Vandy Wins College World Series!!!

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

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

Well done, Vandy!

Messi's Incredible Free Kick

No matter how many times I've seen Lionel Messi play the beautiful game, I always see something special each time.  To end the first half against Nigeria today, Messi delivered a perfect free kick.  It was his second goal of the game and fourth of this World Cup.  The image below shows one view of the initial setup (click on the image for a larger view).

Messi is just about to connect.  He is about 27 yards (24.7 meters) perpendicular distance from the goal line.  The image below shows a good look at the defensive wall (click on the image for a larger view).

Messi launched the ball off his left boot with a speed of 55.4 mph (89.1 kph) and launch angle of 18.5 degrees.  Note that the Nigerian goal keeper is left of center in the goal (as seen by Messi).  The goal keeper's initial position was critical because Messi imparted a great deal of clockwise spin (as seen from above) on the ball.  His target was well away from the goal keeper!  The image below shows Messi introducing his left boot to Brazuca (click on the image for a larger view).

Note how his foot is left of center on the ball so that he can drive his boot through, thereby torquing the ball.  Note, too, the lean in his legs.  He has moved his rotation radius so as to increase his boot's distance from that axis.  The pitch provides the counter-torque to keep Messi stable because his right boot pushes to his left, which means the pitch pushes on his boot to his right.  The torque from the pitch nearly balances the torque from his weight; balance is further aided by his arm movements.

It took the ball just 1.2 seconds to reach its target.  The image below shows a three-dimensional trajectory (click on the image for a larger view).

The red curve is the real trajectory; the red dashed curve is the shadow on the pitch.  The thin black curve is what the kick would have looked like with no spin and no knuckling (black dashed curve is the shadow of that kick).  Now you see why the kick was perfect!  Messi used the Magnus effect to curl the ball into the upper-right portion of the goal.

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

Once again, Messi has dazzled the soccer world!

Penalty Kick Sends Greece to Knockout Stage!

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

The image below shows Samaras as he starts his motion toward the ball.  Ivory Coast goal keeper Boubacar Barry is waiting at the center of the goal.  Click on the image for a larger view.

It will take Samaras about 1.46 seconds to reach the ball from the image you see above.  Barry, like all goal keepers, will have to rely on scouting reports, Samaras's body language, and a good bit of luck if he is to block the kick.  After nearly 0.46 seconds, Barry is seen in the video initiating his lean to his left (right for Samaras).  After another 0.58 seconds, Barry is clearly moving toward his left, either guessing the direction of the kick or seeing something in Samaras's body language, such as an open hip.  Almost 0.42 seconds after that, Samaras kicks the ball.  The image below shows Samaras's right boot just making contact with the ball (click on the image for a larger view).

You can clearly see that just as boot meets ball, Barry has committed to blocking a shot he believes will be down and left of him.  Notice how low to the pitch he is before the ball has even left Samaras's boot!  He has also moved forward so as to reduce the projected area of the goal as seen by the ball at the kick point.  The image below shows another view of Barry just before the kick (click on the image for a larger view).

You can once again see how committed Barry is to blocking down and to his left (down and to Samaras's right).  The ball took only 0.375 seconds to reach the goal plane, so don't blame goal keepers for committing to a guess just as the ball is kicked.  The goal area is (24 feet) x (8 feet) = 192 square feet (17.8 square meters).  Throughout the 0.375 seconds the ball took to reach the goal plane, Barry probably blocked a total of around 9% of the projected area, though that percentage drops to no more than 5% or so once the ball reaches Barry.

Barry just missed getting the block!  Check out the image below (click on the image for a larger view).

Greece's ticket to the knockout stage is mere inches from Barry's fingers.  The next image shows that the cropped video I took can't distinguish Barry's glove from the ball (click on the image for a larger view).

The final image I show below is a closer look from the back of the goal (click on the image for a larger view).

Look how close that ball is to being blocked!  That is the difference between moving on to the knockout stage (Greece) and heading home (Ivory Coast).  There is no way Ivory Coast wanted anyone else defending that kick.  It is interesting to note, though, that Barry is listed at 5 feet 10 inches (1.80 meters) tall.  The backup goal keeper for Ivory Coast, Mandé Sayouba, is listed at 6 feet 3 inches (1.93 meters) tall.  Ivory Coast had already made three substitutions when the decisive penalty kick was taken.

Of course I had to model the trajectory of the ball.  The image below shows the three-dimensional trajectory with the goal plane shown as a rectangle (click on the image for a larger view).

I show the trajectory shadow on the pitch, plus the no-spin trajectory and shadow.  The ball had slight counterclockwise spin (as seen from above), and thus curved very slightly toward Barry.  Brazuca was launched 7 degrees off the pitch at 71.0 mph (114 kph).  The ball had only slowed to 63.1 mph (101.5 kph) when it passed the goal plane.  At that launch speed, the drag force on the ball is the same as the ball's weight!

Congratulations to Greece for making the knockout stage!

From a Jones Smash to a Ronaldo Punch in the Stomach

World Cup action takes one across the entire spectrum of emotions.  During yesterday's match with Portugal, I was elated when Jermaine Jones smashed an equalizer in the 64th minute.  I was really cheering 17 minutes later when Clint Dempsey used his stomach to move the US ahead, 2-1.  Fearing the five minutes of extended time, I was on pins and needles hoping my team could hold on and earn a berth in the knockout stage.  Instead, the great Cristiano Ronaldo, who had not had a great game to that point, fired a cross for the ages in the final half minute to give Portugal a draw.  I felt like someone had punch me in the stomach.  Now the US must go for at least a draw on Thursday against a powerful German team.

The image below shows Jermaine Jones as he fires his smash (click on the image for a larger view).

That smash was at the goal plane in just 0.97 s.  As the image above shows, Portuguese goal keeper Beto was partially screened from Jones, which explains why Beto looked slow to react to the shot.  The ball trajectory is shown below (click on the image for a larger view).

Three-dimensional graphics are always challenging!  I show the plane of the goal, plus the shadow of the trajectory on the pitch.  I also show a no-spin trajectory, but because counterclockwise (as seen from above) spin was small, there wasn't much curve.  There was enough curve, however, because the no-spin trajectory is just outside the goal plane!  Jones fired his shot at a phenomenal 73.8 mph (118.8 kph).  Note how Jones's right leg is fully extended from his rotation axis, which he moved by leaning, thus guaranteeing a lot of speed.

Ronaldo's cross was a thing of beauty.  The image below shows Ronaldo just as he kicked the ball (click on the image for a larger view).

As with Jones, Ronaldo leaned so as to increase his leg's rotation radius.  Both Jones and Ronaldo benefited from enhanced stability through their leans, too.  Note that Varela, who is about to head Brazuca right into my stomach, has yet to enter the penalty area.  The image below shows Varela as he is heading the neutralizer (click on the image for a larger view).

Ronaldo's cross was timed perfectly.  The ball left Ronaldo's boot with lots of counterclockwise spin (as seen from above) at a launch speed of 62.6 mph (100.8 kph), and then reached Varela's head 1.4 seconds later at a speed of 45.1 mph (72.6 kph).  The image below shows the trajectory of Ronaldo's cross (click on the image for a larger view).

The red curve is the actual trajectory; the thin, black curve is what the trajectory would have looked like without all that counterclockwise spin.  The spin pulled the ball back toward Varela, which meant it wasn't running away from him as much as the no-spin trajectory.

First and foremost, I was sick that my US team lost a win in the final seconds of the match.  After getting over the feeling of being punched in the stomach, I realized just how special Ronaldo's cross was.  There truly is beauty in a dark moment!

Tim Cahill: Goal of the Tournament!

"It's the goal of the tournament!"  My summer research student, Chad Hobson, uttered those words immediately after seeing Australia's Tim Cahill strike as incredible a goal as you are ever to see.  We were watching Netherlands take on Australia in my office,  hoping not only to see some great soccer, but some great physics.  We weren't disappointed as the quality of play was top notch, and there was plenty to dissect from a physics viewpoint.

Just a minute before Cahill's great goal, Holland's Arjen Robben scored an incredible goal of his own.  Firing with his left boot from the left side of the penalty box, he sent Brazuca through the Australian defense as one would thread a needle.  Check out Robben's shot below (click on the image for a larger view).

It appears Australia has a great chance to block the shot, right?  Well, watch Brazuca sneak under the first defender's boot (click on the image below for a larger view).

The ball had only the goal keeper to beat, which it did (click on the image below for a larger view).

What a shot!  We could hardly believe what we had just seen, and then Tim Cahill struck the equalizer.  What's great about the start of the play is the Ryan McGowan met a pass moving almost perpendicular to his run.  He in fact kicked the ball without a single dribble (click on the image below for a larger view).

Not only does McGowan kick the ball just 15 yards (13.7 m) from the halfway line, he is kicking the ball to Cahill (in yellow on the far right above) who will have to catch it while looking into the sun.  Look at the stadium shadow on the pitch!  When thinking about what Cahill did, don't forget that he was staring into the sun.  The view below shows that Cahill was about 9 yards (8.2 m) from the penalty box when McGowan kicked the ball (click on the image for a larger view).

The straight-line distance from McGowan's kick to the point where Cahill catches the ball with his left boot was about 41 yards (37 m).  The ball took a bit more than 2.7 seconds to reach Cahill, and Cahill struck the ball immediately upon receiving it.  He never dribbled the ball; the ball never touched the pitch.  The image below shows Cahill receiving the ball (click on the image for a larger view).

The timing was exquisite!  McGowan was running about 15 mph (24 kph) when he kicked the ball.  He launched it off his boot with a speed of approximately 51 mph (82 kph).  Cahill was running forward at roughly 11 mph (18 kph) when he caught/kicked the ball, which was around 2 feet (0.6 m) off the pitch.  The ball was traveling about 37 mph (60 kph) when it hit Cahill's left boot.  The image below shows a better look at the catch/kick (click on the image for a larger view).

Note the players' shadows.  The ball came right out of the sun from Cahill's perspective.  He kicked Brazuca into the middle of the top crossbar, which then ricocheted into the goal.

If you haven't seen this goal, go online and find it.  It's worth watching!

USA Corners Its Way to Win!

Two days have passed since I was jumping up and down after my home country defeated Ghana, 2-1.  Ghana has had our number in recent World Cups, so a win was sweet, and even more so given the quality of competition in our group.  The Wall Street Journal published today a little blurb I sent them on the corner kick that set up the winning goal.  I've only now had time to add a few more comments beyond what the Wall Street Journal published.

About four minutes following a great equalizing goal by Ghana in the 82nd minute, USA had a corner kick right of the goal as seen by someone looking at the goal from the middle of the pitch.  The image below shows Graham Zusi in the 86th minute about to deliver the corner kick (click on the image for a larger view).

He kicked the ball with his right boot, which imparted counterclockwise spin (as seen from above) on the ball.  He launched the ball at a speed of about 59 mph (95 kph).  The ball curved to his left, creating a perfect banana trajectory.  John Brooks headed the ball into the goal after the ball spent 1.47 seconds in the air.  The image below shows Brooks with Brazuca on his head (click on the image for a larger view).

The magnitude of the force Brooks exerted on the ball, which is the same magnitude force he felt from the ball, was nearly 120 pounds!  As great as Brooks's header was, I really love the corner kick that set it up.  Check out the trajectory below (click on the image for a larger view).

The solid red curve is the actual trajectory.  The red dashed curve shows the shadow on the pitch.  The dark thin curve is what the trajectory would have looked like has there been no spin on the ball, i.e. no banana kick made from whipped air using the Magnus force (that kick's shadow is also shown).  The real ball moved nearly 6 yards (5.5 m) laterally to the left.  Moving toward Brooks helped him with his header.  He could give the ball speed into the goal by almost reversing the normal component of the ball's impact velocity.

Isn't that corner kick a thing of beauty?

Torque that Brazuca!

The first two goals in Switzerland's 2-1 win over Ecuador gave us great banana kicks from the left side into the penalty area.  The assists were every bit as spectacular as the headers that provided the goals.  Both relied on left-booted kicks that put clockwise spin (as seen from above) on the ball.  The left-to-right curve due to the the Magnus force meant the ball had a component of its velocity away from the goal and toward the waiting head of a teammate.  Both kicks were things of beauty!

Ecuador's Walter Ayoví kicked the ball by swinging his left leg across and upward.  Look at the image below (click on image for a larger view).

What a great image!  Notice the body lean.  The planted right boot pushed on the pitch to the right (as we see it in the image).  The pitch, by Newton's third law, pushed the right boot to our left.  That created a torque in the clockwise direction (again, as seen by us), which nicely balanced the counterclockwise torque created by Ayoví's weight.  That weight torque was clearly present because Ayoví's center of mass was not over his feet.  Enner Valencia was set up perfectly.

By swinging his left boot across Brazuca, Ayoví created the necessary torque to get the ball spinning.  That same type of torque was put on Brazuca by Ricardo Rodriguez of Switzerland as he sent the ball into the penalty area on a corner kick so that Admir Mehmedi could head in the equalizer.  I cropped the image below from my video feed (click on image for a larger view).

The net partially obstructs the view, but you should be able to see the body lean and Brazuca coming off Rodriguez's left boot.  Like the previous kick, boot must meet ball left of center as seen by the player.  A nonzero lever arm distance from the contact point to Brazuca's center of mass is necessary to get the ball spinning.

I can't leave this Sunday of World Cup action without commenting on the incomparable Lionel Messi.  After incredible footwork to get to one of his favorite spots on the pitch, Messi took advantage of an opening to send the ball off the left post and into the goal.  Look at the image below (click on image for a larger view).

Another left boot, but this time the line of force from the boot went above Brazuca's center of mass.  Messi's left boot is moving upwards in the above image.  Messi's genius was on full display not only in getting to the perfect spot for a shot on goal, but knowing to give Brazuca topspin.  Messi kicked the ball from 18 yards out, right on the center of the line for the penalty area.  The ball stayed low, and bounced just before hitting the left post.  There was no way the goal keeper could get such a shot.  The topspin meant there was a Magnus force pointing down, which helped keep the ball low to the pitch.  Watch that goal, and be amazed at one of the best to ever play the beautiful game.

To Spin or Not to Spin?

The two goals scored in the first half of Italy's match with England were great, both from a strategic point of view and from physics point of view.  Claudio Marchisio scored the match's first goal after Italy executed a perfect corner kick play.  Instead of powering the ball into the penalty area, Marchisio received the ball after some fancy and tricky footwork from teammates.  He then kick the ball low to the pitch with almost not spin.  Check out the image below (click on image for larger view).

The image I cropped from the video feed I was watching shows the ball low to the pitch with very little spin.  Note how clear the ball is compared to the players.  Marchisio's shot looked to have a slight knuckle effect, which I estimate from one replay that showed the shot from the back of the goal.  At the speed and angle of the launch, the ball would not have laterally deflected more than about 2% of its horizontal range (from boot to the first time the ball hit the pitch).  He opted for no spin because he was after a straight shot on goal.

England tied the match just two minutes later when Wayne Rooney found Daniel Sturridge with a beautiful cross off his left boot.  The ball had lots of clockwise spin (as seen from above), which meant it curved left to right as Rooney would have seen it.  Look at the image below (click on image for a larger view).

Rooney is off to the right, out of frame of the video feed I cropped.  His perfectly placed ball is heading for Sturridge.  The ball's spin meant that it arced a little toward Sturridge, which made for easy handling by the forward.

The first half goals showed when it's good to kick with little-to-no spin and when a lot of spin is needed.  Great physics on those two goals!

Italy got the winning goal on a well-timed header by Mario Balotelli just five minutes into the second half.  An excruciatingly close miss by Rooney and several errant kicks by England late helped Italy close out a 2-1 win and three very big points on the heels of Costa Rica's stunning win over Uruguay.

Great Header, Robin van Persie!

What a great goal by Robin van Persie just before halftime of the Netherlands match against Spain!  Daley Blind fired the ball off his left boot from just past the middle of the pitch near the left touch line.  The ball had lots of clockwise spin (as seen from above), and curved left to right.  The ball met the head of a diving van Persie about 16 yards from the center of the goal.  The trajectory of the kick was perfect, and so was van Persie's header, which sent the ball upward and over the Spanish goal keeper.  Is the image below great, or what?!?

Click on the above image for a larger view.  Spain is in trouble as Arjen Robben just used some fancy footwork to score in the 53rd minute.  This great game is better than the rain-soaked match between Mexico and Cameroon that saw two goals taken from Mexico in the first half by truly awful refereeing.

Almost World Cup Time!

Like millions and millions of other people around the world, I'm anxiously awaiting for tomorrow to bring the start of the World Cup in Brazil.  I've had a lot of fun researching the new ball, which is called Brazuca.  That research, getting ready for the Tour de France, and working on a couple of books have kept me very busy -- and away from blogging.  I hope to get a few posts written during the World Cup.

My research student this summer is Chad Hobson, who just completed his first year here at Lynchburg College.  Chad will be helping me with Tour de France modeling.  He is also a soccer player and avid fan of the beautiful game.  We spent part of the afternoon today examining the flight of Brazuca.  The photo below shows my ball, which is just like the one my colleagues in Japan tested in a wind tunnel (we published our research on Brazuca a couple of months ago -- go here to download a copy of our paper for free).

Click on the image for a larger view.  Note the texturing on the surface.  Note, too, the long seam paths, which help make the six-panel Brazuca's surface rougher on average than the eight-panel Jabulani surface.  The research I did with my colleagues in Japan shows that Brazuca will be more stable than Jabulani.  There should not be so many erratic trajectories this time around!

To get a feeling for how a soccer ball curves, check out the image below (click for a larger view).

Chad kicked the ball with counterclockwise spin as seen from above (also a little topspin component).  I show the path the ball takes with the red trajectory curve.  Brazuca's spin causes air to be whipped off back and to the right.  There is thus a leftward deflection, creating the nice banana trajectory you see above.

It now World Cup time!