No Huddle asked me to analyze a nice touchdown thrown by Washington Redskins' quarterback Kirk Cousins to Ryan Grant. Unfortunately for the Redskins, the New Orleans Saints had a monster 4th-quarter comeback and won the game in overtime. The play I analyzed took place late in the 3rd quarter with the shot clock winding down. The Redskins faced a 3rd and 7 from the Saints 40-yard line. Cousins (#8) was in the shotgun and just prior to the snap, the Saints sent both safeties in for a blitz into the middle of the Redskins' line. Washington had seven blockers, including running back Samaje Perine (#32). But the Saints had eight rushing the quarterback and it doesn't take a rocket scientist to know that 8 is greater than 7. Kirk Cousins was about to get smashed! The Saints' safeties had a running start on the blitz. Cousins received the ball 0.43 s after it was snapped and the hungry Saints defenders were rushing for the sack. Ryan Grant (#14) was on the right side of the Washington formation. Check out the start of the play below from the screen capture I took (click on image for a larger view).
Grant sprinted to the right sideline as Cousins held the ball long enough for Grant to get open. The left side of the Redskins' line broke down and Cousins was going to be blindsided by defensive end Alex Okafor (#57). Cousins had taken four big steps back and threw the ball a full 2 s after he received the snap. Just as he threw, he became the meat in a Saints sandwich as he got crushed by Okafor and safety Vonn Bell (#48). Safety Rafael Bush (#25) piled on after the initial hit for added damage. Check out the carnage below (click on image for a larger view).
Not much fun for Cousins, was it? But he got the ball where it needed to be! Cousins released a great spiral into low-Earth orbit at the speed of 46 mph at 30.7 degrees above the horizontal. The ball traveled just over 38 yards in total horizontal distance, reaching a maximum height of about 8 yards above the turf, and took 2.1 s to reach Grant. It landed in his hands at about 41.6 mph. An air resistance force of about 15% of the ball's weight was acting on the ball while in flight. Check out the graph below of the ball's trajectory (click on image for a larger view).
Grant had run past two unsuspecting Saints defenders and was wide open for the catch. Check out just how open he was (click on image for a larger view).
Where was the defense?!? All that was left for Grant was a stroll into the end zone with perhaps a little taunting thrown in. After scoring, he tossed the ball into yet another low-Earth orbit.
For the audio on TuneIn Radio, click here. Gary O'Reilly of Playing with Science joined me on the show and did a wonderful job setting up the play. During my analysis of the play, I was interviewed by Alissa Smith of the Lynchburg News & Advance. Gary O'Reilly was kind enough to give Alissa a few comments for her story. Click here for the story that appeared in the Monday, 20 November 2017 edition of the paper.
For this week's appearance on TuneIn Radio, I got to discuss a great fake punt in the Jacksonville Jaguars' overtime win against the Los Angeles Chargers. At the end of the first quarter with no score, the Jaguars were lined up for a punt. It was 4th and 7 on their own 44-yard line. Brad Nortman was set to receive the snap from long snapper Matt Overton. Corey Grant was behind the Jaguars' line to the right of Overton. Check out the screen capture I got of the formation below (click on the image for a larger view).
I circled Nortman, Grant, and Paul Posluszny, who followed my yellow arrow into an incredible block. Nobody was lined up across from Overton, and thus a lineman didn't notice that Overton was ever-so-slightly angled toward Nortman's right. He would direct snap the ball to Grant. Check out the hole that the Jaguars' line opened up for Grant, and note Posluszny's great block to seal the side of the hole to Grant's right (click on the image for a larger view).
Notice Grant is headed toward the massive hole as Posluszny runs right in front of him. Grant had faked to his right to give Posluszny time to get in the hole for the seal block. Nortman rolled out to his left to help sell the fake.
The Chargers had two shots at stopping Grant. The first was by #40, Chris McCain. Grant stiff-armed McCain at the Jacksonville 45-yard line as McCain dove toward Grant. The problem with McCain's tackle attempt is that McCain's force mostly pulled downward on Grant's legs. That wasn't going to alter Grant's forward linear momentum! Check out the screen capture below (click on the image for a larger view).
McCain tried for Grant's feet, but Grant stabilized himself just a like a tightrope walker does. Notice both his arms are extended outward. That makes it harder to move Grant's center of mass outside his shoes, which would cause a gravitational torque to make him fall.
The second and last hope for the Chargers was #20, Desmond King. He had an open-field shot at Grant near the Los Angeles 42-yard line. But once Grant spied King, Grant shot to his left. When King drove for Grant, Grant hurdled over nine feet horizontally to avoid having his legs taken out. Look at Grant's athleticism below (click image for a larger view).
King dove, but Grant leapt to daylight. Once Grant cut hard to his right at the Los Angeles 35-yard line, he outran the defense to the goal line. Those hard cuts can lead to well over 100 pounds of force on a running back's legs. It's no wonder the average career length for an NFL running back is only about four years!
What I especially loved about the play is that it took nearly 11 seconds to complete. Someone could have jogged 10.6 mph along the sideline at the snap of the ball and gone 56 yards to the goal line in the time it took Grant to score. Grant was through the initial hole at 15 mph, and then hit a maximum speed of about 19 mph halfway into Los Angeles territory before scoring at nearly 18 mph. A sideline jogger that went 56 yards would have watched Grant run a total of about 85 yards!
Chuck Nice of Playing with Science joined me on today's radio segment. Chuck did a great job setting up the play and then I yapped some physics. Click here for our segment on TuneIn's No Huddle. It was a lot of fun talking football physics!
I returned from my visit to Kenyon College today. Friends and colleagues know why the trip was difficult for me. Kenyon College has been a special place for me since 1999. Unfortunately it now represents a place of broken promises and betrayal. What helped me considerably was the warm reception I received upon meeting up with former colleagues. It was great chatting with old friends again. I also enjoyed meeting new people and spending a few minutes discussing my research with Kenyon's bright physics majors. I had fun giving my talk. The photo below shows me a couple minutes before my talk began (click on the image for a larger view). Pizza helped attract a few extra students!
The chalkboard shows some belated Halloween math I used to entertain people before I got introduced. Nothing like a little mathematical nonsense to lighten an audience!
I will return this Friday to where my post-doctoral career began, Kenyon College in Gambier, Ohio. There are many reasons why I look forward to being back at Kenyon, but there are several personal reasons why the trip will be difficult for me. I'll do my best to put those reasons aside and have a great trip to a place that still means a lot to me. I certainly look forward to discussing three of my research areas with the good people at Kenyon. Either click here or on the poster below for information about my Friday talk.
The Philadelphia Eagles rolled over the Denver Broncos yesterday to the tune of 51-23. Gary O'Reilly and I represented Playing with Science on yesterday's No Huddle segment on TuneIn, during which I analyzed Jay Ajayi's impressive 46-yard touchdown run in the second quarter. Click here for the No Huddle segment. Ajayi's touchdown run was so fun to analyze that I decided to write a bit more in my blog post. Linear momentum, forces, and the laws of physics played crucial roles in the touchdown, like they do in most everything else that happens in the world. Look at the screen capture below for the start of the play (click on the image for a larger view).
The Eagles have 1st and 10 at the Broncos' 46-yard line. Quarterback Carson Wentz is in the shotgun and Ajayi is lined up on Wentz's right. Note there are four defensive lineman and five offensive lineman. Eagles' center Jason Kelce is not lined up against anyone. Kelce is about to play a major role in the play with some key blocking. Before that, he had to snap the ball to Wentz. The ball took about 0.4 s to reach Wentz, which is about the time it takes for a major-league fastball to reach home plate. Once he snapped the ball, Kelce pulled to his left, Ajayi took two strides to his left to receive the ball from Wentz, and then he witnessed the most beautiful blocking open up before him. Check out the blocking in the image below (click on the image for a larger view).
Eagles' left tackle Halapoulivaati Vaitai had Broncos' outside linebacker Shane Ray (#56) blocked. See the yellow circle in the above screen capture. Eagles' left guard Stefen Wisniewski had Bronco's defensive end Shelby Harris taken care of. See the orange circle in the above image. Look at the hole Ajayi is about to run through! After getting the ball from Wentz, Ajayi needed just five strides to get to the hole. Note the white arrow on lead blocker in the hole, center Jason Kelce. He has his eyes on Broncos' strong safety Justin Simmons. Take a look at the blocking scheme from another view (click on the image below for a larger view).
That's quite a hole, right? The Eagles' lineman employed their intuitive physics knowledge of linear momentum to set up the great run. Isaac Newton taught us that a net, external force is needed to change an object's linear momentum. The product of an object's mass times its velocity is an object's linear momentum. Beefy lineman have lots of mass and thus need lots of force to stop. A couple hundred pounds of force to stop a defensive lineman are not out of the ordinary. Offensive lineman intuitively know that linear momentum and force are vectors, which means they have directions as well as magnitudes. Keep that in mind for the end of the play.
The great line blocking allowed Ajayi to hit the hole at a speed of about 19 mph (31 kph). He was able to maintain that speed while running down the left sideline. While running toward the goal line, Ajayi's linear momentum was pointed right at the goal line. Broncos' free safety Darian Stewart was Denver's last hope on the play. Unfortunately for Stewart and Denver, linear momentum was working against them. Check out the screen capture below as Stewart hit Ajayi at the Broncos' 3-yard line, just below Ajayi's hip (click on the image for a larger view).
Stewart hit Ajayi with a force nearly perpendicular to Ajayi's linear momentum. That certainly changed Ajayi's linear momentum, but mostly perpendicular to the left sideline. Despite a force of several hundred pounds over less than 0.1 s, Ajayi's linear momentum change was mostly toward the out-of-bounds area. That works great unless an athlete like Jay Ajayi is a couple yards from glory and he is able to contort his body. He still had much of his linear momentum that was pointed toward the goal line after the hit.
Just as he was hit, Ajayi rotated toward his right. That ensured that after he was hit, his ball-carrying left arm would be above his body and ready to pass over the orange pylon for a touchdown. See what I mean in the screen capture below (click on the image for a larger view).
From the terrific blocking at the start of the play to Ajayi's contorted body over the pylon, linear momentum was the 12th man on the field for the Eagles!
Last night's episode of StarTalk's Playing with Science focused on the World Series. We discussed many iconic moments, such as Willie Mays' famous over-the-shoulder catch in the 1954 World Series and Kirk Gibson's lone at-bat in the 1988 World Series. Click below for a link to the episode.
The above episode aired a week earlier only on TuneIn. Click here for that link.
Last night the Astros evened up this year's Fall Classic with a thrilling 11-inning win. Game 3 will be in Houston tomorrow night. I love baseball and I love the World Series, but I grew up with the Astros in the National League. This year's World Series has a weird feel for me!
I had a lot of fun analyzing Eddie Jackson's second interception in yesterday's Bears' win over the Panthers. Jackson, a rookie safety out of Alabama, perfectly timed his run to a tipped ball and took Cam Newton's pass 76 yards for his second TD. His first came on a 75-yard interception, meaning Jackson became the first defensive player in NFL history to have two 75+-yard returns for touchdown in one game. Check out my screen capture below as Jackson just gets to the deflected pass (click on the image for a larger view).
Can you tell which player is moving fastest? It should be obvious by the amount of blur! The Panthers' Kelvin Benjamin was the intended receiver. He appears to have a good bead on the ball after Prince Amukamara got his right arm on Benjamin's chest just as Newton's pass arrived. But that blur coming from the right is Eddie Jackson, moving at nearly 17 mph. That running start was all he needed to snag the ball and take off for a pick six. I'm sure the fact that Cam Newton went to Auburn made the interception all the sweater!
The above play is the one I discussed on TuneIn yesterday. Gary O'Reilly joined me as we pitched the wonders of Playing with Science. Click here for our segment on yesterday's No Huddle.
Chuck Nice, Gary O'Reilly, and I joined Brian Webber and Nick Ferguson on TuneIn's 1st & Goal this past Sunday. We discussed Golden Tate's great touchdown run during Detroit's loss to New Orleans. There was some terrible tackling during the play, but Tate capped his touchdown run with a spectacular front flip into the end zone. Check out the screen capture I took of Tate crossing the goal plane (click on the image for a larger view).
I analyzed the play and provided physics commentary. As he crossed the goal plane upside down, Tate was moving 12 mph and rotating at 60 rpm. Think you could score a touchdown like that?!?
Click here for the seven-minute segment that contains more of my physics analysis of the Tate's touchdown. It was a lot of fun doing a live show!
I meant to write a blog post about my appearances on StarTalk's Playing with Science, but my life, both professional and personal, has kept me extremely busy in recent months. Appearing on the show and talking about sports physics has been a lot of fun! Chuck Nice and Gary O'Reilly are great hosts of the show and I always enjoy my interactions with them. Below is a list of the episodes I've appeared on. Click on the links to access the episodes.
After his performance in the Alps and in yesterday's time trial, there was no doubt that Chris Froome would win his fourth Tour de France. He now has a three-peat (should I send Pat Riley money for using that term???). Froome didn't win a stage this year, but was clearly the best cyclist. Staying near the winners in the mountains and in the time trials, Froome was simply better than everyone else. His Team Sky mates played a large role in his victory. It doesn't hurt to be supported by a powerful team!
Dutch cyclist Dylan Groenewegen won today's final stage. How did our model perform today? We saved our best for last, as you'll see below.
As tough as it is to predict the mostly-ceremonial final stage, I'm thrilled to end this year's Tour de France with a near-perfect prediction. How did our model perform overall? After summing the stage-winning times, I found we were 1.11% slow. I'll definitely need to spend time thinking about how much athletes and technology have improved since last year.
I never cease to be amazed by elite athletes. A total of 167 cyclists finished the Tour de France. I would be hard-pressed to finish a long flat stage during daylight hours. As for those grueling mountain stages, forget it. I need more time in the gym! My model estimates energy burn, i.e. internal energy burn with an average efficiency of about 20% and not just energy output needed to power the bike. During the entire race about 115,000 Calories could have been burned. Published cyclists' data may be below that number, but an estimate has to be made of internal energy efficiency. Our published papers on Tour de France modeling cite sources that are consistent with our energy estimates. The point is that a LOT of energy is burned during the three-week race. At 550 Calories apiece, those 115,000 Calories amount to nearly 210 Big Macs. That averages to 10 Big Macs per stage! I don't recommend eating Big Macs before cycling, but it does give you some idea of how much energy those cyclists burn each day. You may have heard that 3500 Calories matches the energy content in a pound of fat. That's roughly true, but you may have to burn about twice the Calories to get a pound of fat off because of the complicated way the body converts energy. Either way you think about it, 115,000 Calories represent one or two bowling balls of fat weight. No wonder elite cyclists stay in such great shape. Their job is a wonderful form of exercise!
I once again thank rising high-school senior Ryan Wainer from New York for his work this year. He acquired all the terrain data, which led to a successful set of predictions. How successful? We had one bad prediction with Stage 5 (9.24% error) and five good-a-decade-ago-but-want-to-do-better-today predictions in the error range of 4% - 8%. But that leaves 15 predictions to better than 4%, 11 of which were better than 2%. Five of those 11 were better than 1%, including our best prediction today. A nice way to end!
Chris Froome did what he needed to do in today's individual time trial. He came in third, just six seconds behind Poland's Maciej Bodnar. Froome now leads the overall classification by 54 seconds over Colombia's Rigoberto Urán Urán. Unlike the first individual time trail in Stage 1, today's result was slower than I thought it could be. We were a bit more than 5% off, as you'll see below.
One of the first things to look at after this year's Tour de France will be the two individual time trials. We were short on power in the first time trial and had too much power today. Tomorrow's final stage will be mostly ceremonial until the big sprinters go for the stage win once they are in Paris. Froome will probably be seen with some champaign and four fingers up (three in a row!). The last stage is always tough to predict because of the ceremonial nature of the stage. We've done well in the past by backing off on power. Our final prediction is given below.
Stage 21: 2h 25' 50" (prediction)
Chris Froome showed today why he's the best cyclist in the world.
That makes 12 of 19 stages that we've hit better than 3%. Strategies on long flat stages are hard to predict because the peloton dictates so much of the pacing. Boasson Hagen and 19 other cyclists came in within two minutes of the winning time. Chris Froome and the rest of the peloton came in 12' 27" after Boasson Hagen. I would therefore claim that our prediction was spot on!
Tomorrow's individual time trial will be the last chance Romain Bardet (23 s back) and Rigoberto Urán Urán (29 s back) have of catching Chris Froome. Below is our prediction.
Stage 20: 26' 42" (prediction)
We were a bit slow on the first individual time trial, which was the opening stage this year. I'll be anxious to see if we do a little better tomorrow.
Warren Barguil made France proud today with his second mountain stage win in this year's Tour de France. We predicted the two big mountain stages in the Alps really well. Look below to see how well we did today.
Chris Froome came in fourth today with a group just 20 s behind Barguil. He has a 23-s lead over Romain Bardet. The goal for Team Sky in tomorrow's long flat stage will be to keep Froome with the cyclists just behind him. The individual time trial on Saturday looks like it could be a lot of fun! Below is our prediction for tomorrow's Stage 19.
Stage 19: 5h 11' 09" (prediction)
If Chris Froome is to secure a three-peat, his team will have to have a great day tomorrow.
Michael Matthews won his second stage today. Racing turned out to be fast on the downhill, which is what I mentioned in yesterday's post. There is no way to predict team strategies! Below is a comparison between reality and our prediction.
Not a bad error, but yesterday's result spoils me for more sub-1% predictions. The next two stages in the Alps will likely decide this year's winner. Our prediction for tomorrow's stage is given below.
Stage 17: 5h 09' 36" (prediction)
Monster climbs in tomorrow's stage, but the finish will be a downhill sprint. Can anyone sneak across the finish line in under five hours?
The stage is classified as flat, but it's quite hilly for the first half. The middle of the stage is mostly downhill. Depending on racing strategies coming off a rest day, the above prediction could be slow. I'll be anxious to see if cyclists push themselves to high speeds on the downhills.
There are some stages I watch come to an end and hope the winning cyclist can give just a tiny bit more effort in the last kilometer. Check out the comparison between Bauke Mollema's winning time with our prediction for today's Stage 15.
Come on, Bauke! Just 21 seconds faster today and we reach perfection. He won by 19 seconds, so he didn't need to rush the final few hundred meters. But I'll definitely take today's result. Missing a nearly five-hour stage by 21 seconds is a lot of fun! I'm glad I didn't make the mistake I made with yesterday's prediction and alter power output. Our model did its thing today.
Chris Froome remains in yellow. Nairo Quintana, who I loved watching battle Froome in the mountains in 2015's Tour de France, slipped to #11 in the overall classification, more than six minutes behind Froome.
Tomorrow is a rest day. Teams will plot strategies for the next day's flat stage and the two, grueling stages in the French Alps that follow. I'll post our prediction for Stage 16 tomorrow.
Chris Froome got 25 s on Fabio Aru in today's Stage 14 and turned a 6-s deficit into a 19-s lead on the Italian cyclist. Michael Matthews won what I consider to be a slow stage today. Below is a comparison between the winning time and our prediction.
We were too slow on hilly Stages 5 and 8, so power was upped slightly for today's stage. We would have been under 1% without the change! Oh well, that's what makes this so much fun. We can't predict team strategies, crashes, and weather. Below is our prediction for tomorrow's hilly stage.
Stage 15: 4h 41' 26" (prediction)
I'm not tweaking the power in our model for tomorrow's stage. Will I regret that with a rest day to follow???
Our error isn't too large, but I've gotten used to hitting the mountain stages a little closer. Tomorrow's mountain stage isn't even half as long as today's stage, but it has three category-1 climbs and a speedy downhill finish. Our prediction is given below.
Stage 13: 2h 34' 22" (prediction)
Aru Fabio picked up time on Chris Froome today and wrested the yellow jersey away from the three-time champion. Will Froome get it back tomorrow?
Marcel Kittel is dominating the flat stages in this year's Tour de France. He won his fourth flat stage of this year's race. I thought someone might come in under four hours. Kittel was just a minute over that time. Below is a comparison between Kittel's time and our prediction.
I was traveling yesterday, so I missed watching Stage 9 of the Tour de France. That grueling mountain stage is one I'll have to catch on replay. Below is a comparison between the actual winning time and our prediction.
I'll definitely take that error! We nailed the first mountain stage. Below is our Stage 10 prediction:
Stage 10: 4h 05 31" (prediction)
I fully expect at least one cyclist to come in under four hours. But what will strategies be like? Will a relatively short flat stage after a rest day be competed for in an all-out manner? Will cyclists save up for a longer flat stage the next day? The leaders in the full classification certainly won't be going all-out for the win. But will their teams reign in breakout cyclists going for glory? It will be interesting to see what happens after the first rest day.
I'll be most interested to see why we were a bit slow on the past two hilly stages. Tomorrow is a travel day and I'll miss watching Stage 9, which contains three brutal climbs. I'll definitely check it out on replay!
Stage 4 finished for us rather well, but not so well for the riders involved in the controversial crash. It's a shame Peter Sagan won't be in the rest of the race. He is a great cyclist to watch, but his elbow cost him a chance at another points title. I'll also miss seeing Mark Cavendish, who was the unfortunate recipient of Sagan's elbow.
Today's Stage 5 had a grueling climb at the finish, but cyclists completed the stage much faster than we anticipated. We thought perhaps a little energy would be kept in storage today, but only three of the 193 cyclists were slower than our prediction. Below are comparisons for the past two stages.
When I return from traveling, I'll need to look at Stage 5 more closely and determine where we were slow. The first part of the stage to check will be the final climb. Below are predictions for the next four stages. That will take us to the first rest day on Monday.
Stage 6: 4h 56' 51" (prediction)
Stage 7: 4h 56' 08" (prediction)
Stage 8: 4h 51' 54" (prediction)
Stage 9: 5h 11' 15" (prediction)
With Chris Froome in the yellow jersey and the big climbs still to come, can anyone keep him from winning his fourth Tour de France???
I'm currently in West Virginia while traveling. I had to sneak a few minutes away from other activities to report on the first three stages of the Tour de France. Our model is doing well! I thought we might be a tad slow on the time trial, and we were, but we've nailed Stages 2 and 3. Below are the comparisons for the first three stages.
It's great being under 2%, not to mention being under 1%! I'll try to check in on the next two stages and then get more predictions online while on my travels. Team Sky certainly looks strong again this year!
I see that I made a mistake in my previous blog post. I wrote that the Tour de France begins this Sunday, but of course it begins tomorrow, which is Saturday. My research student has accumulated terrain data and I've run the data through my model. I won't be able to watch the first few stages as I'll be traveling. I'll thus put our predictions for the first five stages in today's post and then do my best to comment on the results when I'm able to do so.
Stage 1: 0h 16' 48" (prediction)
Stage 2: 4h 42' 08" (prediction)
Stage 3: 5h 04' 57" (prediction)
Stage 4: 4h 48' 37" (prediction)
Stage 5: 4h 04' 49" (prediction)
Stage 1 is a short time trial. I always worry that we'll be a bit slow, especially when such a time trial takes place at the start of the race when cyclists are well rested. Will a new time-trail record be set tomorrow? I'll be checking in when I can. Stages 2 and 4 are flat stages with a few small climbs. Stage 3 is hilly and Stage 5 is definitely medium-mountain with a category-1 climb at the finish. I will have to do a lot of reading and catching up when I finish traveling. In past years, riders have taken the first couple of stages a bit easier than later stages. We've been a tad fast early in the race on the flat stages. I'll be curious to see if that's the case this year.
It has been 281 days since my last blog post. I have missed writing about the Cubs winning the World Series after 108 years of rebuilding. A thrilling overtime Super Bowl passed without a word from me in this space. I've missed a lot of opportunities to write. Even the ongoing 2017 FIFA Confederations Cup in Russia has been off my radar (will Germany take it???). The reason for my long absence is that a personal tragedy befell me just eight days after my last blog post -- nine months ago today. Many friends, family members, and colleagues have kept me going during incredibly difficult times, but none more than my two wonderful daughters. They remind me on a daily basis that I can survive inconceivable betrayal.
To those of you who have contacted me in recent months and asked about my blog writing, I offer a heartfelt "thank you" for your interest. I hope to return to more regular blog writing, beginning with the upcoming Tour de France, the 104th edition set to begin this Sunday in Düsseldorf. My former student, Chad Hobson, who helped me with the past three Tours de France, graduated Lynchburg College last May and is off to study physics at the graduate level at University of North Carolina at Chapel Hill. This summer I have Ryan Wainer, a rising high-school senior in the state of New York, working with me. He has collected terrain data and I'll run them through the latest model that Chad and I put together after last year's race. I will not be able to put the kind of detail into my Tour de France blog posts that I have inserted in the past. But I will get predictions up soon. I can't wait to see if anyone can knock off Chris Froome! I also hope to get a blog post written that highlights my appearances on Star Talk Radio. It's good to stroll my fingers across a keyboard once again.