Tom Allen

Quasi-static characterisation and impact testing of auxetic foam for sports safety applications

This study compared low strain rate material properties and impact force attenuation of auxetic foam and the conventional open-cell polyurethane counterpart. This furthers our knowledge with regards to how best to apply these highly conformable and breathable auxetic foams to protective sports equipment. Cubes of auxetic foam measuring 150 × 150 × 150 mm were fabricated using a thermo–mechanical conversion process. Quasi-static compression confirmed the converted foam to be auxetic, prior to being sliced into 20 mm thick cuboid samples for further testing. Density, Poissons ratio and the stress–strain curve were all found to be dependent on the position of each cuboid from within the cube. Impact tests with a hemispherical drop hammer were performed for energies up to 6 J, on foams covered with a polypropylene sheet between 1 and 2 mm thick. Auxetic samples reduced peak force by ~10 times in comparison to the conventional foam. This work has shown further potential for auxetic foam to be applied to protective equipment, while identifying that improved fabrication methods are required.

Effect of friction on tennis ball impacts

There are currently no restrictions on the coefficient of friction of tennis courts or strings. The aim of this paper was to determine the effect of friction on tennis ball impacts. Finite element models were used to determine the effect of friction for oblique spinning impacts both between a tennis ball and a rigid surface and between a tennis ball and the string bed of a freely suspended racket. The results showed that during an oblique impact a tennis ball can behave in any of the following ways: first, it can slide, second, it can slide and then ‘overspin’, or, third, it can slide, overspin, and then converge towards rolling. The ball will slide throughout the majority of impacts on the court during play. Therefore, the rebound topspin of the ball will increase with increasing court friction and the horizontal rebound velocity will decrease. The ball will roll off the string bed for the majority of groundstrokes, and the rebound properties will effectively be independent of string bed friction.

Effect of tennis racket parameters on a simulated groundstroke

Abstract Composite materials have given manufacturers the freedom to develop a broad range of tennis rackets, allowing them to change key parameters such as the structural stiffness, mass, and position of the balance point. The aim of this research was to determine how changing these parameters could affect ball resultant rebound velocity and spin for a simulated groundstroke. A finite element model of a freely suspended racket and strings was used to determine the effect of racket parameters for oblique spinning impacts at a range of locations on the stringbed. The finite element simulations were conducted in the laboratory frame of reference, where the ball is projected onto an initially stationary racket. The mean rebound velocity of the ball was 9% higher for a structurally stiff racket, 37% higher for a heavy racket, and 32% higher for a head-heavy racket. In addition, the mean rebound topspin of the ball was 23% higher for a heavy racket and 21% higher for a head-heavy racket. Therefore, in relation to a groundstroke with an impact location away from the node, the rebound velocity of the ball is likely to increase with the structural stiffness of a racket. The effect of changing the mass and position of the balance point is more complex, as it is dependent on the relationship between the transverse moment of inertia and maximum pre-impact swing velocity.

Effect of inter-string friction on tennis ball rebound

Tennis players report anecdotally that the choice of string material affects the amount of spin applied to the ball by the racket. Previous research on the effect of the coefficient of friction of tennis strings has concluded that ball rebound is mostly, but not always, independent of the string friction. To understand this better, tennis balls were projected at a fixed racket at 25 m·s−1 with backspin varying from 0 to 400 rad·s−1 at an angle of 40° and 60° to the normal with strings made from either nylon or polyester. Each string type was modified by lubricating it to give low friction or sanding it to give high friction. It was shown that the inter-string friction μs had different consequences depending upon whether the strings slid across each other during contact. The ball tended to roll at high μs, unless the inbound backspin was high enough to induce slipping. A decrease in μs allowed slipping of the strings over each other which reduced the horizontal impulse applied to the ball. At very low μs the ball was induced to overspin at steep impacts or slip at shallow angles. It was concluded that the dominant effect of a change in inter-string friction was in the string movement rather than the coefficient of friction between the ball and strings, and that the effect was dependent upon impact angle and spin.

Effect of temperature on the dynamic properties of soccer balls

Soccer is played over a wide range of temperatures. Previous research has shown that the dynamic properties of sports balls, such as squash balls, tennis balls, and baseballs are dependent on temperature. The aim of this research was to determine whether the dynamic properties of soccer balls are temperature dependent. Quasi-static tensile testing was conducted on samples of soccer ball material, at nominal temperatures of 0, 20, and 40 °C. Normal impact testing at speeds up to 22 m/s was undertaken at nominal ball temperatures of 0, 20, and 40 °C. The stiffness of the material decreased as the temperature increased. The coefficient of restitution, contact time, and maximum deformation of the ball all increased with temperature. The mean coefficient of restitution was 0.82 ± 0.03 at 40 °C in comparison to 0.73 ± 0.02 at 0 °C. A foot-to-ball impact model combined with a trajectory model was used to simulate a penalty kick directed at the top corner of the goal. The results showed that the time available to the goalkeeper was 7 per cent shorter at 40 °C in comparison to that at 0 °C. Therefore, the time available for a goalkeeper to prevent a goal decreases as temperature increases.

Experimental Validation of a Finite-element Model of a Tennis Racket String-bed (P21)

An explicit finite-element (FE) model of a tennis racket string-bed was produced in Ansys/LS-DYNA 10.0. This model was used to simulate a range of impacts between a tennis ball and string-bed, which were validated against experimental data. The laboratory validation was undertaken by firing balls, with backspin in the range from 0 to 600 rad·s-1, from a pitching machine onto a head-clamped tennis racket. Inbound velocities and angles in the range from 20 to 30 m·s-1 and approximately 20 to 60° respectively were tested. Results were obtained for rebound spin, angle and velocity, with good agreement between the model and experiment.

Experimental Validation of a Tennis Ball Finite-element Model for Different Temperatures (P22)

An explicit finite-element (FE) model of a pressurised tennis ball was produced in Ansys/LS-DYNA 10.0 and validated at room temperature. This model was successfully updated to simulate temperatures of 283.15 and 313.15 K (10 and 40 oC), by adjusting the internal pressure and material properties of the ball’s rubber core. The validation experiment was undertaken using an impact rig in a climate chamber, for perpendicular impacts on a rigid surface with inbound velocities in the range from 15 to 30 m·s-1. The impact rig consisted of an air-cannon, for firing the balls, a set of light gates for calculating coefficient of restitution (COR), and a force plate for measuring contact time. The model was found to be in good agreement with the experimental data across the entire range of temperatures tested.

Auxetic Foam for Snow-Sport Safety Devices

Skiing and snowboarding are popular snow-sports with inherent risk of injury. There is potential to reduce the prevalence of injuries by improving and implementing snow-sport safety devices with the application of advanced materials. This chapter investigates the application of auxetic foam to snow-sport safety devices. Composite pads—consisting of foam covered with a semi-rigid shell—were investigated as a simple model of body armour and a large 70 × 355 × 355 mm auxetic foam sample was fabricated as an example crash barrier. The thermo-mechanical conversion process was applied to convert open-cell polyurethane foam to auxetic foam. The composite pad with auxetic foam absorbed around three times more energy than the conventional equivalent under quasi-static compression with a concentrated load, indicating potential for body armour applications. An adapted thermo-mechanical process—utilising through-thickness rods to control in-plane compression—was applied to fabricate the large sample with relatively consistent properties throughout, indicating further potential for fabrication of a full size auxetic crash barrier. Further work will create full size prototypes of snow-sport safety devices with comparative testing against current products.

Finite Element Model of an Impact on a Palmar Pad from a Snowboard Wrist Protector

Wrist injuries are the most common types of injury in snowboarding. Protectors can reduce injury risk by limiting wrist hyperextension and attenuating impact forces. There are a range of wrist protector concepts available, but it is unclear if any particular design is more effective. The aim of this study was to develop and validate a finite element model of an impact on the palmar pad from a protector. Pad material from a protector was characterised to obtain stress vs strain data, and determine whether it was rate dependent. Material data was implemented into a finite element model to predict impact behavior at 2.5 J. Four material models were investigated, with an Ogden model paired with a Prony series providing the best agreement to experimental data. Future work will build a model of a complete protector for predicting the protective levels of these products.

Spin generation during an oblique impact of a compliant ball on a non-compliant surface

Oblique impacts between a ball and surface are a key part of many sports. Previous work has shown that a ball can slide, over-spin or roll at the end of an impact, depending on impact conditions. Inbound spin ratio was analysed to determine if it could be used to identify what is likely to happen at the end of impact for all sports regardless of surface, ball type, impact velocity, angle and spin. A predictive model, in the form of a finite element model, of a tennis ball was validated against experimental data for oblique impacts with inbound spin ratios in the range of –1 to 1. Spin ratio is defined as the product of the ball’s angular velocity and radius divided by the centre of mass velocity tangential to the surface. The finite element model was then used to determine the effect of impact conditions and ball parameters on outbound spin ratio. The study showed that for constant inbound spin ratio, outbound spin ratio was dependent on inbound velocity and angle. For constant inbound velocity and angle, decreasing the mass and increasing the stiffness of the ball through a change in material properties resulted in an increase in the maximum outbound spin ratio. Inbound spin ratio can be used to predict how a ball will rebound from a surface; however, inbound velocity and angle must be constant. Spin ratio can therefore be used to compare the impact characteristics for different ball and surface scenarios.