Available online www.jocpr.com Journal o Chemical and Pharmaceutical Research, 14, 6():11-1114 Research Article SSN : 97-784 CODEN(USA) : JCPRC Monte carlo experimental research on table tennis size aects paddler experience sense and audience ornamental Jianguo Liu School o Physical Education and Science, Quu Normal University, Quu, Shandong, China ABSTRACT Dierent diameters table tennis bring out paddler dierent experience qualities, meanwhile it gives audience dierent ornamental quality. Take paddler universal serve strength 4N as striking orce, according to inormation, it works out that best visual table tennis shiting eect is 1.9 m/s and table tennis best radius is 4mm.Then consider rom paddler hitting percentage, table tennis collides the table, the bigger original route deviation angle is, the more diicult paddle receive would be, so that ewer times o back and orth would be. Based on this theory, with the same strength, calculate diameter 4mm table tennis collides table deviation angle is 16.1, diameter 8mm table tennis collides table deviation angle is.1, so that deine 4mm table tennis has an advantage over 8mm table tennis. inally by Monte Carlo simulation experiment deines that best table tennis radius is 4mm. Key words: Experience quality, deviation angle, table tennis diameter, Monte Carlo Simulation NTRODUCTON Any one sport event should have higher ornamental. Otherwise, it will lose audience. And sport events that lose audience are no vitality. With regard to table tennis audience has deceasing tendency since 197s, table tennis technical ornamental research has already become an important subject in table tennis theoretical cycle. n order to increase table tennis air resistance in lying, slow down its running speed in competition so that achieve urther increasing and enriching table tennis proessional paddlers striking techniques and skills, inally increase table tennis competitions overall ornamental, international table tennis ederation let international table tennis proessional tournament oicial table tennis adopted diameter increase rom 8mm to 4mmm in. However, the coming o large ball era has always suered table tennis coaches and paddlers disputes. To solve the problem, Chinese and oreign scholars always adopt investigation method, carry out simple statistical analysis o results appeared by paddler using two kinds o table tennis [1-]. Though it can solve these problems, shortcoming still exist on theoretical aspects. National associated scientiic committee researchers have made dierent diameters and weights table tennis aect striking speed and rotation experiment. Experiment conclusions are big diameter table tennis speed is slower than that o small diameter one, while its rotation is weaker than that o small diameter one; or same diameter table tennis, large weight and elastic orce one has quicker speed and stronger rotation than small weight and elastic orce one. n eb.rd,, international table tennis ederation extraordinary general meeting and congress have passed 4mm large ball reorm scheme in Kuala Lumpur, decided that table tennis competition would use diameter 4mm, weight.7g large ball to substitute 8mm small ball since Oct.1 st, that was also ater Sydney Olympic Games [4-6]. To urther improve table tennis paddler experiment quality and audience ornamental quality, analyze table tennis eatures rom mechanics perspective, utilize computer making simulation on table tennis dynamic process so that ind best table tennis diameter. 11
Jianguo Liu J. Chem. Pharm. Res., 14, 6():11-1114 MODEL DESGN n order to ind out 8mm and 4mm such two table tennis dierences in paddler experience sense and ornamental, convert problems into researching two table tennis in speed, rotation as well as its dropping to opponent table and bounce generates angle oset problems. Adopt mechanics principle, research table tennis initial movement situation and rebound movement trajectory, and establish two table tennis models based on that as table tennis initial movement model and rebound trajectory model [7-9]. Preparation beore model establishment n international ormal competitions, international table tennis ederation normally adopt length 74cm, width 1.cm, height 76cm, net height 1. cm table, as igure 1 shows [1]. When serving table tennis, it should irst through its own table, then bounce to opponent table through net. n continuously striking, table tennis should directly drop to opponent table without through its own table. These are basic rules. igure 1: Table tennis table schematic igure Conditional assumption in researching: Except table tennis diameter is variable, other conditions not changing that table tennis competition table tennis table, net, rule and competition environment all achieve current international table tennis ederation stipulation; Table tennis hardness owns rigidity, and mass distribution is evenly. Use symbol explanation in researching process, reer to Table 1. Table 1: Symbol convention m Table tennis mass R Table tennis diameter v Table tennis running speed ω Table tennis angular speed reer to rotational inertia r Table tennis radius µ riction coeicient riction orce J impulse ϑ delection angle υ swinging speed Table tennis suered joint orce Table tennis ornamental sense model establishment and solution Because racket aects table tennis mechanical analysis is extremely complicated, in order to simpliy problems, this paper ignores all very little action orce, now assume that racket eects on table tennis are two orces eects that are vertical to racket orce as well as table tennis and racket tangential riction orce, and table tennis initial speed and angular speed are.let table tennis mass to be m, diameter as R. As igure shows, let racket and horizontal included angle to be, time that racket eects on table tennis as t, swinging speed as v [, 1]. igure : Racket initial parameter analysis igure orce impulse in the time t t is dt that expressed by, impulse in the time t t is dt that 116
Jianguo Liu J. Chem. Pharm. Res., 14, 6():11-1114. goes through table tennis mass center and tangents with expressed by and table tennis, thereore riction R orce generates table tennis a torque, torque s impulsive moment in the time t R t dt is, that R ( R c = mr r = ) is.table tennis mass center rotational inertia is, end speed along v direction is, end v speed along direction is, end angular speed is ω.according to momentum theorem and angular momentum theorem, it can get ollowing ormula: = mv = mv R = cω (1) Solve: v = m v = m R ω = c = mr () () (4) urther deduce ormula (4), it gets: D t = = = mr mr c t t dt = = µ mr mr ω () n ormula, µ expresses riction coeicient ( µ value normally is.~.8 [], According to the model, this paper 1 t values µ =.6 = ), 1 second [4]. Table tennis competition appreciation perspective analysis: Table tennis competitions ornamental mainly are related to technical quality, tactics changes, paddler instrument and stroking motion aesthetic perception as well as competition times and other actors. But or research problems, it mainly analyzes rom table tennis technical mass that is to evaluate 8mm and 4mm two dierent diameters table tennis ornamental through analyzing table tennis speed and turns. Because most o audience selects to watch table tennis competitions by TV, only consider competition ornamental watching by TV, and audience best translational visual angle is / s [], While viewing angle that watches TV is not changing, root cause o changing is camera converted certain included angle that moves with table tennis movement, thereore regard camera as human eyes, take rotation as best point, according to data, it indicates that general camera distance rom competition court is around meters[6]. Thereore best audience sense table π = 1.9m / s tennis movement speed is: 6. Analysis when diameter is 8mm ( m =. 1 kg ) : Assume that outside world vertical orce on table tennis is t 4 1 v = = = =4N, so. 1 m m 1 =16 m / s 117
Jianguo Liu J. Chem. Pharm. Res., 14, 6():11-1114 1 ω =.6 4 - - According to ormula (), it gets:. 1 8 1 1 =81. rad / s Analysis when diameter is 4mm ( t 4 1 v = = = so.79 1 m m 1 =14.69 m / s m =.79 1 kg ): Similarly assume =4N, 1 ω =.6 4 - -.79 1 4 1 1 =698.9 rad / s Through comparing 8mm and 4mm more ornamental. v with 1.9m/s, it is obviously that adopt 4mm diameter table tennis is Judge competition is wonderul or not, it tends to check whether there are many two paddlers back and orth times or not, according to data indication, it is clear that applause would appear when paddlers have 7 to 8 back and orth times [6], thereore evaluate audience ornamental can be up to paddlers back and orth times, the more back and orce times are, the happier audience would be. Turns are normally related to paddlers strength and table tennis speed as well as delection angle. The aster speed is, the ewer turns would be; the larger table tennis delection angle is, the larger diiculties receive would be, the ewer turns would be. Through 4...1 analysis as well as ollowing delection angle analysis, it shows that 4mm diameter table tennis speed is slower than 8mm diameter table tennis, and delection angle is also smaller than 8mm diameter table tennis, thereore 4mm diameter table tennis would let competition turns increasing, and increase ornamental. Paddler experience sense and best diameter model establishment and solution Through above model analysis, it gets that 4mm diameter table tennis is really better than 8mm diameter table tennis in ornamental perspective, but it doesn t solve paddler experience sense and best table tennis diameter problems. Table tennis running trajectory analysis: n movement process, table tennis mainly suers three orces inluences that are respectively gravity, air resistance and Magnus orce, as igure shows. igure : Table tennis orce dissolution igure M shows Magnus orce, D Among them, G shows gravity, movement speed, ω shows table tennis angular speed. shows air resistance, v shows table tennis = G + M + D = mgkˆ G D 1 = ρc D ( πr) v v CD n ormula, ρ shows air density, shows resistance coeicient, R shows table tennis radius. According to Magnus ormulas, M = ρ (πr) ( ω v). (6) (7) (8) 118
Jianguo Liu J. Chem. Pharm. Res., 14, 6():11-1114 Table tennis rebound model establishment and solution: t mainly researches movement speed, angular speed, linear speed as well as impulse change situations beore, during and ater table tennis drops to table to explain table tennis delection angle. As igure 4 variable symbols, it shows each variable change beore and ater table tennis drops to table. igure 4: Variable change situations beore and ater table tennis drops to table n igure 4, v and shows table tennis speed, ω and ω shows table tennis angular speed, u and u J shows table tennis and table relative speeds; r shows impulse caused by table riction, J z shows upwards impulse. When table tennis is stroking rom one party to another party s table and ast rebounds, table tennis movement speed v direction and angular speedω direction will occur to delection, which would lead to table tennis running trajectory shits comparing to original running trajectory. While dierent diameters table tennis caused table tennis running trajectory oset angles dierent. By researching dierent diameters table tennis delection angles, to deine paddlers experience sense and audience ornamental brought by 8mm and 4mm two table tennis and deine best table tennis diameter. Corresponding table tennis and racket angle oset model has already proved by experiment [8].This paper based on the model; establish table tennis and table angle oset models. According to previous analyzed table tennis running movement speed v and angular speedω, it gets table tennis parallel to table speed u when takes movement, its expression is: u = vxy + ( ω r) n ormula, vxy represents v projection in coordinate xoy plane. (9) According to table tennis rigidness hypothesis, table tennis speed v vertical direction component expression is = ε z v z n ormula, z represents ater table tennis rebounding v vertical direction speed, vz rebounding v vertical direction speed, ε represents elastic deormation coeicient. (1) represents beore Table tennis impulse in coordinate xoy plane has connections with impulse in z Positive coordinate axis direction that can express with ollowing ormula: J = J xy µ z u u n ormula (11), J xy represents impulse in Coordinate xoy plane, direction, µ and represents table tennis and table sliding riction coeicient. J z (11) represents impulse in z axis positive 119
Jianguo Liu J. Chem. Pharm. Res., 14, 6():11-1114 According to impulse-momentum theorem: m mv = J (1) As well as angular momentum and rotational inertia principle: ω ω = r J (1) Get two equations as: J = m( 1+ ε ) z v z 1 r u u = µ J ( + ) + u m u (14) (1) n ormula (1), u represents speed when table tennis touches table. Due to table tennis and table touching time is quite short, we assume that touches table. Thereore establish u and proportion relationship, the expression is: u = c ( xy isn t changing when table tennis c ) (16) Through ormula (1) (1) and (16), it can get: vz c = 1 µ (1 + ε ) = 1 α u (17) Among them, v z α = µ( 1 + ε) u. Through combining ormula (1) (1) and (17), it can get v and relationship: v = Avv + B v ω ω = A v + Bωω ω (18) (19) n physics, when c > shows it is sliding riction status, but this paper don t get involved in physical constraints o c sizes. 1 α αr A v = 1 α B v = αr ε, And α α 1 r = α A α B ω ω = 1 r 1, n physics, c indicates it is rolling riction status. When c =, u =, table tennis is ully rolling.at this 111
Jianguo Liu J. Chem. Pharm. Res., 14, 6():11-1114 α = time,.since rolling status is zero sliding constraint status, so: A v = ε, B v = r r, And: A ω = r r, B ω = 1 rom (16) and (17), it gets: = v sin1 cos1 + r ω sin cos v sin1 cos1 r ω sin cos εv z Among them,, respectively shows speedυ and z axis included angle, speed υ projection in xy plane and x axis included angle, expresses angular speedω and z axis included angle, angular speedω projection in xy plane and x axis included angle, as igure. y ϑ = Then delection angle expression is x. igure : Delection angle (serve) n case that, are the same, ϑ becomes bigger, then it indicates when table tennis touches table, it is prone to get delection, and it is more diicult to predict remote curve ater table tennis collides with table, then paddler is also more diicult to stroke the table tennis, back and orth times would be more and more ewer, audience ornamental quality not high; Since it is diicult to stroke expected received table tennis, paddler experience mass is also not high. or 8mm and 4mm comparison, with regard to, these our variables, since paddlers stroking ways are dierent, table tennis and table colliding angles are also dierent, we irst take random values o, ϑ respectively as,,,, 8 ϑ =.1, 4 =16.1. t is clear that8mm delection angle is larger than that with 4mm, so that is to say 8mm table tennis is more diicult to stroke than 4mm table tennis. Best radius selection: Just as previous delection angle problems, when, these our variables still value as,,,, change table tennis radius, then it can get ollowing one tendency igure that delection angles changing ollowed by radius, igure as ollowing igure 6: 1111
Jianguo Liu J. Chem. Pharm. Res., 14, 6():11-1114 igure 6: Table tennis best radius selection igure t is ound when r=1mm, that is to say when table tennis diameter changes into 4mm, table tennis delection angle is the minimum one. t is also thought when table tennis diameter changes into 4mm; it is paddler best experience radius. Because best visual angular speed is1.9 m / s, similarly can get best running radius is 4mm. MODEL TEST RESEARCH Above result is deined in case angle is ixed. n order to get more precise calculation result and provide above our angles size rom to 9 at random so that deine, dierent situations best radius, when test times is 1, running result is 4 mm diameter table tennis is best table tennis that accounts or 6%, is ar higher than other types table tennis. Calculation result is as ollowing igure 7 shows. igure 7: 1 times testing Monte Carlo simulation result When testing times is, simulation result still indicates that 4mm diameter table tennis is the best table tennis that accounts or 68%, is ar higher than other types table tennis. Running result is as ollowing igure 8 shows. igure 8: times testing Monte Carlo simulation result When testing times is 1, simulation result still indicates that 4mm diameter table tennis is the best table tennis 111
Jianguo Liu J. Chem. Pharm. Res., 14, 6():11-1114 that accounts or 7%, is ar higher than other types table tennis. Running result is as ollowing igure 9 shows. igure 9: 1 times testing Monte Carlo simulation result When testing times is 1, simulation result still indicates that 4mm diameter table tennis is the best table tennis that accounts or 7%, is ar higher than other types table tennis. Running result is as ollowing igure 1 shows. igure 1: 1 times testing Monte Carlo simulation result When simulation times arrive more than 1, there is 7% probability that best radius is 4mm, or other % probability why it is not 4mm, we think,.values between and 9, some might not value but it still takes, such as table tennis might not vertical to table and stroke upwards, but to sum up it gets best radius is 4mm. CONCLUSON Through applying table tennis movement model, analyze model movement speed and angle, and took people best ornamental table tennis running speed (1.9 m / s ) as measurement criterion, it got that running speed at 14.69 m / s diameter 4mm table tennis ornamental result had an advantage over that running speed at 16 m / s diameter 8mm table tennis. Meanwhile, only took speed as measurement criterion, it was obvious that 4mm table tennis speed was slower that was more helpul or paddler experiencing. By establishing table tennis rebound trajectory model to measure dierent diameters table tennis rebound angle osets, it got that table tennis with 4mm diameter had the lowest oset that can improve paddler experience sense more. And through dierent diameters table tennis Monte Carlo simulation, it got that 4mm diameter table tennis accounted or largest percentage, thereore 4mm diameter table tennis was the best table tennis. REERENCES [1] HU Leyong. Sports & Science, 1, (), 4-4. [] Chun, yan. Journal o Hubei Sports Science,, 1(4), 4-4. [] Li Jin-Liang, Zhao Xia, Zhang Chao-Hui. Journal o Beijing Sport University,, 8(1), 1414-1416. 111
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