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Research Article

Optimal barbell force-velocity profiles can contribute to maximize weightlifting performance

Abstract

Maximal barbell power output (Pmax) and vertical barbell threshold velocity (vthres) are major determinants of weightlifting performance. Moreover, an optimal force-velocity relationship (FvR) profile is an additional variable that has the potential to maximize sports performance. The aims of this study were (i) to present a biomechanical model to calculate an optimal FvR profile for weightlifting, and (ii) to determine how vthres, Pmax, and the optimal FvR profile influence theoretical snatch performance (snatchth). To address these aims, simulations were applied to quantify the respective influence on snatchth. The main findings confirmed that at constant vthres and Pmax, snatchth is maximized at an optimal FvR profile. With increasing Pmax and decreasing vthres, the optimal FvR profile becomes more force dominated and more effective to enhance snatchth. However, sensitivity analysis showed that vthres and Pmax have a larger effect on snatchth than the optimal FvR profile. It can be concluded that in weightlifting, training protocols should be designed with the goal to improve Pmax and to reduce vthres to ultimately enhance snatchth. Training programs designed to achieve the optimal FvR profile may constitute an additional training goal to further develop weightlifting performance in elite athletes that already present high Pmax levels.

Citation: Sandau I, Granacher U (2023) Optimal barbell force-velocity profiles can contribute to maximize weightlifting performance. PLoS ONE 18(8): e0290275. https://doi.org/10.1371/journal.pone.0290275

Editor: Javier Peña, University of Vic - Central University of Catalonia: Universitat de Vic - Universitat Central de Catalunya, SPAIN

Received: November 17, 2022; Accepted: August 4, 2023; Published: August 18, 2023

Copyright: © 2023 Sandau, Granacher. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: All relevant data are within the paper.

Funding: This study is part of the research project KT 1-17 at the Institute for Applied Training Science, Leipzig, Germany and was funded by the German Federal Ministry of the Interior and Community. We acknowledge support by the Open Access Publication Fund of the University of Freiburg.

Competing interests: The authors have declared that no competing interests exist.

Introduction

In ballistic sports such as track and field or weightlifting, performance is ultimately determined by the athlete´s capability to maximally accelerate their body mass (e.g., sprinting, jumping) or a maximal external load (i.e., weightlifting) [1, 2]. In all of these examples, the velocity reached at the end of the propulsive phase is related to mechanical output parameters produced through efficient work of the neuromuscular system [3]. In this context, a linear force-velocity relationship (FvR) has frequently been used to assess mechanical parameters such as the theoretical maximal velocity at zero force (v0) and the theoretical maximal force at zero velocity (F0). From v0 and F0, maximal power output (Pmax) and the FvR profile (i.e., slope of the FvR; sFvR) can be computed [4]. Previous research has shown that Pmax is a major determinant of maximal ballistic performance [5, 6]. In addition, Samozino and colleagues further reported that for a given Pmax level, performance in vertical jumping and sprinting is (theoretically) maximized at an optimal FvR profile [4, 7, 8]. Accordingly, a customized resistance training program to improve ballistic sports performance should aim to maximize Pmax through optimization of the FvR profile. Although the benefits of an optimal FvR profile for practical use are still under debate [9], there is partial evidence that resistance training programs designed to optimize the FvR profile were more successful than standard (i.e., non-optimized) resistance training protocols in improving vertical jump height in trained soccer, rugby, and futsal player [10–12].

In weightlifting, maximal performance is determined by the lifters neuromuscular capabilities to produce a high power output combined with well-developed lifting technique (e.g., turnover and catch phase) [13]. The technical mastery and effectiveness of the lift is reflected by the individual’s vertical threshold velocity (vthres) [14]. The vthres is the minimum peak vertical barbell velocity (vmax) an individual athlete needs to lift a maximal barbell load successfully in the overhead position. For example, the vmax during a one-repetition maximum (1RM) lift in the snatch is denoted as vthres in the snatch. In general, vthres ensures a necessary vertical travel distance and flight time of the maximal barbell load (i.e., projectile motion) at the end of the acceleration phase, which allows the athlete to squat under and catch the barbell in the overhead position.

Consequently, weightlifters who have better technical skills in the turnover and catch phase can lift with lower levels of vthres. For example, better technical skill performance is indicated through larger amounts of “residual work” and a shorter time-span of the turnover phase [14, 15]. term “residual work” has previously been defined as the vertical distance the barbell travels beyond the theoretical distance from projectile motion (i.e., vmax) due to an acting vertical force component that is initiated through the upper extremities [14]. In addition, a low vthres corresponds to a smaller amount of force that needs to be utilized to accelerate the barbell. Hence, higher force levels can be achieved to overcome gravitational forces which results in better weightlifting performance. As recently presented, weightlifting is a good example to use FvR-parameters (i.e., F0, v0, Pmax) to monitor progression during training and to predict weightlifting performance [16, 17]. In agreement with results from vertical jumping [4], for individual time-series data Pmax has been shown to be highly–but not perfectly (i.e., cross-correlation coefficients range from 0.86–0.88)–associated with the theoretical snatch performance (snatchth) in elite weightlifters [17]. Due to the imperfect correlation of snatchth and Pmax, the specific FvR profile was assumed to be another determinant of weightlifting performance [17] as it has been previously presented for the vertical jump [4]. Accordingly, a given Pmax level in combination with an optimal FvR profile may maximize snatch performance.

Therefore, the main aim of this study was to determine how the optimal FvR profile (if any), vthres, and Pmax influence weightlifting performance. Considering the aforementioned relation between maximal vertical jump performance and an optimal FvR profile [7], we hypothesized that for a given level of Pmax and vthres, the FvR profile has an impact on the theoretical snatch performance (H1), and that the theoretical snatch performance is maximized at an optimal FvR profile (H2). Further, we were interested to elucidate the extent to which Pmax, the FvR profile, and vthres influence snatchth. With reference to the literature [4, 14], we hypothesized that changes in Pmax and vthres influence snatchth to a larger degree compared with changes of the FvR profile (H3).

To address these aims, first, we present the biomechanical concept of optimal FvR profile applied to weightlifting (i.e., snatch pull model) from which the maximal theoretical snatch performance () can be computed. In the second part, we used mathematical simulations to apply the snatch pull model with data from the literature. The simulations were used to quantify the influence of the optimal FvR profile, vthres, and Pmax on snatchth.

Methods

Theoretical background

This section is dedicated to the theory of optimal FvR profile and how an optimal FvR profile may positively influence weightlifting performance. For this purpose, we briefly recap the established biomechanical model from vertical jump and transfer it to weightlifting.

In a linear modelled FvR profile from loaded vertical jumps, Pmax is located at 0.5F0 and 0.5v0, respectively [3]. Consequently, Pmax can be calculated as: (1)

In this context, the vertical force at Pmax (i.e., 0.5F0) is associated with an external load condition during the jump. For a given FvR profile, the load at Pmax conditions is interpreted as the optimal load [18]. In case of a vertical jump, when Pmax is located at a load that corresponds to the jumpers body mass (i.e., body mass = optimal load) an optimal FvR profile is achieved [4]. Under optimal FvR profile conditions (i.e., Pmax is located at body mass), the vertical take-off velocity of the body´s center of mass–and hence the maximal jump height–is maximal. In contrast, even at constant Pmax level, with a non-optimal FvR profile (i.e., Pmax is located at loads smaller or larger then body mass), the achieved vertical take-off velocity is less than the maximal vertical take-off velocity at an optimal FvR profile. In other words, with a non-optimal FvR profile, the actual external mechanical power-output during a jump is less than the jumper’s maximal power capacities (Pmax) [19]. The concept of delivering Pmax at the load condition corresponding to the targeted movement (here unloaded vertical jump) can be used as a starting point to find an optimal FvR profile that maximize performance in weightlifting.

Transferring theory from jumping to establishing optimal barbell FvR profiles in weightlifting

Performance in weightlifting is simply defined as the maximal load that can be lifted in the snatch and the clean and jerk [20]. However, a successful maximal lift requires acceleration of the barbell load up to an individual vthres during the acceleration phase [2, 14]. As previously outlined for the vertical jump [21], performance in weightlifting can also be described by two interacting constraints: i) movement specific barbell velocity conditions (i.e., vthres in m∙s-1) (black line in Fig 1A) and ii) mechanical output produced by the neuromuscular system (i.e., barbell FvR; dashed black line in Fig 1A).

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Fig 1.

Graphical example of two barbell force–velocity relationships (FvR) (dashed black lines) with corresponding barbell power outputs (dotted black lines) representing non–optimal (A) and optimal profiles (B) during the specific snatch pull test (Pmax = maximal vertical barbell power, v0 = theoretical maximal vertical barbell velocity at zero mean barbell force, = theoretical maximal vertical mean barbell force at zero maximal vertical barbell velocity, = vertical barbell power at snatchth, = vertical mean barbell force at snatchth, = optimal mean barbell force at , vthres = individual vertical barbell threshold velocity for 1RM snatch, opt = optimal).

https://doi.org/10.1371/journal.pone.0290275.g001

In this context, it has recently been shown, that for the individual weightlifter, the theoretical snatch performance (snatchth in kg) can be calculated from the linear snatch pull FvR profile and the known vthres of a 1RM snatch [16]. For example, vthres is a highly individual constant that can be obtained from 1RM snatches in competitions using video-based analysis of barbell kinematics. The interaction of the two aforementioned mechanical constraints can be visualized by the intersection of the two lines, giving the mean barbell force at vthres ( in N) (black dot in Fig 1A) from which snatchth can be calculated. According to the approach outlined by Sandau et al. [16], to compute snatchth, first needs to be computed from vthres, v0 (in m∙s-1), and sFvR (in m∙s-1∙N-1) as follows: (2)

Of note, as adjustment to the approach proposed by Sandau et al. [16], in Eq (2) v0 and sFvR were extracted from a snatch pull FvR modelled with maximal (instead of mean) vertical barbell velocity (ordinate) and mean vertical barbell force (abscissa). Therefore, the slope of the FvR is calculated as: (3)

represents the sum of the barbell force due to gravity (g in m∙s-2) and the barbell force due to the mean vertical barbell acceleration to achieve vthres ( in m∙s-2). Consequently, snatchth is obtained by: (4)

In Eq (3), can be calculated using vthres and the vertical distance of barbell acceleration (i.e., hacc in m; vertical height of the barbell at the instance of vthres minus the radius of barbell plates [0.225 m]): (5)

Substitution Eqs (1) and (4) in Eq (3), and after simplification, snatchth can be expressed as: (6)

To express snatchth as a function of sFvR and Pmax, using Eqs (1) and (3), v0 can be calculated as: (7)

Finally, substituting Eq (7) in Eq (6) gives: (8)

As mentioned above, maximal ballistic performance is achieve, when the actual external power-output during a movement equals Pmax. For the individual weightlifter, the actual vertical power output during snatchth is highly associated with the absolute load of snatchth [17]. Since power is the product of force and velocity, using Eq (2), the actual vertical power output during snatchth ( in W) can be calculated as: (9)

With being the mean vertical barbell force at snatchth (Eq (2)). Substituting Eq (2) in Eq (9) gives: (10)

As can be seen for the exemplary barbell FvR profile in Fig 1A, is not located at Pmax. Following the same mechanical principle presented for the vertical jump, a mismatch of and Pmax can be interpreted as a non-optimal barbell FvR profile that results in a non-maximal snatchth. In this case, only a fraction of Pmax can be used to accelerate the barbell load to vthres. In turn, an optimal barbell FvR profile that enables the weightlifter to accelerate the barbell with the maximal possible vertical barbell power output (Pmax) may result in a maximized snatchth performance (). Again, even with a given Pmax level, snatchth is maximized at an optimal sFvR (). Graphically, this is achieved, if Pmax is exactly located at (Fig 1B). In the presented example, is reached when Pmax is shifted towards (to the right) by an increase in and a decrease in v0. In other words, the non-optimal sFvR in this case is caused by a force “deficit” or a velocity “surplus”, respectively. For example, if Pmax needs to be shifted to the left to match , the non-optimal sFvR is caused by a velocity “deficit” or a force “surplus”, respectively.

As previously mentioned for the optimal FvR profile in vertical jumps, under conditions, vthres equals and equals . Since vthres is an individual known constant for a 1RM snatch lift, can be simply calculated as: (11)

Using Eqs (2) and (3), and after simplification, the can be calculated as: (12)

Finally, is obtained by substituting Eq (12) in Eq (8).

Model simulation

In the theoretical background, we presented a biomechanical model from which the optimal FvR profile (i.e., ) and the maximal theoretical snatchth () can be computed. This model is based on a snatch pull linear two-point FvR (i.e., only two loading conditions were applied during the snatch pull test) that is obtained using linear regression in eight elite male weightlifters [22]. In order to illustrate how changes in Pmax and vthres may moderate and , typical ranges of Pmax and vthres were applied for simulations using Eq (8). Furthermore, the simulations were used to quantify the respective contribution of Pmax, sFvR, and vthres on snatchth.

For the applied simulations, no new experimental data were collected. Instead, we used data from previous (published) studies of our research group [16, 17, 22]. In total, these experiments were conducted with 10 elite male and 3 elite female weightlifters, modeling the barbell FvR profile and snatchth using the aforementioned snatch pull test. From these experiments, typical value for Pmax range from 2000 to 4000 W, for sFvR from -0.0005 to -0.0025 m∙s-1∙N-1, and hacc was on average 0.8 m [16, 17, 22]. In addition, the magnitudes of maximal vertical barbell velocities during the 1RM snatch (i.e., vthres) can also be obtained from the literature. Typical values for vthres during the snatch 1RM range from 1.70 to 2.0 m∙s-1 [15, 23, 24].

First, changes in and were analyzed for different Pmax (at constant value of vthres) and vthres values (constant value of Pmax), and as a variation of both variables. Second, the influence of vthres, Pmax, and sFvR on snatchth were analyzed through sensitivity analysis. Within the sensitivity analysis, the relative (i.e., percentage) variation of each independent variable was plotted against the relative snatchth change to assess the relative importance of each variable. Although hacc has an influence on snatchth, this variable was treated as a constant in the simulations as it depends on the athlete’s anthropometric characteristics that cannot be influenced through training.

Results

Influence of Pmax and vthres on snatchth and sFvR

The simulated influence of Pmax and vthres on snatchth and sFvR is depicted in Fig 2. Findings from the simulation study showed that both Pmax and vthres influence snatchth. Furthermore, at high Pmax or a low vthres levels, changes in sFvR have a larger potential to moderate snatchth due to the more prominent apex of the snatchth-sFvR-function (Fig 2). As mathematically presented, snatchth is maximized (i.e., ) at an optimal value of sFvR (i.e., , red lines in Fig 2).

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Fig 2. Changes in theoretical 1RM snatch performance (snatchth) as a function of the slope of the barbell force–velocity relationship (sFvR) for different values of vertical maximal barbell power (Pmax) at a fixed vertical barbell threshold velocity (vthres) of 1.85 m∙s–1 (left), and for different values of vthres at a fixed Pmax of 3000 W.

The distance of vertical barbell acceleration (hacc) was set to 0.8 m. The red line represents at .

https://doi.org/10.1371/journal.pone.0290275.g002

In fact, it is obvious that with increasing Pmax and decreasing vthres, is shifted towards a more force dominated FvR profile (Figs 2 and 3).

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Fig 3. Changes of maximal theoretical 1RM snatch performance () and the optimal slope of the barbell force−velocity relationship as a function of the threshold velocity (vthres) and vertical maximal barbell power (Pmax).

The distance of the vertical barbell acceleration (hacc) was set to 0.8 m.

https://doi.org/10.1371/journal.pone.0290275.g003

Since equals 2vthres (Eq (11)), under optimal FvR profile conditions, is a constant and does not depend on the absolute value of snatchth. Therefore, in theory, improvements in weightlifting performance solely may depend on increased theoretical maximal vertical barbell force capabilities (i.e., ) (Fig 4). This relation results in an improved force at vthres and thus a higher barbell load that can be lifted. According to the example in Fig 4, at a constant vthres of 2.0 m∙s-1, an increase in by +500 N is associated with an increase in Pmax of +500 W that corresponds to an increase in of about +20 kg.

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Fig 4. Theoretical model for athlete specific improvements in snatch performance at a fixed theoretical optimal maximal vertical velocity () of 4.0 m∙s–1, a fixed vertical acceleration distance (hacc) of 0.8 m, and constant vertical threshold velocity of 1RM snatch (vthres) of 2.0 m∙s–1 at optimal barbell FvR conditions.

Increased theoretical maximized snatch performance () as a result of increased theoretical optimal maximal vertical mean force () from 3000 N (black dashed line) to 3500 N (light grey dashed line) to 4000 N (grey dashed line) and the associated increase in maximal power (Pmax) from 3000 W (black dotted line) to 3500 W (light grey dotted line) to 4000 W (grey dotted line).

https://doi.org/10.1371/journal.pone.0290275.g004

Relative contribution of Pmax, vthres, and sFvR on snatchth

The sensitivity analysis showed that relative snatchth performance is primarily influenced by Pmax and vthres rather than sFvR (Fig 5). Of note, Fig 5 shows that Pmax and vthres have a continuous positive or negative effect on snatchth, while sFvR has its maximal effect at .

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Fig 5. Relative changes in modelled 1RM snatch performance (snatchth) in response to relative parameter variation of vertical maximal barbell power (Pmax), slope of the barbell force–velocity relationship (sFvR), and vertical barbell threshold velocity (vthres).

The reference parameter values (i.e., 1.0) are: Pmax = 3000 W, sFvR = –0.0011 m∙s–1∙N–1, vthres = 1.85 m∙s–1. The distance of vertical barbell acceleration (hacc) is 0.8 m. Grey lines represent positive and negative identity lines.

https://doi.org/10.1371/journal.pone.0290275.g005

Discussion

This study aimed to introduce the theoretical base of an optimal barbell snatch pull FvR profile (i.e., ) to maximize theoretical snatch 1RM performance () in weightlifting. We additionally examined the influence of , Pmax, and vthres on snatchth performance. In line with our study hypotheses, we observed at constant levels of Pmax or vthres that snatchth is influenced by sFvR and maximized at an optimal sFvR value (i.e., ). We further confirmed that changes in Pmax and vthres have a larger influence on snatchth than changes in sFvR.

Competitive weightlifting requires both well developed technical skills and high mechanical power output to lift a maximal load in the overhead position in the snatch and the clean and jerk [25, 26]. The snatch pull FvR is an approach to quantify the external mechanical output at the barbell and to assess training related changes in v0, , Pmax and vthres. While the parameters v0, , Pmax are related to neuromuscular capabilities, vthres is related to sport-specific technical skills. Our study findings revealed that besides training-induced improvements in neuromuscular capabilities, well-developed technical skills (i.e., amount of vthres) are needed and affect snatch performance. From the perspective of the neuromuscular capabilities, Pmax presented the largest contribution to increase weightlifting performance. The leading effect of Pmax to enhance ballistic performance is in agreement with evidence from the literature [27]. In addition, with an increased performance level (i.e., high Pmax), an optimal barbell FvR profile becomes more relevant to further maximize weightlifting performance. In this context, our simulations showed that the optimal barbell FvR profile is primarily force driven as Pmax increases. This finding seems reasonable, given that the snatch 1RM is highly associated with the weightlifter´s maximal strength capabilities (i.e., 1RM squat) [25, 26, 28].

From the perspective of weightlifting technical skills, the simulations showed that changes in vthres have a large influence on snatchth. For instance, if two lifters have the same Pmax level to accelerate a maximal barbell load, the lifter with lower vthres will achieve the higher snatch performance. In this context, Richter [29] postulated that increased maximal muscle strength and power have a larger impact to improve weightlifting performance than increased technical skills (ratio 10:1). In theory, however, if improved technical skills are associated with lowered vthres, the aforementioned ratio is ≈ 1:1.5 (Fig 5). Nevertheless, the large potential influence of vthres on snatch performance should be put in perspective, since technical skills in weightlifting level off after 4–5 years of systematic training [30]. Therefore, elite weightlifters with a long history of systematic training (>5 years) are more likely to benefit from increased muscle strength and power (i.e., , Pmax) to improve snatch performance than from lowering vthres.

A few limitations of this study should be acknowledged. First, we should mention that the present findings are based on a biomechanical model that was verified using simulations. Although the concept of an optimal FvR to maximize performance seems to work for the vertical jump [10, 11], the validity for practical application in weightlifting has not yet been shown. Second, although the measurement error of FvR parameters (i.e., , v0, Pmax) derived from the snatch pull test is rather small [22], the measurement error for and has not been assessed yet. However, knowledge of measurement error for and is essential to guide training programming for the individual athlete. Finally, the modelled changes in snatch performance are based solely on changes in mechanical parameters during the acceleration phase (lift-off until maximal vertical barbell velocity) without accounting for the effect of an increased barbell load on the execution of the subsequent movement phases (i.e., turnover, catch, stand up) that also limit the performance outcome.

Conclusions

Weightlifting performance can be improved through an increase in mechanical power output (Pmax), improved technical skills (vthres) and optimized FvR profile (). During long-term athlete development as well as in elite sports, improvements of Pmax should be the main focus of training to further develop weightlifting performance [13, 17, 31]. In addition, a well-developed snatch technique enables weightlifters to efficiently lift loads at low vthres. This point can be declared as a major goal during the early stages of the long-term athlete development process [30]. For weightlifters with high Pmax levels, the contribution of to maximize snatch performance becomes more relevant. This finding is of great importance for elite weightlifters as the contribution of increased Pmax and lowered vthres to improve performance is strongly limited in world class athletes. Therefore, designing elite weightlifters training to achieve an optimal FvR profile has the potential to maximize performance. Even if optimization of the FvR profile can provide only small improvements in weightlifting performance, it may be of importance in competitions. As pointed out by Sandau and Lenz [32], on average, only 1.0% (≈ 3.7 kg) of total weightlifting performance (sum of snatch and clean and jerk) was the difference of making it to the podium or not (3rd vs. 4th place) at the Olympic Games.

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