Football physics: The "impossible" free kick - Erez Garty

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In 1997, Brazilian football player Roberto Carlos set up for a 35 meter free kick with no direct line to the goal. Carlos’s shot sent the ball flying wide of the players, but just before going out of bounds it hooked to the left and soared into the net. How did he do it? Erez Garty describes the physics behind one of the most magnificent goals in the history of football.

Lesson by Erez Garty, animation by TOGETHER.

In 1997,
in a game between France and Brazil,

a young Brazilian player
named Roberto Carlos

set up for a 35 meter free kick.

With no direct line to the goal,

Carlos decided to attempt
the seemingly impossible.

His kick sent the ball flying
wide of the players,

but just before going out of bounds,
it hooked to the left

and soared into the goal.

According to Newton's first law of motion,

an object will move
in the same direction and velocity

until a force is applied on it.

When Carlos kicked the ball,
he gave it direction and velocity,

but what force made the ball swerve

and score one of the most magnificent
goals in the history of the sport?

The trick was in the spin.

Carlos placed his kick
at the lower right corner of the ball,

sending it high and to the right,
but also rotating around its axis.

The ball started its flight
in an apparently direct route,

with air flowing on both sides
and slowing it down.

On one side, the air moved in the opposite
direction to the ball's spin,

causing increased pressure,

while on the other side, the air moved
in the same direction as the spin,

creating an area of lower pressure.

That difference made the ball curve
towards the lower pressure zone.

This phenomenon is called
the Magnus effect.

This type of kick,
often referred to as a banana kick,

is attempted regularly,

and it is one of the elements
that makes the beautiful game beautiful.

But curving the ball
with the precision needed

to both bend around the wall
and back into the goal is difficult.

Too high and it soars over the goal.

Too low and it hits the ground
before curving.

Too wide and it never reaches the goal.

Not wide enough
and the defenders intercept it.

Too slow and it hooks too early,
or not at all.

Too fast and it hooks too late.

The same physics make it possible

to score another
apparently impossible goal,

an unassisted corner kick.

The Magnus effect was first documented
by Sir Isaac Newton

after he noticed it while playing a game
of tennis back in 1670.

It also applies to golf balls,
frisbees and baseballs.

In every case, the same thing happens.

The ball's spin creates a pressure
differential in the surrounding air flow

that curves it
in the direction of the spin.

And here's a question.

Could you theoretically
kick a ball hard enough

to make it boomerang
all the way around back to you?

Sadly, no.

Even if the ball didn't
disintegrate on impact,

or hit any obstacles,

as the air slowed it,

the angle of its deflection
would increase,

causing it to spiral into smaller
and smaller circles

until finally stopping.

And just to get that spiral,

you'd have to make the ball spin
over 15 times faster

than Carlos's immortal kick.

So good luck with that.