06 August 2012

Some say, "Football!" Some say, "Soccer!"

Each time I check scores on a US website or listen to a US sports commentator, I read or hear about soccer in the Olympics.  Given where the Olympics are being played right now and given that the international governing body is the Fédération Internationale de Football Association (FIFA), football might be the better term to use.  What one calls the beautiful game is, of course, not nearly as important as the action taking place on the pitch (or field, if you prefer).

My girls and I have been following the football action.  They are, no surprise, more interested in the women's tournament than the men's.  We plan to watch the US team take on Canada later today in the semifinals.  The winner plays the winner of the match pitting Japan against France. My girls love the big stars like Amy Wambach and Hope Solo, but they especially enjoy the all-out white-haired enthusiasm expressed in the play of Megan Rapinoe.  Of delight to them as well is The Albert, which is the ball being used in the Olympics.

Adidas created a special Tango 12 series ball for the London Olympics, and it was named The Albert.  It is easy to find online close-up images of the ball (click here for one example).  According to Adidas, the new ball's woven carcass and improved bladder are capable of holding its air better and keeping water out of its interior.  The latter feature is especially important for matches in Great Britain where summer rain is not so uncommon.  Football designers do their best to make balls as spherical as possible.  The balls in the Tango 12 series have 32 thermally-bonded triangles with a grip texture.  As someone who does research on footballs, those details are important to me.  For my young girls, they love the color scheme.

Football trajectories are of special interest to me, and I pay close attention to the ball's flight on corner kicks and shots on goal.  If you see a shot with lots of sidespin, imagine viewing the ball from above.  The Magnus force due to the counterclockwise spin often imparted by a right-footed player causes the ball to deflect to the left.  Clockwise spin is associated with balls getting deflected to the right.  Those "banana" kicks are tricky for goalkeepers.  Even trickier are the low-spin "knuckleball" kicks.

The Magnus force comes about because the boundary layer of air around the ball separates asymmetrically (as defined by the line of the velocity vector) from the back of the ball.  Think of what a boat's rudder does to the water moving around a boat's hull.  There is no sideways deflection if you see a symmetric wake behind a boat.  Turning the rudder, however, causes the wake to deflect to one side, allowing a component of the water's force on the boat to push the boat to one side.  Think about Newton's third law.  If the rudder pushes water in one direction, the water has to push on the rudder in the opposite direction.

The low-spin "knuckleball" kicks present slowly-varying profiles of the ball to the oncoming air.  Because of the places where the panels are joined, there are parts of the ball that are rougher than others.  Rough area usually delay the boundary layer's separation.  Allow the ball to slowly rotate and the the deflection direction changes.  Tough for the goalkeeper!

Air drag is the force that slows the ball down during its flight.  Those rough areas on the ball help reduce drag.  If that seems counterintuitive, check out the graph below (click on the image for a larger view).
That image comes from an invited article I wrote for Physics Today before the 2010 World Cup (click here for the article or here for the Japanese version in the magazine Parity).  The drag coefficient is plotted versus Reynolds number, which is proportional to the ball's speed (to convert to speed, note that the "2" on the horizontal axis corresponds to a ball speed of about 14.1 m/s or 31.5 mph).  What you see is that in the speed range for football, a perfectly smooth ball would have a lot more drag on it.  The two inset images show that as speed increases through the "drag crisis" the boundary layer's separation ultimately moves farther back on the ball, leading to a smaller drag coefficient.

The above is but a flavor of the wonderful physics behind the beautiful game.  My pre-Olympics football picks were US on the women's side and Brazil on the men's side.  Both teams are still alive.  My girls and I will enjoy great semifinal action on the women's side today as we root for our home country!

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