ABLE OF CONTENTSIntroduction Brief description of the projectProject Identification and Definition31 CFD Seam Simulation4 EquiRules for Tenackets41 Qualities of modern tennis rackets5 Kinematical analysis of the Tennis game6 Bio-mech22349257 Theoretical grounds of alternative phase mod2 Collision of mechanical objects3 Loading the tennis rackpment data278
1 Collecting information8 2 Experimental data for the bending of the body of the tennis racket9 Grounds for setting up the principle concept andement9 1 Analysis of the racket-ball dynamic interaction system92 Calculations of the striking strength when the ball hits the string93 Calculating the travelling speeds of the two colliding solid bodiracket and ball9 4 The maximum ball speed when hitting the racket and the bouncing95 Load analysis for the head and body of the racket and eventualcollations and deformationoading the frame and body by the horizontally acting forceDeformation estimations9 7 Determining the forces in the handleReference list
1 Introduction Brief description of the projectn some ways tennis has become a truly high tech sport Advances in racketdesign and compositioe changed the speed of thewooden frames, and made the game easier and more enjoyable at the recreationallevision coveragetches makes use oflysis toexplain the outcome of matches in terms of winners, errors, serving percentages andball placement Players study the statistical tendencies of opponents in an effort to getut at the most basic level of understanding there is no clear picture of whathappens to the tennis ball during therse of a teh
The radial velocity of the serves, but beyond that very little is really known about whathe game New types of strikes rescomplicated rotationcreasing service speed of ball shootingmaximum upper rotationSlice resulting in simultaneous bottom and side rotationIckets nowadaysto be constantly re-developed Design andanuracturing proe most essentiacan have, are subjected to aerodynamical change This book seeks to study tennisrom a new perspective - the perspective of design aerodynamics, setting outdetermine what we can learn about the flight of the tennis ball When the ball hits theacket during play, some dynamic stresses and deformations occith the loadhis results in oscillations (vibrations) in the racket andditions the phenomenon "resesonance conditions exist the periodically changing stress might lead to damagesthe racket caused by gradually forming cracks in the material2 Project dentification and Definitionhe wider popularity of tennis as a sport game on a world-wide scale, the
reasing quality of the play of both professional and amateur players has setgrounds for expanding the production of aids and accessories, such as tennis racketss gamehere is a wide variety of tennis rackets presently available on the market andthese could be basically assessed on the basis of the following characteristicsof material used for manufactureSize altensions of racket head2345 String t6 Degree of damping and vibrationshe first 5 characteristics are quantitative and could easily be determined andhe sixth characteristibrationesistance, is the appealing element The value of these vibrations is important andhard to determine with formulas due to the complexity of the friction process, thefriction and the air resistance losses [2]3 Equipment Rules for Tennis Ballsennis ball data such as the balls size the bell as other dIstinguishing shaperoughly a 635-mm(2
5-inch)sphiform outesurace a cois hourglass shaped seam and a felt-like fuzz The ball has to bewhite or yellow in colour It has to be more than 567-grams(two ounces)and lesshan 585-grams( two and one-sixteenth ounces)in weight The average professiorennIshe ball at 120kmph and the spin of the ball during a serve canreach around 1000 rpm [2he seam of the ball is a very important issue to deal with Internationalequipment regulations dictate for the minimum seams to appear in the surface of athermore these should be stitchless the seam makes the surface of thetennis-ball very porous and non-uniform3 1 CFD Seam SimulationMy interest on the seam feature and its consequences led me to start simulating
he tennis-ball Computers are used extensively throughout aeronautics to aid in thedesign and analysis of aircraft, watercraft, and even sports equipment Scientists haveed mathematical models, which emulate the physics of fluidsmathematical fluid models are programmed into software applications, which can bused onAn engineer can take an object, like an aeroplane or ball, and use the fluid modelto analyse how this object wororm in flight It is like having a virtual windtunnel Therefor this type field of work It's called"ComputatioDynamics"or "CFD"for short
We decided not to include the whole simulationprocedure step by step in this section We would like though, to feature some of theset up madeigures 1 and 2 above show two different cases Comparing them, we could finddifferences in the ball's speed and spinEquipment Rules for Tennis RacketsRackets faiot approvedder the ruleslected to a frame and alternately interlaced or bonded where theycross I ne stringing pattern sand in particular notle centre than in any other area the strings shall be free of attached objects anddand tear or vibration and which are reasonable in size and placement for suchessional play the frame of the racket shall not exceed 7366-cm( 29chesoverall length, including the handle, as from 1st January 1997 For non-
professional play, the frame of the racket shall not exceed 7366-cm(29 inches)anuary 2000,the maximum length of a racket for non-professional play shall be 8128-cm(32cket shall not exceed 3175-cm(12 1/2 inches)in ovewidth The strung surface shall not exceed 3937-cm 15 1/2 inches in overall lengthhe frame, including the handle, shall be free of attached objects and devicesother than those utilized solely and specifically to limit or prevent wear and tear olvibration, or to distribute weight
Any objects and devisesThee handle, and the strings, shall be free of any device,which makes it possible to change materially the shape of the racket Or to change theweight distribution in the direction of the longitudinal axis of the racket, which wouldalter the swing moment of inertia, during the playing of a point41 Qualities of modern tennis racketsamiliar with the basrformance characteristics of modern tennisackets contributes to the most suitable choice of a racket for both the beginner andthe professionalidering his individual nature(physical chskills, manner of playing, etc ) and the requirementshe competition (courthardness, ball brand,
etc ) This knowledge alsomaximum of a given racketmaximum capabilities out of a racket"[6] To achieve this leading players even ordthe basic modelof the manner and skills of the player The striking technique for a wooden racketvery much different to that of a racket made of modern compositterials Everyevolutionary change to the rackets results in modifications in striking techniquesModern rackets are manufactured and tested mainly to provide the followingbasic mechanical and dynamic customer performance characteristicsRacket Lengtis is the distance from the tip of the racket to the end of the handle a commonthe racket to provide more powerful strike anddynamic inertia To preventd increase of racket lengths ITF approved adocument at its congress in Lozane in 1997 according to which professional playerscan use rackets of maximum 29S Long body rackets are made of 28, 285 and29length [6directly proportional to the length weight, dynamic inertia and powernversely proportionady rigidity, manageability and controlhis is theof the string flred on the inside of theis measured in square centimetres or square inches Various companies offer racketsof 500 to 750 sqfor this parameterhis charactedirectly proportional to the length dynamic inertia, power and controhe rigidity of the string area flat, body rigidity andmanageabilityhis is the distribution of the static weight of the racket along its entire length
It isan indication of the distance measured from the low end of the handle to the crosswhere the racket would stand horizontally if we supported it at this cross point Highervalued weight on the head onfor the weight on thhandle and lower values indicate the opposite balance of weight The lightest racketheads for adults have a balance figure of 300 and the heaviest heads have a balanceof380-mm[6]directly proportional to the length, weight, dynamic inertia and poweiversely proportional to manageability and controlhis is the static weight of the racket measured in grams Kids rackets are theeight starts from 200ofessional rackets are the heaviest Thep to 367-370 gr [7 Profesattachdditional weights to the head of the racket to change its balance and add to theweight of the racket
his parameter isinversely proportional to manageability and conhis is the number and positioning of the string knit openings in the body of thedensity and structurea According toumber of knit openings modern rackets usually have between 16 and 20 longitudinalstrings and 18 to 22 transverse strings though there are some exceptions Accordinghe positioning of the string openings some rackets feature uniformther nonuniform and denser in the striking zone(centre) string area [7]directly proportional to the rigidity of the string area, the dynamic inertia andcontinversely proportional to tensioning and powerensioninghis is the tension applied to the string when knit
Tensioning is usuallyperformed within 18 to 35 kg Tension is "equal when longitudinal and transversestringsidentically tensioned and is differential"whetudinal strings arensioned heavier than transverse ones this difference is usually between 1 and 2 kgand is defined by the shape of the head of the racket [7] Rackets featuring largerdifferencesthe lenglongitudinal and transverse strings are usually kndifferent tensiordirectly proportional to the rigidity of the string area and controlString area rigidityhis is the pressure pliability of the knit string area not counting the racket bodyelasticity This property depends on the knit, tensioning and the shape and sizeof racket head this is resultant characteristic and is an exactation of the rackete important to know the final result of the knit and not the exact value ofapplied to the string whe most pliable surface has a figure of 5for this parameter and the hardest one comes up to 75 kg[7
his propertytly proportional to the knit, terinversely proportional to the surface area of the string flat, the dynamic inertiaand powee pliability of tket body Thiprofessional rackets this figure is between 50 and 75 kg[7his propertybility and colh headDynamic inertiais is a set of energetic characteristics of the racket indicating how the racketansfers the energy from the hand during the movement Until very reproperty was disregarded from measurements and was only determined and senseby the playerelf Now that computer measurement has been introduced into thetennis sport this is a characteristic that is being followed very closely and is the latestfeature established so far
It is dependent and functionally incorporates all other racketoperties indicating the result of the combination between them Satisfactocorporation of opposite parameters is achieved by distributing the mass andelasticity along the racket mainframe Leading racket brands are made lighterprovide better control and manageability but at the same time they provide muchhe dynaertia This makes the racket powerful and precise (control and manageabilitychieved by improving the balance characteristics andarbon fibre compounds thisparameter usually varies within 290 and 360 units [8]his parameter isdirectly proportional to the length, string surface area, balance, weight, bodyidity and powerinversely proportional to the knit, tensioning, string area rigidity manageabilit
his is the ability of the racket to obey to the movementaim is for the player to exercise minimum effort to change the position of the racketand the string area surfaceis measured within 50 and 100 ar [8his propertydirectly proportional to the body rigidity and contreinversely proportional to the length, head size, balance, weight and dynamicneriagy being transmitted from the racket to themum effort fromhand to have the racket transmitting maximumenergy to the ball Modern rackets have figures for this parameter between 25 and 80unitshis propertyectly proportional to the length, head size, balance, weight, body rigidityinversely proportional to the knit, tensioning, string area rigidity, manageabilityhis is the ability of the racket to provide precisely (and quickly) the rightdirection traiectory aball
Considering the relative shareunprovoked mistakes this is a very essential parameteracket this80his property is pidirectly proportional to the area and size of the head to the knit, tensioningidity, body rigidity andinversely proportional to the length, balance, weight, dynamic inertia andwing Coative table of the basic characteristic palters of mostcommonly used professional rackets indicates how manufacturers achieve thecombination between opposite characteristics and what are the trends in thedevelopment of these qualities