How to kick a cool "banana ball" in the World Cup by bypassing the human wall and turning halfway?

The World Cup comes once every four years

I don't know if you still remember

2018 World Cup

Portugal and Spain meet in the group stage

C Ronaldo saved the day at the last minute

Kicked out by the commentator

"As graceful as a startled swan and as graceful as a dragon"

"C-type" free kick equalizes the score

Why does a kicked ball rise and fall quickly?

Why does it "turn"?

First, let's take a look at free kicks.

What is a free kick?

A free kick is a type of penalty kick. It is a method of restarting play in football (or handball) after a foul.

There are two types of free kicks: direct free kicks, where the kicking player can shoot the ball directly into the goal of the offending team to score; indirect free kicks, where the kicking player cannot shoot directly into the goal and the ball must be kicked or touched by another player before it enters the goal. After a free kick is awarded in the frontcourt, a foam spray is used to mark the position of the ball and the position of the human wall. When taking a free kick, the player needs to touch the ball with his hands and then kick it after the referee blows the whistle.

Banana balls? Can you eat them?

In fact, this kind of free kick taken by Ronaldo is not uncommon in football matches.

In 1997, during a soccer match between Brazil and France, Brazilian soccer player Roberto Carlos took a free kick from 35 meters away with no direct path to the goal. His shot caused the ball to fly past the players and, just before it went out of bounds, veered sharply to the left and smashed into the goal.

Image source: Internet Banana Ball Diagram

The sudden turn of the ball left the players, especially the French goalkeeper, no time to react. This most beautiful, iconic and physics-defying free kick in history is called the "banana shot". French physicists have studied this for several years and finally explained it with the "Magnus effect".

Magnus Effect

Image source network

When the rotational angular velocity vector of a rotating object does not coincide with the object's flight velocity vector, a lateral force will be generated in the direction perpendicular to the plane formed by the rotational angular velocity vector and the translational velocity vector. Under the action of this lateral force, the object's flight trajectory will be deflected. This is a phenomenon in fluid mechanics.

Source: Schematic diagram of the Magnus effect from the School of Physics and Information Science, Shaanxi Normal University

The reason why a rotating object can generate a lateral force is that the rotation of the object can drive the surrounding fluid to rotate, causing the fluid speed on one side of the object to increase and the fluid speed on the other side to decrease.

Did you feel confused after hearing this?

Banana ball trajectory

When a ball moves in an airflow, if its rotation direction is the same as the airflow, low pressure will be generated on one side of the ball and high pressure will be generated on the other side of the ball. The athlete's force is directed to the right, so the ball rotates counterclockwise. At the turning point, low pressure is generated on the left side of the ball and high pressure is generated on the right side, which causes a lateral pressure difference in the ball and forms a force to the left.

Image source: NKPhysics

According to the physical formula, the farther the distance, the slower the speed, and the greater the angle of deviation of the ball. Therefore, we can see that at the end of the banana ball, a more violent deflection will occur, giving the goalkeeper a huge "scare".

Can I play like Ronaldo?

Back to the free kick in which Ronaldo "turned the tide" mentioned at the beginning of the article, this ball not only embodies the concept of the "banana ball" mentioned above, but also mixes in the "elevator ball", which refers to a football kicked with great force, falling very quickly, like falling from an elevator. It is actually the trajectory of a high-speed flying football under the resistance of gravity and a large Reynolds number.

Image source: Chinese Physical Society Journal Network Pirlo's "Elevator Ball"

Professor Ge Weikun explained: "A key factor in kicking an elevator ball is that the ball's initial speed must be fast." To kick an elevator ball, the ball's initial speed should be close to 150 kilometers per hour, which is the speed of a car speeding on a highway.

Image source: Science World

When simulating a scenario, the researchers found that in order for a free kick at a speed of more than 100 kilometers per hour to avoid the human wall (assuming that there are five opposing players with a height of 1.8 meters lined up at a distance of about 9 meters) and be successfully shot, the angle between the ball and the ground when it leaves the ground must be controlled between 15° and 17°, which means an accuracy range of only 2° (at a distance of 25 meters from the goal, kicking out a side-spinning arc with a rotation speed of 8 revolutions per second).

If it is a football, rotating 8 times per second at a speed of 90 kilometers per hour, the ball will bend more than 3 meters within this distance.

See watermark for source

The key to kicking an arc is to place the foot off the center of the ball. The greater the deviation from the center of the ball, the faster the ball will spin. Some researchers say that excellent free-kick players such as Andrea Pirlo will tilt the ball's axis of rotation at a greater angle than the side spin, allowing the Magnus force to tilt downward, thus kicking a "fast, sharply curved, and sharply downward" ball path.

Source: Science World, Journal of the Chinese Physical Society

Science and Technology Daily, Tianjin Science Popularization, NKPhysics

Compiled by: Dong Xiaoxian

Editor: Guru