Competitive distance runners are faced with a unique challenge in sports: generating fast running speeds while making movements as economical as possible (26). Fast running speeds are believed to result from generation of high vertical forces on the ground while minimizing the time that the foot is in contact with the ground (25). However, a shorter ground contact time (tc) has been repeatedly shown to correlate with a higher mass-specific metabolic cost of running in both humans and animals (12,14,18,22,24). Therefore, it can be argued that the competitive elite distance runner must find a way to generate some critical amount of velocity for the distance being raced, perhaps with tc as long as possible at that velocity to minimize the metabolic cost of locomotion—that is, to maximize running economy. Because very small changes in running economy can result in very large changes in performance in elite distance runners (5,7,19), how the distance runner alters tc and gait with increasing speed may be important to performance outcomes.
Running economy is known to differ between athletes specializing in middle-distance (MD) events (e.g., 800 through 1500 m) and those specializing in long-distance (LD) events (e.g., 5000 m through the marathon), with each group demonstrating lower oxygen uptake values than the other at paces corresponding to their specialty racing distance (7,20). Similarly, elite male distance runners have a significantly lower oxygen uptake at any given submaximal speed compared with elite female distance runners (7). Although these differences in economy may be due to contrasting physiological traits between men and women or between MD and LD specialists, it may also be the result of differences in tc or other components of running mechanics. For example, in a group of 31 subjects, submaximal V˙O2 showed a significant positive correlation with tc (26), and in both humans and bipedal animal runners, 70%–90% of the increase in metabolic cost with increasing running speed can be explained by the decrease in tc (18). Ultimately, whether measures of tc, known to be proportional to the mass-specific metabolic cost of running, follow the same pattern with increasing speed as measures of oxygen uptake in groups of men versus women or MD versus LD specialists is unknown.
Therefore, the purpose of this investigation was to characterize changes in tc and select kinematic variables as a function of speed in elite distance runners. Specifically, this study examined if differences existed between a) elite male and female distance runners and b) MD and LD specialists. Our working hypotheses were that a) elite female distance runners have shorter tc compared with elite men running at common running speeds and b) elite MD and LD specialists demonstrate differing rates of change in tc with an increase in running speed, each of the above paralleling the already published metabolic responses to exercise in these groups.
Twelve men and six women agreed to participate in the study. Of the 12 men, 8 were classified as elite distance runners. All eight elite men were professional distance runners and had met the qualifying time for their respective nation’s 2008 Olympic Trials in track and field. Each elite male posted a competitive mark in 2007 or 2008 that placed them in the top 250 in the world for their primary competitive event distance. The specialty racing events of these elite male distance runners included the 1500 m/mile (n = 4), 5000 m (n = 1), and the 10,000 m (n = 3). From these event area specialties, the elite males were grouped for comparison into MD (1500-m/mile specialists, n = 4) and LD (5000- and 10,000-m specialists, n = 4) classifications, as has been done elsewhere (20). Four additional men were classified as collegiate distance runners, on the basis of age, educational status, and competitive performance level. These four men were all accomplished members of the Indiana University cross-country and track-and-field teams. All six women were classified as elite. Although not as accomplished in performance history as the elite men’s group, the elite women’s group included one US Olympic Trials participant, one US large city marathon champion, and three athletes who were conference champions or All-Americans in their respective events while in college. Subject characteristics are presented in Table 1. All subjects gave written informed consent before testing, and all protocols and procedures used in testing were approved by the Institutional Review Board of Indiana University.
To measure variables related to running gait, subjects completed separate 30-s running stages at constant speeds on a motorized treadmill (model 18-72; Quinton, Bothell, WA). Male subjects ran at nine speeds in ascending order from 5 to 7 m·s−1 with stage increments of 0.25 m·s−1, whereas female subjects ran at eight speeds in ascending order from 4 to 5.75 m·s−1 with stage increments of 0.25 m·s−1. These starting and ending speeds were specifically selected because they match competitive running speeds achieved by high-level distance runners in events ranging from 1500 m to the marathon (42.2 km). Running speed was verified with a laser tachometer (DT-2234C; Kernco, El Paso, TX) and revolutions per minute-versus-speed charts specific for the treadmill belt length. For all tests, subjects wore lightweight racing flats and had a warm-up period of no less than 10 min of running. Each 30-s stage was separated by a period of standing rest, with the duration selected by the subject. Subjects were instructed to recover fully between stages, with a typical recovery time lasting ∼120 s. At each speed, subjects lowered themselves onto the moving treadmill belt, while supporting their weight with their upper body via the treadmill’s handrails. Typically, subjects needed approximately four to eight steps to be running unassisted, and it was at this point that the 30-s data collection period started.
Selected gait kinematic variables were measured via accelerometry. Separate wireless triaxial 10-g accelerometer devices (G-Link; MicroStrain, Williston, VT) were attached to the top of each shoe, using plastic ties to attach the device to the shoelaces. The accelerometers were attached as securely as possible to minimize any inertial artifacts from movement of the device on the shoe. The accelerometers sampled each axis at a rate of 1024 Hz, with data from each 30-s stage stored in separate files and wirelessly downloaded after the completion of the testing session for later analysis. Accelerometer raw data were analyzed using a custom in-house computer program, following a procedure similar to the one described elsewhere (24). Briefly, the unfiltered and unprocessed waveform output from the y axis (oriented relative to the frontal plane) and z axis (oriented relative to the transverse plane) of the accelerometer was used to identify markers corresponding to the precise times of the foot contacting the ground and the foot toeing off (breaking contact) from the ground. An example of the accelerometer output waveform used for ground contact and toe-off identification is shown in a representative trace in Figure 1.
From this accelerometric output, we were able to measure or calculate the following for each foot: a) tc, defined as the time (s) from when the foot contacts the ground to when the foot toes off from the running surface; b) swing time (tsw), defined as the time (s) from toe off to initial ground contact of consecutive footfalls of the same foot; c) stride frequency, defined as the number of ground contact events (i.e., steps taken) per second; and d) stride length, defined as the length (m) the treadmill belt moves from toe off to initial ground contact in successive steps. Values of tc, tsw, stride length, and stride frequency were determined and calculated from the average of accelerometric values obtained from a minimum of 20 consecutive steps of the same foot, starting 5 s into each 30-s stage. Furthermore, because previous studies have indicated that the metabolic cost of locomotion per unit of body weight is proportional to the inverse of tc:
where Emetab is the rate of energy consumption (W), Wb is body weight (N), and C (J·N−1) represents a “cost coefficient” dependent upon the species and biped/quadruped mode of locomotion (11,14,18,21,24), we examined 1/tc at all speeds for men and women, as well as for MD and LD specialists.
For all parameters, a normal distribution was confirmed using the Shapiro–Wilk test. A separate 2 × 4, subject groups (sex) × condition (speed), split-plot repeated-measures ANOVA was followed by tests of a priori simple main effects to determine sex differences at common speeds for all dependent variables. Least squares regression was used to determine differences in the rate of change in dependent variables as a function of speed, with differences in slopes between groups determined by using Student’s t-tests. The α for statistical significance for all comparisons was set at P < 0.05. For comparisons not reaching statistical significance, the Cohen d statistic was calculated to determine an estimate of effect size because of the small sample sizes used in some comparisons.
Gait characteristics and sex differences
As running speed increased, tc and tsw were reduced in both sexes, whereas stride length and stride frequency increased (Fig. 2). The response of the previously listed variables to increasing speed within each sex was linear, with R2 values of 0.98 or greater for all comparisons. The rate of change in tc with increasing speed was similar between men (regression slope = −0.0198 s·m−1·s−1) and women (regression slope = −0.0239 s·m−1·s−1) and did not reach statistical significance (P = 0.10, d = 1.1). Men displayed a significantly larger reduction in tsw with increasing speed (men’s regression slope = −0.0235 s·m−1·s−1, women’s regression slope = −0.0091 s·m−1·s−1, P = 0.02). However, both sexes seemed to be approaching a common functional minimum in tsw as speeds increased. As speed increased, men seemed to rely slightly more on increasing stride frequency (men’s regression slope = 0.213 Hz·m−1·s−1, women’s regression slope = 0.171 Hz·m−1·s−1, P = 0.28, d = 0.8), whereas women seemed to rely slightly more on increasing stride length (men’s regression slope = 0.189 m·m−1·s−1, women’s regression slope = 0.234 m·m−1·s−1, P = 0.29, d = 1.8), although neither comparison reached statistical significance.
Because men and women ran at common speeds of 5.00, 5.25, 5.50, and 5.75 m·s−1, comparisons could be made between sexes at these specific paces. At each of the four common speeds, men displayed significantly longer tc, longer tsw, longer stride lengths, and lower stride frequencies compared with women (Fig. 2). When data for these variables were normalized to standing height, no significant sex differences were present at any speed for tc, tsw, and stride length; however, women still demonstrated significantly larger stride frequencies per unit of standing height (Fig. 3).
Women displayed significantly smaller values of tc, compared with men running at the same speeds (Fig. 4A), suggesting a higher mass-specific metabolic cost to run at any submaximal pace compared with elite men. The rate of increase in 1/tc as speed increased was not different between men and women.
Event speciality differences
When elite males were grouped by event specialty (MD vs LD), MD specialists demonstrated a significantly smaller rate of change in tc as speed increased compared with LD specialists (MD regression slope = −0.0169 s·m−1·s−1, LD regression slope = −0.0202 s·m−1·s−1, P = 0.01). Figure 5 displays the mean values for tc, tsw, stride frequency, and stride length versus speed for the MD and LD men. MD specialists showed a trend toward a smaller increase in stride frequency (P = 0.06, d = 0.7) and a larger increase in stride length (P = 0.07, d = 0.8) as speed increased, compared with LD specialists. The MD and LD groups were well matched for height (MD height = 179.7 ± 6.6 cm, LD height = 180.5 ± 5.9 cm); therefore, unlike the differences between men and women at common speeds, differences between event area specialties are not explained by standing height.
Comparing elite men by event area specialty, LD specialists demonstrated a larger increase in 1/tc with increases in speed, compared with MD specialists (MD regression slope = 0.198, LD regression slope = 0.234, P = 0.01), suggesting a larger increase in metabolic cost as speed increased in the LD specialists.
The primary findings of this investigation are a) men and women demonstrated significant differences in tc at common speeds, suggesting differences between sexes in metabolic cost of locomotion, and b) elite male MD and LD specialists demonstrated significant differences in the rate of change in tc as speed increased, suggesting speed-dependent differences between groups in metabolic cost. Our use of accelerometers represents an extension of the use of this technique to determine tc and selected gait kinematic variables in humans (16,24). However, the elite nature of the sample (both male and female) used in this study represents a unique cohort with minimal data in the literature.
General changes in gait with increasing speed
As treadmill speed increased, we observed steady linear decreases in mean tc and tsw and steady linear increases in stride length and stride frequency (Fig. 2). The linear response of these variables to changes in speed is consistent with measures reported elsewhere in humans (4,20,25) and terrestrial animals (14,18). However, our observed rate of change in variables like stride length and stride frequency as speed increased differs from other published data. These differences may be a function of the measurement techniques used, the different running speeds used, or differing abilities of the subject cohorts. For example, in a group of 12 male recreational runners running at much slower speeds of 3.15 to 4.12 m·s−1, Cavanagh and Kram (4) observed a regression slope of step length versus speed of 0.299 m·m−1·s−1, 58% larger than the 0.189-m·m−1·s−1 slope produced by the elite male runners at speeds ranging from 5.0 to 7.0 m·s−1 in the present study. For step frequency versus speed, the cohort of Cavanagh and Kram displayed a regression slope of 0.115 Hz·m−1·s−1, compared with 0.213 Hz·m−1·s−1 for our elite cohort. Note that both the cohort of Cavanagh and Kram and our male subjects were well matched for mean height (179.6 vs 181.6 cm); therefore, these differences are likely not dependent upon leg length or stature differences. Our data would suggest that in elite distance runners running at speeds corresponding to elite race pace, there is a greater reliance on increasing stride frequency and a smaller dependence on increasing stride length per unit change in speed, compared with recreational runners at much slower speeds. This concept would be supported by early research by Högberg (10), who demonstrated that increases in running speed in humans are primarily achieved by increasing stride length at lower speeds (<6.0 m·s−1) and increasing stride frequency at higher speeds, with this relationship subsequently confirmed by others (25).
Comparing times for tc in the present investigation to other published data, Williams et al. (27) (using a runway-mounted force platform) showed a mean tc in a group of elite women of 0.157 s at a speed of 5.31 m·s−1, similar to our observed tc of 0.152 s at 5.25 m·s−1. In men, Bushnell and Hunter (2) used high-speed video during overground running with a 10-m capture zone to determine tc. The authors reported a mean tc value of 0.177 s for a group of 10 male collegiate distance runners running at a speed of 5.81 m·s−1. At a slightly slower speed of 5.75 m·s−1, our cohort of men displayed a substantially shorter mean tc of 0.155 s. However, although Bushnell and Hunter used a group of men that is perhaps one of the most talented endurance-trained cohorts available in the literature for comparison with our subjects, the authors did not report standing heights or leg lengths for their subjects. Therefore, we do not know if differences in tc values between studies are dependent upon the measurement technique used, the running ability of the subjects, or potential differences in height.
Sex differences—common running speeds
At common running speeds from 5.0 to 5.75 m·s−1, women demonstrated significantly shorter tc and tsw, greater stride frequency, and shorter stride length compared with men. The most logical explanation for these differences is that the cohort of women had a mean height 10.4 cm shorter than that of the group of men. In other words, to maintain the same pace, the group of shorter women selected a strategy of higher stride frequencies and shorter stride lengths than the group of taller men. As a result, tc at common speeds was significantly shorter in the women versus the men. When tc, tsw, and stride length were normalized to standing height, the differences in these variables between sexes were not present (Fig. 3). However, stride frequency remained significantly greater in the women at each speed, even when normalized to standing height. It is important to note that these underlying sex differences in kinematic variables at common running speeds may not be solely due to anthropometric differences but could certainly be due to other factors that may differ between our male and female cohorts: e.g., application of greater ground forces by the men (23,25) or differences in muscle fiber type distribution (23).
tc as an indicator of metabolic cost of locomotion
It has been proposed that the energy cost of running is primarily determined by the metabolic cost of producing a force to support body weight (14,18,22). Expanding on this concept, Kram and Taylor (14) hypothesized that the energy used per unit weight of active muscle should be inversely proportional to the time available to produce force in each step—that is, tc. In walking and running humans, the measured absolute metabolic cost of locomotion has been tightly correlated (R2 = 0.93) with body weight divided by tc (12). In bipedal animal and human runners, 70%–90% of the increase in metabolic cost with increasing speed can be explained by the decrease in tc (18). Our cohort of elite women demonstrated significantly shorter values of tc compared with elite men running at the same speeds, which suggests that women should have a higher mass-specific metabolic cost than men to run at common speeds. Although we did not measure oxygen consumption in this study, insight on the differences in metabolic cost of submaximal running in elite distance runners has been published by Daniels and Daniels (7). In a group of 20 elite women distance runners, mass-specific V˙O2 (mL·kg−1·min−1) was significantly higher in women at common running speeds, compared with a group of 45 elite men, paralleling the response observed in our data of 1/tc (Figs. 4A, B). Daniels and Daniels reported that elite men are 6%–7% more economical than elite women across four submaximal running speeds. Our tc data at four slightly faster speeds suggest elite men are 8%–9% more economical than elite women. Comparatively, Taylor et al. (22) speculated that smaller mammals with higher cycle rates during locomotion (and thus faster muscle shortening velocities) likely would demonstrate higher metabolic costs to run at any given speed. This concept is consistent with our observed differences in contact times between the larger, taller men and the smaller, shorter women. Simultaneous measures of tc and oxygen consumption in elite male and female runners would be an appropriate next step to determine precisely how much of the observed sex difference in running economy can be explained by differences in tc.
Event specialty differences—MD and LD athletes
The LD group had a significantly larger decline in tc compared with the MD group as running speed increased (Fig. 5A). Following the concept that the inverse of tc is proportional to the metabolic cost, the MD athletes saw a 25.4% increase in metabolic cost as running speed increased from 5 to 7 m·s−1, whereas the LD athletes demonstrated a 31.1% increase in cost. However, the longer tc in the LD specialists at the slowest speed may be a preferred trait in this group, perhaps allowing for a lower metabolic cost (i.e., better running economy) at the slower speeds that correspond to their preferred racing distance. Again, from the work of Daniels and Daniels (7), comparisons of elite male marathoners to elite male 800-m/1500-m specialists found that the marathoners were more economical (i.e., exhibited ∼5% lower V˙O2) at a slower speed (∼270 m·min−1) compared with the 800-m/1500-m group. The marathoners also demonstrated significantly higher oxygen consumption (∼8% higher) compared with the 800-m/1500-m specialists at a faster speed corresponding to 1500-m race pace, and the regression slope relating V˙O2 to running speed was significantly higher in the marathoners (∼24% higher), compared with the 800-m/1500-m specialists. The steeper increase in our accelerometer-derived data of 1/tc versus running speed in elite male LD athletes parallels the metabolic data from Daniels and Daniels. Using either study’s measure (or proportional estimate) of metabolic cost, the differing rates of increase in energy cost between MD and LD athletes with increasing speed may be a predominant factor in event area selection and competitive success.
We could ask if the slower decline in tc as speeds increased within the MD athlete cohort is a direct result of adaptations to prolonged training at speeds faster than those that the LD athletes typically use. From a 300- or 600-Hz video (Exilim EX-F1; Casio, Tokyo, Japan) collected on four elite male subjects (two MD, two LD), all demonstrated a midfoot or forefoot ground contact at the fastest running speed, independent of event area specialty. However, at the slowest running speed, the two LD athletes demonstrated a consistent heel strike ground contact, whereas the two MD athletes consistently landed with a midfoot strike. Because faster running speeds typically require a shift more toward a midfoot or forefoot strike (3,11), chronic training at faster speeds commonly achieved by MD athletes may have caused an adaptation where the MD athletes naturally select a mid/forefoot strike mechanic, even at slower speeds where it may be less economical (26). The shorter tc in the MD group versus the LD group at the slowest running speed, despite the same standing height, would lend support to this notion, as do data that indicate that sprint athletes have shorter tc than endurance athletes at a common speed of 5.81 m·s−1 (2). Other investigations have indicated lower oxygen consumption in athletes who are more prominent heel strikers or who have a smaller shank angle at the point of ground contact (26,27). It would logically follow that athletes who are heel strikers would likely have longer tc, with more time available for force generation and thus a lower metabolic cost, compared with midfoot or forefoot strikers. However, this concept needs to be measured directly.
Alternatively, does a smaller increase in energy cost as speed increases somehow predispose an individual to success in MD events, causing the athlete to choose this distance as his or her specialty? Within a group of 10 male national-class MD runners, energy expenditure at 7 m·s−1 showed significant negative correlations to Type II fiber distribution (r = −0.67), Type II fiber area (r = −0.64), and the percentage of myosin heavy chain II isoforms (r = −0.61) (15). This indicates that the more Type II fibers an athlete had, the less energy he or she expended running at elite 1500-m competition speed, and elite MD runners as a group have been shown to possess more Type II skeletal muscle fibers than elite LD runners (6). It has been argued that as more motor units are recruited at fast running speeds corresponding to MD race pace, MD athletes rely on an increased contribution from Type II fibers and glycolytic energy production to meet the energy demand of running, compared with LD athletes who rely more on an increased oxygen consumption to meet the additional adenosine triphosphate demand (15). As Type I/Type II fiber type distribution is generally believed to be fixed and not substantially altered with chronic training (1,8,13), one could argue that the genetically determined fiber type distribution is still the primary determinant of event specialty success, as has been traditionally suggested (9,17). However, experienced athletes, coaches, and scientists involved with the discipline of competitive distance running would certainly point out there are many other likely factors (both physical and psychological) related to MD or LD event selection. Therefore, it is unlikely that one factor, such as muscle fiber type distribution, is solely responsible.
There are limitations that need to be considered when interpreting and applying the data presented in this study. Several comparisons did not reach statistical significance despite an adequate effect size because of a small sample size resulting in a lack of statistical power. The elite nature of the cohort studied does make the data set valuable and unique despite these limitations; however, the relationships and outcomes suggested in this article should be confirmed in larger cohorts. Clearly, the relationship between tc and metabolic cost and the apparent difference between sexes should be confirmed by simultaneous measurement of kinematic variables and oxygen uptake at multiple speeds. Our observations suggest that future studies examining differences in metabolic cost between MD and LD athletes would benefit from the inclusion of additional kinematic measures, such as shank angle at the point of ground contact and documentation of heel or forefoot strike at different speeds. Similarly, it would be enlightening to know if improvements in running economy with chronic training are manifested by changes in tc.
In conclusion, elite male and female distance runners displayed differing gait responses at common running speeds, with the significant differences in tc observed at common speeds suggesting differences between sexes in the metabolic cost of locomotion. Elite male MD and LD specialists demonstrated differences in the rate of change in tc as speed increased, suggesting speed-dependent differences between groups in metabolic cost. The known differences in running economy at common speeds between elite male and female distance runners, as well as between elite MD and LD specialists, may be largely influenced by differences in foot tc.
This study was supported by a grant from the Amateur Athletics Union/Bell-Updyke-Willett Kinesiology Research Fund, Indiana University School of Health, Physical Education, and Recreation, and a grant from the High Performance Division of USA Track and Field.
None of the authors of this article has any conflicts of interest or financial conflicts to report.
The results of the present study do not constitute endorsement by the American College of Sports Medicine.
1. Barnard RJ, Edgerton VR, Peter JB. Effect of exercise on skeletal muscle. I. Biochemical and histochemical properties. J Appl Physiol. 1970; 28: 762–6.
2. Bushnell T, Hunter I. Differences in technique between sprinters and distance runners at equal and maximal speeds. Sports Biomech. 2007; 6: 261–8.
3. Cavanagh PR, Lafortune MA. Ground reaction forces in distance running. J Biomech. 1980; 13: 397–406.
4. Cavanagh PR, Kram R. Stride length
in distance running: velocity, body dimensions, and added mass effects. Med Sci Sports Exerc. 1989; 21 (4): 467–79.
5. Costill DL. The relationship between selected physiological variables and distance running performance
. J Sports Med Phys Fitness. 1967; 7: 61–6.
6. Costill DL, Daniels J, Evans W, Fink W, Krahenbuhl G, Saltin B. Skeletal muscle enzymes and fiber composition in male and female track athletes. J Appl Physiol. 1976; 40: 149–54.
7. Daniels J, Daniels N. Running economy
of elite male and elite female runners. Med Sci Sports Exerc. 1992; 24 (4): 483–9.
8. Gollnick PD, Armstrong RB, Saltin B, Saubert CW, Sembrowich L, Shepherd RE. Effect of training on enzyme activity and fiber composition of human skeletal muscle. J Appl Physiol. 1973; 24: 107–11.
9. Gollnick PD, Matoba H. The muscle fiber composition of skeletal muscle as a predictor of athletic success. An overview. Am J Sports Med. 1984; 12: 212–7.
10. Högberg P. Length of stride, stride frequency
, “flight” period and maximum distance between the feet during running with different speeds. Arbeitsphysiologie. 1952; 14: 431–6.
11. Hoyt DF, Wickler SJ, Cogger EA. Time of contact and step length: the effect of limb length, running speed, load carrying and incline. J Exp Biol. 2000; 203: 221–7.
12. Hoyt RW, Knapik JJ, Lanza JF, Jones BH, Staab JS. Ambulatory foot contact monitor to estimate metabolic cost of human locomotion. J Appl Physiol. 1994; 76: 1818–22.
13. Ingjer F. Effects of endurance training on muscle fibre ATP-ase activity, capillary supply and mitochondrial content in man. J Physiol. 1979; 294: 419–32.
14. Kram R, Taylor CR. Energetics of running: a new perspective. Nature. 1990; 346: 265–7.
15. Kyrolainen H, Kivela R, Koskinen S, et al.. Interrelationships between muscle structure, muscle strength, and running economy
. Med Sci Sports Exerc. 2003; 35 (1): 45–9.
16. Le Bris R, Billat V, Auvinet B, Chaleil D, Hamard L, Barrey E. Effect of fatigue on stride pattern continuously measured by an accelerometric gait recorder in middle distance runners. J Sports Med Phys Fitness. 2006; 46: 227–31.
17. Rall J. Energetic aspects of skeletal muscle contraction: implication of fiber types. In: Terjung R, editor. Exercise and Sport Sciences Reviews. New York (NY): MacMillan; 1985. p. 33–74.
18. Roberts TJ, Kram R, Weyand PG, Taylor CR. Energetics of bipedal running. I. Metabolic cost of generating force. J Exp Biol. 1998; 201: 2745–51.
19. Saunders PU, Pyne DB, Telford RD, Hawley JA. Factors affecting running economy
in trained distance runners. Sports Med. 2004; 34: 465–85.
20. Svedenhag J, Sjodin B. Body-mass–modified running economy
and step length in elite male middle- and long-distance runners. Int J Sports Med. 1994; 15: 305–10.
21. Taylor CR. Force development during sustained locomotion: a determinant of gait, speed and metabolic power. J Exp Biol. 1985; 115: 253–62.
22. Taylor CR, Heglund NC, McMahon TA, Looney TR. Energetic cost of generating muscular force during running: a comparison of large and small animals. J Exp Biol. 1980; 86: 9–18.
23. van Ingen Schneau J, de Koning JJ, de Groot G. Optimization of sprinting performance
in running, cycling and speed skating. Sports Med. 1994; 17: 259–75.
24. Weyand PG, Kelly M, Blackadar T, et al.. Ambulatory estimates of maximal aerobic power from foot–ground contact times and heart rates in running humans. J Appl Physiol. 2001; 91: 451–8.
25. Weyand PG, Sternlight DB, Bellizzi MJ, Wright S. Faster top running speeds are achieved with greater ground forces not more rapid leg movements. J Appl Physiol. 2000; 89: 1991–9.
26. Williams KR, Cavanagh PR. Relationship between distance running mechanics
, running economy
, and performance
. J Appl Physiol. 1987; 63: 1236–45.
27. Williams KR, Cavanagh PR, Ziff JL. Biomechanical studies of elite female distance runners. Int J Sports Med. 1987; 8 (2 suppl): 107–18.