Mathematical model to crouch start in athletics

Transcription

1 Mathematical model to crouch start in athletics 1 Amr Soliman Mohamed, 1 Lecture in Department of kinesiology faculty of physical education - Minia University, Egypt 1. Introduction Science is the cause of development in many fields, particularly the sport field with its various activities, especially the track and field sport, which is fertile ground to various applications of science, especially the biomechanics, which aims to study the development of millimeters of vertical or horizontal distance traveled (throwing and jumping), or parts of a second (the running), and that when dealing with the performance of elite players. The results of biomechanical studies in track and field are considered the basis for the development of the motor skills of running, jumping and throwing (5)(17)(15)()(13)(7), As for the races of short distances, we find that all the runners use crouch start, which is one of the international legal requirements to start (9). There are numerous studies dealt with the issue of start with variety ways, such as Brooks (1981)(4), who tried to study the relationship between the length of the runner's leg and the horizontal distance between the front of the starting block template and the start line, in addition to the impact of changing that distance on the speed of start, As well as hoster (1986)(10), Schot and knutezen (199)(17), Harland and Steele (1997)(8) who tried to develop a new start technique or to compare between more than one technique or to identify the mechanical variables values affecting on the start. Some researchers have tried to identify the impact of blocking start type, aiming at a comparison between the vacuum blocking start and normal one such as the study of Adel Abd Elhafez (1981)(1). Others have aimed to reach the most appropriate distributions to the start based on the values of the dynamic variables result from testing these distributions and its impact on start-up phase and launch from the blocking start such the study of Khaled Abdel Hamid (006)(11). Many of the scientific references and studies indicated that to achieve the most appropriate possible starting from the crouch start, you have to put the body joints in a certain angles to enable the body to achieve maximum power in the least possible starting time, and the most common angles are: -The front knee angle (90 degrees). - The front and rear ankles angles (90 degrees). - Rear knee angle (10 degrees)(3)(1)(14)(16)(17)(6). Therefore, the researcher tried to put a mathematical model of crouch start depending on the player anthropometry measurements by which we can determine the horizontal distance between the parts of blocking start and the starting line and its tilt angles on the ground there for it ensures that the player is able to reach the optimum position and angle of departure including the angles of knees and ankles, which contribute to increase the speed and power off and thus reducing the total time of start.. Materials and Methods The researcher has used the descriptive method that fits the field of the research. The researcher derived a foundation of mathematical model from references and scientific studies which dealt with the topic of block starting in many ways, in addition to the basic mechanical rules. The research has been applied on a sample of three different players in the length (176.5±10cm) to confirm the starting of players from the optimal angles, and then re-applied to another sample (139.7±8cm) to confirm the impact of the model in start time.

2 Mathematical model Table (1) Symbols used in illustrations and in the mathematical equations of the model N S Description 1 A Foot length B shank length 3 C Thigh length 4 D The length of the trunk 5 E fully arm Vertically length 6 Vertical Distance between the point of the shoulder and the horizontal line passing through the hip F point and parallel to the surface 7 G Vertical distance between the shoulder point and horizontal line passing horizontally of hip point 8 H Connecting line between the toe of the rear foot and hip point 9 I Horizontal distance between hip point and toe of the rear foot 10 j Horizontal distance between hip point and the vertical line pass-through shoulder point 11 K Connecting line between knee point and toe of front foot 1 1 Front knee angle 13 Rear knee angle 14 3 Front ankle angle 15 4 Rear ankle angle 16 5 Front block angle 17 6 Rear block angle 18 x1 The distance between the front block and start line 19 x The distance between the rear block and start line Mathematical model-building steps First: There are five basic variables are known from the diverse scientific sources as follow: 1-The relative or real distribution of the body mechanical segments lengths (Anthropometric measurement) (a, b, c, d) which is measured directly or calculated based on the opinions of (braune & fischer) (1889) (dempster)(1955) bernstein)(plagenhoof) ( 1988) (zatsiorsky & seluyanov) (1993 ) (deleva) ( 1996), Or averages of those ratios extracted from these tables by the researcher. - Front knee angle (90 deg) (1). 3- Rear knee angle (10 deg) (). 4-The front and rear ankles angle (90 deg) (3, 4). 5- Front block angle (60 deg) as theoretical output (5). Second: There are five unknown variables shown in Figure (1) as follows: 1-Vertical distance between the point of the shoulder and the horizontal line passing through the hip point and parallel to the surface (f). - Vertical distance between the shoulder point and horizontal line passing horizontally of hip point (g). 3- Rear block angle (6). 4- The distance between the front block and start line (x1). 5- The distance between the rear block and start line (x) Third: to calculate the distance between the front block and start line: f x1 = = ( c sin (( d 60 f b sin ) 30 ( c sin a sin 30 )) 60 ) e (( b sin 60 ) ( a sin 30 ))

3 3 Fourth: To calculate the distance between the rear block and start line: h = (( a b c ) ( a b ) c (cos( 10 (tan ( a / b)))) )(1) i = h g () j = d f (3) from 1,,3 x = i j Fifth: To calculate the Rear block angle: 6= (180 ((sin ( g / h)) (cos (( h b a c )/( h ( a b )))) (tan ( b/ a)))) Figure (1) steady phase position at the crouch start Figure () Extraction stages of the mathematical model variables, respectively

4 4 3. Results and Discussion Table () Relative body segment lengths, according to views of the scientists and the its overall average Table (3) Relative distribution of different lengths which applied the mathematical model on it theoretically Table (4) Results from the applied of mathematical model on various lengths theoretically by using the overall average lengths (by the researcher) Table (5) Overall average of the application results of mathematical model on a sample of three players to confirm the results of the angles starting practically segment length (cm) segment Results of the Variables (cm) body height body height Head nick Ratio to all body (%) whole trunk Rear block distance (%) upper arm Ratio to all body (%) arm forearm rear angle (deg) hand front knee angle (deg) total arm differences thigh rear knee angle (deg) leg shank differences foot front ankle angle (deg) ankle height differences front block angle rear ankle angle (deg) front block distance differences

5 5 Table (6) Overall average of the application results of mathematical model on a sample of three players to confirm the results of the time and velocity of starting practically Player data Calculated (cm) nom Height(cm) x1 ratio x ratio f. Angle b. Angle Player data Measurements (cm) nom Height(cm) model thigh shank foot trunk arm 1 13 calc real calc real calc real The overall average for three trials (S) Player data mathematical model traditional model Differences (%) nom Height(cm) T. start T, 10m T. start T, 10m T. start T, 10m Table () clarifies the arguments between scientist's opinions on the lengths proportions of the body anatomy segment, which prompts the researcher to find the average of those values and uses it in the mathematical model to recognize the least possible differences between measurements of different types of objects. Tables (3,4) prove the application of mathematical equations model on the values of the average of body length ratio on different and progressive default height in the starting from (130 cm) to (10 cm). Equations of the model was applied until extraction of the variables required, the value of horizontal distance between the front block and the start line was the largest in all the circumstances of the shank player length, ratio of the horizontal distance between the front block and the start line equal value (8.3%) of the almost total length of the body. As the percentage of the distance between the rear block and the start line was equal (5.4%), these values differed slightly at (± 5) when applying the model on different rates for different length of the body and this is accepted by the researcher. Table (5) shows the practical results which assert the validity of the mathematical model, as it has been applied on three players of different heights and then blocking start variables were calculated in accordance with the proposed mathematical model, and then photographed them and calculated their joints legs angles. They were all around the optimal values of the start angles, the difference between real and theoretical values (1: deg) which is acceptable to the researcher. Table (6) it is clear that practical results and the differences between the start according to mathematical model method and traditional method being applied on a sample of three players, each has three trials of every method and then calculated the general average of results to every one. It is clear to us that the ratio of change between the two methods was for the benefit of the mathematical model method, as the difference between the two methods is (17.74% : 6.67%) on start time, and (1.81% :.05%) on 10m running time. 4. CONCLUSIONS Through the research procedures. To achieve the aim of it in the light of these results, using former scientific studies and the views of scientists, the researcher formulated his research concludes on the following: -The researcher is able to design the mathematical model to crouch start in the light of the measurements Anthropometry of the player.

6 6 - The proportion of horizontal distance between the front templates and the start line (8.3%) of the total length of the player body. -The proportion of horizontal distance between the rear template and the start line (5.4%) of the total length of the player body. - The relationship between the horizontal distance from the front template and rear to the line of the start line was (1: 1.85). - For each player, there are start Variables suit his total body lengths and anatomical links to enable him to put his body joint in the best angles of departure and assist him to reduce the start time. - Best front template angel with the ground is (60 degrees) because it suits his optimum starting body angels. - The Proposed Calculation model to start saves (17.74%: 6.76%) in the start time as well as (1.81%:.05%) in 10m running time. REFERENCES 1-Adel m. Abd Elhafez (1983). Impact type of blocking in start, Fourth Scientific Conference for the Study of Sport and Education Research, Faculty of Physical Education for Boys, Helwan University,. - Bartlett, R. M., Müller, E., Lindinger, S., Brunner, F., and Morris, C. (1996). Three-dimensional evaluation of the kinematics release parameters for javelin throwers of different skill levels. Journal of Applied Biomechanics, 1, 58-71,. 3- Borzov, v.,( 1979). The optimal starting position in sprinting, soviet sports review, no Brooks, c.,( 1981). Women's hurdling, leisure press, west point,. 5- Chapman, a.e., & Caldwell, g.e., (1983). Kinetic and limitations of maximal sprinting speed, journal biomechanics, vol, 16, no, 1,. 6- Čoh, M., kastelic j.& printaric, s., (1998). A biomechanical model of the 100m hurdles of Brigita Biekovec, track coach, no. 14, winter. 7- Feltner, m.e., & nelson, st., (1981). Three dimensional kinematics of the throwing arm during the penalty throw in water polo, journal of applied biomechanics, vol, 1, no, 1,. 8- Harland, M., & Steele, J. (1997). Biomechanics of the Sprint Start. Sports Medicine, 3 (1), 11-0,. 9- Hay, J.G. (1993). The Biomechanics of Sports Techniques (Fourth Edition). Prentice-Hall, Inc, Englewood Cliffs. ISBN , 10- Hoster, m., (1986). Sprint, the crouch start, technique, no, 95, spring,. 11- Khalid a, Shafi (000). Analytical study of the different distributions of the start and its Impact to some parameters in the dynamic start-up phase of the race and support for 100 young people, unpublished PhD, Faculty of Physical Education - University of Menoufiya,Egypt,. 1- Mero, A., Luhtanen, P., & Komi P. (1983). A biomechanical study of the sprint start. Scand J Sport Sci, 5(1), Newton, r.u.k,. Kraemer, w.j., Hakkinnen, k., Humphries, b.j., & Murphy, a.j., (1966). Kinematics and kinetics and muscle activation development, journal of applied biomechanics, vol, 1, no,. 14- Pronk, c.n., von Niewenhuyzen, j.f., & Stam, h.j.,( 1985). Comparative study of Isokinetic force measurements of the knee extensor in d. winter, r. Norman, r. wells, k., hays, & a. patla, (eds), biomechanics 1x, champing il, human kinetics,. 15- Ritzdorf, w., & Conrad, a., (1990). High jump. In G-P Brüggemann & B. Glad (Eds.), scientific research project at the Games of the XXIVth Olympiad-Seoul 1988: final report (pp ). London: International Amateur Athletic Federation,. 16- Sale, d.,( 1991). Natural adaptation to strength training in strength and power in sport, p.v. komi (ed) London Blackwell,. 17- Schot, P., & Knutzen, K. (199). A Biomechanical Analysis of Four Sprint Start Positions. Research Quarterly for Exercise and Sport, 63 (), ,. 18- Sung, r.j., Chung, c.s., & shin, l,s.,( 1990). A kinematics analysis of the Fosbury flop techniques of Korean male elite high jumpers, Korean journal of sport science Seoul,.