Marcel Kittel won his fourth stage of this year's Tour de France with a great sprint to the finish line. The image below shows Kittel just ahead of Alexander Kristoff (click on the image for a larger view).
With Tony Martin's two stage wins and a stage win for AndréGreipel, German cyclists won 7 of the 21 stages. Below is Kittel's winning time and a comparison with our prediction.
We'll take that error on such a hard stage to predict! Kittel's average speed is given below.
Stage 21: 11.41 m/s (41.08 kph or 25.53 mph)
Cyclists hit speeds around 63 kph (39 mph) a few times on the streets of Paris. That's faster than they would drive on those streets! Seeing the cyclists loop around Paris made me want to return there for another visit.
The man of the hour is of course Vincenzo Nibali, winner of the 101st Tour de France. There were times when he simply looked on a different plane of athleticism compared to his competitors. I grabbed a screenshot as Nibali crossed the finish line (click on the image for a larger view).
I also grabbed an image of Niabli on the podium with Péraud and Pinot and the Arc de Triomphe in the background (click on the image for a larger view).
Nibali was the only cyclist to finish the entire Tour de France under 90 hours. His winning time was 89h 59' 06". With the 3 km removed from Stage 5 because of two dangerous cobblestone sections, the total distance biked came to 3660.5 km (2274.5 mi). That gives Nibali an average speed of 11.30 m/s (40.68 kph or 25.28 mph).
It was a great Tour de France! Stages were well planned, and there was plenty of cycling variety. Kudos to Ji Cheng, the first Chinese cyclist to compete in the Tour de France. There were 164 cyclists who finished this year's Tour de France, and Cheng came in last. But, he did what 34 cyclists who finished Stage 1 could not do; he finished the entire race. He may have been just over six hours behind Nibali, but he will surely return to China amidst cheers. Tour de France athletes are as good as it gets. I couldn't even finish a single stage of the Tour de France, much less come close to what Ji Cheng did in July. Congratulations to all those who finished!
My research student, Chad Hobson, helped make modeling this year's race a lot of fun. We are happy with the improvements we made to our model. Except for Stages 4, 5, and 6, where massive tailwinds made our predictions too slow (the rain-soaked and shortened Stage 5 at 7.79% was our worst error), all of our predictions came in under 5%, including five stages under 1%. Predicting stage-winning times isn't easy!
There was only one cyclist I was interested in watching today: Tony Martin. He was a veritable machine on his bike in the individual time trail with his powerful legs and strong core moving him along French roads faster than anyone else. Below is a comparison between Martin's time and our prediction.
Just ONE cyclist beat our prediction today! Throw out Martin's time and we miss the second-place time by only FIVE SECONDS. But, we can't do that! We'll take our error because watching Martin was watching time-trial cycling at its best. The image below shows Martin at the start and at the finish (click on the image for a larger view).
Note that Martin wore the distinctive rainbow jersey that signifies that he is the racing world champion. I snagged a few more images of Martin in today's race. The two below show his aerodynamic bike, streamlined helmet, and powerful body (click on the image for a larger view).
I love the rainbow-colored back wheel! The image below shows Martin on a downhill (click on the image for a larger view).
Note how he is off the saddle and compressed. He minimized his frontal area so as to reduce air drag. You simply won't find better time-trial technique! Below is Martin's impressive average speed.
Stage 20: 13.56 m/s (48.83 kph or 30.34 mph)
The 2014 Tour de France comes to a close tomorrow with a 137.5-km (85.44-mi) flat stage that will be mostly ceremonial. Beginning in the commune of Évry, the stage finishes on the famous Champs-Élysées in Paris. Below is our prediction.
Stage 21: 3h 17' 50" (prediction)
Vincenzo Nibali has this year's race wrapped up. He came in fourth today and extended his overall lead to nearly eight minutes. Italy will celebrate a Tour de France champion, but France will have lots to celebrate tomorrow as well. Jean-Christophe Péraud at 37 years old will take second place, and fellow Frenchman and white-jersey wearing 24-year-old Thibaut Pinot will be in third place. Pinot won Stage 8 in the 2012 Tour de France. He may be one of the favorites to win it all next year.
Lithuanian Ramūnas Navardauskas led the field the entire way through the rain-soaked finish in Bergerac. He held off a ferocious sprint in the final kilometer to take the stage by seven seconds. I grabbed the image below as Navardauskas crossed the finish line (click on the image for a larger view).
Though it rained for much of the stage, speeds were not affected much. As cyclists neared Bergerac, they were navigating some fairly narrow roads at speeds reported to be as high as 64 kph (40 mph). That's pretty fast on wet roads! Earlier in the race, there were crosswinds and tailwinds reaching 25 kph (16 mph). Winds and rain thus canceled each other a bit in this stage. Below is a comparison between our prediction and Navardauskas's winning time.
That makes five stages for us with an error under 1%. Navardauskas's average speed is given below.
Stage 19: 12.25 m/s (44.10 kph or 27.40 mph)
Given all the rain and wind, that's a great average speed! Navardauskas was lucky to have missed a crash that happened just inside the magic 3-km (1.9-mi) mark. The image below shows the crash (click on the image for a larger view).
Because the crash happened inside 3 km, riders did not lose much time, even if they could no longer compete for the stage win.
Tomorrow's Stage 20 picks up in Bergerac. The stage is the only time trial in this year's Tour de France. Moving north by northeast, the individual time trial finishes 54 km (33.6 mi) away in the commune of Périgueux. Our prediction is given below.
Vincenzo Nibali essentially won the 2014 Tour de France today with a dominating performance in the race's final mountain stage. The image below shows the moment with 8 km (5 mi) left when The Shark decided to chomp all his competition by zooming past Team Sky's Mikel Nieve Iturralde (click on the image for a larger view).
Nibali finished more than a minute ahead of the rest of the field in winning today's stage, his fourth stage win in this year's Tour de France. The image below shows Niabli crossing the finish line with the look of a man who knows he'll be on the podium in Paris on Sunday (click on the image for a larger view).
Below is a comparison between Nibali's winning time and our prediction.
Just 24 riders out of 164 (14.6%) beat our time, so we feel like we did well with this stage. Nibali's average speed is given below.
Stage 18: 9.927 m/s (35.74 kph or 22.21 mph)
Nibali now has an incredible 07' 10" lead over France's Thibaut Pinot, who, with fellow Frenchman Jean-Christophe Péraud, leapfrogged over Spain's Alejandro Valverde Belmonte, who had been in second since Stage 13. Tomorrow's Stage 19 is a 208.5-km (129.6-mi) flat stage that begins in Maubourguet Pays du Val d'Adour, and takes riders north away from the Pyrenees to the finish in the commune of Bergerac. Below is our prediction.
Stage 19: 4h 46' 18" (prediction)
Of most interest in tomorrow's stage is the fight for the spots behind Nibali. Cyclists will jockey for position so that they will be able to make their move in Saturday's individual time trial.
Rafał Majka has now done what no other Polish cyclist has done -- win two Tour de France stages. He earned his polka dot jersey today by besting all his competitors up the grueling final climb. The image below shows Majka crossing the finish line and picking up 50 climbing points in the process (click on the image for a larger view).
We did much better predicting Majka's second stage win than we did when he won Stage 14 last Saturday, as the comparison below demonstrates.
I continue to be impressed by the vistas in the Pyrenees. The Tour de France is doing a great job making me want to visit southern France! I snapped the image below from my video feed (click on the image for a larger view).
Not a bad place to end a Tour de France stage, huh? Tomorrow's 145.5-km (90.41-mi) is this year's final mountain stage. Cyclists begin in the commune of Pau and face the hors catégorie climb to the 2115-m (6939-ft) peak of Col du Tourmalet just a little past the stage's halfway point. For the second day in a row, riders will have to contend with an hors catégorie climb to finish the stage. The ski resort of Hautacam sits at the end of Stage 18 at an elevation of 1520 m (4987 ft). Below is our prediction.
Stage 18: 4h 09' 45" (prediction)
After the monster climb in the middle, how much will riders have left for the demanding climb at the end?
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.
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?
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!
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.
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.
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.
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!
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.
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?
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.
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!
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.
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!
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!
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.
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.
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, AndréSchürrle 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.
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.
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.
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.
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!
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.
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!
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!
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.
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 ofÉpernay, 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!
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.
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!
