It's spring in Manchester.

Old trees draw new branches, young grass breaks new shoots, birds chirp on branches, and young men and women form groups of threes and twos.

There is a smell called spring in the air.

Carrington Training Base.

Chu Ge, who may be the most expensive single dog in history, seriously placed the football twenty-seven places away from the goal.

He stood in front of the ball and looked at the goal.

At the end of the day's training, the teammates had basically left the training ground and headed for a spring date. On the current training ground, only Chu Ge is left.

The entire Carrington has been contracted by Chu Ge.

"There are two kinds of rotation of the football: one is horizontal rotation and the other is vertical rotation. And behind these rotations, there are certain rules to follow. For example, Bernoulli's principle in physics. ”

"Bernoulli's principle explains where the force of the ball's rotation comes from, but it does not quantitatively explain the specific trajectory of the ball. Because this principle is for incompressible fluids, while air is actually compressible fluids. ”

"To explain the trajectory of football quantitatively, we need to use the Magnus effect."

"In Bernoulli's principle, it is mentioned that due to the interaction of ball speed and air pressure, the football is subject to a force F in addition to its own gravity when it operates. The magnitude and direction of this force F are determined by three factors. These three factors are: the coefficient (which is related to the viscous resistance of the surface), the vector angular velocity of the rotation of the football while flying, and the vector velocity of the football. The vector angular velocity fork multiplied by the appropriate amount of velocity and multiplied by the coefficient to calculate the magnitude of the deflection force of the football. The right-hand rule determines the direction of F. ”

"The Magnus effect is not only in football, but also in almost all ball games, such as basketball, table tennis, tennis, volleyball and other sports, and its main feature is spin."

"And because of the peculiarity of football, there is another situation, that is, there is almost no strong spin, but it can still kick a weird arc. For example, the S-shaped free kick that swings from side to side, and the tomahawk elevator ball that Cristiano Ronaldo and I are good at, and which falls rapidly. ”

"The flight trajectory of this type of football is affected by the air resistance F generated by its high-speed movement, and its magnitude is equal to 1/2ρV?? CdA。 ”

"ρ is the density of the air, V is the speed of the ball, Cd is a coefficient, and A is the cross-sectional area."

"In football, it's clear that the biggest impact is the speed of the ball, V?? This will significantly affect the size of the resistance. When a football is in flight, it is subject to drag in addition to being affected by gravity. The faster the ball speed, the greater the resistance, which causes the ball to slow down. After the soccer ball flies a certain distance, the horizontal speed of the soccer ball slows down rapidly due to the influence of drag, and the biggest factor affecting the trajectory of the soccer ball is the gravity of the soccer ball. Under the influence of gravity, the football will fall significantly. ”

"Going up quickly, falling down suddenly, that's the elevator ball."

"This phenomenon is very evident when fireworks are set off. The principle of the elevator ball is based on this. ”

"The key to kicking a lift ball is that you have to have a lot of resistance. The core element that affects the resistance of the football is the initial speed at which the ball runs. This means that if you want to kick the elevator ball, you have to use enough force to give the ball great speed. Just like I did with Cristiano Ronaldo, take a free kick at 120 kilometers per hour and there will be a lift ball. ”

"Theoretically, the trajectory of a free kick can be split into these three. But in fact, the vast majority of free kicks are a combination of the above three trajectories. ”

"When a soccer ball flies, it is not simply horizontal or vertical, but it is tilted. Whether it's Bernoulli's principle, the Magnus effect, or air resistance, there will be all at the same time. ”

"It's just that banana balls and defoliant balls focus more on the rotation of the football, while the elevator ball emphasizes the speed of the football."

"In addition, in the high-speed movement of football, turbulence can occur. However, the turbulence phenomenon cannot be quantitatively analyzed at present. It is also the existence of turbulence that makes the flight trajectory of the football erratic. Left then right, or right and then left, that's why. ”

Chu Ge didn't have the proficiency to brush free kicks as usual.

He faced the goal, constantly thinking, reviewing what homework he had done before.

Since Go can only make the right decision through calculation, can the laws of physics determine the trajectory of the soccer ball's flight in football?

It's an interesting topic.

In actual football, confrontation is everywhere, and there are so many factors to consider that it is very complicated to calculate.

Therefore, Chu Ge focused his research on free kicks.

Some players take free-kicks, mainly by talent; Some people mainly rely on skill, but only "feet" are familiar. Combined, the two have produced many free-kick masters.

Chu Ge also took this path before.

Now, after being inspired, he has come to trust science.

For other players, using science to guide free-kicks is theoretically feasible, but it lacks operability in practice.

But Chu Ge is different.

He is systematic.

After Chu Ge thought of using a scientific method to calculate the trajectory of a free kick and did a lot of homework, the way of football in the system was subdivided into an experience of the way of free kicks.

At present, Chu Ge's experience has reached 60%.

This shows that his current method is effective.

With the assistance of the system, Chu Ge can constantly revise the calculation formula and use experience to summarize the impact of various values, so as to obtain the best way to shoot free kicks.

Previously, after Chu Ge's passing attribute reached SS, the system could estimate his success rate.

This gave Chu Ge an inspiration.

All the assistance of the system is based on Chu Ge's own ability. And if Chu Ge figured out the principle of the flight trajectory of the free kick and used practice to correct the routine, would the system also remind the success rate of various free kick penalty methods and routes, so as to improve the efficiency of Chu Ge's free kick goals?

"Through calculations, AI can become a great chess player."

"Well, by calculating, the penalty of a free kick can also reduce the uncertainty. Maybe I'll be able to figure out a free-kick routine that will kill me. ”

Start doing it when you think of it.

Chu Ge set the ball.

Start targeted exercises.

His previous free-kick practice was just a simple brush of proficiency, like an oil seller.

And now, science has become Chu Ge's weapon.

……

Chu Ge hadn't mainly practiced free kicks for a while, and after he had a goal, after the end of each day's training, he would spend a lot of time on special practice for free kicks.

"It's not terrible to have talent, but it's terrible that people who are better than you work harder than you."

Seeing Chu Ge, who practiced free kicks every day, even Ibu couldn't help but sigh.

1 second to remember Aishang:. m.