Effect of materials and manufacturing on the bending stiffness of vaulting poles C L Davis and S N Kukureka The University of Birmingham, Department of Metallurgy & Materials, Edgbaston, Birmingham, B15 2TT, UK ABSTRACT: The increase in the world record height achieved in pole vaulting can be related to the improved ability of the athletes, in terms of their fitness and technique, and to the change in materials used to construct the pole. For example in 1960 there was a change in vaulting pole construction from bamboo to glass-fibre reinforced polymer (GFRP) composites. The lighter GFRP pole enabled the athletes to have a faster run-up, resulting in a greater take-off speed, giving them more kinetic energy to convert into potential energy and hence height. The GFRP poles also have a much higher failure stress than bamboo, so the poles were engineered to bend under the load of the athlete thereby storing elastic strain energy that can be released as the pole straightens, resulting in greater energy efficiency. The bending also allowed athletes to change their vaulting technique from a style that involved the body remaining almost upright during the vault to one where the athlete goes over the bar with their feet upwards. Modern vaulting poles can be made from GFRP and / or carbon-fibre reinforced polymer composites (CFRP). The addition of carbon fibres maintains the mechanical properties of the pole, but allows a reduction in the weight. The number and arrangement of the fibres determines the mechanical properties, in particular the bending stiffness. The vaulting poles are also designed for an individual athlete to take into account each athlete's ability and physical characteristics. The poles are rated by ‘weight’ to allow athletes to select an appropriate pole for their ability. This paper will review the development of vaulting poles and the requirements to maximize performance. The properties (bending stiffness and pre-bend) and microstructure (fibre volume fraction and lay-up) of typical vaulting poles will be discussed. INTRODUCTION Pole-vaulting has a long history, but from the late 19th century the sport as we know it began to be developed seriously with improvements in materials and vaulting techniques throughout the 20th century (Haake, 2000). Early poles were solid, made from ash or hickory before hollow bamboo poles became common in the first half of the 20th century. Whilst being lighter than solid poles they were still essentially rigid. After the Second World War, steel and aluminium poles were also tried. Glass-fibre composites were first used in the late 1950’s and by 1961 the world record was broken with a composite pole with multiple composite sheet layers to achieve the optimum properties (figure 1). Since then there has been a rapid improvement in heights achieved and it is clear that the performance improvements directly follow from materials improvements and design changes (figure 2). However the more recent availability of carbon-fibre composite poles has not had such a significant effect. The techniques of vaulting have changed too and the flexibility of composite poles has been utilised to great effect by athletes as they swing into the jump then rock back while the pole flexes so that they approach the bar feet first. This maximises the athlete’s ability to use energy effectively and achieve the greatest possible return for their kinetic energy and muscle power. UD Fibre Filament wound core Plain Weave Twill Fig. 1. The filament wound structure of a vaulting pole (Jenkins, 2002) Bamboo Glass fibre composites Solid wood Fig. 2. Change in Olympic record heights over last 100 years and associated vaulting pole material changes. REQUIREMENTS FOR A VAULTING POLE The International Association of Athletics Federations rules state that ‘The pole may be of any material or combination of materials and of any length or diameter…….’ (IAAF, 2003). The key requirements are length, stiffness and the appropriate design or selection for each individual athlete. The versatility of fibre-composites makes all of these more easily variable through changes in design and manufacture. Length Several studies have considered the length and stiffness of the pole and found that there is an optimum value of both which maximises performance. Ekevad and Lundberg (1997) modelled the effects of pole length and stiffness on energy conversion from kinetic energy to potential energy during the vault by finite element analysis. They found that there was an optimum length that allowed sufficient polebend and time for the vaulter to rock back and rotate appropriately. Relatively short and stiff poles were found to straighten almost completely and the vault height could be limited by the pole-length. However, longer poles, when bent completely, may not be able to provide sufficient force to lift the vaulter to the optimum height. Stiffness Pole flexibility and the ability to tailor the properties of fibre-composite poles to required values are key advantages. Linthorne (2000) found that whereas for a rigid pole, the vaulter’s trajectory is always concave to the planted pole-end, for a flexible pole the trajectory changes from convex through take-off and maximum pole bend, to concave from pole release to peak height. The stiffness of the pole and its ability to bend both have an effect on the changes in energy through the vault (Schade et al 2000). The total energy of the vaulter decreases from a high point at take-off, when kinetic energy is high, to a minimum at the time of maximum pole bend as this energy is stored as potential energy in the elastically-strained pole. This energy is returned to the vaulter as the pole unbends – first as kinetic and finally as potential energy. Ekevad and Lundberg (1997) found that as with pole length there was an optimum stiffness value for effective vaulting. Equality between the weight of the vaulter and the Euler buckling load gives the minimum pole stiffness. A pole with too low a stiffness straightens incompletely and the vaulter does not achieve a great height. A pole which is too stiff straightens too quickly and the vaulter reaches peak height too early. Burgess (1996) further optimised the design by considering a tapered pole with greater thickness in the middle where the stresses are greater than at the ends. An appropriate combination of pole length and pole stiffness, optimised for the individual athlete is required. Biomechanics and individual selection of poles For the same pole geometry a heavier vaulter will require a stiffer pole to achieve the same height. Also an individual athlete may use different poles at different stages in a competition. Most elite vaulters will specify a certain length, ‘flex rating’ (ie pole stiffness) and possibly mandrel size for winding the composite layers (Gill Athletics, 2003). VAULTING POLE CHARACTERISTICS Introduction Glass-fibre composites are light and stiff and have a much greater failure strain than that of bamboo (Haake, 2000). Carbon fibre-composites generally have a higher stiffness and this can be a limitation since the vaulter has less time to swing and rotate before the pole unbends. Carbon fibre laminae also have a higher strength and a typical laminate of carbon fibres in epoxy at 50 % volume fraction would have a strength of 1000 MPa compared with 700 MPa for a similar laminate of polyester and glass fibres (Harris, 1999) Most vaulters still use glass-fibre poles and considerable experience is necessary to use carbon-fibre poles. Published information on materials and manufacture indicates multiple layers for bending and torsional stiffness (figure 1) but there is less detail available on the number and thickness of the layers. Pre-bend Vaulting poles often have a ‘pre-bend’ to aid the athlete by making it easier to ‘plant’ the pole and bend it initially. A ‘pre-bend’ is where the vaulting pole is not straight but has a permanent curvature that is introduced during pole manufacture, for example by allowing the pole to bend the prescribed amount by self weight during the curing process. It should be noted that for these poles the stiffness around the circumference is constant, as will be discussed below. For glass fibre reinforced polymer (GFRP) composite poles the pre-bend has been found to be 20 – 30 mm. The athletes need to ensure that the vaulting pole is orientated correctly when planted at the beginning of the vault otherwise torsional stresses will be introduced in the pole as it twists to the preferred bending position. A vaulting pole with a significant pre-bend will naturally orientate itself when the athlete rests the tip of the pole on the ground. Vaulting poles without a pre-bend may be designed to have variable stiffness around its circumference, i.e. the pole having a ‘soft’ and ‘stiff’ side, with the athletes having to orientate the pole with the ‘soft’ side facing them at the plant to aid bending of the pole during the vault. For these poles the athlete needs to orientate the pole using a mark on the side of the pole; incorrect orientation may cause injury because of twisting of the pole during the vault. Stiffness The stiffness of a vaulting pole will affect the ease with which the athlete can bend it during a vault. The stiffness of a pole is related to the stiffness of the material it is made from (the material’s modulus of elasticity, E) and its shape (diameter and wall thickness). The relative stiffness of a pole is displayed as a ‘weight rating’, which the athlete should not exceed. The weight rating is calculated by the manufacturers and is related to how much the pole bends when loaded in the centre with a 50lb (22.3 kg) mass. The method of testing may vary between manufacturers (e.g. free or constrained support of pole ends, length of free span etc.). For GFRP vaulting poles the material’s modulus of elasticity will be related to the volume fraction, and orientation, of the fibres (silica glass E ≈ 76 GPa) compared with the epoxy resin (E = 4 – 5 GPa). It was found that for GFRP vaulting poles of the same length (4.2 m), outside diameter (32 mm) and wall thickness (2 mm) the bending stiffness ranged from approximately 900 Nm-1 to 1100 Nm-1 with the mass of the poles ranging from approximately 1.64 kg to 1.76 kg respectively. The increase in density, and consequently bending stiffness, reflects an increase in the volume fraction of glass fibres (density 2.65 Mg m-3) compared with epoxy resin (1.2 Mg m-3), rather than a change in fibre orientation to change the stiffness. A change in fibre orientation, for example to be more parallel to the pole axis in order to increase bending stiffness, would also reduce the torsional stiffness of the pole, which is not desired. For a predominantly carbon fibre reinforced polymer (CFRP) vaulting pole labelled as having a ‘soft’ side it was found that the bending stiffness varied between approximately 835 Nm-1, for the soft side, to 900 Nm-1 when tested in the other orientation. It is possible to change the bending stiffness by altering the volume fraction and / or the fibre orientation around the circumference of the vaulting pole. For this pole it was found that the difference in bending stiffness was achieved by changing the wall thickness of the pole, with the ‘soft’ side having a wall thickness of 1.75 mm, over 90o around the circumference, compared with an average wall thickness of 2.25 mm over the remaining 270o. The use of CFRP rather than GFRP allows the vaulting pole mass to be reduced due to the higher modulus of elasticity of carbon fibres (235 GPa) compared with glass fibres (76 GPa). Microstructure The microstructure of the GFRP vaulting poles, figure 3, showed the existence of several distinct composite layers. An inner ply, approximately 200 µm thick, was observed around the entire circumference of the pole. The majority of the pole crosssection was comprised of bundles of fibres, embedded in the polymer resin matrix, separated by thin, approximately 10 – 20 µm, plies. In total for the GFRP composite vaulting poles examined there were five regions of fibre bundles separated by the thin plies, only two of which are clearly visible in figure 3. For the CFRP vaulting pole the ‘soft’ side was observed to have three layers of fibre bundles, whereas the ‘stiffer’ side had five layers of fibre bundles and more separating plies. Additionally the CFRP pole had both inner and outer plies (with fibres oriented at 80-85o for the inner ply but at approximately 25o for the outer and separating plies). Closer inspection of the microstructure, figure 4, revealed approximately 300 fibres in each bundle. Image analysis showed the fibres in the bundles to be orientated at approximately 45o to the pole length, whilst the fibres in the inner ply and the plies separating the bundles were at angles of approximately 80-85o to the pole length, i.e. they run almost perpendicular to the pole length. Fibres at an angle of 45o provide bending stiffness and torsional stiffness, both requirements for the vaulting pole. The fibres at 80-85o provide hoop stiffness and also act as crack arrestors. For example in figure 4, a crack can be observed in the microstructure running from the outer surface of the pole through two fibre bundles then stopping on reaching a ply with fibres running around the circumference of the pole. The majority of the vaulting poles are manufactured by filament winding where the fibres, and fibre bundles, are wound onto a mandrel in the various orientations required. The fibres / fibre bundles are pre-coated by pulling them through a bath of resin. Resin Inner ply Fibre bundle 200µm Ply Fig.3. Optical micrograph of a transverse section through a GFRP vaulting pole showing the different composite layers. Individual fibres 50µm Fig. 4. Optical micrograph showing individual glass fibres in the fibre bundles During the vault the pole bends most in the middle part of its length, thus to ensure sufficient strength (to avoid fracture) in this region additional composite plies could be used (Burgess 1996). At the ends of the poles, where less strength is required, fewer plies could be used, thereby reducing the overall weight of the pole. This can be achieved by using a ‘sail piece’, a trapezoidal pre-preg composite sheet that is wrapped around the mandrel resulting in an increased number of composite layers in the middle section of the pole. Failures During vaulting poles can fail catastrophically by fracture of the pole, usually half way along the pole during the swing phase where the bending stresses are greatest. Fracture of the pole can result in injuries to the athlete, as well as a failed attempt at clearing the bar, and should therefore be avoided. Cracks can exist in the composite from manufacturing (fibre damage; incomplete curing causing delamination), or can occur in service (by fatigue). The fracture surface from a GFRP pole that failed during use is shown in figure 5. The crack runs through the fibre bundle (right hand side of image) with little fibre pull out and brittle (flat) fracture of the fibres. When the crack reaches the ply with fibres at 80 – 85o the fibres generally remain intact with the crack running between them, having to deviate in path. Fig. 5. SEM image of the fracture surface from a broken GFRP vaulting pole. CONCLUSIONS The design of vaulting poles requires not only a knowledge of mechanics, biomechanics and the characteristics of the individual athlete but also of materials properties and manufacturing conditions. Modern glass and carbon fibre vaulting poles are complex structures in which the multiple layers and components provide flexibility and energy storage whilst ensuring bending and torsional stiffness. Fibre bundles and the relative orientation of the layers not only give stiffness and strength but they can help arrest incipient failures. Future designs utilising the manufacturing flexibility available with fibre composites will further enhance performance. ACKNOWLEDGEMENTS We would like to thank Amy Cleeton and Blake Rayner for their help with this work. REFERENCES Burgess, S (1996) The Engineering of Sport 83, ed S Haake (Balkema, Rotterdam). Ekevad, M and Lundberg, B (1997), Journal of Biomechanics, 30 (3), 259. Gill Athletics, private communication, 2003. Haake, SJ (2000), Physics World, September 2000. Harris, B (1999), Engineering Composite Materials, 2nd ed, IoM. IAAF Competitition Rule 183 (2003), Int Assoc of Athletics Federations, Dec 2003. Jenkins, MJ (2002), Interdisciplinary Science Reviews, 27 (1), 61. Linthorne, NP (2000), Sports Engineering, 3, 205. Schade, F, Arampatzis, A and Bruggemann, G, (2000), Journal of Biomechanics, 33, 1263.
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