І І І м і ж н а р о д н а н а у к о в о - п р а к т и ч н а к о н ф е р е н ц і я “ З д о р о в ’ я н а ц і ї і в д о с к о н а л е н н я ф і з к у л ь т у р н о - с п о р т и в н о ї о с в і т и ” 79 СЕКЦІЯ 2. ПРОФЕСІЙНИЙ ТА ДИТЯЧО-ЮНАЦЬКИЙ СПОРТ BIOMECHANICAL ANALYSIS OF THE DEPENDENCE OF THE HIGH JUMP RESULT ON THE HEIGHT AND WEIGHT OF AN ATHLETE Egoyan A.E., Gobirakhashvili A.D., Moistsrapishvili K.M. Georgian State Teaching University of Physical Education and Sports, Georgia, Tbilisi, alexegoyan@gmail.com Abstract. This paper presents the results of a complex biomechanical analysis of the high jump. The data of the world's best high jumpers (39 men and 36 women) were studied. Based on these data, we calculated the average height and weight of athletes for men and women and determined the dependence of the jump result on the athlete's height, weight and vertical speed of the centre of gravity at the moment of the jump. Keywords: high jump, computer modelling, centre of gravity, biomechanical analysis. Introduction. The biomechanics of the high jump has been studied quite well, the average values of the main biomechanical parameters such as the speed of the athlete’s centre of gravity (COG) during the take-off, the duration of the take-off phase and the take-off force have been estimated [1, 2]. However, the dependence of these parameters on the height and weight of the athlete, which ultimately determines the final result, has not been sufficiently studied. Purpose of research. The main purpose of this study is to determine how the result of the high jump depends on the height and weight of the athlete. To do this, we studied the results of the world’s best high jumpers and, using a simple biomechanical model and computer modelling, established how the athlete’s height and weight affect the position of the centre of gravity at the take-off moment and the vertical component of its velocity. I I I i n t e r n a t i o n a l s c i e n t i f i c a n d p r a c t i c a l c o n f e r e n c e “ N a t i o n ’ s h e a l t h a n d i m p r o v e m e n t o f p h y s i c a l a n d s p o r t s e d u c a t i o n ” 80 Results of the research and their discussion. We have studied the weights and heights of 39 men and 36 women world’s best high jumpers [3]. The results of the statistical analysis are presented in Table 1. Table 1 - Average values of the characteristic parameters of men and women world’s best high jumpers. Parameter Men Women High jump result (Mean), cm 238.82 204.14 Height (Mean), cm 192.69 180.72 Height (Mean Absolute Deviation), cm 5.63 4.21 Height (Standard Deviation), cm 6.69 5.54 Weight (Mean), kg 76.67 60.94 Weight (Mean Absolute Deviation), kg 5.11 4.43 Weight (Standard Deviation), kg 5.93 5.3 BMI (Mean), kg/m2 20.65 18.65 BMI (Mean Absolute Deviation), kg/m2 1.01 0.95 BMI (Standard Deviation), kg/m2 1.28 1.27 From Table 1, we can see that both men and women high jumpers have low enough values of BMI – 20.65±1.01 kg/m2 for men and 18.65±0.95 kg/m2 for women. This is because most of them are tall – average men’s height is 192.69±5.63 m, while women’s 180.72±4.21 m and have relatively light body masses - 76.67±5.11 kg for men and 60.94±4.43 kg for women. To understand how the final result of the high jump depends on the sportsman’s weight and body mass we use the following formula: 𝐻 = ℎ𝐶𝑂𝐺 + 𝑉𝑦 2 2 ∙ 𝑔 , (1) where H - is the highest position of the sportsman’s COG, hCOG – is the vertical position of COG at the take-off moment, Vy – is the vertical velocity of COG at the take-off moment, and g≈9.8 m/s2 – is the gravitational acceleration on the Earth's surface. І І І м і ж н а р о д н а н а у к о в о - п р а к т и ч н а к о н ф е р е н ц і я “ З д о р о в ’ я н а ц і ї і в д о с к о н а л е н н я ф і з к у л ь т у р н о - с п о р т и в н о ї о с в і т и ” 81 From Fig. 1 we can identify the positions of the athlete’s body during the take-off (position #8) and bar clearance (position #16). Using athletic body proportions from [4] and segment inertia parameters from [5] we can calculate COG coordinates for men and women having average heights from Table 1. Figure 1 - Positions of the sportsman’s body in the high jump, using the Fosbury Flop technique. The results of computer modelling are shown in Fig. 2. Figure 2 - The results of computer modelling of COG positions for an upright standing athlete and an athlete at the taking-off moment (a.) – men, b.) – women). The calculated vertical coordinates of COG are shown in Table 2. I I I i n t e r n a t i o n a l s c i e n t i f i c a n d p r a c t i c a l c o n f e r e n c e “ N a t i o n ’ s h e a l t h a n d i m p r o v e m e n t o f p h y s i c a l a n d s p o r t s e d u c a t i o n ” 82 Based on the data presented in Table 2, we can calculate COG coordinates for athletes of arbitrary height h using the following formulas: hCOG=135ꞏ(h/193)=0.699ꞏh – for men, hCOG=124ꞏ(h/181)=0.685ꞏh – for women. From these formulas we can find, that increasing the height h by 10 centimetres increases the jump result by about 7 centimetres. Table 2 - The calculated vertical coordinates of COG for men and women. Gender Height (cm) COG vertical coordinate (cm) Increase (cm) Upright standing At the take-off moment Men 193 106 135 29 Women 181 99 124 25 Knowing the sportsman’s high jump result H and his/her COG vertical position hCOG, we can calculate Vy – the vertical velocity of COG at the take-off moment: 𝑉𝑦 = √2 ∙ 𝑔 ∙ (𝐻 − ℎ𝐶𝑂𝐺), (2) At the next stage of the research, we can estimate how the result of the jump will change if the athlete's weight changes by a few kilograms, while the take-off force F and the take-off time ∆t do not change. From the impulse-momentum change equation: 𝐽 = 𝐹𝑦 ∙ ∆𝑡 = 𝑚ꞏ𝑉𝑦 , (3) From (3) we can calculate J for men and women having parameters shown in Table 1: J = 348.176 kgꞏm/s for men and J = 241.917 kgꞏm/s for women. And then from (1) and (2) we can calculate Vy and H for different values of body weight m. The sportsman’s body mass changes ∆m and the corresponding changes in the high jump result ∆H are shown in Table 3. Table 3 - The changes in the high jump result ∆H caused by the changes in body weight ∆m. ∆m (kg) -5 -4 -3 -2 -1 0 1 2 3 4 5 ∆H (cm), men 14.9 11.7 8.6 5.6 2.7 0.0 -2.6 -5.2 -7.6 -10.0 -12.3 ∆H (cm), women 14.9 11.6 8.4 5.5 2.6 0.0 -2.5 -5.0 -7.3 -9.5 -11.6 І І І м і ж н а р о д н а н а у к о в о - п р а к т и ч н а к о н ф е р е н ц і я “ З д о р о в ’ я н а ц і ї і в д о с к о н а л е н н я ф і з к у л ь т у р н о - с п о р т и в н о ї о с в і т и ” 83 Conclusions. Based on the conducted research, we can make the following conclusions: 1. The vertical speed at the take-off moment is the main parameter that determines the result of the jump - its increase by 0.1 m/s will increase the result of the jump by about 4-5 centimetres. 2. Among the world’s best high jumpers, the average height of men is 193 cm, and the average height of women is 181 cm. Increasing the height parameter by 10 centimetres increases the jump result by about 7 centimetres. 3. Reducing/increasing the weight parameter by 1 kilogram will increase/decrease the jump result by 2.7 centimetres. This means that the athlete should not have extra weight except muscle weight. List of sources of information: 1. Dapena, J., Gordon, B. J., and Meyer, B. W. (2006). High Jump (Women), Indiana University, 106 pp. 2. Dapena, J., and Ficklin, T. K. (2007). High Jump (Men), Indiana University, 136 pp. 3. Athlete Data. (Retrieved on December 20, 2022). http://athletedata.weebly.com/high-jump.html. 4. Human Proportion Calculator 2.0 (Beta), http://humanproportions.com/. 5. de Leva, P. (1996). Adjustments to Zatsiorsky-Seluyanov's segment inertia parameters. Journal of biomechanics, 29 (9), 1223–1230. http://athletedata.weebly.com/high-jump.html http://humanproportions.com/