and you'll see Cassano on the left side of the penalty area.  He kicked the ball with his left boot, and the ball was spinning clockwise (as seen from above).  There was so much spin on the ball that the Magnus force pushed it left to right (as seen from Cassano's viewpoint).  By the time the ball reached Balotelli's head, which was centered about 5 m (5.5 yards) from the goal, the ball had a velocity component toward Balotelli.  It was the perfect cross into the box and Balotelli nailed it.


Balotelli's second goal came in the 36th minute as the German defense let him slip through for a shot at the goal about 16.5 m (18 yards) out.  This goal was pure power.  Click on the image below for a larger view of the trajectory of Balotelli's goal.

The red curve shows the actual trajectory; the blue curve shows what the trajectory would have looked like had there been no spin on the ball.  Balotelli smashed the ball with his right boot with a right-to-left motion as he drove his foot into the ball.  That gave the ball a clockwise (as seen from above) rotation that caused the ball to veer toward the upper right corner of the goal. Balotelli thus kicked a "screwball" in the baseball sense (click here for my post from six days ago on that topic).

I estimate that Balotelli's shot took about 0.544 seconds (after averaging several viewings of the goal) to reach the goal plane.  The ball's initial speed was 32.7 m/s (73.1 mph).  Couple that enormous speed with a screwball effect and Manuel Neuer, Germany's goal keeper, had no chance whatsoever to prevent the goal.  All Neuer could do was what the rest of us did -- watch with awe the power and beauty of Mario Balotelli's game-winning shot.

Italy moves on!

After 90 minutes of scoreless football in Kiev, England and Italy played two additional 15-minute periods of scoreless football.  Italy had possession for 68% of those two hours, and had taken 36 shots (8 on goal) to England's 9 shots (1 on goal).  Italy passed better, attacked better, and looked much crisper than England.  Despite looking so much better than England, Italy simply could not score.  England's goal keeper, Joe Hart, played great, as did the Three Lions' defense.  Two hours of dominant play got thrown out for Italy as the match moved to penalty kicks.


When Riccardo Montolivo missed Italy's second penalty attempt, I thought England had lucked out the win.  Instead, Ashley Long's penalty kick for England hit the crossbar.  Gianluigi Buffon made the sole goal-keeper save of the penalty-kick session when he stopped England's fourth kick by Ashley Cole.  Italy had the victory with a 4-2 penalty kick score.


Imagine how difficult it is for a goal keeper during penalty kicks.  The ball is kicked from just 11 meters (12 yards) out.  A hard-kicked ball may leave the kicker's boot at roughly 30 m/s (67 mph), though penalty kickers may opt to bring speed down to improve accuracy.  Andrea Pirlo's penalty kick for Italy was quite slow and down the middle, which fooled Joe Hart.  For all the advanced study of penalty-kick tendencies, luck plays a major role.  A ball kicked at nearly 30 m/s will reach one of the upper corners of the goal in about 0.4 seconds.  That's the same time it takes for a Major-League fastball to reach home plate after the pitcher lets go of it.  Studies in human reaction time suggest that eye-hand reactions take place on the order of 0.20 seconds, whereas eye-leg reactions need nearly twice that time.  In short, if a goal keeper stands in the center of the goal and simply reacts to a penalty kick, there is no way to stop the kick.  The goal keeper must guess ahead of time.  Gianluigi Buffon made a great guess on Ashley Long's kick.


Italy moves on to face Germany in the semifinals.  Italy will need to finish much better against the Germans compared to how they did against England.

Germany's Screwball Goal ...

Germany was much too powerful for Greece in today's Euro 2012 quarterfinal action.  Earning a 4-2 victory in Gdańsk (Poland), Germany moves on to the semifinal round against the winner of Sunday's England versus Italy match.


The goal I most enjoyed in Germany's win was the first one.  Click here for ESPN's GameCast of the match.  Click on The Team's first goal and enjoy Philipp Lahm's smash from about 22 m (24 yards) out.  Go to the 0:47 mark in the video for a great slow-motion look at Lahm's goal.  Note that Lahm hit the ball with his right boot.  Note, also, that Lahm's right leg moved powerfully across his body, meaning that he was twisting counterclockwise (as seen from above).  His twist was so strong that he lost his balance upon returning to the pitch after his brief moment in the air.  That kicking motion gave the ball a clockwise (as seen from above) component to the spin.  The video shows quite well that the ball tailed away from the Greek goal keeper, Michail Sifakis, in a left-to-right manner (as seen by Lahm) as it slammed into the upper right portion of the goal.  Without the rotation and the curve due to the Magnus force, the goal keeper would have blocked the ball (Sifakis managed to just get his left pinkie on the ball).


If a right-handed baseball pitcher throws the ball with a component of spin that is clockwise (as seen from above), we call that pitch a screwball.  Not too many pitchers throw that pitch because it is hard on the arm.  Old timers like Christy Mathewson and Carl Hubbell were famous for throwing the "fadeaway" or screwball.  From my youth, I recall Fernando Valenzuela lighting up Major League Baseball in 1981 with a look to the sky before throwing his screwball.  Today's pitchers rely more on a circle change because it is much easier to throw compared to a screwball.  Anyway, a screwball moves from left to right (as seen by the pitcher) for a right-handed pitcher.  That is the same type of motion that Sifakis had to deal with from Lahm's great kick.


The Magnus force makes for some wonderful trajectories!

Ukraine's no goal ...

I am happy to see England move on to the quarterfinals of Euro 2012, but today's win over Ukraine shows why replay needs to be a part of professional football.  The image below (cropped from televised replay) shows that Marko Devic's shot was clearly a goal, despite not being called a goal.  Click on the image for a larger size.

The referee standing along the goal line did not call this a goal.  I really can't blame the referee given how fast the above play moved in real time.  There may have been poetic justice in the "no goal" call because Ukraine was offside earlier in the attack, but that doesn't change the fact that replay is needed to decide calls like the one shown above.  Goal-line technology is here and is easy to implement.  The above image could have been created seconds after the play and a decision could have been made within a minute of stopping play.  There aren't that many goals in a typical football game, and there certainly aren't that many controversial goals.  In a given tournament, there are, what, one or two (at most) controversial goals that could benefit from replay?

Join the 21st century and get the call right!

Portugal and Germany Dominate Group B!

Father's Day allowed me the opportunity to take in a little world-class football today.  The quality of play by the Portuguese and Germans did not let me down.  As much as I love the physics associated with football aerodynamics, what dropped my jaw today was the physics of the ball on the pitch.


The Navigators are lucky to have Cristiano Ronaldo on their club.  Ronaldo is fortunate to have teammates with the incredible skill to put the ball in the just the right place for him to shine.  Click here for the ESPN GameCast of Portugal's 2-1 win over Netherlands in Kharkiv.  Joao Pereira set up Ronaldo's first goal in the 28th minute with a fantastic ball through the Dutch defense.  About 30 meters (33 yards) from the goal, Pereira sent the ball off the outer portion of his right boot to meet Ronaldo nearly 14 meters (15 yards) from the goal.  The timing was perfect as the ball met Ronaldo in stride.


Ronaldo's second goal came in the 74th minute after an even more impressive setup.  Nani was racing down the right side of the pitch and kicked the ball about 27 meters (30 yards) from the goal line along the right boundary line of the penalty area.  Nani booted the ball with his right foot.  Note the counterclockwise rotation (as seen from above) Nani gave the ball.  That rotation caused the ball to curve to the left as it rolled along the ground, reaching Ronaldo in stride about 11 meters (12 yards) left of center of the goal.  The friction force from the pitch on the ball was responsible for the force that pushed Nani's ball to the left.  As the ball reached Ronaldo, it was literally moving sideways into Ronaldo's left boot.  A truly spectacular pass from Nani!  I urge you to watch the video on the ESPN GameCast page, especially the winning goal for Portugal.


Click here for the ESPN GameCast of Germany's 2-1 win over Denmark in Lviv.  Take a look at The Team's opening goal in the 19th minute by Lukas Podolski.  The flick from Mario Gomez to redirect the ball to Podolski was a thing of beauty.  The Germans showed how teamwork and precision passing led to a goal.  Human reaction time is at least 0.2 seconds or so.  Once Gomez flicked the ball and Podolski was in place for the smash into the net, The Olsen Gang could not react fast enough -- no team could.


Portugal and Germany move on to the quarterfinals of the Euro 2012.  The Czech Republic (against Portugal) and Greece (against Germany) will have to defend great movement of the ball on the pitch!

Three Goals for Three Lions!

England had a spectacular win against Sweden today in Group D action of the Euro 2012.  Olympic Stadium in Kiev was the venue for the exciting match.  The Blue-Yellow is guaranteed to finish in the bottom two of Group D.  To see all the goals in England's 3-2 win, click here for ESPN's GameCast page.  I found delightful physics in all three goals.

• Andrew Carroll opened scoring in the match in the 23rd minute.  Steven Gerrard's cross was amazing!  From about 36 meters (39 yards) down the right side of the pitch, Gerrard sent a perfect cross to Carroll, who was about 11 meters (12 yards) from the center of the goal.  Go to the one-minute mark of the short video showing the goal.  Carroll is in the air in slow motion executing a wonderful header.  Once off the ground, Carroll's angular momentum is conserved.  Note how his head whips to his left while his right arm swings behind his back.  Those two rotations are in opposite directions.  Carroll's left leg rotates toward the right side of his body.  All of those rotations are such that Carroll's angular momentum in the air matches the angular momentum he had when he left the ground.  Watch Carroll while in the air!  He is poetry in motion after receiving Gerrard's wondrous cross.
• Theo Walcott drew England even in the 64th minute, just about five minutes after Sweden had taken a 2-1 lead.  About 24 meters (26 yards) out, Walcott send a scorching shot through a crowd of players.  Go to the 43-second point in the video for the slow-motion replay.  Watch the flight of the Adidas Tango 12 ball.  The is a component of spin that is counterclockwise (as seen from above).  There is also a topspin component to the ball's spin.  That topspin component helps the ball dip into the goal.  Walcott had to kick the ball high enough to clear the wall of defenders, and he needed just enough topspin for the ball to have a downward deflection from the Magnus force.  A great kick!
• The winner for England was simply mind-boggling.  In the 78th minute, Theo Walcott fired the ball from the right side of the box and connected with Danny Welbeck.  Go to the 55-second point in the video for slow motion of Welbeck's goal.  You will see Welbeck spinning clockwise (as seen from above) as he receives the ball on the heel of his right boot.  Welbeck's back was to the goal!  His rotation continued after he kicked the ball so that he could witness his winning goal.  Imagine the incredible control and balance needed to do what Welbeck did.  Though he fell to the pitch after rotating toward the goal, he was in complete control as the ball reached his right heel.  Stability physics tells us that strong cores are needed to maintain balance and control during top athletic competition.  Keep doing those sit-ups!

England will be back in Donetsk next Tuesday to take on Ukraine.  Lots more football and physics to be seen!

Gerrard to Lescott!

Given their injuries and the suspension of Wayne Rooney, England was fortunate to escape with a 1-1 draw against France in today's Group D match-up in the 2012 UEFA European Football Championship.  The players looked to be taxed in the evening heat of Donbass Arena in Donetsk, Ukraine.


I loved Steven Gerrard's long kick to Joleon Lescott in the 30th minute.  Lescott received the ball perfectly just inside the 6-yard box, nearly centered by the plane of the goal.  Click here for video highlights and go to the 0:46 point in the video.  Below is my model of Gerrard's kick (click on the graph for a larger image).

The red curve is Gerrard's kick; the blue curve is what Gerrard's kick would have looked like had the ball not possessed counterclockwise spin (as seen from above).  There is no goal without the lovely Magnus force curving the ball towards Lescott!  I estimated that the time of flight of the ball was 1.73 seconds and that it left Gerrard's boot at about 25 m/s (90 km/hr or 56 mph).  Lescott was able to sneak past the French defense for the header that put England on top, a lead they would hold for only about 9 minutes before Samir Nasri tied the score with a great shot left of goal just outside the box as England's defenders looked a little lost.

England and France play again in four days.  The Three Lions will take on Sweden; Les Bleus will face Ukraine.

Grand Tour Modeling

A short video describing the Grand Tour modeling that I have been working on with my research student, Brian Ramsey, appears on my college's home page.  Click here for the Lynchburg College home page or here for a direct link to the video on YouTube.  Many more details behind Grand Tour modeling appear in Chapter 4 of my book (click on cover image on the right).

Ryder Hesjedal takes the Giro d'Italia!

Canadian Ryder Hesjedal edged Joaquim Rodríguez of Spain by just 16 seconds to take this year's Giro d'Italia.  Road conditions shortened the final stage, which most definitely affected my prediction!  Below are the results with the average speed for Marco Pinotti of Italy, who won today's time trial.

• Stage 21:  33' 06" (actual), 39' 39" (prediction), 6' 33" slow (19.79% error - not real!)
• Stage 21:  14.2 m/s (31.8 mph)

But, wait!  Don't kill me for that large error.  I didn't know until just as the race began that the final stage would be shortened from 31.5 km (19.6 miles) to 28.2 km (17.5 miles).  That 10.48% reduction in distance makes all the difference.  Using my predicted average speed with the new distance, my prediction changes to 35' 30", which reduces my error to 7.25% slow.  Pinotti still completed the stage faster than I would have predicted, but my prediction was not nearly as bad as it first seemed.

It's now on to preparation for the Tour de France.  Modeling the final week of the Giro d'Italia has been fun, partly because it's been such a good learning experience.  Check back in early July for predictions of Tour de France stage-winning times.

A little better on Stage 20 ...

Belgian Thomas De Gendt's great solo breakaway did the job in today's Stage 20 of the Giro d'Italia.  Below are the results with De Gendt's average speed listed afterwards.

• Stage 20:  6h 54' 41" (actual), 6h 30' 56" (predicted), 23' 45" fast (-5.73% error)
• Stage 20:  8.80 m/s (19.7 mph)

It boggles my mind just how good those athletes competing in the Giro really are.  That final climb was amazing.  I love the snow!  The past two mountain stages have given me a new appreciation for the challenge of completing the Giro with such a strenuous ending.  As someone heretofore more familiar with the Tour de France, my respect for the Giro and desire to model it more completely in the future have grown considerably this week.

Below is our prediction for tomorrow's final stage, which is an individual time trail.

• Stage 21:  39' 39" (prediction)

It should be a fun ending in Milan tomorrow!

Too fast on Stage 19!

Roman Kreuziger of the Czech Republic won today's Stage 19 of the Giro d'Italia.  Below are the results with Kreuziger's average speed listed afterwards.

• Stage 19:  6h 18' 03" (actual), 5h 43' 12" (prediction), 34' 51" fast (-9.22% error)
• Stage 19:  8.73 m/s (19.5 mph)

Having our prediction under 10% is of little consolation!  As I noted yesterday, we were worried that our prediction might be too fast.  Cyclists looked to be gassed by the time they reached the final climb.  We simply had too much power in our model.

At 219 km (136 miles), tomorrow's Stage 20 is even longer than today's stage.  Cyclists end tomorrow at the famed Passo Dello Stelvio (Stelvio Pass), which is the highest paved mountain road in the eastern part of the Alps.  The final 44 km (27 miles) of Stage 20 will have riders climb over 2 km (1.2 miles) of elevation as they ascend to the 2757-m (9045-ft or 1.713-mile) peak of Stelvio Pass.

Moving on to our prediction for tomorrow's stage, we obviously rethought our power outputs.  The last 10 km (6.2 miles) of today's Stage 19 saw Kreuziger average less than 5 m/s (11 mph), which was about 10% less than what we thought riders would do.  Below is our prediction for tomorrow's stage.

• Stage 20:  6h 30' 56" (prediction)

The best thing about being wrong in science is the opportunity to learn something.  I hope we now have a better feeling for power outputs in tomorrow's stage.

Stage 18 results and Stage 19 prediction ...

Italian Andrea Guardini won Stage 18 of the Giro d'Italia today, just beating out Mark Cavendish of Great Britain.  Below is a comparison of the winning time with our prediction, followed by Guardini's average speed for the 139-km (86.4-mile) stage.

• Stage 18:  3h 00' 52" (actual), 3h 11' 49" (prediction), 10' 57" slow (6.05% error)
• Stage 18:  12.8 m/s (28.7 mph)

I'll take a 6% error on a race I just started modeling this year, and at the end of the race at that.  As  I have noted in previous posts, modeling these cycling stages is not only a great deal of fun, it is hard.  If my model is too simple, I am glossing over complexities that influence a race.  If my model is too complicated, I am making too many a priori assumptions, many of which are certain to be incorrect in the actual race.

Okay, on to Stage 19, which looks to be a brutal mountain stage.  Starting in the north Italian city of Treviso, the stage ends 198 km (123 miles) later in Alpe di Pamepago, which is in the heart of the Dolomites.  Beginning at just 15-m (49-ft) elevation, cyclists will reach the 2047-m (6716-ft or 1.27-mile) peak at Passo Manghen after 123.3 km (76.6 miles) of biking.  The final 8 km (5 miles) will make for a grueling uphill to the finish line.  Here is our prediction:

• Stage 19:  5h 43' 12" (prediction)

I hope cyclists have enough fuel in the tank to make it up the final climb fast enough that our prediction is not too fast!

Giro d'Italia Stage 18 Prediction

Our prediction for tomorrow's Stage 18 is below.

• Stage 18:  3h 11' 49" (prediction)

The downhills from San Vito Cadore to Vedelago should make for some wonderful racing!  Riders should not kill themselves on tomorrow's stage because two monster mountain stages await them on Friday and Saturday.

Not a bad first stage!

Joaquin Rodríguez won today's Stage 17 of the Giro d'Ialia.  The Spaniard just edged Italian Ivan Basso in an exciting finish.  Below is how today's result compares to the prediction I posted yesterday.

• Stage 17:  5h 24' 41" (actual), 5h 28' 26" (prediction), 3' 45" slow (1.15% error)

I told my student, Brian Ramsey, that that's not bad for his very first stage prediction!  Below is how the average speed came out for Joaquin Rodríguez in the 187-km (116-mile) stage.

• Stage 17:  9.60 m/s (21.5 mph)

Check back soon for a prediction for tomorrow's Stage 18, which looks to have a lot of fast downhills.

A try at Giro predicting ...

The 2012 Giro d'Italia is nearly over.  I've only modeled a couple of stages of this race in the past, mostly because my spring semester keeps me extremely busy as the race gets underway.  This year has been no exception.  A rising sophomore Lynchburg College physics student, Brian Ramsey, is working with me this summer in preparation for modeling the 2012 Tour de France.  We thought a nice warm-up exercise would be to model a few stages of this summer's Giro.


To introduce Brian to what it's like to stick one's neck out for science, I had him model tomorrow's Stage 17 using the model I developed for the Tour de France.  Tomorrow's stage is a wonderful mountain ride that takes cyclists from Falzes to Cortina d'Ampezzo.  Here is our prediction for tomorrow's stage:

• Stage 17:  5h 28' 26" (prediction)

We shall see what happens!

Ping-Pong Physics and Vlogging

One of my favorite results from Classical Mechanics has to do with the stability of rigid bodies as they rotate about certain axes.  I demonstrate this theorem in a YouTube video, which is my first attempt at vlogging (though these words may render my attempt but a partial one!).  Click on the video below (or click here) to see and hear me talking about rotating ping-pong paddles.  If you don't own a ping-pong paddle, try my demonstration at home with your television's remote control.  You should easily be able to find the axis about which rotation is unstable.  That's how I discovered one of nature's beautiful workings when I was a teenager.

Way to go Owls!

Ever since my family and I lived in Sheffield, England during my last sabbatical (2008-09 academic year), I have followed the ups and downs of Sheffield's two football clubs, Sheffield Wednesday (the Owls) and Sheffield United (the Blades).  After the Owls defeated the Wycombe Wanderers 2-0 yesterday, they secured the #2 spot in the Football League One table.  The Owls join top club Charlton Athletic for automatic promotion to Football League Championship for next season.


The Blades finished in the #3 spot in the table, just three points behind the Owls, after yesterday's draw against Exeter City, a club that will be relegated to Football League Two for next season.  The Blades now join Huddersfield Town, Milton Keynes Dons, and Stevenage for the League One play-offs.  Two matches with Stevenage (11 May and 15 May) await Sheffield United.


Congratulations to the Owls!  Go Blades!

Earth Day, Feynman, Science, and Beauty

Today is Earth Day, which, having also been born in 1970, is as old as I am.  International celebrations of Earth Day began 20 years later.  Like anything else, the way in which people observe Earth Day will be varied, from complete apathy to total euphoria.  As science helps us understand our less-than-special place in the universe, we slowly come around to the idea that we share our environment with our fellow animals.  We abuse our environment to our own peril.  What constitutes "abuse" is sometimes cause for great debate.  Instead of adding fuel to that fire, I wish to focus here on the beauty of the natural world.


We all experience the world in different ways.  I am unfortunate enough to speak only English.  I envy those, like my wife, fluent in both English and Japanese, who possess ways of formulating thoughts for which the English language is not adequately equipped.  They are capable of seeing the world in ways that I cannot.  As someone who speaks English, I may have ways of seeing my surroundings that someone in, say, China cannot.  Then again, a person living in China may have some ways better than mine for seeing his or her environment.  Language helps us formulate thoughts, communicate them to others, and learn from others.


Mathematics is a language, and a very special one at that.  What makes it special is that it is universal.  I have been around people from other countries who I could not talk to in English.  But, once we started putting equations on a chalkboard, we could share our thoughts.  Physics enhances the beauty of mathematics by helping us understand our natural world.  I have always enjoyed the idea that mathematics is the language of the universe, but physics is the poetry.  Just like the words we think of when hearing the word "language," mathematics is a language that provides us with a unique way of seeing the world.


Unfortunately, too few people possess enough fluency in mathematics to really "see" the world in the way some scientists can.  The joy I acquire when probing for a physical understanding of what happens in a great sporting moment is as heart-stopping for me as the moment itself.  Keeping with the definition Socrates gave us for a wise person, the more I know, the more I realize what I don't know.  The desire to "know" why something happens pushed me into being a physicist.


There were other influences that pushed me into physics.  One was seeing Richard Feynman drop an O-ring into ice water during a hearing to determine the reason why the Challenger shuttle exploded on 28 January 1986.  I was mesmerized seeing a world-class physicist make something so complicated seem so simple.  Like many physicists of my generation, Feynman was one of several that we admired greatly.  Though I know that I'll never see the world as well as he did, I love the life-long struggle to see how close I can come.


I usually share a little bit of Feynman with my classes once or twice a semester.  Just this past Friday, I showed my Classical Mechanics students a few minutes of Feynman lecturing in 1964 to an audience at Cornell as part of his lecture series entitled The Character of Physical Law.  This was just about a year before Feynman got the call from Stockholm.  With all his charisma, charm, and enthusiasm for physics, Feynman ended the second lecture with some wonderful words about how mathematics helps us see beauty in the universe.  Click here for a YouTube video of his second lecture.  Go to about the 51:30 mark and watch until the end (about two-and-a-half minutes).  As Feynman says, "For you who don't know mathematics, it's really quite difficult to get a real feeling across as to the beauty, the deepest beauty, of nature." Mathematics may be difficult, but it's well worth the effort to learn some of that wonderful language.


So, I celebrate Earth Day today by doing physics.  I hope to gain a little more understanding of the natural world and further appreciate its beauty.  

Baseball Turns 65 Today!

On 15 April 1947, Jackie Robinson took to the diamond in Brooklyn's Ebbets Field.  Robinson did not get a hit that day, but the Dodgers beat the Boston Braves 5-3 (click here for the box score).  What made that day special 65 years ago is that Robinson broke the color line in Major League Baseball.  Robinson became the first black man to play Major League Baseball in the 20th century.  There are many, many books you can read about how the courageous Brooklyn general manager, Branch Rickey, selected the even-more-courageous Robinson to bring forth enlightenment to a racist sports world.  I'll not retell that story, but offer the perspective of a 41-year-old physicist who loves baseball.


Born in 1970, I grew up in love with baseball.  Baseball was fully integrated on the field, but not so much in management.  Color didn't mean much to be when I watched baseball and when I played the game as a child.  I etched E-5 on my glove just like Brooks Robinson did; I flapped my elbow like Joe Morgan.  Greatness appealed to me and I never thought about a great "white" player or a great "black" player, just a great "baseball" player.


I also relished baseball history.  Somehow baseball stats just stuck in my head, even to this day.  I collected baseball cards, got autographs, and read book after book on what seemed the perfect game to me.  I certainly read about the Negro Leagues, but like everything that happens to us before we are born, the idea of blacks having their own league because they couldn't play with whites was an abstraction for me.  I felt sick over the idea that great black players weren't allowed to compete in the Major Leagues, but that feeling arose only because of words I read in a book.


So what did I do as a geeky baseball-playing kid?  I wondered if Babe Ruth could have hit 60 homers in 1927 if, every now and then, he had to face a cocky 21-year-old Satchel Paige.  Would Lefty Grove have gone 31-4 in 1931 if, every now and then, he had to look over to first base and see a 28-year-old Cool Papa Bell in the prime of his career ready to take off for second at the first hint that Grove was about to deliver his pitch?  Both Jimmie Foxx (in 1932) and Hank Greenberg (in 1938) challenged the great Babe Ruth's single-season home run record.  Imagine Josh Gibson playing his age 18 to age 27 seasons in the hitter-friendly 1930s.  Would Gibson have broken Ruth's record?


We'll never know the answers to those questions (and many more) that floated around in my young head.  But look at what we do know.  Science is about acquiring data and evidence.  Jackie Robinson won the Rookie of the Year award in 1947 and the National League MVP award two years later.  When the Hall of Fame voted in Robinson and Bob Feller in 1962, affirmative action played no role in the former's vote total.  If Feller's fastball could make a Major League hitter flinch, imagine what seeing Jackie Robinson dance back and forth on second base did to Major League pitchers.  The data and evidence were there in abundance.  Not only did Jackie Robinson belong in the Major Leagues, so did his peers in the Negro Leagues.


Think about where science has taken us in the past 65 years.  The work Watson and Crick did in the early 1950s on DNA gave us biochemical understanding of who we are.  I've always loved it that Watson and Crick were awarded their Nobel Prize in 1962 -- the same year as Jackie Robinson's election to the Baseball Hall of Fame.  Science does not think of people as divided into "tribes" and "races."  We are all part of a species of primates called homo sapiens.  No matter our gender, race, or country of origin, variations in our collective DNA are incredibly tiny compared to other animals (click here for an interesting research paper on this topic).


Our biochemical understanding of ourselves couples quite well to the evolutionary ideas put forth by Darwin in 1859.  Researchers across many scientific disciplines have provided enormous amounts of data and evidence to give us an understanding of how we got here.  We know, for example, that our human origins date back about 200,000 years in Africa, meaning that we are all Africans.  Think about how much science and reason enlighten us.  Push credulity, hatred, and ignorance aside, then think about how cool it is that you and I share common ancestors with Jackie Robinson.  Now that is something to celebrate!


Finally, ponder how short a time length 65 years is.  Nearly 13% of the more than 313 million people in the US are at least 65 years old.  About 1 in 8 people in the US were alive when Jackie Robinson took the field on that pioneering day 65 years ago.  About 9% of our population is at least 70 years old, meaning that about 1 in 11 people probably have memories of Jackie Robinson breaking the color line.  If you know someone of that advanced age, talk to him or her today about Jackie Robinson.  We lose living witnesses to history every year.  Let's keep their stories alive.

Magnus at the Masters!

NOTE:  I wrote the following analysis on the evening of Sunday, 8 April 2012, not long after Bubba Watson won the Master's.  I've been delayed getting my analysis posted.

Bubba Watson's second shot on the second playoff hole of the Master's was a thing of beauty.  If you have not seen it, click here (go to the 5:13 mark on the video).  It not only won him the Masters, it was a great example of a golfer intentionally using the Magnus force to his advantage.  The Magnus force is the force associated with a spinning ball.  It helps explain curveballs in baseball and banana kicks in soccer.  A spinning ball whips air around its back in an asymmetric way.  What that means is that the air is whipped off to one side or the other instead of straight back.  Think of how a boat rudder works.  Turn the rudder to one side and water gets deflected, which makes the boat turn.  Newton's third law tells you that if a ball deflects air in one direction, the air must deflect the ball in the opposite direction.

Golfers use the Magnus force all the time.  Their club faces are grooved to help get the ball spinning.  On tee shots, a well-hit ball will have backspin.  The Magnus force associated with that backspin has an upward component, which fights gravity and helps keep the ball in the air a little longer than if the ball wasn't spinning.  Think about a good Major League fastball.  The backspin prevents the ball from dropping so much on the way to the plate.  A left-handed golfer like Bubba Watson will slice if he hits the ball in such a way that it has a component of spin that is counterclockwise (as seen from above).  What Watson did on the 10th at Augusta was go for a hook.  Seen from above, his ball had a component of its spin that was clockwise.  The ball thus came out of the trees spinning in such a way that the ball curved to the right.  Given that Watson was in the trees on the right side of the fairway, it was the perfect shot.  Most amateur golfers will hook or slice without trying to do so.  Watson showed us when a hook is a good thing.

The physics fun didn't stop with the ball in the air.  Once the ball hit the green, its spin caused it to take a right turn in front of the hole.  The ball eventually stopped rolling and a green jacket lay just ten feet from the hole.  Watson was then able to two-putt for the win because Louis Oosthuizen was not able to find the green with his second shot.  Bubba Watson can thank the Magnus force for the new addition to his wardrobe!