In recent years, the force-velocity-power (FVP) profiling method has gained prominence within the sports performance industry, establishing itself as a popular diagnostic tool for evaluating sprinting ability. This method aims to evaluate critical indicators of performance during the acceleration phase of a sprint, emphasizing the application of horizontal force within specified time constraints (Hunter et al., 2005; Morin et al., 2015, 2011). The growing interest in sprint FVP profiling within the sports performance literature may primarily be attributed to its ability to uncover mechanical insights that may have previously only been accessible in a cost- and labour-intensive lab setting, thus contributing to our continued pursuit of the ‘lab-to-field’ concept (Verheul et al., 2020).
Conceptual frameworks are now in place for the individualisation of training through sprint FVP profiles, offering insights into tailored physical, biomechanical and technical training recommendations for optimising performance (Hicks et al., 2023, 2020; Morin and Samozino, 2016). However, the utility of this method has recently received criticism (Bobbert et al., 2023; Ettema, 2023; Jon Goodwin & Dan Cleather, 2023). Ettema (2023) contends that the FVP profiling concept for sprint running may be a “dead end,” raising concerns over the logic underpinning the method and questioning its effectiveness. Other work has also shed light on the FVP profile for jumping, emphasising the importance of understanding what it is and, perhaps more importantly, what it is not (Bobbert et al., 2023). As such, this next post is one of a series that reviews the FVP profiling method, discussing the FVP concept from a mechanical perspective and reflecting on the recent concerns proposed by authors and leading biomechanists. Crucially, though, this series will aim to not leave practitioners scratching their heads, thinking, ‘where do we go from here?’. Instead, we will present alternative, practical approaches that can still present as a step forwards in our evaluation of sprinting performance.
How to Establish an Athlete’s Sprint Force-Velocity-Power Profile
Developing a sprint FVP profile typically involves conducting maximal sprints over distances of 20–40 metres. Split times (e.g., 0–10 m, 10–20 m, and 20–40 m) are recorded using timing devices, such as photocells, or with systems that capture instantaneous velocity-time or position-time data, such as high-speed cameras, optical lasers, portable motorised resistance training devices, or global positioning systems. The recorded velocity-time or position-time data is then analysed to determine the athlete’s step-averaged kinematics (Hicks et al., 2023).
Using the fundamental principles of dynamics in the horizontal plane, FVP profiling quantifies the net horizontal antero-posterior ground reaction force acting on the whole-body centre of mass over time. To establish an athlete’s horizontal sprint profile, required measurements include body mass, height, and displacement-time running data. Additionally, accounting for air friction requires knowledge of wind speed, air temperature, and barometric pressure. The comprehensive FVP profile is then computed by modelling the derivative of the velocity-time curve, resulting in modelled horizontal acceleration data (J.B. Morin et al., 2019; Samozino, Rabita, Dorel, Slawinski, Peyrot, Saez de Villarreal, et al., 2016). Linear force-velocity and polynomial power-velocity relationships can subsequently be derived from this data (see Figure 1). Although a variety of metrics can be determined via this approach, the ‘headline’ variables commonly used are provided in Table 1 below.
Links with Performance and Injury Risk
Importantly, the outputted metrics of interest have been shown to differentiate among sports, age groups, genders, playing positions, and performance levels (Cross et al., 2015; Delaney et al., 2018; Haugen et al., 2019; Watkins et al., 2021). A plethora of research has now investigated the associations of the aforementioned variables derived from FV profiling and linear sprinting performance (Buchheit et al., 2014; Escobar-Álvarez et al., 2020; Lahti et al., 2020; Marcote-Pequeño et al., 2018; Morin et al., 2012; Rabita et al., 2015). Strong correlations have been identified between the FVP sprint variables F0 (r = -0.89), V0 (r = -0.87) and PMAX (r = -1.00) with 10-meter sprint times, whereas SFV and DRF have demonstrated stronger relationships to 40-meter sprint times (Haugen et al., 2019). These mechanical variables have also shown to differentiate between elite sprint performers (Stavridis and Paradisis, 2019). In an analysis of world-class athletes, FVP profiles for both male and female sprinters showed strong negative linear relationships between F0 (r = -0.66), V0 (r = -0.78), PMAX (r = -0.87), and 100-meter sprint times (Stavridis and Paradisis, 2019).
The correlations among mechanical variables have been found to shift across the velocity-time curve as sprint distances increase (Buchheit et al., 2014; Escobar-Álvarez Juan Antonio AND Fuentes-García, 2020; Marcote-Pequeño et al., 2018; Nicholson et al., 2021). For example, athletes who demonstrated more force-dominant mechanical profiles (higher F0) were linked to faster sprint times in segments under 20 meters (Nicholson et al., 2021). Conversely, athletes with velocity-oriented profiles (V0), alongside demonstrating the ability to limit the decrement in mechanical effectiveness with increasing speeds (i.e., DRF), exhibited stronger correlations with sprint times in segments exceeding 20 meters (Nicholson et al., 2021). With that said, the SFV and PMAX variables appear to be a performance indicator of both short and long-distance sprints because their computations are based on F0 and V0.
Interestingly, a significant body of literature is now emerging that demonstrates the role that sprint mechanical variables can have in identifying sprint-related injury risk. Of particular interest is the F0 variable, where prospective cohort studies now support the potential relevance of including frequent F0 evaluation for hamstring muscle strain injury risk management (Edouard et al., 2021; Lahti et al., 2022). Additionally, studies have noted a distinct reduction in FH0, without alterations in V0, upon return to football post-hamstring strain injury (Mendiguchia et al., 2016, 2014). The documented F0 decrease may also be consistent with reported reductions in hamstring muscle strength post-injury (Maniar et al., 2016; Tol et al., 2014). It has been suggested that this decrease in F0 may stem from compromised hamstring muscle function, impeding efficient force production during sprinting, particularly during the early acceleration phase (Edouard et al., 2021).
Clearly, these new approaches are opening up avenues that are allowing us to have a deeper understanding of applied sprint analysis than ever before, and the empirical basis for these pursuits is growing in concert. However, before chasing this goal and evolving our practise, we may need to take a step back and truly understand the methods that underpin these new insights. Therefore, the next section we will aim to unpick the mechanical constructs that underpin the FVP to try and determine what is relevant and, perhaps, what is not.
Power: A Meaningless Metric to Look at During Sprinting?
It has been proposed that the FVP slope (SFV), established through the axis intercepts of each variable (F0/V0), elucidates the linear force-velocity relationship, serving as indicators for coaches to determine whether a greater emphasis on ‘high-velocity’ actions or ‘force-based’ strength training should be prioritised during preparation periods (Hicks et al., 2023, 2020; Morin and Samozino, 2016). It has been proposed that there is an ‘optimal’ SFV value, that is, a F0/V0 ratio, for a given PMAX, that leads to the best sprinting performance for different distances. A deviation from this optimal SFV is called a ‘force–velocity imbalance’, which can be used to inform individualised training modification to optimise SHFV, and thus, sprinting performance.
A premise of this approach, therefore, relies on using power output as the key performance indicator for sprinting performance. However, Dan Cleather explains the common misconceptions when interpreting power in their most recent book (Cleather & Goodwin, 2023). Indeed, power is often defined as the product of force and velocity. Yet this definition can cause confusion and make people think that sprinting requires high power output, which is not entirely true. A common error is to assume that because sprinting involves fast movement and high force production, power output must also be high. The mistake in this assumption is to compare horizontal velocity with vertical force. Power is a scalar quantity and thus lacks directionality, so ‘horizontal power’ is actually a misleading term. However, evaluating the power formula requires aligning its constituent components belonging to the same vectors (i.e., horizontal force and velocity).
An alternative way of demonstrating the power output of a given activity is to determine the rate of which work is done, with work being the product of force and displacement in the direction of force application, which is divided by time to calculate power. Sprinting involves both positive and negative work that is contributed to by the direction and magnitude of the ground reaction force and the COM displacement. During acceleration, the work done is at its highest in the first few steps, as the sprinter applies a large propulsive force and increases the horizontal velocity of the COM. However, as the sprinter approaches maximum velocity, the work done actually decreases. Although power is scalar, as above, the vector components that calculate it (i.e., force and displacement) still need to be compared like with like. As such, due to the shift in orientation during upright sprinting, vertical force production is at its highest, yet vertical COM displacement per unit of time is minimal. Conversely, during maximum velocity, while horizontal displacement is at its highest, and by definition, horizontal velocity at its peak, braking and propulsive forces largely cancel each other out, resulting in net minimal horizontal force, and thus, a lower amount of mechanical work. Therefore, power output during sprinting is relatively low, despite the high speeds and resultant forces apparent during sprinting.
What may further confuse things is that the FVP approach aims to calculate power through the force and velocity derived from the exponential curve of the horizontal displacement-time characteristic during the linear sprint (Figure 1a). Therefore, information is ascertained from step-averaged data captured in the horizontal plane, while the vertical components are mostly assumptions (Samozino et al., 2016). This may lead to further confusion when interpreting where ‘peak power’ actually occurs during a linear sprint. As demonstrated in Figure 2, peak instantaneous power derived from GRF data is identified towards the end of the sprint (around 3-4s) (Chelly and Denis, 2001). In contrast, step-averaged ‘horizontal’ power typically occurs around the 0.5-1.5s mark of a FVP (Figure 1b), which begs the question as to how tangible power output, derived from step-averaged horizontal velocity data, is as a metric to base sprint training recommendations on.
As has just been alluded to, another important aspect to consider in this approach is that the FVP curves generated represent smoothed average values of the COM horizontal movement. However, due to the alternation of ground contact and flight during sprinting, instantaneous velocity and acceleration fluctuate around a smoothed ‘net averaged’ line (Figure 1a). This distinction is crucial, as these smoothed curves might lead to the misinterpretation that sprinting at higher speeds involves lower forces than during initial acceleration (Figure 1c). Therefore, if there is any oversight of the fact that this profile is derived from horizontal displacement data, it could be easy for one to assume that an athlete who is ‘velocity-dominant’ (i.e., high V0 or a ‘flatter’ SFV slope) demonstrates low force production capabilities, which is likely not the case, and can lead to suboptimal conditioning strategies. The vertical component of GRF generation is particularly significant in distinguishing linear sprinting ability (Bellon et al., 2019; Clark and Weyand, 2014; Weyand et al., 2000) and instantaneous GRF data is crucial in revealing the impact-phase mechanism influencing gait features in competitive sprinters (Figure 3). The observed asymmetrical force application pattern, particularly among the fastest sprinters, represents a distinct GRF signature optimised for maximising running speeds during brief contact periods in sprinting (Clark and Weyand, 2014). Therefore, in the FVP approach, approximated, step-averaged force values are derived directly from kinematic data, making them entirely dependent on calculated velocities for a specific athlete. There is no possibility for force to vary independently of velocity. Consequently, two athletes with the same mass and velocity data will exhibit identical derived force data, even if their ground reaction force profiles during contact differ (Goodwin & Cleather, 2023) (Figure 3).
Back to Basics
A rationale for FVP profiling is that the re-arrangement results in variables (F0 and V0) that are simpler to understand and interpret for practitioners and this offers insights that may not be as apparent before the re-arrangement. However, with perhaps the most reductionistic interpretation of F0 and V0 being the goals of improving acceleration and maximum velocity performance, this can still be determined by examining how quickly velocity develops (quantified by τ or, simpler still, short-distance split times) and how high it becomes (maximum velocity or longer-distance splits), all of which can be extracted from the velocity-time trace. A reference curve can also be easily added to the velocity-time curve for visual analysis, making it more direct and easier to interpret than a single numerical value. Although re-arranging information doesn’t create new data, it may still be useful; for instance, differences in initial acceleration, represented by the slope of the velocity-time trace (i.e., τ), may not be well-shown in the original trace, but become more visible after transformation and allow small yet important details to be better visualised. In the FVP profile, however, the time/distance aspect of sprinting has been removed, making the information more abstract and harder to grasp.
Put more simply, if an individual runs 5 m in 1.2 seconds, do we really need a FVP to inform us that horizontal force application is sub-optimal and that they need to work on acceleration characteristics? Examining velocity-time data and developing performance standards across key distances or split times of interest can inform our training priorities to the same level as the FVP approach (Hicks et al., 2023; Morin and Samozino, 2016). In actuality, as will be discussed in more detail in Part 2, by not limiting ourselves to ‘F0’ or ‘V0’ groups, we can gain more insight into distinct linear sprinting phases and apply more targeted training strategies (Bellon et al., 2019). Ultimately, it is impulse, and thus, an ability to effectively apply and tolerate high relative net forces over increasingly abbreviated ground contact times, that underpins sprinting performance (Nagahara et al., 2019). Through position-time data alone, these aspects can’t realistically be indicated, only inferred.
Can We Really Combine Vertical and Horizontal Force-Velocity-Power Profiles?
Practitioners and sports scientists will often use jump data extracted from force platforms to glean insights into an athlete’s underpinning neuromuscular function. By analysing force platform GRF waveforms from jumping, insights can be ascertained into an athletes braking and propulsive characteristics. Numerous investigations have also pointed to correlations between jump variables and sprinting, deceleration and change of direction performance (Harper et al., 2020; Jones et al., 2009). This has subsequently led inferences to be made linking ‘vertical’ performance parameters to ‘horizontal’ performance indicators. -1
As such, a common approach aims to compare FVP profiles generated from sprinting with those generated from the jumping profiles (Morin and Samozino, 2016). However, it has recently been highlighted that ‘vertical’ FVP profile generated from squat jumping at varied loads misrepresents the intrinsic force-velocity relationship and may not have added value over plotting jump height or take-off velocity as a function of the truly independently manipulated load (Bobbert et al., 2023). This is because effective work is not determined by how fast the lower extremity moves on average, but by how the velocity changes over time (Bobbert et al., 2023). For example, at the same average velocity, less work can be done during jumping than during isokinetic lower extremity extension at the same velocity (Bobbert et al., 2023). This is because jumping involves accelerating and decelerating the lower limbs within the interaction of segmental dynamics (Bobbert, 2012), while isokinetic extension involves moving the lower extremity at a constant velocity. In their study, Bobbert et al. (2023) demonstrated by different simulation models that the vertical FVP profiles developed from this approach are task-dependent, since the effective work is different for varied tasks that involve lower extremity extension, such as jumping, sprinting, or cycling, and even within the intra-individual variation of the same jumping task itself. Therefore, the velocity–time history of the task is fundamentally important to determine the changes in velocity and effective work over time for a given task and as such cannot be arbitrarily assigned (i.e., 0.5 times the take-off velocity).
It is, therefore, to no surprise that most of the force-oriented metrics have low correlations with sprint performance, particularly over greater distances (Marcote-Pequeño et al., 2018; Nicholson et al., 2021). Sprinting involves a complex interaction of muscle-tendon unit interactions comprising of eccentric, isometric and concentric muscle action that are all phase, angle and velocity dependent. Force platform data during the stance phase of sprint acceleration has identified that the duration of the braking phase (≤ 90ms) likely accounts for ≤20% of contact time (Hunter et al., 2004; Mero, 1988). It has been suggested that faster athletes may express a higher RFD at earlier time points (e.g. ≤ 90ms) during sprinting, thus suggesting that faster athletes develop eccentric braking forces at a superior rate in comparison to their slower counterparts (Bellon, 2016). Therefore, by developing a greater eccentric force for the concentric part of the stance phase, faster athletes may “potentiate” propulsive force in the later part of ground contact (Morin et al., 2015) and may subsequently lead to a higher GRF and sprint speed (Weyand et al., 2000), therefore, substantiating the aforementioned points (Clark and Weyand, 2014).
As such, aiming to isolate the propulsive component of sprint and jump profiling may indeed have a stronger rationale for early-acceleration (Bellon, 2016; Kugler and Janshen, 2010; Morin et al., 2015); however, when seeking to uncover the mechanical underpinnings of ‘vertical’ and ‘horizontal’ performance, of which the FVP approach proposes to reveal, we may be limiting ourselves. Isometric, eccentric and reactive strength components should not be ignored, and can be garnered from well-established and widely adopted performance assessment options, such as those attained from isometric and dynamic testing using force platforms. Alternatively, those with lower resources may do just as well ascertaining maximal strength capabilities using traditional methods (e.g., 1RM), utilising jump height and reactive strength measures from squat jumps, CMJs, drop jumps or repeated jumps (e.g., 10-5), all of which can be derived using contact time and flight time metrics using low-cost equipment.
So What Now?
Criticism comes easy and it is not the sole intention of this article to simply pick holes in the FVP method without discussing what alternative steps we can take from here. The authors of the method should be commended for their efforts and contributions to the field, in part for highlighting that more granular approaches need to be considered beyond performance times to guide us on more objective and targeted speed training prescription. The fact that numerous investigations have demonstrated the benefits of using this approach in improving sprinting performance and identifying relative injury risk should not be disregarded. The method demonstrates that the individualisation of movement profiles can be ascertained from instantaneous velocity data in order to deliver more targeted speed training interventions. What’s more, some metrics derived from the FVP method certainly do have worth, such as those representative of the mechanical effectiveness concept (i.e., ratio of forces).
With that said, there are evident concerns in the FVP method, some of which have been briefly discussed here. Readers are encouraged to refer to some excellent resources that address these issues in more detail; for example, the recent publications from Ettemma and Bobbert (2023), alongside Cleather & Goodwin’s book chapter on power and FVP profiling, alongside Peter Weyand’s feature on Sportsmith’s podcast channel. It is also worth reviewing the rationale and processes underpinning the FVP to fully understand the construct and its aims (Morin et al., 2019; Morin and Samozino, 2016). For sports scientists and practitioners to make an informed decision on their own practise, there needs to be opportunity to review a balanced argument and see what works for them in their own context and training philosophy.
We are not finished here, though. As mentioned previously, this article is one of a series in which we will demonstrate that there are approaches that may offer more targeted focus for sprinting analysis and are simpler to implement. For example, velocity traces can indeed be transformed to demonstrate the more subtle developments of initial acceleration. Using velocity and/or acceleration at key instances, or grouping sprinting distances into specific zones, we may ascertain important phase-specific information that enables more focused gym and field conditioning strategies. Furthermore, the more recent developments of FVP method relating to ‘in-situ method’ will also be discussed as a key gateway into the invisible monitoring concept in team sports.
Summary
- The FVP method has been popularised as it proposes to be a relatively low-cost, field-based approach to derive key insights into an athlete’s underpinning mechanical performance in relation to linear sprinting performance.
- The FVP has shed light on a more individualised approach to sprinting development which has been demonstrated through improved performance, alongside highlighting potential injury risk factors.
- Optimisation for power should not be the goal during sprinting; rather, impulse is king, which translates to the ability to effectively apply and tolerate high relative net forces over increasingly abbreviated ground contact times.
- The FVP is merely a re-arrangement of velocity-time trace, which can be more simply created, rather than replacing time-series data for arbitrary values with limited meaning (F0/V0).
- If FVP were to truly uncover an athlete’s maximal neuromuscular capabilities, we would want to identify eccentric, isometric and concentric strength qualities. To uncover this, we need more than step-averaged velocities.
- A one-dimensional approach to speed assessment (i.e., only forwards) will lead to an oversight of other high intensity, multi-directional speed qualities that, currently, cannot be evaluated through the same approach.
References
Bellon, C.R., 2016. The relationship between strength, power, and sprint acceleration in division 1 men’s soccer players (Electronic Theses and Dissertations). East Tennesse State University.
Bellon, C.R., Deweese, B.H., Sato, K., Clark, K.P., Stone, M.H., 2019. Defining the early, mid, and late subsections of sprint acceleration in division 1 men’s soccer players. J Strength Cond Res 33, 1001–1006. https://doi.org/10.1519/JSC.0000000000003088
Bobbert, M.F., 2012. Why is the force-velocity relationship in leg press tasks quasi-linear rather than hyperbolic? J Appl Physiol 112. https://doi.org/10.1152/japplphysiol.00787.2011
Bobbert, M.F., Lindberg, K., BjØrnsen, T., Solberg, P., Paulsen, Gø., 2023. The Force-Velocity Profile for Jumping: What It Is and What It Is Not. Med Sci Sports Exerc 55. https://doi.org/10.1249/MSS.0000000000003147
Buchheit, M., Samozino, P., Glynn, J.A., Michael, B.S., Haddad, H. Al, Mendez-Villanueva, A., Morin, J.B., 2014. Mechanical determinants of acceleration and maximal sprinting speed in highly trained young soccer players. J Sports Sci 32, 1906–1913.
Chelly, S.M., Denis, C., 2001. Leg power and hopping stiffness: relationship with sprint running performance. Med Sci Sports Exerc 33, 326–333.
Clark, K.P., Weyand, P.G., 2014. Are running speeds maximized with simple-spring stance mechanics? J Appl Physiol 117, 604–615. https://doi.org/10.1152/japplphysiol.00174.2014
Cross, M.R., Brughelli, M., Brown, S.R., Samozino, P., Gill, N.D., Cronin, J.B., Morin, J.-B., 2015. Mechanical Properties of Sprinting in Elite Rugby Union and Rugby League. Int J Sports Physiol Perform 10, 695–702.
Delaney, J.A., Olson, T.M., Morin, J.-B., 2018. Sprint acceleration mechanical profiling for the NFL draft. Sports Performance and Science Reports 27.
Edouard, P., Lahti, J., Nagahara, R., Samozino, P., Navarro, L., Guex, K., Rossi, J., Brughelli, M., Mendiguchia, J., Morin, J.B., 2021. Low horizontal force production capacity during sprinting as a potential risk factor of hamstring injury in football. Int J Environ Res Public Health 18. https://doi.org/10.3390/ijerph18157827
Escobar-Álvarez Juan Antonio AND Fuentes-García, J.P.A.N.D.V.-C.F.A.A.N.D.J.-R.P., 2020. Association between vertical and horizontal force-velocity-power profiles in netball players.
Ettema, G., 2023. The Force–Velocity Profiling Concept for Sprint Running Is a Dead End. Int J Sports Physiol Perform 1–4. https://doi.org/10.1123/ijspp.2023-0110
Harper, D.J., Cohen, D.D., Carling, C., Kiely, J., 2020. Can countermovement jump neuromuscular performance qualities differentiate maximal horizontal deceleration ability in team sport athletes? Sports 8. https://doi.org/10.3390/sports8060076
Haugen, T.A., Breitschädel, F., Seiler, S., 2019. Sprint mechanical variables in elite athletes: Are force-velocity profiles sport specific or individual? PLoS One 14. https://doi.org/10.1371/journal.pone.0215551
Hicks, D.S., Drummond, C., Williams, K.J., Pickering, C., van den Tillaar, R., 2023. Individualization of Training Based on Sprint Force-Velocity Profiles: A Conceptual Framework for Biomechanical and Technical Training Recommendations. Strength Cond J 45.
Hicks, D.S., Schuster, J.G., Samozino, P., Morin, J.-B., 2020. Improving mechanical effectiveness during sprint acceleration: Practical recommendations and guidelines. Strength Cond J 42, 45–62. https://doi.org/10.1519/SSC.0000000000000519
Hunter, J.P., Marshall, R.N., McNair, P.J., 2005. Relationships between ground reaction force impulse and kinematics of sprint-running acceleration. J Appl Biomech 21, 31–43. https://doi.org/10.1123/jab.21.1.31
Hunter, J.P., Marshall, R.N., McNair, P.J., 2004. Segment-interaction analysis of the stance limb in sprint running. J Biomech 37, 1439–1446. https://doi.org/10.1016/j.jbiomech.2003.12.018
Jon Goodwin & Dan Cleather, 2023. The Biomechanics of Sprinting: Force 2.
Jones, P., Bampouras, T.M., Marrin, K., 2009. An investigation into the physical determinants of change of direction speed. Journal of Sports Medicine and Physical Fitness 49, 97–104.
Kugler, F., Janshen, L., 2010. Body position determines propulsive forces in accelerated running. J Biomech 43, 343–348. https://doi.org/10.1016/j.jbiomech.2009.07.041
Lahti, J., Jiménez-Reyes, P., Cross, M.R., Samozino, P., Chassaing, P., Simond-Cote, B., Ahtiainen, J.P., Morin, J.-B., 2020. Individual sprint force-velocity profile adaptations to in-season sssisted and resisted velocity-based training in professional rugby. Sports 8, 74. https://doi.org/10.3390/sports8050074
Lahti, J., Mendiguchia, J., Edouard, P., Morin, J.B., 2022. A novel multifactorial hamstring screening protocol: association with hamstring muscle injuries in professional football (soccer) – a prospective cohort study. Biol Sport 39. https://doi.org/10.5114/biolsport.2022.112084
Maniar, N., Shield, A.J., Williams, M.D., Timmins, R.G., Opar, D.A., 2016. Hamstring strength and flexibility after hamstring strain injury: A systematic review and meta-analysis. Br J Sports Med. https://doi.org/10.1136/bjsports-2015-095311
Marcote-Pequeño, R., García-Ramos, A., Cuadrado-Peñafiel, V., González-Hernández, J.M., Gómez, M.Á., Jiménez-Reyes, P., 2018. Association Between the Force–Velocity Profile and Performance Variables Obtained in Jumping and Sprinting in Elite Female Soccer Players. Int J Sports Physiol Perform 14, 209–215. https://doi.org/10.1123/ijspp.2018-0233
Mendiguchia, J., Edouard, P., Samozino, P., Brughelli, M., Cross, M., Ross, A., Gill, N., Morin, J.B., 2016. Field monitoring of sprinting power–force–velocity profile before, during and after hamstring injury: two case reports. J Sports Sci 34. https://doi.org/10.1080/02640414.2015.1122207
Mendiguchia, J., Samozino, P., Martinez-Ruiz, E., Brughelli, M., Schmikli, S., Morin, J.B., Mendez-Villanueva, A., 2014. Progression of mechanical properties during on-field sprint running after returning to sports from a hamstring muscle injury in soccer players. Int J Sports Med 35. https://doi.org/10.1055/s-0033-1363192
Mero, A., 1988. Force-time characteristics and running velocity of male sprinters during the acceleration phase of sprinting. Res Q Exerc Sport 59. https://doi.org/10.1080/02701367.1988.10605484
Morin, J.-B., Bourdin, M., Edouard, P., Peyrot, N., Samozino, P., Lacour, J.-R., 2012. Mechanical determinants of 100-m sprint running performance. Eur J Appl Physiol 112, 3921–3930. https://doi.org/10.1007/s00421-012-2379-8
Morin, J.B., Edouard, P., Samozino, P., 2011. Technical ability of force application as a determinant factor of sprint performance. Med Sci Sports Exerc 43, 1680–1688. https://doi.org/10.1249/mss.0b013e318216ea37
Morin, J.B., Samozino, P., 2016. Interpreting power-force-velocity profiles for individualized and specific training. Int J Sports Physiol Perform. https://doi.org/10.1123/ijspp.2015-0638
Morin, J.-B., Samozino, P., Murata, M., Cross, M.R., Nagahara, R., 2019. A simple method for computing sprint acceleration kinetics from running velocity data: Replication study with improved design. J Biomech 94, 82–87. https://doi.org/https://doi.org/10.1016/j.jbiomech.2019.07.020
Morin, J.B., Slawinski, J., Dorel, S., de villareal, E.S., Couturier, A., Samozino, P., Brughelli, M., Rabita, G., 2015. Acceleration capability in elite sprinters and ground impulse: Push more, brake less? J Biomech 48, 3149–3154. https://doi.org/10.1016/j.jbiomech.2015.07.009
Nagahara, R., Kanehisa, H., Fukunaga, T., 2019. Ground reaction force across the transition during sprint acceleration. Scand J Med Sci Sports 30, 450–461. https://doi.org/10.1111/sms.13596
Nicholson, B., Dinsdale, A., Jones, B., Till, K., 2021. Sprint and Jump Mechanical Profiles in Academy Rugby League Players: Positional Differences and the Associations between Profiles and Sprint Performance. Sports 9. https://doi.org/10.3390/sports9070093
Rabita, G., Dorel, S., Slawinski, J., Sàez-de-Villarreal, E., Couturier, A., Samozino, P., Morin, J.B., 2015. Sprint mechanics in world-class athletes: A new insight into the limits of human locomotion. Scand J Med Sci Sports 25, 583–594. https://doi.org/10.1111/sms.12389
Samozino, P., Rabita, G., Dorel, S., Slawinski, J., Peyrot, N., Saez de Villarreal, E., Morin, J.B., 2016. A simple method for measuring power, force, velocity properties, and mechanical effectiveness in sprint running. Scand J Med Sci Sports 26, 648–658. https://doi.org/10.1111/sms.12490
Stavridis, I., Paradisis, G., 2019. Association between Sprinting Performance and Force-Velocity Mechanical Profile of Men’s and Women’s World-Class Sprinters. https://doi.org/10.3390/proceedings2019025033
Tol, J.L., Hamilton, B., Eirale, C., Muxart, P., Jacobsen, P., Whiteley, R., 2014. At return to play following hamstring injury the majority of professional football players have residual isokinetic deficits. Br J Sports Med 48. https://doi.org/10.1136/bjsports-2013-093016
Verheul, J., Nedergaard, N.J., Vanrenterghem, J., Robinson, M.A., 2020. Measuring biomechanical loads in team sports–from lab to field. Science and Medicine in Football 4, 246–252. https://doi.org/10.1080/24733938.2019.1709654
Watkins, C.M., Storey, A., McGuigan, M.R., Downes, P., Gill, N.D., 2021. Horizontal force-velocity-power profiling of rugby players: A cross-sectional analysis of competition-level and position-specific movement demands. J Strength Cond Res 35. https://doi.org/10.1519/JSC.0000000000004027
Weyand, P.G., Sternlight, D.B., Bellizzi, M.J., Wright, S., 2000. Faster top running speeds are achieved with greater ground forces not more rapid leg movements. J Appl Physiol 89, 1991–1999. https://doi.org/10.1152/jappl.2000.89.5.1991
