© 2001 by The Society for Integrative and Comparative Biology
Energetics and Mechanics of Human Walking at Oscillating Speeds1
1 Department of Exercise and Sport Science, Manchester Metropolitan University, Hassall Road, Alsager ST7 2HL, UK
2 Department of Physiology, Institute of Advanced Biomedical Technology, National Research Council, Via F.lli Cervi 93, 20090 Segrate (MI), Italy
3 Centro Studi Attivita' Motorie, Fondazione ‘Salvatore Maugeri,’ Pavia, Italy
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Seven subjects walked on a programmable treadmill both at constant (3.5 ± 0.0 and 5.0 ± 0.0 km/hr) and oscillating speeds (±0.5, ±1.0, ±1.5, ±2.0 km hr–1), set to sinusoidally change between the two limits in 3 sec. In each condition oxygen consumption measurements were taken. The same experimental protocols were replicated on a walkway by asking subjects to adapt their stride frequency to an audio signal corresponding to the sinusoidal stride frequency changes measured on the treadmill. Differently from what expected, only the ±2.0 km hr–1 oscillation resulted to be metabolically different from the constant speed walking, both for the treadmill and the walkway conditions. The time course of the mechanical energy of the body centre of mass could reveal that a strategy devoted to benefit from the usual energy fluctuations occurring at "constant speed," is likely to be used to cope with speed varying sequences. From the energy curve observed at constant speed, it is possible to derive an energetically equivalent curve by cumulating acceleration portions, and deceleration ones, of a group of strides as to produce a single acceleration and a single deceleration phase, as it is observed in oscillating speed walking. Being aware of the bias introduced by using a non-inertial frame (the treadmill protocol), we are replicating the experiments with a laser beam projected on a wide radius circular path at oscillating speeds, that the subjects have to follow. The preliminary data seem to confirm the invariance of the metabolic requirements in oscillatory walking up to ±1.5 km hr–1.
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INTRODUCTION |
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Most of the scientific literature dealing with the metabolic and mechanical work of locomotion has been based on measurements taken at constant speeds. This is mainly the result both of technology, because of the diffusion of motorized treadmill, and of convenience, due to the need to standardize measurement conditions. While having provided several fundamental insights in the determinants of the different gaits, such a laboratory constraint does not match the daily activity of humans and terrestrial animals, whose locomotion is seldom observed to occur at constant speed. The continuously alternating of acceleration and deceleration is part of everyone's life and, as in cars (FHWA, 1980
), is expected to be associated with a substantial amount of extra energy consumption, with respect to a steady progression at the same average speed (see Fig. 1). We are assisting to a growing interest in the field of intermittent locomotion due to different reasons. Comparative physiologists and biomechanists realised that locomotion in birds and fishes often occurs in bouts rather then at a constant pace, and this could be associated to different strategies devoted to maintain a high muscular efficiency. Human physiologists, nonetheless, are interested in the effects of added loads on the energy cost of walking and running. While it is known that the added mass proportionally increases the metabolic cost of walking, no paper has been published so far on the influence of it on the cost of oscillatory speed motion. In cases as obese patients, for example, the deviation from a constant progression speed could possibly constitute a burden because of a higher mass located in the head-trunk segment.
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The interest on intermittent locomotion is not confined to the biological world. The automotive industry and their outmost technological research in terms of economy of internal combustion engine vehicles recently managed to record the least fuel consumption (more than 3,300 km per liter of gasoline—Mileage Marathon, Eco Marathon Nokia 01.09.1996, www.sci.fi/
fmmc/res96.html) by using an intermittent motion where an active acceleration was followed by a passive deceleration (www.susono.com/nobby/ecorun_eng.html). Aim of this work is to compare the metabolic cost of walking at constant speed with the one observed when different speed changes (about the same average speed) are imposed, and to discuss the relationship with the predictions from mechanics.
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MATERIALS AND METHODS |
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Seven healthy subjects (age 35.7 ± 5.1 yr, mass 69.7 ± 10.8 kg, BMI 22.7 ± 2.4, 2 females), after giving their informed consent, walked on a motorized treadmill (Woodway ERGO-LG, Germany) at constant speeds (3.5 ± 0.0) and 5.0 (5.0 ± 0.0) km hr–1) and with imposed speed fluctuations while maintaining the same average speeds. Four protocols were designed allowing speed changes between the lower and the upper limit every 3 sec (acceleration-deceleration cycle time was 6 sec) for a total duration of 5 min. With respect to the average speed, the imposed changes were ±0.5, ±1.0, ±1.5, and ±2.0 km hr–1. For each protocol the acceleration between the lowest and the highest speed was set as to produce a sinusoid-like speed time course (with no constant speed phase, see Fig. 2).
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The metabolic expenditure was assessed via an automatic oxygen consumption analyser (Vmax, Sensor Medics, USA). The oxygen uptake and heart rate were sampled in the last 30 sec of 5 min periods for both basal (standing) and exercise conditions. The energy cost of walking (C, mlO2 kg–1 km–1) was obtained by subtracting the basal value (mlO2 kg–1 min–1) from the exercise metabolic consumption and by dividing the result by the average progression speed. Each subjects performed the 5 trials 5 times to enhance the signal-to-noise ratio.
Being aware that some of the mechanical work during speed-oscillating walking on the treadmill is done by the electric motor (and some by the human, as it is a non-inertial frame), we replicated the protocols on a long walkway (52.1 m) the subjects had to follow forth and back at a varying step cadence, as acoustically provided by a loudspeaker. The time course of the step cadence was obtained on an individual basis by analysing the footfall sequence for each protocol when subjects were walking on the treadmill. This was done by sampling at 100 Hz the 3D motion of reflective markers (ELITE, B.T.S., Milano, Italy) located on the calcaneus and the fifth metatarsals. After having processed these data as to calculate the precise timing of foot contacts, the corresponding audio sequence (with different sounds for the left and right foot) was repeated as to last 5 min. During the last minute the oxygen uptake was measured by a portable device (Oxylog 2, P.K. Morgan Ltd, UK).
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RESULTS |
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Figure 3 shows the metabolic results for all the investigated protocols, both during walking on the treadmill and on the walkway. The invariance of the oxygen uptake is apparent for oscillation ranges up to ±1.5 km hr–1, while at ±2.0 km hr–1 the tendency is to show a metabolic increase. Since the metabolic cost of walking is calculated as the net oxygen uptake divided by the average speed, we can expect that it would show the same independency on the speed oscillation amplitude.
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DISCUSSION |
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The invariance of the metabolic cost of walking with respect to the different speed oscillation is rather surprising. Mechanics tells us that even the slightest acceleration is associated with some extra work, while the successive deceleration phase can occur by transforming mechanical work into heat. We know from physiology that when biological actuators are used both for acceleration and deceleration, they need extra metabolic energy, although the energy ratio between the two activities, for the same amount of developed force, is 5 to 1 (Abbott et al., 1952
). This notion makes the present findings even more surprising. It is possible to estimate the additional metabolic work associated to the speed oscillations (additional changes in the kinetic energy of the body centre of mass) imposed by the experimental protocol.
Any speed fluctuation (
v, m·sec–1) about a constant average speed (
m·sec–1) implies a kinetic energy changes (KE, J) of:
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where m is the subject mass (kg). If the speed changes in a given time interval (
t, s), the additional mechanical external work (W+EXT, J·kg–1·m–1) that has to be done to accelerate the body, per unit distance, is:
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Also, we have to consider the additional negative external work (W–EXT, J·kg–1· m–1) needed to decelerate the body in the second half of the speed change cycle as
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because of the symmetry of the acceleration/deceleration phases. By assuming muscular efficiency (eff+, eff–) of 0.25 and 1.25 for positive and negative work (Abbott et al., 1952), respectively, the metabolic extra cost (C, expressed in J·kg–1·m–1) can be calculated according to:
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where the constant 0.5 reflects half the speed oscillation duration (from – v to + v in t). To express the expected C in mlO2·kg–1·km–1, i.e., the common unit for the metabolic cost of locomotion, we have to use the equivalence 1 ml O2 = 20.9 J and, for sake of convenience, to introduce the half speed range in km·hr–1 (v). The following equation can be derived:
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By substituting t = 3 sec (the time interval between the low and the high speed in each protocol), we obtain C = 10.6, 22.2, 31.9 and 42.5 mlO2 kg–1 km–1 for ±0.5, ±1.0, ±1.5 and ±2.0 km hr–1 oscillations, respectively. The additional energy expenditure (E, mlO2 kg–1 min–1) can be calculated as
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where the constant is needed to convert the average speed to consistent units, and is equal to
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for the average speeds of 3.5 and 5.0 km hr–1, respectively. Such an additional metabolic work rate, represented as vertically off-set lines with respect to the experimental values at constant speed in Figure 3, does not match the experimental data, although the value for the highest speed oscillation (±2.0 km hr–1) tends to approach it.
The suggested hypothesis, thus, is that the expected extra-mechanical (and consequently extra-metabolic) work is either "buried" in the one already done when walking at constant speed (see below) or is inexistent. In this case, though, we would have at least to take into account the extra-metabolic work involved in walking at speeds for which a non-linear metabolic expenditure and cost was reported (Cavagna and Kaneko, 1977). When departing from 3.5 km hr–1, for instance, the 6 sec oscillating speed phase can span from 2.0 to 5.0 km hr–1 (see Fig. 4). By disregarding the extra energy due to acceleration and deceleration, an estimate of the average cost in that range could be obtained by calculating the average height (cost) of the area limited horizontally by the lower and upper speeds and vertically by the curve and the abscissa. This procedure corresponds to calculate the definite integral of the curve between 
–v and +v ( and v are the average fluctuating speed in km hr–1, see Fig. 4). By describing the experimental curve of metabolic cost of walking with a second degree polynomial equation, as:
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where V is the speed (km·hr–1) and a, b and c the regression constants, it can be shown that the corresponding average cost, when speed oscillation is allowed, is:
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This equation shows that, when compared to the cost of moving at constant average speed, to walk at oscillating speed would imply (at least) an extra metabolic cost which depends on the overall curvature of C (the coefficient a) and on the oscillation speed range squared. By fitting C coefficients as a = 9.69, b = –91.1, c = 302.4 (metabolic data from Minetti et al., 1995), the extra energy expenditure associated to this effect (E, mlO2 kg–1 min–1) can be calculated as
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Figure 5 shows a good match between predictions of this "minimum" extra-cost (solid curve) and the data experimentally obtained for all speed oscillation ranges about 3.5 km hr–1 exception made for the highest, ±2.0 km hr–1, where the prediction underestimate the real values. The hypothesis that no extra-cost due to acceleration-deceleration is required up to a given speed oscillation range is supported so far by these findings.
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A possible explanation for the lack of evident dependency of C on the speed oscillation range is that some motor strategies are used. For example, the inherent forward acceleration/deceleration sequence of walking (at "constant" speed) could have been used to cope with the treadmill speed changes imposed every 3 sec by the present experimental protocols. Figure 6 shows how to construct, from a mechanical energy curve of the body centre of mass obtained at a "constant" speed, a mechanically (and energetically) equivalent curve associated with multi-stride acceleration/deceleration sequence. By pooling together all the energy increase segments of single strides, and by pooling together also the energy decrease ones, the resultant shape is consistent with a sequence of just accelerating strides, followed by a sequence of just decelerating ones, at the same overall mechanical energy cost. In this respect there is a peculiar unit equivalence that can shed light on the likelihood of the illustrated strategy. The mechanical external work, necessary to lift and accelerate the centre of mass during each stride, is about 0.36 J per kg of body mass and per metre travelled, when walking at a speed of about 3.5 km hr–1 (Minetti et al., 1995
). That unit, normally used for the mechanical cost of locomotion, is equivalent to metre per second squared, which is the unit of acceleration. It is interesting that 0.36 m sec–2 is the acceleration involved in the maximum speed oscillation that we used in this investigation, i.e., ±2.0 km hr–1 in 3 sec. This is another clue that with the mechanical work humans have to perform to walk at ‘constant’ speed it is possible also to walk at oscillating speed up to a given level, beyond which some additional mechanical work, reflected by an increase in metabolic consumption, has to be done.
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The authors are aware that the "treadmill protocol" produced biased results, mainly because the subjects were assisted by the motor during the acceleration/deceleration process. This makes the mechanical system "non inertial" and apparent forces should be introduced to fully understand the motion. However, unbiased experiments done on the walkway and more recent research on a wide radius (25 m) circular path, where the subjects have to follow a laser spot projected on the ground at oscillating speeds, confirmed the overall invariance of oxygen uptake up to speed oscillation of about ±1.5 km hr–1. While the illustrated rationale for explaining the metabolic invariance is supported by some preliminary video capture measurements, only a complete study about the motion analysis, with the consequent computation of the mechanical external work, will shed light on the determinants of such a speed range independence of metabolic cost.
In summary, oscillating speed cruising in automobiles is more expensive than steady ones because at constant speed they are optimized to travel cheaply. Differently, it is quite expensive for legged animals to move even at constant speed because of the continuous alternation of increase/decrease of the mechanical energy (the bicycle was invented to prevent this effect). However, this comes to help when they need to move at unsteady speeds, since this can be done within some limits without a remarkable increase in metabolic energy consumption. This is done by reducing the negative work done in each step, if acceleration is desired, and by reducing the positive work, if deceleration is required.
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ACKNOWLEDGMENTS |
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The authors are in debt with Tom McKee for technical support, with John Buckley and Paola Zamparo for assistance during the experiments, and with Prof. Pietro Enrico di Prampero for stimulating discussions and advice.
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FOOTNOTES |
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1 From the Symposium Intermittent Locomotion: Integrating the Physiology, Biomechanics and Behavior of Repeated Activity presented at the Annual Meeting of the Society for Integrative and Comparative Biology, 4–8 January 2000, at Atlanta, Georgia.
2 E-mail: a.e.minetti{at}mmu.ac.uk
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References |
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SYNOPSISINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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Abbott, B. C., B. Bigland, and J. M. Ritchie. 1952. The physiological cost of negative work. J. Physiol, 117:380-390.
Cavagna, G. A., and M. Kaneko. 1977. Mechanical work and efficiency in level walking and running. J. Physiol, 268:467-481.
FHWA (Federal Highway Administration)., 1980. Procedure for estimating highway user costs, fuel consumption and air pollution, U.S. Dept. of Transportation, Washington D.C.
Minetti, A. E., C. Capelli, P. Zamparo, P. E. di Prampero, and F. Saibene. 1995. Effects of stride frequency changes on mechanical power and energy expenditure of walking. Med. Sci. Sports Exer, 27:1194-1202.[Web of Science][Medline]
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