Running velocity over short distances is an important factor for successful performance in most team sports (2,21,26). Velocity is the product of stride length and stride rate or frequency, and to increase velocity, at least 1, if not both, of these parameters must be increased (23,24). From the deterministic model depicted in the Figure, it can be observed that both stride length and frequency are products of the amount and duration of force exerted. That is, the fundamental factors relating to optimizing velocity are the application of force and the time over which it is applied.
What is not apparent from the model is the direction of force application that is most important. That is, is the application of horizontal or vertical force of more importance to increase velocity? Within the literature, there are differing views as to the significance of each during sprint performance. Further ambiguity is added to this issue when additional sport-specific factors need to be considered, such as those encountered during contact situations in rugby and rugby league. Therefore, it is not entirely clear which force component is more important in affecting increased velocity within a sporting situation, such as rugby and rugby league.
The velocity requirements of the sport also need to be considered, such as the distances or durations over which players are commonly required to sprint. In sports where average sprint distances range from 10 to 30 m, it would appear that the ability to achieve maximum velocity within the shortest time frame is more important than the maximal velocity itself. That is, acceleration rather than maximum velocity would seem to be of greater importance to many sportsmen and women. This leads to the question of whether there are different directional requirements to force application when considering maximum velocity and maximum acceleration.
This literature review addresses this contention by (a) investigating the literature on horizontal force production and its effect on velocity and acceleration, (b) investigating the literature on vertical force production and its effect on velocity and acceleration, and (c) suggesting future research directions.
HORIZONTAL VERSUS VERTICAL FORCE PRODUCTION
DETERMINANTS OF VELOCITY
Velocity is the product of stride rate or frequency and stride length, and to increase velocity, at least 1, if not both, of these parameters must be increased without a proportionately similar or larger decrease in the other (9,20,23,24).
If velocity is simply the product of the frequency and length of a runner's stride (Figure), it would be possible to attain faster top running velocities simply by increasing the frequency of steps. Weyand et al. (24) reported that at top velocity during level treadmill running, stride frequencies were 1.16 times greater for a runner with a top velocity of 11.1 versus 6.2 m·s−1(1.8 fold range) (r 2 = 0.30). However, when the same researchers investigated the individual variation at top velocity on −6-degree decline and degree incline treadmill inclinations, no significant difference in stride frequency (4.38 ± 0.08 versus 4.34 ± 0.08 steps·s−1, respectively) was observed despite a significant difference in top velocity (9.96 ± 0.30 versus 7.10 ± 0.31 m·s−1 respectively). Hunter et al. (9) reported that step rate was not significantly related to sprint velocity (r = −0.14), as did Brughelli et al. (3) who reported a trivial correlation between maximum running velocity and stride frequency (r = 0.02). Heglund and Taylor (8) suggested that the range of stride frequencies used at different velocities tends to be narrow; however, these results were based on animal studies using quadrupeds ranging in body size from a mouse to a horse.
Stride frequency is directly influenced by the stride time, which in turn is compromised of swing time or flight time and contact time or stance time (20). That is,
Given swing time comprises the majority of the total stride time at top velocity (approximately 75% of stride time for maximum velocities of 6.2 to 11.1 m·s−1) (24), the relatively weak relationship between top velocity and maximal stride frequency may be the result of runners with different top velocities repositioning their legs in similar periods. That is, similarities between minimum swing times minimize the extent of possible variation in maximal stride frequencies. Regression relationships presented by Weyand et al. (24) showed that minimum swing times were only 8% (0.03 seconds) shorter for a runner with a top velocity of 11.1 versus 6.2 m·s−1 (r 2 = 0.06) during level treadmill running. In contrast, swing times at the slower velocities attained during inclined running were actually 8% shorter than those of the faster decline running (0.331 ± 0.005 and 0.359 ± 0.004 seconds, respectively). This difference, however, was attributed to interruption of the limb's arc because of the inclination of the running surface rather than differences in velocity.
If it is indeed the case that both fast and slow runners and fast and slow running velocities present similar swing times, then differences in maximal stride frequencies between fast and slow runners may result from the contact portion of the stride being shorter in faster runners and velocities. Brughelli et al. (3) reported a low correlation between maximum running velocity and contact time (r = 0.14); however, this is in contrast to other research. Nummela et al. (20) reported that maximal running velocity had a significant negative relationship with ground contact times (r = −0.52). In support of this finding, the contact times at maximum velocity observed by Weyand et al. (24) were significantly shorter for the faster decline running compared with those for the slower incline running (0.098 ± 0.003 and 0.130 ± 0.004 seconds, respectively). Kyröläinen et al. (12) reported that as running velocity increased from 3.45 to 8.25 m·s−1, contact times shortened from 0.227 ± 0.011 to 0.115 ± 0.007 seconds. Munro et al. (18) also reported a decrease in contact time as running velocity increased (0.27 ± 0.020 seconds at 3.0 m·s−1 and 0.199 ± 0.013 seconds at 5.0 m·s−1). It would seem that an increase in velocity because of an increase in stride frequency may be attributable to a decrease in the time the athlete is in contact with the ground.
As stated previously, if velocity is simply the product of the frequency and length of a runner's stride (Figure), then it would also be possible to attain faster top running velocities simply by increasing the stride length. Weyand et al. (24) reported that during level treadmill running, stride lengths at top velocities were 1.69 times greater (4.9 versus 2.9 m) for a runner with a top velocity of 11.1 versus 6.2 m·s−1 (r 2 = 0.78). It was also reported that stride lengths during maximal velocity decline running (4.6 ± 0.14 m at 9.96 ± 0.30 m·s−1) were significantly greater than those of maximal velocity incline running (3.3 ± 0.10 m at 7.10 ± 0.31 m·s−1). This is in agreement with other researchers (3,9) who reported significant correlations between maximum running velocity and stride length (r = 0.66 and r = 0.73, respectively).
Stride length is the sum of the takeoff, flight, and landing distance. However, Weyand et al. (24) reported that contact lengths did not differ between fast and slow runners with regression equations indicating that contact lengths were only 1.10 times greater for a runner with a top velocity of 11.1 versus 6.2 m·s−1 (r 2 = 0.30). Furthermore, when these results were analyzed within groups of men and women, it was reported that contact lengths varied little or not at all in relation to top velocity. Nummela et al. (20) reported that an increase in stride length was related to an increase in both vertical force (r = 0.58) and horizontal propulsion force (r = 0.73), suggesting that an increase in stride length is achieved by increasing both vertical and horizontal ground reaction forces (GRF). These results would tend to suggest that the predominant mechanism used by runners to achieve greater stride length is through greater application of GRF. That is, stride length is determined by the product of force exerted during foot-ground contact and the duration of the applied force (23,24).
It would appear that the major determinants of velocity are the forces applied to the ground and the time of foot-ground contact. That is, the attainment of greater velocity requires the application of greater support forces during briefer contact periods. GRF can be broken down into 3 components; however, typically, the horizontal (anterior-posterior) and vertical components are of most interest (10). Mero and Komi (14) have shown a relationship between running velocity and average net resultant force (vertical and horizontal), when related to body weight (r = 0.65), but there are numerous hypotheses regarding the relative importance of various GRF components to sprint performance. It has been shown that faster running velocity are associated with increased vertical force production (1,3,11,12,18,19,24), although a relationship to horizontal force production has also been shown (3,10,12,18,20). This section investigates the relationship of both components and suggests future directions for research in this area.
VERTICAL FORCE PRODUCTION
It has been theorized that during constant velocity running, there is no or very little horizontal resistance to overcome and that the propulsive forces that increase the body's forward velocity before takeoff simply offset the braking forces that decrease the body's velocity on landing (18,24). Furthermore, it is the vertical portion of stride that needs assistance because of the need to overcome gravity; therefore, applying greater forces in opposition to gravity would increase vertical velocity on takeoff, translating to an increased running velocity.
Weyand et al. (24) reported that an increase in vertical force production was the predominant mechanism used by runners to attain faster top velocities. Regression equations showed that at top velocity, mass-specific forces applied to oppose gravity were 1.26 times greater for faster runners compared with those for slower runners (r 2 = 0.39). Furthermore, when comparing the same subject at different velocities, significant differences in vertical forces were observed between the faster top velocities achieved during decline running and the slower top velocities of incline running (2.30 ± 0.06 and 1.76 ± 0.04 body weight (BW), respectively). Munro et al. (18) reported that as running velocities increased from 3 to 5 m·s−1, peak vertical GRF (relative to body weight) increased from 1.40 ± 0.11 to 1.70 ± 0.08 BW. Similar findings were reported by Nigg et al. (19) whereby vertical forces were found to significantly increase as velocity increased from 3 to 6 m·s−1 (1331 ± 225 to 2170 ± 489 N, respectively). Using the subject's reported mean body weight, these equate to estimated values of 1.9 and 3.0 BW, respectively. Similarly, Kyröläinen et al. (12) demonstrated changes in the GRF as velocity increased from 3.45 to 8.25 m·s−1. Maximal vertical force values increased from 1665 ± 219 to 2134 ± 226 N. As results were not reported by gender, relative values were not able to be calculated. Arampatzis et al. (1) also reported an increase in maximum vertical GRF (N/kg) between velocities of 2.5 and 6.5 m·s−1, although values were not presented. These findings support the theory of an increase in running velocity being achieved through an increase in vertical GRF.
HORIZONTAL FORCE PRODUCTION
In contrast to the above, it has been suggested that the critical factor in maximal sprint running is an increase in horizontal propulsive forces. To maintain velocity, the horizontal propulsive force must be equal to the braking force; however, to increase velocity, the propulsive force must be greater than the braking force (10,15,20), suggesting that horizontal propulsive forces play an important role in velocity development and acceleration.
Using multiple linear regression, Hunter et al. (10) found that relative propulsive impulse explained 57% (r 2 = 0.57) of the variance in sprint velocity, whereas relative vertical impulse did not explain any further variance in sprint velocity. These findings are supported by those of Nummela et al. (20) who also reported a significant correlation between maximal running velocity and mass-specific horizontal forces during the propulsion phase (r = 0.66,). Once again, mass-specific vertical force was not found to be related to the maximal running velocity. Munro et al. (18) reported that propulsive impulses, normalized by body weight, increased 79% from 0.14 ± 0.01 to 0.25 ± 0.2 BWI as velocity increased from 3.0 to 5.0 m·s−1. Over the same velocity range, vertical GRF only increased 21%. Kyröläinen et al. (12) also demonstrated changes in the GRF with increasing velocity. As velocity increased from 3.45 to 8.25 m·s−1, maximal forces in the horizontal direction increased 175% from 235 ± 42 to 675 ± 173 N, whereas vertical forces only increased 30%. As mentioned previously, the estimation of relative values was not possible because of the nonseparation of results by gender. Increases in horizontal forces were also reported by Brughelli et al. (3). As running velocity increased from 40 to 100% of maximum, relative horizontal forces increased 105% from 0.21 ± 0.02 to 0.43 ± 0.06 N/kg, whereas vertical forces only increased 18%. These findings seem to suggest that horizontal force production is more important than vertical force production in allowing an increase in running velocity.
It is worth noting the differences in methodologies used by the various studies. Results from studies using motorized (24) and nonmotorized (24) treadmills have been presented alongside those obtained from ground running (1,10,12,18-20). Although it may be questionable as to whether constant velocity running on a motorized treadmill is an accurate way of deducing cause and effect for overground running, of greater interest may be the conclusion presented by Weyand et al. (24) reporting that an increase in vertical force production was the predominant mechanism used by runners to attain faster top velocities when only vertical force production was measured. This is also true of Arampatzis et al. (1) and Nigg et al. (19) who reported that vertical forces were found to significantly increase as velocity increased. Of the studies who measured both vertical and horizontal force, Kyröläinen et al. (12) and Munro et al. (18) reported increases in both components with an increase in velocity, whereas Hunter et al. (10) and Nummela at al. (20) reported significant relationships only with the horizontal forces.
VERTICAL VERSUS HORIZONTAL
When the vertical and horizontal components are compared, it is apparent that the magnitude of the vertical forces is the larger of the two. Munro et al. (18) reported that at velocities ranging from 3.0 to 5.0 m·s−1, peak vertical GRF are typically 5-10 times greater than the peak horizontal forces. At 3.0 and 5.0 m·s−1, horizontal propulsive impulses were 10 and 15% of average vertical GRF, respectively. From the results presented by Kyröläinen et al. (12) at 3.45 and 8.25 m·s−1, horizontal forces were 14 and 32%, respectively, of vertical GRF. This apparent difference in magnitude is also supported by Brughelli et al. (3) who reported that at 40, 65, and 100% of maximum velocity, relative horizontal forces were 9, 12, and 18%, respectively, of relative vertical forces, which can be attributed to vertical acceleration, that is, 9.81 m·s−2.
Although there does appear to be a difference between vertical and horizontal force production, it seems that the magnitude of this difference decreases as velocity increases. If horizontal components of GRF are expressed as a percentage of the vertical component, then an increase in the reported percentage would imply that the horizontal component has increased proportionally more so than the vertical component. This increase in the percentage contribution of the horizontal component of GRF as speed increases is evident in the studies by Munro et al. (18), 10% at 3.0 m·s−1 increased to 15% at 5.0 m·s−1, Kyröläinen et al. (12), 14% at 3.45 m·s−1 increased to 32% at 8.25 m·s−1, and Brughelli et al. (3), 11% at 40% of maximum velocity increased to 19% at 100% of maximum velocity.
In addition to a nonuniform increase in the 2 main components of GRF, it is also evident that the increases in vertical forces with increasing velocity may not be linear. Although Munro et al. (18) and Nigg et al. (19) indicated that the increases in the vertical GRF were linear with increasing velocity in the range of 3-6 m·s−1, and Keller et al. (11) noted similar linear increases up to 3.5 m·s−1; above these velocities, the relationship has been reported to be nonlinear, and in some cases, there is no further increase in vertical forces. Brughelli et al. (3) reported that as running velocity increased from 40 to 65% of maximum velocity, relative horizontal forces increased 38% (0.21 ± 0.02 to 0.29 ± 0.03 N/kg) and relative vertical forces increased 17% (1.98 ± 0.23 to 2.31 ± 0.18 N/kg). However, as running velocity increased from 65 to 100%, relative horizontal forces increased a further 48% (0.29 ± 0.03 to 0.43 ± 0.06 N/kg), whereas relative vertical forces remained relatively constant and only increased 1% (2.31 ± 0.18 to 2.33 ± 0.30 N/kg). These findings are similar to those of Nummela (20) who also reported that relative vertical force remained constant after approximately 65% maximum velocity. It was observed that vertical force increased with the increasing velocity until the velocity of 7 m·s−1; thereafter, the velocity was increased without further increase in vertical force. As mentioned previously, Keller et al. (11) reported a linear increase in relative vertical forces at lower velocities (1.23 ± 0.10 BW at 1.5 m·s−1 to 2.45 ± 0.28 BW at 3.5 m·s−1); however, as velocity increased from 3.5 to 6 m·s−1, there were no significant increases in relative vertical forces (2.45 ± 0.28 to 2.38 ± 0.28 BW, respectively). Furthermore, a decrease was observed at the highest velocity of 8.0 m·s−1 (1.89 ± 0.49 BW), although this only represented values for 3 trials from 1 subject at this high velocity. Of interest are the findings of Hunter et al. (10) who also reported that the relationship between relative vertical impulse and sprint velocity showed signs of nonlinearity. In this case, however, it was shown that after a certain magnitude, any further increases in relative vertical impulse did not correspond to an increase in sprint velocity. Although these results were only reported in graphical form, they would seem to suggest that a ceiling effect may exist with regard to vertical force production, that is, past a certain point, velocity is no longer increased by increasing vertical GRF.
It has been shown that to reach faster maximum running velocities increases in both vertical and horizontal GRF are required. Although it appears that the vertical component is the larger of the 2 GRFs, it is suggested that running velocity is more dependent on horizontal than on vertical force as the velocities increase toward maximal. This is evident given that linear relationships were not observed between vertical force and running velocity at higher velocities. The significance of the horizontal component seems to be logical because one cannot increase horizontal velocity by increasing vertical force, but acceleration and deceleration of running velocity is produced mainly by changing horizontal force. The next section considers the contribution of vertical and horizontal force production with regard to acceleration.
Although velocity is very important in most sporting situations, acceleration is of relatively greater importance when covering only short distances at maximal effort (6,23). Therefore, it would appear that the ability to achieve maximum velocity within the shortest time frame is more important than maximal velocity itself. That is, acceleration becomes an essential focus when investigating the requirements of many sports.
As discussed previously, there are numerous hypotheses regarding the relative importance of various GRF components to sprint performance. The velocity-time curve can be divided into 3 phases, acceleration, constant velocity, and deceleration (15), and many of these hypotheses were intended to be the most applicable to the constant velocity phase of a sprint (10). It has been suggested that during constant velocity running, the propulsive forces that increase the body's forward velocity before takeoff simply offset the braking forces that decrease the body's velocity on landing (18,24). In contrast, acceleration is achieved by changing horizontal force such that the propulsive force is larger than the braking force (20). This leads to the question of whether there is a different directional requirement to force application when considering peak velocity and peak acceleration.
When investigating vertical and horizontal GRF characteristics, Mero (13) compared the acceleration phase of sprinting (velocity = 4.65 m·s−1) with that of previous work investigating maximal sprinting (velocity = 9.85 m·s−1) (16). The respective average vertical forces were equal (431 ± 100 N and approximately 563 N, respectively), whereas the horizontal forces produced during the acceleration phase of sprinting were about 46% greater than those produced during constant velocity maximal sprinting (526 ± 75 and 360 ± 42 N, respectively). It should be noted that the average vertical force from Mero et al. (16) was estimated from the stated value (1,286 ± 61 N), which was inclusive of body weight, minus the mean subject body weight (73.7 kg).
The vertical and horizontal values during acceleration obtained from Mero (13) at 4.65 m·s−1 can be expressed relative to body weight using the mean body weight and compared with the norms reported by Munro et al. (18) at corresponding velocities of 4.5 and 4.75 m·s−1. Again, it can be seen (Table.) that the respective relative vertical forces during acceleration and constant velocity were equal at comparable velocities, whereas the horizontal force during acceleration was greater than those recorded during constant velocity. These results suggest a greater emphasis on horizontal force during acceleration than there is during constant velocity running.
Hunter et al. (10) reported that both simple and multiple regression results showed a relatively strong trend for faster athletes to produce greater magnitudes of relative propulsive impulse (r 2 = 0.57). It was thought that athletes with the ability to produce higher horizontal propulsive forces would undergo larger increase in horizontal velocity during each stance phase, thereby accelerating faster. This finding is in agreement with the research of Mero and Komi (14) who reported a positive relationship between average resultant GRF during propulsion and sprint velocity between 35-m and 45-m marks (r = 0.84) and with those of Mero (13) who reported a high correlation between horizontal force production in the propulsion phase and running velocity (r = 0.69). These results further emphasize the importance of the propulsion phase during the acceleration phase of sprinting.
Hunter et al. (9) suggested that a high vertical GRF, and therefore, a high vertical velocity of takeoff, had a positive effect on step length; however, it also had a negative effect on step rate. In addition, there was evidence of a strong negative interaction between step length and step rate (r = −0.78). That is, those athletes who had a high step rate tended to have a shorter step length and vice versa. It was thought that more frequent ground contacts, via a low vertical GRF and short flight time, would allow a greater opportunity to accelerate. If flight time is increased during acceleration, as determined by a large relative vertical GRF, this would correspond to a decrease in the percentage of time spent in contact with the ground. Given an athlete can only influence their sprint velocity when in contact with the ground, this would be a disadvantage (10). That is, the most favorable magnitude of vertical GRF is one that creates a flight time only just long enough for repositioning of the lower limbs. If the athlete can reposition the limbs quickly, then a lower relative vertical GRF is sufficient, and all other strength reserves should be applied horizontally. It is only when an athlete cannot achieve or maintain a high step rate such as when fatigued, that a greater relative vertical GRF becomes more important (10).
Therefore, during the acceleration phase of a sprint, greater increases in horizontal propulsion are required to achieve high acceleration (10). Consequently, it is proposed that it would be of advantage to direct most training effort into producing a high horizontal GRF, not vertical GRF.
CONCLUSIONS/FUTURE RESEARCH DIRECTION
It is generally accepted that maximal running velocity requires high force production (2,15,17). As such, strength and power training methods are almost universally promoted as a means of training to improve running velocity (2,5,23). Therefore, the relationship between strength and power and velocity are of considerable interest in attempting to identify possible mechanisms for the enhancement of running performance (2,5,25,27).
It is also generally accepted that the more specific a training exercise to a competitive movement, the greater the transfer of the training effect to performance (5,21,22), and as such, athletes who require power in the horizontal plane, engage in exercises containing a horizontal component, whereas athletes who require power to be exerted in the vertical direction, train using vertical exercises (4,21). Given that a variety of training regimens are commonly used to improve muscular force output with the ultimate goal of enhancing sprinting performance (21,23), it would seem intuitive to focus on the enhancement of the forces, which are the most important in improving velocity.
From the literature, although it is apparent that force production is necessary in both the vertical and horizontal planes, it is the horizontal forces that experience the greatest increase when accelerating to maximal velocity. This becomes even more valid when the demands of rugby, league, or American football are taken into consideration. That is, the need to accelerate quickly over short distances, where increases in horizontal propulsive forces are essential, and the need to overcome large horizontal resistances, in the form of contact from opposing players. It would, therefore, seem critical that a movement-specific approach be applied to the design of strength and power resistance programs for such sports.
Currently, most gym-based resistance programs focus on exercises that principally work the leg musculature in a vertical plane. It is proposed that the transference of gym-based strength gains may be improved if exercises were used that involve both vertical and horizontal force production. That is, if successful performance requires force, velocity, and power (product of force and velocity) in the horizontal plane, improvements may be realized if the design of the resistance training program focuses on horizontal movement-specific exercises as well as traditional vertical exercises. To date, however, the effectiveness of a gym-based lower-body resistance training program with a horizontal component has not been investigated.
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