22 July 2014

Rogers Wins First Pyrenees Stage!

Michael Rogers of Australia won his first Tour de France stage today with an impressive performance in this race's first foray into the Pyrenees.  Riders endured arduous climbs and dangerous downhills.  The scenery was incredible.  Check out a sample below (click on the image for a larger view).
I love the green grass and the evergreen trees.  Check out the scene when José Serpa crossed the peak of today's final monster climb (click on the image for a larger view).
I challenged cyclists to come in under six hours today.  Rogers and the elite cyclists right behind him almost did just that.  Below is Rogers's winning time and a comparison with our prediction.
  • Stage 16:  6h 07' 10" (actual), 5h 59' 36" (prediction), 07' 34" fast (-2.06% error)
With just over six hours in the saddle in a tough stage through the Pyrenees, and with two more to come, I'll take a 2% error!  Rogers was ecstatic to win today, as the screen shot I took shows (click on the image for a larger view).
Not a bad day's work for the 34-year-old!  Below is his average speed.
  • Stage 16:  10.78 m/s (38.81 kph or 24.12 mph)
Cyclists face another mountain stage in the Pyrenees tomorrow, beginning in the commune of Saint-Gaudens.  The 124.5-km (77.36-mi) stage contains three category-1 climbs before the hors catégorie climb that finishes the stage at an elevation of 1654 m (5427 ft) at Saint-Lary  Pla d'Adet, which is close to France's border with Spain.  Below is our prediction.
  • Stage 17:  3h 38' 06" (prediction)
Vincenzo Nibali will once again don the yellow jersey tomorrow.  Can anyone catch him?

21 July 2014

Stage 16 Prediction

Stage 16 is a 237.5-km (147.6-mi) mountain stage that will take riders west from Carcassonne into the Pyrenees.  Cyclists will face a huge hors catégorie climb to the 1755-m (5758-ft) peak of Port de Balès before what should be a high-speed downhill sprint into Bagnères-de-Luchon.  Below is our prediction.
  • Stage 16:  5h 59' 36" (prediction)
Tomorrow's stage will be grueling, especially the aforementioned monster climb near the end.  We challenge cyclists to come in under six hours!

20 July 2014

Kristoff Overtakes Devastated Bauer!

Norwegian Alexander Kristoff sprinted his way to victory in today's Stage 15 of the Tour de France.  New Zealand's Jack Bauer had essentially led the entire stage -- and lost it in the final 30 m (33 yd).  Bauer was in tears after the race, and who can blame him?  Bauer looked like he had the distance in front of the attacking sprint group with just half a kilometer to go.  The group caught Bauer right at the end, leaving Bauer in 10th place.  The image below shows Kristoff just after crossing the line with Bauer on the far left of the image (click on the image for a larger view).
To see how close the sprint group was bunched together at the end, check out the image below (click on the image for a larger view).
Kristoff is just ahead of Australia's Heinrich Haussler with Slovakia's Peter Sagan in green on the left coming in third.  Kristoff has now won the last two flat stages, and we did a great job predicting his winning time, as the comparison below shows.
  • Stage 15:  4h 56' 43" (actual), 4h 58' 57" (prediction), 02' 14" slow (0.75%)
We are pleased to be under 1% error for the fourth time!  With crosswinds gusting up to 30 kph (19 mph) over parts of the stage, sometimes helping and sometime hurting cyclists, it was good that wind did not play a major role in the winning time.  It was also fortunate that the rain that fell for much of the day in Nîmes had abated by the time the cyclists got there.  Below is Kristoff's average speed.
  • Stage 15:  12.47 m/s (44.89 kph or 27.89 mph)
The Tour de France has its second and last rest day tomorrow.  The Pyrenees are lurking, so cyclists better get lots of rest!  I'll post our prediction for Stage 16 tomorrow.

19 July 2014

Majka Takes Stage 14 in his First Tour de France!

Polish cyclist Rafał Majka was king of the Alps today.  The 24-year-old is in his first Tour de France, and now he has a stage win.  Vincenzo Nibali made his move with 4 km (2.5 mi) left.  The photo below shows Nibali going for it at the 4-km sign (click on the image for a larger view).
Yellow-jersey-clad Nibali was not only going for the stage win, he was trying to increase his overall lead.  He wasn't able to catch Majka, but he did add a minute on his overall lead on Alejandro Valverde after Valverde faded a bit on today's final climb.  The image below shows an exhausted Majka after he crossed the finish line (click on the image for a larger view).
Kudos to Majka for a great ride up a final climb that made its debut in this year's Tour de France.  It was exciting to see all the attacking taking place on that final category-1 climb. After thinking our prediction would be fast, I asked yesterday how many riders would come in under five hours.  The answer is zero.  We were fast as the comparison with Majka's winning time and our prediction below shows.
  • Stage 14:  5h 08' 27" (actual), 4h 53' 38" (prediction), 14' 49" fast (-4.80% error)
I was worried watching the final climb that our error would eclipse 5%, so I'm glad we came in under that mark.  Hitting three of the past four stages to better than 1% spoils us!  We'll have lots to learn about today's grueling stage, which is what makes this work so much fun.  Below is Majka's average speed.
  • Stage 14:  9.564 m/s (34.43 kph or 21.39 mph)
Cyclists head southwest tomorrow in the southeastern part of France in a 222-km (138-mi) long flat stage.  Beginning in the commune of Tallard, the stage has a great downhill part in the middle where racing is sure to be fast, and then finishes flat in the city of Nîmes.  Below is our prediction.
  • Stage 15:  4h 58' 57" (prediction)
Riders will enjoy a rest day on Monday before tackling the stages in the Pyrenees.  Unlike today, we expect to see cyclists coming in under five hours tomorrow!

18 July 2014

Nibali is a MACHINE in the Alps!

While his closest competitors had their shirts opens and their mouths gasping for breath, Vincenzo Nibali powered up today's final climb like a machine.  He simply looked like he was on an athletic plane above his fellow cyclists.  Nibali now has more than three minutes on his closest rival for the yellow jersey.  Can anyone catch The Shark?!?

Below is Nibali's time and a comparison with our prediction.
  • Stage 13:  5h 12' 29" (actual), 5h 15' 05" (prediction), 02' 36" slow (0.83% error)
The image below show's Nibali's reaction upon winning today's grueling stage (click on the image for a larger view).
That happens to be the same reaction my research student, Chad Hobson, and I had upon learning that our prediction was once again under 1% off!  Below is Nibali's average speed.
  • Stage 13:  10.53 m/s (37.92 kph or 23.56 mph)
That's pretty good considering the cyclists were biking up a brutal climb to finish off their racing day.  The temperature reached 37 C (99 F) at one point, but at least the riders had great vistas, like the one I snapped below from my online feed (click on the image for a larger view).
Not bad, huh?  More mountains are on the way tomorrow as Stage 14 starts back in Grenoble and then heads east to the 2058-m (6752-ft) peak of Col du Lautaret, a category-1 climb.  Cyclists then have an hors catégorie climb to reach the 2360-m (7743-ft) peak of Col d'Izoard.  To complete the 177-km (110-mi) mountain stage, cyclists end with a category-1 climb to the ski resort on the 1855-m (6086-ft) peak at Risoul.  Below is our prediction for this formidable stage.
  • Stage 14:  4h 53' 57" (prediction)
With such a daunting stage giving riders a second consecutive monster climb to the finish, I will not be surprised if our prediction is a tad fast.  How many riders will come in under five hours?

17 July 2014

Kristoff Gets Us to Under 1% Again!

Norway's Alexander Kristoff had an amazing sprint to the finish line in today's Stage 12 of the Tour de France.  The image below shows Kristoff crossing the finishing line, just edging out Peter Sagan (click on the image for a larger view).
The final sprint was great.  Speeds on the last downhill reached 66 kph (41 mph).  Temperatures reached 34 C (93 F).  That's a hot day to be racing!  Below is Kristoff's time and a comparison with our prediction.
  • Stage 12:  4h 32' 11" (actual), 4h 30" 16" (prediction), 01' 55" fast (-0.70% error)
We are ecstatic to once again have our prediction come in under 1%!  Below is Kristoff's average speed.
  • Stage 12:  11.36 m/s (40.89 kph or 25.41 mph)
Picking back up in Saint-Étienne tomorrow, Stage 13 is a 197.5-km (122.7-mi) long mountain stage.  Cyclists will head mostly east, but a little south into the French Alps.  Once they reach the city of Grenoble, riders will have biked 165.5 km (102.8 mi) and be at an elevation above sea level of 229 m (751 ft).  They will enter Grenoble after a fantastic sprint down from the 1154-m (3786-ft) peak of Col de Palaquit, which will have been reached after a category-1 climb.

The real fun begins at the very end of the stage when cyclists will be greeted with an hors catégorie climb to Chamrousse, a ski resort at an elevation of 1730 m (5676 ft).  It took Lance Armstrong 1h 07' 27" to make that 32-km (20-mi) climb in Stage 11 of the 2001 Tour de France, which happened to have taken place on 18 July.  When Armstrong did it, he was winning an individual time trial from Grenoble to Chamrousse.  How will this year's riders do on the same climb exactly 13 years later after they have already biked 165.5 km (102.8 mi)?  This is not a stage for the faint of heart!  Below is our prediction.
  • Stage 13:  5h 15' 05" (prediction)
If you cannot watch the entire stage, at least watch the last hour.  That final climb will be well worth it!

16 July 2014

Gallopin's Sprint Lifts France!

Two days after France saw the yellow jersey leave one of her countryman on Bastille Day, Tony Gallopin gave France something to cheer about.  His impressive sprint to the finish line, where his speed hit 54 kph (34 mph) through the streets of Oyonnax, earned him the win in Stage 11.  The image below shows Gallopin celebrating as he crosses the finish line with a bunch of his fellow cyclists barreling down on him (click on the image for a larger view).
Below is Gallopin's winning time and a comparison with our prediction.
  • Stage 11:  4h 25' 45" (actual), 4h 33' 24" (prediction), 07' 39" slow (2.88% error)
On a gorgeous French day for racing with tailwinds reaching as high as 10 kph (6.2 mph) in several places, and following a rest day, we are thrilled to be less than 3% slow.  Gallopin's average speed is given below.
  • Stage 11:  11.76 m/s (42.33 kph or 26.30 mph)
Tomorrow's Stage 12 is another of the medium-mountain variety.  Beginning in the French commune of Bourg-en-Bresse, the 185.5-km (115.3-mi) stage takes riders mostly south, but a little west toward the finish in the city of Saint-Étienne.  Two category-4 climbs and two category-3 climbs greet cyclists along the way.  Below is our prediction.
  • Stage 12:  4h 30' 16" (prediction)
If the weather is great, if cyclists enjoy a little tailwind, and if they aren't too worried about the two big mountain stages to follow, we could be a tad slow again.  We hope we can come in under 3% error again!

15 July 2014

A Restful Prediction for Stage 11

The World Cup is over and the Tour de France has its first rest day.  How does one get a sports fix today?!?  The Major League Baseball All-Star game is tonight!  Perfect timing!

Tour de France cyclists are surely resting today and planning strategies for the upcoming stages.  Tomorrow's Stage 11 begins in the commune of Besançon, not too far from France's border with Switzerland.  The 187.5-km (116.5-mi) medium-mountain stage takes riders due south into the Jura Mountains, ending in what will hopefully be a fast downhill sprint into Oyonnax.  Below is our prediction.
  • Stage 11:  4h 33' 24" (prediction)
Will riders be fast after a day of rest?  Or, will they be holding back, knowing they've got serious climbs in the Alps coming up?  How will Contador's absence affect strategies?  Lots to learn over the next few stages!

14 July 2014

Nibali Reclaims Yellow Jersey!

Vincenzo Nibali made his move with about 2 km (1.2 mi) left in today's stage.  He looked like a machine pounding away on his bike as the final climb near the finish line reached an insane 20%.  Below is an image I cropped of Nibali finally catching Joaquim Rodriguez with about 1.2 km (0.75 mi) left (click on the image for a larger view).
Rodriguez rode such an outstanding race to that point, but the final climb belonged to Nibali.  The image below shows Nibali just after he crossed the finish line (click on the image for a larger view).
Below is Nibali's time and a comparison to our prediction.
  • Stage 10:  4h 27' 26" (actual), 4h 25' 53" (prediction), 01' 33" fast (-0.58% error)
My research student, Chad Hobson, and I were quite happy watching Nibali make his move because we knew we would have a great prediction.  We'll take 0.58% error any day!  Below is Nibali's average speed.
  • Stage 10:  10.06 m/s (36.23 kph or 22.51 mph)
That's an impressive speed to have been in the saddle nearly four-and-a-half hours and endured so many categorized climbs.

France looked to be enjoying Bastille Day.  Fans lined the route.  Check out the image below (click on the image for a larger view).
Look at what Rodriguez was staring at with about 5 km (3 mi) left in the stage.  It's a wonder there aren't more crashes than there are.

Today's most notable crash was that of Alberto Contador who badly injured his right knee and had to bow out of the stage and the Tour de France after about 95 km (59 mi) into the race.  Now that Contador is out, the various teams' mountain strategies will surely change.

Tomorrow is a rest day, and cyclists will need it after today's grueling stage.  I'll have our prediction for Stage 11 posted sometime tomorrow.

13 July 2014

It IS Germany's Day!

After Tony Martin won Stage 9 earlier today, I wondered if this would truly be Germany's day.  Now that the 2014 World Cup is in the history books, today really IS all Germany's.  Argentina and Germany showed why they were in the final.  The two best teams in the world were on display, and the defenses did not disappoint.  Each team had its moments to score, but extra time was needed.  The goal that won it all for Germany was as beautiful a goal as you'll ever see.

In the 113th minute, André Schürrle delivered the perfect cross into the box.  He was on the left side of the pitch.  The ball met Mario Götze's chest, and then dropped onto Götze's left boot.  Germany's 4th World Cup win was sealed when the ball flew into the far right side of the net.  I cropped the image below from my video feed (click on the image for a larger view).
That image will be on posters all over Germany!  Götze turned 22 just over a month ago.  That's pretty young to be world famous!

Congratulations to Germany on a well-deserved World Cup title.

Does Tony Martin Start Historic Day for Germany?

Tony Martin dominated Stage 9 of the Tour de France today.  When Martin reached the day's greatest height at Grand Ballon, which took riders to 1336 m (4383 ft), I cropped the image below from my video feed (click on the image for a larger view).
Martin was ahead by about three minutes at that point, and won by nearly that margin.  Below is Martin's time and a comparison with our prediction.
  • Stage 9:  4h 09' 34" (actual), 4h 20' 39" (prediction), 11' 05" slow (4.44% error)
Our error went down slightly from yesterday.  After being fast for all three stages in England, we've been on the slow side for the six stages in France.  Below is Martin's average speed.
  • Stage 9:  11.35 m/s (40.87 kph or 25.40 mph)
With Tony Martin making Germany proud in the Tour de France, this could be a day to remember for the Germans if their national team can beat Argentina later today in the World Cup final.

Tomorrow's Stage 10 is the first mountain stage of this year's Tour de France.  Starting where today's stage ended in Mulhouse, cyclists face a 161.5-km (100.4-mi) long stage that mostly takes them through the Vosges Mountains on a semicircular loop to the north and west.  Riders will face a category-3 climb, two category-2 climbs, and four category-1 climbs, including the finish at Planche des Belles Filles.  Below is our prediction.
  • Stage 10:  4h 25' 53" (prediction)
Tony Martin now has the polka-dot jersey and Tony Gallopin has taken over the yellow jersey.  The French will be excited to see one of their own wearing the yellow jersey on Bastille Day.  We'll be anxious to see if the elite cyclists continue to be faster than our predictions.  A day of rest follows Stage 10, so they may go for top times knowing they'll be resting the next day.

12 July 2014

Kadri Makes France Proud!

Blel Kadri left the field in today's Stage 8 after only about 28 km (17 mi) of cycling -- and never lost the lead.  The Frenchman was a machine on the arduous climbs at stage's end and crossed the finish line more than two minutes before anyone else (click on the image before for a larger view).
Kadri will look good with the polka dot jersey as the leader in the mountains classification.  The battle for second today was between Alberto Contador and yellow-jersey wearer, Vincenzo Nibali.  The image below shows Contador grabbing three seconds off Nibali's lead (click on the image for a larger view).
Below is Kadri's time and a comparison with our prediction.
  • Stage 8:  3h 49' 28" (actual), 3h 59' 54" (prediction), 10' 26" slow (4.55% error)
Wind was not a big factor and the light rain probably helped riders keep their legs cool during the big climbs.  We are happy to be under 5%, but we were thrilled to see Kadri powering his way up the mountains.  He was a star for France today!  Below is his average speed.
  • Stage 8:  11.69 m/s (42.10 kph or 26.16 mph)
Picking up where Stage 8 left off, tomorrow's Stage 9 begins in Gérardmer.  The 170-km (105.6-mi) medium-mountain stage eventually gets riders southeast to Mulhouse, which sits near the French borders with Germany and Switzerland.  Riders are tested with six categorized climbs before a great downhill and flat finish.  Below is our prediction.
  • Stage 9:  4h 20' 39" (prediction)
We hope to be impressed by some great climbing tomorrow.  Though we were about 10 minutes slow today, just 47 of 184 cyclists (~25.5%) beat our prediction.  The world's top cyclists are truly athletic marvels!

11 July 2014

Photo Finish in Stage 7!

Italian Matteo Trentin just barely edged out Peter Sagan of Slovakia in a thrilling sprint to end today's Stage 7 of the Tour de France.  Check out the image below that I cropped from my video feed (click on the image for a larger view).
The red line on the left is the finish line.  Could it get any closer than that?!?  Both Trentin and Sagan were among a fortunate few who managed to avoid the crashes that took place near the end of the stage, including one that happened not too far back from the finish line when the above photo was taken.

There were crosswinds during most of the first half of the stage, and then some tailwind components over the second half.  Wind speeds never really got more than about 15 kph (9.3 mph), so though riders were marginally helped by the wind, it didn't play nearly the role it did in the past three stages.  Below is Trentin's time and a comparison with our prediction.
  • Stage 7:  5h 18' 39" (actual), 5h 27' 13" (prediction), 08' 34" slow (2.69% error)
Now that the wind didn't kill our prediction, we are happy with the above comparison!  Trentin's average speed is given below.
  • Stage 7:  12.27 m/s (44.16 kph or 27.44 mph)
Think about how impressive that average speed is.  Cyclists spent nearly five-and-a-half hours in the saddle today, and the leaders still managed better than 44 kph.  On one of the final steep downhill streets, my video feed claimed speeds reached 85 kph (53 mph).  Now that's flying!

Cyclists continue heading essentially south tomorrow in a 161-km (100-mi) Stage 8, which begins in the French commune of Tomblaine.  Stage 8 is classified medium-mountain because of two big category-2 climbs and the category-3 climb that ends the stage in Gérardmer in the Vosges Mountains.  Below is our prediction.
  • Stage 8:  3h 59' 54" (prediction)
We think the best of the best will surely come in under four hours.  It's time to see what the climbers can do!

10 July 2014

How to Improve Spin Kicks in Karate

I've been taking karate with my family for a little more than two years.  We attend classes a couple of times a week at Super Kicks Karate in Forest, VA.  I really enjoy it, but I'm 43 and I've had three back surgeries, so there are a few advanced kicks that give me problems.  One in particular is the jump spin hook kick.  To execute such a kick, begin in a left-side fighting stance (it doesn't matter which side fighting stance one begins in; I'm just choosing one).  The kick will be made with the back leg, which is the right leg.  After initiating a clockwise (as seen from above) turn with the body, one jumps up, fires a side kick with the right leg, and then immediately bends the right leg 90 degrees (making the "hook" in hook kick).  One should land in the same position in which one began, thus completing a full turn.

If what I just described seems challenging, it is!  While practicing the kick last week at Super Kicks, my instructor, Clifton Abercrombie, offered a tip for doing the kick better.  As soon as Mr Abercrombie said, "Pull your arms in tight to your body as you do the kick," the physics part of my mind said, "Well, duh!"  I had always practiced the jump spin hook kick by trying to increase my hang time and focusing on what my kicking leg was doing.  It never dawned on me to employ a basic concept from physics to help increase my rotation speed.  My "Well, duh!" moment came because I've taught angular momentum conservation more times than I can count!

Mr Abercrombie was kind enough to allow me to film him executing a spin hook kick and a jump spin hook kick, which happen to be the first two moves in our Universal 8 kata.  To illustrate how pulling one's arms in helps with the kicks, Mr Abercrombie performed the kicks first with his arms out, much as I had been doing as a karate novice, and then with his arms in, as a more seasoned martial artist will do.  The first video below shows "arms out."
Now look at the improvement as Mr Abercrombie performs the same kicks "arms in."
Mr Abercrombie leaves the mat at a little more than 4 mph and has a hang time of about 0.4 seconds.  While in the air, there is essentially zero torque about Mr Abercrombie's center of mass (air resistance provides some torque, but that's a small effect).  When there is no net external torque on an object, angular momentum is conserved.  This powerful law in physics not only helps us understand karate kicks, we use it when analyzing the interior of nuclei and the swirling of galaxies.  It's a powerful law!  When you see a figure skater going into her final spin, note that she has her arms and one leg extended far from her body.  Her initially slow spin gets faster and faster as she brings her arms in.  She reduces her moment of inertia as she pulls her mass closer to her rotation axis.  To maintain an essentially constant angular momentum, she has to spin faster as her moment of inertia decreases.

Now think about a jump spin hook kick.  A lot must happen in less than half a second!  Watch Mr Abercrombie perform the "arms out" kicks again.  Then watch the "arms in" again.  You should notice that he spins faster with "arms in."  Because he is spinning slower in the "arms out" case, he must hurry his kick, which leads to a bit more instability than in the "arms in" case.

To better see what is happening, check out the image below (click on the image for a larger view).
The image on the left shows the moment when Mr Abercrombie's right leg is straightened as if it were a side kick.  The image on the right shows the 90-degree bend in his right leg, which is the hook.  Note that his arms are out.

Now check out the "arms in" version of the above photos (click on the image for a larger view).
Note where Mr Abercrombie's side kick position is.  By pulling his arms in, he has rotated faster, meaning his straightened right leg has rotated farther ahead than in the "arms out" case.  Note, too, when he achieves the 90-degree leg bend how much more stable his body is compared to the "arms out" case.  By getting around quicker, Mr Abercrombie doesn't have to hurry the kick and risk instability.  To get a feeling for just how fast such a kick moves, the time interval between the two images above is just 0.133 seconds.  Pulling his lower leg 90 degrees translates to a rational speed in that brief time interval of about 113 rpm.  That's about a quarter the rotational speed of helicopter blades!  Because he was spinning faster in the "arms in" case compared to the "arms out" case, the "hook" part of his hook kick was about 20% faster.  That translates into more pain for the unlucky target!

I'll close with a look at the "arms in" case from the other direction.  The image below shows Mr Abercrombie landing after executing the "arms in" jump spin hook kick (click on the image for a larger view).
Many years of training and skill development go into what you see above.  Note his eyes are forward on the target he was just imagining hitting.  Note that his arms are in, but they are on the way out to help arrest his rotation and return him to a left-side fighting stance.  Note his perfectly vertical left leg during the landing, while his right leg is perfectly parallel to the floor.  I've got many years of work ahead of me before I could come close to that kind of skill.  At least now I've got a great physics tip to help me!

The Gorilla Sprints to Victory!

German André Greipel, nicknamed the Gorilla, won Stage 6 today with a thrilling sprint to the finish line.  The image below shows Greipel just edging out his closest competitors (click on the image for a larger view).
Below is Greipel's winning time and a comparison with our prediction.
  • Stage 6:  4h 11' 39" (actual), 4h 29' 39" (prediction), 18' 00" slow (7.15% error).
Greipel's average speed is given below.
  • Stage 6:  12.85 m/s (46.25 kph or 28.74 mph)
Why are we slow again?  We are slow for the same reason we were slow the past two stages:  tailwinds.  Cyclists traveled essentially southeast today.  Winds from the northwest to the southeast in the range 15 kph (9.3 mph) - 20 kph (12.4 mph) dominated the stage.  Check out the image below from early in the race (click on the image for a larger view).
Look at the flags!  The wind is blowing right in the direction of the stage's route.  I saw flags like those all through the stage while I watching the race online.  Below is another screen shot I took, this one near the end of the race (click on the image for a larger view).
The poor guy holding the French flag can barely hold it as the wind is blowing right in the direction the cyclists are moving.  Tailwinds have been a theme in the past three stages.  We aren't making excuses for bad predictions, but we are putting into context why we are slow.  We simply didn't have weather information before making predictions.  Had we averaged over all the winds, including the crosswinds near the end of the stage, and put in a 5 kph (3.1 mph) horizontal tailwind for the entire stage, we would have been just 22" fast.  In the future, we may have to guess weather conditions based on what we've learned about northern France.

Stage 7 is the second-longest stage in this year's Tour de France.  Cyclists will bike 234.5 km (145.7 mi) tomorrow.  Beginning in the commune of Épernay, riders will move mostly east for the first half of the stage, followed by an essentially southeast route toward the finish in the city of Nancy.  Sprinters need to get good times tomorrow before hills and mountains greet riders in the following three stages before the Tour de France has its first rest day on 15 July.  Below is our prediction for Stage 7.
  • Stage 7:  5h 27' 13" (prediction)
If you are watching tomorrow's action and note tailwinds, our prediction will likely be too slow.  We are hoping to see a stage without significant contributions from the wind!

09 July 2014

Rain and Crashes Mar Stage 5!

Today's Stage 5 was a mess.  The start of the race saw winds blowing from the northwest to the southeast at 30 kph (19 mph).  Because the stage took riders mostly due south, they had tailwind components for the majority of the stage.  Winds slowed a little as the stage wore on, but stayed at least 15 kph (9.3 mph) and in the 20 kph (12 mph) - 25 kph (16 mph) range over the last third of the stage.  When I saw the huge tailwinds, I knew our prediction would be too slow.

Winds helped riders, but they also had to contend with a lot of rain.  There was enough water on the roads that two of the nine cobblestone sections were deemed too dangerous and removed from the route.  The stage was 3 km (1.9 mi) shorter than it was supposed to be, and the entirety of the 3 km removed was cobblestone road.  Coupled with the tailwinds, losing 3 km of slow cobblestones meant that our prediction would be really slow.

The image below is one I cropped from my video feed.  It shows the first section of cobblestones (click on the image for a larger view).
Note how dangerous the edges of the road are.  I saw many crashes, and some riders almost got stuck in the muck.  The image below is one I cropped from the second cobblestone section.  It shows the seven lead riders at that time (click on the image for a larger view).
The most notable crash today was that of Christopher Froome, who won the Tour de France last year.  His second crash of the day cost him the rest of the Tour de France as he had to limp into a car and retire from the race.  That leaves Team Sky without a leader because Bradley Wiggins was left off the team.

Despite the terrible racing conditions, the lead riders were averaging about 48 kph (30 mph) after two hours in the saddle.  I knew the tailwinds helped a great deal, but I was still impressed riders could bike that fast in the rain.  The seven cobblestone sections slowed them down in the latter part of the race.

Lars Boom of Netherlands was spectacular today.  He navigated all the cobblestone sections flawlessly and was a tour de force at the stage's end.  He was pumping his pedals like crazy to make sure he would get the stage win.  The image below shows Boom crossing the finish line (click on the image for a larger view).
Note his muddy face.  Riders finished up today with mud all over their faces, clothing, and bikes.  Below is a comparison between Boom's time and our prediction.
  • Stage 5:  3h 18' 35" (actual), 3h 34' 03" (prediction), 15' 28" slow (7.79% error)
The tailwinds and 3 km less cobblestones killed our prediction, so I'm not terribly perturbed by the error given that we modeled a longer stage without wind!  At our average speed prediction, taking 3 km off removes just over 4' off our prediction.  Tacking on a continuous horizontal tailwind of 4 kph (2.5 mph) knocks another 12' off our prediction, which would have gotten us a lot closer to Boom's time.  If only we could know the weather ahead of time and know if a stage will be shortened!

Boom's average speed is given below.
  • Stage 5:  12.80 m/s (46.08 kph or 28.63 mph)
The tailwinds helped, but that's an amazing average speed with seven cobblestone sections.

Tomorrow's flat Stage 6 begins in the northern French city of Arras and then moves 194 km (120.5 mi) southeast to Reims.  There are a couple of category-4 climbs, but the stage has a flat finish.  Below is our prediction.
  • Stage 6:  4h 29' 39" (prediction)
We hope there aren't huge tailwinds and rain tomorrow!

08 July 2014

Kittel Blasts Our Time!

Marcel Kittel has done it again!  He's won three of the first four Tour de France stages.  Below is a comparison between Kittel's winning time and our prediction.
  • Stage 4:  3h 36' 39" (actual), 3h 49' 16" (prediction), 12' 37" slow (5.82% error)
A decade ago, I would have thought our error was fine.  Now, I think it's too large!  I was unable to watch any of the stage.  I did, however, see reports of 20 kph (12.4 mph) tailwinds in a few places and crosswinds in other places.  There appeared to be a tailwind component for much of the race.  Those who watched the race will surely let me know how much wind played a role in today's action.  Kittel's average speed is given below.
  • Stage 4:  12.578 m/s (45.28 kph or 28.14 mph)
That's a great speed, but not so large as to raise eyebrows.  To give you a feeling for just how sensitive times are to environmental conditions like wind, if we add a 4 kph (2.5 mph) horizontal tailwind to the entirety of Stage 4, we are slow by only 4".  That's all it takes!  We need to research the stage a little more to see if wind played a role or if Kittel was just flat-out amazing.  We know the latter is true!

Tomorrow's 155.5-km (96.6-mi) flat stage begins just across the border into Belgium in Ypres.  After a bit to the northeast, the stage mostly takes riders south, finishing in Arenberg Porte du Hainaut.  What makes Stage 5 so fun is that is has nine sections of cobblestones in the latter half of the stage.  Cobblestone roads make up a total of 15.4 km (9.57 mi) of the final 68.5 km (42.6 mi) of the ride into Arenberg Porte du Hainaut; that's more than 22% of that last 68.5 km.  We will be anxious to see how the cobblestones affect racing.  Below is our prediction.
  • Stage 5:  3h 34' 03" (prediction)
Despite winning three of the first four stages, Kittel sits in 147th place at 19' 50" behind Vincenzo Nibali's, whose great ride in Stage 2 keeps the yellow jersey on his back.

07 July 2014

Kittel Makes It Two Out Of Three!

German Marcel Kittel just beat out Peter Sagan in a great sprint to end Stage 3 of the Tour de France.  Jan Barta and Jean-Marc Bideau battled each other for the lead for much of the entry into London.  The peloton eventually ate Bideau and then consumed Barta with about 6 km (3.7 mi) left in the race.  The image below is what I cropped from my video feed as Kittel crossed the finish line (click on the image for a larger view).

Below is Kittel's winning time and a comparison with our prediction.
  • Stage 3:  3h 38' 30" (actual), 3h 33' 10" (prediction), 5' 20" fast (-2.44% error)
Rain began to fall in London, though it didn't seem to affect speeds too much.  There was a crash just behind the leaders with about 1.7 km (1.1 mi) left, but I couldn't see if rain played a role.  Below is Kittel's average speed.
  • Stage 3:  11.823 m/s (42.56 kph or 26.45 mph)
Cyclists bid farewell to England and cross the Channel for tomorrow's flat Stage 4, which begins in the commune of Le Touquet.  The 163.5-km (101.6-mi) stage has a couple of category-4 climbs as it takes riders east to the city of Lille, which sits near the French border with Belgium.  Below is our prediction.
  • Stage 4:  3h 49' 16" (prediction)
We were a bit fast during the three stages in the UK.  We'll see if cyclists pick it up a bit when they get to France.

06 July 2014

Nibali's Great Ride Into Sheffield!

Italy's Vincenzo Nibali was impressive in winning today's second stage of the Tour de France.  It seemed all of Yorkshire turned out to witness the world's most famous cycling event.  Despite a few problems with crowd interference, it was a perfect day for racing.  Jenkin Road proved to be a real test for riders as they neared the finish line.  The image below shows the moment when Nibali made his final push to stay in front for good (click on image for a larger view).
Nibali is in a teal color and is at the far left portion of the road at the right in the image.  This happened just 1.9 km (1.2 mi) from the finish line.  The image below is another crop I took from my video feed; it shows Nibali crossing the finish line (click on image for a larger view).
Below is Nibali's winning time and a comparison with our prediction.
  • Stage 2:  5h 08' 36" (actual), 5h 03' 00" (prediction), 5' 36" fast (-1.81% error)
We are definitely happy to be under 2% error!  Below is Nibali's average speed.
  • Stage 2:  10.856 m/s (39.08 kph or 24.28 mph)
It was a lot of fun watching today's stage.  I saw many familiar sites in the Peak District and in Sheffield.  Tomorrow's Stage 3 will see the last of England as riders commence the flat stage in Cambridge and finish in London.  Vincenzo Nibali will don the yellow jersey as the overall leader.  Below is our prediction.
  • Stage 3:  3h 33' 10" (prediction)
The 155-km (96.3-mi) is much flatter than what cyclists faced in the first two stages.  We were  a bit fast with our first two prediction.  We'll see if cyclists pick it up tomorrow and come in under our prediction.

05 July 2014

Kittel Takes Stage 1!

Marcel Kittel won the first stage of this year's Tour de France, finishing ahead of Peter Sagan.  Mark Cavendish crashed near the end of the stage, but managed to finish in obvious pain.  Below is Kittel's winning time and the comparison with our prediction.
  • Stage 1:  4h 44' 07" (actual), 4h 30' 23" (prediction), 13' 44" fast (-4.83% error)
I am surprised we were a bit fast, but I'm always glad to have the first stage prediction come in under 5%.  We never know what strategies teams will employ.  Despite being classified a flat stage, the category-4 climb and the two category-3 climbs seemed to take a bit out of the riders.  We'll see if they were just saving up for the rest of the race.

Kittel, who also won last year's first stage, won today's stage with an average speed a good bit behind where he was last year.
  • Stage 1:  11.175 m/s (40.23 kph or 25.00 mph)
Last year's opening stage was 22.5 km (14.0 mi) longer than this year's first stage, yet Kittel was able to achieve an average speed last year 7% greater than what he did today.  The two category-3 climbs must have held him back a little today.

Tomorrow's Stage 2 begins in the historic city of York and ends in Sheffield, which is where I lived for nearly a year during my last sabbatical.  It would be great to be there tomorrow!  There are nine categorized climbs in tomorrow's 201-km (125-mi) stage.  Cyclists will enjoy wonderful scenery in the Peak District.  Here is our prediction for tomorrow's hill stage:
  • Stage 2:  5h 03' 00" (prediction)
Sneaking in under five hours tomorrow will be tough!

A Great Luiz Free Kick!

Brazil erupted yesterday when David Luiz sent a free kick into the upper-right portion of the goal in the 69th minute to put Canarinho up 2-0 in its match against Columbia.  Check out the setup below (click on image for a larger view).
Luiz was roughly 34 yards (31 meters) from his target.  The overhead shot below shows that Luiz was slightly left of center on the pitch (click on image for a larger view).
With the Colombian wall set up to defend the left side of the goal (as seen by Luiz), Colombian goal keepr David Ospina is set up in the middle of the goal.  Given the placement of the defensive wall, I don't understand Ospina's placement.  With what's in front of him, Luiz will clearly aim for the upper-right part of the goal.  The image below shows Luiz from the front (click on image for a larger view).
Luiz has opened up his so as to direct the ball toward his right.  He's got a great lean when he plants his left boot.  His right boot will drive up through the ball, giving Brazuca a slight topspin.  The image below shows the kick from the back (click on image for a larger view).
You can easily see Luiz's open hip and the ball heading toward his right.  What is strange is the image of Ospina behind the wall.  Given that the ball took just 1.1 seconds to reach its target, any visual obstruction would have been costly to Ospina.  The image below shows that Luiz put the ball in exactly the right spot (click on image for a larger view).
Ospina got his left index finger on the ball, but it wasn't enough.  My model trajectory is shown below (click on image for a larger view).
Besides the trajectory shadow on the pitch, I show with the light black curve what the trajectory would have looked like without the little bit of topspin.  There were even some slight wobbles from knuckling effects.  Without those lovely aerodynamic influences, the ball would have just missed high.

I calculated a whopping 77 mph (124 kph) launch speed at a little more than 15 degrees off the pitch.  The ball had slowed to about 56 mph (89 kph) when it crossed the goal plane.  It was a powerful and accurate kick that justifiably put Brazil's fans into a frenzy!

04 July 2014

It's Tour de France Time!

The 101st Tour de France commences tomorrow in Leeds.  The first three stages of this year's big race will take place in the UK.  Tomorrow's 190.5-km (118.4-mi) flat stage heads north from Leeds, loops through Yorkshire Dales, and then south into Harrogate.

As I've done each of the past three years, I will put stage-winning time predictions on my blog.  One of my talented students, Chad Hobson, who just completed his first year at Lynchburg College, has been working with me this summer.  We've made what we hope are a few positive refinements to the model my research group has employed for more than a decade.  Science and technology continue to improve bike and helmet design, and cutting-edge training methods elevate the performances of the elite athletes who compete for the famed yellow jersey.  The latter part of last year's Tour de France left us stunned with never-before-seen speeds, all of which are described in our most recent paper on Tour de France modeling (click here for the paper that was published last month in the Journal of Sports Engineering and Technology).

Our goal is to predict the winning time for each stage.  We do not try to model a specific cyclist.  Based on published research on biker's power output, air drag, etc, we try to incorporate the dominant physics contributions in our model.  There is no way we can predict with any accuracy what the weather will be like on a given stage, if there will be crashes, or if teams' strategies dictate slowed or increased pace.  If we find a stage-winning time is much longer than our prediction, we aren't bothered much if it turns out there was lots of rain and a couple of crashes.  When our model ran slow in the latter part of last year's race, our curiosity was certainly piqued!

With all those qualifications out of the way, here is our prediction for this year's first stage:
  • Stage 1:  4h 30' 23" (prediction)
Who will don the yellow jersey after tomorrow's stage?  Given the location of the stage, I wouldn't bet against Mark Cavendish!

With the World Cup and the Tour de France now overlapping, it's a busy and fun time of year for me!  I hope to catch most of the action as two more countries will leave the World Cup today.  I'll also celebrate my country's 238th birthday while anxiously awaiting for tomorrow's start of cycling's biggest event.

01 July 2014

Congrats to Belgium

My country is now out of the World Cup after losing 2-1 to Belgium.  Congratulations to the Red Devils; they looked like the better team.  They just kept attacking and attacking until finally they broke through early in extra time.  Belgium would have scored a lot more had Tim Howard not played the game of his career.  He put on a clinic for how goalkeeping should be done.  His 16 saves set the World Cup record in the half century that that stat has been kept.  He was magnificent!

The goals by Kevin De Bruyne, who played a wonderful match, and Rmelu Lukaku were rife with top skill.  But I really love Julian Green's goal for the US.  He turned 19 just 25 days ago.  The image below shows his first World Cup touch (click on the image for a larger view).
Michael Bradley sent in a perfect through ball from 39 yards (36 m) out and Green nailed it with his swinging right leg from about 10 yards (9 m) out.  The ball had plenty of backspin to help its upward trajectory toward the right side of the goal.  It was a beautiful play from a player US soccer fans will surely get to know better in the future.

All eight group winners won their opening games in the knockout stage.  There have been some great matches so far!  Congrats to the US for making the knockout stage and providing fans like me with lots of thrills.  Congrats to Belgium for enduring a record-setting goal keeping performance and earning the win.

26 June 2014

Vandy Wins College World Series!!!

My beloved alma mater, Vanderbilt University, just won the College World Series!  It's Vandy's first men's national title, and it's the first time I've seen one of my two schools win a national title since they became my schools (my graduate school is Indiana University).  My four years at Vandy were 1988-92, which means I graduated from Vandy just over 22 years ago.  What's great about one's school is that it's with you for life.  I've seen my two schools win big games, and I've seen them lose in heartbreaking fashion.  Tonight is the first time I've seen one of them end a sport's season on top.  What a great feeling!

Kudos to Virginia for a great season.  They are an admirable national runner-up.  We hung on to win tonight's third and deciding game, 3-2.  We needed great pitching and a timely home run, which was rare in this College World Series.

Well done, Vandy!

25 June 2014

Messi's Incredible Free Kick

No matter how many times I've seen Lionel Messi play the beautiful game, I always see something special each time.  To end the first half against Nigeria today, Messi delivered a perfect free kick.  It was his second goal of the game and fourth of this World Cup.  The image below shows one view of the initial setup (click on the image for a larger view).
Messi is just about to connect.  He is about 27 yards (24.7 meters) perpendicular distance from the goal line.  The image below shows a good look at the defensive wall (click on the image for a larger view).
Messi launched the ball off his left boot with a speed of 55.4 mph (89.1 kph) and launch angle of 18.5 degrees.  Note that the Nigerian goal keeper is left of center in the goal (as seen by Messi).  The goal keeper's initial position was critical because Messi imparted a great deal of clockwise spin (as seen from above) on the ball.  His target was well away from the goal keeper!  The image below shows Messi introducing his left boot to Brazuca (click on the image for a larger view).
Note how his foot is left of center on the ball so that he can drive his boot through, thereby torquing the ball.  Note, too, the lean in his legs.  He has moved his rotation radius so as to increase his boot's distance from that axis.  The pitch provides the counter-torque to keep Messi stable because his right boot pushes to his left, which means the pitch pushes on his boot to his right.  The torque from the pitch nearly balances the torque from his weight; balance is further aided by his arm movements.

It took the ball just 1.2 seconds to reach its target.  The image below shows a three-dimensional trajectory (click on the image for a larger view).
The red curve is the real trajectory; the red dashed curve is the shadow on the pitch.  The thin black curve is what the kick would have looked like with no spin and no knuckling (black dashed curve is the shadow of that kick).  Now you see why the kick was perfect!  Messi used the Magnus effect to curl the ball into the upper-right portion of the goal.

The ball crossed the goal plane at 42.0 mph (67.6 kph).  Had the ball not been spinning, it would have crossed the goal plane about 10.8 feet (3.28 meters) left of where it actually crossed the goal plane.  The goal keeper would have surely blocked the kick.

Once again, Messi has dazzled the soccer world!

Penalty Kick Sends Greece to Knockout Stage!

In the 93rd minute of yesterday's deadlocked match between Greece and Ivory Coast, Giorgos Samaras sent a penalty kick into the back of the net, which put Piratiko into the knockout stage.  It's the first time in that stage for Greece, a comment that could have been made for Ivory Coast had the Samaras kick been just a few inches off its trajectory.

The image below shows Samaras as he starts his motion toward the ball.  Ivory Coast goal keeper Boubacar Barry is waiting at the center of the goal.  Click on the image for a larger view.
It will take Samaras about 1.46 seconds to reach the ball from the image you see above.  Barry, like all goal keepers, will have to rely on scouting reports, Samaras's body language, and a good bit of luck if he is to block the kick.  After nearly 0.46 seconds, Barry is seen in the video initiating his lean to his left (right for Samaras).  After another 0.58 seconds, Barry is clearly moving toward his left, either guessing the direction of the kick or seeing something in Samaras's body language, such as an open hip.  Almost 0.42 seconds after that, Samaras kicks the ball.  The image below shows Samaras's right boot just making contact with the ball (click on the image for a larger view).
You can clearly see that just as boot meets ball, Barry has committed to blocking a shot he believes will be down and left of him.  Notice how low to the pitch he is before the ball has even left Samaras's boot!  He has also moved forward so as to reduce the projected area of the goal as seen by the ball at the kick point.  The image below shows another view of Barry just before the kick (click on the image for a larger view).
You can once again see how committed Barry is to blocking down and to his left (down and to Samaras's right).  The ball took only 0.375 seconds to reach the goal plane, so don't blame goal keepers for committing to a guess just as the ball is kicked.  The goal area is (24 feet) x (8 feet) = 192 square feet (17.8 square meters).  Throughout the 0.375 seconds the ball took to reach the goal plane, Barry probably blocked a total of around 9% of the projected area, though that percentage drops to no more than 5% or so once the ball reaches Barry.

Barry just missed getting the block!  Check out the image below (click on the image for a larger view).
Greece's ticket to the knockout stage is mere inches from Barry's fingers.  The next image shows that the cropped video I took can't distinguish Barry's glove from the ball (click on the image for a larger view).
The final image I show below is a closer look from the back of the goal (click on the image for a larger view).
Look how close that ball is to being blocked!  That is the difference between moving on to the knockout stage (Greece) and heading home (Ivory Coast).  There is no way Ivory Coast wanted anyone else defending that kick.  It is interesting to note, though, that Barry is listed at 5 feet 10 inches (1.80 meters) tall.  The backup goal keeper for Ivory Coast, Mandé Sayouba, is listed at 6 feet 3 inches (1.93 meters) tall.  Ivory Coast had already made three substitutions when the decisive penalty kick was taken.

Of course I had to model the trajectory of the ball.  The image below shows the three-dimensional trajectory with the goal plane shown as a rectangle (click on the image for a larger view).
I show the trajectory shadow on the pitch, plus the no-spin trajectory and shadow.  The ball had slight counterclockwise spin (as seen from above), and thus curved very slightly toward Barry.  Brazuca was launched 7 degrees off the pitch at 71.0 mph (114 kph).  The ball had only slowed to 63.1 mph (101.5 kph) when it passed the goal plane.  At that launch speed, the drag force on the ball is the same as the ball's weight!

Congratulations to Greece for making the knockout stage!