Patrick Willems

Effect of load and speed on the energetic cost of human walking

It is well established that the energy cost per unit distance traveled is minimal at an intermediate walking speed in humans, defining an energetically optimal walking speed. However, little is known about the optimal walking speed while carrying a load. In this work, we studied the effect of speed and load on the energy expenditure of walking. The O2 consumption and CO2 production were measured in ten subjects while standing or walking at different speeds from 0.5 to 1.7xa0mxa0s−1 with loads from 0 to 75% of their body mass (Mb). The loads were carried in typical trekker’s backpacks with hip support. Our results show that the mass-specific gross metabolic power increases curvilinearly with speed and is directly proportional to the load at any speed. For all loading conditions, the gross metabolic energy cost (Jxa0kg−1xa0m−1) presents a U-shaped curve with a minimum at around 1.3xa0mxa0s−1. At that optimal speed, a load up to 1/4xa0Mb seems appropriate for long-distance walks. In addition, the optimal speed for net cost minimization is around 1.06xa0mxa0s−1 and is independent of load.

The energy cost of walking in children

Abstract. Size, morphology and motor skills change dramatically during growth and this probably has an effect on the cost of locomotion. In this study, the effects of age and speed on the energy expended while walking were determined during growth. The rate of oxygen consumption and carbon dioxide production were measured in 3- to 12-year-old children and in adults while standing and walking at different speeds from 0.5xa0m·s–1 to near their maximum aerobic walking speed. Standing energy expenditure rate decreases with age from 3.42±0.48xa0W·kg–1 (mean±SD, n=6) in the 3- to 4-year-olds to 1.95±0.22xa0W·kg–1 (n=6) in young adults. At all ages the gross cost of transport has a minimum which decreases from 5.9xa0J·kg–1·m–1 in 3- to 4-year-olds to 3.6xa0J·kg–1·m–1 after 10xa0years of age. The speed at which this minimum occurs increases from 1.2xa0m·s–1 to 1.5xa0m·s–1 over the same age range. At low and intermediate walking speeds the net cost of transport is similar in children and adults (about 2xa0J·kg–1·m–1). In young children walking at their highest speeds the net cost of transport is 70% (3- to 4-year-olds) to 40% (5- to 6-year-olds) greater than in adults.

The role of gravity in human walking: pendular energy exchange, external work and optimal speed

1 During walking on Earth, at 1.0 g of gravity, the work done by the muscles to maintain the motion of the centre of mass of the body (Wext) is reduced by a pendulum‐like exchange between gravitational potential energy and kinetic energy. The weight‐specific Wext per unit distance attains a minimum of 0.3 J kg−1 m−1 at about 4.5 km h−1 in adults. 2 The effect of a gravity change has been studied during walking on a force platform fixed to the floor of an aircraft undergoing flight profiles which resulted in a simulated gravity of 0.4 and 1.5 times that on Earth. 3 At 0.4 g, such as on Mars, the minimum Wext was 0.15 J kg−1 m−1, half that on Earth and occurred at a slower speed, about 2.5 km h−1. The range of walking speeds is about half that on Earth. 4 At 1.5 g, the lowest value of Wext was 0.60 J kg−1 m−1, twice that on Earth; it was nearly constant up to about 4.3 km h−1 and then increased with speed. The range of walking speeds is probably greater than that on Earth. 5 A model is presented in which the speed for an optimum exchange between potential and kinetic energy, the ‘optimal speed’, is predicted by the balance between the forward deceleration due to the lift of the body against gravity and the forward deceleration due to the impact against the ground. 6 In conclusion, over the range studied, gravity increases the work required to walk, but it also increases the range of walking speeds.

Effect of speed on the energy cost of walking in unilateral traumatic lower limb amputees

In this work, the effect of walking speed on the energy expenditure in traumatic lower-limb amputees was studied. The oxygen consumption was measured in 10 transfemoral amputees, 9 transtibial amputees and 13 control subjects, while they stood and walked at different speeds from 0.3xa0mxa0s−1 to near their maximum sustainable speed. Standing energy expenditure rate was the same in lower-limb amputees and in control subjects (≈1.85xa0Wxa0kg−1). On the contrary, during walking, the net energy expenditure rate was 30–60% greater in transfemoral amputees and 0–15% greater in transtibial amputees than in control subjects. The maximal sustainable speed was about 1.2xa0mxa0s−1 in transfemoral amputees and 1.6xa0mxa0s−1 in transtibial amputees, whereas it was above 2xa0mxa0s−1 in control subjects. Among these three groups, the cost of transport versus speed presented a U-shaped curve; the minimum cost increased with the level of amputation, and the speed at which this minimum occurred decreased.

Mechanical work and muscular efficiency in walking children

SUMMARY The effect of age and body size on the total mechanical work done during walking is studied in children of 3–12 years of age and in adults. The total mechanical work per stride (Wtot) is measured as the sum of the external work, Wext (i.e. the work required to move the centre of mass of the body relative to the surroundings), and the internal work, Wint (i.e. the work required to move the limbs relative to the centre of mass of the body, Wint,k, and the work done by one leg against the other during the double contact period, Wint,dc). Above 0.5 m s–1, both Wext and Wint,k, normalised to body mass and per unit distance (J kg–1 m–1), are greater in children than in adults; these differences are greater the higher the speed and the younger the subject. Both in children and in adults, the normalised Wint,dc shows an inverted U-shape curve as a function of speed, attaining a maximum value independent of age but occurring at higher speeds in older subjects. A higher metabolic energy input (J kg–1 m–1) is also observed in children, although in children younger than 6 years of age, the normalised mechanical work increases relatively less than the normalised energy cost of locomotion. This suggests that young children have a lower efficiency of positive muscular work production than adults during walking. Differences in normalised mechanical work, energy cost and efficiency between children and adults disappear after the age of 10.

The resonant step frequency in human running

Abstractu2002At running speeds less than about 13 km h–1 the freely chosen step frequency (ffree) is lower than the frequency at which the mechanical power is minimized (fmin). This dissociation between ffree and fmin was investigated by measuring mechanical power, metabolic energy expenditure and apparent natural frequency of the body’s bouncing system (fsist) during running at three given speeds with different step frequencies. The ffree requires a mechanical power greater than that at fmin mainly due to a larger vertical oscillation of the body at each step. Energy expenditure is minimal and the mechanical efficiency is maximal at ffree. At a given speed, an increase in step frequency above ffree results in an increase in energy expenditure despite a decrease in mechanical power. On the other hand, a decrease in step frequency below ffree results in a larger increase in energy expenditure associated with an increase in mechanical power. When the step frequency is forced to values above or below ffree, fsist is forced to change similarly by adjusting the stiffness of the bouncing system. However the best match between fsist and step frequency takes place only in proximity of ffree (2.6–2.8 Hz). It is concluded that during running at speeds less than 13 km h–1 energy is saved by tuning step frequency to fsist, even if this requires a mechanical power larger than necessary.

Stability of the Braced Ankle A Biomechanical Investigation

We measured the bare ankle and the braced angle- torque relationships in 12 uninjured volunteers under static and dynamic conditions within the full range of inversion motion. These relationships were measured with a specially designed mechanical device that al lowed inversion movements with angular velocities up to 850 deg/sec. In testing the bare ankle under static conditions, the torque showed a 10-fold increase within the full range of motion (average, from 0.9 N-m at 7° to about 8 N-m at 48° of inversion). The slope of the angle-torque relationship increased under dynamic conditions giving higher torque values (up to 18 N-m on average). Both orthoses induced similar additional torques that increased linearly, up to about 6 N-m at 45°, with higher angles of inversion. These additional torques are small compared with the amount of stress applied to the foot during a typical ankle sprain situa tion, such as recovering from a jump. Therefore, we propose that orthotic devices increase the ankle torque, counteracting the inversion movement, and also prevent the start of the inversion movement by preloading and maintaining the ankle in a proper ana tomic position with optimal contact between the artic ular surfaces.

Energy cost, mechanical work and muscular efficiency in swing-through gait with elbow crutches

Crutches are widely used to assist ambulation in disabled people. Many authors have shown that the use of crutches increases the energy cost as compared to normal walking. In this study we have measured the energy consumed and the mechanical work performed during swing-through crutch gait in order to assess if the greater energy expenditure is accompanied by an equivalent increase of the work done to move the body. Our results show that, depending upon the speed, the energy expenditure is 2-3 times higher in swing-through gait than in normal walking. On the other hand, the mechanical work increases only 1.3-1.5 times. Thus the extra cost of swing-through gait cannot be explained solely by an increase of the mechanical work, but is due at least in part to a reduction in the efficiency of positive work production.

Biomechanics of locomotion in Asian elephants

SUMMARY Elephants are the biggest living terrestrial animal, weighing up to five tons and measuring up to three metres at the withers. These exceptional dimensions provide certain advantages (e.g. the mass-specific energetic cost of locomotion is decreased) but also disadvantages (e.g. forces are proportional to body volume while supportive tissue strength depends on their cross-sectional area, which makes elephants relatively more fragile than smaller animals). In order to understand better how body size affects gait mechanics the movement of the centre of mass (COM) of 34 Asian elephants (Elephas maximus) was studied over their entire speed range of 0.4-5.0 m s−1 with force platforms. The mass-specific mechanical work required to maintain the movements of the COM per unit distance is ~0.2 J kg−1 m−1 (about 1/3 of the average of other animals ranging in size from a 35 g kangaroo rat to a 70 kg human). At low speeds this work is reduced by a pendulum-like exchange between the kinetic and potential energies of the COM, with a maximum energy exchange of ~60% at 1.4 m s−1. At high speeds, elephants use a bouncing mechanism with little exchange between kinetic and potential energies of the COM, although without an aerial phase. Elephants increase speed while reducing the vertical oscillation of the COM from about 3 cm to 1 cm.

Walking on Mars

Sometime in the near future humans may walk in the reduced gravity of Mars. Gravity plays an essential role in walking. On Earth, the body uses gravity to ‘fall forwards’ at each step and then the forward speed is used to restore the initial height in a pendulum-like mechanism. When gravity is reduced, as on the Moon or Mars, the mechanism of walking must change. Here we investigate the mechanics of walking on Mars onboard an aircraft undergoing gravity-reducing flight profiles. The optimal walking speed on Mars will be 3.4 km h−1 (down from 5.5 km h−1 on Earth) and the work done per unit distance to move the centre of mass will be half that on Earth.