Mechanics of pole vaulting: a review Julien Frère a ; Maxime L'Hermette a ; Jean Slawinski b ; Claire Tourny-Chollet a a

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1 This article was downloaded by: [Frère, Julien] On: 12 July 2010 Access details: Access Details: [subscription number ] Publisher Routledge Informa Ltd Registered in England and Wales Registered Number: Registered office: Mortimer House, Mortimer Street, London W1T 3JH, UK Sports Biomechanics Publication details, including instructions for authors and subscription information: Mechanics of pole vaulting: a review Julien Frère a ; Maxime L'Hermette a ; Jean Slawinski b ; Claire Tourny-Chollet a a CETAPS, Faculty of Sport Sciences, University of Rouen, Mont Saint Aignan Cedex, France b Scientific Department of Team Lagardère, Research Center for Expertise, Evaluation and Programming, Paris, France Online publication date: 12 July 2010 To cite this Article Frère, Julien, L'Hermette, Maxime, Slawinski, Jean and Tourny-Chollet, Claire(2010) 'Mechanics of pole vaulting: a review', Sports Biomechanics, 9: 2, To link to this Article: DOI: / URL: PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

2 Sports Biomechanics June 2010; 9(2): Mechanics of pole vaulting: a review JULIEN FRÈRE 1, MAXIME L HERMETTE 1, JEAN SLAWINSKI 2,& CLAIRE TOURNY-CHOLLET 1 1 CETAPS, Faculty of Sport Sciences, University of Rouen, Mont Saint Aignan Cedex, France, and 2 Research Center for Expertise, Evaluation and Programming, Scientific Department of Team Lagardère, Paris, France (Received 19 June 2009; revised 7 May 2010; accepted 7 May 2010) Abstract A good understanding of the mechanics of pole vaulting is fundamental to performance because this event is quite complex, with several factors occurring in sequence and/or in parallel. These factors mainly concern the velocities of the vaulter-pole system, the kinetic and potential energy of the vaulter and the strain energy stored in the pole, the force and torque applied by the athlete, and the pole design. Although the pole vault literature is vast, encompassing several fields such as medicine, sports sciences, mechanics, mathematics, and physics, the studies agree that pole vault performance is basically influenced by the energy exchange between the vaulter and pole. Ideally, as the athlete clears the crossbar, the vaulter mechanical energy must be composed of high potential energy and low kinetic energy, guaranteeing the high vertical component of the vault. Moreover, the force and torque applied by the vaulter influences this energy exchange and these factors thus must be taken into consideration in the analysis of performance. This review presents the variables that influence pole vault performance during the run-up, take-off, pole support, and free flight phases. Keywords: Kinematics, kinetics, performance, mechanical energy, joint torque Introduction The aim of pole vaulting is to jump over a crossbar with the help of a long pole. The rules of the International Association of Athletics Federations (IAAF, 2006) state that The pole may be of any material or combination of materials and of any length or diameter.... Consequently, the poles used for vaulting have changed considerably throughout the twentieth century, explaining the sharp increase in the world record from 3.15 m in 1849 to the present world record of 6.14 m, set in 1994 by Sergey Bubka. The improvement in height was most significant when fibreglass poles, along with landing mats, were introduced in The mean progression in the world record became 3.97 cm per year with the introduction of fibreglass poles, whereas it had previously been 1.63 cm per year (Anderson, 1997). Vault performance with a fibreglass pole generated a great deal of research, including university theses (Dillman, 1966; Barlow, 1973; Gros, 1982; McGinnis, 1984), scientific publications (Steben, 1970; Hubbard, 1980b; McGinnis and Bergman, 1986; McGinnis, Correspondence: Julien Frère, CETAPS, Faculty of Sport Sciences, University of Rouen, Boulevard Siegfried, Mont Saint Aignan Cedex, France. julien.frere@univ-rouen.fr ISSN print/issn online q 2010 Taylor & Francis DOI: /

3 124 J. Frère et al. 1987; Angulo-Kinzler et al., 1994), and project reports and books (Ganslen, 1961; Gros and Kunkel, 1990; Arampatzis et al., 1999), in order to provide a complete analysis of this sport for researchers, coaches, and athletes. The early studies of the pole vault can be distinguished by method: experimental or simulation. The first method had the advantage of measuring actual vault data but was limited by the invasiveness of the research materials and the evaluation of vault performances in a competitive context. The aim of the second method was to model and predict performance but the complexity of the pole vault imposed limits on the conclusions that could be drawn. Several models sought to decompose the event, leading to discrepancies concerning the performance factors (Vaslin and Cid, 1993). Although the quantity of scientific data about pole vaulting mechanics continues to grow with the ongoing development of technologies, such as computer, motion analysis software or force plates, the pole vault has been the subject of only one literature review, which classified the obvious, dubious, and other factors of performance (Vaslin and Cid, 1993). This review proposed no model of the pole vault and, since its publication, knowledge in the field has grown considerably. Thus, the goals of the present review were to compile and update the mechanical data on pole vaulting through the presentation of a new model that incorporates all its phases and to highlight the performance factors in each phase within kinematics, energies, and kinetics processes. How to model the pole vault? Classically, coaches have divided the pole vault into seven stages: (i) run-up, (ii) transition with arm elevation in the last three steps, (iii) take-off including the pole plant, (iv) swing phase, (v) rock-back, (vi) inversion position, and (vii) bar clearance. However, this movement cut-out has differed among authors and according to the mechanical approach. Hay modelled the pole vault with a four-height division of the final vault height: H 1 is the height of the vaulter s centre of gravity (CG v ) at take-off, H 2 is the height of the CG v when the pole is straightened, H 3 is the height of the CG v when the vaulter releases the pole, and H 4 is the vertical difference between the peak height of the CG v and the height of the crossbar (Hay, 1980). This model was useful for identifying some of the basic performance factors which influence these partials heights, such as the morphology and position of the vaulter s body for H 1, the vertical velocity at pole release for H 3, and the vaulter s body position in the free flight phase for H 4. Also, the partial height H 2 could be influenced by the pole length and amount of potential energy transferred to the vaulter by the pole at pole release. However, this model was limited in the analysis of kinematic variables, such as the vaulter s horizontal and vertical velocities and the pole bending rate. The biomechanical analysis of the 1992 Olympic finals for the men s pole vault (Angulo- Kinzler et al., 1994) divided the vault into four phases and defined instants of interest (events) within each phase. The first phase was the run-up, including the touchdown (TD) and take-off (TO) of every support. The second phase was the take-off, which included the last touchdown (TD1), the pole plant (PP), and the last take-off (TO1). The third phase was the pole support with maximum pole bend (MPB), pole straight (PS), and pole release (PR). The last phase was the free flight phase from PR to bar clearance, including the peak height (HP) of CG v. This division was useful for analysing the many mechanical variables of the vault, which was limited with Hay s model. Nevertheless, it remained impossible to evaluate the pole-athlete interaction during the vault or to analyse its influence on performance. More recently, the vault was modelled using an energetic approach that included the interaction between the pole and the vaulter (Schade et al., 2000; Arampatzis et al., 2004).

4 Mechanics of pole vaulting 125 The energy calculation of this model was based on the vaulter s limb motion and CG v, which allowed the computation of the athlete s external work but not the internal work of the individual muscles. Despite this limitation, two criteria were defined to evaluate the athlete s behaviour during the vault and to determine patterns in pole vaulting, for example, and malesfemales (Schade, Arampatzis, Brüggemann et al., 2004). The vault phase was divided into two segments: the first began at TD1 and ended at MPB. During this segment, the vaulter s kinetic energy is transferred to the pole and stored as strain energy. The second segment began at MPB and ended at HP. Here, the strain energy of the pole is delivered up to the vaulter as potential energy. This last model concerned strictly energetic processes during the vault phase and did not analyse the vaulter s action before planting the pole, that is, the running phase. A new model can now be proposed that further elucidates the pole vault event and takes into account the energy exchange between the athlete and the pole. This model is based on previous studies (Angulo-Kinzler et al., 1994; Arampatzis et al., 2004) and divides the pole vault into four phases, each containing relevant instants (Figure 1):. The run-up phase corresponds to the run-up and includes the TD and TO of every support of the approach except the last stance. During this phase, the vaulter s aim is to gradually increase kinetic energy by increasing horizontal velocity.. The take-off phase includes TD1, PP, and TO1. Any pole vault model needs to specify this phase for two reasons. First, the last stance finishes the run-up and is the longest stance with a high vertical component (McGinnis, 1987; Angulo-Kinzler et al., 1994). Second, the vaulter s kinetic energy begins to be transferred to the pole, which is already planted in the take-off box. Consequently, the take-off phase is a real transition between the run-up and the flying part of the vault.. The pole bending phase, from TO1 to MPB, is characterised by the energy transfer from the vaulter to the pole. During this phase, the vaulter s mechanical energy is transferred to the pole as strain energy. Figure 1. Pole vault model. (1) Run-up phase; (2) Take-off phase, including the last touchdown (TD1), the pole plant (PP) and the last take-off (TO1); (3) Pole bending phase until maximum pole bending (MPB); (4) Pole straightening phase, including pole straight (PS); pole release (PR); and peak height of the CG v (HP).

5 126 J. Frère et al.. The pole straightening phase, from MPB to HP and including PS and PR, is the vaulter s restitution of energy from the pole. During this phase, the strain energy of the pole is transferred to the vaulter as potential energy, permitting the maximum elevation of the CG v. Except for the run-up phase, which presents only few scientific data, the kinematic (velocities), energy, and kinetic (forces and torques) analysis of each phase of this new model provides a good understanding to improving pole vault performance. The run-up phase The aim of this section is to present the fundamental principles of the run-up and to discuss the effects of carrying a pole on sprint coordination. However, few data can be found in the scientific literature. The role of the arm swing and impact of pole carriage The relationship between the CG v horizontal velocity and jump performance has been the subject of a great deal of research in order to simulate or predict final performance. Correlation coefficients between approach run velocities and crossbar height were significant for men (r ¼ 0.69) (Adamczewski and Perlt, 1997) as well as for women (r ¼ 0.77) (McGinnis, 2004). Thus regression analyses could serve as standard to predict the future performance, but it could also indicate technical improvement over the years, while the approach velocities remained almost the same, the men and women vaulters managed to improve final performance (Adamczewski and Perlt, 1997; McGinnis, 2004). However, the vaulter s horizontal velocity cannot be as high as in free running for two reasons: (i) pole carriage and (ii) the crucial need for accuracy in positioning the take-off foot (Angulo-Kinzler et al., 1994). The first reason seems to contribute more to the loss of horizontal velocity. A decrease of 0.8 to 1.2 m/s in horizontal velocity was observed for elite pole vaulters compared with a free run-up (Gros and Kunkel, 1990). This difference represented 7.5% to 11% of the two horizontal velocities (with and without a pole, respectively). However, other studies determined that this loss corresponded to 0.5 m/s, that is, a difference of 4.5% between the two conditions of run-up (Linthorne, 1994, 2000). Also, the restricted arm swing causes a loss in horizontal velocity by a decrease in the shoulder rotations around the longitudinal axis. This decrease in shoulder rotations affects the coordination of the legs and the pelvic rotations, thus leading to a loss of speed (Novacheck, 1998). If loading the arm by means of additional weight induces a loss of speed (Ropret et al., 1998), carrying a pole would have a similar effect because of the pole weight. More than the effective weight of the pole (up to 3 kg), the relative weight of the pole has a major effect on the decrease in velocity. The relative pole weight should be understood as an increasing gravitational torque developed by a pole carried in front of the athlete and moving from a vertical to a horizontal position. This change in the pole position causes a forward shift in the centre of gravity of the athlete-pole system in front of the foot ground contact and leads to less time to recover the swing leg in order to accelerate the foot before ground contact (Frère et al., 2009). Consequently, pole carriage is the major cause of the loss of horizontal velocity, rather than the need for accuracy in positioning the take-off foot. The restricted swing of both arms causes a less efficient run. Only one study dealt with the influences of carrying a pole on run-up coordination (Frère et al., 2009). This is surprising because knowledge about the run-up with a pole has

6 Mechanics of pole vaulting 127 a direct impact on training programmes and consequently on the possibility to increase performance by improving the run-up. The authors determined that the loss in horizontal velocity was due to significantly smaller stride length associated with significantly reduced maximum hip and knee flexion during the swing phase. According to running biomechanics, stride length is under the influence of hip and knee flexion-extension at toe-off and the end of the swing phase (Schache et al., 1999). Moreover, in the stance phase, it appeared that the braking phase was significantly longer when the athlete was carrying the pole (Frère et al., 2007, 2009). This was in accordance with the results of biomechanical reviews on running, which concluded that the faster the athlete ran, the shorter the stance and braking phases were (Vaughan, 1984; Williams, 1985; Mero et al., 1992; Novacheck, 1998; Schache et al., 1999). Consequently, improving the run-up in pole vault requires a training programme based on a large range of exercises with pole carriage, including sprinting, jumping, and hopping on one foot. All these exercises would have the same goal: to improve sprint velocity with this specific running pattern and strengthen posture with a pole in the hands. The take-off phase The take-off phase is defined as the last support, between TD1 and TO1, and includes PP (Figure 1). Planting the pole in the take-off box creates a shock between the ground and the vaulter-pole system. Velocity Horizontal velocity is lost in the take-off phase. As in the long jump, a re-orientation of the CG v trajectory occurs during the last stance, with a higher vertical component to allow the following jump. It was shown that take-off velocity decreased with an increase in the take-off angle (Linthorne, 2000; Linthorne et al., 2005), when take-off velocity referred to the resultant velocity of the CG v as the vaulter left the ground. The vaulter had a take-off velocity directed at an angle f to the horizontal, where f refers to the take-off angle. Moreover, the shock generated at PP also decreases the horizontal velocity. The Olympic gold medallists in 1988 (Gros and Kunkel, 1990) and 1992 (Angulo-Kinzler et al., 1994) respectively cleared 5.90 m and 5.80 m, and both showed a loss in CG v horizontal velocity of about 2 m/s between the penultimate TO and TO1 (from 9.86 to 7.90 m/s and 9.74 to 7.74 m/s, respectively). Another study (McGinnis, 1987) reported a 2 m/s decrease in horizontal velocity from the analysis of 16 vaults in the range of 5.50 to 5.81 m, whereas the analysis of three elite French pole vaulters clearing 5.50 m indicated a loss in resultant CG v velocity from 0.9 to 1.8 m/s between TD1 and TO1 (Durey, 1997). The estimation of the optimal take-off angle with flexible vaulting poles was reported to be 188 (Linthorne, 2000), meaning that (i) the vaulter should favour a forward directed take-off to minimise loss in CG v horizontal velocity and (ii) the initiation of pole bending markedly slows down the vaulter (Durey, 1997; Morlier, 1999). Energy At take-off, the amount of mechanical energy in the vaulter-pole system is influenced by the vaulter s initial kinetic energy and the behaviour during interaction with the pole (Hubbard, 1980b; Gros and Kunkel, 1990; Ekevad and Lundberg, 1995; 1997; Arampatzis et al., 1999; 2004). During the take-off, the CG v horizontal velocity is higher than the vertical velocity.

7 128 J. Frère et al. Given that the amount of kinetic energy is reflected by the vaulter s CG v horizontal velocity, the vaulter s kinetic energy decreases during the take-off. The vaulter s mechanical energy decreases because of the decrease in the kinetic energy (Schade, Arampatzis, Brüggemann et al., 2004). Between TD1 and TO1, the loss in kinetic energy is reflected at two levels: (i) in the lower limbs with the increasing vertical component of the last support and (ii) in the trunk and upper limbs with the pole plant and initial bending of the pole (Angulo-Kinzler et al., 1994; Linthorne, 2000; Schade, Arampatzis, Brüggemann et al., 2004). The initial pole bending reveals the interaction between an active vaulter and a passive pole, with the transfer of the vaulter s kinetic energy to strain energy within the pole. Mathematical models of the pole vault take-off demonstrated that a certain amount of kinetic energy was dissipated as heat in the vaulter s body using a rigid pole (Linthorne, 1994) and a flexible pole (Linthorne, 2000). The first model gave results close to vaulting performance with rigid poles (bamboo or steel). In contrast, when the perfectly rigid rod was replaced by an elastica pole in this model, thereby simulating pole vault performance with a flexible pole, realistic results were not generated because of the lack of an energy dissipation mechanism. The model gave a maximum vault height of 7.70 m with an optimum take-off angle of 08 (Linthorne, 2000). The model was thus revised to include a mechanism of energy dissipation in the athletepole system, where only the athlete s body is subjected to energy dissipation by taking into account the vaulter s actions during the take-off phase. The vaulter was modelled by a heavily damped linear spring, which was characterised by stiffness: the constant k (in N/m). The author of this model assumed that the value of k reflected the level of resistance in the vaulter s arms and torso (Linthorne, 2000), but he suggested that a multi-segment model of the vaulter would make the model more accurate. Also, the model was based only on energy dissipation in the athlete s body, whereas it was shown that 6 10% of the energy transferred to the pole is lost during the interaction between athlete and pole (Arampatzis et al., 2004; Schade et al., 2006). This energy loss was probably due to the viscoelastic properties of the pole and to friction between the take-off box and the pole. A more accurate version of Linthorne s model would thus need to take into account this energy loss from the pole, the non-uniform stiffness of the pole along its length, and a pole pre-bend (Burgess, 1998; Davis and Kukureka, 2004; Moore and Hubbard, 2004; Morlier et al., 2008). However, from this energy dissipation model highlighted principles for improving vault performance such as, the heavier the vaulter is, the lower the energy dissipation is, the higher the stiffness of the pole and more parallel to the pole the take-off angle are, the higher the energy dissipation is. Finally, with regard to the energy processes observed in mechanical and simulation studies, the vaulter has to (i) produce a high amount of kinetic energy just prior to the take-off phase in order to compensate for its inevitable decrease and (ii) be able to develop high muscular strength in the shoulders, arms, and trunk to limit energy dissipation in the body and store more strain energy in the pole. Force and torque The elastic capacities of the flexible poles (fibreglass or carbon) allow the vaulter to store strain energy in the pole. With this type of pole, it is possible to keep a greater distance between the two hands than with rigid poles (steel), which allows for easier control of pole bending by the application of force perpendicular to the longitudinal axis of the pole and

8 Mechanics of pole vaulting 129 Figure 2. Hand location and components of hand forces at TO1 with (a) a steel or bamboo pole and (b) a flexible pole. in opposite directions (Figure 2). Indeed, the upper hand exerts forward and downward resultant force, whereas the lower hand applies forward and upward resultant force (Hay, 1980; Dapena and Braff, 1983; Angulo-Kinzler et al., 1994; Morlier, 1999; Morlier and Mesnard, 2007). Hubbard modelled the flexible pole as a large slender rod and used large deflection theory to calculate pole deformation as a function of the force and moment applied by the vaulter (Hubbard, 1980a, 1980b). His model determined that the reaction force of the pole (F p, in N), was linearly related to its shortening chord, when there was no applied moment and in considering the stiffness of the pole (the Euler buckling load) and its chord shortening. In beam mechanics, the Euler buckling load is defined as the critical compressive load limit that will never be overstepped. If the applied compressive load is higher than the Euler buckling load, the beam will have an irreversible buckling or will be broken. In case of vaulting pole, the definition of Euler buckling load is confusing within the literature. From Ekevad and Lundberg (1997), a simply supported straight pole model was computed in considering that the Euler buckling load was equal to the weight of the vaulter. In such a case, this definition indicated the minimum stiffness of the pole which was able to straighten entirely under the weight of the vaulter. Also this definition was in the way of the model proposed by Hubbard (1980a, 1980b), where the compressive load must be higher than the Euler buckling load to flex the pole. On the contrary, Burgess (1998) mentioned that the flexible pole is not in case of buckling instability due to its elastic properties and that the pole could not be fully collapsed. That is why the compressive load allowing the flexion of the pole is under the critical Euler buckling load. In addition, the vaulter applied a bending moment with the lower grip hand around the upper grip hand to initiate the pole deflection at the beginning of the vault. Moreover, in the case of over-bending the pole, the vaulter jumps over the plane of the crossbar before the pole straightens (Ekevad and Lundberg, 1997). Hubbard (1980a, 1980b) and Dapena and Braff (1983) demonstrated that the resultant ground reaction force (GRF) of the pole decreased when a bending moment was applied to the top end of the pole in addition to compressive force, especially for low percentages of pole deflection. For instance, when pole deflection was under 10% with a moment of 250 N m, the resultant GRF was decreased by 28% (Hubbard, 1980b). This finding explained that a greater distance between the hands induced opposite resultant forces from each hand and thus increased the torque to bend the pole, which is fixed by the tip in the take-off box (Dapena and Braff, 1983). The wider the distance between both hands was, the lower the GRF of the pole was. This result indicated the significant advantage of using flexible poles compared with rigid poles, which allow only a small distance between the hands.

9 130 J. Frère et al. This decrease in the GRF allowed the vaulter to use a higher upper hand grip without increasing the take-off angle, thus preserving high kinetic energy during the take-off phase (Linthorne, 1994, 2000). A recent study developed a 3-D calculation model of the torque action applied to the pole by vaulters at a point mid-way between the two hands (Morlier and Mesnard, 2007). The vaulters were digitised into 14 articulated rigid solids and mechanical joints for the calculation of the torque (ultimately materialised by the CG v ) on the pole (the mid-point between the hands). During take-off, the vaulters applied force mainly on the vertical and horizontal axis as well as a bending moment around the transverse axis. In such a way, the vaulters attempted to resist the GRF of the pole by applying a vertical and a horizontal force of about 1000 and 1500 N, respectively, and a high positive moment ranging from 200 to 1800 N m between TD1 and TO1 (Morlier and Mesnard, 2007). These efforts increased the angle between the pole and the horizontal axis, which favoured the initial bending of the pole and consequently increased its accumulated strain energy. Thus, during the take-off phase, the studies showed that the applied torque on the pole has a major importance compared to the compressive force. The pole vaulter has two aims during take-off: (i) to resist the GRF of the pole by increasing the time of the last support (TD1 to TO1) and (ii) to increase the angle between the pole and the horizontal axis (Morlier, 1999; Morlier and Mesnard, 2007). The demonstration of this double aim highlighted the predominant role of the shoulder muscles at take-off (Frère et al., 2008). At take-off, the vaulter has high horizontal velocity and a great elevation of the dominant arm, and begins to resist the load from the pole. This combination of factors is such that the vaulter is subjected to high loads that may lead to injuries like rotator cuff tendonitis, shoulder instability, low back pain or spondylolysis (Gainor et al., 1983; Beattie, 1992; Bird et al., 1997; Brukner et al., 2004) when the take-off is not executed with accuracy. Accuracy refers to the placement of the last support relative to the upper hand. The elevation of the dominant arm increases the pole-ground angle and the push action of the non-dominant arm applies torque to the pole in order the initiate bending. However, another pole vault take-off model should be mention in this review. This model is widely used by coaches and corresponds to the Russian free take-off, mastered by Sergey Bubka and developed by his coach Vitaly Petrov. There is a free take-off when PP coincides with the TO1 (Petrov, 2008). This take-off way has advantages such as, higher pole-ground angle at PP, greater horizontal velocity and impulse at the take-off allowing the use of longer and stiffer poles (Launder and Linthorne, 1990). Nevertheless, the free take-off implies the vaulter to be able to produce high muscular strength with the upper-limbs, because of the risk to be backward leaned. Moreover, the free take-off doesn t allow applying some force and moment on the pole while the athlete is still on the ground. Even if the free take-off appears to be relevant for high pole vaulting performance, there is some lack of published scientific research and the free take-off only concerned technical articles and coaches knowledge. Indeed, it would be interesting for further scientific and mechanic studies to analyse the effects of the free take-off on the pole vaulting performance, the pole vaulter s velocities, and the applied force into the pole and to compare it with the classical take-off. The pole bending and pole straightening phases The pole bending and pole straightening phases of the pole vault model described in this review includes the pole support phase and the free flight phase. Although pole bending can be clearly differentiated from pole straightening because of the energetic processes specific to each phase, it is important to focus on obtaining a better understanding of the event rather

10 Mechanics of pole vaulting 131 than strictly following the model. The following sections thus describe the events from TO1 to HP of the CG v. Velocity Experimental studies (Gros and Kunkel, 1990; Angulo-Kinzler et al., 1994; Morlier, 1999) showed a smooth decrease in the horizontal velocity from TO1 to PS, whereas the vertical velocity increased (Figure 3). In the pole bending phase, the horizontal velocity was greater than the vertical velocity and the inverse characterised the pole straightening phase. Ideally, the time at which the two velocities are identical corresponds to MPB. Before MPB, the vaulter s body is in forward motion in relationship to the bending pole and, after MPB, the vaulter is in upward motion from the straightening pole. Measurements of the angular velocity of the pole chord during the vault confirmed these forward and upward motions (Angulo-Kinzler et al., 1994). The vaulter reaches maximal vertical velocity at PS and HP occurs when this velocity is null. The greater the vertical velocity at PS is, the greater this velocity will be at PR, and the higher H 3 (Hay, 1980) will be, allowing a high elevation of the CG v during the free flight phase. For instance, at the 1992 Olympic finals in Barcelona (Angulo-Kinzler et al., 1994), the gold medallist had a vertical velocity of 1.81 m/s at PR, whereas the velocity of the 7 th -ranked vaulter was 1.12 m/s (HP ¼ 5.91 and 5.74 m, respectively). Consequently, irrespective of the grip height, the Olympic champion benefited from a CG v elevation 11 cm higher than the 7 th between PR and HP. Thus, in addition to the grip height, this higher free flight phase offers the possibility to increase the final performance. After its peak at PS, the vertical velocity of CG v decreases until the end of the vault (Figure 3). This relationship demonstrates that the vaulter loses vertical velocity from PS to HP, despite the final push-off. The maximal vertical velocity should thus be considered as a performance factor because the final height could be determined by the vertical velocity at PS and could estimate the influence of the vaulter s final push-off on the performance. Figure 3. Typical curves of horizontal (dashed line) and vertical (solid line) velocities of the CG v during the pole vault. Data from Gros and Kunkel (1990), Angulo-Kinzler et al. (1994), and Morlier (1999).

11 132 J. Frère et al. At TO1, the vaulter initiates the vault with high horizontal velocity, which progressively decreases until MPB and then stabilises until the end of the vault. The maintained horizontal velocity ranged from 1.5 to 2 m/s and permitted the vaulter to safely clear the cross bar (Gros and Kunkel, 1990; Angulo-Kinzler et al., 1994; Morlier, 1999). Energy The fundamental principle of pole vaulting is the interaction between vaulter and pole to transfer kinetic energy to potential energy through the strain energy of the pole (Dillman and Nelson, 1968; Hay, 1971; Schade et al., 2000; Sheehan, 2002; Arampatzis et al., 2004; Schade, Arampatzis, and Brüggemann, 2004; Schade, Arampatzis, Brüggemann et al., 2004; Schade, 2006; Schade et al., 2006; Schade and Brüggemann, 2006). The maximum height of CG v was found to be significantly correlated with the vaulter s maximal mechanical energy at HP, both for men (r ¼ 0.88, p, 0.01) and women (r ¼ 0.86, p, 0.01) (Schade, Arampatzis, Brüggemann et al., 2004). The energetic patterns were calculated as follows (Dillman and Nelson, 1968; Morlier, 1999; Schade et al., 2000; Schade, Arampatzis, Brüggemann et al., 2004; Schade et al., 2006): As the pole bending phase began, the vaulter s mechanical energy decreased caused by the reduction in kinetic energy, which attained the minimum after MPB. Next, the mechanical energy increased until PS, due to the constant increase in the vaulter s potential energy from TO1 to HP (Figure 4). The energetic interaction between the vaulter and pole during a vault was analysed and performance criteria were then developed (Arampatzis et al., 2004). It was found that vaulters benefited from pole flexibility during the pole bending phase. The strain energy stored in the pole was calculated by the relationship between the GRF measured in the planting box with the pole deformation summed with the relationship between the bending moment at the top end of the pole with the location of both vaulter s hand relative to the pole chord. This study also pointed out that the amount of total energy transferred to the pole was greater than the decrease in the vaulter s mechanical energy (Figure 4). This additional energy came from muscular work (Arampatzis et al., 2004). However, no detail was given about the muscular work of each limb relative to the total muscular work allowing this Figure 4. Typical curves of kinetic energy (black line), potential energy (grey line), and mechanical energy (dashed lined) of the athlete and total strain energy of the pole (dotted line) during the pole vault. Data from Dillman and Nelson (1968), Gros and Kunkel (1990), Morlier (1999), Arampatzis et al. (2004), and Schade et al. (2006).

12 Mechanics of pole vaulting 133 increase of energy of the vaulter/pole system. Further calculations (e.g. inverse dynamics) should be made or another approach (e.g. electromyography) could be considered to complete the muscular contribution into pole-vaulting performance. A similar process was reported during the giant swing before dismounts and flight elements on the high-bar in acrobatic gymnastics (Arampatzis and Brüggemann, 1998, 1999). An energetic interaction between the gymnast and the high-bar occurs, with the greatest mechanical power and torques achieved by the shoulder joint (about 2500 watts and 500 N m, respectively). The best values were observed when the gymnast began the ascending phase of the giant swing. These similarities with the pole vault allow us to hypothesise that the shoulder joint and muscles provide similar work to add energy to the pole. After MPB, the strain energy of the pole is transferred to the vaulter as potential energy. The pole energy decreases until PS, whereas the mechanical energy of the vaulter increases until PR because of the increase in potential energy (Schade et al., 2000; Arampatzis et al., 2004; Schade, Arampatzis, Brüggemann et al., 2004; Schade et al., 2006). Moreover, the increase in the vaulter s mechanical energy is greater than the decrease in the pole strain energy. Consequently, the flexible pole appears to provide an efficient tool for the transfer of pole strain energy to the vaulter s potential energy. However, this transfer was found to be efficient only if the vaulter effectuated muscular work, principally at the shoulders, during the pole bending and restitution phases (Arampatzis et al., 1997, 1999). Despite the different methods of energy calculation, the results and conclusions of this experimental study (Arampatzis et al., 2004) agreed with those of a previous simulation study (Hubbard, 1980b) that found (i) greater final mechanical energy than the vaulter s initial energy and (ii) greater work (in Joules) performed by the shoulder joint rather than the wrist and hip joints. Force and torque Even though the vaulter had left the ground, he could apply some forces and torques on the pole. These actions allowed the vaulter to increase the bending of the pole and to push on the pole before PR. Measured results and modelled findings all agreed that these post-take-off actions of the vaulter increased the final pole vault performance. The strain elastic energy stored in the pole was calculated from the compressive force and the bending moment of the athlete on the pole which represented about 75 and 25% of the pole energy, respectively (Arampatzis et al., 2004). First, the horizontal component of the GRF was larger than the vertical one, indicating pole compression that was more forward than upward at the beginning of the vault (Figure 5, until 0.2 s). The vertical component was then higher than the horizontal one until the end of the vault, indicating that the vaulter-pole interaction was principally in the vertical direction. The vertical GRF before and after MPB followed a bell-like curve and was explained by the vaulter s downward compression on the pole and by the pole s upward extension, respectively. The comparison of the vertical force applied to the pole by vaulters with several performance levels allowed to observe differences in time and maximal vertical force, which ranged from 1000 to 1350 N and was explained by technical differences between the pole vaulters. The best pole vaulter produced greater vertical force in a shorter time (Morlier and Mesnard, 2007). A cinematographic study revealed a significant correlation between the degree of extension of the elbow of the lower arm and the final performance (Steben, 1970). This elbow extension allowed applying forward and upward resultant force and creates a support, which permits the bending moment around the upper hand. A 2-D inverse dynamic analysis of the pole vault (McGinnis and Bergman, 1986) was in agreement with this previous kinematic finding.

13 134 J. Frère et al. Figure 5. (a) Direction and magnitude of the resultant GRF at the take-off box during a pole vault; (b) Approximation of the vertical (y, black line), horizontal (x, grey line), and resultant Fp (dashed line) GRF at the take-off box during the pole vault. Data from Arampatzis et al. (2004), Morlier and Mesnard (2007), and Schade et al. (2006). The inverse dynamic analysis computed different torques during the pole support phase of the vault including the moment produced on the top of the pole and the resultant shoulder joint moment. After TO1, the moment produced on the top of the pole ranged from 100 to 250 N m with a mean duration of 0.2 s and corresponded to the early stage of the swing of the pole vaulter. Simultaneously, a shoulder flexion moment increased up to a mean peak value of 89.8 N m and represented the activity of the shoulder flexor muscles. Then, a long period

14 Mechanics of pole vaulting 135 of activity of the shoulder extensor muscles occurred with a high shoulder extension moment reaching a mean peak value of N m. According to this 2-D analysis, a 3-D inverse dynamic study of the pole vault (Morlier and Mesnard, 2007) determined that the maximal global moment applied on the pole ranged from 210 to 410 N m and occurred during the bending of the pole and when the athlete swung to attain the rock-back position before MPB. Through the measurements of the applied moments, it was possible to (i) identify the swing to rock-back position as a relevant performance factor and (ii) demonstrate that the action of the shoulder joint muscles was of major importance. These inverse dynamic measurements about the moments applied by the vaulter on the pole and joints moments were all in agreement with a previous simulation study using a three segments model of the vaulter (Hubbard, 1980b). Indeed, this simulation highlighted that without the pole-buckling moment at the top of the pole just after TO1, the vaulter model was not able to attain the plane of the crossbar. Also, it appeared that the values of moment around the top of the pole were higher than those at the shoulder joint which were higher than those at the hip joint. Again, the inverse dynamic findings (McGinnis and Bergman, 1986) served as limit to impose maximum moments of 600, 500, 300, and 130 N m around the top of the pole and at the shoulders, hips, and knee, respectively, to a smart pole vaulter model (Ekevad and Lundberg, 1995) in order to manage a vault as real as possible. Simulation studies have also emphasised the role of the vaulter s muscular actions in pole vaulting relative to pole stiffness and length (Ekevad and Lundberg, 1995, 1997). By modelling a smart pole vaulter, that is, an active pole vaulter, with six segments and five pin joints, the authors demonstrated that the performance ratio (maximum vaulter s potential energy divided by the initial kinetic energy of both vaulter and pole) was clearly higher for a smart pole vaulter than a passive (materialised as a point) vaulter. Also, the pole characteristics for the smart pole vaulter appeared to be inferior to those of a passive athlete. This meant that an active pole vaulter that is, who performed muscular work produced a more efficient vault and had a higher vault than a passive with the same pole. Finally, the analysis of the vaulter s angular momentum confirmed that the swing to rockback position was a performance factor. The angular momentum around the transverse axis was higher than those around the two other axes (Morlier and Cid, 1996) and the maximal values were reached before MPB. This pattern highlighted that the pole vaulter carries out muscular work to bend the pole more and thus store more strain energy (Gros, 1982; Gros and Kunkel, 1990; Angulo-Kinzler et al., 1994; Arampatzis et al., 2004; Schade, Arampatzis, Brüggemann et al., 2004). Conclusion and implications This review of the literature on the mechanics of pole vaulting points up the major performance factors. Although athletes produce forces, velocities, and energies during the run-up and take-off phases of classic jumps (e.g. long jump or high jump), in the pole vault they can also influence the trajectory after take-off by exerting force and torque on the pole and storing strain energy in the pole. Flexible poles have many advantages compared with rigid poles, including a smaller optimal take-off angle, which permits the maintenance of high horizontal velocity at take-off, and a greater distance between the hands, which facilitates pole bending by increasing the moment applied on the pole. The torques applied by the vaulter on the pole have a direct influence on final performance because they can increase the bend and thus increase the strain energy stored in the pole.

15 136 J. Frère et al. During the run-up, the leg muscles are more important than the arm muscles, conversely to the pole support phase, whereas the take-off requires a high activation of both arm and leg muscles for the double contact with the ground, one with the pole planted in the take-off box and the other with the take-off foot. All the interactions between the vaulter and the pole require strength production, especially from the shoulder and trunk muscles. During pole bending, the upper body muscles are most activated to produce this strength so that the vaulter can transfer energy into the pole and then benefit from the pole s elastic properties to clear the crossbar. However, the activity of the shoulder and trunk muscles requires further study to determine their role in the strength applied on the pole and in the energy production relative to the final pole vaulting performance. There is much work to be done in this area and efforts are needed to improve our knowledge about the effects of force production, especially from the shoulder muscles, on pole vault performance. Acknowledgements No sources of funding were used to assist in the preparation of this review. The authors have no conflicts of interest that are directly relevant to the content of this review. The authors are grateful to Catherine Carmeni for help in writing the English manuscript. References Adamczewski, H., and Perlt, B. (1997). Run-up velocity of female and male pole vaulting and some technical aspects of women s pole vault. New Studies in Athletics, 12, Anderson, G. K. (1997). The limits of human performance in the pole vault. Track Coach, 138, , Angulo-Kinzler, R. M., Kinzler, S. B., Balius, X., Turro, C., Caubet, J. M., Escoda, J., et al. (1994). Biomechanical analysis of the pole vault event. Journal of Applied Biomechanics, 10, Arampatzis, A., and Brüggemann, G.-P. (1998). A mathematical high bar-human body model for analysing and interpreting mechanical-energetic processes on the high bar. Journal of Biomechanics, 31, Arampatzis, A., and Brüggemann, G.-P. (1999). Mechanical energetic processes during the giant swing exercise before dismounts and flight elements on the high bar and the uneven parallel bars. Journal of Biomechanics, 32, Arampatzis, A., Schade, F., and Brüggemann, G.-P. (1997). Pole vault. In H. Müller, and H. Hommel (Eds.), Biomechanical Research Project at the 6th World Championships in Athletics, Athens 1997: Preliminary Report (Vol. 12, pp ). Monaco: New Studies in Athletics. Arampatzis, A., Schade, F., and Brüggemann, G.-P. (1999). Pole vault. In G.-P. Brüggemann, D. Koszewski, and H. Müller (Eds.), Biomechanical Research Project at the VIth World Championships in Athletics, Athens 1997: Final report (pp ). Oxford: Meyer & Meyer Sport. Arampatzis, A., Schade, F., and Brüggemann, G.-P. (2004). Effect of the pole-human body interaction on pole vaulting performance. Journal of Biomechanics, 37, Barlow, D. A. (1973). Kinematic and kinetic factors involved in pole vaulting. (Unpublished PhD thesis, Indiana University, Indiana) Beattie, P. (1992). The use of an eclectic approach for the treatment of low back pain: A case study. Physical Therapy, 72, Bird, S., Black, N., and Newton, P. (1997). Sports injuries. Cheltenham, UK: Stanley Thornes. Brukner, P., Khan, K., and Kron, J. (2004). The encyclopedia of exercise, sport and health. Sydney: Allen & Unwin. Burgess, S. C. (1998). The modern Olympic vaulting pole. Materials and Design, 19, Dapena, J., and Braff, T. (1983). Use of separate hand location to calculate ground reaction force exerted on a vaulting pole. Medicine & Science in Sports & Exercise, 15, Davis, C. L., and Kukureka, S. N. (2004). Effect of materials and manufacturing on the bending stiffness of vaulting poles. In M. Hubbard, R. D. Mehta, and J. M. Pallis (Eds.), The engineering of sport 5 (Vol. 2, pp ). Winfield, KS: Central Plain Books Manufacturing. Dillman, C. J. (1966). Energy transformations during the pole vault with a fiberglass pole. (Unpublished Master s thesis, Pennsylvania State University, Pennsylvania)

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