speeds about double the maximum walking speed of an average person with a less

Transcription

1 J. Physiol. (1981), 315, pp With 5 text-figurew Printed in Great Britain MECHANICS OF COMPETITION WALKING BY GIOVANNI A. CAVAGNA AND P. FRANZETTI From the Istituto di Fisiologia Umana dell' Universita' di Milano and the Centro di Studio per la Fisiologia del Lavoro Muscolare del C.N.R., Milano, Italy (Received 31 July 1980) SUMMARY 1. The work done at each step to lift and accelerate the centre of mass of the body has been measured in competition walkers during locomotion from 2 to 20 km/hr. 2. Three distinct phases characterize the mechanics of walking. From 2 to 6 km/hr the vertical displacement during each step, Sv, increases to a maximum (3 5 vs. 6 cm in normal walking) due to an increase in the amplitude of the rotation over the supporting leg. 3. The transfer, R, between potential energy of vertical displacement and kinetic energy of forward motion during this rotation, reaches a maximum at 4-5km/hr (R = 65 %). From 6 to 10km/hr R decreases more steeply than in normal walking, indicating a smaller utilization of the pendulum-like mechanism characteristic of walking. 4. Above 10km/hr potential and kinetic energies vary during each step because both are simultaneously taken up and released by the muscles with almost no transfer between them (R = 2-10 %). Above km/hr an aerial phase (25-60 msec) takes place during the step. 5. Speeds considerably greater than in normal walking are attained thanks to a greater efficiency of doing positive work. This is made possible by a mechanism of locomotion allowing an important storage and recovery of mechanical energy by the muscles. INTRODUCTION In level walking, as in cycling, the efficiency of positive work (i.e. positive work done/net energy expenditure) attains a maximum at intermediate speeds (Dickinson, 1929; Cavagna & Kaneko, 1977); high walking speeds are uneconomical because of a steep increase in the energy expenditure. Competition walkers, however, attain speeds about double the maximum walking speed of an average person with a less steep increase in the energy expenditure (Menier & Pugh, 1968). This suggests two possibilities: (1) less mechanical work is done to move forwards and/or (2) the efficiency of positive work is greater. In order to distinguish between these two possibilities we measured the mechanical energy changes of the centre of mass during competition walking and compared them with those met in normal walking /81/ $07.50 D 1981 The Physiological Society

2 244 G. A. CA VAGNA AND P. FRANZETTI METHODS List of Symbols M Body mass Vf instantaneous speed of forward motion of the centre of mass Vv instantaneous speed of vertical motion of the centre of mass Vf average speed of locomotion; Vf = LIT g acceleration of gravity Sv sum of the upward displacements of the centre of mass taking place during a cycle of movement r; Sv = Wy/Mg EK, kinetic energy of forward motion of the centre of mass EK,V kinetic energy of vertical motion of the centre of mass Ep gravitational potential energy of the centre of mass Etot total mechanical energy of the centre of mass; Etot = EK,f + EKV + Ep Wf positive work done at each step to increase the forward speed of the centre of mass; Wr is the sum of the increments of EK,f during T WV positive work done at each step to lift the centre of mass; Wv is the sum of the increments of Wp during T Wext positive work done at each step to increase the mechanical energy of the centre of mass; Wext is the sum of the increments of Etot during T R transfer of mechanical energy with the pendulum-like mechanism characteristic of walking; R = ((IWfl + IWlI- Wext)/( Wr +twvi)) 100 Wint positive work done during each step to accelerate the limbs relative to the centre of mass; a complete transfer of mechanical energy is assumed betwen the two segments of each limb Wtot total positive work done at each step, WtOt = Wextl + Wind (WIT). This mechanical power is smaller, about half or less, then the average power developed by the muscles during contraction; in fact not only positive work, but also negative work is done during r; in addition T may include a 'flight' period W/(LM) positive work done per unit distance and per unit of body mass; W/LM = W/MVf = WT/TML T step period, i.e. period of repeating change in forward and vertical velocity of the centre of mass tse fraction of the period T during which one foot only contacts the ground (single contact) tdc fraction of the period T during which both feet contact the ground (double contact) AV fraction of the period T during which the body is off the ground L length of the step; L = VrT LSC forward displacement of the centre of mass taking place at each step of walking when one foot only is in contact with the ground; L., = Vr tse Ldc forward displacement of the centre of mass taking place at each step of walking when both feet contact the ground; LdC = Vf tdc Lv forward displacement of the centre of mass taking place when the body is off the ground, Lv= Vf tv Measurements The mechanical work done during each step to lift and accelerate the centre of mass of the body in the forward and vertical directions was measured by means of a strain-gauge platform (4 x 0'5 m) sensitive to the vertical and the horizontal components of the force exerted by the feet against the ground. The procedure used to calculate the mechanical energy changes of the centre of mass from the platform's records has been described by Cavagna (1975). At the end of each run over the platform, the mechanical energy changes of the centre of mass (gravitational potential and kinetic energy) were plotted automatically as a function of time using a microcomputer (Fig. 1). Each set of curves in Fig. 1 shows the oscillations of the mechanical energy of the centre of mass taking place during one step at the indicated speed. The upper curve indicates the changes in kinetic energy of forward motion, E, - 1/2Vf2 where M is the body mass and Vf the instantaneous forward velocity of the centre of mass. The dotted line in the middle tracing indicates the changes in

3 COMPETITION WALKING potential energy, Ep, due to the vertical displacement of the centre of mass, S, (AEp = Mg Si, g being the acceleration of gravity); the continuous line of the middle tracing indicates the gravitational potential energy plus the kinetic energy of vertical motion (Ep+EKV where EK,V = 1/2MVV2, Vv being the instantaneous velocity of the centre of mass in the vertical direction). The lower curves give the total mechanical energy Etot = EKf+Ep+EK,V (continuous line) and the sum EK,r + Ep (dotted line). The increments of EKJ represent the positive work necessary to accelerate forward the centre of mass during each step (Wf), the increments of Ep the positive work 2-5 km/hr 61 km/hr 10-4 km/hr * 4' 245 o * km/hr 152 km/hr 17 7 km/hr 2,, Epk+fEk, I l E+ Ek f 0* Time (sec) Fig. 1. Computer plots of the mechanical energy changes of the centre of mass of the body during one step of competition walking at different speeds (subject M.C., 5000 m indoor world-record holder, 74 kg, 1P75 m, 26 years). In each set of tracings the upper curve refers to the kinetic energy, EKf = 1/2MVf2; the middle curve to the sum of the gravitational potential energy, EP, and of the kinetic energy EK,v = 1/2MV 2; and the bottom curve to the total energy, Etot = EKr + EP + EK,V. The curves EP and EKf + EP are also given (dotted lines). The arrows indicate the instant when the front foot contacts the ground (continuous) and when the back foot leaves the ground (interrupted). The step cycles are plotted so that all the tracings begin about 90 msec before the front foot contacts the ground. against gravity (Wv) and the increments of Etot the mechanical work done by the muscles against the external forces to increase the mechanical energy of the centre of mass (Wext). The decrements of Etot represent the negative work done by the muscles to decelerate the body; the negative work done by the muscles is practically equal to positive work because air resistance is small. The positive work done during each step (1Wf, Wv and Wext) was calculated by a microcomputer from the increments in the curves in Fig. 1. The vertical displacement of the centre of mass during each step (Fig. 2) was calculated by dividing the vertical work by the weight (Sv = Wv/Mg). Since Wv is the sum of the increments of the Ep curve during one step, Sv is also the sum of the vertical displacements when these occur in more than one phase of the step (as at 10-4 km/hr in Fig. 1). The experiments have been made on eight competition walkers of the Italian national team; an average of thirty runs were made by each subject. The data obtained from all the subjects were used to plot the curves in Figs. 2 and 4; each point in these curves represents the average (plus and minus the standard deviation) of the co-ordinates of all the data within 1-2 km/hr, 2-3 km/hr

4 246 G. A. CA VAGNA AND P. FRANZETTI etc. The time of single contact during which only one foot contacts the ground (t,,), and the time of double contact during which both feet contact the ground (tdc) were recorded in six subjects with the procedure described by Cavagna, Thys & Zamboni (1976) (Fig. 3). The presence of an aerial phase, tv, was determined by the lack of any electrical contact between the feet with the metallic surface of the platform; the duration of tv was measured from the length of the horizontal tracts of the EKJf tracing (Fig. 1). RESULTS The work against gravity and the three phases of walking The vertical displacement of the centre of gravity (Sv) taking place during each step is plotted as a function of the average speed of walking in Fig. 2. The relationship shows two reversals of slope, one at 6-7 km/hr and another at km/hr, which clearly separate three different phases of the mechanics of walking. 6 tl.. l E _ 3i~ 13N Average speed forwards, Vf (km/hr) Fig. 2. The vertical displacement of the centre of gravity during each step is plotted as a function of walking speed. Each point represents the average of the data obtained from the eight subjects studied; the bars indicate the standard deviation of the mean, and the figures near each point give the number of items in the mean. The arrows separate the three phases of walking (see text). The dotted line gives the trend of the data obtained in normal walking by Cavagna et al. (1976). The first phase is characterized by a progressive increase of Sv. This is accompanied by an increase of the forward displacement during the time of single contact (Lsc in Fig. 3) with almost no change of the forward displacement when both feet are on the ground (Ldc in Fig. 3). During single contact the body rotates over the foot on the ground as an inverted pendulum, with the consequence that potential energy of vertical displacement, Ep, and kinetic energy of forward motion, EKf, are almost completely out of phase. The amplitude of this rotation increases up to 6-7 km/hr. As shown by Coates & Meade (1960) and by Cavagna et al. (1976) this leads to an increase of the vertical displacement of the body. In the second phase, from 6-7 km/hr to km/hr, Sv decreases progressively to a minimum (note the flattening of the Ep+ EKv curve at 10'4 km/hr in Fig. 1). This is accompanied by a reduction of Ldc due to a progressively greater extension of the foot which is about to leave the ground (Fig. 3). As in normal walking, the

5 COMPETITION WALKING 247 vertical lift due to this extension opposes the lowering of the centre of gravity (while accelerating it forwards), with the consequence that the total vertical excursion is reduced (Cavagna & Margaria, 1966; Cavagna et al. 1976). The mechanism of the first two phases of competition walking is therefore similar to that already described for normal walking; however the maximal vertical displacement during each step in competition walking is almost half that in normal walking (dotted line in Fig. 2) > L LSC# 1* I I ' o~~~~~~~-r E 0*4 td ~~~~~~~~tv Average speed forwards, Vf (km/hr) Fig. 3. The step length, L, the forward displacement of the centre of mass when only one foot is on the ground, LS, and the forward displacement of the centre of mass when both feet are on the ground, LdC, are given as a function of speed in the upper part of the Figure. Above 13-14km/hr LdC is substituted by a forward displacement taking place with no contact with the ground, L, (filled squares; the half-filled square at km/hr indicates the average of some LdC data (two subjects) and some Lv data (four subjects)). The corresponding step period, r time of single and double contact, tsc and tdc, and time spent in the air, tv, are given in the lower part of the Figure. Bars, dotted lines and arrows are as in Fig. 2 (the numbers of items in the mean, as indicated, refer to six subjects only). In the third phase of competition walking (from to 20 km/hr) Sv increases again as a consequence of the increasing push of the foot which is about to leave the ground. The forward displacement taking place when both feet are on the ground, Ldc, reaches a minimum at km/hr. At higher speeds it is substituted by a forward displacement which occurs during an aerial phase (Lv in Fig. 3). This is shown in Fig. 1 by an interval of time during which the total mechanical energy of the centre of mass Etot remains constant. At the end of the aerial phase Etot increases a little due to an increase of EK J; this is likely due to the backward velocity of the foot relative to the ground at the instant of contact (Fenn, 1930).

6 248 G. A. CA VAGNA AND P. FRANZETTI Transfer between gravitational potential energy and kinetic energy offorward motion The tracings at 6 1 km/hr in Fig. 1 show that the changes of EKr and Ep+EK,V are almost completely out of phase (as in a pendulum) so that Wext < WfI + Wvj. Above 104 km/hr the curves EKf and Ep+EK v are almost completely in phase, indicating that the work done by the muscles is required both to acclerate forward the centre of mass and to lift it against gravity, i.e. Wext l WfI + Wvj. 70 x x k, k + + k L- 0 Cu cj W _- Q Average speed forwards, Vf (km/hr) Fig. 4. The % recovery, R, and the external work done per unit distance. Wext/(LM), during competition walking are given as a function of speed in the upper part and in the lower part of the Figure respectively. The % recovery indicates the extent of mechanical energy re-utilization through the shift between gravitational potential energy and kinetic energy: in the range of speed over which the % recovery is maximum the work done per unit distance is minimum and vice versa. Bars, dotted lines and arrows are as in Fig. 2. A measure of the transfer of mechanical energy with the pendulum-like mechanism characteristic of walking is given by the % recovery (Cavagna et al. 1976): R = ((I WfI+ IWv- Wext)/(l WfI+ I WvI))100. (1) In a frictionless pendulum Wext = 0 and R = 100 because all of the potential energy is 'recovered' as kinetic energy and vice versa during a cycle. On the contrary, if

7 COMPETITION WALKING 249 WfI + WvI = Wext then R = 0 and all of the potential and kinetic energy changes are due to muscle activity. The % recovery in competition and normal walking is plotted as a function of speed in the upper part of Fig. 4. In the lower part of Fig. 4 we plotted the external work done per unit distance, WeXt/LM, to show how it is affected by the % recovery. It is apparent that the work is at a minimum in a range of speeds over which the % recovery is at a maximum and vice versa. From 6 to 12 km/hr the % recovery is smaller in competition walking than in normal walking, and consequently the external work per unit distance is greater. DISCUSSION The net energy expenditure per unit distance during normal and competition walking is given as a function of speed in Fig. 5. As shown by Menier & Pugh (1968), the two kinds of locomotion are about equally expensive up to 6-7 km/hr, whereas at greater speeds competition walking becomes much less expensive than normal walking. The present data also show that the mechanics of normal and competition walking are similar up to 6-7 km/hr and differ thereafter (Figs. 2 and 4). The lowered vertical displacement (Fig. 2) is probably due to the hip and shoulder movements which characterize the mechanics of competition walking (Payne, 1978). Above 6-7 km/hr the external work done per unit distaince, We~t/LM, is greater in competition walking than in normal walking. As mentioned above, this is due to a reduction of the transfer between kinetic and potential energies (as shown by a reduction of the % recovery which is a measure of this transfer) and, consequently, to an increase of the transfer between external energy and muscular activity. A greater amount ofwork done on and by the muscles with a smaller energy expenditure suggests a greater efficiency of doing positive work. In order to make a comparison between mechanical work output and energy expenditure one has to take into account the total mechanical work done by the muscles, including the work required to accelerate the limbs relative to the centre of mass (internal work, Wint). It seems reasonable to assume that Wint does not differ appreciably in competition and normal walking because the step period at a given speed is nearly the same (r in Fig. 3). The total mechanical work done in competition walking has therefore been calculated by adding Wext measured in competition walking and Wint measured in normal walking. The equation used to calculate the internal work was gint (cal/(kg. min)) = V214 (km/hr) which gives a minimum value of Wint assuming a complete transfer of mechanical energy between the two segments of each limb (Cavagna & Kaneko, 1977). A minimum value of Wint has been used to compensate for a possible error made by assuming no transfer between Wint and text in the calculation of 'tot* The total mechanical work done per unit distance, Wtot/LM, together with the energy expenditure both for competition and for normal walking is given in the bottom part of Fig. 5. The ratio between the two, i.e. the efficiency of positive work, is given in the upper part of Fig. 5. A maximum of efficiency (< = 0 25) is to be expected at intermediate speeds when the positive mechanical work is derived from the transformation of chemical energy by the contractile machinery of muscles (as

8 A. CA VAGNA AND P. FRANZETTI 0*5 C.0 M* ot... ~Energy expenditure 03_ Ui 0-3 I I Energy expenditure 1.0 a 05 CL 0. Q a; ~~~~~ML Average speed forwards, Vf (km/hr) We~tI + W~IJ and the net energy expenditure Fig. 5. Below: the total positive work Wtot (total - standing) per unit distance are given as a function of the speed for competition walking (continuous lines) and normal walking (dotted line). The energy expenditure curve of normal walking (dotted line) was traced over the average of the data of Margaria (1938), Ralston (1958), Cotes & Meadle (1960) and Dill (1965); that of competition walking was calculated from the line in Fig. 1 of Menier & Pugh (1968) for speeds greater than 8 km/hr, and from the average of the data of Menier & Pugh and those of normal subjects at lower speeds. Energy expenditure at speeds greater than 14-5 km/hr is extrapolated from the line given by Menier & Pugh (1968). Above: the efficiency of positive work, Wtot/energy expenditure, is given as a function of speed for competition walking (continuous line) and for normal walking (dotted line). The interrupted part of the energy expenditure and efficiency curves indicates that at these speeds an oxygen debt may be necessary to meet the mechanical power output. in cycling: Dickinson, 1929). An efficiency greater than 0-25 and increasing with the velocity of movement is to be expected when positive work is mainly due to the recoil of previusly stretched muscles (as in running: Cavagna & Kaneko, 1977; Cavagna, Citterio & Jacini, 1980). The curves in the upper part of Fig. 5 show that walking is mainly sustained by the 'contractile' mechanism in normal walking and in competition walking at low speeds. At high speeds of competition walking the efficiency increases with speed, as in man running and the kangaroo hopping (Alexander & Vernon, 1975). In all these cases the increase in efficiency with speed

9 COMPETITION WALKING 251 is associated with the mechanics of locomotion which allows a maximum storage of mechanical energy in the muscles (EKrf and EP + EKV curves in phase with a negligible % recovery). We wish to thank Professor G. Boella from the Istituto di Fisica, dell 'Universita' degli Studi di Milano who made it possible to process on-line the signals from the platform, Maestro dello sport T. Assi for his encouragement and stimulating discussions, and the athletes and the Federazione Italiana di Atletica Leggera for their enthusiastic participation in the experiments. REFERENCES ALEXANDER, R. MCN. & VERNON, A. (1975). The mechanics ofhopping by kangaroos (Macropodidae). J. Zool., Lond. 177, CAVAGNA, G. A. (1975). Force platforms as ergometers. J. apple. Physiol. 39, CAVAGNA, G. A., CITTERIO, G. & JACINI, P. (1980). Elastic storage: role of tendons and muscles. In Comparative Physiology: Primitive Mammals, ed. SCHMIDT-NIELSEN, K. Cambridge University Press. CAVAGNA, G. A. & KANEKO, M. (1977). Mechanical work and efficiency in level walking and running. J. Physiol. 268, CAVAGNA, G. A. & MARGARIA, R. (1966). Mechanics of walking. J. apple. Physiol. 21, CAVAGNA, G. A., THYS, H. & ZAMBONI, A. (1976). The sources of external work in level walking and running. J. Physiol. 262, COTES, J. E. & MEADE, F. (1960). The energy expenditure and mechanical energy demand in walking. Ergonomics 3, DICKINsoN, S. (1929). The efficiency of bicycle-pedalling, as affected by speed and load. J. Physiol. 67, DILL, D. B. (1965). Oxygen used in horizontal and grade walking and running on the treadmill. J. apple. Physiol. 20, FENN, W. 0. (1930). Work against gravity and work due to velocity changes in running. Am. J. Physiol. 93, MARGARIA, R. (1938). Sulla fisiologia e specialmente sul consumo energetic della marcia e della corsa a varie velocity ed inclinazioni del terrono. Atti Accad. naz. Lincei Memorie 7, MENIER, D. R. & PUGH, L. G. C. E. (1968). The relation of oxygen intake and velocity of walking and running, in competition walkers. J. Physiol. 197, PAYNE, A. H. (1978). A comparison of the ground forces in race walking with those in normal walking and running. In Biomechanics, VIA, vol. 2A, ed. ASMUSSEN, E. & JORGENSEN, K. Copenhagen: University Park Press. RALSTON, H. J. (1958). Energy-speed relation and optimal speed during level walking. Int. Z. angew. Physiol. 17,