hand push in selected side horse vaulting stunts

14
Japanese Society of Physical Education NII-Electronic Library Service Japanese Sooiety of Physioal Eduoation Hatano Y ‘‘ Skii Analysis of Kick and Hand Pusb Actiens in Sei ted Side Hor8e Vaulting Stunts Reseatvh o ¢ ’劭 al Mncation VoL 20 No 6March 1976 pp 339 352339 37 SKILL ANALYSIS OF KICK AND HAND PUSH ACTIONS IN SELECTED SIDE HORSE VAULTING STUNTS Yoshiro HATANO 7bO Galt gei σve 5丿 運動 にお 踏切 りと 着手 分析 (東京 学芸大学 跳馬 跳箱運動 技術指導 示唆 を来 真分 折法 適用 して 踏切 着手 ic考察 競技経験者 IO よる 屈身 とび とび 前転 び屈身宙返り演技 分析 にその 重心軌跡 ら力 学的 を踏切 着手 いて ような結果を得 1 決定 け る特 定 技術的 力掌限定する 不可能 助走 着手 条件 条件 補 償的動 作 めに の出 えを必 し も支 配 していないと れる 2 重心移動 ズに まれ る よ う な助走 t ドが 最後 ける 蹴り だ第 飛躍 にと て有 と考えられる 3 所要 時間 蹴り 着手 引続 され ag して 有利 4 蹴り 直下 はやや 陵方 向 け られ 般的 着手 前下方 多 く見 られ 5 転回系 跳躍 にお 体幹 前方 助走 続く下方 蹴り によ 生 まれ この 重心 転系 技と大差 なか 6 跳躍 実施 lcts 体幹 前方 転を るが 着地以前 戻す 振 りや腰 屈伸運動 を用 いているこ とが明 らかで Abstract In order to find certai 3uggestions for improvements in performances ln vaulting stunts and in its skill instruction kk king and hand push actions of selected side horse vaulting stunts were studied by use of cinematographical analysis technique Ten coilege gymnasts volunteeled as 8ulectg who performed squat vault handspring vault and front somersault vau t for picture taking Upon analyzing Projected pictures the center of gravity movements were traced fr m which v tn y es f kicking and hand pu h acti ns were attempted The outcomes included the followings N 工工 Eleotronio Library

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Page 1: HAND PUSH IN SELECTED SIDE HORSE VAULTING STUNTS

Japanese Society of Physical Education

NII-Electronic Library Service

Japanese  Sooiety  of  Physioal  Eduoation

Hatano, Y .,‘‘Skii垂Analysis of Kick and  Hand ・Pusb  Actiens in Sei  ted Side・Hor8e

Vaulting Stunts” Reseatvh/o岬 剛 ¢ ’劭 」師 ‘al Mncation , VoL 20,

 No.6, March , 1976,

pp.339〜352.

339(37)

SKILL  ANALYSIS  OF  KICK  AND  HAND ・PUSH  ACTIONS

   IN SELECTED  SIDE・HORSE  VAULTING  STUNTS

Yoshiro   HATANO

7b海ツO Galt#gei σ”’ve ア5蕗丿

跳 馬運動 に お け る 踏切 り と着手の 技術分析

波 多 野  義  郎

      (東京学芸大学)

 跳馬 ・跳箱運動の 演 技 や 技術指導 へ の 示唆 を来 め て , 写 真 分 折法 を 適用 し て ,特 に そ の 踏 切 りと 着手 icつ い て

考察 し た .即 ち ,体操競技経験者 IO 名に よ る 屈身 と び 。腕立 て 前転とび 。前転 とび屈身宙返 り, の 演技 を分析

し , 特に そ の 重心軌跡か ら力学的 ベ ク トル 解 析 を 踏 切 りと 着手 に つ い て 試み , 次 の よ うな結果を得 た .

 1. 優れ た演技 を 決定 づ ける特定 の 技術的・力掌的条件を限定す る こ とは , 不可能 に 近 い .即ち,助走 ・踏切

  り ・着手な ど の ある一つ の 条件 の 優劣は,他 の 条件 に お け る補償的動作が あるた め に ,総合的演技 の 出 来ぱ

  え を 必 ずしも支配 して い な い と思わ れる.

 2. 重心移動 が ス ム ーズ に 踏切 り動作に 持 ち こ まれ る よ う な助走 ス t“一ドが あ る こ と と,そ の 最後の

一歩 に お

   け る 踏 切 板へ の 重心 入射角 が 小 さ い こ とが ,強い 蹴 りと ,ス ケール に 富ん だ第一飛躍 に と っ て 有 効 で あ る

      と 考 え られ る,

 3. 所 要 時間 の 短 い ,鋭い 蹴 りや 着手 は , 引続 き展 開 さ れ る ag−  ・第 二 局 面 の ス ケール に 対 し て 有利 に 働 く.

 4. 踏 切 りに お ける 蹴 りは ,直下 よ りは や や 陵方 に 向けられ る の が 一般的で あり,一方 , 着手 で は 前下方へ の

  突 きが 多 く見 られ た .

 5. 転回系の 跳躍技に お ける 体幹 の 前方回転は , 速い 助走に 続く, 後下方 へ の 蹴 りに よ っ て 生まれ る 例が 多 い

  が,こ の 時 の 重心軌跡 は ,特に 非回 転系の 跳躍技と大差 が なか っ た.

6. 非回 転系の 跳躍技で も, その実施前半lctsい て 体幹は 前方回 転をす るが ,着地以前 に そ の 回 転を逆に 戻す

  た め に ,腕の 前上方向 へ の 振 りや腰 の 屈伸運動 を用い て い る こ とが明 らか で あ る、

Abstract

  In order  to find certai 旦 3uggestions  for improvements  in performances  ln vaulting  stunts

and  in its skill  instruction, kk:king and  hand−push actions  of  selected  side 。horse vaulting

stunts  were  studied  by use  of  cinematographical  analysis  technique.  Ten  coilege  gymnasts

volunteeled  as 8ulectg  who  performed   squat  vault ,  handspring  vault   and   front  somersault

vau [t  for picture taking .  Upon   analyzing  Projected pictures, the  center  of  gravity  movements

were  traced, fr。m  which  v   t… n ・晝y・es ・f  kicking and   hand−pu・h acti ・ns   were   attempted ・

The  outcomes   included  the  followings;

N 工工一Eleotronio  Library  

Page 2: HAND PUSH IN SELECTED SIDE HORSE VAULTING STUNTS

Japanese Society of Physical Education

NII-Electronic Library Service

Japanese

:・

'

'

Society of Physical Education

340(13S) RlrsE ARCH JOCrRtVAL OE PHYSrcAL EDUCATIOIV Vol. 2o, No. 6, (Oversets Edition No. 13>, March, 1976.

I'. No single technical andlor meehanical prernises to dec{de the successful performance

were found. The execusion in one of the prernises, such as pteceding run, kick and

hand-push would be compensated in other premises, and hence, the total performance

weuld not be ruled by one.

2. Satisfaetory speed in preceding run to be carried over to kicking action and smoothness

in the last step of the run vv'ould provide effective pre-fLight.

,', Sharp kick and hand-push actions with short duration of time would provide effective

pre- and post-flights, respectively.

4. The kicking for take-off is generally directed to down-backward, while the hand-push, to down-forward.

5. Forward rotartory move of the trunk in rotatory vaulting stunts is generally produced

by fast preceding run follewed by a down-backward klck, while the center of grayity

trajectory would not be so different between rotatory and non-rotatory stunts.

6. In the case of non-rotatory stunts, the trunk starts to rotate forward in the first half

of the performance, though such rotation is reversed in the latter half, by wiggling

the hips and up-lifting swinging of the arms.

1. Introductio"

Human movement is so versatile that a movement performed by a person at a time may

'i・r},

from any other movements he has ever made before, Yet it is such specific at certain

phases of skillful aetivities that established ski{ls and habits, are diffieult to be changed.

Analysis of skillful body movements, for this reason, may constitute analysis of the skM

it3elf. '

Mechanical analysis of body movents may be attempted for merely a scientific interest,

hut also for finding certain suggestions fer skill instruction. As a matter of fact, a few

[・,:umptes of studies, the results of which may be used as useful suggestions for instructional

t-?L'hniques, have been reported in variety of sports. However, instructional andlor coaching

Euggestions for horse vaulting stunts in gymnestics, for exampte, have been more frequentiy

provided from intuitional considerations by instructors and eoaches than from results of

.htientific studies.

Certainl.v a performance is usually given by a gyrnnast who is not necessarily always

concerned about the mechanics of the skill, rather he performs as a whole person to whom

c,th/-r suggestions from psychological and phys{erogicat viewpoints may be also necessary.

X,'et,

certa{n mechanical considerations should provide opportunities to improve some aspects

ofthe perforrnancet'tO). For this reason, mechanical studies of various physical skills, forthe

purpose of finding ¢ ertain general mechanicai principles which govelrn the skill and ef pro・

v!'ding useful suggestions to improve perforrnances, should be conducted more frequently7)8).

Thus, in this study, certain side-horse vaulting stunts in gyrnnastics are taken into movie

t'ilms for the purpose of mechanical analysis so that useful suggestions for improvement of

p?rt'ormances and teach{ng techniques may be provided

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Japanese Society of Physical Education

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JapaneseSociety ofPhysical Education

Hntateo : Skill Analysis of Kick atnt HZ nd-Ptish Actiens in Slalectect Slde-Hbrse Vautting stsmts 3"(3g)

Purpose ef the Study

The purpose of the study then is to analyze the mechanics of certain side-horse vaulting

stunts in gymnastics by applying previously established experimental technique of cinemato-

graphical analysis, so that the sequential body movement throughout each of the stunts and

the specific charactaristcs of the stunts may be explained by use of certain parameters, such

as quality and quantity of ferce invelved in various phases of each performance made by

certain novice and advanced college gymnasts. Accumulation of such study results may be

expected to make contributions tewards more therough understanding in variety of human

rnovernents involving certain skills.

2 Methodelogy

In order to analyze the mechanics of certain side-vaulting stunts in gymnasties, the

processes of (1) stoop vault (SV-INSV-7), (2) handspring vault (HS-1--HS6) and (3) frontsomersault vault (YV-1 and YV-2) were selected for cinematographical analysis.

2. 1. Subjects

Ten college gymnasts majoring in health and physical education at Tokyo Gakugei

Unfversity, two rnales and eight females, whose carrier length in this sport ranged betweenthree and six years, volunteered as subjeets, The reason why experienced gymnasts were

exclusively used for the experiment was because for beginners these stunts are rather

difficult to perform.

During the performance, the female subjects wore tightly fitted gymastic uniform and

the rnale, shorts, for the benefitof the picture'analysis to take place later. Further, certain

landmarks of the body, such as wrist, knee and ankle of the camera side of each subject

were taped for the same reason.

The subjects warmed up thernselves properly to the peint at which they would be on

the top level physical condition for performance. The runway and vaulting board for the

approach of vaulting as well as mats at the landing area were provided as in the rnanner'a

competition would take place. The vaulting horse was placed sideways, with its height

being t20cm.

2. 2. Picture Taking Devices

Each performance to be analyzed was taken into 16mm high speed mevie films by use

of a camera, produced by Bolex Co., West Germany. Using a tripod, the camera was set at

an appropriate height, 120crn from the floor, and at a certain distance apart from the vaulting

horse in the transverse direction to the pathway of the performer to be fully able te catch

the perfermance within the camera view.

Fuji Neopan R 250 blaek-and-white positive filrn with its ASA being 250, each role

having 1oo feet of length, was used fer entire picture taking.

While the accurate shutter speed of each picture taking needs to be determined for this

NII-Electronic

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Japanese Society of Physical Education

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Page 5: HAND PUSH IN SELECTED SIDE HORSE VAULTING STUNTS

Japanese Society of Physical Education

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JapaneseSociety ofPhysical Education

Hatano

wouldeverymance

: Skil1 Analysis of Kitk nd IEIhnd-Ptish Actians in Selected Side-Hbrse Vdtdti'ng Stwtts 243(")

be shown, provided the resultant drawing looks simple. For this /reason, drawings of

8 or 10 frames, with sorne exceptions when necessary, were combined in each perfor-

for analysis of sequential body movements.

3. Parameters

3. 1. Sequential Movement of Bedy Segrnents

Sagittal movements of certain landmarks of the body, such as the ear, shoulder, hip,

knee, ankle, elbow and wrist, all on the camera side of the subject, were traced in each

performance. Then combining any adjacent three !andrnarks, the sequential changes in angles

of extremities and trunk were also analyzed. Likewise, the changes in angle betvveen the

trunk and the vertieal line, which would indicate the process of body rotation, were recorded.

3. 2. Center of Grayity

The center of gravity of the body ef the performer was estimated in each frame of

drawing. The estimation of center of gravity in variety of eomplexed body position shown

on the course of performance was made by applying methods proposed by Matsui"), modified '

by the current investigator earlier5).

3. 3. Vector Analysis

Upon obtaining the sequential course of center.of gravity movement in each performance,

the velocity and acceleration of center of gravity rnovement at each moment rnay be obtained

when the time length for eaeh frame is taken into account. When the vertical distance -

between center of gravity positions at the moment of take-off and at the heighest point

during the pre-flight in a given vaulting performence is given, for instance, the vertical

component of initial veloeity for the pre-flight is, by applying Formula 2, determined. At

the same time, the horizontal velocity of a proje ¢ ted object is always constant, and hence,

the horizontal component of initial velocity for the same may be simply given, by app!ying

Formula 3. Substituting above values into Formula 4, the initial aerial velocity of the center

ef gravity and its arrgle of take-off rnay be ealculated. Likewise, the velocity and incidented

angle, right before the kicking action for take-off is taken, would be calculated.

Elements of the initial velocity that the center of gravity obtained right after the take-off,

when mechanieal consideration is given, should be the combining result of elements of

center of gravity movement right before the take-off and that ef kicking force which the

body, particularly the !ower extremities, applies to the vaulting board. It is indeed an

example of vector. Applying vector analysis procedure, the amount of kick at the take-off

(though the unit being velocity) may be ealeulated, using Formula 5.

After finding the amount of kick at the take-off, amount of acceleration, or the quantity

of shock that the center of gravity receives may be calculated by Formula 6, provided the

time Iength of take-off is given. Taking the hody weight of the subject and the gravity

force inte account, when using Formula 7, the amount of force the center of gravity

}..

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JapaneseSociety ofPhysicalEducation

sc"e<4D

reeeives would also be ca!culated.

4. Results and Discussiens

4. 1. Analysis of Data

In this study, certain side-horse vaulting stunts in gymnastics were filmed for mechanical

analysis and the loci of body segments and those of ¢ enter of gravity were traced. In this

manner, general ¢ haracteristics of each stunt aad specific characteristics of each performance

may be clatified. Each frame of picture was darwn en sheets of paper, and these drawings,

when sequentially combined, provided body moves in the time course. Representing fifteen

sequentially combined pietures which were produced in this study, Figure 1 is presented,though in the figure, for qvoiding complexed drawings, onty drawings of every eight frames

are included. Heavy line in the figure represents the locus of center of gravity, which

appear to be consistent with mechanical principles.

The mechanical elements in each experimental performance, which were calculated from

the analysis of drawings, sequential drawings and loci of center of gravity along the time

mo e-

,--.

Fig. 1Sequential drawings

aooemM

of SV-4 with locus of eenter of gravity.

Fig. 2

A'=s.75mlsecA =7・41m!sec

Vector analysis of

moment of kicking

B' :3.19m!sec

B =8・24mlsec

force exerted by the center of gravity at theand hand-push in SV-4.

C'=7.15mfsec a'=30, 2' P'= 38. 40 r'= 7. 5'

C =4. 73mfsec a :93. 00 B=45. 00 r=ls.oe

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Page 7: HAND PUSH IN SELECTED SIDE HORSE VAULTING STUNTS

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Japanese  Sooiety  of  Physioal  Eduoation

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346(44)

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Hbtano : Skill Analysis of KVck nd Hdnd-Push Actions in Sttected Side-Hbrse vaulting St"nts 347(45)

course, are listed in Tables 1 and 2. While various vector elements involved in the kick

and hand-push in each performance are included in these Tables, such vector elements along

the loci of center of gravity were drawn on other sheets of paper. An examp!e of such

vector analysis is demonstrated in Figure 2,

The changes in joint angles at shoulder, hip and knee, ZS, .tH, ZK, respectively,

during the tirne course of performance, in which the extension position being marked as OO,

are demonstrated in Figure 3. Then, upon measuring the angle of the trunk with vertical

line in each drawing, the proce$s of body rotation was analyzed. In order to examine the

relationship between the angular ve!ocity of trunk, AV (degreelsec), and the body length

(maximurn distance between two furthest body segments), BL (cm), were compared also in

Figure 3.

115

9e

45:H,t,

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45

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±melen6thattertelce-eff(sec)-

kickingfirstprodectileband-push secendprodectileien

Fig. 3 Sequential changes in

and angular veloeity

O.2 O.5 O.4 O.S O,6 O.7 O.8 O,9 1.0

'

f

iendtns ,

jeints, body length (BL) l shoulder (.ttS), hip (.(H) and knee (IK) of trunk rotation (AV) {n the time course of SV-4 performanee. It

.-

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'll;-i'ilt

i'.tte.1・I

N"")

The analytical procedure in this study included 7oo drawings, 15 sequential drawings,and 4,OOO parametric deta. Upon e)tEmining given figures and tables and obtained data,fellowing discussions may be made.

4. 2. General Discussion en Vaulting

General principles governing vaulting event may be numerically described when one

carefully examines the Tables 1 and Z Speed of approaching running, for e)tample, varies

so widely that the fastest runner (HS5) with 8mlsec velocity, or equivalent to 135 secl

1oom dash speed, shows more than twice as fast asa noviee girl vaulter (SV-5), who

actually made a significant preceding jump before the take-off action (incidenta1 angle being46 degrees). The case of SV-5 being an exception, the incidental angle, ranging between

O and 25 degrees, did not show strong relationship with the skill itself, while greater speed

of approaching running seemed to produce better performance.

The angle of backward body leaning, recorded as the angle between the level and the

line connecting the center of gravity and the toes at the moment of kick, was found not to

be necessarily consistent within an individual in different attempts, while all the recordings

stayed within ± 9 degrees. The actual kicking time length appeared to be slightly longer

than .100 second in each case, and the involved acceleration ranging between 2G and 7G,

both values seem to be somewhat similar to the cases of somersault in tumbling and floorf:xercise events, as to compare with the previous reports by the present investigator3)D5).

The direction of kick varied between 78 -v 135 degrees (zero degree being straight forward

at the level, and 90 degree, exactly downward), though generally, prevalent tendency was

to kick slightly down-backward.

The amount of force exerted during the hand-push action within a tirne length of

slightly less than .200 seconds appear to be nearly half of that in kicking. The difference

in time length between kicking and hand-push and the differences in the velocities in

preceding body moves may be two major factors for this tendency. The hand-push was

gL・nerally directed to down-forward, (angle less than 90 degrees). Certainly in no cases it

was directed to down-backward in the squat vault. Only exception to this principle was the

front somersault vault (YV-1 and 2) which requires rather fast body rotation, using the

oppasite reaction of the hand-push.

As the kiek was directed forward, the amount of force involved in kieking inereases,

while this direction is not likely to be the only influential element on the seale of the first

projectile. When the velocity of preeeding run is larger and the kick is directed down-

backward, forward body rotation may well be provided and the projectile may become rather low

and forceful. In contrast, when the running speed is slovv and kick is directed down-forward,

forward rotation is provided and the projectile may become short and high. It seerns, no

single factor deterrnines the total performance, rather, each element probably interact each

other to produce the total perfermance. In other words, there is no definite ideal type ef

kick, projectile, hand-push, or landing, but rather, only inbalanced mechanical distribution

would cause a poor performance. Example of such poor perforrnances are seen in HS-2, 3

/

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Hlatano : Sh"l An`zlysis ef Kick atsd H7dnd-Ptash Actions i" Selected Stlde-Horse Vdalting Ststnts 349(47)

and 4 in which time lengths of hand-push were particularly long, resulting in extrernely

small amount of acceleration in hand-push and in poor post f!ight, or second projectile.

The initial flight angle ef the center of the gravity during the pre-flight ranged between

21.0 and 45.6 degrees and the initial velocity of the sarne, 5.4 and 11.6mlsec. The kinds of

vaulting stunt (whether rotatory er not) did not affect the scale of such parameters. The

center of gravity trajectory durlng the preceding run-kick-pre-flight, does not vary

according to the vaulting stunt, though in the case of leng-herse vault (in contrast to the

current method, side-horse vault), the result may be different. However, certain differences

were observed in the rotational movements of the trunk and the lower limbs between the

rotatory and non-rotatory stunts. For example, upon examining figures (not presented here

exeept SV-4 due to the limited availability of space) to show the process of trunk rotation

during the time course of each performance, it was neticed that in the non-rotatory vaults,

certain wiggling actions at the hips are taken during the post-flight in an attempt to recover

from the already-leant-front trunk before the landing.

The initial flight angle of the center of gravity during the post-flight ranged between

15.1 and 48.8 degrees and the initial velocity of the sarne, 3.2 and 9.8 mlsec. These values

are slightly smaller than the case of the pre-flight. In general, a sharp hand-push with

short time length of hand-placing resulted in large scaled post-flight, and hence, judged to

be a

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'

1

'

'y;k

350(48)

4. 4. Coaching Suggestions

Within the limitation of the experiment taken here in the present study, it seerns that

no single mechanical elements overwhelmingly rule the success of a performance, because

variety of elements interaet each other. However, ¢ ertain instructional and coaching

suggestions may be made from the diseussions presented above.

In general, it was understood that the kick and hand-push actions in each performance

may be contrelled in relation with the preceding run and body rotation. However, a powerful

preceding run may be the key for producing an effective kick. The last step of the prece-

ding run before the kicking should net be a jump with a large vertical element, but rather,

it should be of sliding type. A sharp kick, which may result in great kieking acceleration,

rnay well be advantageou$. for an effective pre-flight. The directien of kick should be

deterrnined according to the kind of vault (rotatory or not), L e., provided the center of gravity

trajectory being the same, kicking down-backward would produce more body rotation. When

provided that same body rotation is kept, kicking down-forward would produce greater height

in pre-flight trajectory of the center of gravity.

Regarding the angle of hand-push, down-forward hand-push seem to be necessary for

non-rotatory vaults, in contrast to slightly down-backward for rotatory vaults. A sharp hand-

push, which may result in great hand-push acceleration, rnay be advantageous for an effec-

tive post-flight.

Teachers and coaches, when instructing vaulting events, may utMze such suggestions as

rnentioned above, because any bodily performance has certain aspects for mechanical consi-

derations and the performers may be benefitted by such information.

5. Summsry

Certain side-horse vaulting stunts in gymnastics were mechanically analyzed to find

principles governing each stunt and to provide certain suggestions for skill improvement.

That no single mechanical elements overwhelmingly rure the success of a performance and

that the ideal performance may be sought after accumulating similar efforts were among

the findings.

Appendix ,

Formula 1.

In the free falling object, the following relationship exists betyveen the vertical distance of the

center of gravity movement, h, and the time length invotved, t;

t=vt kh while g=gravity force.

Formula 2.

Likewise, the relationship betyveen vertical element of velocity, Vs, and the vertical distance, h,

is;

Vs=V 2gh

FermDla 3. The horizontal element of the velocity in a projected object, V:, is always constant and is

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Hatano : SkiU Analysis of Kiah atid Hl ,uiLPash Aciions in Sttuted Sldle-Hbrse Vatdting St"nts 351(4g)

calculated from the horizental distance, D, divided by time length to move such dlstanceq t;

v..,D . t

Formula 4. '

The initial velocity, Ve, and its prejected angle, e, in the projected obicct are calcu!ated as

follews; ve=lt!-Vtwtv, .

ll tane

='vx

FOrlnUloard5ir

to obtain B-t and p in i ABD, whereas Arii/, AD, a and e are known, the follovving

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,,,

asKsd)

Porinlls T. '

The ameunt of force, F, an object receives an acceleration equals to the mass (m=ll I, whereas

W stands for weight and m, mass) multiplied by accelration.

F=mt= W x a g '

Selected References

l ) Bunn, fohn W. ScientMc Princlptee of Coschinx, Prentice-Hall, lgso.

2) Cureton, Thomas K., "Elementary Principles and Technigues ef Cinematqgraphical As!ysis as

Aids ln Athletie Research," lo:3-24, May, Resesrch quarterly, lo: 3-24, May, lg3g.

3) Hatane, Yoshiro, "The

Cinematographie Analysis of Standing Baek Somersault;' Unpublished

paper, University of Oregon, l964. '

4 ) ,

"The Mechanics of the Double ;Beck-Somersault;' Mester's thesis, IMichigan State

University, 1961・

s) - "Mechanical

Analysis of Tumbling Stunts in Gymnastics," Bulletin of Tokyo

Gakugei University. Mst\ttX\re-, 22-5: 222-37, 1971 (in Japanese language).

6) -

Osamu Kado and Ryuji Takagi, "Cinematographical Analysls af Tennis Ball Re-

bound at Various Artificial Tennis Court"' Jonrnst ot Heslth, Phrsical Education and Recrea-

tion, "fi(DptS!, 25-4: 256-6q April, tg7s (in Japanese language).

7) McCloy, Charles H., `CThe

Application of Mechanical Principles to the Teaehing of Sports and

Athletics," Unpublished paper, State University of Iowa, 1950.

s) - `tSome

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