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Physical Football - Bend It Like Roberto Carlos

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Brazil versus France. Everybody remembers France '98, which saw France's 3-0 pasting of the favourites, Brazil, in the Football World Cup Final. Quite a bit of drama there, with the mystery of what happened to Brazil's star player Ronaldo on that dark night before the final1.

However, just a year before, in the pre-World Cup warm-up tournament of Le Tournoi, jaws dropped in astonishment, aghast at the skill and exploit of one player of the Brazilian football team in their match against France.

It wasn't Ronaldo, their star player. It wasn't Rivaldo, who scores goals as frequently as rabbits breed. It wasn't even Romario, the veteran of the Brazilian squad.

Instead, it was the second-shortest player in the squad, with thighs the size of tree-trunks and a tendency to put a new spin on things when they came to him.

Brazil v France

Le Tournoi, Lyons, 3 June, 1997, 22nd Minute of the Match...

The score is 0-0. France have conceded a free-kick from about 25 yards from the goal. The French team set up a nice defensive wall of players, and Fabien Barthez2 was gearing himself up to make a nice save when required. It seemed like a normal free-kick that would hopefully be unable to penetrate the French lines of defence.

However, one of the diminutive players on the Brazilian team stepped forward to take it, which seemed to be a very strange choice indeed. A defender taking a free-kick? Well, it's not completely unheard of, but still, it's quite peculiar for this to happen.

Perhaps it is, but not if the defender is one Roberto Carlos, left-footer extraordinaire, standing at a grand height of 5'6''/168cm...

The Free-kick Is Taken...

The ball is slightly to the right of middle of the goal, 25 yards out. The French wall is ready to block all incoming objects, protecting the most important thing on the pitch. Fabien Barthez has assumed the position.

Roberto Carlos does a short run-up and strikes the ball with his trusty left foot. However, he appears to have botched the job completely, with the ball flying further out to the right than where it was before.

The ball flew so far right that one of the ball-boys between the right corner-flag and the right goalpost ducked in fear for himself. However, something was not quite right.

As if by magic, the ball swung around sharply to the left, around the bewildered French wall and into the back of the net, leaving the baffled Fabien Barthez standing - that was all he could do.

Roberto Carlos had scored a magnificent bendy 'banana' free-kick, and Brazil were in the lead at the 22nd minute3.

Physics According to Roberto Carlos

Apparently, Roberto Carlos practised this style of free-kick on the training ground all the time. This would mean that it was second nature to him on where to strike the ball, what velocity and what force.

This puts it down more to luck than to actual physical equations, but physics still had its part to play in Roberto Carlos' glory.

The Free-kick According to Physics

When taking a free kick, you have at least four forces to consider...

Use the Force

  1. The Force of the Kick - If unchecked, this will send the ball on a linear trajectory4 forever.

  2. The Drag (caused by air viscosity) - This will slow the ball down on the linear trajectory until it eventually stops.

  3. Gravity - Gravity will bend the linear trajectory towards the ground.

  4. The Magnus Force5 - This only comes into play when the ball is spinning.

The fourth force will be used to explain the banana-kick.

The Magnus Force

Actually, the physics is the same whether you're talking blasting a curve ball at Babe Ruth, bending a ball over the six-yard box from a corner flag, or kicking6 your second serve on a grass court.

The Magnus Force (or Effect) is quite but not entirely similar to Bernoulli's Principle, where you have different dynamic pressures on two sides of an object moving in a fluid. This is what allows planes to fly.

Picture an aeroplane wing. Move the whole wing forward. Air passing over the top of the wing has to move faster than air passing underneath, because of the aerofoil profile - it has further to travel in the same time. When a fluid7 moves faster, its pressure reduces. So, you have more pressure under the wing than on top. This means you have lift.

Now, instead of a wing, picture a cylinder. The path of air over and under the cylinder is the same - a circle is symmetrical. However, if you rotate the cylinder so that the 'leading edge' is moving up, it will drag the air along its surface with it, speeding it up, and reducing the pressure. Similarly, on the underside, it'll slow it down and increase the pressure. Yet again, there is lift.

The irregularities of a football - the stitches, and so on - will be causing different forces on different sides of the rotating ball, because it swirls the air around. This causes some turbulence on the respective sides of the ball, because one side is turning against the moving direction of the ball, and the other side is rotating with the moving direction. Hence, there are two different forces on both sides of the ball, hence the curving. The faster side will be the one apparently 'pushing' the trajectory in. The slower side will be apparently 'pulling' the trajectory in.

Therefore, if you kick the ball with a top-spin, the ball will fall down faster. If you give it a bottom spin, it will apparently have an extra up-component. If you kick the ball with an oblique spin you get those banana curves.

There are more effects that could be considered, such as the air humidity8 and other more complicated variables.

Bend It Like Roberto Carlos

Ever fancied trying to bend a ball like Roberto Carlos? Well, here's a possible way of recreating that magical moment:


  • A football pitch (goalposts and corner-flags recommended)

  • A dry day

  • A football

  • Some friends (a minimum of seven, including yourself, but if you feel like overdoing it, go with two full teams)

And, if you're really feeling pedantic, get everyone kitted out in the respective kits - the blue for les Bleus, and the yellow and blue for the Samba Boys.


  1. First of all, take into account the vital statistics of the small guy himself:

    Physical Statistics

    • Height - 5'6''/168cm9

    • Thigh Circumference - 23.4in/58.5cm10

    • Average speed of ball - 94mph/150kph

    Despite his diminutive height, there is a substantial amount of muscle in his thighs that goes into engineering such a kick.

    So, probably some kind of training would be in order.

  2. Now, assuming you are Roberto Carlos, sort yourself and your friends into the following positions:

    • Roberto Carlos - stand 25 yards from the goal-line

    • The French Wall - four people, 10 yards from the ball

    • Fabien Barthez11 - one person, standing on the goal-line, opposite the ball

    • The Ball-boy - one person, an entire goal-length to the right of goal, behind some imaginary hoardings

    In the case of a surplus of friends, here are a few extra positions so they don't feel left out:

    • French Defender 1 - one person, standing one yard wide of the wall to your right, and ten yards from goal

    • French Defender 2 - one person, standing to French Defender 1's left

    • French Defender 3 - one person, same distance away from goal as French Defender 1, only on the other side

    • Brazilian Attacker 1 - one person, standing just to French Defender 3's left

    • Brazilian Attacker 2 and 3 - two people, one standing just to French Defender 1's left, another just behind him respectively

    • Brazilian Attacker 4 - one person, same distance away from the goal as Roberto Carlos, standing on a par with Brazilian Attacker 2

    • The Crowd - variable, but not on the pitch, as of yet

    • The Pundits - again, variable, but nicely critical; sheepskin coats optional

  3. Dry your boots and the ball. Place it in front of you, slightly to the right of the centre of goal, 25 yards out. Step about five yards away from the ball to give yourself a good run-up.

  4. Run up to the ball with determination and vigour - don't fall over in the process!

  5. Kick the bottom of the right side of the ball with the outside of your left foot on the up-swing towards the Ball-boy, with an aim to getting the ball to a velocity of at least 70mph and a height of about ¾ the height of a goalpost. What you want to do is to get the ball to dip just as it passes by the defensive wall - as it dips, the linear velocity of the ball will decrease, allowing the Magnus Force to take effect, but you don't want the ball to be so slow that it curls too early, or too fast so that it curls too late. You also want it high enough off the pitch so that it has enough time to curl in, but not so high that it misses the goal completely.

  6. Make sure the French wall does a little jump and watches the flight of the ball. This also applies to all the other players.

  7. Watch. The ball should appear to go about a yard wide of goal, straight towards the ball-boy. Make sure the ball-boy ducks at this point. Then, it should appear to take a sharp left-turn, clip the right goalpost and dip into goal.

  8. Here's how you and your friends should react:

    • If you are representing the Brazilians, jump into the air and celebrate appropriately.

    • If you are representing the French, look suitably stunned and shocked. More specifically, if you are playing Fabien Barthez, look behind you at the ball in complete bafflement.

    • If you have a crowd, make sure they react appropriately.

    • If you are one of the pundits, either pour scorn Alan Hansen-style on the French defence or shower praise on the free-kick.

So, as we see, there's a lot of physical magic involved in a banana kick. And much skill from the free-kick taker in question. That's how to bend a ball like Roberto Carlos.

1Sounds quite scary, but a more detailed explanation can be found here.2Who was, back then, making a reputation for being one of the best goalkeepers in the world.3Unfortunately, the free-kick was not enough to secure a win as France equalised in the 60th minute.4A straight line.5Sometimes also referred to as the Robins-Effect. Hendrik G Magnus was the first to properly explain that Force in 1852, even though Newton had already thought about the problem before in 1672. Robins showed in 1742 how to detect the effect.6For a more detailed definition of a kick serve, look here.7A fluid can be either a liquid or a gas.8Meaning it would be easier to do a kick on a dry day rather than a humid day due to the levels of moisture in the air.9Second only to Juninho Paulista, who is a mere 3cm shorter than his compatriot.10Note: this is for one thigh only. It is also the same thigh circumference as Muhammed Ali's when he was at his peak.11Again, if you really want to be pedantic, if your friend is not already bald, arrange for him to be so, prior to the free-kick. This would also mean you would have to have your head shaved too, to concur with Roberto Carlos' hair, or lack of.

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