Physics and Football ?

Any action that is taken in nature is governed by the laws of physics and football is no exception to this either unless you are Axel Blaze from a childhood tv series called ‘Inazuma Eleven’ which is the person in the picture above, then physics will have to take centre bench on the matter. However, in reality, we cannot be Axel Blaze unfortunately and physics takes command over the many things that occur during a game of football. We will look at some situations in a football match that involves physics and explain how physics works during these instances in some detail.

Roberto Carlos Understood the Assignment

Roberto Carlos of Brazil scores the perfect free kick against France (Courtesy: Press Association)

Many of us may not have seen this beautiful goal in real life but if you were even a small bit interested in football, you would have come across this fabulous goal by Roberto Carlos during the Tournament of France in 1997 against France. Roberto Carlos took a free kick about 30m away from the goal and when he kicked the ball, the ball looked as though it was going miles wide but then it magically started bending around the wall at such an alarming angle and back into the goal and led to one of the most iconic goals to existed to this day.

What kind of sorcery is this ?

The fundamental mechanics of a curving ball in football is basically the same for a ball in cricket, golf, baseball and tennis. Think of a ball that is spinning around and axis that is perpendicular to the direction of the air flowing across it. The air travels faster at the part of the ball that is moving in the same direction as the airflow across the ball which reduces pressure at that side of the ball. The opposite happens at the other side of the ball where the air travels slower relative to the centre of the ball. This makes the forces on each side of the ball to be unbalanced causing a lateral deflection of the ball during flight. This is known as the ‘Magnus Effect’.

Picture representation of the Magnus effect where the pressure is reduced where the airflow across the ball is in the same direction as the spin of the ball (top left) and the opposite happens on the other side of the ball (bottom right) which causes the ball to deflect.

There are two types of forces acting on a ball that is spinning in the air. These two forces are the lift and drag forces. The lift force is the upwards or sidewards force responsible for the Magnus effect and the drag force is the force that acts in the opposite direction to path of the ball. The drag force on a ball increases with square of the velocity of the ball but the drag coefficient which is a constant number also depends on the velocity of the ball. The drag coefficient actually drops suddenly when the airflow across the ball goes from being smooth to being violent and unsteady. When the airflow is smooth and the drag coefficient is high, the layer of air on the ball ‘separates’ quite early and creates whirling masses of air (whirlwinds) as the ball passes through the air. When the air is unsteady and violent, the layer of air sticks to the ball a lot longer which produces a late separation of the layer of air on the ball which results in less drag.

Picture representation of  turbulent (violent and unsteady) air flowing across the ball causing late separation and less drag on the ball.

So basically, if you can hit the ball fast enough so that the airflow across the ball is unsteady, then the ball will experience a smaller drag force. You can say the goalkeeper is in ‘double trouble’ because the ball isn’t just moving at a high speed but the ball won’t slow down as much as you would expect it to slow down. You could say that the best goalkeepers understand more physics than they realize from such experiences.

If you increase the spin on the ball, you get a bigger lift coefficient which gives a bigger Magnus force but if you increase the speed of the ball for the same amount of spin, then you would get a smaller lift coefficient and therefore, a smaller Magnus force. This means that if the ball is moving at a slower speed but you give it a lot of spin, then the ball will have a more dramatic curve in its trajectory than if you kicked the ball with a lot more speed and the same amount of spin. From this you could also say that as the ball slows down at the end of its trajectory, the curve of the ball becomes more evident and dramatic.

Let’s Put the Pieces Together

Using what we’ve learned so far, we can breakdown what happened during Roberto Carlos’ free kick. He kicked the ball with the outside of his left foot causing the ball to have an anticlockwise spin. The airflow through the ball at the start was unsteady and the drag was low but after a few meters the ball slowed down and the airflow across the ball became smooth which increased the drag on the ball and slows the ball down even more. This the Magnus effect to start and the ball started bending toward the goal. If we assume the spin on the ball is almost still the same then the drag coefficient increases and causes the ball to bend even further. Finally, as the ball gets slower at the end of its trajectory, the curve on the ball becomes more exaggerated until the ball hits the back of the net leaving the whole world speechless (unless you understood the Magnus effect back then, because if that was the case, then you would have felt like the smartest person in the world for sure).

I’m Just Speaking My Mind Here

This actually reminded me of Lamine Yamal who is an up and coming youngster that has taken the footballing world by storm. Whenever he takes a shot after cutting in on a player, he always has this perfect curl on the ball but the ball moves so slow and still looks unreachable for the goalkeeper and many times the goalkeeper does not reach the ball and the ball goes into the back of the net. The Magnus effect explains clearly how his slow but dramatically curling shots goes in the net but he is still physically growing as he is only 17 years of age. It makes me wonder if when he gets more physically strong if he will lose that lovely curl on the ball because he will instinctively shoot the ball faster or if he can keep his strength in control and keep making those shots for a long time to come or will he change his shooting completely and put more emphasis on power purposefully ?

Is the Ref Blind or Misaligned ?

Reporting an offside is not easy and some mistakes might not be the fault of the linesman but because of optical and perspective errors. This kind of mistake might be large in number but they are inevitable because it is caused by the physical limitation of the human eye. As the linesman is running up and down the pitch, they can’t always be perfectly in line with the last defender so that they can be in line with the suspected offside position. This is the very reason for these errors. Looking at the image below, when the attacker is between the defender and linesman, the players look in line and the offside is not declared. If the defender is between the attacker and linesman, the linesman sees the positioning to be irregular even if the players are in line and declares an offside. This is why VAR is used so that you have the correct observation point at all times and oversights can be avoided. So next time you are upset because of an offside during a match or the referee is taking too long to call an offside, just know that referee might have been blind for that one moment, not because he is but because of his physical limitations as a human.

Picture showing how how the misalignment of the linesman (black) with the defender (yellow) and attacker (red) can cause errors when declaring offside.

Physics in football can show us how an amazing moment in the sport can involve so much complex theories but it can be simplified in a way so that everyone can see how amazing the players that make these moments happen are. We can also see how there are still things that can be improved in a sport for fairness purposes by using physics to understand where such errors come and creating a solution to the problem. There is so much more you could talk about like, penalties, the likelihood of scoring a goal, the knuckleball, why goalkeepers jump forward when diving, why goalkeepers put water on their gloves and many more but we’ll leave that for another time.

References:

• physicsworld (June 1998), “The physics of football”, Everyday Science, Available at: https://physicsworld.com/a/the-physics-of-football/
• Maria, G. D. (September 2021) “The Laws of Physics in Football”, EE Times Europe, Available at: https://www.eetimes.eu/the-laws-of-physics-in-football/