External mechanical work done during the acceleration stage of maximal sprint running and its association with running performance

Among human locomotive movements, sprint running is the most powerful. The mechanical power output during sprint running reaches about 3000 W step⁻¹ in sprinters (Fukunaga et al., 1981). Sprint running from a stationary state inevitably involves a period of time until the running velocity reaches the maximum, i.e. the acceleration stage. In this stage, runners are required to maximally accelerate their bodies to attain a high running velocity within a short period. Thus, examining the mechanics of the acceleration stage of maximal sprint running is essential to elucidate how runners are capable of achieving a high power movement. To realize this, it is necessary to continuously obtain data on kinetics and/or kinematics at each step during the entire period of maximal sprint running from the start of the run, because these markedly vary with increasing running velocity (Nagahara et al., 2014, 2018a,b,c). Owing to methodological difficulties, available information on this subject is very limited.

One useful approach to examine the mechanics of human locomotive movements is to evaluate mechanical work done during the movements (Willems et al., 1995). Many studies calculated the work done and/or power generated during running by analyzing the ground reaction force (GRF) during the stance period (Cavagna, 1975; Cavagna et al., 1964, 1971, 1976; Cavagna and Kaneko, 1977; Fenn, 1930a,b; Fukunaga et al., 1980, 1981). In these studies, the work done at every step in running has been divided into two parts on the basis of the horizontal anterior–posterior GRF during the stance period: the work done during the braking phase (negative work) and propulsive phase (positive work), in which the runner's body decelerates and accelerates, respectively. However, only one provided extensive data on the changes in the work done at each step during the acceleration stage of maximal sprint running (Cavagna et al., 1971), although the presented data were limited to those in the horizontal anterior–posterior direction. From the previous findings, at about 7 m s⁻¹, the negative work done at each step, which immediately precedes the positive work, begins to increase, while the propelling force stops decreasing and becomes constant. On the basis of these findings, Cavagna et al. (1971) suggested that during low velocity running, the contractile component of the muscles is responsible for the power output, whereas during high velocity running, the mechanical energy is stored in the ‘series elastic elements’ during the negative work phase, and used to enhance power output in the positive work phase. This is indirectly supported by musculoskeletal modeling studies (Hof et al., 2002; Lai et al., 2014, 2016), indicating that the relative contribution of tendon elastic strain energy to the mechanical work done during sprint running expands with increasing running velocity.

In the report of Cavagna et al. (1971), however, it should be noted that the data on GRFs obtained during a single sprint were measured over only a few steps, because of the limitation in the length of force plates used (0.5 m×4). For constructing GRF data to recreate the entire acceleration stage of sprint running, the participants were required to perform several sprints on different days starting at various distances from the force plates. This approach calls into question the continuity of data acquisition and/or consistency of maximal effort by the runners. In addition, Cavagna et al. (1971) used only three sprinters as the participants and presented only individual data. In spite of these conditions, no studies have been conducted to corroborate the prior findings obtained over about half a century. The fastest intra-individual sprinting within a single session consisting of three to five maximal trials can be characterized by: (1) the exertion of a sufficient vertical impulse during the short support duration from the fourth step; (2) the large propulsive impulse and mean force during the initial acceleration; and (3) a large mean net anterior–posterior force during initial and middle acceleration (Nagahara et al., 2018c). These suggest that if one intends to elucidate the mechanics of maximal acceleration sprint running in relation to the performance, GRF data at every step should be measured continuously over the whole acceleration stage in the fastest intra-individual trial within a single session consisting of multi-sprints covering the entire distance examined.

Apart from the calculation of mechanical work, GRF data during accelerated sprint running over 10–50 m have been extensively analyzed to explain the inter-individual differences in running performance (Hunter et al., 2005; Kawamori et al., 2013; Morin et al., 2011, 2012, 2015; Nagahara et al., 2018a,b). Based on these findings, maintaining a high GRF during the propulsive phase and a low value during the braking phase in the horizontal anterior–posterior direction are essential to achieve a high running velocity. As a general rule, the execution of accelerated sprint running requires the runners to maximally accelerate their bodies in the forward direction. Considering these aspects, maximizing the work done during the propulsive phase in the horizontal anterior–posterior direction while suppressing any increase in the work done during the braking phase can be a strategy to achieve a high running velocity. However, this would partially contradict the idea described by Cavagna et al. (1971). Namely, if the relative contribution of the elastic strain energy stored during the braking phase to power output during the propulsive phase expands with increasing running velocity, work done during the braking phase might contribute to achieve high running performance (Hunter et al., 2005). Examining this will provide useful information concerning the energetics for achieving a high velocity in accelerated sprint running.

The present study aimed to elucidate the magnitude of the mechanical work done in each of the braking and propulsive phases during the acceleration stage of 60 m maximal sprint running and the associations of the work variables with running performance. To this end, we adopted a 50 m force plate system (Nagahara et al., 2018a,b,c) to continuously obtain GRFs at every step during the acceleration stage. We hypothesized that in maximal sprint running from a stationary start, while the work done during the propulsive phase in the horizontal anterior–posterior direction gradually decreases with increasing running velocity, it accounts for the majority of the total external work done during the acceleration stage and its difference from the work done during the braking phase can be a major factor affecting running performance.

Twelve young males were recruited as the participants (age, 21.2±2.9 years; height, 1.736±0.062 m; mass, 69.8±11.4 kg; means±s.d.). Each of the subjects participated in sporting events involving sprint running (e.g. track and field, soccer or basketball). This study was approved by the Ethics Committee of the National Institute of Fitness and Sports in Kanoya and was consistent with the institutional ethical requirements for human experimentation in accordance with the Declaration of Helsinki. The participants were fully informed of the purpose and risks of the experiment and gave written informed consent.

After warm-up, the participants were asked to perform maximal acceleration sprint running over 60 m 3–5 times on a 110 m indoor runway from a crouched position with starting blocks, wearing running shoes. The participants started to run on hearing a signal produced by an electronic starting gun connected to a computer linked to force plates, initiating the recording of GRF. A rest period of 5 min or more was set between the trials. At each step, GRFs in each of the horizontal medio–lateral, horizontal anterior–posterior and vertical axes was measured with a 50 m force plate system (Nagahara et al., 2018a,b,c), which consisted of 54 individual force plates (Tec Gihan Co. Ltd, Uji, Japan) consecutively placed from the starting area to 50 m mark. Among the force plates, four were set in the starting area: two for hands and two for feet. Each force plate for hands was 0.550 m wide, 0.300 m long and 0.085 m thick, and its mass was 23 kg and that for feet was 0.32 m wide, 1.20 m long, and 0.12 m thick, and its weight was 47 kg. The force plates set in the starting area were equipped with starting blocks. Each force plate set from the starting line to 50 m mark was 0.90 m wide, 1.00 m long, and 0.13 m thick, and its mass was 68 kg.

All force plates involved in the system were covered with the track surface (Resin Ace, Hasegawa Sports Facilities Co. Ltd, Tokyo, Japan) and designed to measure the force (F) applied to its top surface with strain gauges in the three axes of an orthogonal x-, y- and z-coordinate system: horizontal medio-lateral (F_x), horizontal anterior–posterior (F_y), and vertical (F_z) axes (Fig. 1). The natural frequency of each of the force plates laid under the ground was determined by analyzing the damped oscillation of the force curve, induced by hitting the force plates with a hammer. The average value of the natural frequency for 54 force plates was 145 (±3.2) Hz for F_x, 145 (±3.8) Hz for F_y, and 217 (±7.0) Hz for F_z. In the present study, therefore, the GRF data were digitized with 1 kHz and analyzed using a low-pass filter with a cut-off frequency of 100 Hz. The nonlinearity of the force plates was within ±1%. For the ground contact on the force plate, touchdown and toe-off were identified from the raw F_z data with a threshold of 30 N using a computer software program (MATLAB R2018a, MathWorks). The F_z data were also used to calculate the center of pressure (COP) position at each step in the horizontal anterior–posterior direction using a computer software program (Fig. 1D).

The duration of foot contact with the ground and that from toe-off of one leg to the next foot strike of the other leg were determined using MATLAB and defined as the support and aerial times, respectively. Similarly, the mean COP position 10 ms before and after the halfway point during foot contact was also calculated using MATLAB and defined as the location of foot contact. As a parameter representing sprint running performance, the time required to run 50 m (T_{50 m}) was calculated from changes in the position of COP. In the present study, the running velocity (V) at each step was obtained by differentiating the change in COP displacement between the two consecutive steps with respect to the time required. The peak value of V was referred to as the maximal running velocity (V_max). In addition to the absolute value, V at each step was expressed as the value relative to V_max (% V_max). The present study defined the running stage from block clearance to the point at which V_max appeared as the acceleration stage. With reference to a previous study (Nagahara et al., 2018c), the trial in which the highest V_max among the 3–5 sprints was observed was subjected to the following analysis.

The sum of E_kap and E_v at every step was defined as external mechanical energy (E_ext). External mechanical work (W_ext) at every step was calculated on the basis of the changes in E_ext.

In each of E_kap (Fig. 2A), E_v (Fig. 2B) and E_ext (Fig. 2C), the periods between landing and the point at which the energy value became minimal and between the point at which the minimum value appeared and toe-off were defined as the braking and propulsive phases, respectively. The W_kap, W_v and W_ext values in the braking phase were referred to as −W_kap, −W_v and −W_ext, respectively, and those in the propulsive phase as +W_kap, +W_v and +W_ext, respectively. In addition, the differences between |−W_kap| and +W_kap (ΔW_kap), between |−W_v| and +W_v (ΔW_v), and between |−W_ext| and +W_ext (ΔW_ext) were calculated. Each work parameter was expressed as the value relative to body mass. The total values of each work parameter at every step over 50 m and in each of 0–10, 10–20, 20–30, 30–40 and 40–50 m sections were calculated to examine their associations with T_50 m. In addition, the mean values of mechanical power (P_kap, mech) and force (F_y, mech) in each of braking (−P_kap, mech and −F_y, mech, respectively) and propulsive (+P_kap, ech and +F_y, mech, respectively) phases at every step in the horizontal anterior–posterior direction were calculated by dividing the relevant work and impulse parameters by the corresponding time to examine the associations between the power and force variables. Each of power and force variables was expressed as the value relative to body mass.

Descriptive data are presented as means±s.d. In this study, %V_max had already reached around 20% at block clearance (Fig. 3). Thus, the means and s.d. for the analyzed variables are presented at intervals of 10% V_max in a range of 20% V_max or higher. The value at every 10% V_max for each participant was obtained by applying a cubic method to two known data points adjacent to the corresponding %V_max. In this process, two participants exceeded 20% V_max at block clearance, and so the mean and s.d. for each variable at 20% V_max were calculated using data for the remainder (n=10). Pearson product–moment correlation coefficients (r) were calculated to determine the relationships between +P_kap, mean and each of |−P_kap, mean|, +F_y, mean and |−F_y, mean| and between each of the work variables and T_{50 m}. The significance level was set at P<0.05. All statistical analyses were performed using MATLAB.

T_{50 m} and V_max were 7.11±0.54 s and 8.67±0.75 m s⁻¹, respectively. The total number of steps over 50 m, including block clearance, was 30.3±1.8. Velocity sharply increased from block clearance and reached 50% V_max within 1 s, and then increased in a hyperbolic convex upward manner until about 3–4 s (Fig. 3). V_max was reached at 36.87±7.76 m (5.49±0.65 s) from the starting line. In terms of the average value, the runners reached 90% V_max at a running distance corresponding to 35.4% of that required to attain 100% V_max (Table 1), indicating that the runners had already achieved a running velocity close to V_max in the earlier period of the acceleration stage.

In terms of the average value, +W_kap at every 10% V_max was more than 3.6 J kg⁻¹ with relatively small changes until 70% V_max, and then it decreased to 2.4 J kg⁻¹ at 100% V_max (Fig. 4A). |−W_kap| was less than 0.3 J kg⁻¹ at 70% V_max or lower, but it nonlinearly increased at 80% V_max or higher and reached 1.9 J kg⁻¹ at 100% V_max. +W_v decreased from 1.7 J kg⁻¹ at 20% V_max to 0.6 J kg⁻¹ at 50% V_max, and |−W_v| was less than 0.4 J kg⁻¹ even at 100% V_max (Fig. 4B). +W_ext linearly decreased from 6.0 J kg⁻¹ at 20% V_max to 2.8 J kg⁻¹ at 100% V_max, and |−W_ext| was less than 0.5 J kg⁻¹ until 80% V_max, and then it abruptly increased to 2.3 J kg⁻¹ at 100% V_max (Fig. 4C).

At 70% V_max or lower, while the change in ΔW_kap was small (Fig. 5A), ΔW_v abruptly decreased (Fig. 5B). At 70% V_max or higher, ΔW_kap sharply decreased, but ΔW_v was mostly constant. ΔW_ext linearly decreased with increasing running velocity (Fig. 5C).

On comparing the average values of the total of each work parameter at every step over 50 m, +W_kap was greater than |−W_kap|, +W_v, and |−W_v| by 2.3, 5.8 and 7.9 times, respectively (Table 2). Reflecting the difference between +W_kap and |−W_kap|, the total of +W_ext at every step was 2.1 times greater than that for |−W_ext|.

+F_y, mech linearly decreased until 80% V_max and then it became mostly constant (Fig. 6A). |−F_y, mean| gradually increased with increasing running velocity. +P_kap, mean and |−P_kap, mean| increased with increasing running velocity until 100% V_max (Fig. 6B). Differences between +F_y, mean and |−F_{y, mean}| and between +P_kap, mean and |−P_kap, mean| became negligible at 100% V_max.

+P_kap, mean was more strongly correlated with +F_{y, mech} at every 10% V_max in a range from 20 to 100% V_max (Table 3). On the other hand, there were no significant correlations between +P_{kap, mean} and either |−F_{y, mean}| or |−P_{kap, mean}| and between +F_{y, mean} and |−F_{y, mean}| at every 10% V_max, with the exception that the association between +P_{kap, mean} and |−F_{y, mean}| at 100% V_max was significant.

The total value of ΔW_kap over 50 m was more strongly correlated with T_{50 m} as compared with those of the other work variables (Table 4). In terms of the total work over each 10 m section, too, the ΔW_kap values in all distance sections except for the 40–50 m section were highly correlated with T_{50 m}, notably in the first two distance sections.

The findings obtained here indicated that in maximal sprint running over 50 m, +W_kap accounted for the majority of the total external work done during the acceleration stage, and the total value of ΔW_kap at every step over 50 m was closely correlated with T_50 m. These results support our hypothesis set at the start of this study.

+W_v was relatively large at 20% V_max. For most of the participants, 20% V_max corresponded to the running velocity just after the completion of block clearance (Fig. 3). Thus, the greater +W_p at 20% V_max may be a result reflecting the work requirement during block clearance in which the runners need to raise their bodies from a crouched position through block clearance, accompanying a propulsive action in the forward direction. Regardless of %V_max, however, the parameters of W_v were markedly smaller than +W_kap (Fig. 4). This suggests that the runners sprinted over 50 m while doing more work in the propulsive phase of the horizontal posterior–anterior direction, and minimizing work done in the vertical direction.

Reflecting the changes in +W_kap and |–W_kap| until 70% V_max from the start of the run (Fig. 4), the reduction in ΔW_kap in the velocity range was relatively small (Fig. 5). Considering that the runners reached 70% V_max at 4.1 m from block clearance (Table 1), the current results indicate that in the early period of the acceleration stage, the runners propelled their bodies in the forward direction with less deceleration. This will be partially associated with the changes in the runner's posture and/or motion during the acceleration stage. Greater accelerations can be generated by more forward-oriented forces, and the orientation of the GRF vector is closely associated with the forward lean of the body at toe-off (Kugler and Janshen, 2010). In addition, it has been shown that in accelerated sprint running, the foot position on ground touchdown changes from behind to in front of the center of gravity of the body after the fourth step (Nagahara et al., 2014). The horizontal anterior–posterior distance between the center of gravity of the body and metatarsophalangeal joints of the support leg becomes a primary reason for the decrease in running velocity during the stance period (Mero et al., 1992), and a smaller distance suppresses the magnitude of the horizontal ground reaction impulse during the braking phase (Hunter et al., 2005). In the current results, the runners reached 60–70% V_max at the 4th–5th steps (Table 1). Thus, the changes in +W_kap and −W_kap at around 70–80% V_max may be partially attributable to the magnitude of forward lean of the body at toe-off and/or the foot position on ground touchdown during the initial phase of the acceleration stage.

−W_kap increased at 80% V_max or higher and its difference from +W_kap became small at 100% V_max. Cavagna et al. (1971) reported that the negative work done at each step began to increase when the running velocity reached about 7 m s⁻¹. In the current study, the average running velocity corresponding to 80% V_max, at which −W_kap started to increase, was 6.94 m s⁻¹ (Table 1). This agrees with the results of Cavagna et al. (1971), in spite of the difference in the procedure for measuring GRFs between the present (single-sprint) and previous (multi-sprint) studies. At the start of this study, we questioned the validity of GRF data obtained by multi-sprints in terms of the continuity of data acquisition and/or the consistency of maximal effort by the participants. With respect to the running velocity at which the negative work done in the horizontal anterior–posterior direction starts to increase, the current results support the previous findings (Cavagna et al., 1971). The present study analyzed the fastest intra-individual sprint among three to five 60 m sprints with reference to the report of Nagahara et al. (2018c). In their results, however, it is also true that there was no clear difference between the fastest and slowest intra-individual trials in the changes of step-to-step spatiotemporal variables and GRFs across the step number. Thus, the difference between the procedures to obtain GRF data (single sprint vs multi-sprints) might have produced a difference in the magnitude of the work values, but not induced that in the pattern of changes of the work values across running velocities.

It has been considered that the power output during the early stage of accelerated sprint running is mainly derived from the contractile components of the muscles, and the augmentation of the negative work at a high running velocity increases the mechanical energy stored in the elastic elements and enhances its contribution to power output during running (Cavagna et al., 1971). As evidence to support this, it has been shown that concentric force and power development are critical to sprint performance over a very short distance (less than 10 m) (Chelly and Denis, 2001; Sleivert and Taingahue, 2004; Young et al., 1995). In addition, musculoskeletal modeling studies (Hof et al., 2002; Lai et al., 2014, 2016) have shown that the relative contribution of tendon elastic strain energy to the mechanical work during sprint running increases with increasing running velocity, although these focused on the behavior of a given muscle-tendon unit. Considering these findings, at 80% V_max or higher, in which +W_kap decreased and −W_kap largely increased with increasing running velocity, either |−F_y, mean| or |−P_kap, mean| might be positively associated with +P_kap, mean. Certainly, the current result that at 80% V_max or higher, +P_kap, mean still increased while +F_{y, mean} became mostly constant suggests the contribution of tendon elastic energy to power generation at a high velocity running (Cavagna et al., 1971). At increments of 10% V_max ranging from 20 to 100% V_max, however, only the |−F_{y, mean}| at 100% V_max was significantly correlated with +P_kap, mean. By contrast, P_kap, mean was closely related to +F_{y, mean} at every 10% V_max over the entire acceleration stage until 100% V_max. These results indicate that until 90% V_max from block clearance, i.e. in most of the acceleration stage, muscle work done during the propulsive phase mainly contributes to generate +P_{kap, mean}, and the contribution of tendon elastic energy stored in the braking phase (Cavagna et al., 1971), if present, could be realized at around 100% V_max.

The total of each of ΔW_kap at every step over 50 m was strongly correlated with T_{50 m}. This agrees with previous reports indicating that maintaining a high GRF during the propulsive phase and a low value during the braking phase in the horizontal anterior–posterior direction are major determinants for achieving a high running velocity (Kawamori et al., 2013; Hunter et al., 2005; Morin et al., 2015; Nagahara et al., 2018a). In terms of the total work done in each 10 m section, ΔW_kap was highly correlated with T_{50 m} in all distance sections except for 40–50 m, notably in the 0–20 m section (Table 4). Thus, it can be said that at least on maximal sprint running over 50 m, maximizing +W_kap while suppressing an increase in |−W_kap|, notably in the early stage (less than 20 m) of the running distance, is one of the major determinants for achieving better total running performance. At the same time, the observed association between ΔW_kap and T_{50 m} rules out the possibility that the tendon elastic energy stored during the braking phase in the horizontal anterior–posterior direction (Cavagna et al., 1971) might contribute to better performance in accelerated sprint running over 50 m.

In addition to the horizontal anterior–posterior GRFs, many studies have already examined the influences of the vertical GRF during sprint running on running performance (Hunter et al., 2005; Kawamori et al., 2013; Morin et al., 2011, 2012, 2015; Nagahara et al., 2018a,b; Weyand et al., 2000). Among these studies, only one attempted to separately analyze the vertical GRF for each of braking and propulsive phases and to examine their associations with sprint performance (Nagahara et al., 2018b). From the limited findings, no significant correlations were found between sprint performance and vertical ground reaction impulses of either braking or propulsive phases (Nagahara et al., 2018b). In the current results, the total +W_v and |−W_v| over 50 m and specific running distances were positively correlated with T_{50 m}. This indicates that, in a similar way to the work done during the braking phase in the horizontal anterior–posterior direction, how the runner can minimize the work done during the braking and propulsive phases in the vertical direction will also be a factor leading to a high running performance over 50 m.

The present study had some limitations. It involved only young adult males as the participants, and notably did not involve elite sprinters. Further investigation including these subjects is required to elucidate the mechanics of maximal acceleration sprint running in elite athletes specifically trained to maximize the acceleration ability and determine factors for better sprint running performance. In addition, the present study did not conduct measurements concerning body kinematics and orientation during maximal sprint running. In the future, studies involving measurements of both kinetics and kinematics during sprint running will be needed to elucidate the association between body kinematics and work variables during sprint running.

In summary, the present study indicates that in maximal sprint running over 50 m, work done during the propulsive phase in the horizontal anterior–posterior direction accounts for the majority of the total external work done during the acceleration stage, and maximizing it while suppressing work done during the braking phase is essential to achieve a high running performance.