The Physics of Beckham

By Mark Trodden | June 23, 2006 6:03 am

I had a great time in England, visiting my parents and catching as much of the World Cup as was reasonable. On Tuesday night we watched England as they managed a draw against Sweden to finish the first round at the top of their group, ensuring a second round match-up against Ecuador on Sunday. I’ll be watching that one back in the U.S., since I flew back yesterday, and although I’ll enjoy it, it won’t be quite the same as watching the game back in England.

Despite his reputation, David Beckham hasn’t really been pulling his weight in my opinion. Nevertheless, there have been a few moments of that wonderful Beckham touch, such as the one that led to the very first goal in England’s first game against Paraguay.

For those of you unfamiliar with Beckham’s specialty, it is the perfectly weighted curving ball, sometimes used as a direct shot on goal from a free kick, and other times used from a corner to land precisely on the head of a waiting striker. Since in both cases Beckham strikes the ball from a stationary position (the ball that is, not Beckham, I should point out in uncharacteristically David Foster Wallace-like style) after other players have positioned themselves strategically (a set piece), he is often referred to as a “dead-ball specialist”. The extent to which the path of the ball curves is particularly impressive, and is the source of the title of the well-known 1998 2002 movie Bend it Like Beckham.

Here‘s a clip to show you what it looks like.

Anyone who plays football knows instinctively (by which I mean through extended practice and through watching experts do it) how to curve a ball. The trick is to put an appreciable amount of spin (or “english” for all you American pool players) on it, while being sure to strike the ball hard enough so that it goes some distance over which the spin can have its effect.

But the kids out there (and most of the adults, I’m guessing), have no idea why this works. So if you fall into this category, or you know someone who does and you’re looking or a resource to help explain it to them, SoccerBallWorld has the site for you.

The site contains an online version of a wonderful article that was first published in Physics World magazine, June 1998 pp25–27.

You can read over the FAQs about the physics of soccer balls. For example, you might be interested in the whether atmospheric pressure affects how soccer balls fly – an important question given the very different places World Cup finals are held. You’ll be told that

The atmospheric air pressure (the air surrounding the ball) also plays a role in how far a ball travels. At lower pressure, there’s less air friction. You can compare it to kicking the ball in a tank of water to kicking the ball on the moon. Balls go farther at high altitude because of the reduced drag from the air, which is thinner as you go higher up. So there’s a case where “reduced” air pressure makes the ball go farther.

But let’s face it, you’re almost certainly there because you feel in your bones that England will win the World Cup (OK, you always feel this way, but surely it’ll be different this time, won’t it?), and want to understand the physics behind Beckham’s contributions. Right?

If so, then you’ll want to start off reading about the aerodynamics of soccer balls; Bernouilli’s principle; the Magnus effect; the lift force and the drag force; and laminar flow.

Once you’ve absorbed that, then you might want to read on about the work that Japanese researchers at Yamagata University performed using finite-element analysis to simulate how people kick footballs. Finally, at this point, you should have a decent understanding of the Physics of Beckham.

Having done your solemn duty as a physicist, you are now free to sit back and watch England play Ecuador in the second round at 11am EST on Sunday.

I love the World Cup.

[Update: Jorge Pullin pointed me to this very cool site (in Spanish) about the physics of football. (Also, England won against Ecuador.)]

  • anon

    Finally, at this point, you should have a good understanding of the Physics of Beckham.

    Minor addition: if you watch very closely, you will also notice that the strings, or laces, of his boots are neither curled nor entangled. His physics doesn’t trip him up repeatedly.

  • peter

    Dont forget that his voice is high pitched enough for echo location, and his skull dense enough to be a singularity. In fairness, he has set up almost all of our goals. And what if there’s quantum entanglement between Owen’s anterior cruciate ligament and something else in the universe, which broke simultaneously? We look to physicists for anwers.

  • Dan

    The one on the video looks more like Rivaldo than Beckham…

  • Mark

    Thanks Dan! I was looking at a bunch of different clips and pasted the wrong one into the post. I’ve replaced it now.

  • Navneeth

    I’m not sure how many movies with the title Bend it Like Beckham were made, but if you’re referring to this one, I think you’re off by 4 years. 😉

  • citrine

    OK, here’s a question from someone who is woefully ignorant of sports.

    If the specialty moves of an athlete can be analyzed in such great detail, how come others who play the same sport cannot (do not?) seem to adopt the same technique(s) to equal effect?

  • Eugene

    It’s all Steven Gerrard so far.

  • Mark

    Thanks Navneeth – fixed!

  • Leo

    You should mention that the goal against Paraguay was in fact an own goal of a Paraguayan. So much about Beckham. Everyone knows that Germany will win :)

  • Mark

    Germany do look great Leo – I agree. As for the Paraguayan own goal; Beckham’s delivery was inch-perfect and if the defender hadn’t got that slight touch, then two England strikers were there to head it in, so I think it was essentially a perfect free kick.

  • JoAnne

    Mark, I’ve been waiting for a World Cup post from you! Glad you didn’t disappoint…

  • Aaron

    Wow, what an exciting post. On more than one occasion I’ve tried to explain to people how to create that bending effect you see occur on a well struck soccer ball. It’s interesting to see the physics broken down and explained in detail. Now I have a little bit better understanding of something that I seem to have grasped very early life, and eventually applied to my time on the soccer field as a right wing.

    My understanding of how to effectively bend a soccer ball began when I was six or seven years old learning to chop wood with a double bladed ax in the Sierra Nevadas of northern California. The individual who taught me was a local Native American, whose name I can’t recall any longer. But well I remember that first day of my training when he showed me the advantages of “pulling” the ax handle at the precise moment just before the ax head struck the wood. Anyone who’s ever used an ax or a pickax will immediately understand what I’m talking about. For reasons that I’m sure the physicists can better explain than I, this action seems to increase the effectiveness of an ax stroke by 1 to 3 times. When you’re a kid it seems almost magical because you have very little strength in comparison to an adult, and learning this little trick enabled me to split much larger pieces of wood much more easily than I had previously.

    Some years later when I learn to play soccer at age 8, I began to unconsciously employ the same technique I’d learned splitting wood to the ball on the soccer field. To my mind at the time, the effect was amazing. Whenever I had time to set up the ball, as in a free kick, I was able to produce that bending effect which allows you to launch the ball in one direction, and at a specific point in flight the curvature, which initially it was only slight, seems to overcome the forward inertia to some degree allowing for that dramatic change in direction midflight.

    Later in life I was able to create this same effect in a volleyball serve, and later in a golf drive. Unfortunately my ability to make the golf ball radically change direction 150 yards out from the point of strike was never particularly desirable. I believe they call it a slice, and I have one that seems to be able to make near perfect right angle turns sending my ball off into the woods or through a neighbor’s window. Apparently once you learn this ability, it’s rather hard to stop doing it.

    In the world of volleyball it allowed me to develop a trick serve, which I always referred to as the “Death Drop Serve.” By striking the ball with just average or light force, while at the same time dropping to the ground at the precise moment, I was able to create a serve which seem to bend at a right angle in midair. So what the opponents saw was a ball coming straight at them over the net at a relatively high velocity, and at a specific point it would drastically change direction and drop to the ground in front of them, seemingly dead, totally depleted of its energy. This little trick serve won me many a must-have point on on the volleyball court.

    I was never a great soccer player, but even to this day I can still bend the ball around a half a dozen players standing in front of the net, leaving them rather bewildered as to what just happened.

    Everyone always thought I had some special ability, but I guess all I really did was develop an instinctual grasp of physics early in my youth.

  • Simon

    Did Joe Cole intend to slice the ball like that?

  • Mark

    I honestly don’t know Simon, although my best guess would be no. Great looking goal in any case though!

  • Simon

    I agree – I think he’s becoming our key player, along with Gerrard.

  • Mark


  • Eugene

    For a sometime I’ve always wondered why I can hit curveballs better when I was playing in Chicago. I moved from malaysia to Chicago, and suddenly my curveball rules. Then I realized that it must be because it’s much dryer in Chicago (it’s 99% humidity back home) so my boot (cleats to you USians) doesn’t slip on the ball so much.

  • Say Lee

    Apparently the work of the japanese researchers did not help their countrymen at all. Japan is at the bottom of the group and became a first-round casulty, a fate shared by other Asian aspirants.

    Because of the dimples on golf balls, they behave differently in mid-flight and I believe that was analyzed too in one of the issues of Physics Today (Working Knowledge).

    And speaking of Germany being the favorite, the prediction now finds support in Physics Today too (June, 2006, Soccer obeys Bessel-function statistics ).

  • donncha

    Robert Carlos from WAY back. My jaw dropped the first time I saw this.

  • damtp_dweller

    Isn’t that the goal he scored in Le Tournoi?

  • Paul Valletta

    Being born in Wales, we have had to suffer in soccer! Whilst having some great individual soccer palyers, we never Gel as a team. But I LOVE and support “soccer” and am not biased in any way. I enjoy football, I admire good footballers, and if a player “of any nation”, shows some exquisite skills on the pitch, I love it. This world cup, has seen the emergence of some interesting players, and football nations I had not heard a lot of, until now.

    I am rooting for England, I want to see some underdog nation do well, but as far as I can predict the final, I believe it will be the reverse of 1966:England v Germany-score 2-2, Germany wins 4-2 after extratime.

    40 years ago it was the other way around, England home nation, 2-2 England won after extra time.

    About the physics of Beckham, does not the balls “inside pressure” have a lot to do with it motion?..the pressure give the ball weight, the more pressure inside the ball will, according to the accepted Newtonian view?..produce the “less” curved passage from an impact force?..example a lighter ball will curve and bend (a slice-shot) as it will be more affected by the surrounding air presure?

    Getting the ball to “bend”, “slice”, “swerve” and generally decieve the goalkeeper whilst in transit, is one of the most spectacular sporting skills in existence, as clearly shown by the amazing Joe Cole goal, and early in the competition, by Germany’s Miroslav Klose.

    Amazing for us football fans!

  • Mark

    Those of you who are intersted will have seen the latest example of the physics of Beckham today, as his fabulous free kick goal sent England through to the quarter finals.

  • Say Lee

    Beckham bent it a few more times today, one of which led to the English fans going wild, including Victoria, in today’s game against Ecuador.

  • Alan Reifman

    The journal American Scientist also just came out with an interesting article on soccer ball design. I briefly discuss this, as well as Mark’s post, on my blog (click on my name above).

  • Amara

    I used to play a little soccer when I was in my early 20s, so I am far from immune to the thrill of the sport, but now living in Italy, I have not yet understood the level of ‘insanity’ that people here have towards football/soccer. When national clubs play each other, fans go to the neighborhood of the coach of the opponent’s team and spray-paint the street with sloagans and make as much ruckus as they can in the middle of the night to wake everybody up. Probably the more popular or fashionable something is, the more resistant I am at looking at it, so Italy’s indulgance saturated me a bit. Therefore, when the World Cup began, I didn’t pay attention to the event. Until the last few days.

    On a short business trip to France last week I read an article on the plane in the June 10 The Economist comparing the World Cup to the Olympics and why the World Cup is ‘better’. The article made a strong case that the World Cup is pleasantly divorced from the global pecking order because it has its own hierarchy and reflects a satifying characteristic of the global game. The article said that despite the undoubted prestige to be had by becoming champions of the world, it is extremely hard – if not impossible- for a determined and well-resourced government to create a World Cup-winning team. Moreover, a winning football team needs not just athleticism but also a spark of creativity and style that cannot be manufactured by sport’s centeral planners. It is the capacity to surprise that helps make the World Cup such a gripping event.

    So after my daylong business meeting, I ducked into a cafe to relax, and with a nice coincidence, it was 15 minutes before the start of the France-Togo match. I stayed in that cafe for the entire game watching it with the two French girls running the cafe and experienced for the first time in years, the thrill of the World Cup and with two enthusiastic supporters of their country’s team. So now, I must say, ‘Thank You, World Cup’ for giving all of the world such a wonderful event.

  • chapieau04

    Dear Mark,

    as I teach Mathematical Methods of Physics here in Naples, I
    felt obliged to explain the physics behind those kind of stikes, using
    a simplified two-dimensional model (plane flow around a cilinder)
    and conformal maps. You will perfectly understand that I called it
    the Maradona effect.

    Best regards

  • Mark

    I just added an update linking to the following cool site, in Spanish)

  • Amara

    Did I say the Italians were ‘insane’ about football? I need another superlative. One doesn’t need to own a television here to know when a score was made. Firecrackers, horns, voices spontaneously, simultaneously emerged from my little Castelli Romani town. Deafening. There must be something in the genes… :-)

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About Mark Trodden

Mark Trodden holds the Fay R. and Eugene L. Langberg Endowed Chair in Physics and is co-director of the Center for Particle Cosmology at the University of Pennsylvania. He is a theoretical physicist working on particle physics and gravity— in particular on the roles they play in the evolution and structure of the universe. When asked for a short phrase to describe his research area, he says he is a particle cosmologist.


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