Computer Simulation of Splash Control and Research of the Rip Entry Technique in Competitive Diving

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1 ISSN (print) Intrnational Journal of Sports Scinc and Enginring ol. 4 (1) No. 3, pp Computr Simulation of Splash Control and Rsarch of th Rip Entry Tchniqu in Comptitiv Diving JingGuang Qian 1, Songning Zhang, Haiquan Jin 3 1 Naning Institut of Physical Education,Naning, China Th Univrsity of Tnnss, Knoxvill, USA 3 Jiangsu Provincial Diving Tam, Naning, China (Rcivd January 8, 1, accptd March 1, 1) Abstract. Th purpos of this study was to xamin ffcts of diffrnt hand pattrns usd by divrs on th minimization of splash at th instanc of watr ntry for comptitiv diving. An impact modl was dvlopd with th human body modld as a wdgd solid obct and th watr as an idal fluid. Th quations of motion for th solid obct wr stablishd with satisfactions of control functions and initial boundary conditions of th fluid. A finit lmnt mthod was usd to simulat th impact procss in customizd computational softwar. Th rsults indicatd a proportional rlationship btwn th highst point of th unrstraind wav surfac and th wdg angl during th impact. Th simulation rsults indicatd a squard obct as th idal shap for th watr ntry. In practic, instad of having palms facing ach othr to form a wdg at th watr ntry, th divr should intrnally rotat th arms and form a flat impact surfac with th palms towards th watr to ffctivly limit th watr splash. Furthr mchanical analyss also suggstd that, th palms should b maintaind in a dirction ust opposit to th rsultant vlocity of th watr in a massaging motion during th impact in ordr to ffctivly control th splash. Kywords: Diving, Finit Elmnt, Computr Simulation, Splashlss Entry, Rip Entry 1. Introduction A rip ntry is a ky lmnt for watr ntry in comptitiv diving. Th siz of watr splash may dirctly influnc th outcom of a diving comptition. Thrfor, it has bcom a focal point of both practical and thortical intrsts as to how to minimiz th splash siz by using various body positions and ntry tchniqus during th ntry from th initial impact to th total submrg of th ntir body undr watr. Th splash control tchniqu has bn around for a whil. At th bginning, most divrs manipulat thir limbs to form a sharp shapd form for th ntranc. If th ntry starts from th hands, both palms ar usually placd facing ach othr with straight arms so that th body forms a wdg that has a sharp part and a blunt part. If th ntry starts with th ft, th ft ar fully plantarflxd with th tos ntring watr first. Such a body formation minimizs impact forcs at th ntry but usually causs a significant amount of splash. It was latr accidntally discovrd that a mor dorsiflxd ankl position at th watr ntry actually causd lss watr splash (Rackham, 1975). Hnc, divrs and coachs startd to xprimnt foot ntry tchniqu with mor dorsiflxion and hand ntry with hyprxtndd wrist (Rackham, 1975). It has gradually volvd into th currnt rip ntry tchniqu that rquirs a flat ntry surfac formd by ovrlappd hands with fully flxd and intrnally rotatd shouldr oints. Through trials and rrors, coachs and divrs hav alrady accumulatd som practical xprincs and mthods for th splash control tchniqu. Howvr, no brakthrough rsarch has bn prformd on th thortical basis of th tchniqu; many aspcts of th tchniqu such as mchanisms of splash formation and optimization of splash control tchniqu dsrv furthr invstigation (Brown, t al., 1984). Body watr ntry and splash formation ar rathr complicatd phnomnon of impacts and intractions btwn a solid body and fluid. Impact btwn fluids and solids is a hot rsarch topic; rlativly ffctiv mthods analyzing th impact hav bn proposd ovr th yars with som simplification procss. Among thm, mor influntial mthods includ th thory of similarity flow by Macki (Macki, 1969) and Dobrovol'skaya (Dobrovol'skaya, 1969), mthod of matching and gradually dvloping by Armand (Armand and Coint, 1986) and Coint (Coint, 1989), and spcially th Laplac transformation adoptd by Publishd by World Acadmic Prss, World Acadmic Union

2 166 JingGuang Qian, t al: Computr Simulation of Splash Control and Rsarch Gavrilnko and Kubnko with applications in impact btwn rigid body and fluid during ntry of a squard rigid body (Gavrilnko and Kubnko, 1985), an oval obct (Gavrilnko, 1986), a symmtrical obct (Kubnko and Gavrilnko, 1987) and, lastic sphrical shll (Gavrilnko, 1989). In addition, numrical mthods for th impact phnomnon hav sn som furthr improvmnts in th 9-nod isoparamtric rctangular lmnt (Maral, 1978) and nonlinar boundary lmnt mthod (Zhao and Faltinsn, 1993). All ths rsarch rsults hav providd foundations for studying impact btwn human body and watr. As to th splash formation during diving, many factors may influnc th final outcom. Howvr, th formation procss can b dividd into thr diffrnt stags: 1) th procss of initial impact btwn th human body and watr; ) th procss from th initial body watr ntry till th complt submrgnc of th divr; 3) th procss of turbulnt flow formation aftr th complt ntry. Thrfor, th purpos of this study was focusd on xamining rlationship btwn hand pattrns and splash hights during th initial impact stag of non-rotating diving using a finit-lmnt modl.. Matrials and Mthods In ordr to study th rlationship btwn hand pattrns and watr splash hights, following simplifications wr mad during modling and computr simulation. Th watr was tratd as an idal fluid (incomprssibl and non-viscous) and th human body as a wdg-shapd solid obct (Figur 1). A physical and mathmatical modl of th wdgd solid obct and th idal fluid during th impact was first stablishd. Th quations of motion (intraction quations btwn fluid and solid) for th solid obct wr stablishd, which satisfid control functions and initial boundary conditions of th fluid. Computational softwar was dvlopd using a finit lmnt mthod to simulat th impact procss of th wdgd obct with th fluid with th wdg angl changd from 4 to 8. Simulations and Computation of Impact Procss with Watr. Th human body was simplifid as a wdgdshapd solid obct and th watr ntry of th divr during th impact was tratd as th impact btwn th wdgd obct and th watr. According to th consrvation of mass and nrgy, principl of momntum, and th principl of fluid viscosity, quations of continuity, quations of motion (momntum quations), nrgy and constitutiv quations can b drivd. Ths quations, stat quations, and basic quation sts of fluid dynamics ar formulatd in th following forms of diffrntial quations: R 1 Figur 1. Initial stag prior to th impact btwn th wdg and fluid. p div( ) t d F divp dt du P S div( kgrad ( T )) q (1) dt 1 P pi ( S Idiv ) ' Idiv 3 p f (, T ) Whr ρ is th watr dnsity, th vlocity vctor of th fluid fild, F th body forc applid to th watr, P a strss tnsor of th fluid fild, p th prssur of th fluid fild, T th watr tmpratur, I th unit tnsor, U intrnal nrgy of watr, S th vlocity tnsor du to dformation in th fluid fild, k th cofficint of watr hat conduction, q th hat radiation cofficint, μ th first cofficint of watr viscosity, μ th scond cofficint of watr viscosity, and div divrgnc. With rspct to th idal and incomprssibl fluid of a non-rotating motion, th fluid motion should satisfy th control quation: Z H r SSci mail for contribution: ditor@ssci.org.uk

3 Intrnational Journal of Sports Scinc and Enginring, 4 (1) 3, pp t p gz Th abov quation is formd by a scond-ordr linar partial diffrntial quation and a potntial function, and can b usd to dtrmin unknown φ (potntial) and p (prssur). Bcaus of its symmtrical physical natur of th wdgd solid, th original thr-dimnsional problm can b rducd to a two-dimnsional planar problm by using a cylindrical coordinat systm and th computation procss can b thrfor gratly simplifid. Th opposit dirction of motion for th wdg rprsnts z-axis and th lft horizontal th r-axis (Figur 1). Th origin of th coordinat systm is st at th intrsction point btwn th z-axis and th bottom of th pool; th quation () bcoms th following undr th cylindrical coordinat systm: f (t) 1 r z r r (3) p gz f (t) t Whr φ and p ar functions of r, z and t. Th quation abov has an infinit numbr of solutions. Howvr, only thos solutions satisfying boundary and initial conditions ar maningful. Thrfor, th quation (3) must b solvd undr crtain initial and boundary conditions. Initial Conditions. During th watr ntry of th wdgd obct, th focus of discussions in this papr is on th first stag (t = ) and scond stag (t > ) whr th first stag is th initial condition of Z th ntir impact procss (Figur 1). Mor spcifically, th stats associatd with th wdg and watr in th initial stag ar th initial L conditions at t =. = ( r R, z H,) z=f (r) p = gz ( r R, z H) whr φ is th vlocity potntial function of th fluid fild, P th function of prssur in th fluid fild, ρ th watr dnsity, and g th gravitational acclration. Boundary Conditions. Th scond stag of th solid and fluid intraction, th impact stag (t > ), is th main intrst of this study (Figur ). Th fr surfac of th watr xprincs dramatic changs during th impact btwn th wdg and watr, and th ntry of th solid into watr in this stag of th procss. Th watr boundary conditions must b known in ordr to dtrmin th stat of th fr watr surfac in th computation procss L 4 β β Figur. Impact stag btwn th wdg and fluid z () r SSci mail for subscription: publishing@wau.org.uk

4 168 JingGuang Qian, t al: Computr Simulation of Splash Control and Rsarch v r r p P v n vl cos( ) n L cos prdr MG v r r v z z Ma = 1 for pool sid = for fluid surfac = 3 for intrfac btwn wdg and fluid (4) = 4 for vrtical cross-sctional ara = 5 for pool bottom During th impact of th solid and fluid, th boundary conditions ar formd by th intrfac surfac btwn th solid and fluid, and th fluid surfac. Th boundary conditions of th fluid surfac ar ssntial boundary conditions whil th natural boundary conditions includ th intrfac of th fluid with th impact solid, and th sids and bottom of th pool. According to th quation of motion for th wdgd solid and th charactristics that a non-adhsiv fluid has a zro vlocity along th normal dirction of th wdg wall, th fluid boundary conditions can b xprssd as: whr β is th obliqu angl of th wdg wall (Figur ), L th half lngth of th intrfac of th wdg and fluid, φ th vlocity potntial function of th fluid fild, v t th instantanous vrtical vlocity of th solid, and g th gravitational acclration. Solution of vlocity potntial of idal fluid using finit diffrnc mthod. It is assumd that th approximat function (Li and Yuan, 1987; Zhang, 1986) in lmnt of th vlocity potntial function φ (r, z, t) has this form: i ( t) i (5) i Whr is an intrpolation function of th slctd vlocity potntial, I = 1,,,, th dfinit function of vlocity in th lmnt, φi(t) th valu of th vlocity potntial function at th tim t and th knot i. By slcting th intrpolating function of th vlocity potntial as a wightd function and stablishing control functions of Galrkin intgration (Wang and Shao, 1997), th strong form of intgration of th vlocity potntial is found with considration of th natural boundary conditions. In addition, th quation of motion (4) for th wdgd obct is combind into th quation (5). By stting in th quation for th lmnt and through propr simplification, th following finit-lmnt systm quations for th lmnt ar drivd: [ k ] ( t) [ k ] (6) Whr [ k ] [ k i F ] ( r i r i [( ) r ( v cos ) i i i i i 1 i ) d z r r i i d d r z 4 ( z d i F ) ] d 5 d Whr i = 1,, 8 and = 1,, 8. By using a diffrnc mthod, a discrt solution is sought as a function of tim in quation (6) and th N i N i SSci mail for contribution: ditor@ssci.org.uk

5 Intrnational Journal of Sports Scinc and Enginring, 4 (1) 3, pp unstady motion is convrtd into a stady motion within th unit tim. Thn a gnral matrix of th finit lmnt functions is drivd through assmbly of an ntir matrix of stiffnss: [ K ] { } { F} (7) NN This is a st of N th -ordr linar quations. By solving this st of linar quations within th boundary conditions, th vlocity potntial for th ntir fluid fild at th tim of L+1 [ ( r, z, l 1) ] and vlocitis of r and z within all knots across th fluid fild can b found. Thrfor th prssur p can b solvd for vry knot. For th unrstraind surfac of th fluid during th impact procss, its shap is solvd using an itration mthod (Zhu, 1986). Assuming th unrstraind surfac as z = f(r) with th flow shapd as proctil motion in gnral and th flow closst to th wdg as a straight lin, th prssur P (n) can b approximatd by vrifying th boundary conditions of th unrstraind surfac. Th rror prssur btwn th approximatd prssur and th actual prssur for th unrstraind surfac is givn as: P P P ; th watr splash hight can b thn computd as: N N P P h H (8) P Whn th itration rror h is within a prdtrmind rang (ε < 1-4 ), it is considrd a succssful solution. Othrwis, propr corrctions ar mad to th unrstraind surfac functions. Onc h is solvd, th shap of th unrstraind surfac is dtrmind. Through rpatd itrations, th unrstraind fluid surfac shap at vry instant during th ntir impact procss is obtaind. Du to th importanc of splash hight in udging a div during comptition, h was chosn as th outcom masur of th modl. Th watr splash hight was simulatd during th impact at svn diffrnt obliqu angls: β = 4, 1,, 3, 45, 6, and 8. Th splash hight during th impact was xprssd as a prcnt of th maximum hight obtaind for th obliqu wdg angl at 8 during th simulation. In addition, a -dimnsional isoparamtric 4-nods lmnt with an arbitrary boundary shap was usd in th study. On additional nod was intrpolatd on ach sid rsulting an 8-nods isoparamtric lmnt to rprsnt th curvd fluid surfac. Whn finit lmnt msh is dividd, a gratr amount of lmnts was usd in th aras clos to th impact sit with smallr distanc btwn th adacnt nods whras a smallr amount of nods was usd in th aras furthr away towards th walls and bottom of th pool. With this approach, th splash hight was ffctivly computd and th computation dmand was gratly rducd. 3. Rsults Th simulatd splash hight during th impact for ach of th svn wdg angls was prsntd in Tabl 1. Th rsults indicatd that th highst point of th unrstraind wav surfac aftr th impact incrasd with an incras in th wdg angl (slop). Th gratst (sharpst) wdg angl licitd th highst watr splash during th impact. Th diffrnc in th splash hight btwn th wdg angls of 8 and 4 was almost tims. In addition, a sparat simulation was run for two wdgd obcts of 3 and 6 kg. Th rsult suggstd that th gratr body mass and impact forc incrasd th splash at th sam obliqu angl. Prcnt Splash Hight 4. Discussion Tabl 1. Prcnt splash hights from diffrnt obliqu angls. Obliqu Angl 4º 1º º 3º 45º 6º 8º 5.% 1.5% 5.% 31.3% 5.% 6.5% 1% During comptition, th succss of a div is partially udgd by th succss of th rip ntry and its splash hight. Th lowr th splash hight, th highr th scor for th tchnical componnt associatd with th splash control. During impact btwn a solid and fluid, a part of impact nrgy is transfrrd to th fluid, which crats a motion of th fluid and formation of splash. Howvr, th splash formation is also rlatd to many othr factors. SSci mail for subscription: publishing@wau.org.uk

6 17 JingGuang Qian, t al: Computr Simulation of Splash Control and Rsarch First of all th splash formation is rlatd to fluid charactristics. Watr as a spcial form of fluid has following uniqu faturs. (1) Incomprssibility: comprssibility of its volum is rathr small; undr th forc application, it can b only displacd but not comprssd. () Minut adhsivnss: du to this charactristic, watr motion displays non-uniformity undr a forc application; parts of watr may mov in dirctions othr than th dirction of th forc. (3) Undr comprssion, watr tnds to mov in a dirction whras last prssur is prsnt (so calld th most scapabl dirction). According ths charactristics, motion charactristics of watr during impact can b analyzd. Th splash is also rlatd to th shap of th impact obct. Whn th wdgd obct impacts th watr with its sharp dg, watr is comprssd diagonally downward. Th dirction of th forc is prpndicular to th inclind surfac (Figur 3). Th watr closst to th wdg movs in th dirction of th forc application undr th comprssion. Du to raction forcs from th surrounding watr, its intndd motion is rstraind and forcd to mov upwards along th wall of th sharp wdg, i.. in th most scapabl dirction. Th first layr of watr undr th comprssion will scap in th dirction first. As th wdg continus to pntrat into watr, th fluid at th top has alrady scapd along th wall; its location bcoms th most scapabl dirction for th watr blow. Thrfor, th undrlind watr continus to scap along this dirction and forms th watr splash. Gratr is th impact, highr th spd and thus th splash. F Figur 3. Impact btwn th wdgd obct and watr F Figur 4. Impact btwn th squard obct and watr. Evn though th watr scaps upwards along th slop of th wdg surfacs undr prssur and forms th watr splash, th splash hight is rlatd to th obliqu angl of th wdg wall, which is also th proction angl of th splash. Th splash hight incrass with incrasd proction angl whn th scap vlocity is hld constant. This was also vrifid in our computr simulation. Whn th pntrating obct is not wdg-shapd but rctangl-shapd, th rsults of th impact ar diffrnt. Aftr th obct submrgs into watr, th prssur is applid vrtically downward. Th watr, undr such prssur, disprss circumfrntially. It dos not form a most scapabl dirction du to th raction forcs from th surrounding watr. Undr such raction forcs (prssur) parts of watr may mov upwards along th vrtical wall of th obct (Figur 4). At th sam tim, howvr, th impacting obct is moving downwards bringing its surrounding watr with it bcaus of its high impact vlocity. Whn such a vlocity is gratr than that of th watr vlocity travling upwards along th wall, no apparnt watr splash is formd. Thrfor, instad of having palms facing ach othr to form a wdg at th watr ntry, th divr can intrnally rotat th arms and form th impact surfac with th palms facing towards th watr to ffctivly limit th watr splash. In practic, a comptitiv divr not only prforms simpl vrtical movmnts but also high-spd rotations and somrsaults. Whn an obct impacts watr with high-spd rotation and somrsault, its vlocity s dirction is not purly downward and is actually dtrmind by th translational ( v ) and rotational (ω) vlocitis of th obct with th rsultant vlocity () dircting diagonally downward at th tim of impact (Figur 5). If th divr wr to impact th watr with th flat palms aftr th initial ntry, th squard obct would mov towards on of th connrs. Th watr would scap along th surfac of th palms and th sids of th arms rsulting in th similar wdg ffct; th divr would fail to contain th splash. At this tim, th divr should chang th dirction of th palms as it dscnds in th watr, so that th palms could b always b dirctd 9º angl to th on-coming watr flow (Figur 6a & 6b). Onc th divr contacts th watr, th rsistanc from th watr can crat a rsistiv torqu that has a dirction ust opposit to th angular motion of th body, caus a dramatic dcras of its angular vlocity quickly(ω), and produc a vrtically downward rsultant vlocity of th body (Figur 6c).. At this tim, th palms should b turnd SSci mail for contribution: ditor@ssci.org.uk

7 Intrnational Journal of Sports Scinc and Enginring, 4 (1) 3, pp downwards from its prvious diagonally downward dirction to rmain opposit to th rsultant vlocity of th watr In a forward somrsault, th divr should push downward with th bas of palms and th littl fingr s sid, and kp th palm facing antriorly downward at th watr ntry. In a backward somrsault, th divr should push downward with th sid of th thumbs and kp th palms facing postriorly downward instad. Onc th divr contacts th watr, th raction forc from th watr instantly crats a rsistiv torqu that is applid in a dirction ust opposit to th body rotation, and dramatically rducs th spd of th body s rotation. At this tim, it is critical to push with th palms in th opposit dirction to kp th palms prpndicular to th dirction of th watr spd as discussd prviously in ordr to rotat th palms towards a vrtically downward v dirction in a massaging motion. In ordr to ffctivly control th splash, th divr not only flxs and intrnally rotats th shouldr oints and pushs th palms outwards to maintain th squard shap for watr Figur 5. Impact btwn th ntry, but also massags th watr succssfully. Th dirction, th squard obct with high rotating rang of motion, and th magnitud of th massag motion ar rlatd spd and watr. to th dirction of body rotation and spd at th instanc of th watr ntry, th position of th cntr of gravity of th body bfor th div, and th body wight of th divr. 5. Training study Aftr obtaining th simulatd and thortical rsults, twlv divrs from th Jianshu profssional diving tam wr rcruitd as subcts in a training study during a - month training priod. Th training mphasizd squard rip ntry concpt, and implmntd a tchniqu that rquird th divrs to hav tight body, straight body lin, rigid wrist and hand, straight shouldr angl, and prompt watr massaging, and a dscnt into watr as dp as possibl. v (a) v (b) Figur 6. Wrist s motion to kp th palm prpndicular to th watr s rsultant vlocity. In a platform diving vnts that hav high dscnding vlocity, it is asir to contain th splash than a springboard vnt with propr control. Both ffctivnss and quality of th rip ntry ar actually bttr in platform vnts, mainly du to its gratr dscnding hight and longr tim so that th athlt has nough prparation for watr ntry. According to our prvious thortical analysis, th dscnding body with high vlocity causs th watr flow closst to th body to mov downward. Whn this movmnt vlocity is gratr than th upward scaping vlocity of watr du to raction to th downward comprssion, no apparnt splash will occur. In addition, th vrtical dscnding vlocity of th palm is far gratr than th horizontal vlocity du to th rotation of th body at th tim of ntry; th rang of ncssary massaging motion is smallr. Thus th rip ntry tchniqu for a platform vnt is simplr. With sufficint strngth in th wrist, lbow and shouldr oints and capabl to maintaining a rigid and straight body postur, a platform divr can obtain smallr splash and crispr ntry sound to provid good imprssion to udgs and audinc. If th divr dos not hav nough strngth and cannot maintain a squard rigid body postur, any giving in a body oint would rsult a significant amount of watr splash. Furthrmor, high impact forcs ar usually xprincd using a flat hand pattrn and may caus an inury with any such giving (l it, t al., 1993). Thrfor, w dvotd a larg amount of training on tchniqus with mphass placd on th rip ntry tchniqu so that th participating divrs could mastr th skill. Spcific strngth training was also introducd with aims to prvnt inuris. v (c) SSci mail for subscription: publishing@wau.org.uk

8 17 JingGuang Qian, t al: Computr Simulation of Splash Control and Rsarch Th training of watr massaging tchniqu is paid spcially attntion for th ntry action with high vlocity of forward or backward somrsault so that to maintain th hand is vrtical to th dirction of sum of vlocity. Diffrnt standards ar proposd in th practic of training for th dfrnt lvl of diving athlts. Th training for thos xprimntal athlts is mphasizd on xplaining th mchanism and principal of th rip ntry tchniqus and th movmnt practic to improv thir prciving and capability on th rip ntry tchniqus. Ths xprimntal athlts usually hav bn traind for a long tim and hav som of xprimnts on th ntry tchniqus, howvr thy ar not so clar in th dtails of th movmnt so that thy oftn faild to complt th movmnt sinc thir prciving on th rip ntry tchniqus is passiv. Th training for thos young divrs is mphasizd on som assistant practic to lt thm prciv watr massaging tchniqu on th basis of undrstanding th tchniqu of flat hand pattrn. Th training priod for th rip ntry tchniqus can b shortd in this way. Undr th guidanc of th thortical and practical xprimntal rsults, th participating divrs all mastrd th rip ntry tchniqus with a combination of th squard obct ntry and massaging. In past training practic, it usd to tak long-trm and rpatd practic for athlts to passivly prciv and mastr th tchniqu. With th undrstanding of th mchanisms of splash control, th divrs wr mor activly involvd in th training procss and w wr abl to improv th training fficincy and lvls. Th succss rat of th rip ntry of two of th bst divrs of th group rachd abov 8% in practic. Xu Hao rcivd gold mdals in th doubl vnt in th Asian, and Yang Lan arnd th gold mdals in th doubl vnt of th Chins National Diving Championship. 6. Conclusion Th simulation rsults indicatd that th slop of th wdg was invrsly proportional to th impact magnitud and th dclin of th body vlocity, but proportional to th splash hight. Th splash hight changs by a factor of narly tims btwn 8 and 4 wdg angls. () Th splash hight is also closly rlatd to th hand pattrn usd in diving at th tim of impact. Using a tchniqu with an intrnally rotatd and fully flxd (straight) shouldr oint and both hands forming a squard surfac, a divr can ffctivly rduc th splash but incras th risk of inury. (3) It is imprativ to massag th watr aftr th initial ntry to maintain th palms opposit to th dirction of th watr vlocity to ffctivly minimiz th splash according to th dirction and spd of th body rotation. (4) Th rip ntry tchniqus with a combination of th squard obct ntry and massaging is mphasizd in th training for divrs, th training priod for th rip ntry tchniqus can b shortd and th succss rat can b improvd in this way. Th limitations of th study ar mainly associatd with ncssary simplifications of th impact procss btwn th wdg and watr. Th human body is modld as a wdgd obct, watr is tratd as idal fluid, and th splash hight is stimatd with a finit lmnt mthod. Du to ths simplifications, th simulatd rsults can crtainly dviat from a ralistic situation and cannot yild prcis outputs. Thrfor, much of discussion was basd on qualitativ obsrvations. Furthr studis ar warrantd to improv th modl and simulation tchniqu to achiv mor prcis quantification of th outcom. 7. Rfrncs [1] Armand, J. L. and R. Coint. Hydrodynamic impact of a cylindr. In: Offshor Mchanics and Arctic Enginring Symposium. Tokyo, Japan. 1986, pp [] Brown, J. G., L. D. Abraham and J. J. Brtin. Dscriptiv analysis of th rip ntry in comptitiv diving. Rsarch Quartrly for Exrcis and Sport. 1984, 55: [3] Coint, R. Two-dimnsional watr-solid impact. Journal of Offshor Mchanics and Arctic Enginring. 1989, 111: [4] Dobrovol' skaya, Z. N. On som problms of similarity flow of fluid with a fr surfac. Journal of Fluid Mchanics. 1969, 36: [5] Gavrilnko,... Transint loading as an llipsoid of rvolution pntrats a fluid. Sovit Applid Mchanics. 1986, : [6] Gavrilnko,.. Dtrmination of th strss-strain stat of thin lastic sphrical shlls pntrating into a comprssibl fluid. Sovit Applid Mchanics. 1989, 4: SSci mail for contribution: ditor@ssci.org.uk

9 Intrnational Journal of Sports Scinc and Enginring, 4 (1) 3, pp [7] Gavrilnko,.. and. D. Kubnko. Plan problm of rigid body pntration into a comprssibl fluid. Sovit Applid Mchanics. 1985, 1: [8] Kubnko,. D. and.. Gavrilnko, Axisymmtric problm of th pntration of rigid bodis into a comprssibl fluid. Sovit Applid Mchanics. 1987, 3: [9] Li, D. and G. Yuan. Th numrical mthod for two dimnsional unstabl fluid motion. Biing: Scinc Prss, [1] Macki, A. G. Th watr ntry problm. Quartrly Journal of Mchanics and Mathmatics. 1969, : [11] Maral, P.. Hydrodynamic impact analysis. (EPRI NP-84, Rsarch Proct 81-3). California: Elctric Powr Rsarch Institut, [1] Rackham, G. Entry Tchniqus. In: G. Rackham (Eds.). Diving complt. London: Fabr and Fabr LTD. 1975, pp [13] Wang, C. and M. Shao. Fundamntal principls and numrical solutions in finit lmnt mthods. Biing: TsingHua Univrsity Prss, [14] Zhang, B. Finit lmnt mthods in fluid mchanics. Biing: Mchanics and Industry Prss, [15] Zhao, R. and O. Faltinsn. Watr ntry of two-dimnsional bodis. Journal of Fluid Mchanics. 1993, 46: [16] Zhu, J. Computational fluid mchanics. Biing: Scinc Prss, SSci mail for subscription: publishing@wau.org.uk