Mechanical energy oscillations of two brachiation gaits: measurement and simulation

How do arm‐swinging apes locomote effectively over a variety of speeds? One way to reduce the metabolic energy cost of locomotion is to transfer energy between reversible mechanical modes. In terrestrial animals, at least two transfer mechanisms have been identified: 1) a pendulum‐like mechanism for walking, with exchange between gravitational potential energy and translational kinetic energy, and 2) a spring‐like mechanism for running, where the elastic strain energy of stretched muscle and tendon is largely returned to reaccelerate the animal. At slower speeds, a brachiator will always have at least one limb in contact with the support, similar to the overlap of foot contact in bipedal walking. At faster speeds, brachiators exhibit an aerial phase, similar to that seen in bipedal running. Are there two distinct brachiation gaits even though the animal appears to simply swing beneath its overhead support? If so, are different exchange mechanisms employed? Our kinetic analysis of brachiation in a white‐handed gibbon (Hylobates lar) indicates that brachiation is indeed comprised of two mechanically distinct gaits. At slower speeds in “continuous contact” brachiation, the gibbon utilizes a simple pendulum‐like transfer of mechanical energy within each stride. At faster speeds in “ricochetal” brachiation, translational and rotational kinetic energy are exchanged in a novel “whip‐like” transfer. We propose that brachiators utilize the transfer between translational and rotational kinetic energy to control the dynamics of their swing. This maneuver may allow muscle action at the shoulder to control the transfer and adjust the ballistic portion of the step to meet the requirements for the next hand contact. Am J Phys Anthropol 115:319–326, 2001. © 2001 Wiley‐Liss, Inc.     

The mechanics of hopping by kangaroos (Macropodidae)

Force platform records and films have been made of kangaroos and a wallaby hopping.
The maximum forces exerted on the ground were about six times body weight. The force exerted on the ground changes direction, throughout the period when the feet are on the ground, so that it is always more or less in line with the centre of mass. Consequently the animal decelerates a little and then accelerates again, during the contact phase.
The fluctuations of potential energy which occur in each hop are slightly smaller at high speeds than at low ones. Fluctuations of external kinetic energy increase with speed and account for most of the energy cost of hopping at high speeds. Fluctuations of internal kinetic energy (due to acceleration and deceleration of the limbs) are relatively small. While the feet are on the ground the extensor muscles of the hip do positive work, those of the knee negative work and those of the ankle negative work followed by positive work. The energy cost of hopping is reduced substantially by elastic storage of energy in the Achilles tendon. In the case of a wallaby hopping at moderate speed the calculated saving was 40%. The maximum stresses developed in leg muscles, tendons and the tibia have been calculated and are discussed in relation to the known properties of muscle, tendon and bone. The trunk pitches as the animal hops because the two legs swing forwards and back simultaneously. Appropriate tail movements reduce, but do not eliminate, this effect. A mathematical theory of hopping is presented and used to investigate the merits of different hopping techniques.
Dawson & Taylor's (1973) discovery that the rate of oxygen consumption of kangaroos decreases a little, as hopping speed increases, is probably to be explained by the increased role of elastic storage of energy at high speeds.     

Relative shortening velocity in locomotor muscles: turkey ankle extensors operate at low V/V(max)

The force-velocity properties of skeletal muscle have an important influence on locomotor performance. All skeletal muscles produce less force the faster they shorten and typically develop maximal power at velocities of approximately 30% of maximum shortening velocity (V(max)). We used direct measurements of muscle mechanical function in two ankle extensor muscles of wild turkeys to test the hypothesis that during level running muscles operate at velocities that favor force rather than power. Sonomicrometer measurements of muscle length, tendon strain-gauge measurements of muscle force, and bipolar electromyographs were taken as animals ran over a range of speeds and inclines. These measurements were integrated with previously measured values of muscle V(max) for these muscles to calculate relative shortening velocity (V/V(max)). At all speeds for level running the V/V(max) values of the lateral gastrocnemius and the peroneus longus were low (<0.05), corresponding to the region of the force-velocity relationship where the muscles were capable of producing 90% of peak isometric force but only 35% of peak isotonic power. V/V(max) increased in response to the demand for mechanical power with increases in running incline and decreased to negative values to absorb energy during downhill running. Measurements of integrated electromyograph activity indicated that the volume of muscle required to produce a given force increased from level to uphill running. This observation is consistent with the idea that V/V(max) is an important determinant of locomotor cost because it affects the volume of muscle that must be recruited to support body weight.     

Muscle mechanical work requirements during normal walking: the energetic cost of raising the body's center-of-mass is significant

Inverted pendulum models of walking predict that little muscle work is required for the exchange of body potential and kinetic energy in single-limb support. External power during walking (product of the measured ground reaction force and body center-of-mass (COM) velocity) is often analyzed to deduce net work output or mechanical energetic cost by muscles. Based on external power analyses and inverted pendulum theory, it has been suggested that a primary mechanical energetic cost may be associated with the mechanical work required to redirect the COM motion at the step-to-step transition. However, these models do not capture the multi-muscle, multi-segmental properties of walking, co-excitation of muscles to coordinate segmental energetic flow, and simultaneous production of positive and negative muscle work. In this study, a muscle-actuated forward dynamic simulation of walking was used to assess whether: (1). potential and kinetic energy of the body are exchanged with little muscle work; (2). external mechanical power can estimate the mechanical energetic cost for muscles; and (3.) the net work output and the mechanical energetic cost for muscles occurs mostly in double support. We found that the net work output by muscles cannot be estimated from external power and was the highest when the COM moved upward in early single-limb support even though kinetic and potential energy were exchanged, and muscle mechanical (and most likely metabolic) energetic cost is dominated not only by the need to redirect the COM in double support but also by the need to raise the COM in single support.     

Patterns of mechanical energy change in tetrapod gait: pendula, springs and work

Kinematic and center of mass (CoM) mechanical variables used to define terrestrial gaits are compared for various tetrapod species. Kinematic variables (limb phase, duty factor) provide important timing information regarding the neural control and limb coordination of various gaits. Whereas, mechanical variables (potential and kinetic energy relative phase, %Recovery, %Congruity) provide insight into the underlying mechanisms that minimize muscle work and the metabolic cost of locomotion, and also influence neural control strategies. Two basic mechanisms identified by Cavagna et al. (1977. Am J Physiol 233:R243-R261) are used broadly by various bipedal and quadrupedal species. During walking, animals exchange CoM potential energy (PE) with kinetic energy (KE) via an inverted pendulum mechanism to reduce muscle work. During the stance period of running (including trotting, hopping and galloping) gaits, animals convert PE and KE into elastic strain energy in spring elements of the limbs and trunk and regain this energy later during limb support. The bouncing motion of the body on the support limb(s) is well represented by a simple mass-spring system. Limb spring compliance allows the storage and return of elastic energy to reduce muscle work. These two distinct patterns of CoM mechanical energy exchange are fairly well correlated with kinematic distinctions of limb movement patterns associated with gait change. However, in some cases such correlations can be misleading. When running (or trotting) at low speeds many animals lack an aerial period and have limb duty factors that exceed 0.5. Rather than interpreting this as a change of gait, the underlying mechanics of the body's CoM motion indicate no fundamental change in limb movement pattern or CoM dynamics has occurred. Nevertheless, the idealized, distinctive patterns of CoM energy fluctuation predicted by an inverted pendulum for walking and a bouncing mass spring for running are often not clear cut, especially for less cursorial species. When the kinematic and mechanical patterns of a broader diversity of quadrupeds and bipeds are compared, more complex patterns emerge, indicating that some animals may combine walking and running mechanics at intermediate speeds or at very large size. These models also ignore energy costs that are likely associated with the opposing action of limbs that have overlapping support times during walking. A recent model of terrestrial gait (Ruina et al., 2005. J Theor Biol, in press) that treats limb contact with the ground in terms of collisional energy loss indicates that considerable CoM energy can be conserved simply by matching the path of CoM motion perpendicular to limb ground force. This model, coupled with the earlier ones of pendular exchange during walking and mass-spring elastic energy savings during running, provides compelling argument for the view that the legged locomotion of quadrupeds and other terrestrial animals has generally evolved to minimize muscle work during steady level movement.     

Elastic energy savings and active energy cost in a simple model of running

The energetic economy of running benefits from tendon and other tissues that store and return elastic energy, thus saving muscles from costly mechanical work. The classic “Spring-mass” computational model successfully explains the forces, displacements and mechanical power of running, as the outcome of dynamical interactions between the body center of mass and a purely elastic spring for the leg. However, the Spring-mass model does not include active muscles and cannot explain the metabolic energy cost of running, whether on level ground or on a slope. Here we add explicit actuation and dissipation to the Spring-mass model, and show how they explain substantial active (and thus costly) work during human running, and much of the associated energetic cost. Dissipation is modeled as modest energy losses (5% of total mechanical energy for running at 3 m s^-1) from hysteresis and foot-ground collisions, that must be restored by active work each step. Even with substantial elastic energy return (59% of positive work, comparable to empirical observations), the active work could account for most of the metabolic cost of human running (about 68%, assuming human-like muscle efficiency). We also introduce a previously unappreciated energetic cost for rapid production of force, that helps explain the relatively smooth ground reaction forces of running, and why muscles might also actively perform negative work. With both work and rapid force costs, the model reproduces the energetics of human running at a range of speeds on level ground and on slopes. Although elastic return is key to energy savings, there are still losses that require restorative muscle work, which can cost substantial energy during running.     

Asymmetric interlimb role-sharing in mechanical power during human sideways locomotion

Sideways movement at a wide variety of speeds is required in daily life and sports. The purpose of this study was to identify the characteristics of asymmetry in power output between lower limbs during sideways gait patterns. Seven healthy men performed steady-state sideways locomotion at various speeds. The mechanical external power of each limb was calculated and decomposed to the lateral and vertical components by the center of mass velocity and ground reaction force. We acquired data from 126 steps of sideways walking at 0.44–1.21 m/s, and from 41 steps of sideways galloping at 1.04–3.00 m/s. The results showed asymmetric power production between the limbs during sideways locomotion. During sideways walking, the trailing limb predominantly produced positive external power and the leading limb produced predominantly negative external power, and these amplitudes increased with step speed. In contrast, during sideways galloping, negative and subsequent positive power production was observed in both limbs. These differences in asymmetric interlimb role-sharing were mainly due to the vertical component. During sideways galloping, the trailing limb absorbs vertical power produced by the leading limb due to the longer flight time. This characteristic of vertical power production in the trailing limb may explain the presence of a double-support phase, which is not observed during forward running, even at high speeds. Our results will help to elucidate the asymmetric movements of the limbs in lateral directions at various speeds.     

Changes in relative work of the lower extremity joints and distal foot with walking speed

The modulation of walking speed results in adaptations to the lower limbs which can be quantified using mechanical work. A 6 degree-of-freedom (DOF) power analysis, which includes additional translations as compared to the 3 DOF (all rotational) approach, is a comprehensive approach for quantifying lower limb work during gait. The purpose of this study was to quantify the speed-related 6 DOF joint and distal foot work adaptations of all the lower extremity limb constituents (hip, knee, ankle, and distal foot) in healthy individuals. Relative constituent 6 DOF work, the amount of constituent work relative to absolute limb work, was calculated during the stance and swing phases of gait. Eight unimpaired adults walked on an instrumented split-belt treadmill at slow, moderate, and typical walking speeds (0.4, 0.6, and 0.8 statures/s, respectively). Using motion capture and force data, 6 DOF powers were calculated for each constituent. Contrary to previously published results, 6 DOF positive relative ankle work and negative relative distal foot work increased significantly with increased speed during stance phase (p < 0.05). Similar to previous rotational DOF results in the sagittal plane, negative relative ankle work decreased significantly with increased speed during stance phase (p < 0.05). Scientifically, these findings provide new insight into how healthy individuals adapt to increased walking speed and suggest limitations of the rotational DOF approach for quantifying limb work. Clinically, the data presented here for unimpaired limbs can be used to compare with speed-matched data from limbs with impairments.     

Power in sports: A literature review on the application,assumptions, and terminology of mechanical power in sport research

The quantification of mechanical power can provide valuable insight into athlete performance because it is the mechanical principle of the rate at which the athlete does work or transfers energy to complete a movement task. Estimates of power are usually limited by the capabilities of measurement systems, resulting in the use of simplified power models. This review provides a systematic overview of the studies on mechanical power in sports, discussing the application and estimation of mechanical power, the consequences of simplifications, and the terminology. The mechanical power balance consists of five parts, where joint power is equal to the sum of kinetic power, gravitational power, environmental power, and frictional power. Structuring literature based on these power components shows that simplifications in models are done on four levels, single vs multibody models, instantaneous power (IN) versus change in energy (EN), the dimensions of a model (1D, 2D, 3D), and neglecting parts of the mechanical power balance. Quantifying the consequences of simplification of power models has only been done for running, and shows differences ranging from 10% up to 250% compared to joint power models. Furthermore, inconsistency and imprecision were found in the determination of joint power, resulting from inverse dynamics methods, incorporation of translational joint powers, partitioning in negative and positive work, and power flow between segments. Most inconsistency in terminology was found in the definition and application of ‘external’ and ‘internal’ work and power. Sport research would benefit from structuring the research on mechanical power in sports and quantifying the result of simplifications in mechanical power estimations.     

Lower-limb joint work and power are modulated during load carriage based on load configuration and walking speed

Soldiers regularly transport loads weighing >20 kg at slow speeds for long durations. These tasks elicit high energetic costs through increased positive work generated by knee and ankle muscles, which may increase risk of muscular fatigue and decrease combat readiness. This study aimed to determine how modifying where load is borne changes lower-limb joint mechanical work production, and if load magnitude and/or walking speed also affect work production. Twenty Australian soldiers participated, donning a total of 12 body armor variations: six different body armor systems (one standard-issue, two commercially available [cARM1-2], and three prototypes [pARM1-3]), each worn with two different load magnitudes (15 and 30 kg). For each armor variation, participants completed treadmill walking at two speeds (1.51 and 1.83 m/s). Three-dimensional motion capture and force plate data were acquired and used to estimate joint angles and moments from inverse kinematics and dynamics, respectively. Subsequently, hip, knee, and ankle joint work and power were computed and compared between armor types and walking speeds. Positive joint work over the stance phase significantly increased with walking speed and carried load, accompanied by 2.3–2.6% shifts in total positive work production from the ankle to the hip (p < 0.05). Compared to using cARM1 with 15 kg carried load, carrying 30 kg resulted in significantly greater hip contribution to total lower-limb positive work, while knee and ankle work decreased. Substantial increases in hip joint contributions to total lower-limb positive work that occur with increases in walking speed and load magnitude highlight the importance of hip musculature to load carriage walking.     

Calf muscle work and segment energy changes in human treadmill walking

The relation between changes in potential and kinetic energy in a seven-segment model of the human body and the work of m. triceps surae was investigated in four subjects walking on a treadmill at speeds between 0.5 and 2.0 m/s. Segment energy levels were determined by means of tachometers attached with strings to various points on the subject's body. Muscle work was assessed by electromyogram to force processing. M. triceps surae is active during stance, first doing negative (eccentric) work and ending with a short period of positive (concentric) work at “push-off”. It turned out that in normal walking these muscles provide the major part of positive work for the initiation of swing at push-off. Only at large step lengths, when push-off starts well before contralateral heel contact, is there a minor pushing forward of the trunk. In the negative work phase, m. triceps surae seem to check the forward speed of the trunk. A related decrease of trunk kinetic energy is not present, however, but this may be obscured by the simultaneous action of m. quadriceps femoris and, in a later stage, by a transfer of energy from the decelerating contralateral (swing) leg to the trunk. Energy of the trunk segment shows a sharp decline in double stance and a more gradual increase in the first half of single stance. Evidence is given that this effect is due to quadriceps action in the knee flexion-extension movement during stance. The presented results are incorporated in a general picture of energy flows in human walking.     

An energy 'sources' and 'fractions' approach to the mechanical energy expenditure problem--III. Mechanical energy expenditure reduction during one link motion

Mechanical energy economy and transformation during one link motion are analyzed on the basis of the theory developed in the previous publications (parts I and II of this series, J. Biomechanics 19, 287-300). The 'compensation coefficient' characterizing mechanical energy economy is introduced. The attempts to estimate MEE using only energy curves and neglecting the powers of real sources of energy implicitly lead to replacement of real force and moment systems by the systems reduced to the centers of mass. But such an unintentional substitution of imaginary sources for real ones, specifically, the reduction of forces acting on the link to the equivalent system, changes estimates of mechanical energy expenditure (MEE). That is why the methods of calculating MEE economy based on the determination of so-called 'quasi-mechanical' work (the sum of the kinetic and potential energy increases per one cycle of motion) are not correct. There are two mechanisms to reduce the MEE using the antiphase fluctuations (corresponding to energy transformations) of the (a) rotational and translational fractions of the total energy (at the expense of the F-sources); (b) potential and kinetic energies (at the expense of the mg-source).     

Calf muscle moment, work and efficiency in level walking; role of series elasticity

Moment and work of the human calf muscles in level walking were determined by means of an EMG to force processor, based on a muscle analogue (Hof and Van den Berg (1981) J. Biomechanics, 14, 747-758, 759-770, 771-785, 787-792). Nine subjects (four women, five men) walked on a level treadmill at speeds between 0.5 and 2.5 ms-1, in their self-chosen pace and at forced pace with steplengths between 0.3 and 1.1 m. The calf muscles are normally only active in the stance phase. The moment increases, with a variable course, to a peak just before push-off. This peak moment increases with the walking speed, from the reference moment (the value in standing on the toes with one leg) at zero speed, to 1.5-2.1 times this value at a speed of 2 ms-1, and decreases at still greater speeds. During the roll-over phase work is done on the calf muscles ('negative work'), followed by positive work in push-off. The negative work is constant, 0.20-0.36 J kg-1, depending on the subject. The positive work increases linearly with steplength--not with speed--from zero at ca. 0.35 m to 0.50 J kg-1 at a steplength of 1.1 m. The interaction between the contractile and the series elastic component in the muscle could be studied by means of the analogue. A great part of the work done on the muscle and of the positive work done by the contractile component are stored in the series elastic component. The stored energy is released at a high rate in push-off. This mechanism ideally requires a concerted contraction, i.e. a contraction in which the activation is matched to the load to the effect that the length of the contractile component remains constant. The muscle then behaves like a spring. Consequences are (a) only little of the negative work gets lost, (b) the length of the contractile component remains close to the optimum of the force-length relation, (c) the shortening speed of the contractile component is now in the range where the muscle works at a high efficiency, and (d) high power peaks can be delivered due to the 'catapult action'.     

Simultaneous positive and negative external mechanical work in human walking.

In human walking, the center of mass motion is similar to an inverted pendulum. Viewing double support as a transition from one inverted pendulum to the next, we hypothesized that the leading leg performs negative work to redirect the center of mass velocity, while simultaneously, the trailing leg performs positive work to replace the lost energy. To test this hypothesis, we developed a method to quantify the external mechanical work performed by each limb (individual limbs method). Traditional measures of external mechanical work use the sum of the ground reaction forces acting on the limbs (combined limbs method) allowing for the mathematical cancellation of simultaneous positive and negative work during multiple support periods. We expected to find that the traditional combined limbs method underestimates external mechanical work by a substantial amount. We used both methods to measure the external mechanical work performed by humans walking over a range of speeds. We found that during double support, the legs perform a substantial amount of positive and negative external work simultaneously. The combined limbs measures of positive and negative external work were approximately 33% less than those calculated using the individual limbs method. At all speeds, the trailing leg performs greater than 97% of the double support positive work while the leading leg performs greater than 94% of the double support negative work.     

Rheodynamic model of cardiac pressure pulsations

To analyse parametrically (in terms of the qualitative theory of dynamical systems) the mechanical influence of inertia, resistance (positive and negative), elasticity and other global properties of the heart-muscle on the left ventricular pressure, an active rheodynamic model based on the Newtons's principles is proposed. The equation of motion of the heart mass centre is derived from an energy conservation law balancing the rate of mechanical (kinetic and potential) energy variation and the power of chemical energy influx and dissipative energy outflux. A corresponding dynamical system of two ordinary differential equations is obtained and parametrically analysed in physiological conditions. As a result, the following main conclusion is made: in physiological norm, because of the heart electrical activity, its equilibrium state is unstable and around it, mechanical self-oscillations emerge. In case the electrical activity ceases, an inverse phase reconstruction occurs during which the unstable equilibrium state of the system becomes stable and the self-oscillations disappear.     

Force platforms as ergometers.

Walking and running on the level involves external mechanical work, even when speed averaged over a complete stride remains constant. This work must be performed by the muscles to accelerate and/or raise the center of mass of the body during parts of the stride, replacing energy which is lost as the body slows and/or falls during other parts of the stride. External work can be measured with fair approximation by means of a force plate, which records the horizontal and vertical components of the resultant force applied by the body to the ground over a complete stride. The horizontal force and the vertical force minus the body weight are integrated electronically to determine the instantaneous velocity in each plane. These velocities are squared and multiplied by one-half the mass to yield the instantaneous kinetic energy. The change in potential energy is calculated by integrating vertical velocity as a function of time to yield vertical displacement and multiplying this by body weight. The total mechanical energy as a function of time is obtained by adding the instantaneous kinetic and potential energies. The positive external mechanical work is obtained by adding the increments in total mechanical energy over an integral number of strides.     

Air resistance and its influence on the biomechanics and energetics of sprinting at sea level and at altitude

Following an examination of the processes by which chemical energy is converted into useful work during running, a mathematical model of the energetics of sprinting is constructed. This is used in conjunction with a careful analysis of Olympic records, in particular those obtained in the 1968 Games at Mexico City, to determine the magnitude of the rate of working against air resistance during running. It is established that times in the 100 m, 200 m and 400 m events at the Mexico Olympics were approximately 1.7% lower than they would otherwise have been if the races had been run at sea level. This information is used to deduce that the external work done per unit time against air resistance is about 7.5-9% of the total power output of a sprinter, running at maximum speed at sea level. These figures compare well with the value of 7.8% obtained independently by Davies (J. appl. Physiol 48, 702-709, 1980). The analysis provides evidence that a linear relation exists between running speed and the rate of degradation of mechanical energy into thermal energy up to the highest sprinting speeds attainable. The maximum power generated by a sprinter is approximately 3 kW.     

Pygmy locomotion

The hypothesis that Pygmies may differ from Caucasians in some aspects of the mechanics of locomotion was tested. A total of 13 Pygmies and 7 Caucasians were asked to walk and run on a treadmill at 4–12 km · h^–1. Simultaneous metabolic measurements and three-dimensional motion analysis were performed allowing the energy expenditure and the mechanical external and internal work to be calculated. In Pygmies the metabolic energy cost was higher during walking at all speeds (P < 0.05), but tended to be lower during running (NS). The stride frequency and the internal mechanical work were higher for Pygmies at all walking (P < 0.05) and running (NS) speeds although the external mechanical work was similar. The total mechanical work for Pygmies was higher during walking (P < 0.05), but not during running and the efficiency of locomotion was similar in all subjects and speeds. The higher cost of walking in Pygmies is consistent with the allometric prediction for smaller subjects. The major determinants of the higher cost of walking was the difference in stride frequency (+9.45, SD 0.44% for Pygmies), which affected the mechanical internal work. This explains the observed higher total mechanical work of walking in Pygmies, even when the external component was the same. Most of the differences between Pygmies and Caucasians, observed during walking, tended to disappear when the speed was normalized as the Fronde number. However, this was not the case for running. Thus, whereas the tested hypothesis must be rejected for walking, the data from running, do indeed suggest that Pygmies may differ in some aspects of the mechanics of locomotion.     

High-speed running performance: a new approach to assessment and prediction.

We hypothesized that all-out running speeds for efforts lasting from a few seconds to several minutes could be accurately predicted from two measurements: the maximum respective speeds supported by the anaerobic and aerobic powers of the runner. To evaluate our hypothesis, we recruited seven competitive runners of different event specialties and tested them during treadmill and overground running on level surfaces. The maximum speed supported by anaerobic power was determined from the fastest speed that subjects could attain for a burst of eight steps (approximately 3 s or less). The maximum speed supported by aerobic power, or the velocity at maximal oxygen uptake, was determined from a progressive, discontinuous treadmill test to failure. All-out running speeds for trials of 3-240 s were measured during 10-13 constant-speed treadmill runs to failure and 4 track runs at specified distances. Measured values of the maximum speeds supported by anaerobic and aerobic power, in conjunction with an exponential constant, allowed us to predict the speeds of all-out treadmill trials to within an average of 2.5% (R2 = 0.94; n = 84) and track trials to within 3.4% (R2 = 0.86; n = 28). An algorithm using this exponent and only two of the all-out treadmill runs to predict the remaining treadmill trials was nearly as accurate (average = 3.7%; R2 = 0.93; n = 77). We conclude that our technique 1) provides accurate predictions of high-speed running performance in trained runners and 2) offers a performance assessment alternative to existing tests of anaerobic power and capacity.     

Old men running: mechanical work and elastic bounce

It is known that muscular force is reduced in old age. We investigate what are the effects of this phenomenon on the mechanics of running. We hypothesized that the deficit in force would result in a lower push, causing reduced amplitude of the vertical oscillation, with smaller elastic energy storage and increased step frequency. To test this hypothesis, we measured the mechanical energy of the centre of mass of the body during running in old and young subjects. The amplitude of the oscillation is indeed reduced in the old subjects, resulting in an approximately 20% smaller elastic recovery and a greater step frequency (3.7 versus 2.8 Hz, p=1.9x10(-5), at 15-17 km h(-1)). Interestingly, the greater step frequency is due to a lower aerial time, and not to a greater natural frequency of the system, which is similar in old and young subjects (3.6 versus 3.4 Hz, p=0.2). Moreover, we find that in the old subjects, the step frequency is always similar to the natural frequency, even at the highest speeds. This is at variance with young subjects who adopt a step frequency lower than the natural frequency at high speeds, to contain the aerobic energy expenditure. Finally, the external work to maintain the motion of the centre of mass is reduced in the old subjects (0.9 versus 1.2 J kg(-1) m(-1), p=5.1x10(-6)) due to the lower work done against gravity, but the higher step frequency involves a greater internal work to reset the limbs at each step. The net result is that the total work increases with speed more steeply in the old subjects than in young subjects.