i am gun king

Chapter 210 Chapter 213 Science and Persistence
The final draw is acceptable to both sides, and although they missed the league championship, the two teams still have a Champions League match, ignoring the crazy media reports

Li Yuxin has something to do now, which is to reflect. This game has taught him a deep lesson. When Arsenal fell into a difficult battle, he stood up, and now his teammates can also provide support.
At this time, he remembered that story, and remembered why he practiced the elevator ball at that time. That Wu's good friend, Chris Fan
October 2006, Mallorca, Spain
Characters: Feng Shuo, Chris, a physics fan, Li Yuxin
"At first I thought it was the luck of the kicker players."

Hearing this, Li Yuxin also read the headline. He also thought so at the beginning. Cristiano Ronaldo was just lucky, so what's there to brag about?
"But I found that no matter whether it is Cristiano Ronaldo, Juninho, or Pirlo, there have been such free kicks. It is not an isolated example. One person can get in one by luck, but can so many people get in by luck? So I started to study this kind of free kick... I found that this free kick is definitely not lucky. There is an inevitable law and connection between free kicks and goals."

Speaking of this, Chris himself was a little excited. He waved his fist, excited as if he had discovered some new element...

"I can even say that as long as you stick to the correct way of kicking the ball, you can kick this kind of elevator ball that looks like luck. Why do I dare to say that? This is based on science..."

"Science?" Li Yuxin couldn't help interjecting when he heard this, what science is there in kicking a free kick?
Seeing Li Yuxin's surprised expression, Chris smiled.

"Science, of course," he said in a very affirmative tone. "Why does the elevator ball appear in such a state? This involves fluid mechanics. Because the football is a sphere, it will form a streamlined contact with the surrounding air, which will cause turbulence or turbulence. A transverse force will be generated in the direction perpendicular to the plane formed by the velocity vector, and this transverse force will cause the flight path of the object to deflect.

"To put it simply, the arcball we see is actually the embodiment of the Magnus effect. The rotating object can generate force laterally because the rotation of the object can drive the surrounding fluid to rotate, so that the fluid velocity on one side of the object increases, and the fluid velocity on the other side decreases. According to Bernoulli's theorem, the increase in fluid velocity leads to a decrease in pressure, and the decrease in fluid velocity will lead to an increase in pressure, which leads to the lateral pressure difference of the rotating object and forms a lateral force. At the same time, because the lateral force is perpendicular to the direction of motion of the object, this force mainly changes the direction of the flight speed, that is, forms the centripetal of the object's motion. force, thus causing a change in the direction of the object's flight...

"This is the physical principle of the curve ball. Let's take Beckham's curve ball as an example. We can see that the ball speed becomes slower as it reaches the goal, and the ball spins faster. According to the Magnus effect, the difference in air pressure on both sides of the ball causes the ball to deflect to the opposite side of the angular velocity direction and the direction of travel.

"What about the elevator ball? It doesn't apply to the Magnus effect. Because the ball spins at a very low speed, or even does not rotate, the foot force is almost all applied to the kinetic energy required for the forward direction. The moment the football goes out, it gains a very high speed. At the beginning, the ball will move forward in a straight line at high speed. However, as the air acts on the streamlined surface of the ball, any position of the ball can produce an air pressure difference, which directly leads to erratic movement of the ball, from left to right, even up and down.

Speaking of this, Chris suddenly stopped his eloquent speech, and then asked Feng Shuo who was stunned beside him: "Do you have any paper and pen?"

"Here I want to talk about why I think the elevator ball can be successfully copied, rather than luck. Because there is only a reason. I concluded that when Cristiano Ronaldo and Juninho kicked the elevator ball, I found that the two people have a common reading, that is, they are good at long shots, and they can take direct free kicks from far away from the goal. Juninho has scored many free kicks very far from the goal. What does this mean? It means that both of them have very strong feet, yes , Strong feet, this is one of the conditions that must be met for kicking the elevator ball, that is, the hitting power.

"Similarly, the kicked elevator ball, because the football itself does not rotate, so the football itself will not generate a very strong lateral force. When the football passes through the air, it encounters air resistance, and the air will form a vortex street behind it, which will cause the football to start to vibrate. This is why the football will go up and down, left and right in the air. When the vibration frequency is too high, there will be a relatively large directional deviation, just like the Tacoma Bridge under the influence of the vortex street. .

Having said that, Jose Kreis took out his mobile phone, found the video of the goal in the video, and played it for two people.

Chris took it and didn't even look at it.
I wrote it directly.

"You see, the football is almost non-spinning in the air. The black color block on the football has a positional shift, but this is not caused by the rotation, but just proves the result of the air exerting pressure on the football from different directions... The goalkeeper therefore has no reaction to the ball at all..."

Junior Juninho once scored a very famous free kick in Ligue 37. The football changed direction twice in the air, and finally drew a B-shaped arc and drilled into the goal.If I remember correctly, the ball was [-] to [-] meters away from the goal, which is farther than the distance you are practicing now... I remember I saved the video of this goal in my phone..."

He wrote down the formula of Newton's second law on paper, and at the same time kept talking with his mouth and hands.

Then Chris continued to talk, eloquently.

"This phenomenon can be calculated theoretically, and it is related to a ratio called the Reynolds number. The Reynolds number is the ratio of the force you kick a ball to the viscous force of the air on the football. This number is called the Reynolds number. The elevator ball is related to the Reynolds number... I have found through calculations that for a non-rotating ball, when the initial speed is lower than the terminal speed, the ball will move in a parabola, and when the initial speed is much greater than the terminal speed, the ball will fall sharply when it falls... That is to form an elevator ball. The basic formula is Newton's second law..."

Feng Shuo didn't react at all, and just mechanically handed him the paper and pen in his hand.

After writing the formula of Newton's second law, I wrote down the second formula: "...Because it is an elevator ball, the ball does not rotate, so the data of lateral force can be ignored. When only air resistance is considered, and it is a large Reynolds number, that is, when the initial speed is very fast, this formula can be simplified to"

"The hitting force must be strong enough to allow the football to achieve the highest initial speed, so that an elevator ball can appear. Otherwise, you will not be able to kick an elevator ball at all. This is different from a curve ball. A curve ball does not require an initial speed, and there is no way to require an initial speed, because kicking a curve ball will increase the friction between the sneakers and the football. Increasing friction will reduce the speed. Playing an elevator ball requires the ball to be touched as short as possible. The shorter the speed, the faster the ball.

"Then why do you have to hit the ball vigorously to kick the elevator ball? Here I want to introduce a famous theory called 'Karman Vortex Street' theory. This theory was put forward by the famous aerodynamics expert von Karman, so it is named after him. What is the Vortex Street Theory? It means that when the water flow and air flow are blocked by an object, the regular arrangement of vortex after vortex is formed behind the object. Resonance. In terms of architecture, if it is serious, it will cause collapse accidents, such as the famous collapse of the Tacoma Bridge in the United States...

"The basic formula of the vortex street theory is very simple, that is, F is equal to KV divided by B divided by 0, V can be regarded as the running speed of the sphere, the dam is the diameter of the sphere, K is the Strouhal number, which is related to the medium of the sphere and the properties of the fluid, and is the shaking frequency. From this formula, we can see that the faster the ball speed, the smaller the diameter of the ball, the higher the frequency of the football shaking. The diameter of the football is fixed, and the Strouhal number is also relatively fixed, so the only thing that can play a role is the speed of the ball, and the speed of the ball depends on you The force applied to the football...is the force of your shot. The greater the force of the shot, the higher the frequency of the football shaking in the air after being affected by the vortex street theory. This is why kicking the elevator ball must be strong enough. If the force is not strong and the ball is not fast, it will not be successful.

"...From this formula, we can finally get a final velocity Hc. Note that the final velocity I'm talking about is not the final velocity we usually understand, but the velocity when the acceleration is equal to zero, which means that the velocity will not change anymore...It is a square root form, related to the radius of the ball, related to the damping coefficient, and related to the air density...In short, we can calculate a final velocity...The relationship between the final velocity and the initial initial velocity determines the shape of the ball's trajectory...That is, according to the formula just now, we can calculate the speed with time The change of the speed...and if the speed is integrated with the time, the change of the distance with time can be obtained, that is, the trajectory of the football is given..."

He started drawing XY-axis graphs on paper.

"...Look at this arc, the initial speed is about 37 meters per second, and the angle is 38 degrees. The calculated arc should look like this... Do you see it? A typical elevator ball running route. At the beginning, it goes up a relatively gentle slope, and then descends very steeply... So, there are rules for kicking the elevator ball.

Having said this with great interest, Chris raised his head from his calculation formula, looked at Li Yuxin and Feng Shuo who were already stunned, as if petrified, and said...

(End of this chapter)