Introduction
Linear sprinting is an important action in match deciding events of field-based sports such as soccer. However, time-motion studies in soccer reveal that not all sprints are linear (Caldbeck, 2019; Fitzpatrick et al., 2019) and that many are curvilinear with varying radii (Brice et al., 2004). Whilst far less research has been conducted on curvilinear sprinting compared to linear, many studies mainly from an athletics track perspective reveal that curvilinear sprint running evokes biomechanical asymmetries between limbs outside of that typically observed between limbs whilst running at maximal linear running speed (Alt et al., 2015; Churchill et al., 2015; 2016). These biomechanical asymmetries present ramifications for physical and technical development to best prepare athletes for curvilinear sprint demands in sport. This blog highlights the importance of curvilinear sprint running for multidirectional speed athletes and examines the biomechanical characteristics of curvilinear sprint running and the implications for field- and gym-based drill/ exercise prescription.
The Importance of Curvilinear Sprint Running
Linear running speed is no doubt an essential quality regarding expressions of agility in sport. Indeed, data in male soccer highlights that sprint (or linear advancing motions) are the most common actions by an attacker preceding a goal (Faude et al., 2012; Martinez et al., 2022; Martinez et al., 2023) and sprint capacity is typically a discriminating factor in playing levels across numerous sports (Gabbett et al., 2008; Dobbin et al., 2019; Thomas et al., 2016). However, it is also important to recognise that particularly in the case of field-based sports such as soccer and American football, many sprints are not directly linear. Caldbeck (2019) in an analysis of maximum velocity sprinting in EPL soccer, found that 85% of sprints are curvilinear. Similarly, based on time-motion analysis on 10 EPL matches, Caldbeck & Dos’Santos (2022) found 86% (78 ± 13) of actualisation phase (the key movements that ultimately decide the degree of success of the movement, be these key sporting actions or a moving to a position as quickly as possible [Caldbeck, 2023]) sprint efforts were curvilinear. Further, sprint activities in soccer have been shown to be rarely linear (Fitzpatrick et al., 2019) and may vary from 3.5 to 11 m in radii (Brice et al., 2004), suggesting that whilst the ability to sprint is no doubt important, the ability to modify technique and maintain speed whilst running along a curvilinear path is perhaps even more important. This curvilinear sprint ability is otherwise known as manoeuvrability.
“Manoeuvrability is the ability to maintain velocity during a change of direction that does not involve a clear ”plant” step (i.e., a curvilinear path of movement or ‘arc’ run) or the ability to perform or change mode of travel to and from ‘transitional’ movements (i.e., side shuffle or back pedal)”
DeWeese & Nimphius, 2016; Jones & Nimphius, 2018
Mechanical Basis of Curvilinear Sprinting
Figure 1 is a deterministic model for sprint running performance and shows that the time to complete any sprint is dependent on average speed, with average speed dependent on the interaction between step length and step frequency. Step length can be broken down into touchdown, flight, and take-off distances, whereas as step frequency is the reciprocal of step time which is broken down into stance and flight times. Both flight distance and time are influenced by take-off parameters: height of the centre of mass, angle and speed at take-off of each foot contact. The latter two are influenced by the vertical and horizontal velocities achieved at the point of take-off, which fundamentally are dependent on the net vertical and horizontal impulses (force × time) generated during ground contact (impulse-momentum relationship). Figure 1 can be applied to different phases of a sprint, however, each phase is characterised by differing locomotion mechanics (e.g., acceleration phases involve greater forward lean with triple lower limb extension behind the centre of mass, whereas maximum velocity running is characterised by a more upright trunk position). Essentially, during acceleration there is greater focus on generating net horizontal impulse (increasing propulsive impulse, whilst minimising braking impulse) rather than vertical impulse (Hunter et al., 2005; Kawamori et al., 2013; Morin et al., 2015), thus, the direction of force orientation is critical here. Throughout acceleration, applying force more horizontally as a ratio of the total force applied, which has also recently been termed mechanical effectiveness (Morin et al., 2011; Morin et al., 2012; Rabita et al., 2015). As a sprint progresses to maximum velocity and the runner becomes more upright it becomes difficult to increase net horizontal impulse further (0 acceleration), and thus, the emphasis in on vertical force and impulse generation to maintain an optimal flight phase (Weyand et al., 2000).
The challenge with curvilinear or ‘bend sprinting’ as known in athletic circles is that the athlete is required to evoke a directional change with each footfall as the athlete progresses around the bend (the athlete can only cause a directional change whilst in contact with the ground). Thus, the athlete needs to generate centripetal force toward the centre of curvature of the bend (Figure 2). To do this the athlete with each footfall needs to place the leg lateral to the centre of mass, as force and impulse are 3-dimensional vector quantities, and thus, to cause a resultant change in momentum along the curved path then impulse needs to be generated medially towards the centre of curvature (Figure 2). Centripetal force (F) is calculated as the following:
m × v2/ r
Where m = athlete or objects mass, v = velocity of the athlete or object and r = the radius of the curvilinear path.
Thus, the centripetal force required is greater the faster the athlete is travelling around the bend and/ or the shorter the radius of the curvilinear path of the athlete. This added requirement with each footfall with curvilinear sprinting causes asymmetrical biomechanical differences between the inside and outside leg (beyond typical side to side variation you may see with athletes running maximally in a straight line) and with the limbs during linear sprinting (Figure 2). The following section provides an overview of these biomechanical differences.
Biomechanical Characteristics of Curvilinear Sprinting
As might be expected, most of the research into curvilinear sprint running focuses on athletics track sprinters who regularly compete in 200 m races, thus, running anticlockwise (left leg acts as the inside leg, right leg acts as the outside) with radii of curvature ≥36.5 m equal to lane 1 of a standard 400 m running track. Most of the research in this context tends to focus on maximum velocity sprinting after approximately 40 m of running. Whilst this may not be reminiscent of curvilinear sprint demands of field sports like soccer whereby radii might vary from 3.5 to 11 m (Brice et al., 2004) and involve running in a clockwise rather than just anti clockwise direction. Nevertheless, this literature provides a basis to understand the biomechanical demands of curvilinear running.
Curvilinear sprint running is characterised by greater lean into the curve to place the foot laterally in the frontal plane relative the centre of mass to generate centripetal force with each footfall to evoke a directional change along the curvilinear path (Figure 3). This task requirement leads to alterations in step characteristics between inside and outside limbs, for instance, during maximum or near maximum (>90%) velocity sprinting (after 40m of running) inside step length is longer than outside, but step frequency is greater for the outside limb leading to similar velocities with either limb (Churchill et al., 2015; Churchill et al., 2016). The lower step frequency of the inside limb is a result of longer ground contact times as flight time tends to be unchanged from linear sprint running (Alt et al., 2015; Churchill et al., 2015), whereas flight time is shorter outside limb (Churchill et al., 2015; Churchill et al., 2016). The inside limb experiences lower vertical and resultant ground reactions forces compared to linear sprint running and the outside limb, owing to the need to generate greater inwardly directed forces to evoke the directional change with each footfall (Smith et al., 2006; Churchill et al., 2016). As a result, greater centre of mass rotation for the inside compared to the outside limb is evident (Churchill et al., 2015; Churchill et al., 2019) highlighting the importance of the inside limb in travelling along a curvilinear path. Although, Ishimura & Sakurai (2016) in an analysis of sprinters with a greater radii 43.51 m found the opposite owing to greater estimated centripetal forces. The inside limb also experiences greater braking impulse and duration during ground contact (Churchill et al., 2016), which is perhaps related to the greater touchdown distance observed in male sprint athletes (Churchill et al., 2015; Ishimura & Sakurai, 2016).
The prolonged ground contact of the inside leg also exhibits increased ankle eversion, hip adduction and hip external rotation than the outside limb and straight running (Alt et al., 2015), whereas the outside limb tends to involve more hip abduction (Churchill et al., 2016) and external ankle rotation and knee internal rotation (Alt et al., 2015). Furthermore, these kinematic adaptations seem to occur early within the acceleration phase (Churchill et al., 2020a). Greater ‘whole-body’ lean is evident at touchdown for the right outside limb compared to inside limb (Churchill et al., 2015). Greater thigh separation at touchdown, hip extension and hip flexion are evident for the inside limb (Churchill et al., 2015). Another significant biomechanical difference between the inside limb and the outside limb is that the lean into the bend may lead to the inside foot using the oblique foot axis, rather than the transverse foot axis for the right limb, which may lead to compromised propulsion for the left limb (Churchill et al., 2016). Indeed, Judson et al., (2019) during analysis of the acceleration phase in male sprinters found that left (inside) step medio-lateral centre of pressure position was more lateral relative to the 2nd metatarsal head compared to straight running, thus, using the oblique foot axis rather than the transverse foot axis to push off. The authors found this coincided with compromised antero‐posterior force and propulsive impulse and an increase in peak eversion of the midfoot and ankle for the inside limb (Judson et al., 2019).
The differing joint kinematics associated with the inside and outside leg understandably results in neuromuscular and joint load differences between limbs. Early research (Smith et al., 1997) reported temporal muscle activity adaptations (from linear motion) in the gluteus maximus, medial and lateral gastrocnemius, tibialis anterior, peroneus brevis and tensor fascia latae of soccer players whilst jogging (4.4 m∙s-1) and running (5.4 m∙s-1) for both legs along curved paths of 5, 10 and 15 m radii; highlighting that muscles involved with multiplanar control of the ankle and hip adapt activity during curvilinear motion. Filter et al., (2020b) found that curvilinear sprinting (radius 9.5 m) in soccer players resulted in greater adductor and semitendinosus activation for the inside leg and biceps femoris and glute medius activation outside leg suggesting muscles of the inside leg adduct and internally rotate the hip, whereas the outside leg abduct and rotate the hip to support the differing mechanical requirements. Furthermore, it appears that curved sprinting results in increased peak left hip adduction moments and greater metatarsal phalangeal joint plantar flexor moments left and right steps and greater ankle plantar flexor and eversion moments in left vs. straight (Judson et al., 2020). The changes in frontal plane kinematics and consequently moments experienced during curved sprinting highlights the need to perform curvilinear sprint running in training to enable the athlete/ player to experience the larger lateral forces evoked by curvilinear running.
Less research has been conducted on curvilinear sprinting during the acceleration phase. Judson et al. (2019) examined mid-acceleration (10-17 m) phase sprint running in 9 male sprinters (200m < 23.5 s) and as with maximum velocity sprinting the inside limb experienced more prolonged ground contact times compared to straight sprinting and the outside limb of bend sprinting. Mediolateral force was found to be greater during ‘bend’ sprinting than straight from 3 to 96% of stance to help maintain curvilinear motion, but this led to lower ratio of forces (a measure of force orientation relative to total force [horizontal force/ resultant force]) for the inside and outside leg. Mediolateral force during bend sprinting was greater in the right step compared to the left during 1%‐12% of the stance phase, whereas later in stance (75%‐100%), mediolateral force was greater in the left step than right, thus further establishing the left foot as fulfilling a different role to the right foot during bend sprinting (Judson et al., 2019). Therefore, it appears that to negotiate the ‘bend’ the ability to apply force and the orientation of force is a limiting factor for acceleration due to the need to generate medio-lateral force and likely relate to the use of the oblique rather than transverse metatarsal phalangeal joint axis noted above (Judson et al., 2019). Figure 4 summarises the biomechanical differences between inside and outside limb during curvilinear sprinting and compared to linear sprint running.
“Exposing the athlete to curvilinear sprint running of differing radii is essential to prepare athletes in multidirectional sports to experience the differing force, loading demands and differing technical adjustments required to run efficiently along a range curvilinear paths.”
paul jones
Effects of Differing Radii
As might be expected, reducing the radii of curvature during sprint running reduces sprinting velocity (Churchill et al., 2019; Chang & Kram, 2007). Churchill et al., (2019) in a comparison of male sprinters running in lane 8, 5 and 2 of a standard 400 m running track (radii: 45.10, 41.41 and 37.72 m, respectively) found significantly more turning was achieved with the left (inside) leg compared to right in all lanes, but more right turning occurred in lanes 5 and 2 of shorter radii than in lane 8. Furthermore, more body lateral lean (both limbs) was used when radii reduced (greater lean right step than left) and greater ground contact times were experienced with the inside leg which increased with lower radii. However, it does appear that much shorter radii of curvature alters force production characteristics between limbs. For instance, Chang and Kram (2007) examined differences in a low sample of 5 recreational males between straight running and running with radii of curvature of 1, 2, 4 and 6 m. As expected, the inside leg produced lower vertical ground reaction force and peak propulsive forces, however, braking forces were lower with reduced radii and higher on the outside leg (unlike sprint running with greater radii >36.5 m). Furthermore, the outside leg produced greater lateral forces compared to inside, similar across each radii and again differs to studies with greater radii (>36.5 m). In support of these observations, Smith et al., (2006) examining curvilinear sprint running in 6 male soccer players on natural turf with a radii of 5 m and different running intensities and again found lower total forces in curved vs. straight sprinting. However, again in curved motion, all vertical force measures were greater for outside leg, with anterior–posterior forces showing the outside leg provided greater propulsion forces and impulse with less braking. Moreover, medially directed forces (average and peak) and impulse were greater outside leg vs. inside leg which were both greater than straight running unlike previous literature with greater radii (>36.5 m) (Churchill et al., 2016; Judson et al., 2019), suggesting that the outside limb may play a major role to generate forces required to change direction along curved paths of shorter radii. It is likely that to run along paths of such short radii athletes may use a strategy akin to repeated ‘crossover’ and ‘side-step’ cuts for the inside and outside leg respectively, as suggested by Rand and Ohstuki (2000). Therefore, what is clear is that exposing the athlete to curvilinear sprint running of differing radii is essential to prepare athletes in multidirectional sports to experience the differing force, loading demands and differing technical adjustments required to run efficiently along a range curvilinear paths.
Methods to Evaluate Curvilinear Speed
Although, curvilinear sprint performance is commonly associated with some track events (e.g., 200 and 400 m running), tests of such qualities are infrequently carried out in the literature particularly for multidirectional speed athletes. Filter et al. (2020a) developed a curvilinear sprint test for football, that used the D of the penalty area of a football pitch. Players were required to sprint in both a clockwise and anticlockwise manner around the D of the penalty area – a known length of 17 m and a radius of 9.15 m, with timing cells at the start and end of the D and at the mid-point (8.5 m). The authors reported acceptable reliability for each variable reported (ICC = 0.75 – 0.96; Typical error = 0.03 – 0.06 s; CV = 0.5 – 1.97%). Interestingly, the authors reported low association between a linear 17 m sprint test and curvilinear sprints in either direction (R2= 0.35-0.37), suggesting that the curvilinear sprints are assessing different qualities to a linear sprint test. This offers avenues for performance testing in soccer to evaluate curvilinear sprint ability alongside linear sprint ability. Given the Pearson’s correlation between linear and curvilinear sprint performance could be viewed as large (R = 0.59 – 0.6), does suggest that curvilinear sprint performance maybe influenced by linear running speed. Thus, like the change of direction deficit subtracting a linear sprint time from a curvilinear sprint time to reveal a curvilinear sprint or manoeuvrability deficit may also provide a more isolated measure of one’s ability to adapt technique and perform a curvilinear sprint. Further research is required to adapt such protocols with other sports where curvilinear sprint ability is a prerequisite for performance and may require a multitude of different length and radii to be assessed to provide a curvilinear speed profile for an athlete in a specific field-based sport.
Implications for Training
The asymmetrical running patters, in particular the changes in frontal plane kinematics and consequently moments experienced during curved sprinting, presents implications for both field and gym-based training. It is recommended that curvilinear sprints should be integrated into training to enable the athlete/ player to experience the larger lateral forces evoked by curvilinear running. Sprint drills should be of diversified radii to enable athletes to effectively make technical adjustments associated with varying radii and experience the frontal and transverse plane loads associated with curvilinear running. Sprints should also be performed clockwise and anticlockwise to ensure players are equally adept at curvilinear sprinting in differing directions and avoid the development of asymmetries. Figure 6 presents potential curvilinear drills that could be performed. Additionally, athletes should potentially perform strength and plyometric exercises in ‘leaning’ positions (Churchill et al., 2016; Elstub & Churchill, 2023). Using a jammer bar maybe one way to enable this in a gym environment by performing landmine single leg squat and single leg Romanian deadlift with inside and outside leg (Figure 7), lateral step ups and lateral sled pulls, whereas variations of lateral bound and crossover hops (Figure 8) could be used to evoke the multiplanar loading requirements of ‘bend’ sprinting. Finally, given the large eversion loads and energy absorption experienced in the inside limb during ‘bend’ running (Judson et al., 2020) then exercises targeting the tibialis posterior and tibialis anterior (Figure 9), along with intrinsic foot muscles such as abductor hallucis and flexor digitorum Brevis could influence curved sprint performance and support injury mitigation. Use of minimalist footwear (Elstub & Churchill, 2023) could be one way to target the intrinsic foot muscles along with isometric exercises such as short foot exercise, toe spread out exercise and tower curl (toe flexor exercise) (see Tourillon et al, 2019).
Summary
Whilst linear sprinting ability is important in many field-based sports, time-motion studies in soccer reveal that many sprints are curvilinear with varying radii. Whilst far less research has been conducted on curvilinear sprinting compared to linear, many studies mainly from an athletics track perspective reveal that curvilinear sprint running evokes biomechanical asymmetries between limbs outside of that typically observed between limbs whilst running along a straight path. The inside limb involves greater ground contact times, lower force production (vertical, resultant, and horizontal), greater ankle eversion and hip adduction and use of the oblique metatarsal phalangeal joint axis compared to the outside limb and straight running, whereas the outside limb involves more hip abduction. These biomechanical asymmetries present ramifications for physical and technical development to best prepare athletes for curvilinear sprint demands in sport, with suggestions provided within this blog. For more in-depth discussions regarding linear and curvilinear sprinting see Elstub & Churchill (2023) and Wild & Goodwin (2023) in Multidirectional Speed in Sport: Research to Application by Routledge.
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