Teuns Conquers Final Brutal Climb!

Belgian Dylan Teuns outlasted Italian Giulio Ciccone on the 24% grade over the final 100 m in today's Stage 6.  I sat in my air-conditioned office watching the stage this morning.  Never more accomplished on a bicycle than a few leisurely 20-km rides, I was in awe watching the world's best do what only a tiny fraction of the world's population could do.  Check out Teuns crossing the finish line as the gradient "softened" to 21% (click on image for a larger view).

You can see Ciccone about to come in second.  He'll take it because Julian Alaphilippe struggled mightily over the last few meters and barely crossed the finish line in sixth place.  That cost Alaphilippe the yellow jersey; he's 6 seconds behind in second place.  We'll see Giulio Ciccone in yellow tomorrow.  Check out Teuns's winning time and how it compares with our prediction.

• Stage 06:  4h 29' 03" (actual), 4h 24' 40" (prediction), 04' 23" fast (-1.63% error)

I'm ecstatic that our model did so well today!  We would have had to trim less than 1% off our model cyclist's power output to exactly match the winning time.  Below is Teuns's average speed.

• Stage 06:  9.94 m/s (35.79 kph or 22.24 mph)

That average speed is a typical sprinter's speed in a 100-m dash.  Going up the final climb, cyclists could only manage a third of that speed.

Tomorrow's 203-km (143-mi) flat stage is the race's longest.  Cyclists begin in Belfort, which is very near the border with Switzerland.  They'll travel southwest to the commune of Chalon-sur-Saône.  Our prediction is given below.

• Stage 07:  5h 21' 48" (prediction)

It would be great to see our prediction come in under 2% again!

Sagan EXPLODES to Stage 5 Win!

I love watching Peter Sagan on a bicycle!  Peter the Great absolutely exploded inside 200 m to the finish line and won Stage 5.  No second place for Sagan today!  Check him out going across the line (click on image for a larger view).

He then went into Hulk mode, perhaps letting the cycling world know that the green jersey is his and his alone (click on image for a larger view).

Today's hilly stage had some impressive climbing.  Check out Xandro Meurisse after he was the first to reach the top of Côte des Cinq Châteaux (click on image for a larger view).

His was hitting a speed of 20 kph (12 mph) on a 10% part of the climb.  Wow!

We did a lot better today with our prediction, as you'll see below.

• Stage 05:  4h 02' 33" (actual), 4h 13' 41" (prediction), 11' 08' slow (4.59% error)

I still want that error under 3%, but I'll definitely take today's error after the past two stages.  Racing conditions were perfect today.  The European heat wave is gone, temperatures were in the 21°C - 25°C (70°F - 77°F) range, and climbs where crosswinds could have been a problem had lovely trees around the riders.  Racing was just a tad faster than we thought it would be.  Sagan's average speed is given below.

• Stage 05:  12.06 m/s (43.41 kph or 26.98 mph)

Tomorrow's 160.5-km (99.7-mi) Stage 6 is the year's first mountain stage, and it looks to be a fun ride.  The stage begins in Mulhouse, very near the French borders with Germany and Switzerland.  Riders will have a mostly category-1 climb to near the peak of Grand Ballon.  They'll reach a stage-high altitude of 1336 m (4380 ft).  A category-1 climb to near the peak of Ballon d'Alsace occurs just past halfway into the stage.  What I'm anxious to watch is the final category-1 climb to the finish at La Planche des Belles Filles, right in the Vosges Mountains.  Climbers will be on full display tomorrow!  Our prediction is given below.

• Stage 06:  4h 24' 40" (prediction)

Will we be a bit slow again?  The cyclists impress me this year!

GREAT Sprint by Viviani in Stage 4!

I got to watch today's stage, and I wasn't disappointed.  Elia Viviani made Italy proud with a stupendous sprint in the last few meters to just take today's stage win.  Check out Viviani crossing the finish line (click on image for a larger view).

Viviani is on the right in blue, just ahead of Alexander Kristoff in the center in white and Peter Sagan on the left in green.  Viviani is 11 kg (24 lb) lighter than Kristoff and Sagan.  Did that help?  I don't know, but Viviani did a great job sneaking out of a slipstream near that wall on the right and charging toward the finish line at just the right time.

Now we come to our prediction.  It's wasn't great, but I'm fascinated nonetheless.  While watching the stage, there were comments about crosswinds and sluggish cycling.  I thus knew our prediction would be too fast as I watch the race unfold.  But it turns out that we had yesterday's stage and today's stage exactly backwards.  The slower pace we expected in yesterday's stage showed up today.  The high speed we thought would pervade today's stage was on display yesterday.  We missed today's stage by the exact same time that we missed yesterday's stage, but in the opposite direction!

• Stage 04:  5h 09' 20" (actual), 4h 42' 50" (prediction), 26' 30" fast (-8.57% error)

What's funny is that we have exactly matched the sum of yesterday's winning time and today's winning time, but that's little consolation for two less-than-stellar predictions.  Viviani's average speed is given below.

• Stage 04:  11.50 m/s (41.41 kph or 25.73 mph)

Tomorrow's Stage 5 is a 175.5-km (109.0-mi) hilly stage that begins in the commune of Saint-Dié-des-Vosges and ends in Colmar.  The stage has a couple of category-3 and a couple of category-2 climbs, but the finish looks to be very fast.  Our prediction is given below.

• Stage 05:  4h 13' 41" (prediction)

I hope we get back on track tomorrow!

Alaphilippe Wins FAST Stage 3!

I wish I could describe what happened during today's third stage of the Tour de France.  But I wasn't able to watch it.  I bought the gold pass from NBC to watch the entire race, but the website was inaccessible from my office.  I'm not even able to access a replay, several hours after the stage ended.  There will be no screen captures in this post.  I'll have to get to a comparison between our prediction and the actual result, and then get to our prediction for tomorrow's stage.

Julian Alaphilippe won a very fast stage today, and in the process of doing so, secured the yellow jersey for France for at least tomorrow's stage.  Our prediction wasn't great.

• Stage 03:  4h 40' 29" (actual), 5h 06' 59" (prediction), 26' 30" slow (9.45% error)

The days of being happy to get a prediction error less than 10% are long gone.  We clearly missed something today.  After reading a few summaries of the stage, we learned that there were some rather strong tailwinds.  If someone watched the stage, please let me know if it looked as if winds helped riders.  I'm anxious to learn of other reasons, too.  Alaphilippe's average speed was certainly greater than what we thought on a fairly flat, but hilly near the end, stage.

• Stage 03:  12.78 m/s (45.99 kph or 28.58 mph)

Given how long the stage was, I'm shocked at that average speed.  It's 3 kph greater than even what the Tour de France's website thought might be an upper limit for the average speed.

Tomorrow's Stage 04 is classified as flat, though there are a couple of category-4 climbs in the latter half of the stage.  We thought tomorrow's stage would be faster than today's stage.  The 213.5-km (132.7-mi) stage commences in Reims.   Riders will head mostly east where they'll finish the stage in Nancy.  Our prediction is given below.

• Stage 04:  4h 42' 50" (prediction)

Are the cyclists outputting more power than we expected?  Are they and their bikes more aerodynamic than what we've ascertained from recent publications?  I don't know, and that's what makes this so much fun.  It's time to learn something!

An Amazing Ride by Team Jumbo-Visma!

While watching the Tour de France live, the sports fan in me is always shouting louder than the physicist looking for a perfect prediction.  Team Ineos was finished with a time of 29' 17", and was watching team after team come in, trying to beat that time.  Our prediction was set to be just over 1% off.  But then came the last team, Team Jumbo-Visma, led by yesterday's winner, Mike Teunissen, donned in the yellow jersey.  I was on the edge of my office chair as they were about to start (click on image for a larger view).

The team's eight riders knew what time they had to beat, and they definitely proved the adage that last is not least.

In a team time trial, four of the team's riders must cross the finish line.  The team's time is in fact determined by the time when the fourth rider finishes.  I was anxious to see how Dylan Groenewegen looked after yesterday's crash.  He was unfortunately still showing the effects of the crash as he fell off the team's pace with about 17 km (11 mi) left.  But his mates kept up a torrid pace.  It was great watching the way the team members interchanged the tough lead position.  In the screen capture below, Steven Kruijswijk has just moved to the back (click on image for a larger view).

So much great physics in that image!  The closed back wheels help reduce drag by streamlining the wake of air separating off the bikes and riders.  Cyclists are crouched and helmets are tapered at the back.  The cyclist in front works hardest because there is no drafting for the leader.  By taking turns at the front, team members alternate who expends the most energy.  Athletes, trainers, nutritionists, engineers, physicists, and research and development teams in companies all work to creep ever closer to the limits constrained by the laws of physics.

By the time Team Jumbo-Visma was within a couple of kilometers of the finish line, I was rooting for them to sneak under 29 minutes.  Our prediction was going to be worse if they did, but so what?!?  They pulled it off, as you see below (click on image for a larger view).

Four need to finish, but it's always good to have at least five head for the finish, just in case one rider has a problem.  Check out how our prediction fared.

• Stage 02:  28' 57" (actual), 29' 41" (prediction), 00' 44" slow (2.53% error)

I'll most definitely take that error!  The team's average speed was incredible.

• Stage 02:  15.89 m/s (57.20 kph or 35.54 mph)

Try to imagine biking that speed with at least one other cyclist right in front of you and one other cyclist right behind you.  It's much harder than it looks!

Tomorrow's third stage commences in the western Belgian city of Binche.  Riders will leave Belgium and enter the French commune of Jeumont after about 12 km (7.5 mi) of cycling.  The 215-km (134-mi) hilly stage ends in the French commune of Épernay.  A category-4 climb and three category-3 climbs greet riders near the end of the stage, perhaps hinting at more serious climbs to come in later stages.  Our prediction is given below.

• Stage 03:  5h 06' 59" (prediction)

Can Team Jumbo-Visma make it three in a row???

Teunissen Sprints to First Stage Win!

Dutch rider Mike Teunissen sneaked up through the sprinters, drafted at the right moment, and then burst past Peter Sagan (who else would come in second?!?) to win this year's first stage.  This was a huge surprise for Teunissen, who earned his first grand tour stage win.  Check out how close the finish was (click on image for a larger view).

You can see Teunissen on the right, just edging Sagan at the finish line.  I tried getting a screen shot while watching live, but I couldn't tell who won (click on image for a larger view).

I actually thought Sagan had won, but then saw the replay, where I got the first screen capture above.  You can see the winning time in the upper left of my screen shot.  Teunissen will get a 10-second time bonus for the win, and he'll be donned in yellow tomorrow.  That means Sagan will be wearing Teunissen's green jersey.  Check out how Teunissen's time compares to our prediction.

• Stage 01:  4h 22' 47" (actual), 4h 32' 00" (prediction), 09' 13" slow (3.51% error)

It was a beautiful day for racing, and speeds in Brussels near the finish hit 78 kph (48 mph), so racing was just a tad faster than we thought.  I'll still take the relatively small error!  Teunissen's average speed is given below.

• Stage 01:  12.34 m/s (44.41 kph or 27.59 mph)

There were a couple of crashes that hopefully won't have big implications for the rest of the Tour de France.  Teunissen's Team Jumbo-Visma mate Dylan Groenewegen crashed with just about 1.5 km left in the stage.  I got a screen capture of the crash (click on image for a larger view).

I think that's Groenewegen lying face down with the yellow and black jersey.  Inside of 20 km left was a crash that scarred Swiss cyclist Jakob Fuglsang (click on image for a larger view).

The screen capture below shows some of the damage to Fuglsang, who may have been cut by his sunglasses (click on image for a larger view).

The Tour de France will be much better with Fuglsang and Groenewegen healthy and competing in top form.  I hope they're okay!

I have never been to Brussels.  Watching the Tour de France begin there makes me want to visit the Belgium capital!  Check out the peloton entering the city (click on image for a larger view).

Looks amazing!  Cyclist will stay in Brussels for tomorrow's 27.6-km (17.1-mi) team time trial.  I love watching team time trials.  Team strategies will be on full display as riders swap drafting positions.  Lots of great physics!  Below is our prediction for the second stage.

• Stage 02:  29' 41" (prediction)

I hope our prediction is a little better than today's, but a record-setting time could have us too slow again.  We shall see!

It's Tour de France Time!

On the eve of the world's most famous bicycle race, I am once again geared up to post my research team's predictions for the Tour de France's stage-winning times.   We model elite cycling using published values of cyclist power output, air drag, tire/road friction, terrain data, and, of course, the laws of physics that constrain us all.  This year's race looks to dazzle those of us who love watching battles in the high mountains.

Stage 1 commences in the Belgian capital of Brussels.  The 194.5-km (120.9-mi) flat stage takes riders west, then south of Brussels, before returning north back into Brussels.  Our prediction for the first stage's winning time is given below.

• Stage 01:  4h 32' 00" (prediction)

My research students here at the University of Lynchburg are Carl Pilat, who worked with me last summer, and Noah Baumgartner, who joined my research team this summer.

As I sports physicist, I want to understand how elite athletes are able to do what they do.  I also want to understand the equipment and playing surfaces they use.  Modeling the Tour de France is about taking something extremely complicated and simplifying it enough that one begins to understand it on a fundamental level.  Sticking our necks out and posting stage-winning times is merely our way of spicing up what we do.  We can never fully know weather conditions, and we're not privy to the various strategies employed by the cycling teams.  And we certainly can't know ahead of time if there will be crashes, delays, protests by fans, interference by fans, cows roaming onto the road, and so on.  Those aren't excuses for bad predictions, just the reality of trying to model something so complex.  We love it when a prediction is nearly spot on, and when our predictions don't fare so well, we are given an opportunity to learn something.  That's one reason why being a scientist is such a delight!

Ready for the Women's World Cup?!?

The Women's World Cup begins on Friday, 7 June.  I'm excited to see the world's best go for glory in France!  My country will compete in Group F with Chile, Sweden, and Thailand.  The ball the players will use is the adidas Conext 19.  The panel design is exactly the same as the Telstar 18 ball that was used in the Men's World Cup last summer in Russia.  The color scheme, however, is quite different.  The color scheme pays homage to the ball that helped host France win the Men's World Cup in 1998.  That was the adidas Tricolore.

My colleagues at the University of Tsukuba in Japan, Takeshi Asai and Sungchan Hong, have been great collaborators for me.  We've published a few papers on soccer ball aerodynamics, including papers on the balls used in the past three men's Worlds Cup.  They sent me wind-tunnel data for the Conext 19.  The data look very similar to what we published for Telstar 18 (click here for our paper).  The graph below shows the drag coefficient as a function of ball speed (air speed in the wind tunnel).

I've labeled the so-called "critical speed" in green.  That's the speed at which air flow around the ball transitions from laminar below the critical speed to turbulent above the critical speed.  The critical speed above is at a great speed!  Most of the high-speed corner and free kicks will take place at speeds above that critical speed.  That means the players will deal with a ball in flight whose drag coefficient won't change much.

For balls hit with little to no spin, knuckling effects will play a role.  The graph below shows side and lift coefficients for the Conext 19.

Even though the ball wasn't spinning in my colleagues' wind tunnel, the boundary layer of air still separates asymmetrically off the back of the ball.  That's due to the fact that the seam pattern does not preserve spherical symmetry.  Air might separate off the ball near a seam on one side, but near a panel on the other side.  The large fluctuations at small speeds won't be noticed much by players because the side and lift forces are large compared to the ball's weight at those speeds.  For high speeds, kicked balls with little to no spin will wobble a little.  Lateral deflections could reach 6% of the ball's horizontal range on hard kicked balls.

My colleagues have wonderful facilities for testing soccer balls.  They sent me a video that I posted last year when media were contacting me about the Telstar 18 ball.  I'll show the video again below.

Ain't physics grand?!?  Now bring on the Women's World Cup!

Cover for my new book is out!

My second book, The Physics of Krav Maga, is due out this November.  It will be available just in time for holiday shopping!  😃  I now know what the cover looks like.

I wish I could say I am on the front cover, but my body isn't quite cut like the body on one of those guys!  Click here for my book's Amazon page; click here for my book's page with my publisher (Johns Hopkins University Press).  I look forward to the fall season when my book is released.  It will be fun talking about all the great physics in Krav Maga!

Super Bowl LIII Physics

I've heard many say that Super Bowl LIII wasn't very exciting.  Well ... a defensive battle can be just as exciting as an offensive shootout.  A tied Super Bowl more than halfway into the 4th quarter is exciting, no matter what the score is.  The New England Patriots beat the Los Angeles Rams, 13-3.  As much fun as I had watching the game, I had a tiny bit more fun looking at all the wonderful physics in the game.  I was only able to grab some screen captures, so the images I have below aren't the best quality.  But I'll make a few physics observations from last night's game.

The very first play of the game had me thinking about center of mass.  Sony Michel (#26) ran for 13 yards.  What made his run is that after he took a hit near the line of scrimmage, he managed to keep his center of mass over his base.  Check out the screen capture of his run (click on image for a larger view).

Knowing how to keep his center of mass from getting past his shoes, Michel was able to maintain his balance and pick up the game's first 1st down.

The Rams were feeling good a few plays later when they picked off Tom Brady (#12).  Check out the ball in the air after the tip (click on image for a larger view).

An "impulse" is needed to change an object's momentum.  The physics way of thinking of impulse is to imagine the force on an object multiplied by a collision time.  The football received an impulse from Rams cornerback Nickell Robey-Coleman (#23) that redirected the ball's momentum upward.  That allowed Corey Littleton (#58) to make the pick.

Super Bowl MVP Julian Edelman (#11) likely saved himself from sustaining a concussion early in the 3rd quarter.  When Rams free satety Lamarcus Joyner (#20) laid a hard hit on him, Edelman just managed to tuck his head, which prevented a helmet-to-helmet collision.  Check out how close Edelman came to perhaps not competing in much of the rest of the game (click on image for a larger view).

If you click on the above image, you'll see Edelman's helmet just under Joyner's helmet.  Part of good practice involves learning how to get hit, and staying in one piece.

When I saw Rams quarterback Jared Goff (#16) get hit near the end of the 3rd quarter, I was reminded again about how forces add.  Check out Goff getting smashed (click on image for a larger view).

He was getting sandwiched by three Patriots!  Although he was ultimately pushed backwards, Goff experienced a brief moment of no net force.  If the three Patriots exerted forces that add -- as vectors -- to zero, Goff would have had no net force on him.  Of course, getting squashed in a Death Star trash compacter still hurts, even if one's center of mass isn't going anywhere!

At the very end of the 3rd quarter, I saw Sony Michel get hit by Rams defensive tackle Michael Brockers (#90), and like the first play of the game, a run by Michel had me thinking about center of mass.  Check out the hit (click on image for a larger view).

See #90 of the Rams?  He's hitting Michel right at Michel's center of mass!  That didn't cause Michel to rotate for a tackle.  Instead, Michel bounced off Brockers for a 19-yard gain.  The action is incredibly fast on the gridiron, but good fundamentals mean the difference between getting stopped for a 5-yard gain and picking up 19 yards.

Early in the 4th quarter, I saw Jared Goff get hit by Patriots cornerback Jonathan Jones (#31).  But it was only a flash because Jones came flying from the right side of the action and tagged Goff hard just before the Rams quarterback got out of bounds (click on image for a larger view).

The reason Jones looks like a blur in the above image is that he was moving over 15 mph when he closed on Goff.  That was a cornerback who didn't want the opposing quarterback to get back to the line of scrimmage!

Many commentators have lauded the throw Brady made to tight end Rob Gronkowski (#87) that put the Patriots in position to win the game.  I grabbed the screen capture below (click on image for a larger view).

That ball traveled 33 yards in the air and took 1.93 seconds to go from Brady's hand to Gronk's hands.  But look at the tiny window Brady had to make that completion!  Two Rams defenders are behind Gronk, screening him from Brady's sight.  One of those Rams defender is blanketed on Gronk.  A third Rams defender is closing in on the play.  That throw won the Patriots the Super Bowl.  There is a reason Tom Brady is the GOAT!

The Patriots finished off the Rams with a field goal by Stephen Gostkowski (#3) with just over a minute left in the game.  Look how close the ball came to hitting the left upright (click on image for a larger view).

You can just see the ball about a quarter of the way down along the inside of the left upright.  The Coriolis effect didn't make the difference in the kick, but it was pushing the ball in the right direction.  In the northern hemisphere, projectiles, like footballs, get a tiny push to right.  But because the ball was only in the air 2.3 seconds before it crossed the plane of the uprights, the Coriolis push was less than a quarter of an inch.  But if you're not a Patriots fan, it stinks knowing that even Earth was trying to help that kick!

A nerd like me loves watching sports.  But what makes the experience even more fun is seeing the sports world through the eyes of a physicist.

Super Bowl Physics!

Are you getting excited for this Sunday's Super Bowl?  If you like the merging of science and sports, check out the premier episode of Season 4 of StarTalk's Playing with Science.

• Season 4, Episode 1 (January 30, 2019):  SEASON PREMIERE:  2019 Big Game Special, with Neil deGrasse Tyson

I talk about the physics of football during the first portion of the episode.  I also had a pretty nerdy way to predict the winner!

Danger Among the Thrills

If you're like me, you watched the two NFL conference championship games yesterday, thinking perhaps you were watching the most thrilling back-to-back football games you'd ever seen.  Both games were decided in overtime.  Both games saw the visiting team as the victor.  Both games had a terrible official mistake (a non-call in the first game and a call in the second game) that could have given the victory to the home team.  As thrilling as both games were, something unsettled me late in the first quarter of the first game.

With less than six minutes to go in the opening quarter, the Saints enjoyed a 6-0 lead over the Rams.  They were looking to extend their lead on a drive that had them with 1st and 10 on their own 32-yard line.  Saints quarterback Drew Brees (#9) threw a short pass to tight end Josh Hill (#89).  Hill caught the ball near the line of scrimmage and ran for a first down and more.  The play netted the Saints 24 yards.  But I cringed at the hit Hill received from Rams linebacker Cory Littleton (#58).  Check out the screen capture below (click on image for a larger view).

I could tell from the sound of the collision that Hill's helmet and Littleton's helmet collided with a great deal of force.  Hill was slow to get up, and Littleton could be seen waving for help for Hill.  Below is another view of the collision, but if you'll have to watch the video if you desire to see and hear just how violent the collision was (click on image for a larger view).

Hill reached a speed near 15 mph on his run, and only slowed a little prior to the collision.  The Saints removed Hill from the game and entered him into concussion protocol.  It was later determined that Hill did indeed suffer a concussion.

Josh Hill weighs 250 pounds and Cory Littleton weighs 226 pounds.  Throw in more than 20 pounds per player for pads, gear, and helmet, and yesterday's collision involved more than 500 pounds of total weight.  The average force during a collision like that is comparable to that 500-pound weight.  The maximum instantaneous force can be three times that average force.

Acceleration is the real concussion culprit.  The brain sits in cerebrospinal fluid, which provides cushioning during normal, every-day accelerations.  But if the brain is subjected to an acceleration of about 100 times the acceleration due to gravity, a concussion will be the likely result.  Usually, the torso takes the brunt of that acceleration during a tackle, but a hit to the head means the brain will feel the full acceleration.  Really hard hits to the helmet can actually lead to accelerations as large as 150 times the acceleration due to gravity.  Keep in mind that a fighter pilot only feels one tenth of that acceleration while executing some maneuvers (though the fighter pilot deals with the large acceleration for much longer than the football player does). A severe car crash may have one third the acceleration of a dangerous hit to the helmet in football.  Collision times in football are very short, and the time of the large instantaneous accelerations is even shorter.  But the time is long enough for the brain to hit the skull and leave the player with a concussion.

Today's helmets do a decent job with linear accelerations.  Padding and helmet design help extend collision times (think air bags and catcher's mitts!), which reduces collision forces.  But modern helmets have still not solved the problem of large angular accelerations.  Look at the second screen shot above.  The two players were nearly coming at each other perpendicularly.  The hit to the top of Hill's helmet caused his head to rotate to toward his right shoulder.  Padding does little to help prevent large rotational accelerations.

The football action yesterday was thrilling to say the least.  I just hate to see the darker side of the sport, a side that leaves a player with brain trauma.

Can't Blame Coriolis!

The Chicago Bears lost a heartbreaker at home yesterday to the Philadelphia Eagles, 16-15, in an NFC wild card playoff game.  Cody Parkey missed a 43-yard field goal at the end of the game that would have given the Bears the victory.  The ball he kicked first hit the left upright, then hit the crossbar on the way down, bouncing off in the wrong direction for the Bears.  Check out the the ball hitting the left upright (click on image for a larger view).

The Bears play their home games at Soldier Field, which is at a latitude of 41.8632 degrees north, according to Wikipedia.  A closer look at the stands in the background shows section 151 (click on image for a larger view).

I looked at the seating chart for Soldier Field, and then checked that the field does indeed run south to north.  Section 151 is behind the north end zone, which means Parkey's kick left his foot traveling north toward the left goalpost.

The Coriolis effect arises because the Earth turns on its axis, which means we here on Earth's surface are not in an inertial reference frame.  Earth turns once on its axis in 24 hours, which gives a rotational speed of about 0.73 microradians per second or 15 degrees per hour.  Just after the kick and before the ball hit the upright, the ball was in the air for 2.33 seconds.  At the latitude of Soldier Field, Parkey's kick would have only deflected about a tenth of an inch due to the Coriolis effect.  But what's really important is that a ball kicked to the north in the northern hemisphere will be deflected to the right, i.e. east.  That means that the Coriolis effect actually helped Parkey's kick!  Without the added tenth of an inch to the right, the ball still would have hit the left upright, but just a tiny bit closer to the center of the upright.

I feel bad for Cody Parkey.  His kick would have won the game for the Bears.  The snap was perfect, and the hold was perfect.  Parkey just missed the kick.  He even got a little push in the right direction from the Coriolis effect.

Trickeration at Lambeau Field!

The Detroit Lions entered their season finale at Green Bay with a 5-10 record.  They throttled the usually home-dependable Packers, 31-0.  The Packers knew they wouldn't make the playoff, so there must have been no incentive for them to play well.  A little trickeration early in the second quarter helped the Lions secure victory.  Hey, why not?  When you're 5-10 and your season ends today, why not pull out all the tricks?  The Lions faced 4th & 3 at the Green Bay 8-yard line with 10:42 to go in the second quarter.  Sam Martin (#6) was set to receive the snap at the Packers 16-yard line from long snapper Don Muhlbach (#48).  Matt Prater (#5), the Lions kicker, who happens to hold the NFL record for the longest field goal (64 yards), was ready for a chip shot.  Check out the starting formation (click on image for a larger view).

Count the number of Lions players you see in the above image.  You see only 10, right?  That's because tight end Levine Toilolo (#87) was lined up on the far left side of the Lions formation (right side in the above image).  You can't even see him in the above view!  Now count the number of Packers players you see in the above image.  You see all 11, right?  On the far right is rookie cornerback Josh Jackson (#37).  Toilolo was all alone, and the situation was ripe for a trick play.

Muhlbach snapped the ball directly to Prater.  Toilolo was headed toward the end zone and Prater showed off his quarterback abilities (click on image for a larger view).

You can see Jackson at the bottom right of the above image heading toward Toilolo (not seen in the image).  The throw was right on the money and Toilolo caught the ball at face level (click on image for a larger view).

The ball left Prater's hand at 40.7 mph at a lofty angle of 35.2 degrees above the horizontal.  The ball's flight time was 2.1 s, and it landed in Toilolo's hands while moving at 37.5 mph.  Because of the relatively low throw speed, the ball's initial air resistance force was only about 11% of the ball's weight.  Despite being credited with an 8-yard touchdown pass, Prater's ball traveled a bit more than 32 yards in the air.  Remember than an American football field is 53 1/3 yards wide.  Instead of the 500 pounds of average force he needed for his record field-goal kick (and nearly a ton instantaneous force!), Prater needed only an average force of nearly 17 pounds to accelerate the ball from behind his head to its release point.  The trajectory of Prater's pass is shown below (click on image for a larger view).

One thing I love about Prater's pass is that he threw the ball without using the laces.  Kickers love to kick the ball with "laces out".  Matt Prater must like to throw the ball with "laces out."  Check out the image below (click on image for a larger view).

See the laces on the opposite side of Prater's hand?  The ball rotated between 16 and 17 times on its way to Toilolo.  That meant the ball had an average rotation rate of about 470 rpm, which is less than the roughly 600 rpm quarterbacks make on hard throws.  Prater's throw's rotation rate gives a frequency of about 7.85 Hz, which is nearly 8 times that frequency of a resting person's heartbeat.

It was fun talking about this play on TuneIn's 1st & Goal Check Down segment.  Chuck Nice of Playing with Science was scheduled to appear with me on the show, but I ended up flying solo on the segment.  Click here for the audio of the segment.

Jaylon Smith Shows SPEED on Defense!

The Dallas Cowboys beat the Tampa Bay Buccaneers today, 27-20.  For this week's appearance on TuneIn's 1st & Goal Check Down segment, I got to analyze a defensive play.  Late in the 1st quarter, the Bucs had 3rd & 5 on the Cowboys 34-yard line.  Bucs quarterback Jameis Winston (#3) was lined up in the shotgun (click on image for a larger view).

In the above screen capture, I circled two defensive players for Dallas:  linebacker Jaylon Smith (#54) and defensive end Randy Gregory (#94).  Seeing #94 on the right end gave me flashbacks to seeing the great Charles Haley in that position a quarter century ago.  Gregory channeled some Charles Haley on this play!

After the snap, Gregory was looping around, trying to get to Winston.  Bucs tackle Donovan Smith (#76) pushed Gregory almost to the Dallas 45-yard line, which you can see below (click on image for a larger view).

You can Donovan Smith and Gregory on the far right of the action.  Jaylon Smith is still eyeing the play at the Dallas 30-yard line.  After nearly 4.5 seconds since the snap, Gregory caught Winston on the Dallas 37-yard line (click on image for a larger view).

When I watched the replay, Winston looked stunned that he got caught from behind.  Given the space in front of him, Winston would have been better off running for the first down.  Gregory knocked the ball out with his right hand    Check out Winston's surprised face in the screen capture below (click on image for a larger view).

As Gregory was tackling Winston, check out Gregory's left hand on the ball, which got pushed in the direction needed for what came next (click on image for a larger view).

After three fortuitous bounces of that delightful near prolate spheroid, Jaylon Smith scooped up the ball between the Dallas 30- and 31-yard lines (click on image for a larger view).

It was now off to the races for the former high-school track star.  The left sideline became his track lane.  Check out Smith hitting 20.4 mph on the left sideline (click on image for a larger view).

The Bucs couldn't catch Smith.  He scored about 8.6 seconds after he scooped up the ball (click on image for a larger view).

Jaylon Smith got most of the glory with his great return.  But the play doesn't happen if not for Randy Gregory running about 25 yards around the back of the Bucs line to catch Winston, and then nudge the ball in the direction that proved perfect for Smith.

In a game decided by a touchdown, the Cowboys sure needed that play from Gregory and Smith!  Chuck Nice of Playing with Science joined me on the show today.  Click here for the audio.

Westbrook Takes It to the HOUSE!

The Jacksonville Jaguars were beaten at home today by the Washington Redskins, 16-13.  The most exciting play of the first half was likely Dede Westbrook's (#12) punt return just before halftime.  The Redskins faced a 4th and 6 at their own 22-yard line with about 23 seconds left in the first half.  Punter Tress Way (#5) is waiting for the snap in the screen capture below (click on image for a larger view).

Though the average force during the collision between a punter's shoe and the ball is in the neighborhood of a quarter ton, the maximum force reaches about a ton.  The collision time is less than 10 ms, but the maximum force happens over a much shorter time interval than that.  Check out Way's punt (click on image for a larger view).

The ball looks to have been kicked just past the Washington 12-yard line.  The punt had a hang time of 4.3 s, but the punt could have used just a couple tenths of a second more hang time.  That would have allowed Washington's coverage to get a little farther down the field.  Another half second could have put the coverage about 4 or 5 yards closer.

Jacksonville's Dede Westbrook caught the ball on the Jaguars 27-yard line, which meant the punt traveled about 61 yards in the air.  Check out where Westbrook caught the ball (click on image for a larger view).

Westbrook then turned on the jets and ran down the right sideline at a speed that prevented the Washington pursuit from picking the best angles for tackles.  He hit a top speed of 21.9 mph, which he was able to stay close to for about 25 yards in the middle of his return.  Usain Bolt once hit a top speed of 27.8 mph, but 22 mph in the NFL, with pads and helmet on, is definitely an elite speed.  Check out the screen capture I got of Westbrook running nearly 22 mph (click on the image for a larger view).

An easy conversion to remember is 15 mph = 22 ft/s (exactly).  Westbrook's near 22 mph is over 32 ft/s.  An athletic and fit lineman running 15 mph next to Westbrook running nearly 22 mph loses 10 feet every second.  That's why tackling angles are so important.

Something curious happened at the end of the run.  Washington's Byron Marshall (#34) looked to have a perfect tackling line on Westbrook.  Check out the action just after Westbrook crossed the Washington 20-yard line (click on image for a larger view).

Marshall actually put a hit on Jacksonville's Rashad Greene (#13) instead of closing in on Westbrook.  Look at the screen capture below (click on image for a larger view).

It looks like Marshall was blocking Greene out of bounds at about the Washington 14-yard line!  I've looked at the video several times, and I simply can't figure out what Marshall was doing.  Westbrook turned left where Marshall's "block" occurred and scored easily (click on image for a larger view). 

The Redskins got the game-winning field goal as time expired, but Jacksonville fans were treated to a great punt return by Dede Westrbook.  I analyzed his return for TuneIn's 1st & Goal Check Down segment.  Chuck Nice of Playing with Science joined me on the show.  Click here for the audio of our segment.