Prediction and dynamic model of high jump performance based on block growth model

Transcription

1 ISSN : Volue 8 Issue 0 Prediction and dynaic odel of high jup perforance based on block growth odel Junqing Chen Institute of Physical Education, Gannan Noral University, Ganzhou 34000, Jiangxi, (CHINA) E-ail : tiyuxi@qq.co BTAIJ, 8(0), 03 [337-34] ABSTRACT In order to iprove the achieveent of high jupers, this study first approxiately launches a jup height odel based on the three stage odel as the run-up, take-off and crossing bar. In the take-off stage, to accelerate the run-up velocity and strength athlete the power to jup are two ain directions to enhance the perforance. And to increase the take-off velocity in the crossing bar stage plays an iportant role in enhancing the results. Then based on the en s and woen s high jup chapion achieveent data in the Olypic Gaes, this study establishes the block growth prediction odel of en s and woen s high jup perforance and predicts that the scores of en s and woen s high jup chapion of the 30th Olypic Gaes are accordingly.3845 and The predicted results are highly in coincide with the existing 30th Olypic Gaes results of en s and woen s high jup, which are.38 and.05 respectively, indicating that this odel is suitable for the prediction of high jup perforance and can provide a reference for the training work of high jup coaches and athletes.. 03 Trade Science Inc. - INDIA KEYWORDS High jup; Block growth odel; Dynaic odel; Prediction. INTRODUCTION After 00 years of developent, the high jup has reached a very high level. Whereas, studies on the dynaics and echanical characteristics of the high jup, as well as on predicting athletes perforance still have great significance to proote the iproveent of the jup high level. There are a large nuber of scholars in the past studying on the dynaics of the high jup, but ostly they focus on the analysis of the kineatic characteristics of all aspects of high jup. And studies on the various stages of oveent of the athlete as a whole are very rare. In fact, different technical stages of the high jup are closely linked. Therefore, to conduct echanical analysis of the high jupers height in general is very necessary. High jup results are in a rising process and scientific predictions of future achieveents can specify the day-to-day training of athletes. In the past, prediction on the high jup perforance is usually about the gae tie and scores based on the regression odel and gray prediction odel. However, with the gradually slow growth rate of the high jup achieveents, the predicted results with the above ethods tend to have larger differences with the actual situa-

2 338 Prediction and dynaic odel of high jup perforance BTAIJ, 8(0) 03 tion. In this study, first create a dynaic odel of the high jup height and analyze the various factors effect on the jup height. Then establish block growth prediction odel according to the en s and woen s chapionship results in the Olypic Gaes. This study ais at providing certain referencing basis for the training work of high jup coaches and athletes. RESEARCH ON THE DYNAMIC MODEL OF HIGH JUMP Fundaental analysis of the high jup process and height The Fosbury Flop can be divided into three steps: () Run-up: run-up line is generally J. The preparatory segent of the run-up is a straight line or a sall curvature line, and then gradually transfers to arc, with the arc curvature fro big to sall, to gradually increase the body internal frequency. () Take-off: the horizontal velocity obtained fro the run-up can be rapidly transferred to vertical upward oveent velocity, so that the body is fully upward Juping and ready to cross the bar. Take-off action can be divided into the juping leg s landing, buffering and stretching, three stages in general and the coordination between the swing legs and ars. (3) Crossing bar and landing: the crossing bar is to ake full use of the take-off flight tie to change body posture, and take advantage of the range of otion of the body and rotate over the bar. High jup height H is coposed of three parts: () H : The height of body center of gravity before vacation. It depends on the athlete s height and leg length, and apparently the athletes with tall height and long legs have a clearly advantage on the height of gravity center. It can be decoposed into h, h. h eans the height fro the ground to the body center of gravity when the knees buffer to the greatest extent since the take-off foot s landing. h eans the result that the height of body center of gravity at the take-off oent inus h.() H : The vertical distance fro the highest point in the vacation to the height of body center of gravity height before the vacation. (3) H 3 : The vertical distance fro the body center of gravity to cross bar in the highest point of vacation. It depends on the air posture when the athlete reaches the highest point and the body oveents when crossing the rod. H H H H3 Construction of the atheatical odel Run-up stage: Assuptions: The preparatory segent of run-up is uniforly accelerated linear otion. The curve segent is variably accelerated circular otion. Do not consider the resistance fro winds to the body. Man is taken as a particle. Sybol Description: a - Acceleration of the uniforly accelerated linear otion; F - Friction suffered by the body; R - Radius of the curve. The eventually established atheatical odel is: Line segent: v at ; Curve segent: v 0 FR/ Take-off stage: Model assuptions, Buffering stage: fro the landing to the hopping foot to knees buffering to the axiu extent. As this takes place in an instant, the dropping of the center of gravity can be regarded as a unifor decelerated otion. And the body receives only the supportive force in the vertical direction fro the ground, gravity and the resistance in the horizontal direction. Changes of horizontal velocity and vertical velocity are independent of each other. Kicking stage: the center of gravity is on a rapid shift and the thighs kick straight. Besides, the center of gravity of the person is in the sae line with the reaction force. The huan body is in upward swing in the vertical direction. This happens in a short tie and the force in this process is constant force, so this stage can be approxiately regarded as a uniforly accelerated otion. The eventually established atheatical odel: Buffering: Horizontal direction: f t0 v x v [Theore of ipulse] Vertical direction: Kicking: F t v y v y Crossing bar stage: Assuptions: v y g f / / t0; H gt. [Theore of ipulse] The athlete is regarded as a particle, i.e. the center of gravity is the particle. When people do projectile otion in the air, the body only receives the force of

3 BTAIJ, 8(0) 03 Junqing Chen 339 gravity and the air resistance is ignored. Sybol Description: a- Flight angle; d - The vertical distance of juping-off point to the rod; h - The take-off vertical height; v - The take-off velocity. Modeling: Horizontal direction: v cos a t d [Projectile Motion] Vertical direction: v sin a t g t h By the odels of the three stages: the run-up, take-off and the cross bar, it can be approxiately established that: H H H H H v sin a t gt H 3 3 Analysis on the atheatical odel of the takeoff stage and the crossing bar stage: () Forula for the take-off stage: Buffering: Horizontal direction: f t0 v x v [Theore of ipulse], Vertical direction: H g f / t v y g f / / t0; 0 (The dropping height of the center of gravity is in fact the rising height of the center of gravity) Kicking: F t v y ( v y ) [Theore of ipulse] Therefore, factors affecting the take-off velocity v and flight angle a are the vertical rising height of the center of gravity H and take-off tie t in the take-off stage. To increase the take-off velocity eans to increaseand. As for, the increasing ofwill increase. So fast runup can increaseand shorten the ipact tie. Judging fro, it can be drawn that increases. As for, the increasing of F and decreasing v v y of y will both increase. However, to reducewill be reduce, so to increaseis a ajor factor. In suary, to accelerate the run-up velocity and the athlete s power to jup are the ain directions to increase H. In the take-off stage, with the fast upward swing of swing legs and ars and stretching the joints of hopping foot, a strong kicking action will be fored. This will increase the power of people to jup and can increase the take-off power. () Forula for the crossing bar stage: v cos at d ; v sin a t g t h As can be seen fro the forula: If the center of gravity falls in front of the crossbar, that ay result in that the body will touch the rod in the down process, that is: v sin agt Suppose: v sin a t g t h H (The height of the 0 bar) If the center of gravity falls on the upper back of the crossbar vertical plane, the body will probably touch the bar in the up process, that is: v sina gt Siilarly suppose: sin v a t g t h H0 (The height of the bar) Reasonable take-off velocity and take-off distance should satisfy the following forula: ; sin / v cos a t d v a g H In the forula: H v sin a / g To ake H as larger as possible should increase at the sae tie: () increase the take-off velocity v ; () increase the flight anglea. v v v x y The flight angle of high jup is fored by the horizontal direction and the direction of the initial velocity when the body center of gravity vacates and the body is off the ground. It is related with the ratio of the vertical angle at the take-off instant to the horizontal velocity (when the vertical angle is larger than the horizontal velocity, a 45, when the vertical angle is saller than the horizontal velocity, a 45). Through the sine is the largest when a 90, it is not possible to use the juping angle of90. The ain reason is that the ain purpose of high jup is to cross the bar and at the sae tie to take advantage of the run-up level velocity to accelerate the take-off action. And the sensitivity of a is not high, so that the change scope ofh is liited. Therefore, to increase the take-off velocity v has an ipor-

4 340 Prediction and dynaic odel of high jup perforance BTAIJ, 8(0) 03 tant role in iproving the value of H. RESEARCH ON THE BLOCK GROWTH PREDICTION MODEL OF HIGH JUMP PERFORMANCE The principle of block growth odel Assue that the growth rate of high juper s result r is the linear decreasing function of the original result of high jup x. In other words, the growth rate of high jup result will decline with the increasing of the high jup result: rx r0 sx Therefore athlete high jup result will finally reach saturation and tends to a constant x. When x x, the growth rate is 0. r 0 sx 0 Fro the above relation, it can be derived that: r0 r x x x Substitute the above equation into the equations of exponential growth odel. And based on the initial conditions x t x 0 0, it can be obtained that: x x( t) e t0 After calculation: x r( t x0) Sybol description dx x r0 x dt x x( t0) x0 r - Growth rate of high juper s result; x - Original result of high jup; x - The liit of high jup result Data collection With the en s and woen s high jup chapion achieveents in the Olypic Gaes as research objects, the collected data are shown in TABLE. Model building Prediction odel for Men s high jup perforance: Using the initial condition x ( 4).98, the following can be obtained: dx x r0 x dt x x(4).98 x x( t).98 Calculate: x r( t 4) e Prediction odel for Woen s high jup perforance: Using the initial condition x ( 4).68, the following can be obtained: dx x r0 x dt x x(4).68 x x( t) x.68 Calculate: r ( t 4) e Fitting using the existing data and the calculated solution is: x.404, r ; x.73, r Judging fro the above analysis, the liits of the en s high jup score is.404 and the liits of woen s high jup score is.73. Based on the prediction odel, this study predicts the scores of en s and woen s high jup chapion of the 30th Olypic Gaes, and the predicted results are respectively.3845 and And in fact, the all ready known TABLE : Men s and Woen s high jup chapion achieveents in the Olypic Gaes() Session Year Men Woen

5 BTAIJ, 8(0) 03 Junqing Chen 34 30th Olypic Gaes results of en s and woen s high jup are.38 and.05 respectively. The prediction data for the en s result is quite consistent with the actual data, and the prediction data for the woen s result is slightly different with the actual data. It deonstrates that the block growth prediction odel of high jup result has a favorable prediction result and can be used for the prediction of high jup perforance, as shown in Figure. Figure : The growth curve of en s and woen s chapions achieveent SYMBOL DESCRIPTION f - The takeoff resistance in the horizontal direction f - The take-off supportive force in the vertical direc tion t - Buffer tie 0 v - The horizontal velocity of the hopping foot at last stride in the run-up stage v - Horizontal velocity after the buffering x v y -Vertical velocity after the buffering H -The dropping distance of the center of gravity t - Kicking tie v y - Vertical velocity when the hopping foot is off the ground F - The reaction force of the ground to the body in kicking stage CONCLUSIONS () Fosbury Flop is divided into four stages: the run-up stage, the take-off stage, the crossing bar stage and the landing stage. The jup height consists of three parts: H : The height of body center of gravity before vacation. It can be decoposed into h, h. h eans the height fro the ground to the body center of gravity when the knees buffer to the greatest extent since the take-off foot s landing. h eans the result that the height of body center of gravity at the take-off oent inus h. H : The vertical distance fro the highest point in the vacation to the height of body center of gravity height before the vacation. H 3 : The vertical distance fro the body center of gravity to the crossbar in the highest point of vacation. According to the odels of the three stages: the run-up, take-off and the crossing bar, it can be approxiately established that: H H H H H v sin at gt H 3 3 Through the analysis of take-off stage and crossing bar stage, it shows that to accelerate the run-up velocity and the athlete s power to jup in the take-off stage are the ain directions to increase H, and to increase the take-off velocity v in the crossing bar stage has an iportant role in iproving the value of H () Based on block growth predict odel, the past Olypic Gaes ale and feale high jup chapion achieveent data are fitted to obtain the corresponding function. According to the function, predict the results of the next Olypics. The prediction results show that the liit scores of en s and woen s high jup are.404 and.73 respectively. And the scores of en s and woen s high jup chapion in the next Olypic Gaes are accordingly.3845 and.0707, which are highly in coincide with the already known 30th Olypic Gaes results of en s and woen s high jup, that are.38 and.05 respectively. This indicates that this odel is suitable for the prediction of high jup perforance. REFERENCES [] Xiangdang Du; Re-discussion on Back-style Highjup Run-up Teaching. Journal of Taiyuan Noral University, 5(), 4-4 (006). [] Yaoting He; Kineatic Analysis of the High Jup Run-up for Pantelieng. Journal of Shanghai Physical Education Institute, 6(5), (00). [3] Jinsong Wu; Kineatic Analysis of the Swinging Leg and Support Technique on the Course of the

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