Sporty polymers — polymer use in sports equipment
Sporting performance is a complex mix of mechanics, physiology and psychology, which makes it difficult to ascribe improved performance to specific aspects of the equipment. While much sports apparatus must be light and stiff, favouring composites and polymers, the athlete is intimately connected to the equipment and so the transfer of force from product to athlete needs to be considered. This can result in short- and long-term injuries if the structure is excessively stiff.
The latter has been highlighted by the increased occurrence of tennis elbow associated with the large carbon fibre composite tennis racket frames introduced in the mid-1970s. The product therefore needs to be designed for a specific stiffness range through shape and materials selection.
Damping can also reduce force transfer, but this affects the feel of the equipment, which contributes to the feedback to the athlete. Excessive damping can lead to poor control of the equipment due to its lack of feeling. Feedback to the athlete is one reason why the sound of the equipment, particularly for impact sports, must also be controlled.
Finally, the athlete’s belief that he or she will perform better may be more important than any technical improvement in performance.
Man or machine?
Despite these inter-relationships there are some examples where the sport has been significantly affected by the introduction of equipment that uses new materials.
In 1960, poles for vaulting, which had been constructed from ash, hickory, bamboo and hollow steel, were for the first time constructed from glass fibre-reinforced plastics. The modulus and strength of unreinforced epoxy resin is insufficient for the loads applied during vaulting, but fibre reinforcement increases damping and gives control over the composite modulus (E), by fibre volume fraction and orientation.
The modulus needs to be controlled, as the pole must bend when it is planted at the end of the runway. The buckling force is determined by the mass of the vaulter, his or her speed at the end of the runway and the angle that the pole makes with the ground. The combined force of the vaulter on the pole must exceed the buckling force of the pole, Fbuc, which is given by
(L = length, do = outer diameter and di = inner diameter). Poles with different buckling loads are needed throughout an event as the vaulter warms up and increases speed at the end of the runway so a stiffer, more efficient pole can be used.
Using polymer-matrix composites causes significant strain in the pole, which unloads more slowly than steel tubes, so the vaulter is able to rotate through 180° and cross the bar with feet vertically up rather than swinging over the bar with feet more horizontal. The change in materials and vaulting style caused a significant improvement in vaulting heights (see graph, above right).
Control and distance
The unloading rate of the vaulting pole illustrates the dynamic nature of sports that is coupled with relatively large strains. Any viscoelastic material used in sports equipment would therefore cause mechanical inefficiency due to energy loss through loading and unloading cycles.
Polymers (polyvinyl chloride, polystyrene, polybutadiene [PBD], polyurethane [PU]) and natural materials (cork, leather) are used in many sports balls, which deform to a large strain to store energy during the transfer of kinetic energy from the athlete to the ball. The ‘solid’ golf ball illustrates this behaviour. For an impact at 40m/s, a large strain is induced in the ball.
Such strains are sustained mostly by the core (based on PBD rubber) and by the cover (PU soft or ionomer hard). The viscoelastic nature of PBD results in energy losses of 28-50% depending on impact speed (higher speed equals greater losses) and ball type.
Using diacrylate, oxide and peroxide additives in the PBD increases the proportion of cross-linking so that the hardness and modulus increase results in reduced energy losses. This translates to increased speed off the face and a greater distance for the golfer. This effect is heightened if a hard (ionomer) cover is used.
Golf balls, however, need to combine speed off the face with control, which is achieved by generating backspin. This requires the ball cover to deform into the grooves on a club face and roll up the face rather than slide. A harder ball does not deform into the grooves and so control is lost. The situation is made worse as the torque causing backspin is dependent on the contact area of the ball on the face – a harder ball gives a smaller contact area.
Varying the mix of polymer properties allows this trade-off of distance for control to be circumvented. A softer core causes a large impact strain and so a large contact area – the cover is made from a thin layer of soft PU and readily deforms into the grooves. A soft cover and core should give large viscoelastic energy losses, but separating core and cover is a hard ionomer mantle. This layer acts in a more linear elastic manner and unloads at a faster rate than the core. This forces the core into a faster recovery with less energy loss and therefore faster speed off the face. The distance and spin behaviour of the balls can be correlated to the hardness differences across the various layers.
The ability to alter dynamic properties in polymeric and polymer-matrix composites allows better optimisation of these materials for sporting applications, provided that the sporting action and hence materials merit indices can be determined.
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