Tennis Rackets Research Articles

Using sports equipment for student exploration of vibration and structural acoustics phenomena

The familiarity which many undergraduate and graduate students have with sports implements (bats, sticks, clubs, rackets, and balls), renders such objects as suitable subjects for student exploration through laboratory projects and homework problems. This paper will illustrate how problems and projects involving baseball bats, tennis rackets, hockey sticks, and golf clubs can arouse student interests in structural acoustics. Homework problems in which students model the contact time between ball and racket, the frequencies of a golf club shaft, the vibration of the face plate in a golf driver responsible for the trampoline effect, and the radiation of sound from structural modes in hollow and spherical balls provide engaging applications of the theory for membranes, flexural bending in beams, boundary conditions, and radiation. Examples will be shown for using baseball bats, cricket bats, hurling and hockey sticks, ping pong paddles, and tennis rackets in more involved laboratory projects. Sports implements also have the advantage of being non-uniform and asymmetric (wide body and thin handle), non-isotropic (wood grain), or involving complicated geometrics (ellipses) so that students can compare simple theory to more complicated realistic systems.

The characteristics of the coefficient of restitutions of table tennis rackets made of wooden laminated plate

The characteristics of the coefficient of restitutions of table tennis rackets made of wooden laminated plate

Performance Evaluation of Tennis Rackets by Using Finite Element Analysis of String-Bed

Performance Evaluation of Tennis Rackets by Using Finite Element Analysis of String-Bed

Dynamical analysis of stroke induced vibrations in tennis racket

Tennis rackets are mostly designed disregarding the boundary condition managed by the player's hand on the handle. This process leads to a lack of accuracy in the mechanical parameters the manufacturers provide to their rackets in order for them to be reliable and comfortable to the player. Our work aimed at providing a better understanding of the effect of the tennis player's hand on the racket's dynamical behavior. For this purpose, a dedicated experimental procedure involving 14 tennis players and 5 tennis rackets has been carried out. Vibrations propagated from the racket toward the upper-limb have been collected synchronously with kinematic and electromyographic data during forehands of various intensities. Additionally, an analytical model of the hand/racket interaction has been designed based on operational modal analyses. This model provides a straightforward tool to predict changes in the dynamical behavior of a tennis racket under playing conditions. Results indicated that tennis players adjust their grip-force to tune the vibrational content entering into his upper-limb. Besides, a noteworthy outcome is that grip-force induces modifications in the racket's dynamical behavior that are at least as important as the differences observed under free boundary conditions due to the rackets' own mechanical parameters.

Vibroacoustic analysis of table tennis rackets and balls: The acoustics of ping pong

Table Tennis rackets (ping-pong paddles) exhibit a large number of structural vibration modes which follow patterns first observed by Ernst Chladni and Mary Waller for elliptical plates. Vibrational mode shapes and frequencies obtained through experimental modal analysis will be shown. Acoustic analysis reveals that one structural mode of the paddle, in particular, dominates the sound produced by the ball-paddle impact. The rubber padding provides some damping, and a significant mass loading to the paddle vibrations. The hollow cellulose nitrate balls exhibit a number of vibrational mode shapes typical of a hollow spherical shell, starting at frequencies around 5900 Hz; these will be demonstrated from experimental and computational results. However, the contact time between ball and paddle is such that the lowest acoustic modes of the ball do not contribute to the radiated sound. Instead, the ball appears to radiate sound at a much higher frequency sound (10-12 kHz) most likely due to snap-through buckling common to spherical shells undergoing deformation while impacting a rigid surface at high speeds.

Water absorption experimental analysis of an orange peel and coconut shell particulate blend reinforcement material for composite fabrication

The extant literature on composites has downplayed the merits of orange peel particulates (OPPs) and coconut shell particulates (CSPs) as fillers in mixed forms despite their engineering purposes. An OPP-CSP mixture can be used to suppress the weight disadvantage of CSPs, exploit the water resistance advantage of CSP, enhance the mechanical properties and improve the wear resistance of OPPs as a result of the oily secretions of the OPP. Launching a new research direction of mixed filler experiments, this work examines the water absorption properties of mixed OPPs-CSPs of up to 30 cm3 mixtures by volume, according to filler literature norms and previous sensitivity tests. A principal result is that the average free swell of the particulate blend increased up to 164.61%, a value attained with an initial volume of CSPs equal to 10 cm3 in a combined initial volume of 30 cm3. Thus, the mixing ratio is 10 CSPs:20 OPPs (Type I). This free swell value can cause considerable changes to loadings and structures, which is a negative outcome. Sensitivity analysis showed that the higher-OPPs-in-particulate blend produced the most favourable free swell values. In practice, the findings of this study meet the growing needs of the composite industry for materials having unusual combinations of the properties of water-resistance for lightweight applications in tennis rackets, household interior decorations and agricultural silos. This novel contribution pioneers efforts to produce filler blends of particulate orange peels and coconut shells in independently varied proportions rather than being embedded in composites. Sensitivity analysis of the critical process parameters was carried out to understand the degree of responsiveness of model parameters of the blends. This is the first time such information has been reported in the literature.

Study on string pattern of tennis rackets

In this study, the effect of string pattern on coefficient of restitution (COR) and the amount of spin was evaluated by the dynamics rebound test using the tennis ball. Two kind of rebound test were conducted. In first test, the tennis balls were launched from normal direction of string-bed to evaluate the COR. In the other test, the tennis balls were launched from 45°direction of string-bed to evaluate the amount of spin. This test system had displacement sensor to measure the deformation of string-bed contacting the ball. As a result of tests, in case the distance between strings was large, the contact time between string-bed and tennis ball was long. In addition, the COR was independent on the string diameter and the string pattern. But the COR was dependent on approaching velocity of ball. On the other hand, the string pattern has effect on the amount of spin.

テニスラケットのゴム輪による除振効果（有限差分法による数値解析）

テニスラケットのゴム輪による除振効果（有限差分法による数値解析）

高分子ストリングの直径がテニスラケットの打球面に与える影響

In this study, Effect of string diameter on the hitting surface for tennis rackets were evaluated. The newly designed aluminum jigs were developed which were able to evaluate only the mechanical properties of the hitting surface. Two experiments were conducted to evaluate effect of string diameter on the hitting surface. One was tensile test for the string used for tennis. As a result, three kinds of strings did not have the difined difference in the rerlationship between strain and stress. The other is loading test of the hitting surface. As a result, increasing the diameter of the string showed the same effect as increasing the tension of string.

テニスラケットのストリングベッドの動的特性に与えるストリングの直径の影響

テニスラケットのストリングベッドの動的特性に与えるストリングの直径の影響

Vibrational analysis of hollow and foam-filled graphite tennis rackets

The game of tennis is plagued with wrist and elbow injuries. Most players use light, stiff hollow graphite rackets. A recent foam-filled racket design appears to reduce the risk of wrist injury. A vibrational analysis of a wide variety of rackets was conducted in attempt to understand the science behind this racket’s apparent success. Damping rates were measured for the bending and torsional modes for a wide variety of hollow and foam-filled rackets. No significant difference among the rackets was found, suggesting the benefit of the foam-filled racket design is not due to damping. An extensive modal analysis was conducted for several rackets over the frequency range of 100 Hz to 1.5 kHz to identify the bending, torsional, and string modes. In this paper, the damping rates, mode shapes, and frequencies, will be compared for several hollow and foam-filled rackets. Results will be interpreted in light of the relevant forces between the racket, ball, and arm.

Methodological contribution to study the vibratory behaviour of tennis rackets following real forehand drive impact

Vibrations of tennis rackets induce discomfort in the player (Stroede et al. 2002). Vibrations with frequencies less than 200 Hz are further thought to stress players' upper extremities and potenti...

Safe clinical use of carbon nanotubes as innovative biomaterials.

Carbon nanotubes (CNTs) are structurally described as sheets of six-membered carbon atom rings (i.e., graphene) rolled up into cylinders. CNTs with only one layer are known as single-walled CNTs (SWCNTs), and those with two or more layers are known as multiwalled CNTs (MWCNTs). Cup-stacked carbon nanotubes and carbon nanohorns are also sometimes called CNTs.1−3 Currently, these very attractive carbon materials and nanomaterials are a subject of vigorous product development in a broad range of fields.4−11 The reasons are that CNTs have useful electrical, thermal, and mechanical characteristics, and their base material performance can be improved by combination with other materials.12−23 A recent industrial application of CNTs as an electrode additive to lithium-ion batteries is based on their excellent electrical characteristics. Addition of CNTs prevents battery deterioration and substantially lengthens time to recharging. It is doubtless that the demand for high-performance batteries will grow increasingly with multifunctionalization of personal computers and mobile phones, development of new mobile terminals, spread of electric vehicles, and other factors.24−30 Composite materials with the excellent mechanical characteristics of CNTs have already been used in sporting goods such as golf clubs, tennis rackets, and bicycles. CNTs are also expected to have applications that reduce the weight of aircraft and automobiles.10,14,31−35 A wide variety of advantages are gained from the use CNTs in precision parts as well. CNTs are also used in transistors and memory devices, and enhance their efficiency. The use of CNTs in various displays and TV screens continues to increase in rate. CNTs are also widely used in products designed to prevent static electricity, to shield electromagnetic waves, to store electricity, and for other purposes.36−45 Furthermore, Japan is now facing nuclear energy issues stemming from the accident at Tokyo Electric Power Company’s Fukushima No. 1 nuclear power plant. As a result, CNTs are expected to play a major role in developing new energy sources such as solar photovoltaic power generation and wind power generation.46−52 In the medical field, extensive research activities are underway to develop new CNTs biomaterials for use in the treatment and diagnosis of disease. For example, application of CNTs to cancer treatment and diagnosis, such as in drug delivery systems (DDSs) for treatment of cancer, hyperthermia, and in vivo imaging, has been investigated.53−57 In a study that aimed at applying CNTs to regenerative medicine, CNTs were found to work excellently as scaffold materials for nerve and bone tissue regeneration.58−63 Furthermore, R&D activities are underway to improve the mechanical strength and durability of implants by combining CNTs with existing biomaterials.64−67 Besides, numerous ideas have been put forth about how CNTs can be used in the treatment of a variety of diseases. Figure ​Figure11 shows the trend in the number of articles found in the PubMed database (http://www.ncbi.nlm.nih.gov/pubmed/) (accessed 20 March 2014) by searches using “carbon nanotubes” and “biomaterials” as keywords. The number has been soaring since 2005, suggesting that CNTs research has become a highly competitive field worldwide over the past few years. Of course, numerous articles on the biological applications of CNTs do exist that cannot be captured with these two simple keywords, and the graphic representation of this trend is no more than an indicator of the increase in this research over time. Figure 1 Time trends for the number of articles found in the PubMed database (http://www.ncbi.nlm.nih.gov/pubmed/) (accessed 20 March 2014) by search using “carbon nanotubes” and “biomaterials” as keywords. Recent years have seen ...

Tennis Rackets and the Parallel Axis Theorem

This simple experiment uses an unusual graph straightening exercise to confirm the parallel axis theorem for an irregular object. Along the way, it estimates experimental values for g and the moment of inertia of a tennis racket. We use Excel to find a 95% confidence interval for the true values.

The tool as the last piece of the athlete’s gesture imagery puzzle

The present study tested whether and how motor experience with a specific tool affects motor representation of a specific movement. To this aim, we considered a group of expert tennis players and a control group of athletic individuals without tennis experience. Participants were asked to execute 20 single forehands into the wall with a tennis racket (movement execution – ME) and, afterward, to produce a kinesthetic image of themselves while executing the same movements (motor imagery – MI). During MI participants handled one of the following tools: a tennis racket, a tennis-like racket and an umbrella. Results showed that the duration of the real and the imagined movements were almost similar when participants of both groups held the tennis rackets. In contrast, when tennis players handled the tools not specific for tennis the duration of the imagined movements increased significantly compared to the MI duration with a tennis racket. On the opposite, the handled tool did not modulate MI performances of the control group. In conclusion, this study showed that motor representation of subjects who developed motor skills associated to tool-use is reliant on the object used to practice movements. This finding suggests that, although MI mainly relies on the activity of cortical motor regions, non-motor information – as the use of the tool to practice movement – strongly affects the MI performance.

Measuring the Inertial Properties of a Tennis Racket

Simple and bifilar pendulum were used to measure the mass moments of inertia of three tennis rackets. The pendulum setups were filmed using an off-the-shelf camcorder, with a stopwatch in view to provide timing data. The measurement accuracy was assessed using calibration rods of known mass moment of inertia. The simple pendulum method was found to be most accurate (<1.0% difference to theoretical value) when a square profile rod was used as a pivot. The bifilar pendulum was found to be very accurate (0.0% difference to theoretical value) but sensitive to non-parallel support wires. A Babolat Racket Diagnostic Centre (RDC) was assessed using four calibration rods, of known mass moment of inertia. Measurement agreement was greater than 99.0% for mass moments of inertias within the range of 220 – 380 kg·cm2.

Vibro-acoustic of Table Tennis Rackets. Influence of the Plywood Design Parameters. Experimental and Sensory Analyses.

The performances of a table tennis racket can be qualified with several adjectives like: fast, slow, stiff, adhesive, controllable, etc. These qualifications are subjective since they are relative to the sensory analysis made by each player. It appears that the noise produced at the ball impact on a racket has a great influence on the opinion that a player can give about a racket. Moreover, the sound emitted at the stroke can be appreciated differently among several players. Hence a good sound may give a positive a priori to the player abut the racket appreciation.The study is based on a previous work that demonstrated: the correlation between the acoustic frequency spectrum and the vibration frequency spectrum of a racket following the ball impact – two vibrations modes of the racket blade are responsible of the sound emitted. The influence of the blade plywood composition is studied. Several prototype racket blades have been specially realized with some differences between them on: the thickness of the plies, the wooden essences. The analysis is first performed on the racket blades without rubbers glued on. The vibro-acoustic of each racket is analyzed by experiments on a lab test bench. The results obtained permit to clearly state on the effectiveness of these design parameters on the impact sound.In the second part, the experimental observations obtained at the laboratory are compared with the results of a sensory analysis performed with the same prototype rackets by a panel of high level players which were asked to classify the sounds of the rackets. It is shown that the classification made by the players is consistent with the experimental laboratory observations.

Impact of New Composite Material Technology on the Performance of the Tennis Rackets

With the continues improving of people's living standards, more and more people work out in all kinds of sports fields beyond the busy work. On the other hand, the development of the modern competitive sports also requires that the sports experts should not only strive for the scientific training, but should also pay much attention on the improvement and development of the sports equipment at the same time, which makes the sports equipment market have achieved unprecedented prosperity. This paper introduces the application of the fiber reinforced composite materials in the field of sports equipment, which is described mainly from the advantages of the fiber reinforced composite materials used in sports equipment areas, and from the aspects of the principles of material selection, the product varieties, the application examples and the status.

Understanding the Dynamic Behaviour of a Tennis Racket under Play Conditions

The ‘feel’ of tennis rackets is of increasing importance to manufacturers seeking product differentiation in a context where further performance enhancements are prevented by a combination of mechanical limits and regulations imposed to protect the integrity of the sport. Vibrations excited during a shot contribute greatly to the perception of ‘feel’. Previous studies have been reported but none has covered the full set of mode families or the frequency range in this study. In-plane vibrations associated with the routine use of topspin shots in modern tennis have not been documented so far in the literature. To consider modal behaviour, multiple measurements during play conditions are required but this is practically impossible. This paper proposes an alternative approach and successfully relates a comprehensive modal analysis on a freely suspended racket to vibration measurements under play conditions. This is achieved through an intermediate stage comprising a necessarily more limited modal analysis on a hand-gripped racket and use of the mass modification modal analysis tool. This stage confirmed the prevailing view that hand-gripping can be considered as a mass modification distributed along the handle of the freely suspended racket but the associated mass was much lower than that of an actual hand and the hand also increased the damping ratio of frame modes significantly. Furthermore, in frame vibration measurements during forehand groundstrokes, a greater reduction in bending mode frequencies was observed, consistent with a mass-loading of around 25 % of the actual hand as a consequence of the tighter grip. In these play tests, the first two bending modes, the first torsional mode, the first eight stringbed modes, the first three hoop modes and the third in-plane bending mode were identified, with the stringbed modes being particularly prominent.

Body and Object Effectors: The Organization of Object Representations in High-Level Visual Cortex Reflects Body–Object Interactions

The principles driving the functional organization of object representations in high-level visual cortex are not yet fully understood. In four human fMRI experiments, we provide evidence that the organization of high-level visual cortex partly reflects the degree to which objects are typically controlled by the body to interact with the world, thereby extending the body's boundaries. Univariate whole-brain analysis showed an overlap between responses to body effectors (e.g., hands, feet, and limbs) and object effectors (e.g., hammers, combs, and tennis rackets) in lateral occipitotemporal cortex (LOTC) and parietal cortex. Region of interest analyses showed that a hand-selective region in left LOTC responded selectively to object effectors relative to a range of noneffector object control conditions (e.g., graspable objects, "act-on" objects, musical instruments). Object ratings showed that the strong response to object effectors in hand-selective LOTC was not due to general action-related object properties shared with these control conditions, such as hand priming, hand grasping, and hand-action centrality. Finally, whole-brain representational similarity analysis revealed that the similarity of multivoxel object response patterns in left lateral occipitotemporal cortex selectively predicted the degree to which objects were rated as being controlled by and extending the body. Together, these results reveal a clustering of body and object effector representations, indicating that the organization of object representations in high-level visual cortex partly reflects how objects relate to the body.