Optimal Stride Frequency Research Articles

Changing Stride Frequency Alters Average Joint Power and Power Distributions during Ground Contact and Leg Swing in Running.

Runners naturally adopt a stride frequency closely corresponding with the stride frequency that minimizes energy consumption. Although the concept of self-optimization is well recognized, we lack mechanistic insight into the association between stride frequency and energy consumption. Altering stride frequency affects lower extremity joint power; however, these alterations are different between joints, possibly with counteracting effects on the energy consumption during ground contact and swing. Here, we investigated the effects of changing stride frequency from a joint-level perspective. Seventeen experienced runners performed six running trials at five different stride frequencies (preferred stride frequency (PSF) twice, PSF ± 8%, PSF ± 15%) at 12 km·h-1. During each trial, we measured metabolic energy consumption and muscle activation, and collected kinematic and kinetic data, which allowed us to calculate average positive joint power using inverse dynamics. With decreasing stride frequency, average positive ankle and knee power during ground contact increased (P < 0.01), whereas average positive hip power during leg swing decreased (P < 0.01). Average soleus muscle activation during ground contact also decreased with increasing stride frequency (P < 0.01). In addition, the relative contribution of positive ankle power to the total positive joint power during ground contact decreased (P = 0.01) with decreasing stride frequency, whereas the relative contribution of the hip during the full stride increased (P < 0.01) with increasing stride frequency. Our results provide evidence for the hypothesis that the optimal stride frequency represents a trade-off between minimizing the energy consumption during ground contact, associated with higher stride frequencies, without excessively increasing the cost of leg swing or reducing the time available to produce the necessary forces.

Effect of a Fatiguing Ultratrail on the Graded Energetically Optimal Stride Frequency.

To study the consequences of a fatiguing ultratrail run of 6hours on self-optimizing capability during uphill and downhill (DR) running. The authors collected temporal stride kinematics and metabolic data in 8 (experimental group) male runners before and after the ultratrail run and in 6 (control group) male ultramarathon runners who did not run but stayed awake and performed normal, daily physical activities avoiding strenuous exercises over the 6-hour period. For each subject, preferred and optimal stride frequencies were measured, where stride frequency was systematically varied above and below the preferred one (±4% and ±8%) while running 3 conditions on level, 5% uphill, or 5% DR in a randomized order. Preferred and optimal stride frequencies across grade, group, and time showed no significant differences (P ≥ .184). Metabolic cost and the energetically optimum metabolic cost showed a grade × group × time interaction (P ≥ .011), with an ∼11% increase in the 2 variables only during the DR bouts (P ≥ .037). Despite maintaining similar dynamics of stride frequency adjustments during the DR bout, the experimental group was not able to optimize its gait. This suggests that the DR section of ultratrail runs can introduce a perturbing factor in the runners' optimization process, highlighting the need for incorporating DR bouts in the training programs of ultratrail runners to minimize the deleterious effects of DR on the energetically optimal gait.

Energetically optimal stride frequency is maintained with fatigue in trained ultramarathon runners

ObjectivesAt a given running speed, humans naturally endeavor to achieve an optimal stride frequency that minimizes metabolic cost. Research has suggested that runners select this near optimal stride frequency in some process of self-optimization even during fatiguing tasks up to 1-h of high-intensity running. Here, we studied whether runners demonstrate a similar self-optimizing capability after an ultramarathon of 6 h. DesignControlled pre-post study. MethodWe collected temporal stride kinematics and metabolic data in nine (experimental group) male runners before and after 6 h of running and in six (control group) male ultramarathon runners who did not run, but stayed awake and performed normal, daily physical activities avoiding strenuous exercises over the 6-h period. For each participant, preferred and optimal stride frequencies were measured, where stride frequency was systematically varied above and below PSF (±4% and ±8%). ResultsPreferred and optimal stride frequencies across time and group showed no significant differences (p ≥ 0.276). Furthermore, neither the overall relationship between metabolic cost and stride frequency, nor the energetically optimal stride frequency changed substantially after several hours of running. ConclusionsSimilar dynamics of stride frequency adjustments in the experimental group occurred as those found in a non-fatigued state. This suggests that after an ultramarathon of 6 h, runners were still able to optimize their gait, and automatically adjust it in order to converge on the energetically optimal gait.

Connecting the legs with a spring improves human running economy.

Human running is inefficient. For every 10 calories burned, less than 1 is needed to maintain a constant forward velocity - the remaining energy is, in a sense, wasted. The majority of this wasted energy is expended to support the bodyweight and redirect the center of mass during the stance phase of gait. An order of magnitude less energy is expended to brake and accelerate the swinging leg. Accordingly, most devices designed to increase running efficiency have targeted the costlier stance phase of gait. An alternative approach is seen in nature: spring-like tissues in some animals and humans are believed to assist leg swing. While it has been assumed that such a spring simply offloads the muscles that swing the legs, thus saving energy, this mechanism has not been experimentally investigated. Here, we show that a spring, or 'exotendon', connecting the legs of a human reduces the energy required for running by 6.4±2.8%, and does so through a complex mechanism that produces savings beyond those associated with leg swing. The exotendon applies assistive forces to the swinging legs, increasing the energy optimal stride frequency. Runners then adopt this frequency, taking faster and shorter strides, and reduce the joint mechanical work to redirect their center of mass. Our study shows how a simple spring improves running economy through a complex interaction between the changing dynamics of the body and the adaptive strategies of the runner, highlighting the importance of considering each when designing systems that couple human and machine.

CSM 2019 American Academy of Sports Physical Therapy Poster Presentations (Abstracts SPO1–SPO132)

CSM 2019 American Academy of Sports Physical Therapy Poster Presentations (Abstracts SPO1–SPO132)

Hybrid Locomotion Evaluation for a Novel Amphibious Spherical Robot

We describe the novel, multiply gaited, vectored water-jet, hybrid locomotion-capable, amphibious spherical robot III (termed ASR-III) featuring a wheel-legged, water-jet composite driving system incorporating a lifting and supporting wheel mechanism (LSWM) and mechanical legs with a water-jet thruster. The LSWM allows the ASR-III to support the body and slide flexibly on smooth (flat) terrain. The composite driving system facilitates two on-land locomotion modes (sliding and walking) and underwater locomotion mode with vectored thrusters, improving adaptability to the amphibious environment. Sliding locomotion improves the stability and maneuverability of ASR-III on smooth flat terrain, whereas walking locomotion allows ASR-III to conquer rough terrain. We used both forward and reverse kinematic models to evaluate the walking and sliding gait efficiency. The robot can also realize underwater locomotion with four vectored water-jet thrusters, and is capable of forward motion, heading angle control and depth control. We evaluated LSWM efficiency and the sliding velocities associated with varying extensions of the LSWM. To explore gait stability and mobility, we performed on-land experiments on smooth flat terrain to define the optimal stride length and frequency. We also evaluated the efficacy of waypoint tracking when the sliding gait was employed, using a closed-loop proportional-integral-derivative (PID) control mechanism. Moreover, experiments of forward locomotion, heading angle control and depth control were conducted to verify the underwater performance of ASR-III. Comparison of the previous robot and ASR-III demonstrated the ASR-III had better amphibious motion performance.

Optimal stride frequencies in running at different speeds.

During running at a constant speed, the optimal stride frequency (SF) can be derived from the u-shaped relationship between SF and heart rate (HR). Changing SF towards the optimum of this relationship is beneficial for energy expenditure and may positively change biomechanics of running. In the current study, the effects of speed on the optimal SF and the nature of the u-shaped relation were empirically tested using Generalized Estimating Equations. To this end, HR was recorded from twelve healthy (4 males, 8 females) inexperienced runners, who completed runs at three speeds. The three speeds were 90%, 100% and 110% of self-selected speed. A self-selected SF (SFself) was determined for each of the speeds prior to the speed series. The speed series started with a free-chosen SF condition, followed by five imposed SF conditions (SFself, 70, 80, 90, 100 strides·min-1) assigned in random order. The conditions lasted 3 minutes with 2.5 minutes of walking in between. SFself increased significantly (p<0.05) with speed with averages of 77, 79, 80 strides·min-1 at 2.4, 2.6, 2.9 m·s-1, respectively). As expected, the relation between SF and HR could be described by a parabolic curve for all speeds. Speed did not significantly affect the curvature, nor did it affect optimal SF. We conclude that over the speed range tested, inexperienced runners may not need to adapt their SF to running speed. However, since SFself were lower than the SFopt of 83 strides·min-1, the runners could reduce HR by increasing their SFself.

Energy Expenditure of Trotting Gait Under Different Gait Parameters

Robots driven by batteries are clean, quiet, and can work indoors or in space. However, the battery endurance is a great problem. A new gait parameter design energy saving strategy to extend the working hours of the quadruped robot is proposed. A dynamic model of the robot is established to estimate and analyze the energy expenditures during trotting. Given a trotting speed, optimal stride frequency and stride length can minimize the energy expenditure. However, the relationship between the speed and the optimal gait parameters is nonlinear, which is difficult for practical application. Therefore, a simplified gait parameter design method for energy saving is proposed. A critical trotting speed of the quadruped robot is found and can be used to decide the gait parameters. When the robot is travelling lower than this speed, it is better to keep a constant stride length and change the cycle period. When the robot is travelling higher than this speed, it is better to keep a constant cycle period and change the stride length. Simulations and experiments on the quadruped robot show that by using the proposed gait parameter design approach, the energy expenditure can be reduced by about 54% compared with the 100 mm stride length under 500 mm/s speed. In general, an energy expenditure model based on the gait parameter of the quadruped robot is built and the trotting gait parameters design approach for energy saving is proposed.

Effects of stride frequency and foot position at landing on braking force, hip torque, impact peak force and the metabolic cost of running in humans.

Endurance runners are often advised to use 90stridesmin(-1), but how optimal is this stride frequency and why? Endurance runners are also often advised to maintain short strides and avoid landing with the feet too far in front of their hips or knees (colloquially termed 'overstriding'), but how do different kinematic strategies for varying stride length at the same stride frequency affect economy and impact peaks? Linear mixed models were used to analyze repeated measures of stride frequency, the anteroposterior position of the foot at landing, V̇O2 , lower extremity kinematics and vertical ground reaction forces in 14 runners who varied substantially in height and body mass and who were asked to run at 75, 80, 85, 90 and 95stridesmin(-1) at 3.0 m s(-1). For every increase of 5stridesmin(-1), maximum hip flexor moments in the sagittal plane increased by 5.8% (P<0.0001), and the position of the foot at landing relative to the hip decreased by 5.9% (P=0.003). Higher magnitudes of posteriorly directed braking forces were associated with increases in foot landing position relative to the hip (P=0.0005) but not the knee (P=0.54); increases in foot landing position relative to the knee were associated with higher magnitudes (P<0.0001) and rates of loading (P=0.07) of the vertical ground reaction force impact peak. Finally, the mean metabolically optimal stride frequency was 84.8±3.6stridesmin(-1), with 50.4% of the variance explained by the trade-off between minimizing braking forces versus maximum hip flexor moments during swing. The results suggest that runners may benefit from a stride frequency of approximately 85stridesmin(-1) and by landing at the end of swing phase with a relatively vertical tibia.

Design for Several Hydraulic Parameters of a Quadruped Robot

For a quadruped robot with 12 active joints driven by linear hydraulic actuators, some important parameters, such as the oil flow of the hydraulic system and the needed maximum output force of eac h actuator, are hard to calculate precisely with kinematics and dynamics equations. The oil flow is mainly determined by the walking speed o f the quadruped robot, but also influenced by the stride frequency, gait type and the foot trajectory. This paper planned the fo ot trajectory with cubic polynomial firstly. Then selected optimal stride frequency referred to that of four-legged mammals and stride length according to the required walking speed of the quadruped robot. Furthermore, displacement curves and velocity curves with respect to time for all linear hydraulic actuators can be obtained easily with inverse kinematics equations in MATLAB. The needed maximum output force of each actuator can be obtained from dynamic simulation with MSC.ADAMS. Then the effective area of the hydraulic actuator can be calculated according to the output force of actuator and oil pressure of the hydraulic system. Lastly, the oil flow can be calculated precisely by summing all the products of the velocity and the effective area of each actuator.

Stride frequency in relation to oxygen consumption in experienced and novice runners

We hypothesised that experienced runners would select a stride frequency closer to the optimum (minimal energy costs) than would novice runners. In addition, we expected that optimal stride frequency could simply be determined by monitoring heart rate without measuring oxygen consumption (V̇O2). Ten healthy males (mean±s: 24±2 year) with no running training experience and 10 trained runners of similar age ran at constant treadmill speed corresponding to 80% of individual ventilatory threshold. For two days, they ran at seven different stride frequencies (self-selected stride frequency±18%) imposed by a metronome. Optimal stride frequency was based on the minimum of a second-order polynomial equation fitted through steady state V̇O2 at each stride frequency. Running cost (mean±s) at optimal stride frequency was higher (P < 0.05) in novice (236±31 ml O2·kg−1.km−1) than trained (189±13 ml O2·kg−1.km−1) runners. Self-selected stride frequency (mean±s; strides.min−1) for novice (77.8±2.8) and trained runners (84.4±5.3) were lower (P < 0.05) than optimal stride frequency (respectively, 84.9±5.0 and 87.1±4.8). The difference between self-selected and optimal stride frequency was smaller (P < 0.05) for trained runners. In both the groups optimal stride frequency established with heart rate was not different (P > 0.3) from optimal stride frequency based on V̇O2. In each group and despite limited variation between participants, optimal stride frequencies derived from V̇O2 and heart rate were related (r > 0.7; P < 0.05). In conclusion, trained runners chose a stride frequency closer to the optimum for energy expenditure than novices. Heart rate could be used to establish optimal stride frequency.

Computational study of blood flow in lower extremities under intense physical load

This work is aimed at computational study of the blood flow in lower extremities under intense physical load. We present a modified 1D cardiovascular system model describing skeletal-muscle pumping and autoregulation effects on the blood flow in lower extremities. Skeletal-muscle pump effect is introduced as an external time-periodical pressure function applied to a group of veins. The period of this function is associated with the two-stride period during running. The computational study reveals the explicit optimal stride frequency providing the maximum blood flow through the lower extremities. It is shown that the optimal stride frequency depends on personal parameters. The model is validated by a comparison to the stride frequencies of a number of top-level athletes, therefore, providing a method to assess the level of physical conditioning.

Sacrificing economy to improve running performance—a reality in the ultramarathon?

ultramarathons have become increasingly popular in recent years. Although complex tactical and psychological-motivational factors play important roles in performance ([Fig. 1][1]), running velocity sustained over a prolonged time is directly proportional to maximal sustainable Vo2 and inversely

ELASTIC ENERGY STORAGE DOES NOT SOLELY DETERMINE OPTIMAL STRIDE FREQUENCY

When training as a cross-country runner during her college days, Kristine Snyder recalls her coach telling her to run at a specific stride frequency and wondering where the number came from. ‘The reality is that optimal stride frequency varies from person to person,’ says Snyder, who adds, ‘If you can run at a stride frequency that is going to minimise your metabolic cost – the optimal stride frequency – that is going to allow you to go farther and faster.’ But what determines an individual's optimal stride frequency? ‘There has been this idea in the literature for a while that the reason our optimal stride frequency is optimal is because our elastic energy storage is maximal at that frequency,’ explains Snyder, but no one had successfully tested this theory. Intrigued by the problem at a scientific and personal level, Snyder teamed up with Claire Farley at the University of Colorado, USA, to find out whether elastic energy storage determines optimal stride frequency (p. 2089).‘We decided to see what would happen if we could reduce elastic energy storage, which may allow us to determine what happens when it is present,’ says Snyder. She explains that when you run on the flat you store elastic energy in your tendons as your foot strikes the ground and recover a great deal of this energy when you push off again. However, when running up an incline, the energy stored in the tendons as the foot lands is insufficient to lift you up the slope when you push off next, so muscle provides the additional energy. Conversely, when descending a hill more energy could be stored in the tendons than is needed, so the muscles dissipate the excess to maintain a constant speed. Essentially, Snyder and Farley could alter runners' maximal elastic energy usage by making them run uphill or downhill to find out if elastic energy usage sets a runner's optimal stride frequency.The duo decided to measure the metabolic effects of running at different stride frequencies on flat and inclined surfaces. They reasoned that if elastic energy storage is a significant factor in determining a runner's optimal stride frequency then the metabolic rates of athletes running at different stride frequencies on sloped surfaces would vary less than the metabolic rates of athlete's running at different stride frequencies on a flat surface.Recruiting outstanding runners from Boulder, Colorado, Snyder identified each runner's preferred stride frequency and set a metronome ticking to test whether they could run at 85%, 92%, 100%, 108% and 115% of their natural running frequencies. ‘They really strongly did not like using anything besides their preferred frequency,’ remembers Snyder, but having established that they could, she measured their metabolic rates as they ran at each frequency on the flat and angled treadmills.Plotting the athlete's metabolic rates against their stride frequencies for each of three treadmill angles, the duo expected each parabola to have a different gradient if the optimal stride frequency was determined by the runner's ability to store elastic energy. However, the parabolas were all very similar: optimal stride frequency is not determined solely by elastic energy storage.In that case, what does set a runner's optimal stride frequency? ‘I think we have a combination of things,’ says Snyder. She suspects that optimal stride frequency occurs at intermediate stride frequencies where the athlete's metabolic cost is lowest – as runners' muscles work harder at low and high stride frequencies and they also have to work harder to push off at high stride frequencies.

Energetically optimal stride frequency in running: the effects of incline and decline

At a given running speed, humans strongly prefer to use a stride frequency near their 'optimal' stride frequency that minimizes metabolic cost. Although there is no definitive explanation for why an optimal stride frequency exists, elastic energy usage has been implicated. Because the possibility for elastic energy storage and return may be impaired on slopes, we investigated whether and how the optimal stride frequency changes during uphill and downhill running. Presuming a smaller role of elastic energy, we hypothesized that altering stride frequency would change metabolic cost less during uphill and downhill running than during level running. To test this hypothesis, we collected force and metabolic data as nine male subjects ran at 2.8 m s(-1) on the level, 3 deg uphill and 3 deg downhill. Stride frequency was systematically varied above and below preferred stride frequency (PSF ±8% and ±15%). Ground reaction force data were used to calculate potential, kinetic and total mechanical energy, and to calculate the theoretical maximum possible and estimated actual elastic energy storage and return. Contrary to our hypothesis, we found that neither the overall relationship between metabolic cost and stride frequency nor the energetically optimal stride frequency changed substantially with slope. However, estimated actual elastic energy storage as a percentage of total positive power increased with increasing stride frequency on all slopes, indicating that muscle power decreases with increasing stride frequency. Combined with the increased cost of force production and internal work with increasing stride frequency, this leads to an intermediate optimal stride frequency and overall U-shaped curve.

Preferred and optimal stride frequency, stiffness and economy: changes with fatigue during a 1-h high-intensity run

Metabolic cost of submaximal running at constant speed is influenced by various factors including fatigue and kinematic characteristics. Metabolic costs typically drift upwards during extended running while stride characteristics often shift away from initial. When non-fatigued, experienced runners naturally optimize stride frequency in a manner that minimizes oxygen uptake. An initial objective was to determine whether runners demonstrate a similar self-optimizing capability when fatigued where stride characteristics have perhaps shifted away from the initial state. A secondary objective involved measurement of vertical and leg stiffness characteristics as a potential explanation for frequency changes with fatigue. We hypothesized that runners decrease stride frequency and stiffness with fatigue while optimizing these characteristics to minimize metabolic cost. Sixteen experienced runners completed a near maximal effort 1-h treadmill run at a constant speed. Preferred and optimal stride frequencies (PSF and OSF) were measured near the beginning and end of the hour run using frequencies +/-4 and +/-8% around PSF. From vertical force data recorded throughout the run, leg and vertical stiffness were determined. As expected, oxygen uptake significantly increased during the run from 45.9 to 47.4 ml kg(-1) min(-1) (P = 0.004). There was no difference between preferred and optimal stride frequencies at the beginning or the end of running (P = 0.978), however both PSF and OSF significantly decreased from 1.45 to 1.43 Hz (P = 0.026). All runners self-optimized stride frequency at the beginning and end of one-hour of running despite changes of optimal stride frequency. Stiffness and stride frequency changes were subject specific with some runners exhibiting little to no change. No clear relationship of frequency or stiffness changes to economy was found.

Optimal stride frequency computed from the double-compound pendulum of the leg, and verified experimentally as the preferred stride frequency of jogging

Observations of long-distance runners reveal that the front-finishing runners invariably have smooth and comfortable running gait. Hence, this study is based on the reasoning that a jogger would naturally feel most comfortable to run at the stride frequency corresponding to the natural oscillation frequency of his leg. Under this condition, the jogger would be least tired, as the leg muscles would need to do minimal work to accelerate and decelerate the leg at the start and end of the leg-swing phase of the cycle. Thus, the jogging motion of a runner will appear to be natural and smooth. To elucidate if the leg motion frequency corresponding to its natural frequency of oscillation about the hip joint is the most comfortable jogging mode (causing minimal fatigue to the jogger), both analytical and experimental studies were carried out to determine these frequency values. Analytically, the leg was modelled as a double-compound pendulum and the expressions for the natural oscillation frequencies were derived to compute the stride frequencies (SFs) based on the anthropometric parameters of the volunteers. Also, experimentally, the SFs of these volunteers were determined under running conditions, using a 50 Hz video camera and Peak Motus software. The regression analysis of the model-based stride frequencies versus preferred stride frequencies of natural running yielded a remarkably high correlation coefficient of 0.94. The results obtained in this study suggest that jogging at the natural oscillation frequency of the leg may invoke the least expenditure of energy.

長距離走におけるピッチとストライドの変化が走効率に及ぼす影響

The purpose of this study was to investigate the effects of change in stride frequency and/or stride length on oxygen uptake during distanc6 running, and to compare female runners with male runners in this point. Ten runners, nine table tennis players and eight swimmers underwent treadmill running at three different speeds. Running speed was constant and stride frequency was systematically changed over a range of ±20 strides/min of the free stride frequency (Experiment 1). Five male runners and four female runners ran on a treadmill at stride lengths between 60 cm and 130 cm with a given stride. frequency (160, 180 or 200 strides/min) and at stride frequencies between 150 and 200 strides/min with a given stride length (80 or 100cm) (Experiment 2). The measurements of oxygen uptake and HR were made during steady state in each running. 1) The most economical stride frequency (optimal stride frequency) in males always coincided with the free stride frequency. Both increase and decrease in stride frequency from the free stride frequency caused increase in oxygen uptake in male runners. Regarding female runners, oxygen uptake during distance running was a1most constant over a wide range of stride frequency (170-220). Specific optimal stride frequency was not observed in female runners. 2) Running with a given stride frequency caused a rectilinear relationship between oxygen uptake and stride length in male and female runners. It was suggested that change in stride length scarcely affected running efficiency during distance running. 3) There was an obvious difference between male and female runners in the effect of change in stride frequency on oxygen uptake during distance running with a given stride length. Decrease in stride frequency below 170 strides/min lowered the running efficiency in runners of both sexes. Above 180 strides/min, there was an exponential relationship between oxygen uptake and stride frequency in male runners, and a rectilinear relationship in female runners. Stride frequency higher than 180/min lowered running efficiency in male, but not in female runners. 4) Optimal stride frequency was observed in male runners, table tennis players and swimmers. Optimal stride frequency always coincided with free stride frequency in male subjects, and it was suggested that men without special training can run with the most economical stride frequency. 5) Stride length and stride frequency increased linearly as the running speed increased. Increase in running speed was dependent much more on increase in stride length than that of stride frequency. Contribution of stride frequency to an increase in running speed was more significant in female than male.