Energy and Power Numbers at the Gym

I spent a few more minutes on the elliptical at Ponds Forge this morning compared to my normal workout.  When I was finished, I snapped a photo of the screen, shown below.

I have written about numbers seen on gym equipment before (click here), but I thought I would revisit the topic.  The power reading was dropping precipitously after I stepped off the pedals.  I had burned 684 Calories.  Note that 1 "big C" calorie is the same as 1 kilocalorie, which is 1000 "little c" calories.  Food calories are always in terms of "big C" calories.

To find average power, I need only divide energy output by exercise time.  I will find the time in seconds first.

\[T=(80\,\mbox{min})\,\left(\frac{60\,\mbox{s}}{1\,\mbox{min}}\right)+4\,\mbox{s}=4804\,\mbox{s}\,.\]

Now find the energy output in joules.

\[E=(684\,\mbox{Calories})\,\left(\frac{4184\,\mbox{J}}{1\,\mbox{Calorie}}\right)=2,861,856\,\mbox{J}\,.\]

Sorry about all the digits!  I will truncate soon.  Now get my power output.

\[P=\frac{E}{T}=\frac{2,861,856\,\mbox{J}}{4804\,\mbox{s}}\simeq 596\,\mbox{W}\,.\]

That looks like an impressive power output, right?  After I stopped the machine, I saw the screen below.

Ignoring the extra second on the clock, that page told me that my average power output was 98 W.  Why such a difference in powers?

The answer lies in the thermodynamic inefficiencies associated with energy conversions in the body.  The laws of thermodynamics tell us not only that we cannot get more energy out than what we put in, we cannot even break even.  The glorious second law of thermodynamics tells us, in a hand-wavy way, that there is always waste energy in the workings of a motor.  My body's efficiency may be found as follows.

\[\eta = \frac{P_{output}}{P_{internal}} \cdot 100\% \simeq \left(\frac{98\,\mbox{W}}{596\,\mbox{W}}\right)\,(100\%) \simeq 16.5\%\,.\]

I have added subscripts to the powers.  My output power was not quite that of a 100-W lightbulb.  If you have never tried to keep a 100-W lightbulb on while biking on a stationary bike, you should try it one day.  It is not as easy as it might seem!  But for me to output power at the rate of 100 W, I need to consume food energy in my body at a rate nearly six times what I am able to output.  The waste energy is why I feel hot while working out.  I have estimated Tour de France cyclists' body efficiency to be 20% in my past work.  That is certainly in the ballpark with what I found above.

The MOVEs number is a bit less well defined.  Technogym, who made the elliptical I used, defines MOVEs as "... the ultimate unit of measurement to objectively assess your lifestyle based on the movement and exercise you do and regardless of your gender, age or level."  Technogym gives some examples, such as 50 MOVEs for taking five flights of stairs, 200 MOVEs for a half-hour walk, and 400 MOVEs for a half-hour run.  Technogym further defines Movergy as "... an index of how active your lifestyle is and represents the average of your daily MOVEs over a 14-day period."  If your Movergy is below 500, you are sedentary.  If your Movergy is above 750, you are moderately active.  And if your Movergy is above 1000, you are considered active.  I am thus happy with my 1629 MOVEs!

Do take numbers on gym machines with a grain of salt.  The machine I used had no idea of my gender, age, height, weight, level of fitness, and so on.  I suspect that a human average efficiency of one-sixth is used to compute energy burned.

So Long, Pete Rose

Just after waking up this morning, my wife told me that Pete Rose had died.  I confessed to her when we left our Sheffield house for the gym that the news she passed on to me was quite a gut shot.  I have written and spoken too many times to count about my love of baseball.  Growing up in West Virginia meant living in a state without a professional baseball team.  I thus followed the Baltimore Orioles, the Pittsburgh Pirates, the Philadelphia Phillies, and, of course, the Cincinnati Reds.

I wrote a '5' on my glove because I was enthralled by the way Brooks Robinson played third base.  But the team I rooted for while growing up in the '70s was baseball's first team, the Reds.  Rooting for the Reds in the '70s meant rooting for one of the greatest assemblages of talent on a single team.  The little kid I once was listened to Marty Brennaman and Joe Nuxhall ("the old left-hander, rounding third and heading for home") on the radio at night as names like Bench, Morgan, Concepción, Pérez, Foster, Gerónimo, Griffey, and Rose became larger than life for me.  Long before the internet, newspaper box scores and backs of baseball cards became the sources of numbers for my fertile brain.  Many of the numbers associated with the players I listed above still dance in my mind.

Books on baseball were how I learned baseball's history.  The story of Pete Rose crashing into Ray Fosse to win the 1970 All-Star game in Cincinnati's Riverfront Stadium was familiar to me as a five-year-old baseball junkie.  But that famous play happened 53 days before I was born.  I once looked up that Pete Rose went 2 for 5 on the day I was born.  He would have been 29 years old then.  Despite his age in 1970, Pete Rose had more than 2500 hits to get, a third batting title to win, an MVP to capture, and three World Series rings to earn.  I was jumping for joy when the Reds won the 1975 World Series, but I recall to this day being told by my dad that I had to turn in before extra innings began for the 6th game.  I missed Fisk's home run, but I stayed up to watch the Reds win the thrilling game 7.

I am far back on the list of people who have made the following observation.  Pete Rose fought, clawed, and scratched to win baseball games.  I admired his grit and determination to no end.  A moment in a department store in the summer of 1978 is one I still recall.  I was not interested in shopping with my family.  The televisions drew my attention.  I wanted to see if Pete Rose could keep the streak going.  He hit one of his trademark line drives for a double and I knew the streak was still alive.  Later that summer, I watched on television as Gene Garber, whose sidearm delivery I occasionally mimicked when I pitched in Little League, got Rose to chase an off-speed pitch to end the game and the streak.

Though I was sad to see Pete Rose leave Cincinnati before the 1979 season, I was happy that he was still close in Philadelphia.  He would get 208 hits that year, his last season of at least 200 hits.  I rooted for the Phillies in the 1980 World Series, and I can still see Pete Rose grabbing the ball that Bob Boone muffed near the Phillies dugout.  Rose looked so happy, especially when he bounced the ball on the turf.

Not long after my 15th birthday, Pete Rose passed Ty Cobb.  At that time, Rose was a lock for the Hall of Fame and a glorious post-baseball life.  But just before I turned 19, Rose accepted the permanent ban.  Maybe I had a "Say it ain't so, Pete!" moment that summer of 1989, echoing an apocryphal statement to another one of baseball's permanently banned greats.

It is wise not to turn people into heroes.  Disappointment is almost always the result of doing so.  To this day, I admired the way Pete Rose played baseball.  He inspired me at an incredibly early age.  He was far from being the most physically gifted player of his era.  But he used a grit and determination unlike any player I have ever observed to become a baseball great.  How did that observation manifest itself into my own life?  Growing up lower middle class in West Virginia meant that I had to work hard just to figure out how to get on the academic path I grew to desire.  I loved Rose's example of simply outworking everyone around him so that he could succeed despite any obstacles facing him at the start of his journey.

I repeat that it is wise not to turn intrinsically flawed human beings into heroes.  For me, I could admire and be inspired by the absolute best of a person like Pete Rose even if the very worst of him disgusted me.  Lying was among his vices, and that is one vice I cannot abide.  Pete Rose spent the last 38 years of his life, nearly half of it, answering questions about gambling and the Hall of Fame.  Being a Hall of Fame pariah for all those years probably brought him more fame and notoriety than if he had been inducted in the early '90s.  His gambling vice is now embraced by sports organizations that have enjoyed the money that has rolled in since sidling up to legalized betting.

On the day after he died, I thank Pete Rose for all the wonderful baseball memories.  I thank him for being an astonishing example of how hard work can pay off.  So long, Pete Rose.  You were not my hero, but I sure did admire the best of you.

Learning from Bob Knight

Bob Knight died yesterday (Wednesday, 1 November 2023) at the age of 83.  I love the irony of Coach Knight dying on All Saints' Day.  I learned a long time ago that having heroes is not a good idea.  Nobody is perfect and hero worship inevitably leads to disappointment.  Bob Knight was thus not someone I viewed as a hero, but I definitely admired him.  Though I never had the pleasure of meeting Coach Knight, he did have an influence on me in the role he most thought of himself, that of a teacher.

Webster defines gestalt as "something that is made of many parts and yet is somehow more than or different from the combination of its parts."  The philosophical adage most associated with that idea is that the whole is greater than the sum of its parts.  That was the feeling I had watching Bob Knight's Indiana teams in the 1980s.  At just five-and-a-half years old, I was too young to have memories of his famous 1976 undefeated team.  And I was too into baseball in the late 1970s to pay much attention to college basketball.  But I was part of the growing NBA fan base when Larry Bird and Magic Johnson took basketball to new heights after they left college following their epic national title battle in 1979.  My growing interest in basketball took me to college basketball.  Watching Bob Knight's teams made me realize that a brilliant mind could take rather average talent to extraordinary heights.  The beautiful basketball I watched Indiana play was the result of a team executing better than the sum of its parts.

How did Coach Knight do it?  Over the past couple of decades, I have seen hours of video of Coach Knight discussing his coaching methods, including videos of some of his practices.  Of all that I learned from him about basketball, the one gem I have assimilated into my own teaching is that learning and improving often arises when one feels stress.  Think about how we learn something.  Set aside all of the glorious neurophysiology and consider the following two options.  We are either ignorant of something, which means we have a hole to fill in our brains, or we are wrong about something, which means we have to correct something incorrect in our brains.  I have struggled for years to come up with a better or more simplified way to explain how we learn, but the aforementioned sentence is my best effort to date.  Now consider what many of us feel uncomfortable about admitting.  Who likes to admit to being ignorant or being wrong?  Doing so make us uncomfortable; doing so makes us feel stress.

I could not achieve success as a scientist if I had difficulty admitting I was ignorant or wrong.  I can recall times in my life when I was flooded with great joy when I realized I was wrong about something.  That joy came from learning something new, from discovery.  Not having an accurate understanding of the natural world is more uncomfortable to me than admitting I do not know something or admitting that I am wrong.  Stress over being ignorant or wrong is no longer what pushes me to improvement; my love of learning that came from early days of stress is now what motivates me.

Coach Knight would often say that he wanted his practices to be much harder and more demanding than what his players experienced in games.  I feel the same way about my own teaching.  I want to lay a gauntlet before my students, see them pick it up, and then push themselves to be better than they ever thought they could be.  Coach Knight's practices involved repetition and growing from failure.  Nobody wakes up one day never having played the piano, sits down at a Bösendorfer Opus, and plays one of Chopin's Mazurkas.  And no athlete steps on a basketball court for the first time and drains three-pointer after three-pointer.  Coach Knight also said, "The key is not the 'will to win'...everybody has that.  It is the will to prepare to win that is important."  Athletes must be put in stressful conditions, similar to the old "no pain, no gain" idea, to improve performance.  Students must also be put in stressful conditions.  An enormous amount of preparation that includes frustration, failure, stumbling, inching forward, and gradual understanding must occur before exam success and before career success.   Once a kid says, "Hey, I don't know something and I'm going to work my butt off while failing many times before I really understand what I don't currently know," my work is done.  That student is ready to do good science.  I've seen it happen with many of my students, and it's wonderful to behold.

My fingers could dance across the keyboard for several more hours if I really wanted to discuss all that sits in my head on the topic of Bob Knight.  For now, I will close this blog post with a note of thanks.  Thank you, Coach Knight, for all the memories I have of sitting in Assembly Hall while in graduate school and watching your teams play the best team basketball that I have ever seen as you patrolled the sideline.  And thank you most especially for the lessons you passed on to me about what it takes to learn and improve, be it athletically or mentally.

Jordi Meeus Wins Photo Finish and Jonas Vingegaard Makes it Two in a Row!

Jordi Meeus just barely kept Jasper Philipsen from a fifth stage win in this year's Tour de France.  Meeus lunged his bicycle across the finish line and won by the width of his front tire.

Meeus in on the right in the above screen capture; Philipsen is on the left.  Speeds were quite slow at the start.  It's always hit or miss on this stage, and we missed a little today.

• Stage 21:  2h 56' 13" (actual), 2h 45' 23" (prediction), 10' 50" fast (-6.15% error)

After several years with the average speed well over 40 kph (25 mph) on the final stage, last year and this year have been much slower.  Check out the winner's average speed.

• Stage 21:  10.89 m/s (39.19 kph or 24.35 mph)

If the past two years turn into a trend, we'll have to dial our power down just a hair!  I don't like our error, but the last stage is probably the hardest to predict.  I don't have a line in my code for drinking champagne!

Jonas Vingegaard now has two straight Tour de France general classification wins.  He and Tadej Pogačar were a joy to watch this year.  Unfortunately for Pogačar, Stages 16 and 17 were his undoing.  But there is absolutely nothing wrong with being the second best Tour de France cyclist!

Joining Vingegaard and Pogačar on the podium was Pogačar's teammate and third-place finisher Adam Yates.  It will be fascinating to see if either Vingegaard or Pogačar gets the hat trick next year.  The race won't end in Paris because of the Summer Olympics.  Look for the final stage of next year's Tour de France in Nice next year!

Pogačar Outsprints Vingegaard to Win Stage 20!

Tadej Pogačar won his second stage in this year's Tour de France by outsprinting Jonas Vingegaard in the final hundred meters.  It was great watching Pogačar and Vingegaard ride together through the difficult mountain stage.  And it was wonderful seeing Pogačar get the stage win as a nice consolation to finishing second in the GC.  Pogačar certainly looked thrilled crossing the finish line.

Besides being happy with the penultimate stage action, I'm quite happy with a near-perfect prediction today.

• Stage 20:  3h 27' 18" (actual), 3h 27' 04" (prediction), 00' 14" fast (-0.11% error)

My model seemed to be firing on all cylinders today.  Check out Pogačar's average speed.

• Stage 20:  10.73 m/s (38.64 kph or 24.01 mph)

Tomorrow's ceremonial 115.1-km (71.52-mi) flat stage begins in Saint-Quentin-en-Yvelines and takes riders east into Paris and onto the famed Champs-Élysées.  It will be a day to celebrate Jonas Vingegaard winning his second straight Tour de France.  And it will be a day to see which sprinter earns the famed Parisian stage win.  Our prediction is given below.

• Stage 21:  2h 45' 23" (prediction)

Hard to believe the Tour de France finish is already upon us!

Matej Mohorič Wins Photo Finish!

For the second stage in a row, the breakaway held off the chasers and peloton.  But unlike yesterday, the GC contenders and the rest of the peloton were well behind the finish line when the winner was determined.  I thought Kasper Asgreen was going to get his second straight stage win, but it was Matej Mohorič who just threw his bike at the line for the emotional win.  The screen capture I grabbed will not convince you that Mohorič (on the right) won!

Racing was furious today.  The cyclists began so fast that I wanted to lop 10 minutes off my prediction before they got very far!  My model did a great job modeling the peloton today, but the breakaway and chasers were simply flying during the latter half of the stage.

• Stage 19:  3h 31' 02" (actual), 3h 48' 20" (prediction), 17' 18" slow (8.20% error)

Not doubt about it -- a terrible prediction.  Before additional comments, check out the winner's average speed.

• Stage 19:  13.65 m/s (49.13 kph or 30.53 mph)

I can hardly believe that average speed.  The Tour de France organizers thought the maximum average speed would be 47 kph (29 mph).  The above is, by far, the largest average speed for a stage win this year.  It's simply impossible to know how to program that kind of breakout strategy into my code.  But it's sure fun to watch the fast racing!

Tomorrow's 133.5-km (82.95-mi) mountain stage is the penultimate stage of this year's Tour de France.  It will be a battle for position within the top 10 of the GC.  Riders begin in Belfort and head north to Le Markstein.  Six category climbs will tax cyclists, especially the final two category-1 climbs.  I hope all the sprinters can beat the broom wagon!  Our prediction is given below.

• Stage 20:  3h 27' 04" (prediction)

I sure hope we do better tomorrow.  We could be slow again on a short stage, or the mountains could tame the GC contenders, meaning they'll not go all out for fear of cracking at the end.  It will be interesting to see who rides for glory and who tries to stay safe.

Kasper Asgreen Leads Breakaway to Victory!

Kasper Asgreen lead the four-man breakaway all the way to the finish line in today's thrilling Tour de France stage.  The Danish cyclist got his first stage win at the Tour de France.  As fun as it is too see a massive sprint from the peloton, I was rooting hard for the breakaway to beat the peloton.  It almost didn't happen as the peloton was closing fast in the final few meters, as you can see in the screen capture I grabbed.

Our prediction did quite well today, though there was no way we could have predicted that the breakaway would hold throughout the entire stage.

• Stage 18:  4h 06' 48" (actual), 4h 00' 10" (prediction), 06' 38" fast (-2.69% error)

Check out Asgreen's average speed.

• Stage 18:  12.49 m/s (44.95 kph or 27.93 mph)

The pace was slow at the start, but really kicked up as the peloton realized it would have to fight to catch the breakaway.

Sprinters will be happy that they get another chance to shine tomorrow.  Stage 19 is a 172.8-km (107.4-mi) flat stage that begins in the commune of Moirans-en-Montagne, not too far from Switzerland.  They will head north to the finish line in Poligny.  There is a category-4 climb and a category-3 climb, but the flat classification is probably deserved.  Our prediction is given below.

• Stage 19:  3h 48' 20" (prediction)

I hope our prediction for the final non-ceremonial flat stage does as well as we did on Stages 7 and 11 and not like how we fared on Stages 3 and 4!

Felix Gall Wins BRUTAL Stage!

On a very hot day with slow speeds, Felix Gall held off pursuers and took today's grueling mountain stage.  That final climb cracked one rider after another, including a very famous rider, as I'll get to in a moment.  Cyclists looked utterly drained after they crossed the finish line.

The heat and slower pace made our prediction a bit fast today.

• Stage 17:  4h 49' 08" (actual), 4h 35' 19" (prediction), 13' 49" fast (-4.78% error)

I don't like the error, but I'll offer a hint at how sensitive cyclist power output is to the stage-winning time.  I would have needed about 2% less power on my model cyclist to match today's winning time.  That's all it takes on a mountain stage to go from a perfect prediction to one that is almost 5% off!  Check out Gall's average speed.

• Stage 17:  9.55 m/s (34.39 kph or 21.37 mph)

I don't care how fast we were with our prediction, that average speed is impressive on such a challenging stage!

Tadej Pogačar cracked with about 15 km (9.3 mi) left in the stage.  He looked completely done.  Jonas Vingegaard looks to have wrapped up the general classification with a 07' 35" lead on Pogačar.  I'll always remember yesterday's time trial as the stage when Vingegaard smashed the Tour de France.  I'll always remember today's stage as the stage when Pogačar's dream of catching Vingegaard was smashed.

A 184.9-km (114.9-mi) medium-mountain stage awaits cyclists tomorrow.  They begin in the French commune of Moûtiers and head northwest to Bourg-en-Bresse.  There are only a couple of short category-4 climbs, so the stage might be closer to flat than medium-mountain.  Either way, it will be interesting to see if the sprinters get a chance to go for the stage win.  Our prediction is given below.

• Stage 18:  4h 00' 10" (prediction)

Speeds will hopefully be high as the Tour de France heads towards Sunday's Parisian finish.

Jonas Vingegaard SMASHES Time Trial -- and Tour de France!

Jonas Vingegaard completely smashed his competition in today's time trial.  Tadej Pogačar may regret his bike change.  He came in second today, but Vingegaard blew Pogačar's time away and won by 01' 38".  Vingegaard now has an overall lead of 01' 48" on Pogačar.  Is the Tour de France over???

Our prediction was too fast today.  I realized this morning that terrain data associated with the category-2 climb was a bit off.  That's all on me!  I would have to admit that even if we nailed today's winning time.

• Stage 16:  32' 36" (actual), 30' 22" (prediction), 02' 14" fast (-6.85% error)

I'll have to look at Stage 16 again when the race is over.  That's always when the real science begins!  In the meantime, I'll marvel at what Vingegaard did today, and I'll marvel at his average speed.

• Stage 16:  11.45 m/s (41.23 kph or 25.62 mph)

Vingegaard showed Pogačar -- and the world -- who the best cyclist is.  Pogačar will have to come up with the rides of his life on the two remaining mountain stages if he is to pull off a miracle and get his Tour de France general classification hat trick.

Tomorrow's Stage 17 is 165.7-km (103.0-mi) long and begins in the rest commune of Saint-Gervais-les-Bains.  Cyclists will head south and finish at the Alpine ski resort of Courchevel.  The 28.1-km (17.5-mi) hors catégorie climb at the end of the stage to the 2304-m (7559-ft) peak of Col de la Loze will test riders, but they'll surely enjoy the downhill sprint to the finish line.  I hope the sprinters beat the broom wagon on such a grueling stage.  Our prediction is given below.

• Stage 17:  4h 35' 19" (prediction)

It will be fascinating to see what Pogačar tries tomorrow.  He's got a lot of catching up to do!

Wout Poels Wins First Tour de France Stage!

It was another great day of racing at the Tour de France!  Wout Poels broke away from the lead group and after a wonderful final climb, crossed the finish line all on his own.

He had to have been very happy after earning his first Tour de France stage win.  I was very happy with our prediction!

• Stage 15:  4h 40' 45" (actual), 4h 37' 25" (prediction), 03' 20" fast (-1.19% error)

That's a good way to head into tomorrow's rest day!  Check out the winner's average speed.

• Stage 15:  10.63 m/s (38.25 kph or 23.77 mph)

Wout Poels had a great average speed after so much climbing today!

This has been a Tour de France unlike I've seen in my relatively limited number of years watching the world's most famous bicycle race.  Sports are so much more fun and interesting when rivalries develop.  Jonas Vingegaard (GC winner in 2022) and Tadej Pogačar (GC winner in 2020 and 2021) have been a joy to watch this year.  Pogačar tried a couple of attacks in the final kilometer, but Vingegaard responded like a champion.  Their teams have done all they could do to support the two superstars.  How fitting is this image I grabbed?

Pogačar (16th place) came in just ahead of Vingegaard (17th place); both were 06' 04" behind Poels.

Tomorrow will represent the second rest day in this year's Tour de France.  Cyclists will remain where they finished today, which is in Saint-Gervais-les-Bains.

Stage 16 will be an individual time trial.  Riders will begin the 22.4-km (13.9-mi) stage in the commune of Passy and head in a southwesterly loop to Combloux.  A category-2 climb will be navigated near the end a time trial that will see riders increase elevation by 395 m (1296-ft) from start to finish.  I often wait until the rest day to post the next stage's prediction, but I'll offer our prediction now.

• Stage 16:  30' 22" (prediction)

Many riders who are not GC contenders could take it easy.  But Pogačar and Vingegaard will be the last two riders out.  If Pogačar sets a torrid pace, Vingegaard will have to respond.

Rodríguez Wins on a THRILLING Day of Racing!

If you love to watch elite cyclists battle on a difficult route, this was the stage to watch.  After a very unfortunate crash, which cost several riders the chance to stay in the race, and a 24-minute neutralization, Jumbo–Visma set a torrid pace.  The field of cyclists got split all over the place on the various climbs.  The final climb up Col de Joux Plane is something I won't soon forget.  Jonas Vingegaard and Tadej Pogačar eventually dueled each other for the top of the mountain.  It was a thing of beauty watching the two best in the world push each other.  I felt terrible for Pogačar when his last attack got blocked by motorcycles that were too close to the lead riders.  Fans blocked avenues of attack, too.  The Tour de France organizers must do something about fans swarming on the road.  Pogačar had to give up his attack,  and Vingegaard eventually took the larger time bonus at the top of the mountain.

The descent into the finish line was jaw-dropping.  Speeds were through the roof.  It was Carlos Rodríguez who attacked on the downhill and left his competition is the dust.  Here is the image of Rodríguez getting his first Tour de France stage win.

The torrid pace meant our prediction was once again a tad slow.

• Stage 14:  3h 58' 45" (actual), 4h 07' 21" (prediction), 08' 36" slow (3.60% error)

Not a bad error, but I still want to be under 3%!  Our prediction came in between the riders who finished 11th and 12th.  Out of 158 riders who finished today, roughly 7% beat our predicted time.  My model is just a tad slow on the best of the best.

Rodríguez had quite an average speed.

• Stage 14:  10.60 m/s (38.15 kph or 23.70 mph)

Tomorrow's 179-km (111-mi) 15th stage is the third straight mountain stage.  Beginning in the commune of Les Gets, riders will loop to the southwest and then back northeast toward the category-1 finish at Saint-Gervais-les-Bains.  The Italian border won't be too far away from the finish line.  Our prediction is given below.

• Stage 15:  4h 37' 25" (prediction)

I hope tomorrow's stage has the same fireworks that were on display today!

Kwiatkowski Conquers Grand Colombier!

Polish cyclist Michał Kwiatkowski had the ride of his life today.  With all of France watching on Bastille Day, Kwiatkowski rode the entirety of Grand Colombier all on his own.  Neither the chasers nor the peloton could catch Kwiatkowski, who finished 47" before the next rider crossed the line.

Racing was really fast during the part of the race leading up to the big climb.  And when it was clear that Kwiatkowski would ride to victory, I knew we would be too slow today.

• Stage 13:  3h 17' 33" (actual), 3h 29' 04" (prediction), 11' 31" slow (5.83% error)

I'm no fan of our error today, but I was rooting like mad for Kwiatkowski to make to the end without being caught.  Check out his average speed.

• Stage 13:  11.63 m/s (41.85 kph or 26.01 mph)

Given the end of this stage, that is fast!  It is quite clear that cyclists have increased their power outputs since we modeled the race last year.  I love learning what elite athletes can do!

Right as Kwiatkowski crossed the line Tadej Pogačar attacked Jonas Vingegaard.  With a third-place time bonus, Pogačar managed to knock 8" off Vingegaard's general classification lead.  The Danish defending champion is now just 9" ahead of the Slovenian two-time champ.

Tomorrow's 151.8-km (94.32-mi) mountain stage commences in the French commune of Annemasse.  Cyclists will initially head north toward Lake Geneva before turning back and heading east to the finish line at the commune of Morzine.  A category-3 climb will be followed by three category-1 climbs.  Near the finish will be the hors catégorie climb to the 1691-m (5548-ft) peak of Col de Joux Plane.  Watch for a very fast downhill finish.  Our prediction is given below.

• Stage 14:  4h 07' 21" (prediction)

We've been too slow on the past two stages.  I hope we do better tomorrow!

Izagirre Breaks Away and Rides Solo to the Finish Line!

What a stage!  There was a lot of early jockeying for position.  But it was Ion Izagirre who attacked on the final climb with about 30.9 km (19.2 mi) left in the stage.  He managed to hold onto the lead and cross the finish line all by himself.

It would be 58 seconds before the next two riders came in.  We were a tiny bit slow on a very warm day of racing.

• Stage 12:  3h 51' 42" (actual), 4h 00' 01" (prediction), 08' 19" slow (3.59% error)

That error is just outside my preferred range.  Our prediction fell between the riders who came in 52nd and 53rd today, which meant about 31% of the 167 riders beat our time.  Not a bad prediction, just not elite!  Check out Izagirre's average speed.

• Stage 12:  12.14 m/s (43.71 kph or 27.16 mph)

Race organizers thought 42 kph might be the top speed.  They were off, too!

I've been waiting for tomorrow's stage ever since this year's Tour de France route was released.  The 137.8-km (85.62-mi) mountain stage begins in the eastern French commune of Châtillon-sur-Chalaronne.  Cyclists will head east to the real star of tomorrow's stage, the 17.4-km (10.8-mi) hors catégorie climb nearly to the peak of Grand Colombier.  The riders will cross the finish line at an elevation of 1501 m (4925 ft).  It will be a grueling climb to the finish line!  Our prediction is given below.

• Stage 13:  3h 29' 04" (prediction)

We were too slow today.  Will the Grand Colombier slow riders down?  If we are too slow tomorrow, some cyclist will have had the ride of his life on Bastille Day!

Jasper Philipsen is Simply the Best Sprinter!

Jasper Philipsen has shown the world that he is the best Tour de France sprinter.  His ability to pick a gap on the final sprint and explode to the finish line is awe inspiring.  He finished by more than a bike length ahead of his competition.

With cooler temperatures and some rain today, I thought our prediction would be a tad fast.  But the final hour of racing was incredibly fast.  We did well!

• Stage 11:  4h 01' 07" (actual), 3h 59' 41" (prediction), 01' 26" fast (-0.59% error)

I love that error!  Check out Philipsen's average speed.

• Stage 11:  12.43 m/s (44.74 kph or 27.80 mph)

Philipsen hit a maximum speed of 71.1 kph (44.2 mph) in the final kilometer.  Wow!  I can't even fathom moving at such a speed on a bicycle while on level pavement.

Tomorrow's 168.8-km (104.9-mi) medium-mountain stage begins in the commune of Roanne.  Riders will have a winding stage that sends them east to Belleville-en-Beaujolais.  Our prediction is given below.

• Stage 12:  4h 00' 01" (prediction)

The stage has three category-3 climbs, followed by two category-2 climbs.  It's a perfect stage for a breakaway group to get to the finish line.  Cyclists will compete hard tomorrow, but the Alps are waiting for them!

Pello Bilbao Makes Spain Proud!

Pello Bilbao gave Spain a much-needed stage win at the Tour de France with his great sprint in the final hundred meters.  Six riders in the breakaway managed to get to the finish line without being reeled in by the chasers or the peloton.

Bilbao is now in 5th place in the general classification, 04' 34" behind Jonas Vingegaard.

Racing was fast on a very hot day.  Our prediction was a bit slow.

• Stage 10:  3h 52' 34" (actual), 4h 02' 16" (prediction), 09'42" slow (4.17% error)

As I have noted many times, I want to be under 3%.  It may be that my model will need a tiny bit more cyclist power output for next year.  Check out Bilbao's average speed.

• Stage 10:  11.98 m/s (43.14 kph or 26.80 mph)

My model cyclist was about 1.73 kph (1.07 mph) too slow today.

Tomorrow's 11th stage represents the middle of this year's Tour de France.  Cyclists will begin the stage in Clermont-Ferrand, which is where they rested after the 9th stage.  The 179.8-km (111.7-mi) flat stage will have riders head northwest and then east to Moulins.  Our prediction is given below.

• Stage 11:  3h 59' 41" (prediction)

We were a speck slow in today's heat.  I hope we fare better tomorrow, but if cyclists ride like they did on Stage 8, I will need to give my model cyclist a serious power boost!

Tour de France Stage 10 Prediction

Stage 10 of this year's Tour de France commences at Vulcania, not too far from where yesterday's stage ended and also not too far from where cyclists are resting today.  The 167.2-km (103.9-mi) medium-mountain stage takes riders on a loop to the south where they end up a bit southeast of Vulcania at Issoire.  In the middle of four category-3 climbs is the category-2 climb to the 1451-m (4760-ft) peak of Col de la Croix Saint-Robert.  Our predicted winning time is given below.

• Stage 10:  4h 02' 16" (prediction)

It will be interesting to see how many cyclists survive to the next rest day.  After tomorrow's medium-mountain stage, sprinters will get a chance to shine on Stage 11.  But then another medium-mountain stage, followed by three consecutive mountain stages will get riders to their next day of rest.  A lot of grueling riding coming at the end of the week!

Michael Woods DESTROYS Puy de Dôme!

As someone from the US, I was rooting hard for Matteo Jorgenson to maintain his lead and conquer Puy de Dôme.  But, alas, it was Michael Woods who blasted past Jorgenson with half a kilometer left in the brutal climb to win his first Tour de France stage.  Jorgenson ended up in fourth place today.  Woods won by nearly half a minute.  Here is Woods making Canada proud.

We had a nice prediction today.

• Stage 09:  4h 19' 41" (actual), 4h 25' 28" (prediction), 05' 47" slow (2.23% error)

With such a brutal final climb, I'll definitely take that error!  Check out the average speed for Woods.

• Stage 09:  11.71 m/s (42.14 kph or 26.19 mph)

That was a pretty fast stage!  The top 12 riders (out of 169) beat our predicted time.

After Woods won, the yellow jersey battle got intense when Tadej Pogačar attacked on the 12% grade and Jonas Vingegaard couldn't keep up.  Pogačar ended up knocking 8" off Vingegaard's lead to find himself just 17" behind the yellow jersey.

Tomorrow will be the race's first rest day.  Cyclists will be in the central French city of Clermont-Ferrand.  I will post our prediction for Stage 10 tomorrow.

Pedersen Wins Blisteringly FAST Stage!

If you thought Stage 4 was too slow, you will have loved today's Stage 8.  For such a long stage, it's hard to imagine how elite cyclists were able to sustain the speeds they achieved today.  Mads Pedersen won the final sprint and took the stage win.

Pedersen is on the left with the red helmet.  He just kept Jasper Philipsen from winning his fourth stage this year.

I knew our prediction was in the loo after seeing today's speeds.

• Stage 08:  4h 12' 26" (actual), 4h 37' 16" (prediction), 24' 50" slow (9.84% error)

We have a stage like this every year.  All I can do is tip my cap to the jaw-dropping feats of the best athletes on Earth.  Check out the winner's average speed.

• Stage 08:  13.25 m/s (47.70 kph or 29.64 mph)

Even the announcers were commenting on how quickly the stage ended.  I hate our prediction, but it was great witnessing those speeds!

Tomorrow's ninth stage begins in the commune of Saint-Léonard-de-Noblat and ends near the top of the volcano Puy de Dôme.  The 182.4-km (113.3-mi) mountain stage has riders heading due east until they reach the hors catégorie climb at the finish.  Our prediction is below.

• Stage 09:  4h 25' 28" (prediction)

I hope my model is back on track tomorrow!

Hat Trick for Jasper Philipsen!

Jasper Philipsen denied Mark Cavendish a bit of history today, who is tied with Eddy Merckx with 34 Tour de France stage wins.  Philipsen won his third stage in this year's Tour de France.  He's won all three sprints in all three flat stages.  Check out the finish.

Cavendish is on the left, coming in second.  Philipsen is clearly the top sprinter right now.  And he seems to have a great hold on the green jersey.

We had a great prediction today.

• Stage 07:  3h 46' 28" (actual), 3h 47' 15" (prediction), 47" slow (0.35% error)

It's wonderful to be under 1% again!  Check out Philipsen's average speed.

• Stage 07:  12.50 m/s (45.01 kph or  27.97 mph)

Tomorrow's stage is a long medium-mountain stage at 200.7 km (124.7 mi) in length.  Beginning in the French commune of Libourne, cyclists head northeast to the commune of Limoges.  The stage is fairly flat, but a category-3 climb and two category-4 climbs, all short, await riders in the latter half of the stage.  Our prediction is given below.

• Stage 08:  4h 37' 16" (prediction)

Will sprinters hold back tomorrow?  Will someone in the breakaway win the stage?  Will riders be thinking about the grueling finish to the next day's stage and conserve energy?  Watching the teams' strategies unfold is always a lot of fun!

Pogačar's Attack Gives Him Stage 6!

Tadej Pogačar bided his time behind Jonas Vingegaard and Wout van Aert, who did yeoman's work in keeping Vingegaard in contention for the stage win.  With just 2.7 km (1.7 mi) left, Pogačar attacked and Vingegaard couldn't keep up.  Vengegaard is now in yellow, but Pogačar is only 25" back.  Check out Pogačar winning today's stage.

We did a little better today, but an added amount of power based on yesterday's stage proved to be a colossal mistake.  Such is modeling!

• Stage 06:  3h 54' 27" (actual), 3h 46' 03" (prediction), 08' 24" fast (-3.58% error)

Pogačar's average speed was impressive, but it wasn't blistering.

• Stage 06:  10.30 m/s (37.08 kph or 23.04 mph)

Tomorrow's 169.9-km (105.6-mi) stage is quite flat.  Riders begin in the commune of Mont-de-Marsan and head north to Bordeaux.  After stages 3 and 4, I'm rather apprehensive about tomorrow's prediction!  But it's time to forge ahead.

• Stage 07:  3h 47' 15" (prediction)

Will there be any breakaways by riders who yearn for a stage win?  Or will cyclists play it safe like they did in stage 4?  It will be interesting to see!

Hindley Wins Stage and Grabs Yellow Jersey!

I completely missed today's Tour de France action.  My younger daughter and I spent a good bit of today touring nearby University of Virginia.  I had to watch highlights of Stage 5 after we got back.  A lot happened today!

Jai Hindley took today's stage by more than half a minute on the rest of the competition.  In doing so, Hindley now has possession of the yellow jersey, holding a 47-second lead over last year's winner, Jonas Vingegaard.  Two-time winner Tadej Pogačar now sits in sixth place, 01' 40" behind Hindley.

I think Australia will be celebrating tonight!

My daughter told me the winning time while we were driving to Charlottesville.  It seems we were a bit slow today.

• Stage 05:  3h 57' 07" (actual), 4h 08' 08" (prediction), 11' 01" slow (4.65% error)
  

We fared better today than we did on the two previous stages, but my goal is to get under 3%.  Hindley's average speed is given below.

• Stage 05:  11.44 m/s (41.17 kph or 25.58 mph)

Yet another indication of how slow yesterday's stage was is that today's average speed is almost exactly what the winner averaged yesterday -- on a flat stage!

Tomorrow's 144.9-km (90.04-mi) mountain stage begins in the French commune of Tarbes.  Riders will loop to the southeast before finishing a bit southwest of Tarbes at the commune of Cauterets, which is close to the Spanish border.  The middle of the stage will take cyclists to the 1490-m (4888-ft) peak of Col d'Aspin on a category-1 climb.  The main player in tomorrow's stage will be the hors catégorie climb to the 2115-m (6939-ft) peak of Col du Tourmalet.  As if all that wasn't enough, riders will face a category-1 climb to the finish line.  What a grueling stage!  Our prediction is given below.

• Stage 06:  3h 46' 03" (prediction)

I hope we can sneak under 3% error tomorrow!

Crashes Mar Philipsen's Second Straight Win!

Jasper Philipsen won his second straight Tour de France stage with a great sprint in the final kilometer.  But that final kilometer was marred by a few crashes that took out many of the top sprinters.  Elite cycling can be intense and brutal, as today's finish demonstrated.  Philipsen just edged Caleb Ewan at the finish line.

Now for the comparison between Philipsen's time and our prediction.

• Stage 04:  4h 25' 28" (actual), 4h 06' 01" (prediction), 19' 27" fast (-7.33% fast)

This is our second straight terrible prediction, though yesterday's was due to not having the correct terrain data for the end of the stage.  Today's problem was all about pace.  Halfway into the stage, I could tell we would be much too fast.  I saw this on Cycling News:  "Hopefully the upcoming intermediate sprint will kick the stage into life after a slow day."  Slow is an understatement.  The peloton was moving like molasses today!  Look at the winner's average speed.

• Stage 04:  11.41 m/s (41.09 kph or 25.53 mph)

How slow is that?  Tour de France organizers estimated an average speed range of 43 kph - 47 kph for their time schedules.  I could knock about 18% off my model cyclist's power output and nearly nail today's time.  I've said for years that we cannot predict teams' strategies.  It seems that today was about keeping riders safe while leisurely biking through the south of France.  Only in the final 10 km or so did speeds really kick up.  Oh well, lots to learn from two flat stages that we simply failed to predict well.

Riders hit the Pyrenees tomorrow in this year's first mountain stage.  They begin in Pau and loop around to the southwest before finishing nearly due south of Pau in Laruns.  The 162.7-km (101.1-mi) stage's highlight will be an hors catégorie climb to the 1540-m (5052-ft) peak of Col de Soudet in the middle of the stage.  Our prediction is below.

• Stage 05:  4h 08' 08" (prediction)

I hope we do better in the mountains than we did on the two flat stages!

Jasper Philipsen Wins Thrilling Sprint!

Today's stage was an interesting study in peloton dynamics.  Getting sprinters ready for the finish was the aim of the game in the final part of the race.  Jasper Philipsen prevailed in the final sprint, which was thrilling!  He had to wait for confirmation as race organizers took about 20 minutes to figure out if Philipsen would be penalized for a slight bump on Wout van Aert.  Check out the finish.

Now we come to the comparison between our prediction and reality.  I discovered this morning that my model was using the terrain data for the old 187.4-km stage, not the modified 193.5-km stage.  The additional 6.1 km was due to too much road furniture on the original route.  I won't put a new prediction here because I don't want to brush over the mistake I made yesterday.  I'll compare with the prediction I originally made.

• Stage 03:  4h 43' 15" (actual), 4h 19' 06" (prediction), 24' 09" fast (-8.53% error)

That is obviously a terrible result!  I wish I had the correct terrain data before I wrote yesterday's blog post.  Oh well, I'll have to chalk this one up to a goof!  Below is Philipsen's average speed.

• Stage 03:  11.39 m/s (40.99 kph or 25.47 mph)

What a bizarre stage!  The above speed is quite a bit slower than Tour de France organizers guessed with their time schedules.

Tomorrow's fourth stage begins in the southwest French commune of Dax and takes riders 181.8 km (113.0 mi) mostly east to the commune of Nogaro.  The flat stage will allow sprinters to shine again before the next two grueling mountain stages.  Our prediction is given below.

• Stage 04:  4h 06' 01" (prediction)

After today's disaster, I hope we can get back on track tomorrow.  With such a flat stage, speeds might be higher than my model predicts.  Sprinters might go all-out with the mountains coming up!

Lafay Dominates the Final Kilometer!

The top cyclists were setting a strong pace in the final 20 km (12 mi) of today's second Tour de France stage.  At one point, Jonas Vingegaard and Tadej Pogačar were dueling on the final steep descent.  But for all the position jockeying at the end, it was Victor Lafay who launched out of the group in the final kilometer and took today's stage win.  Does he look happy with the win?

Our prediction fared pretty well today.

• Stage 02:  4h 46' 39" (actual), 4h 50' 54" (prediction), 04' 13" slow (1.47% error)

I have no problem with that error!  Check out Lafay's average speed.

• Stage 02:  12.15 m/s (43.73 kph or 27.17 mph)

So far, my model has done well with the two medium-mountain stages that opened the Tour de France.  Tomorrow's third stage is a flat 193.5-km (120.2-mi) stage (there are conflicting stage distances right now -- 187.4 km versus 193.5 km!) that commences in the north Spanish town of Amorebieta-Etxano and takes riders east and a bit north, just over the French border, to the commune of Bayonne.  Our prediction is given below.

• Stage 03:  4h 19' 06"

I hope to see a fantastic sprint for the win!

Adam Yates Takes the First Stage!

Jumbo-Visma did a lot of work today, but it was the UAE team that got today's first win of the Tour de France.  It was not Tadej Pogačar, who finished third, but Adam Yates who won the day.  Check out Yates crossing the finish line from the screen capture I grabbed.

What was really cool about the end of the race is that Adam's twin brother Simon was with him heading toward the finish; Simon is seen above coming in second.

Now it's time to check on this year's first prediction.

• Stage 01:  4h 22' 49" (actual), 4h 21' 07" (prediction), 01' 42" fast (-0.65% error)

What a great start!  But it's woefully early in the Tour de France, and as the great Han Solo once said, "Don't get cocky!"  I've seen plenty of great predictions in past years get forgotten quickly after some terrible predictions.  The goal is to learn and improve our scientific understanding of cycling at the highest level.  Check out the average speed for Adam Yates below.

• Stage 01:  11.54 m/s (41.55 kph or 25.82 mph)

Tomorrow's second stage begins in the northcentral Spanish city of Vitoria-Gasteiz and takes riders northeast to the coastal city of San Sebastián.  The 208.9-km (129.8-mi) medium-mountain stage is this year's longest stage.  Our prediction is given below.

• Stage 02:  4h 50' 52" (prediction)

A short category-2 climb awaits cyclists near the end of tomorrow's stage.  It will be interesting to see how the pace is set early on.