Toni Kroos' Amazing Bend Beats Sweden!

With just a few seconds left in extended time, Germany got the goal it needed to move past Sweden, 2-0, in yesterday's World Cup action.  The win put Germany in a great position to move on to the knockout stage.  Toni Kroos kicked the game-winner and it was a thing of beauty.  The image below shows Kroos just before he kicked the Telstar 18 (click on the image for a larger view).

The view from behind the goal shows what the Swedish goalkeeper had in mind (click on the image for a larger view).

He is protecting the part of the goal to his right, perhaps thinking the Swedish two-player wall and other defenders would be enough to keep the Kroos kick out of the part of the goal to his left.  One of the defenders in the Swedish wall actually flinched away from Kroos' kick!  Check that out below (click on the image for a larger view).

See the blur of the ball on the back of the Swedish defender at the bottom of the image?  Hey, I'd flinch, too, with a fast-moving ball coming right at me, but I bet they guy wishes his back had at least let the ball graze him.

Now it's time to look at the beautiful trajectory.  The Magnus force helped Germany win the match because Kroos put a lot of counterclockwise (as seen from above) spin on the ball by kicking the ball right of center with his right boot.   That led to a Magnus force pushing the ball to Kroos' left, which meant the goalkeeper might have thought the ball would be wide of the goal.  Check out the trajectory that I've labeled with circles below (click on the image for a larger view).

Look at the lovely bend!  That's a banana kick with whipped air!  As the ball spins counterclockwise, the boundary layer of air is being whipped off the back right part of the ball.  If the ball whips the air that way, Newton's third law says the air has to push the ball to the left.  And did it ever!  Check out the view of the bend from a lower angle (click on the image for a larger view).

Air resistance worked to slow down the ball and Earth's gravity pulled the ball downward, but that gorgeous bend is due to the Magnus effect.  Want to see how close the Swedish goalkeeper came to deflecting the ball?  Check it out (click on the image for a larger view).

See the ball just barely off his outstretched right hand?  Want another view?  Sorry, Sweden, but I've got to show it (click on the image for a larger view).

The image will surely give Swedish fans heartache, but sometimes the beautiful game comes down to mere inches.

Okay, let's get quantitative.  I know the aerodynamic properties of Telstar 18 (click here for my research paper).  Modifying the result in my paper with what we've learned about spinning balls, I modeled Kroos' kick.  Check out the trajectory plot below, which shows the trajectory in red (dashed red line is the shadow on the pitch) and what the trajectory would have looked like without the Magnus force in blue (dashed blue line is the shadow on the pitch).  The goal plane is also shown (click on the image for a larger view).

The perspective I have on my 3D plot isn't quite the same on the actual views I showed above, which is why the red trajectory doesn't look quite as curved as the trajectories I put on the actual images.  Television images are also a bit skewed.  But you can see how much the Magnus effect altered the trajectory from the no-spin case.

The ball was kicked at 67 mph at about 13.6 degrees above the horizontal.  The ball was travelling a bit more than 51 mph when it reached the goal plane, having been slowed by air resistance and converting some kinetic energy into gravitational potential energy.

I'll now show you the sizes of the drag force and the Magnus force on Kroos' kicked ball while in flight.  I scale the forces by the ball's weight.  The ball took almost a second to reach the goal plane (click on the image for a larger view).

Look how close to the ball's weight the two forces are at the moment the ball was kicked!  You can see why the ball slowed so much and curved so much on its way to the goal plane.  Had there been no air resistance, the ball would only have slowed 1 mph or so at the height it reached in the goal plane.

I loved watching the kick and I loved analyzing the kick.  Physics makes the beautiful game all the more beautiful!

Match of a Lifetime for Nigeria's Ahmed Musa!

Ahmed Musa put on a show today as Nigeria defeated Iceland, 2-0, in World Cup Group D action.  The first of Musa's two goals was a thing of beauty.  After a scoreless first half, Iceland had a throw-in early in the second half.  Nigeria got control of the ball and once Victor Moses had the ball down the right side of the pitch, he was off to the races.  He kept looking toward his teammates to his left and he spotted Musa keeping pace.  Look where Moses launched his pass (click on the image for a larger view).

The ball is just leaving the right boot of Victor Moses in the above photo.  He kicked the Telstar 18 down and to the right, which gave the ball a lot of counterclockwise spin (as seen from above).  That meant the Magnus force was on the ball, causing it to curve from right to left (as seen by Moses) off its normal trajectory.  That was the perfect spin because the ball curved in toward Musa.

But the pass, like all passes, was not precisely perfect.  Musa put his athletic skill on full display as he caught the ball.  Check out Musa's outstretched right leg (click on the image for a larger view).

What you have to keep in mind is that Musa not only arrested the majority of the ball's velocity, his right boot was on the underside of the ball.  Whether by design or good fortune, that boot placement caused the ball to rotate counterclockwise -- as seen by Musa!  The ball's rotation axis had been turned 90 degrees.  Look at the closeup below (click on the image for a larger view).

It was great boot placement!  Musa's toes were up to help stop the ball's side-spin, but his ankle was on the bottom of the ball to take advantage of the ball's velocity and create the counterclockwise spin that Musa saw.  That meant that when the ball landed on the pitch, friction with the pitch would cause the ball to move toward the goal.  Muse wisely let the ball hit the pitch (click on the image for a larger view).

By letting the ball bounce off the pitch, Musa allowed the pitch to help the ball move toward the goal, and the ball was in a more stable position to kick with less speed than it would have had had Musa tried kicking the ball before it hit the pitch.  Look at the ball right before the kick (click on the image for a larger view).

Musa has the lean toward his left as his right leg comes through the ball.  He is about to kick the ball with a bit of backspin, so his boot will go through a line below the ball's center of mass.  How close did the ball come to getting blocked?  Check it out (click on the image for a larger view).

Look at how close the Icelandic goalkeeper was to the ball!  But the upward trajectory of a ball kicked at nearly 65 mph with backspin was too much for the goalkeeper.  At the instant shown below, Nigeria was on its way to victory (click on the image for a larger view).

Doesn't Telstar 18 look pretty in the goal plane?  I think so, but not nearly as pretty as Musa's goal!

World Cup Starts Today!

To whet your appetite for the start of the 2018 World Cup, you can listen to Neil deGrasse Tyson and me yap about soccer science on last night's episode of StarTalk's Playing with Science.  Click on the link below to learn about soccer science in the World Cup.

• Season 3, Episode 20 (June 13, 2018):  Extended Classic:  Planet Soccer, with Neil deGrasse Tyson

My only complaint is that the graphics people at Playing with Science didn't use a Telstar 18 ball in the photo!  The last time the traditional 32-panel ball was used in the World Cup was in 2002 when the Fevernova ball was the official ball in South Korea and Japan.  Forget the photo and listen to the podcast!