On The Coefficient Of Restitution Of Tennis Rackets

The evolution of research on tennis equipment has recently introduced some parameters for the evaluation of the racket's efficiency. Among them, the most used in current practice is the coefficient of restitution of the racket (COR), that is simply defined as "the ratio of the rebound speed to the incident speed of the ball for orthogonal impact". Remarkable differences between values of COR reported in the tennis literature are mainly due to the various test conditions adopted. In order to compare different results, some important test parameters must be imposed for a better COR definition. Our recent laboratory tests show that the COR of the same racket is mainly affected by: - kind and conditions of balls kind and tension of strings impact velocity. Moreover, they show that the largest portion of energy is lost because of ball's deformation. Figure 1 shows the coefficient of restitution of a ball, at different impact velocities and on a rigid wall. Furthermore, in a tennis shot, ball deformation for a given velocity is affected by the other test parameters listed above. The augments of string's tension, for instance, increases the ball deformation and consequently decreases COR. This highlights that the traditional coefficient of restitution is not a direct measure of the racket frame efficiency, but it involves the behaviour of ball, strings, frame and grip restraint together. Therefore, in order to be compared by means of COR, rackets must be tested with the same kind of balls and the same kind of strings at equivalent string tension (i.e. tension that gives the same stiffness to the string plane). We suggest to test the racket at four different ball velocities in order to analyse different play conditions; thus we propose a new COR which should contain four values. Moreover, the knowledge of the influence of balls and strings allows to evaluate the portion of COR that is related only to the racket's frame characteristics

HIGH JUMP DIRECT DYNAMIC SIMULATION

INTRODUcrION High jumps are composed of a complex sequence of movements whose single contribution to the whole body motion cannot be intuitively predicted. While most of the movements are well learned by the elite athletes in order to reach the result, few are not effective or negative from the mechanical point of view and are probably performed for an erroneous feeling of their effects. The direct dynamic simulation of jumping can be useful in order to more fully understand the mechanics of high jump techniques; to explain to the athletes the consequences of some errors; and to test possible evolution of the exercise. When the external forces and the relative movements of the limbs are known, the calculation of the whole body trajectory and orientation is a direct dynamic problem

A COMPOSITE MODEL FOR THE SIMULATION OF SKIING TECHNIQUES

INTRODUCTION In this work we present a model for skiing technique analysis and simulation: it consists of a man model, an equipment model and a contact (ski-snow) model. Such a model is the basis for a deeper understanding of the interaction between skier and equipment and its use will be profitable in various applications such as: equipment optimisation and technique improvement. Moreover this simulation technique can be profitably used for teaching the basic principles of skiing. MATERIAL AND METHODS To build our model we combined the methods used for multibody systems dynamic analysis (man model with finite element techniques (ski model). The human body model consists of 3D chains of rigid bodies: according to the "sophistication" of the simulation we use 16 segments, with 39'internal d.0.f (full man model), or 7 segments, with 6 internal d.0.f . To describe rigid body dynamics and kinematics (man model) we adopt a method based on homogeneous matrices (Casolo 1995): both the absolute and the relative position, velocity and acceleration are described by 4x4 matrices, as well as the inertial properties and the external loads. This approach allows to embed both the linear and angular terms in the same formalism. To derive the equation of motion a Lagrangian approach was adopted, leading to this expression: Mq+C(cf.q.t) = Fl(q.q,t) +Ft(q,q) where M is the mass matrix, C contain the weight, the centrifugal and Coriolis effect, Ft contains joint torques, F2 represent the action exchanged with ski through the bindings and the vector q contains joints laws of motion. The model can be used to perform direct and inverse dynamics analysis of skiing, since it allows the input of joint torques and/or joint relative movements, that can be experimental data or can be generated by scratch, by a law of motion preprocessor. Skis are modelled with Finite Element techniques. The internal structure of a ski is quite complex: different material, with complex arrangement, are employed giving rise to properties (stiffness, damping and mass) which can be determined by experimental measures or by complex FE analysis. These properties can be quite well reproduced by means of a simplified model consisting of 3D beam elements . Some geometrical features, such as camber and sidecut, can be easily reproduced. Ski equations of motion, in matrix form, are: M9+ q v r e l + Kq&f = F,,I +Fnlon-ski f F.+.ki - cn,,wn where M, C, K are, respectively, the ski mass, damping and stiffness matrices. The ski load consists of three terms: weight, action exerted by the skier through the bindings and the contact action exerted by the snow. A simple contact model has been also developed, based on the assumption that the snow reacts both to ski deepening, sliding and skidding. This simple model can take into account, for example, the effect of ski vibration on the ski-snow interaction. RESULTS Some simulations have been performed to test model capabilities: we analysed the effect of ski torsional stiffness, as well as the amount of sidecut, on skier trajectory during traverse and turns. The model is also used to simulate the aerial phase of a free-style jump and the following landing phase. In all of these cases simulation can be an useful tool for predicting the effect of changing joint movements (i.e varying skiing technique) and equipment characteristics. A sensitivity analysis can be a first step toward a technique and equipment optimisation. References Casolo F., Legnani G., Righettini P., Zappa B. "A homogeneous matrix approach to 3D kinematics and dynamics", TMM (in press)

Diagnostic work-up of arrhythmogenic right ventricular cardiomyopathy by cardiovascular magnetic resonance

Cardiovascular magnetic resonance (CMR) has become a widespread diagnostic tool. Since its introduction, CMR has been used to image patients with a known or suspected arrhythmogenic right ventricular cardiomyopathy (ARVC). Several abnormalities have been found and described by CMR and at present this diagnostic tool is considered very important for the diagnosis. However, the diagnosis of ARVC relies upon the fulfillment of both clinical and functional criteria and CMR can provide several but not all the information useful for the diagnosis. Furthermore, some findings such as evidence of right ventricular epicardial fat, once considered a peculiar marker of ARVC, have been shown to possess a low specificity. This document was prepared by representatives of the three Italian official Organizations involved in CMR. Its main scope is to highlight the problems encountered when studying patients with suspected ARVC at CMR, to indicate the basic technical equipment needed, to recommend a proper imaging protocol and to offer a consensus on the main features relevant for the diagnosis

Relationships between population traits, nonstructural carbohydrates, and elevation in alpine stands of Vaccinium myrtillus

Premise: Despite great attention given to the relationship between plant growth and carbon balance in alpine tree species, little is known about shrubs at the treeline. We hypothesized that the pattern of main nonstructural carbohydrates (NSCs) across elevations depends on the interplay between phenotypic trait plasticity, plant\u2013plant interaction, and elevation. Methods: We studied the pattern of NSCs (i.e., glucose, fructose, sucrose, and starch) in alpine stands of Vaccinium myrtillus (above treeline) across an elevational gradient. In the same plots, we measured key growth traits (i.e., anatomical stem features) and shrub cover, evaluating putative relationships with NSCs. Results: Glucose content was positively related with altitude, but negatively related with shrub cover. Sucrose decreased at high altitude and in older populations and increased with higher percentage of vascular tissue. Starch content increased at middle and high elevations and in stands with high shrub cover. Moreover, starch content was negatively related with the number of xylem rings and the percentage of phloem tissue, but positively correlated with the percentage of xylem tissue. Conclusions: We found that the increase in carbon reserves across elevations was uncoupled from plant growth, supporting the growth limitation hypothesis, which postulates NSCs accumulate at high elevation as a consequence of low temperature. Moreover, the response of NSC content to the environmental stress caused by elevation was buffered by phenotypic plasticity of plant traits, suggesting that, under climate warming conditions, shrub expansion due to enhanced plant growth would be pronounced in old but sparse stands

Comparison between seismic retrofitting solutions for existing reinforced concrete buildings: a case study

In assessing the safety of existing buildings, the specific actions dedicated to the knowledge of the structure delineate the parameters of the linear or non-linear analysis aimed at identifying the most appropriate structural intervention. In this context, the present paper collects the seismic analysis of a school building in reinforced concrete, illustrating the different stages concerning the acquisition of geometrical and mechanical data, problems about structural modelling and the features of the seismic retrofitting proposed. In closing, a critical comparison between the results derived from some techniques frequently used to seismically improve existing structures

Few simple rules governing hydrogenation of graphene dots

We investigated binding of hydrogen atoms to small Polycyclic Aromatic Hydrocarbons (PAHs) - i.e. graphene dots with hydrogen-terminated edges - using density functional theory and correlated wavefunction techniques. We considered a number of PAHs with 3 to 7 hexagonal rings and computed binding energies for most of the symmetry unique sites, along with the minimum energy paths for significant cases. The chosen PAHs are small enough to not present radical character at their edges, yet show a clear preference for adsorption at the edge sites which can be attributed to electronic effects. We show how the results, as obtained at different level of theory, can be rationalized in detail with the help of few simple concepts derivable from a tight-binding model of the $\pi$ electrons

Scintimammography with 99mTc-MIBI and magnetic resonance imaging in the evaluation of breast cancer

This study was performed to evaluate the sensitivity and specificity of technetium-99m methoxyisobutylisonitrile (99mTc-MIBI) scintimammography (SMM) and contrast-enhanced magnetic resonance imaging (MRI) in patients with breast masses, using the histological findings as the gold standard. Forty-five consecutive patients with a breast lesion, detected by self-examination, physical examination or screening mammography, underwent SMM and MRI. In 38 cases (84.5%), the histopathology was malignant; the breast cancers ranged from 3 to 100 mm in diameter (mean 22 mm). In the overall patient group, MRI showed a slightly higher sensitivity than SMM (92% vs 84%), but SMM showed a better specificity: 71% vs 42%. The accuracy was 82% and 84% for SMM and MRI respectively. To evaluate the influence of lesion size on the results, patients with lesions ≤20 mm and ≤15 mm were examined. In patients with lesions ≤20 mm, the sensitivity of SMM and MRI decreased to 64% and 82% respectively, while SMM again displayed considerably better specificity: 83% vs 50% for MRI. The accuracy of SMM and MRI was 64% and 82% respectively. In patients with lesions ≤15 mm, SMM again showed better specificity (75% vs 50%), while MRI displayed better sensitivity and accuracy (sensitivity, 81% vs 62%; accuracy, 75% vs 65%). In this study the specificity of SMM in patients with breast lesions was thus superior to that of MRI. The combination of SMM and MRI may be used in those patients with equivocal findings at mammography and ultrasound to reduce the number of unnecessary surgical biopsies