Numerical simulation of javelin best throwing angle based on biomechanical model

Transcription

1 ISSN : Voume 8 Issue 8 Numerica simuation of javein best throwing ange based on biomechanica mode Xia Zeng*, Xiongwei Zuo Department of Physica Education, Changsha Medica University, Changsha 41019, (CHINA) E-mai: tiyuxi@qq.com BTAIJ, 8(8), 013 [ ] ABSTRACT This paper uses the motion aerodynamics principe to anayze the javein fight process, integrates reated factors with athetic performance in the study of the force condition and movement condition of the human body and the javein, numericay simuates the different anges of fixed parameters by Mathematic software, obtains the theoretica optimum throwing ange 40, that is when the shot ange is 40 and the ange of the javein s ong axis with the horizonta surface is 31 the throwing distance reaches the greatest. The resuts are very consistent with the actua situation; this artice can make reasonabe suggestions for the promotion of this project s athetic performance, provides a theoretica basis for the javein sports technique, and confirms the reasonabeness of existing theory and technique. 013 Trade Science Inc. - INDIA KEYWORDS Biomechanics; Aerodynamics; Throw ange; Mathematic numerica simuation. INTRODUCTION In the javein movement, moving trajectory and moving resuts of javein are primariy refections of a set of human movement. Using the biomechanica principes can reasonaby prove the maturity of the technique and correct errors of technique. When the javein reeases from the hand it suffers the gravity and air resistance. Due to its shape and mass, it determines that the air resistance of the javein during movement in the air cannot be ignored, so when we study the moving trajectory of javein after disposing the aerodynamics principe is a good theoretica too. Ony by combining the kinetic characteristics and moving trajectory of the javein after disposing can we determine the best shot ange and speed combination of javein. Therefore, using sport biomechanics and aerodynamics principe to conduct objective anaysis of the javein throwing movement has an activey promoting effect on the deveopment of sports technoogy. Javein throwing process incudes: run-up, fina force and javein reeasing fight three phases, where the runup phase takes the ongest time, and this stage provides the best posture for throwing and at this foundation stage the roe of initia kinetic energy is reated to achievements; fina stage is aso used to provide the initia kinetic energy for the javein fight, but its effect is far better than the run-up phase, this stage aso provides the throwing ange of javein fying, which is critica stage reated to athetic performance; During fight javein receives air resistance and gravity, athough the resuts do not have a subjective reation, but it provides resut refer-

2 BTAIJ, 8(8) 013 Xia Zeng and Xiongwei Zuo 1043 ence for the research of vaidity and rationaity of first two phases. In this paper, through biomechanics theory and the aerodynamics theory, it conducts a detaied anaysis for the three stages of javein throwing movement, confirms the reasonabeness of the existing technique of this movement combing with the anaysis resuts, and provides rationaization proposas for the scientific training. SPORTS MECHANICAL ANALYSIS OF LAST FORCE TECHNIQUE (TAKE THE RIGHT HAND THROWING FOR EXAMPLE) The fina stage of javein throwing technoogy starts from the right foot, through series of actions deivering by the egs, hips, torso, shouder, ebow, and hand, and finay throw out the javein. The duration time of the fina stage is about 0.1s-0.15s, which is very short from the time interva. But force sequence and speed change of a aspects of the body are consistent with the biomechanics whipping principes. In the braking process it has shown a very arge instantaneous impuse, makes the javein have greater instantaneous momentum, thus it can have a high initia kinetic energy. In the throwing arm whipping process, when the hand, forearm and upper arm are in the same ine, the three inks do not exist the reative rotation, but have the same anguar veocity reative to the shouder axis, as shown in Figure 1. Figure 1 : The simpe schematic when the arm is in straight ine In Figure 1 Point A represents the shouder joint, point B represents the ebow joint, point C represents the wrist joint, I 1, I respectivey mean the moment of inertia of upper arm and forearm, ù 1 means the anguar veocity of the arm rotates straighty around the shouder joint. But in the throwing process, forearm and upper arm has the reative rotation. We suppose the forearm rotates around the ebow point B, where point B is equivaent to the braking point, as shown in Figure. Figure : Schematic of the forearm rotates reativey around the ebow joint The rotation moment of momentum of the forearm reativey around Point B is as formua (1): M = I â (1) In Formua (1) M represents the torque generated in the forearm musce contraction, â represents the anguar acceeration of the forearm around point B. According to the definition of anguar acceeration the anguar momentum theorem can be obtained as formua () beow: 1 Mt I ( ) 1 t () In Formua () Ät shows the action time of forearm musces torque M; by the formua () the expression of anguar veocity ù can be obtained as formua (3): Mt 1 I (3) The formua (3) shows that the anguar veocity of the forearm is increasing on the basis of ù 1 in the process whipping of throwing arm, and the increased vaue is M t. I When the rotation ange of forearm around point B is very sma, according to the reationship of anguar and inear veocity, we have the expressions in formua (4): v r v r v r r 1 v v1 v In Formua (4) í represents the inear veocity of the point C in wrist reativey to the shouder joint, í 1 represents the inear veocity of the point B in ebow joint reativey to the shouder joint, í represents the inear veocity of the point C in wrist reativey to the ebow joint, and r 1, r respectivey represents the ength of the upper arm and forearm. (4)

3 1044 Numerica simuation of javein best throwing ange based BTAIJ, 8(8) 013 Substitute the formua () and (3) into the formua (4) formua (5) can be obtained: v (r r ) r Mt 1 1 I (5) According to formua (5), when forearm whips, the r Mt ine speed of the wrist increases by comparing with no whipping. In the fina force stage, the body s center of gravity speed is constanty decining; human kinetic energy is aso reducing. The direction of the braking by the eft eg anding and the inertia by the throwing arm on the javein in the acceeration process is opposite to the acceeration direction of the javein. So the body s speed is decining, if in the ast throwing process of throwing arm, throwing objects, the stronger the force of inertia of the throwing matter is, the much thorough that momentum transfer of the body on the javein is. I TABLE 1 : Javein physics parameter tabe for adut mae Parameter name AERODYNAMIC ANALYSIS After disposing in addition to its own gravitationa force Javein aso suffers air resistance. Studying the movement condition of javein reeasing can refect the reationship between movement characteristics and athetic performance when reeasing the Javein, and it is the entry point to study the movement s throwing technique probem of non-forces infuencing factors, so it is necessary to study the movement of the javein after disposing. For any one kind of javein it has its fixed shape and quaity. We can use the poynomia fitting way to dispose each measurement point, and get the physica characteristics parameters of the javein. This paper takes the javein for adut maes as the research object, uses the previous 4 order poynomia function as a mode base beow. The javein physics parameters in TABLE 1 can be obtained. Physica magnitude Tota mass of Javein 811.5g Distance from the gun breech to the centroid Distance from centroid to gun head Surface area of Javein The maximum projected area of javein The rotationa moment of inertia around its own shaft (the axis perpendicuar to the javein direction) The rotationa moment of inertia around its own shaft (the axis aong the javein direction) The rotationa moment of inertia around its own shaft (another axis perpendicuar to the javein direction) The initia kinetic parameters when reeasing javein incude: the shot height of javein centroid is h 0, the shot veocity of centroid is í 0, the ange of javein centroid shot veocity with the horizonta surface is è 0, the ange of javein with the horizonta pane is á 0, the pitch anguar veocity when reeasing the javein is ù 0, the ange of the projection of the javein ong axis in the xoy surface and the projection of the javein centroid veocity in the xoy surface is ã 0 generay known as the yaw ange, the reeasing moment of the javein is in the spatia coordinate system as shown in Figure 3: Javein suffers gravity verticay downward and resistance generated by air during movement in the air. Air resistance is divided into frictiona resistance, pressure drag and the induced drag. The friction resistance is reevant with the air viscosity coefficient, and the 1585mm 1055mm mm mm g*mm g*mm g*mm Figure 3 : The initia state of javein reeasing instant in the coordinate system expression of the friction resistance is in formua (6): 1 F C v ds f f (6) Sf In Formua (6), F f means the friction of air on the javein, ñ means the air density, C f means the viscosity

4 BTAIJ, 8(8) 013 Xia Zeng and Xiongwei Zuo 1045 coefficient of air, S f means the surface area of the javein, and í ô indicates the reative parae veocity of javein centroid to the gas. The expression of the pressure drag is as the formua (7): 1 F C v ds p p // (7) Sp In Formua (7) í means the reative vertica veocity of javein centroid to the gas, and S p means the projected area of the javein. Javein aso receives induced drag during the fight. The air resistance acts on the javein, decompose the resistance in a direction reativey parae to air fow and reativey perpendicuar to air fow. Since in the javein fight the air joint force that it receives does not necessariy act on the javein centroid, it wi produce torsiona moment on the javein. The javein movement can be seen as the pane motion in yoz; according to the synergistic effect of the rotation aw of rigid body and the projectie movement of the objects, the resutant moment equations in the y axia direction and z axia direction can be obtained, as shown in formua (8): 0 1 Fpy sin( ) C pv sin sin f 1 0 F C v cos cosf d fy f F sin( ) C v sin cosf pz p 1 0 F C v cos sin f d fz f M sin( ) C v sin f d p 1 d d The formua (8) shows that the air resistance wi generate rotation torque on the javein, and the gravity goes the Javein center of gravity, so the gravity wi not generate rotating torque and the movement of the two forces can be superimposed. The numerica simuation resuts indicate that when the pitch anguar veocity is zero, for the average athete the range of best shot ange is between [38, 44 ], if the pitch anguar veocity is not zero, we shoud appropriatey increase the shot ange. When the initia attack ange is 0, the throwing distance of javein is the farthest; the smaer the air viscosity coefficient is, the better throwing distance is. (8) INITIAL PARAMETERS AND THROWING DISTANCE NUMERICAL SIMULATION WHEN JAVELIN RELEASES AWAY FROM THE HAND Based on the above force condition of javein after disposing, conduct numerica simuation for formua (6) (7) (8), we can obtain the throwing distance of the javein with different initia parameters. TABLE shows the centroid speed of the javein when shot, the ange of the veocity and the horizonta direction, the ange of javein ong axis and the horizonta surface and the initia yaw ange. In order to expore the probem of shot ange, this paper seects the shot speed 6m/s that athetes generay can reach in major match, the yaw ange is 0, the air viscosity coefficient is 0.003, pressure drag coefficient is 1., the air density is 1.18 * 10-5g/mm3, it uses Mathematic software to conduct numerica simuation for javein throwing distance, the simuation resuts are in TABLE. TABLE : The combination comparison tabe of computer simuation resuts Shot ange 0 Throwing distance (m) The ange 0 of Javein ong axis and the horizonta pane The change trend of throwing distance with 0 when 0 is 30 is shown in Figure 4: Figure 4 : The comparison chart of throwing distance and 0 when 0 = 30

5 1046 Numerica simuation of javein best throwing ange based BTAIJ, 8(8) 013 Because there are too much data, it is shown in the form of bar graph aso the fina resut, respectivey 0 = 3, 34, 36, 38, 40, 4 ; the corresponding 0 is shown in Figure 5 - Figure 10. Figure 9 : The comparison chart of throwing distance and á 0 = 40 Figure 5 : The comparison chart of throwing distance and 0 when 0 = 3º Figure 6 : The comparison chart of throwing distance and á 0 = 34 Figure 7 : The comparison chart of throwing distance and á 0 = 36 Figure 10 : The comparison chart of throwing distance and á 0 = 4 Figure 4 - Figure 10 shows the foowing resuts: 1) When è 0 = 30 and á 0 = 30 the maximum throwing distance is 66.0m; ) When è 0 = 3 and á 0 = 3 the maximum throwing distance is 67.5m; 3) When è 0 = 34 and á 0 = 31 the maximum throwing distance is 68.8m; 4) When è 0 = 36 and á 0 = 7 or 30 the maximum throwing distance is 70.5m; 5) When è 0 = 38 and á 0 = 9 the maximum throwing distance is 71.1m; 6) When è 0 = 40 and á 0 = 31 the maximum throwing distance is 71.3m; 7) When è 0 = 4 and á 0 = 30 the maximum throwing distance is 71.m; According to the simuation resuts, = 40 and á 0 = 31 we have the maximum throwing distance, and then with the assumed parameters, this combination is the best throwing ange. CONCLUSIONS Figure 8 : The comparison chart of throwing distance and á 0 = 38 This paper uses sports biomechanics and aerodynamics to we expain javein movement, and propose the best throwing ange and precautions of throwing; obtains optima throwing ange combination by numeri-

6 BTAIJ, 8(8) 013 Xia Zeng and Xiongwei Zuo 1047 ca simuation. Aerodynamics is the theoretica basis to study the javein movement after reeasing it, which we expains the air resistance of the javein; in the satisfied condition air resistance has a rotationa torque roe on the javein, so that during the fight it can generate rotation; The numerica simuation resuts show that when the shot ange è 0 = 40 and the ange á 0 = 31 of the javein with the ground the throwing distance is the greatest, and this combination is the best throwing ange. REFERENCES [1] Bing Zhang, Yan Feng; The specia quaity evauation of the tripe jump and the differentia equation mode of ong jump mechanics based on gray correation anaysis. Internationa Journa of Appied Mathematics and Statistics, 40(10), (013). [] Cai Cui; Appication of mathematica mode for simuation of 100-meter race. Internationa Journa of Appied Mathematics and Statistics, 4(1), (013). [3] Haibin Wang, Shuye Yang; An anaysis of hurde performance prediction based on mechanica anaysis and gray prediction mode. Internationa Journa of Appied Mathematics and Statistics, 39(9), (013). [4] Hongwei Yang; Evauation mode of physica fitness of young tennis athetes based on AHP- TOPSIS comprehensive evauation. Internationa Journa of Appied Mathematics and Statistics, 39(9), (013). [5] Liao Hong; Study on the optima reease ange of Javein with air resistance. China Sport Science and Technoogy, 43(1), (007). [6] Lu Jian-Ming; The function of eft side support during the reease phase in Javein throw. China Sport Science and Technoogy, 39(4), (003). [7] Wang Qian; Optima initia conditions for Javein performance under new rues. Sport Science, 9(), (1989). [8] Zhou Li; Current state and anaysis of sports biomechanics study in China. Journa of Shanghai Physica Education Institute, 1, 3-6 (1997).