CN110327611A - A kind of platform diving evaluation method that athletic type's coefficient is added - Google Patents

Abstract

The invention discloses a platform diving evaluation method adding athletes' body shape coefficients. The present invention simplifies the diving athlete into a rigid body with rotational motion, and describes the relationship between the diving time of the athlete and the weight and height of the athlete by studying the relationship between the time of the rigid body motion and the quality and length of the rigid body. The specific implementation steps are as follows: Step 1 1. Simplify the diving action of the athlete into five stages; step 2, model the time for the athlete to complete the diving action based on the height and weight of the diver; step 3: establish a new difficulty factor for the diving athlete based on the model obtained in step 2 The evaluation system is to establish a new difficulty coefficient evaluation system for diving athletes based on the mathematical model of the diving athlete's time to complete the diving action and the athlete's height and weight. The present invention can obtain the athlete's body shape coefficient very well.

Description

An Evaluation Method of Platform Diving Adding Athlete's Body Size Coefficient

technical field

The present invention relates to the field of rigid body dynamics, specifically, it is a rotating rigid body motion that adds the body shape coefficient of divers into it, and provides a more fair evaluation method for platform diving

Background technique

The Chinese diving team started to lead the world in the 1990s. The Chinese diving team has achieved brilliant results that have attracted worldwide attention in many world competitions, and is also called the "dream team" by the Chinese. However, with the continuous improvement of the difficulty of movements in world diving and continuous innovation, the Chinese diving team has no obvious advantage in the difficulty of movements. Especially in the men's 10-meter platform event, from the 2004 Athens Olympics in Greece to the 2012 London Olympics, my country has never reached the highest podium in the men's 10-meter platform. Looking at today's diving powerhouses, all of them are constantly making breakthroughs and innovations in terms of movement difficulty on the basis of stable, accurate and beautiful movements. After the difficulty increases, there will be stricter standards for the height and weight of the athletes. Because the current FINA rules for determining the difficulty coefficient of the 10-meter platform diving do not set a body shape correction coefficient, the current evaluation method for the difficulty coefficient There is a lack of fairness.

Contents of the invention

The present invention mainly considers the relationship between divers completing each diving action in the platform diving event and the athlete's body shape (height, weight). Thus, the body shape correction coefficient is obtained, and then a new difficulty coefficient scoring system after adding the body shape correction coefficient is given.

In this paper, the diver is simplified as a rigid body with rotational motion (note: the rigid body mentioned below is the diver), so that the diving time of the athlete can be described by studying the relationship between the time of the rigid body movement and the quality and length of the rigid body Relationship with athlete's weight and height.

Step 1, simplify the diving action of the athlete into five stages;

The five stages described are:

The first stage: pure somersault movement;

The second stage: arms open;

The third stage: rigid body motion with rotation and somersault;

Phase 4: Arms folded in, similar to Phase 2, but the arms move in the opposite direction;

The fifth stage: the pure tumbling rigid body motion after the arms are closed.

Although we have greatly simplified the diver's diving action here, only considering the three movements of the athlete's somersault, twist, and arm opening or closing, this simplification is reasonable. Because if all diving movements, such as knee tuck, knee bend, handstand, etc., are taken into account, it is tantamount to adding difficulty to the model, which may directly lead to the failure of the model to be established, and now this simplification can both Retaining several typical diving movements in diving events can help us establish a model to analyze and discuss the relationship between diving time and athlete's height and weight. Next, we briefly introduce some basic laws of rigid body motion.

Step 2, based on the height and weight of the diver, the modeling of the time for the athlete to complete the diving action is carried out;

We use Ι to represent the constant angular momentum vector in a fixed space frame, and establish a rectangular coordinate system in the fixed frame. Since the influence of air resistance is ignored in the model assumption, the angular momentum is conserved during the motion of the rigid body. The coordinate The origin of the system can be established at any position. At the same time, L is used to represent the angular momentum vector of body motion (human body motion) in the reference frame, and a space coordinate system is established with the center of mass of the person as the original center. Let R represent the rotation matrix from one frame (coordinate system) to another. Use Ω to represent the angular velocity in 3-dimensional space. Let A represent the momentum shift caused by the shape change; use A to represent the momentum shift caused by the shape change;

Relevant literature proposes I=RL, and then proves that and Ω=I ⁻¹ (LA). Then it is derived from the above formula that the rigid body with rotational motion satisfies the following equation of motion:

Among them, l is the constant angular momentum vector in the space fixed frame, φ represents the flip angle of the object, θ represents the tilt angle, Represents the torsion angle, h represents the internal angular momentum caused by the opening or closing of the arm and has nothing to do with time, h=w _d · Ι _d , I ₁ , I ₂ , and I ₃ are the objects on the X-axis, Y-axis, and Z-axis respectively moment of inertia;

Because opening the arm is an instant thing, the time used is relatively small compared to the total time of rigid body motion, so we might as well assume that the completion time of opening the arm to turn 180 degrees is 0.25 seconds, and then get the arm opening. The angular velocity ω _d = 4πrad/s, Ι _d represents the internal moment of inertia caused by opening the arm, here we also simplify the treatment as Ι _d = 2kg m ² , and obtain the internal angular momentum h = 8πN · m caused by the opening of the arm s. According to the principle of conservation of angular momentum, the angular momentum of a rigid body remains unchanged during the entire movement process. We analyze the common sense and combine the angular momentum formula, that is, suppose a female athlete with a weight of 50kg has a radius of rotation of 0.7m, and the angular velocity is the same as above. 4πrad/s, then l＝mr ² ω＝50·0.7 ² ·4π＝307.7N·m·s, here we take a reasonable value l=300N·m·s for the overall angular momentum of the rigid body.

In the formula (1) Respectively represent φ, θ, for dimensionless time The derivative of , and has the following relationship:

in

Here we assume that all the actions in the five stages are symmetrical. In the symmetrical case, there are relationship, so the motion equation (2) can be simplified as:

in

Below we discuss formula (3) according to the five stages mentioned above.

First, let T ₁ , T ₂ , T ₃ , T ₄ , and T ₅ be the time taken to complete the five stages of action respectively, and the corresponding dimensionless time is

Phase 1: Pure somersault movement

In pure somersault action, there is And there is no internal angular momentum caused by the opening or closing of the arm, that is, h=0, so there is and then get the original function

Phase Two: Arms Open

During this movement, we can get There is a slight change in θ. For the convenience of discussion, we uniformly take the value θ=θ _max at this stage. Related literature proposes

This is the first kind of complete elliptic integral. By setting z=sinθ and taking the value γ=19, we can obtain the expression of the above definite integral as

in The k function is a calculation formula proposed by PFByrd et al.

It is not difficult to find that the formula (5) is very complicated, but considering the actual problem, the opening of the arm is only a momentary movement, and this time is very small compared to the total time of the rigid body movement. In order to facilitate our modeling and analysis, here we again right The approximate processing is 0, and the influence of the arm opening on other parts of the body is ignored, that is, the body inclination θ remains unchanged and is still 0.

Phase 3: Tumbling rigid body motion after the arm is opened

Based on the simplified processing in the second stage above, it can be concluded that θ is still 0, still for And at this time, the rigid body is in a pure tumbling balance motion, and there is no internal angular momentum caused by the opening or closing of the arms, that is, h=0, so ρ=0, get the original function

Phase Four: Arm Closure

This stage is similar to stage two, with

Phase 5: Pure somersault movement after arm closure

This stage is similar to stage 1, with

From the analysis here, we can conclude that the total time of rigid body motion is

which is

We find that the moment of inertia I here is a function of mass m, and in three-dimensional space, there is the following relationship:

Among them, x, y, and z represent the distance of the rigid body from the center of rotation in the three-axis direction, respectively.

Based on the analysis of the actual situation, it can be seen that the above three distances are all fixed values, and we also reasonably set the values of x=y=0.5, Equation (7) is transformed into

Put formula (8), h=0, l=300 into formula (1) to get:

Note: Because there is no opening or closing movement of the arm in stage 1 and stage 3, the internal angular momentum h caused by arm swing in these two stages is 0.

It can be obtained from formula (9):

The original function can be obtained

And because φ ₁ = 2πn ₁ , φ ₃ = 2πn ₃ , where n ₁ and n ₃ are the number of tossing cycles in stage 1 and stage 3 respectively, so it can be drawn:

where n=n ₁ +n ₃ .

The above model is verified as follows:

We take Guo Jingjing as an example to verify the rationality of the model. By consulting the data, we can know that Guo Jingjing is 1.63 meters tall and weighs 48 kilograms. Assume that her diving action is to flip twice, that is, put m=48, h=1.63, and n=2 into the formula (12). :

It is consistent with the actual situation, so that the rationality of our model can be verified.

Thinking from a qualitative point of view, it can be seen from formula (12) that the greater the mass, the longer the diving action time. This is consistent with the common sense that the larger the objects in life, the greater the inertia, and their moving speed is relatively slow, which further proves the rationality of our model.

Step 3: Establish a new difficulty coefficient evaluation system for divers based on the model obtained in step 2. Specifically, establish a new difficulty coefficient evaluation system for divers based on the mathematical model of the diver's time to complete the diving action and the athlete's height and weight, and obtain The athlete's body shape correction coefficient is specifically implemented as follows:

The same action, the same degree of difficulty, different athletes need different time to complete it, which is caused by personal physical factors such as personal height and weight, and the three-dimensional image of time T _tot changes with the height and weight of athletes And change, this just shows that the completion time T _tot has specificity for each athlete, that is, each athlete has its own corresponding completion time, assuming that the difficulty coefficient of the diving action completed by the athlete in Figure 3 is D, Putting D into Figure 3 yields Figure 4.

The plane in the figure is the difficulty coefficient D of the diving action. It is stated here that the difficulty coefficient D has no direct functional relationship with the athlete's height/m and athlete's weight/kg in the coordinate axis.

Since the time T _tot to complete the action has an obvious functional relationship with the athlete's height and weight, and can reflect the specificity of different athletes, if the curvature of the time T surface in Figure 4 is applied to the difficulty coefficient D surface, then the difficulty coefficient D The curved surface can also reflect different difficulty coefficients according to the physical parameters of different athletes;

Simply put, this idea is to map the change in the curvature of the time surface T due to height and weight changes to the difficulty coefficient surface D on the basis of the original difficulty coefficient, so that it can reflect the difficulty corresponding to different athletes doing the same action coefficient. The method adopted is to directly add the value of the time surface T to the surface of the difficulty coefficient D to obtain a new difficulty coefficient Surface, it was later found that the difficulty coefficient of obtaining in this way is relatively large, and it is not rigorous, so take a suitable center point value t0 on the time surface T, and get the following expression:

In the formula, T _tot is the actual time calculated by the model built in question 2, t0 is the middle point of the above time T surface, D is the old difficulty coefficient surface, is the new difficulty coefficient surface, is the correction coefficient.

The beneficial effects of the present invention are as follows:

The present invention simplifies the diver into a rigid body with rotational motion (note: the rigid body mentioned hereinafter is the diver), so that the diving of the athlete can be described by studying the relationship between the time of the rigid body motion and the quality and length of the rigid body The relationship between time and athlete's weight and height.

The invention builds a model to reflect the relationship between the time for athletes to complete each diving action and the athlete's body shape (height, weight), obtains the body shape correction coefficient, and then provides a new difficulty coefficient evaluation method after adding the athlete's body shape coefficient.

When discussing the functional relationship between the diving time and the athlete's body shape, some unnecessary parameters were reasonably simplified, and the feasibility of the modeling was improved on the basis of ensuring the correctness of the model. The simplification Ideas can be applied to other modeling problems.

In addition, the model built by the present invention has been correctly verified both qualitatively and quantitatively, showing that the model built is reasonable, more in line with actual conditions, has certain practicability, and has a certain effect on improving the fairness of evaluating diving athletes. Certain reference significance.

Description of drawings

Figure 1 is a diagram of a space coordinate system established with the center of mass of a person as the original center;

Figure 2 shows the existence of inclination angle θ and twist angle The spatial coordinate system diagram of ;

Fig. 3 is the time surface graph that athletes of different heights and weights complete the same action;

Figure 4 is a time surface diagram with the difficulty coefficient surface added as a comparison;

Fig. 5 is a time curve diagram of applying the bending degree of the T curved surface to the D curved surface;

Detailed ways

Based on the previous conclusions: there is a functional relationship between the height and weight of a person and the time it takes for athletes to complete each diving action. Therefore, by collecting a large number of data on the height and weight of divers and using the model obtained earlier, it can be calculated that they are completing the same diving action. Different approximate completion times of actions, and draw it into a three-dimensional graphic time T surface, as shown in Figure 3:

It can be seen from the figure that when completing the same diving movement, the heavier and taller athlete takes longer than the lighter weight and shorter athlete. Similarly, the difficulty of completion is relatively greater; but In actual competitions, different athletes get the same difficulty score for the same action, which is extremely unfair. Small and flexible athletes take a big advantage in terms of body size, so when diving on the platform In sports, it is necessary to set body shape correction parameters in order to achieve fairness in the game.

The same action, the same degree of difficulty, different athletes need different time to complete it, which is caused by personal physical factors such as personal height and weight, and the three-dimensional image of time T _tot changes with the height and weight of athletes And change, this just shows that the completion time T _tot has specificity for each athlete, that is, each athlete has its own corresponding completion time, assuming that the difficulty coefficient of the diving action completed by the athlete in Figure 3 is D, Putting D into Figure 3 yields Figure 4.

The plane in the figure is the difficulty coefficient D of the diving action. It is stated here that the difficulty coefficient D has no direct functional relationship with the athlete's height/m and athlete's weight/kg in the coordinate axis.

Since the time T _tot to complete the action has an obvious functional relationship with the athlete's height and weight, and can reflect the specificity of different athletes, if the curvature of the time T surface in Figure 4 is applied to the difficulty coefficient D surface, then the difficulty coefficient D The curved surface can also reflect different difficulty coefficients according to the physical parameters of different athletes. The specific application method effect diagram is shown in Figure 5.

Simply put, this idea is to map the change in the curvature of the time surface T due to height and weight changes to the difficulty coefficient surface D on the basis of the original difficulty coefficient, so that it can reflect the difficulty corresponding to different athletes doing the same action coefficient. The method adopted is to directly add the value of the time surface T to the surface of the difficulty coefficient D to obtain a new difficulty coefficient Curved surface, it was later found that the degree of difficulty obtained in this way is relatively large and not rigorous, so take a suitable center point value t0 on the time surface T, and at this time t0 corresponds to m=50kg, h=1.6 meters, n is the number of tumbling cycles, n=3, can obtain t0=1.24 second, where, obtain following expression:

In the formula, T _tot is the actual time calculated by the model built in question 2, t0 is the middle point of the above time T surface, D is the old difficulty coefficient surface, is the new difficulty coefficient surface, is the correction coefficient.

Example

Let's take Guo Jingjing's height of 1.63m and weight of 48kg as an example, bring it into the above model, and find a new equation Among them, n is the number of tumbling cycles (half of the number of tumbling circles). The calculation results are shown in the table below. It is obvious that our results are quite different from the original difficulty coefficients in Table 1.

The reason for the difference is consistent with the above answer,

Table 1: Ten-meter platform difficulty coefficient table (partial movements)

[Description of action codes] (1) The first digit indicates the frontal orientation of the athlete before take-off and the direction of somersault, 1, 3 means facing the pool, 2, 4 means facing away from the pool; 1, 2 means somersault outwards, 3, 4 means toss inwards. (2) The third digit indicates the number of tumbling circles, for example, 407, which means turning the back to the pool and tossing inward for 3 and a half weeks. (3) B means flexion, and C means tuck. (4) If the first digit is 5, it means that there is a turning movement. At this time, the meaning of the second digit is the same as that in the explanation (1), the third digit indicates the number of tumbling circles, and the fourth digit indicates the number of turning circles. For example, 5375 means toss inward facing the pool for 3 and a half weeks, and turn for 2 and a half weeks.

Claims (4)

1. A platform diving evaluation method that adds athlete's body shape coefficient, is characterized in that diving athlete is simplified as a rigid body with rotary motion, describes the diving time of athlete by the time of research rigid body motion and the quality of rigid body, the relation of length The relationship between weight and height of athletes, the specific implementation steps are as follows: Step 1, simplify the diving action of the athlete into five stages; The five stages described are: The first stage: pure somersault movement; The second stage: arms open; The third stage: After the arms are opened, rigid body motion with rotation and somersault; Phase 4: Arms folded in, similar to Phase 2, but the arms move in the opposite direction; The fifth stage: pure tumbling rigid body motion after the arms are closed; Step 2, based on the height and weight of the diver, the modeling of the time for the athlete to complete the diving action is carried out; Step 3: Establish a new difficulty coefficient evaluation system for divers based on the model obtained in step 2. Specifically, establish a new difficulty coefficient evaluation system for divers based on the mathematical model of the diver's time to complete the diving action and the athlete's height and weight. Step 4. According to the difficulty coefficient evaluation system, the athlete's body shape correction coefficient is obtained. 2. a kind of platform diving evaluation method that adds sportsman's body shape coefficient according to claim 1, it is characterized in that the modeling concrete realization described in step 2 is as follows: Use Ι to represent the constant angular momentum vector in the fixed frame of space, and establish a rectangular coordinate system in the fixed frame. Since the influence of air resistance is ignored in the model assumption, the angular momentum is conserved during the motion of the rigid body, and the origin of the coordinate system can be It is established at any position; at the same time, use L to represent the angular momentum vector of body motion in the reference system, and establish a space coordinate system with the center of mass of the person as the original center; use R to represent the rotation matrix from one frame to another frame; use Ω Represents the angular velocity in 3-dimensional space; A represents the momentum shift caused by the shape change; Since I=RL, we get And Ω=I ^-1 (LA); then the rigid body with rotational motion satisfies the following equation of motion by deriving the above formula: Among them, l is the constant angular momentum vector in the space fixed frame, φ represents the flip angle of the object, θ represents the tilt angle, Represents the torsion angle, h represents the internal angular momentum caused by the opening or closing of the arm and has nothing to do with time, h=w _d · Ι _d , I ₁ , I ₂ , and I ₃ are the objects on the X-axis, Y-axis, and Z-axis respectively moment of inertia; Assuming that the completion time of opening the arm to turn 180 degrees is 0.25 seconds, and then obtaining the angular velocity ω _d =4π rad/s caused by the opening of the arm, Ι _d represents the internal moment of inertia caused by opening the arm, and the simplified process is Ι _d = 2kg ·m ² , get the internal angular momentum h=8πN·m·s caused by the opening of the arm; according to the principle of conservation of angular momentum, suppose a female athlete whose weight is m1, her rotation radius is r1, and the angular velocity is ω1 as above. Then the angular momentum l=m1r1 ² ω1; In the formula (1) Respectively represent φ, θ, for dimensionless time The derivative of , and has the following relationship: in, Assuming that all actions in the five stages are symmetrical, then relationship, so the motion equation (2) can be simplified as: in, Discuss formula (3) according to the five stages, let T ₁ , T ₂ , T ₃ , T ₄ , T ₅ be the time taken to complete the actions of the five stages respectively, and the corresponding dimensionless times are 3. a kind of platform diving evaluation method that adds sportsman body shape coefficient according to claim 2, is characterized in that the new degree of difficulty evaluation system described in step 3, concrete realization is as follows: Phase 1: Pure somersault movement Have And there is no internal angular momentum caused by the opening or closing of the arm, that is, h=0, so ρ=0, and then get the original function Phase Two: Arms Open Have θ has a change, and the value θ=θ _max is uniformly taken at this stage, then: This is the first kind of complete elliptic integral. By setting z=sinθ and taking the value γ=19, the expression of the above definite integral can be obtained as follows: in The k function is a calculation formula proposed by PFByrd et al.; Considering the practical problems, the The approximate processing is 0, and the influence of the arm opening on other parts of the body is ignored, that is, the body inclination θ remains unchanged and is still 0; The third stage: After the arms are opened, rigid body motion with rotation and somersault; have θ be 0, for Since the rigid body is in a pure tumbling equilibrium motion at this time, there is no internal angular momentum caused by the opening or closing of the arm, that is, h=0, so ρ=0, get the original function Phase 4: Arms folded in, similar to Phase 2, but the arms move in the opposite direction; This stage is similar to stage two, with The fifth stage: pure tumbling rigid body motion after the arms are closed; This stage is similar to stage 1, with Thus, the total time of the rigid body motion is which is Since the moment of inertia I is a function of mass m, in three-dimensional space, there is the following relationship: Among them, x, y, and z respectively represent the distance of the rigid body from the center of rotation in the three-axis direction; Based on the analysis of the actual situation, it can be seen that the above three distances are all fixed values, and their reasonable values are respectively x=y=0.5, Equation (7) is transformed into Put formula (8), h=0, l=300 into formula (1) to get: Since there is no opening or closing movement of the arm in the first stage and the third stage, the internal angular momentum h caused by the swing of the arm in these two stages is 0; It can be obtained from formula (9): The original function can be obtained And because φ ₁ = 2πn ₁ , φ ₃ = 2πn ₃ , where n ₁ and n ₃ are respectively the number of tossing cycles in the first stage and the third stage, thus: Among them, n=n ₁ +n ₃ . 4. a kind of platform diving evaluation method adding athlete's body shape coefficient according to claim 3, is characterized in that the athlete's body shape correction coefficient described in step 4, concrete solution is as follows: Add the value of the time surface T directly to the difficulty coefficient surface D of the diving action to obtain a new difficulty coefficient surface, and take the center point value t0 on the time surface T, the following expression is obtained: In the formula, T _tot is the actual time calculated by the model built in question 2, t0 is the middle point of the above time T surface, D is the old difficulty coefficient surface, is the new difficulty coefficient surface, is the correction coefficient.