ABSTRACT As walking speed increases, humans choose to transition to a running gait at their preferred transition speed (PTS). Near that speed, it becomes metabolically cheaper to run rather than to walk and that defines the energetically optimal transition speed (EOTS). Our goals were to determine: (1) how PTS and EOTS compare across a wide range of inclines and (2) whether the EOTS can be predicted by the heart rate optimal transition speed (HROTS). Ten healthy, high-caliber, male trail/mountain runners participated. On day 1, subjects completed 0 and 15 deg trials and on day 2, they completed 5 and 10 deg trials. We calculated PTS as the average of the walk-to-run transition speed (WRTS) and the run-to-walk transition speed (RWTS) determined with an incremental protocol. We calculated EOTS and HROTS from energetic cost and heart rate data for walking and running near the expected EOTS for each incline. The intersection of the walking and running linear regression equations defined EOTS and HROTS. We found that PTS, EOTS and HROTS all were slower on steeper inclines. PTS was slower than EOTS at 0, 5 and 10 deg, but the two converged at 15 deg. Across all inclines, PTS and EOTS were only moderately correlated. Although EOTS correlated with HROTS, EOTS was not predicted accurately by heart rate on an individual basis.

ABSTRACT Humans have evolved the ability to walk very efficiently. Further, humans prefer to walk at speeds that approximately minimize their metabolic energy expenditure per unit distance (i.e. gross cost of transport, COT). This has been found in a variety of population groups and other species. However, these studies were mostly performed on smooth, level ground or on treadmills. We hypothesized that the objective function for walking is more complex than only minimizing the COT. To test this idea, we compared the preferred speeds and the relationships between COT and speed for people walking on both a smooth, level floor and a rough, natural terrain trail. Rough terrain presumably introduces other factors, such as stability, to the objective function. Ten healthy men walked on both a straight, flat, smooth floor and an outdoor trail strewn with rocks and boulders. In both locations, subjects performed five to seven trials at different speeds relative to their preferred speed. The COT–speed relationships were similarly U -shaped for both surfaces, but the COT values on rough terrain were approximately 115% greater. On the smooth surface, the preferred speed (1.24±0.17 m s −1 ) was not found to be statistically different ( P =0.09) than the speed that minimized COT (1.34±0.03 m s −1 ). On rough terrain, the preferred speed (1.07±0.05 m s −1 ) was significantly slower than the COT minimum speed (1.13±0.07 m s −1 ; P =0.02). Because near the optimum speed the COT function is very shallow, these changes in speed result in a small change in COT (0.5%). It appears that the objective function for speed preference when walking on rough terrain includes COT and additional factors such as stability.

ABSTRACT The ‘cost of generating force’ hypothesis proposes that the metabolic rate during running is determined by the rate of muscle force development (1/ t c , where t c =contact time) and the volume of active leg muscle. A previous study assumed a constant recruited muscle volume and reported that the rate of force development alone explained ∼70% of the increase in metabolic rate for human runners across a moderate velocity range (2–4 m s −1 ). We hypothesized that over a wider range of velocities, the effective mechanical advantage (EMA) of the lower limb joints would overall decrease, necessitating a greater volume of active muscle recruitment. Ten high-caliber male human runners ran on a force-measuring treadmill at 8, 10, 12, 14, 16 and 18 km h −1 while we analyzed their expired air to determine metabolic rates. We measured ground reaction forces and joint kinematics to calculate contact time and estimate active muscle volume. From 8 to 18 km h −1 , metabolic rate increased 131% from 9.28 to 21.44 W kg −1 . t c decreased from 0.280 s to 0.190 s, and thus the rate of force development (1/ t c ) increased by 48%. Ankle EMA decreased by 19.7±11%, knee EMA increased by 11.1±26.9% and hip EMA decreased by 60.8±11.8%. Estimated active muscle volume per leg increased 52.8% from 1663±152 cm 3 to 2550±169 cm 3 . Overall, 98% of the increase in metabolic rate across the velocity range was explained by just two factors: the rate of generating force and the volume of active leg muscle.

ABSTRACT On curves, non-amputees' maximum running speed is slower on smaller radii and thought to be limited by the inside leg's mechanics. Similar speed decreases would be expected for non-amputees in both counterclockwise and clockwise directions because they have symmetric legs. However, sprinters with unilateral leg amputation have asymmetric legs, which may differentially affect curve-running performance and Paralympic competitions. To investigate this and understand the biomechanical basis of curve running, we compared maximum curve-running (radius 17.2 m) performance and stride kinematics of six non-amputee sprinters and 11 sprinters with a transtibial amputation. Subjects performed randomized, counterbalanced trials: two straight, two counterclockwise curves and two clockwise curves. Non-amputees and sprinters with an amputation all ran slower on curves compared with straight running, but with different kinematics. Non-amputees ran 1.9% slower clockwise compared with counterclockwise ( P <0.05). Sprinters with an amputation ran 3.9% slower with their affected leg on the inside compared with the outside of the curve ( P <0.05). Non-amputees reduced stride length and frequency in both curve directions compared with straight running. Sprinters with an amputation also reduced stride length in both curve-running directions, but reduced stride frequency only on curves with the affected leg on the inside. During curve running, non-amputees and athletes with an amputation had longer contact times with their inside compared with their outside leg, suggesting that the inside leg limits performance. For sprinters with an amputation, the prolonged contact times of the affected versus unaffected leg seem to limit maximum running speed during both straight running and running on curves with the affected leg on the inside.

Mechanical energy can be conserved during terrestrial locomotion in two ways: the inverted pendulum mechanism for walking and the spring–mass mechanism for running. Here, we investigated whether diagonal stride cross-country roller skiing (DIA) utilizes similar mechanisms. Based on previous studies, we hypothesized that running and DIA would share similar phase relationships and magnitudes of kinetic energy (KE), and gravitational potential energy (GPE) fluctuations, indicating elastic energy storage and return, as if roller skiing is like ‘running on wheels’. Experienced skiers ( N =9) walked and ran at 1.25 and 3 m s −1 , respectively, and roller skied with DIA at both speeds on a level dual-belt treadmill that recorded perpendicular and parallel forces. We calculated the KE and GPE of the center of mass from the force recordings. As expected, the KE and GPE fluctuated with an out-of-phase pattern during walking and an in-phase pattern during running. Unlike walking, during DIA, the KE and GPE fluctuations were in phase, as they are in running. However, during the glide phase, KE was dissipated as frictional heat and could not be stored elastically in the tendons, as in running. Elastic energy storage and return epitomize running and thus we reject our hypothesis. Diagonal stride cross-country skiing is a biomechanically unique movement that only superficially resembles walking or running.

Although the mechanical function is quite clear, there is no consensus regarding the metabolic benefit of arm swing during human running. We compared the metabolic cost of running using normal arm swing with the metabolic cost of running while restricting the arms in three different ways: (1) holding the hands with the arms behind the back in a relaxed position (BACK), (2) holding the arms across the chest (CHEST) and (3) holding the hands on top of the head (HEAD). We hypothesized that running without arm swing would demand a greater metabolic cost than running with arm swing. Indeed, when compared with running using normal arm swing, we found that net metabolic power demand was 3, 9 and 13% greater for the BACK, CHEST and HEAD conditions, respectively (all P <0.05). We also found that when running without arm swing, subjects significantly increased the peak-to-peak amplitudes of both shoulder and pelvis rotation about the vertical axis, most likely a compensatory strategy to counterbalance the rotational angular momentum of the swinging legs. In conclusion, our findings support our general hypothesis that swinging the arms reduces the metabolic cost of human running. Our findings also demonstrate that arm swing minimizes torso rotation. We infer that actively swinging the arms provides both metabolic and biomechanical benefits during human running.

SUMMARY In level running, humans and other animals store and recover elastic energy during each step. What role does elastic energy play during downhill and uphill running? We measured the fluctuations of the mechanical energy of the center of mass (CoM) of 15 human participants running at 3 m s –1 on the level, downhill and uphill on a force-measuring treadmill mounted at 3, 6 and 9 deg. In level running, nearly symmetrical decreases and increases of the combined gravitational potential and kinetic (GPE+KE) energy of the CoM indicated equal possible elastic energy storage and recovery. However, asymmetrical fluctuations during hill running indicate reduced maximum possible elastic energy storage and return. We analyzed mechanical energy generation and dissipation during level and hill running by quantifying the anatomically estimated elastic energy storage (AEEE) in the arch and Achilles' tendon using peak ground reaction forces and anatomical characteristics. AEEE did not change with grade. At shallow downhill grades, the body must generate mechanical energy, though it dissipates more than it generates. At steeper downhill grades, little to no energy generation is required and only mechanical energy dissipation must occur. The downhill grade at which mechanical energy must no longer be generated occurs at approximately –9 deg, near the metabolically optimal running grade. At shallow uphill grades, mechanical energy must be generated to raise the CoM, and at steeper grades, additional energy must be generated to offset reduced elastic energy storage and return.

SUMMARY Evolution has produced a wide range of body plans, but for a given body mass, the energetic cost of transport (COT) of terrestrial animals falls in a relatively narrow range. Previous research indicates that the COT depends on the proficiency of minimizing mechanical work performed, efficiency of performing that work, and cost of generating force to support weight. Turtles are unique in that their protective shell and shoulder-girdle articulation may eliminate the need for the `muscular sling'. In addition, turtles have slower,more efficient muscles than other vertebrates. However, slow locomotion may raise the COT by confounding mechanical-energy conservation via the inverted-pendulum mechanism. Our goal was to determine the metabolic COT and efficiency of a terrestrial turtle species during locomotion. We studied 18 ornate box turtles, Terrapene ornata . Walking speed was extremely slow (0.07±0.005 m s –1 ). The average minimum COT was 8.0±0.70 J kg –1 m –1 attained at∼0.1 m s –1 . Ornate box turtles consume only half the energy predicted by the allometric relationship for all terrestrial animals(15.9±0.35 J kg –1 m –1 ), and, thus,appear to be very economical walkers. When walking up a 24 deg. incline turtles moved significantly slower (0.04±0.004 m s –1 ),but performed the extra work required to walk uphill with very high efficiencies (>49%). It appears that the co-evolution of a protective shell, the associated shoulder morphology, and very slow, efficient muscles produce both economical level walking and efficient uphill walking.

SUMMARY It has been proposed that muscle-specific factors trigger the human walk–run transition. We investigated if changing the demand on trigger muscles alters the preferred walk–run transition speed. We hypothesized that (1) reducing the demand on trigger muscles would increase the transition speed and (2) increasing the demand on trigger muscles would decrease the transition speed. We first determined the normal preferred walk–run transition speed (PTS) using a step-wise protocol with a randomized speed order. We then determined PTS while subjects walked with external devices that decreased or increased the demand on specific muscle groups. We concurrently measured the electromyographic activity of five leg muscles (tibialis anterior, soleus, rectus femoris, medial and lateral gastrocnemius) at each speed and condition. For this study, we developed a dorsiflexor assist device that aids the dorsiflexor muscles. A leg swing assist device applied forward pulling forces at the feet thus aiding the hip flexors during swing. A third device applied a horizontal force near the center of mass, which impedes or aids forward progression thus overloading or unloading the plantarflexor muscles. We found that when demand was decreased in the muscles measured, the PTS significantly increased. Conversely, when muscle demand was increased in the plantar flexors, the PTS decreased. However, combining assistive devices did not produce an even faster PTS. We conclude that altering the demand on specific muscles can change the preferred walk–run transition speed. However, the lack of a summation effect with multiple external devices,suggests that another underlying factor ultimately determines the preferred walk–run transition speed.

SUMMARY The metabolic cost of running is substantial, despite the savings from elastic energy storage and return. Previous studies suggest that generating vertical force to support body weight and horizontal forces to brake and propel body mass are the major determinants of the metabolic cost of running. In the present study, we investigated how independently altering body weight and body mass affects the metabolic cost of running. Based on previous studies, we hypothesized that reducing body weight would decrease metabolic rate proportionally, and adding mass and weight would increase metabolic rate proportionally. Further, because previous studies show that adding mass alone does not affect the forces generated on the ground, we hypothesized that adding mass alone would have no substantial effect on metabolic rate. We manipulated the body weight and body mass of 10 recreational human runners and measured their metabolic rates while they ran at 3 m s –1 . We reduced weight using a harness system, increased mass and weight using lead worn about the waist, and increased mass alone using a combination of weight support and added load. We found that net metabolic rate decreased in less than direct proportion to reduced body weight, increased in slightly more than direct proportion to added load (added mass and weight), and was not substantially different from normal running with added mass alone. Adding mass alone was not an effective method for determining the metabolic cost attributable to braking/propelling body mass. Runners loaded with mass alone did not generate greater vertical or horizontal impulses and their metabolic costs did not substantially differ from those of normal running. Our results show that generating force to support body weight is the primary determinant of the metabolic cost of running. Extrapolating our reduced weight data to zero weight suggests that supporting body weight comprises at most 74% of the net cost of running. However, 74% is probably an overestimate of the metabolic demand of body weight to support itself because in reduced gravity conditions decrements in horizontal impulse accompanied decrements in vertical impulse.

SUMMARY Why is maximal running speed reduced on curved paths? The leading explanation proposes that an increase in lateral ground reaction force necessitates a decrease in peak vertical ground reaction force, assuming that maximum leg extension force is the limiting factor. Yet, no studies have directly measured these forces or tested this critical assumption. We measured maximum sprint velocities and ground reaction forces for five male humans sprinting along a straight track and compared them to sprints along circular tracks of 1, 2, 3, 4 and 6 m radii. Circular track sprint trials were performed either with or without a tether that applied centripetal force to the center of mass. Sprinters generated significantly smaller peak resultant ground reaction forces during normal curve sprinting compared to straight sprinting. This provides direct evidence against the idea that maximum leg extension force is always achieved and is the limiting factor. Use of the tether increased sprint speed, but not to expected values. During curve sprinting, the inside leg consistently generated smaller peak forces compared to the outside leg. Several competing biomechanical constraints placed on the stance leg during curve sprinting likely make the inside leg particularly ineffective at generating the ground reaction forces necessary to attain maximum velocities comparable to straight path sprinting. The ability of quadrupeds to redistribute function across multiple stance legs and decouple these multiple constraints may provide a distinct advantage for turning performance.

SUMMARY Humans and other animals exchange gravitational potential energy (GPE) and kinetic energy (KE) of the center of mass during level walking. How effective is this energy exchange during downhill and uphill walking? Based on previous reports and our own reasoning, we expected that during downhill walking, the possibility for mechanical energy exchange would be enhanced and during uphill walking, the possibility for exchange would be reduced. We measured the fluctuations of the mechanical energies for five men and five women walking at 1.25 m s -1 . Subjects walked on the level, downhill, and uphill on a force measuring treadmill mounted at 3°, 6° and 9°. We evaluated energy exchange during the single support period based on the GPE and KE fluctuation factors of phase relationship, relative magnitude and extent of symmetry. As expected, during level walking, the GPE and KE curves were out of phase, of similar magnitude, and nearly mirror images so that the fluctuations in combined (GPE+KE) energy were attenuated. During downhill walking, the fluctuations in the combined energy of the center of mass were smaller than those on the level, i.e. mechanical energy exchange was more effective. During uphill walking, the fluctuations in the combined energy of the center of mass were larger than those on the level, i.e. mechanical energy exchange was less effective. Mechanical energy exchange occurred during downhill, level and uphill walking, but it was most effective during downhill walking.

SUMMARY For centuries, elephant locomotion has been a contentious and confusing challenge for locomotion scientists to understand, not only because of technical difficulties but also because elephant locomotion is in some ways atypical of more familiar quadrupedal gaits. We analyzed the locomotor kinematics of over 2400 strides from 14 African and 48 Asian elephant individuals (body mass 116-4632 kg) freely moving over ground at a 17-fold range of speeds, from slow walking at 0.40 m s -1 to the fastest reliably recorded speed for elephants, 6.8 m s -1 . These data reveal that African and Asian elephants have some subtle differences in how size-independent kinematic parameters change with speed. Although elephants use a lateral sequence footfall pattern, like many other quadrupeds, they maintain this footfall pattern at all speeds, shifting toward a 25% phase offset between limbs (singlefoot) as they increase speed. The duty factors of elephants are greater for the forelimbs than for the hindlimbs, so an aerial phase for the hindquarters is reached at slower speeds than for the forequarters. This aerial phase occurs at a Froude number of around 1,matching theoretical predictions. At faster speeds, stance and swing phase durations approach asymptotes, with the duty factor beginning to level off,concurrent with an increase in limb compliance that likely keeps peak forces relatively low. This increase of limb compliance is reflected by increased compression of the hindlimbs. Like other tetrapods, smaller elephants are relatively more athletic than larger ones, but still move very similarly to adults even at <500 kg. At any particular speed they adopt greater relative stride frequencies and relative stride lengths compared to larger elephants. This extends to near-maximal locomotor performance as well - smaller elephants reach greater Froude numbers and smaller duty factors, hence likely reach relatively greater peak loads on their limbs and produce this force more rapidly. A variety of lines of kinematic evidence support the inference that elephants change their mechanics near a Froude number of 1 (if not at slower speeds), at least to using more compliant limbs, if not spring-like whole-body kinetics. In some ways, elephants move similarly to many other quadrupeds,such as increasing speed mainly by increasing stride frequency (except at fast speeds), and they match scaling predictions for many stride parameters. The main difference from most other animals is that elephants never change their footfall pattern to a gait that uses a whole-body aerial phase. Our large dataset establishes what the normal kinematics of elephant locomotion are, and can also be applied to identify gait abnormalities that may signal musculoskeletal pathologies, a matter of great importance to keepers of captive elephants.

SUMMARY Animals must perform mechanical work during walking, but most conserve substantial mechanical energy via an inverted-pendulum-like mechanism of energy recovery in which fluctuations of kinetic energy (KE) and gravitational potential energy (GPE) are of similar magnitude and 180° out of phase. The greatest energy recovery typically occurs at intermediate speeds. Tortoises are known for their slow speeds, which we anticipated would lead to small fluctuations in KE. To have an effective exchange of mechanical energy using the inverted-pendulum mechanism, tortoises would need to walk with only small changes in GPE corresponding to vertical center-of-mass (COM)fluctuations of <0.5 mm. Thus, we hypothesized that giant Galápagos tortoises would not conserve substantial mechanical energy using the inverted-pendulum mechanism. We studied five adult giant Galápagos tortoises Geochelone elephantopus (mean mass=142 kg; range= 103–196 kg). Walking speed was extremely slow (0.16±0.052 m s –1 ; mean ± 1 s . d .). The fluctuations in kinetic energy(8.1±3.98 J stride –1 ) were only one-third as large as the fluctuations in gravitational potential energy (22.7±8.04 J stride –1 ). In addition, these energies fluctuated nearly randomly and were only sporadically out of phase. Because of the dissimilar amplitudes and inconsistent phase relationships of these energies, tortoises conserved little mechanical energy during steady walking, recovering only 29.8±3.77% of the mechanical energy (range=13–52%). Thus, giant Galápagos tortoises do not utilize effectively an inverted-pendulum mechanism of energy conservation. Nonetheless, the mass-specific external mechanical work required per distance (0.41±0.092 J kg –1 m –1 ) was not different from most other legged animals. Other turtle species use less than half as much metabolic energy to walk as other terrestrial animals of similar mass. It is not yet known if Galápagos tortoises are economical walkers. Nevertheless,contrary to biomechanical convention, poor inverted-pendulum mechanics during walking do not necessarily correspond to high mechanical work and may not result in a high metabolic cost.

SUMMARY We studied nine adult horses spanning an eightfold range in body mass( M b ) (90–720 kg) and a twofold range in leg length( L ) (0.7–1.4 m). We measured the horses' walk–trot transition speeds using step-wise speed increments as they locomoted on a motorized treadmill. We then measured their rates of oxygen consumption over a wide range of walking and trotting speeds. We interpreted the transition speed results using a simple inverted-pendulum model of walking in which gravity provides the centripetal force necessary to keep the leg in contact with the ground. By studying a large size range of horses, we were naturally able to vary the absolute walking speed that would produce the same ratio of centripetal to gravitational forces. This ratio,( M b v 2 / L )/( M b g ),reduces to the dimensionless Froude number( v 2 / gL ), where v is forward speed, L is leg length and g is gravitational acceleration. We found that the absolute walk–trot transition speed increased with size from 1.6 to 2.3 m s –1 , but it occurred at nearly the same Froude number (0.35). In addition, horses spontaneously switched between gaits in a narrow range of speeds that corresponded to the metabolically optimal transition speed. These results support the hypotheses that the walk–trot transition is triggered by inverted-pendulum dynamics and occurs at the speed that maximizes metabolic economy.

SUMMARY In the single stance phase of walking, center of mass motion resembles that of an inverted pendulum. Theoretically, mechanical work is not necessary for producing the pendular motion, but work is needed to redirect the center of mass velocity from one pendular arc to the next during the transition between steps. A collision model predicts a rate of negative work proportional to the fourth power of step length. Positive work is required to restore the energy lost, potentially exacting a proportional metabolic cost. We tested these predictions with humans ( N =9) walking over a range of step lengths(0.4-1.1 m) while keeping step frequency fixed at 1.8 Hz. We measured individual limb external mechanical work using force plates, and metabolic rate using indirect calorimetry. As predicted, average negative and positive external mechanical work rates increased with the fourth power of step length(from 1 W to 38 W; r 2 =0.96). Metabolic rate also increased with the fourth power of step length (from 7 W to 379 W; r 2 =0.95), and linearly with mechanical work rate. Mechanical work for step-to-step transitions, rather than pendular motion itself, appears to be a major determinant of the metabolic cost of walking.