1 INTERACTION OF STEP LENGTH AND STEP RATE DURING SPRINT RUNNING Joseph P. Hunter 1, Robert N. Marshall 1,, and Peter J. McNair 3 1 Department of Sport and Exercise Science, The University of Auckland, Auckland, New Zealand Faculty of Health and Sport Science, Eastern Institute of Technology, Hawkes Bay, New Zealand. 3 Physical Rehabilitation Research Centre, School of Physiotherapy, Auckland University of Technology, Auckland, New Zealand INTRODUCTION Sprint-running velocity is the product of step length and step rate. Research conducted on the importance of these factors to sprint performance has shown mixed results (e.g. Armstrong et al., 1984; Mero et al., 1981). However, despite these different opinions, it is clear that increasing step length or step rate will increased sprint velocity, as long as one factor is not increased at the overwhelming expense of the other. (From this point forward, we will refer to the negative effect that step rate might have on step length, and vice versa, as a negative interaction.) In conjunction with knowledge of how to improve step length and step rate, knowledge of how an improvement in one factor will likely affect the other would be of great value to sprint coaches. The negative interaction between step length and step rate has been discussed previously (Hay, 1994), however, has not been researched directly. Therefore, the purposes of this study were to: 1) quantify this negative interaction and determine its likely sources; and ) investigate the effects of manipulation of the negative interaction. METHODS This study involved a total subject pool of 36 athletes (31 males and 5 females) who regularly participated in sports involving sprint running (e.g. athletics, soccer, touch rugby, etc). Mean ± SD for age, height, and body mass of the 36 athletes were 3 ± 5 yrs, 1.76 ± 0.07 m, and 7 ± 8 kg, respectively. Data collection involved each athlete performing a warm-up, followed by maximal effort sprints, 5 m in length, from a standing start. Sagittal plane video data of two steps (sampled at 40 Hz) and ground reaction force data (sampled at 960 Hz) were collected at the 16 m mark of the sprints. The human body was modelled as 1 s: feet, shanks, thighs, truck, head (including neck), and upper and lower arms. Data were smoothed with a fourth-order, low-pass Butterworth filter (Winter, 1990). Cut-off frequency ranged from 7-1 Hz for kinematic data, and was 75 Hz for all ground reaction force data. Twenty-four variables based on the determinants of step length and step rate (see Figures 1 and ) were calculated for each athlete. For each variable, the mean of the fastest three trials of each athlete was used for analysis. The variables included: Sprint velocity: mean velocity of centre of mass of the body (COM) during the step from the force plate. Step length: between point of of one foot (head of nd metatarsals) to that of the following for the opposite foot. Step rate: steps taken per second. Stance and flight : the the COM travelled during the stance and flight phases, respectively. Stance time and flight time: duration of the stance and flight phases. Relative height of : the height of the COM at, to that of. Angle of : the angle, measured to, of the velocity vector of the COM at. Speed of : the magnitude of the resultant velocity of COM at. Horizontal and velocity of and : and velocity of COM at and from the force plate. Horizontal velocity : mean velocity of COM during the stance phase. Touchdown and s: from the head of the nd metatarsals of the stance foot to the COM, at the moments of and. Foot movement : the the head of the nd metatarsal of the stance foot moved during the stance phase. Angles A and C: the angle measured between and a line passing through the stance ankle and the COM, at the moments of (A) and (C). (See Figure 3.) Angles A and C were a measure of positions at and as listed in Figures 1 and Angle B: The range of motion,, of the line passing through the stance ankle and COM. (See Figure 3.) Relative GRI: net (for-aft) ground reaction impulse expressed to body mass. The units are m/s and reflect the velocity of COM during the stance phase (ignoring ). Relative GRI: ground reaction impulse less body weight impulse, then expressed to body mass. The units are m/s and reflect the velocity of COM during the stance phase (ignoring air resistance). To investigate the sources of the negative interaction between step length and step rate, the athletes were paired according to the following criteria: same gender, similar sprint velocity (difference of no greater than 0.05 m/s), similar leg length (difference of no greater than 6.0 cm), and notably different step rate (difference of at least 0.15 Hz). From the total pool of 36 subjects, 8 pairs (7 pairs of males and 1 pair of females) fit these criteria, and were used in the subsequent analysis. Mean ± SD of the 16 subjects for age, height, and body mass were 4 ± 5 yrs, 1.76 ± 0.08 m, and 73 ± 9 kg, respectively. From each pair of subjects, one subject was put into the High Step Rate Group, and the other into the Long Step Length Group, according to the which particular technique they used ( to their partner). It was assumed that the group differences in step rate and step length would be due, at least in part, to the
2 negative interaction discussed earlier. To find the possible sources of this interaction, paired t-tests were used to detect group differences in the determinants of step rate and step length. step rate step time stance time flight time velocity stance height at during flight foot movement vert. velocity postions at inertial paramaters positions at GRI Figure 1: Determinants of step rate (adapted from Hay, 1994). step length stance flight foot movement height at angle speed during flight velocity at postions at inertial paramaters positions at horiz. velocity vert. velocity GRI GRI Figure : Determinants of step length (adapted from Hay, 1994).
3 A B C Figure 3: Angle A is at, angle B is the range of motion, and angle C is at. The lines intersect the ankle joint centre and the centre of mass of the body. To investigate the effects of manipulation of the negative interaction between step length and step rate, a simple simulation was performed. Using the data from the fastest sprinter as a starting point (see Table 1), the flight determining parameters ( and velocity of, and angle and height of ) were individually altered and the effects on step rate, step length, and sprint velocity were calculated. Angle of (θ) and magnitude of the resultant velocity of (v) were calculated using 1 θ = tan ( vv / vh ) and v = v v + vh where v v and v h are the and velocity of, respectively. Flight (D flight ) and flight time (T flight ) were calculated using equations provided by Hay (1994) D flight = v sin cos v cos ( v sin ) g h θ θ + θ θ + g and T flight = v sin ( v sin ) g h θ + θ + g where g is a gravitational constant (9.81 m/s ), h is the height of, and θ is the angle of (in radians). For small changes in the flight determining factors, stance (D stance ) and stance time (T stance ) were assumed to remain constant, therefore, step length (SL), step rate (SR) and sprint velocity (SV) were calculated using SV = SL SR = ( D + D ) (T T ) s tan ce flight s tan ce + flight The validity of the simulation was checked by calculating step length, step rate and sprint velocity from the stance time (0.111 s), stance (0.95 m), velocity of (0.41 m/s), velocity of (8.91 m/s), and height of (0.016 m) of the fastest sprinter. The resulting step length, step rate, and sprint velocity could then be compared to the true life data shown in Table 1. RESULTS AND DISCUSSION For the group of 16 athletes included in the analyses there was evidence of a significant negative interaction between step length and step rate (Pearson r = -0.70, P < 0.01). That is, those athletes whom had a high step rate tended to have a short step length, and vice versa. Table 1 shows the results of the paired t-tests between the Long Step Length and High Step Rate Groups. The athletes in the Long Step Length Group tended to have a longer flight, which was achieved via a longer flight time. This was the product of a greater velocity of, and, in turn, a greater GRI. There were no significant differences in velocity or height of. Nonetheless, even though the longer flight time had a positive effect on step length, it also had a negative effect on step rate. In brief, velocity of (determined largely by the GRI) was the main source of the negative interaction between step length and step rate. The validity check for the simulations resulted in calculated values of 1.95 m, 4.47 Hz, and 8.74 m/s for step length, step rate, and sprint velocity, respectively. These were very close to the true life data of 1.98 m, 4.45 Hz, and 8.80 m/s (as shown in Table 1). The simulations, however, did include two main assumptions: a) was negligible, and b) despite changes in the flight determining parameters, stance time and stance would remain constant. For the purposes of the study, the first assumption was considered acceptable. The second assumption (particularly for stance time) was probably only reasonable for small changes in the flight determining parameters. For example, if an athlete was to significantly increase his velocity of, and therefore his sprint velocity, it would be likely that he would also have to decrease his stance time. Therefore, the results of the simulations should be used only as a guide. The effects (on step length, step rate, and sprint velocity) of altering the flight determining parameters are shown in Figure 4. These simulations showed that, in addition to velocity of, height of was a possible source of the negative interaction between step length and step rate. When velocity or height of was increased, step length increased, step rate decreased, and sprint velocity barely changed. However, when velocity of was increased, step length increased, step rate did not change, and sprint velocity increased. A major cause of a velocity of is GRI. Weyand et al. (000) examined GRI during maximum sprint velocity (on a treadmill) and reported that faster sprinters produced the same GRI as slower sprinters, but in a shorter stance time. This resulted in the faster sprinters having a longer step length (supposedly due to their greater velocity of, to the treadmill belt). Our results suggested that a high GRI had a positive effect on step length; however, it also had a negative effect on step rate, and basically no effect on sprint velocity. More frequent ground contacts (via a low GRI and short flight time) would supposedly allow a greater opportunity for the athlete to combat the effects of wind resistance, and possibly greater opportunity to accelerate (particularly during the mid-acceleration phase of a race). Consequently, we propose it would be of advantage to direct most training effort into producing a high GRI, not GRI, thereby allowing both a long step length and high step rate. This view is supported by reports that better sprinters have a lower velocity of (Mann & Herman, 1985), and both long step
4 lengths and high step rates (e.g. Kivi, 1999). However, such a technique would be ineffective if the athlete did not possess the neuromuscular ability to, among other things, rapidly accelerate and decelerate the swinging lower-limbs. Eccentric strength of the hamstrings (Wood, 1987; Wood et al., 1987) and hip flexors may play important roles here. Table 1: Determinants of sprint velocity, step length, and step rate for the fastest individual, High Step Rate Group, and Long Step Length Group. Fastest Individual High Step Rate Long Step Length Group Group ANTHROPOMETRY Body height (m) ± ± 0.08 Leg length (m) ± ± 0.04 Body mass (kg) ± ± 7.8 SPRINT PERFORMANCE Sprint velocity (m/s) ± ± 0.45 ** Step rate (Hz) ± ± 0.7 ** Step length (m) ± ± 0.11 STEP Determinants of Step length Stance (m) ± ± 0.06 ** Flight (m) ± ± 0.13 Determinants of Step Rate Stance time (ms) ± ± 13 ** Flight time (ms) ± ± 14 FLIGHT Determinants of Flight Distance Relative height of (cm) ± ± 0.3 * Angle of (deg).6 3. ± ± 0.7 Speed of (m/s) ± ± 0.46 Horizontal (m/s) ± ± 0.46 * Vertical (m/s) ± ± 0.10 Determinants of Flight Duration Relative height of (cm) * Vertical (m/s) STANCE Determinants of Stance Distance Touchdown (m) ± ± 0.04 Foot movement (m) ± ± 0.0 Takeoff (m) ± ± 0.04 Angle A (deg) ± 80 ± 3 Angle B (deg) ± 48 ± 4 Angle C (deg) 5 50 ± 5 ± Leg length (m) Determinants of Stance Time Horizontal velocity (m/s) ± ± 0.43 Stance (m) TAKEOFF VELOCITY Determinants of Horizontal Velocity at Takeoff Horizontal (m/s) ± ± 0.44 Change in velocity see footnote Relative GRI (m/s) ± ± 0.03 Determinants of Vertical Velocity at Takeoff Vertical (m/s) ± ± 0.08 Change in velocity see footnote * Relative GRI (m/s) ± ± 0.14 Figures for the groups are mean ± standard deviation. Statistically significant differences between the High Step Rate and Long Step Length Groups are indicated with *P<0.5; **P<0.01. Changes in velocity are not presented in the Table; however, and ground reaction impulse (GRI) would be identical apart from the effects of.
5 Step Length (m) Step Rate (Hz) Sprint Vel. (m/s) Velocity of Takeoff (m/s) Angle of Takeoff (deg) Height of Takeoff (cm) A B C Figure 4: The effects - on step length, step rate, and sprint velocity - of changes in flight determining parameters. A: Effects of changes in either velocity ( ) or velocity ( ) of (original magnitudes of 0.41 and 8.91 m/s, respectively, and are indicated at point 0.0 m/s). B: Effects of changes in the angle of (original magnitude =.6 degrees). C: Effects of changes in the height of (original magnitude = 1.6 cm). Past research suggests that fatigue is also likely to influence the magnitude of velocity of used by a sprint athlete. Towards the end of longer sprint races (e.g. 400 m) an athlete will have a longer step length, lower step rate, increased flight time, and greater than normal oscillations of COM (Mero et al., 199; Mero et al., 1988; Sprague & Mann, 1983). These are all signs of a greater. It appears that a fatigued athlete might attempt to maintain sprint velocity, while simultaneously decreasing the energy demands of a high step rate (van Ingen Schenau et al., 1994), by using the negative interaction between step length and step rate to his or her advantage. SUMMARY Vertical velocity of and height of were highlighted as two possible sources of a negative interaction between step length and step rate. Vertical velocity, at least for the athletes in this study, appeared to be the most prominent source. Increasing step length by increasing height or velocity of will have a negative effect on step rate, and little effect on sprint velocity. A long step length and high step rate combination, typical of elite sprinters, is likely to be achieved by use of a low velocity, and high velocity of. Finally, and GRI obviously play central roles in determining velocity and velocity of, respectively. Consequently, and GRI are important determinants of step length and step rate. Due to their pivotal role in sprint running performance, further research is required to determine how and GRI are optimised for sprint running. REFERENCES Armstrong, L., Costill, D., et al., (1984). Track Technique, 87, Hay, J. (1994). The Biomechanics of Sports Techniques, fourth ed., Prentice Hall International Kivi, D. (1999). Proc. ISB XVII th Congress, 99, 60 Mann, R., Herman, J. (1985). Int. J. Sport Biomech., 1, Mero, A., et al., (199). Sports Med., 13, Mero, A., Luhtanen, P., et al., (1988). Track & Field Quart. Rev., 88, Mero, A., et al., (1981). Scand. J. Sports Sci., 3, 16-. Sprague, P., Mann, R. (1983). Res. Quart. Ex. Sport, 54, van Ingen Schenau, G., et al., (1994). Sports Med., 17, Weyand, P., et al., (000). J. Appl. Physiol., 89, Winter, D. (1990). Biomechanics and Motor Control of Human Movement. Wiley and Sons Wood, G. (1987) In: Medicine and Sport Science. Karger, Vol. 5, Wood, G., Marshall, R., et al., (1987). In: Biomechanics X. Human Kinetics, ACKNOWLEDGEMENTS Thanks to the late James G. Hay for his expert advice and encouragement. His presence is sorely missed. Thanks also to Renè Ferdinands for assisting with data collection.