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When it comes to badminton, everyone must be no stranger. Even if they are not badminton enthusiasts, they will often see players in various sports venues or squares, and they will also hear about famous players such as Lin Dan and Lee Chong Wei.

However, even regular players may not pay attention to the details of badminton flight.

Why is Tu Yuan Pixabay badminton designed like this? Does it always fly with the heavier ball facing forward? How far can badminton fly? Does it spin when it flies? Presumably these questions have aroused everyone's curiosity, so let's go into the text together.

Part 1: the flip of badminton anyone who has ever played badminton will notice that when the ball flies towards you, it is almost always in the front position of the ball. For the sake of others, the opponent is sure to see the same phenomenon. Then there is only one possibility, that is, after each side hits the ball, the badminton will turn over, then turn around and fly back. The question is, is the U-turn done in an instant? Maybe we take it for granted.

Figure 1 (a) a snapshot with an initial velocity of about 18.6m / s and an initial angular velocity of about 206m / s (interval 5ms); (b) a snapshot with an initial velocity of about 10.4m / s and an initial angular velocity of about 28 rad / s (interval 6.5ms). | the picture comes from the literature [1]. Unfortunately, the answer is not like this. As shown in the above picture, the moment of hitting the ball is basically completed around the 1ms, but generally the ball can be flipped around the 20ms. Then it has to go through the process of damping shock in order to make the ball head point in the direction of speed. In order to show this process more intuitively, we draw the evolution of the angle φ between the direction of the ball head and the direction of velocity over time in figure 2. Among them, τ f, τ o and τ s represent the forward time of the first flip to the ball head, the damping oscillation time and the characteristic time to reach stability, respectively.

Fig. 2 the evolution of the angle between the two cases | the picture can be seen in the reference [1]. After 0.1-0.15s, badminton already looks like the head-forward posture of the ball, so except for some special hitting situations, it is difficult for us to catch the process of rapid flipping adjustment after hitting the ball with the naked eye. that. Does this flipping behavior of badminton have anything to do with its own structure?

Fig. 3 Force analysis of badminton when marching | the picture is from literature [1]. Badminton is composed of cork ball head and skirt structure made of goose feather / duck feather or plastic, in which the ball head is heavier and the skirt structure has a larger cross-sectional area. We might as well abstract this feature as the skirt area with large mass and cross-sectional area marked by B and C in the figure, and the ball head area with large mass and small cross-sectional area.

In flight, it is assumed that the direction of the ball head is not consistent with the velocity direction, and there is an angle φ, then the air resistance acting on B and C will produce a moment with the center of mass G as the reference point, respectively. On the one hand, the cross-sectional area of the skirt structure is larger, the air resistance FD is larger, on the other hand, BG is longer than GC, so the ball will inevitably rotate counterclockwise around the center of mass until the ball head points to the direction of velocity.

Fig. 4 Badminton shape illustration | the picture is from the literature [1] if the above weight distribution is easy to think of, then there may be little thought about why badminton chooses an angle close to 45 °. In fact, this is closely related to whether badminton can experience a faster turn to achieve stability. Some scholars have reengraved the shape and mass distribution characteristics of badminton with small iron balls and plastic skirt structures, and released them freely in the water in a skirt-like structure, allowing them to flip in the process of sinking. the following figure shows how its angle affects the turning and stabilization time.

Figure 5 how does the angle affect the flip and stability time? as can be seen from the reference [1], too small and too much angle is not conducive to the stability of the flip, and the range from 30 °to 90 °will experience a stable platform area with fast stability. Obviously, the corner of badminton falls in this area.

Part 2: the flight trajectory of badminton is different from that of tennis. Because the ball itself is lighter and is greatly affected by air resistance when flying, the flight trajectory of badminton seriously deviates from the shape of parabola. Generally speaking, the equation of motion followed by badminton flight can be written.

Where M, ρ and S are the mass, density and cross-sectional area of badminton respectively, U is the velocity, U and g are the vectors of velocity and gravity acceleration, and CD is the constant related to the test conditions. It is not difficult to understand that, in addition to the gravity that causes it to do an oblique throw, the ball will also receive resistance whose size is proportional to the square of the velocity and the direction is opposite to the velocity. The specific trajectory is determined by the magnitude and direction of the initial velocity. For badminton, we can define a quantity related to its flight characteristics, which is called aerodynamic length.

For the badminton we use, the distance is about 4.6m, which determines that the final stable speed of badminton in free vertical fall is U ∞ = 6.7m / s. In the following picture, we can see the comparison between the calculated value (solid line) and the actual value (scatter) of the badminton trajectory at different initial velocities, which shows that the equation of motion can better predict the trajectory.

Fig. 6 comparison of calculated and actual values of badminton trajectories with different initial speeds | the picture is from the literature [1]. So, how far can badminton fly? We might as well look at the changing trend of the distance x0 when the badminton falls to the same height as the starting height after the approximate upthrow movement. According to the above equation of motion, we can find that this distance depends on the initial speed of badminton. By plotting the relationship between the flight distance x0 with respect to the initial velocity elevation θ 0 and the velocity magnitude U0, the following results can be obtained.

Fig. 7 variation of travel distance (m) with initial speed direction (elevation) and speed as long as you have played badminton, this picture must contain some information points that you can empathize with. For example, we find that no matter how hard we use, it seems that the flight of badminton always "stops abruptly" near a certain distance. The speed limit in this picture has reached 140m/s, but the furthest distance that can be reached is only 13.83m. On the other hand, the badminton court we use is 13.4m long, which is why badminton can only play to the other side of the backcourt even with all its strength, even if it is out of bounds.

Fig. 8 Badminton court hint some readers may ask, is it too much to set the speed limit to 140m / s? Can badminton fly so fast? It's not an exaggeration. In July 2013, the famous Malaysian men's doubles player Chen Wenhong shot the ball at the amazing speed of 493km/h under the ideal conditions of the laboratory, which is equivalent to 136.9m/s. It is also reported that Denmark's Codin once played 506km/h 's record of killing the ball, that is, 140.6m/s. Even in the game, Curtin played the 426km/h 's super-fast kill ball. Therefore, badminton is the well-deserved king of ball speed!

Fig. 9 the super-fast kill ball of Codin 426km / h actually, the flight trajectory of badminton is also related to the type of ball. Our common ones are feather balls and plastic balls. The following picture shows the differences in their flight trajectories.

Fig. 10 comparison of trajectories between feather ball making and plastic ball making [1] on the one hand, when the initial angle and speed are the same, the reachable range of plastic balls is larger than that of feather balls; on the other hand, the curvature of the feather ball near the highest point of flight is larger, and the trajectory is closer to the "triangle".

Fig. 11 plastic ball making this is due to the fact that plastic balls tend to be more heavy when they are guaranteed to be sturdy and the cost is low. This also means that the feather ball can fly at a faster speed without going out of bounds, thus reducing the opponent's reaction time. Therefore, feather balls are often more popular.

Part 3: you may have noticed the rotation of badminton. The feathers of badminton are tilted and arranged in the same clockwise direction. Is this an unimportant design? Actually this is not so. We can think of each plume as a thin plate, which is subjected to a force perpendicular to the plane and opposite to the velocity as it travels in the fluid, as shown in the following illustration.

Fig. 12 the force acting on the feather is illustrated by the picture from the literature [1]. We will immediately think that the combined force of these forces will make the badminton rotate around the axis as a whole! When badminton travels at a faster speed, the greater the resistance will be, and the torque generated by the resultant force will increase, making the badminton spin faster. If we multiply the angular velocity Ω by the axial radius R of the feather and get the linear velocity at the pinna, we will find that it is almost linear with the travel speed.

Fig. 13 relationship between linear rotation speed and travel speed of badminton | the picture is from reference [1]. Moreover, compared with plastic balls, badminton balls rotate significantly faster in flight. The analysis shows that faster rotation will limit the advance of the feather ball, which is beneficial to the stability of the feather ball in flight.

It seems that the flight details of badminton is really a great knowledge. In this process, we can not only learn a wealth of physical knowledge, but also help to understand the trajectory of the ball. After watching the push buddy, hurry up and pick up the racket and see if your skills have improved.

Reference:

[1] Cohen C, Texier B D, Q é r é D, et al. The physics of badminton [J]. New Journal of Physics, 2015, 17 (6): 063001.

[2] Badminton-Wikipedia

Kwan M W. It'sa Birdie... It'sa Shuttlecock... It's Badminton: The Physics Behind the Badminton Shuttlecock [J].

[4] the world record of killing the ball has set a new high!

This article comes from the official account of Wechat: Institute of Physics, Chinese Academy of Sciences (ID:cas-iop), author: Yun Kai Ye Luo

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