Energy balance of human locomotion in water
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- Pendergast, D., Zamparo, P., di Prampero, P.E. et al. Eur J Appl Physiol (2003) 90: 377. doi:10.1007/s00421-003-0919-y
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In this paper a complete energy balance for water locomotion is attempted with the aim of comparing different modes of transport in the aquatic environment (swimming underwater with SCUBA diving equipment, swimming at the surface: leg kicking and front crawl, kayaking and rowing). On the basis of the values of metabolic power (Ė), of the power needed to overcome water resistance (Ẇd) and of propelling efficiency (ηP=Ẇd/Ẇtot, where Ẇtot is the total mechanical power) as reported in the literature for each of these forms of locomotion, the energy cost per unit distance (C=Ė/v, where v is the velocity), the drag (performance) efficiency (ηd=Ẇd/Ė) and the overall efficiency (ηo=Ẇtot/Ė=ηd/ηP) were calculated. As previously found for human locomotion on land, for a given metabolic power (e.g. 0.5 kW=1.43 l·min−1 V̇O2) the decrease in C (from 0.88 kJ·m−1 in SCUBA diving to 0.22 kJ·m−1 in rowing) is associated with an increase in the speed of locomotion (from 0.6 m·s−1 in SCUBA diving to 2.4 m·s−1 in rowing). At variance with locomotion on land, however, the decrease in C is associated with an increase, rather than a decrease, of the total mechanical work per unit distance (Wtot, kJ·m−1). This is made possible by the increase of the overall efficiency of locomotion (ηo=Ẇtot/Ė=Wtot/C) from the slow speeds (and loads) of swimming to the high speeds (and loads) attainable with hulls and boats (from 0.10 in SCUBA diving to 0.29 in rowing).
Water locomotion, although more energy demanding per unit distance than locomotion on land, was used by humans for thousand of years. In addition to swimming freely at the surface (or underwater) humans have learnt to use a variety of passive locomotory devices, from tree trunks and floating objects to human-powered boats and watercrafts in the attempt to improve the economy and/or the speed of progression in water. Even though motorized locomotion has now replaced human-powered locomotion, aquatic activities such as swimming, diving, kayaking and rowing are still largely practicised all over the word mostly, if not exclusively, for recreational purposes.
Because of the complexities of the water environment, aquatic locomotion offers an interesting challenge to the understanding of the physiology of human movement; it is traditionally investigated by means of: (1) a biomechanical approach focused on the study of the mechanical determinants and/or (2) a physiological approach focused on the study of the energy requirements.
where Ẇd is the amount of the power dissipated against drag forces (Ẇd=D·v, where D is in N and v in m·s−1). It should also be noted that it is often convenient to define external power as the sum of Ẇd and Ẇk: Ẇext=Ẇd+Ẇk.
When swimming or paddling, the limb/tool that generates propulsion also creates drag (D). Hence, during aquatic locomotion "active drag" is significantly greater than the passive drag that can be measured by towing the subject (or the boat) motionless through the water. Passive drag is easily measured, whereas active drag can only be estimated indirectly.
For swimming active drag can be calculated from measures of sub-maximal oxygen consumption (V̇O2) while the subjects swim at constant speed and are partially towed by a force acting in the direction of motion. Linear extrapolation of the V̇O2 versus towing force relationship to resting V̇O2 yields the towing force which would allow the subject to swim at the given speed without any (net) energy expenditure; this force is assumed to be equal (and opposite) to the active drag at that speed (e. g. di Prampero et al. 1974). This method can be, and has been, used also to estimate the active drag of other forms of aquatic locomotion (kayaking: Pendergast et al. 1989; SCUBA diving: Pendergast et al. 1996; leg kicking at the surface: Zamparo et al. 2002).
Active drag can also be assessed by means of the MAD (measuring active drag) system (e.g. Toussaint et al. 1988). With this device the subject swims by exerting the propelling action of the arms on fixed pads positioned 1.35 m apart 0.8 m below the water surface. The pads are connected to force transducers so that the force exerted by the swimmer at each "stroke" can be recorded; this force is equal to the drag force since, with this set up, the swimmer does not expend any energy in giving water momentum (Ẇk=0). It must be pointed out, however, that only arm propulsion can be investigated with this system because the subject's legs are fixed together and supported by a small buoy.
The component of the total mechanical power "wasted" in accelerating water away from the body (Ẇk) is even harder to assess than the active drag itself. Estimates of the term Ẇk for the arm stroke are reported by Toussaint et al. (1988, 1991) as obtained by means of the MAD system (see above) and by Berger et al. (1997) by means of cinematic analysis.
Studies of animal locomotion (e.g. Lighthill 1975; Alexander 1983, 2003) have shown that, in slender fish, Ẇk can be computed by measuring the speed of the waves of bending which can be observed to travel along the fish's body in a caudal direction (e.g. Alexander 1983, 2003; Lighthill 1975). Indeed, the Froude efficiency of an undulatory movement (ηF) can be calculated from the ratio [(u+v)/2u] (were u is the speed of the bending wave and v is the forward speed). Since ηF is also defined as the ratio Ẇd/(Ẇd+Ẇk) (see Eq. 3 below) it is possible to calculate Ẇk on the basis of values of ηF [e.g. calculated as (u+v)/2u] and Ẇd. This last method was applied to calculate ηF in subjects swimming by using the leg kick (with and without fins) since the action of the leg's muscles indeed produces waves of bending similar to those observed in slender fish (Zamparo et al. 2002). These waves were also observed in subjects swimming the butterfly kick (Sanders et al. 1995) and in monofin swimmers (Zamparo, personal communication).
It goes without saying that, in any form of water locomotion, the term Ẇk can be estimated once the values of ηF (calculated/estimated/assumed) and Ẇd are known.
In most studies regarding aquatic locomotion the contribution of the internal work rate (Ẇint) to Ẇtot has not been considered as a source of mechanical work expenditure; it was recently computed by Zamparo (Zamparo et al. 2002; Zamparo 2003) for the leg kick and the arm stroke. Ẇint was originally defined by Fenn (1930) as the power necessary to accelerate the limbs in respect to the center of mass; as such it is strongly influenced by the frequency of the limbs movement. As shown by Zamparo et al. (2002) Ẇint is a substantial fraction of Ẇtot when swimming by kicking the legs because of the high limb frequencies necessary to produce forward motion. The limb frequency is greatly reduced when leg kicking with fins (Zamparo et al. 2002) and further reduced in the arm stroke (Zamparo 2003) thus leading to a substantial reduction of Ẇint. As a first approximation, in all forms of water locomotion except the leg kick without fins, Ẇint can be neglected and Ẇtot can be assumed to be equal to the sum of Ẇk and Ẇd only (see also Discussion).
Values of propelling efficiency are reported by Zamparo (2003) for the front crawl, by Toussaint et al. (1988, 1991) and Martin et al. (1980) for the arm stroke, and by Zamparo et al. (2002) for surface kicking (with and without fins). Values of Froude efficiency are reported by Samimy (2002) for underwater kicking with SCUBA and by Zamparo et al. (2002) for surface kicking (with and without fins). To our knowledge, the Froude/propelling efficiency for rowing and kayaking was never measured, essentially because of the difficulties in measuring Ẇk in these forms of locomotion; however, there is good agreement on the esteems of this parameter, which, according to several authors, ranges from 0.65 to 0.75 (e.g. Celentano et al. 1974; Dal Monte and Komor 1989; Abbott et al. 1995).
The rate of (net) energy expenditure (Ė) is the sum of the rates of oxidative metabolism, anaerobic glycolysis leading to lactic acid production and creatine phosphate splitting. Whereas the energy cost of locomotion is easy to assess over the range of speeds that can be maintained aerobically (in which case Ė=V̇O2), determining C over the speeds where the anaerobic contribution cannot be neglected is a more challenging task, necessarily implying a certain degree of approximation. At maximal and supra-maximal speeds C was estimated for swimming and kayaking by Capelli et al. (1998), Termin and Pendergast (2001), Zamparo et al. (1999, 2000), and Pendergast et al. (1989).
Estimated/measured values of propelling and Froude efficiency
Speed range (m.s–1)
Froude eff. (ηF)
Propelling eff. (ηP)
Leg kick with fins
Front crawl with fins
The drag efficiency, as calculated from the ratio Ẇd/Ė (Eq. 5), is a useful parameter in aquatic locomotion because it indicates the efficiency with which the overall energy expenditure is utilized to produce "useful" work (thrust). In studies of animal locomotion this efficiency is referred as performance efficiency (Daniel 1991).
Therefore, to calculate the overall efficiency of any form of aquatic locomotion, only four parameters need to be known: v, Ė, D and ηP.
On these premises, this study was carried out with the aim of comparing different forms of locomotion in water. Of all the data collected by the authors over the last three decades, only a limited number of papers were selected. These papers report data obtained while kicking the legs at the surface (L, Zamparo et al. 2002) or underwater (UWF, with SCUBA diving equipment, Samimy 2002), while swimming the front crawl (AL, Zamparo 2003), kayaking (K, Pendergast et al. 1989) and rowing (R, di Prampero et al. 1971; Celentano et al. 1974) and were selected because they report values of energy cost, active drag and cycle frequency as measured, simultaneously, in experienced athletes. These data, once combined with measures/estimates of propelling efficiency, allowed us to attempt a complete energy balance for different forms of human movement in the aquatic environment.
Metabolic power (Ė̇) and energy cost of locomotion (C)
Values of the investigate variables at metabolically equivalent speeds (Ė=0.5 kW throughout). (AL Front crawl swimming, K kayaking, L swimming by kicking the legs, R rowing, UWF underwater SCUBA diving with fins, C energy cost per unit distance, ηP propelling efficiency, ηo overall efficiency, ηd drag (performance) efficiency, Ẇtot total mechanical work, Ẇd work to overcome water resistance). See text for details
Froude (ηF) and propelling (ηP) efficiency
ηP=0.36 for the leg kick without fins (as measured by Zamparo et al. 2002).
ηP=0.58 for fin swimming underwater with SCUBA diving equipment (as measured by Samimy 2002. In the study of Samimy only the Froude efficiency was calculated; however, since the ηF of swimming underwater is the same as that calculated when swimming at the surface with the same kind of fins (0.72 vs. 0.70), it is fair to assume that also the propelling efficiency is similar.
ηP=0.45 for the arm stroke; this value is an average of the values of ηP as measured by means of the MAD system (e.g. by Toussaint et al. 1988, 1991) or calculated by mathematical modelling (Martin et al. 1980) for the arm stroke and of the values of ηP as calculated by Zamparo (2003) for the front crawl with and without fins.
The power to overcome drag (Ẇd), the drag efficiency (ηd) and the overall efficiency (ηo)
Cycle frequency, distance per cyle (dc) and internal work rate (Ẇint)
The internal work in aquatic locomotion was measured only for the leg kick and the arm stroke (Zamparo et al. 2002; Zamparo 2003). Ẇint is a substantial fraction of Ẇtot when swimming by kicking the legs (from 0.25 to 0.65 W·kg−1 at speeds between 0.6 and 1.0 m·s−1) because of the high limb frequencies necessary to produce forward motion (from 1.3 to 1.9 Hz in the same speed range). The limb frequency is greatly reduced when leg kicking with fins (from 0.7 to 1.3 Hz in the same speed range) and when swimming by using the arm stroke (again, from 0.3 to 0.6 Hz at speeds between 1 and 1.4 m·s−1) thus leading to a substantial reduction of Ẇint: in the arm stroke and in the leg kick with fins Ẇint ranges from 0.05 to 0.25 W·kg−1 whereas in the leg kick without fins it is twice that value, ranging from 0.25 to 0.65 W·kg−1 (see above). As shown in Fig. 6 the "average" cycle frequency is about half that of the leg kick without fins in all (the other) forms of water locomotion. Moreover, as indicated below, the external mechanical power of locomotion increases steadily as a function of the speed of movement in water; as such the contribution of Ẇint to Ẇtot, both in absolute and relative terms, is bound to be low and, as indicated in the Introduction, Ẇint can be neglected and Ẇtot can be assumed to be equal to the sum of Ẇk and Ẇd only.
Total mechanical power (Ẇtot)
The total mechanical power for aquatic locomotion could be calculated rearranging Eq. 6 (Ẇtot=Ė·ηo); the values of Ẇtot for all the forms of locomotion investigated here are reported in Table 2 along with the values of ηo, ηd, ηP, C and Ẇd as calculated for a metabolically equivalent speed of 0.5 kW. These data show that, as previously found for human locomotion on land, the use of passive tools for human locomotion in water (e.g. fins or hulls) leads to a decrease of the energy cost of locomotion at a given speed. At variance with locomotion on land, however, these data show that the decrease in the energy cost of locomotion is associated with an increase, rather than a decrease, in the total mechanical power. This is made possible by a continuous increase of the overall efficiency of locomotion from the slow speeds (and loads) associated with human swimming without aids to the high speeds (and loads) attainable with hulls and boats.
In this paper we attempted to draw a complete energy balance of several forms of water locomotion. On the basis (1) of measured values of drag, energy cost and cycle frequency (experimentally determined for each form of locomotion) and (2) of measured or estimated values of propelling efficiency, the drag efficiency and the overall efficiency were computed.
Data reported in this paper show that human locomotion in water can be described by similar rules in spite of the differences in the "type of propeller" (legs or arms), of the different tools that can be utilized for locomotion (fins, kayaks and rowing shells), of the different principles on which the propulsive action is based (e.g. kayaks are propelled by lift on a hydrofoil and rowing shells by drag on the oars, see Alexander 2003) and of the different pattern of movement adopted (the limbs movement is synchronous in rowing and alternate in all other forms of locomotion).
In this paper we aimed to find the trends, similarities and analogies among different strategies of motion in the aquatic environment. The data reported in this study are, therefore, not meant to define unequivocally a form of locomotion but rather to be an example of the relationship between the energetics and mechanics of different strategies of moving in water.
As an example it was shown by Zamparo et al. (1999) that, at speeds between 1 and 2 m·s−1, kayaking with a flat-water sprint K1 scull is more economical (C=0.020 v2.26) than kayaking with a slalom canoe (C=0.098 v1.76, see Figs. 1, 2). As a consequence, the difference in C between competitive rowing shells (as reported in this study: C=0.088 v1.05) and competitive K1 kayaks is less than reported in Fig. 2. It seems also interesting to note here that the energy cost per unit distance of kayaking with a slalom canoe, at the lowest investigated speed (1 m·s−1), is not far from that of sculling a Venetian Gondola (as reported by Capelli et al. 1990) for which C=0.155 v1.67 (in all these examples C is in kJ·m−1 and v in m·s−1).
The difference in the energy expenditure between the two types of kayaks mentioned above was attributed to drag differences between the sculls. Indeed the work expended to overcome drag is the major determinant of the metabolic expenditure in rowing and kayaking for which: Ẇd=Ė·0.21 (r2=0.981, n=30). The slope of this relationship is the drag (performance) efficiency of "boat locomotion"; as shown in Fig. 4, this efficiency is much lower (about 0.07) in all other conditions (L, UWF, AL).
The differences in performance efficiency between aquatic sports in which boats/sculls and paddles/oars are utilized and those in which the human body is moving "alone" in water, propelled only by the upper/lower limbs, can be attributed to several reasons.
The kayak and the rowing shell float on the surface and have a low pressure drag: in these forms of locomotion the wetted surface area is the major determinant of drag. This is not so for the human body where also other factors influence water resistance. Particularly at low speeds (less than 1 m·s−1, e.g. when swimming by kicking the legs only) the swimmers assume an inclined position in the water and their frontal surface area is the major determinant of drag. During forward progression in water the angle of the swimmer with the horizontal, and thus their frontal area, is the result of a balance of torque, or rotational forces around the center of mass, and hydrodynamic lift (Pendergast et al. 1977; Zamparo et al. 1996, 2000; Capelli et al. 1995). As the velocity of progression increases, the hydrodynamic lift increases, the body becomes more horizontal and the frontal area decreases. At these speeds, however, the level of immersion of the body in water becomes important: the larger this underwater weight, the greater the energy cost of swimming. This has also been shown in rowing where drag increased by about 10% for a 20% increase in weight (Secher 1993) and in kayaking where C increased by about 20% for a 20% increase in weight (Pendergast et al. 1989).
On the basis of these equations it is possible not only to characterize different forms of locomotion in water but also to calculate an unknown parameter (e.g. the active drag) from the other two (e.g. Ė and ηd). As an example, for kayaking with a flat-water sprint K1 scull and for sculling a Venetian Gondola only the relationship between Ė and v (Eq. c) is known from experimental data (Zamparo et al. 1999; Capelli et al. 1990). It is fair to assume that the relationship between ηd and v computed for kayaking and rowing in this study (Eq. b, where k2=0.16 and m=0.2) holds also for these two (similar) forms of locomotion. Hence, by combining Eqs. b and c it is possible to compute the D vs. v relationship (Eq. a) for the flat water K1 skull (D=3.2·v2.46) and for the Venetian Gondola (D=24.8·v1.87). These data show that, as expected, the boat opposing the greater resistance in water among these four is the Venetian Gondola and the active drag of a competitive K1 skull is very close to that of a rowing shell.
As pointed out in this paper and by several authors in recent decades (e.g. Toussaint et al. 1988) the drag efficiency is only a "partial efficiency" of water locomotion since it takes into account only the effects of water resistance on the energy expenditure. However, as underlined in studies of fish locomotion (Daniel 1991), this parameter is rather important in practical terms since it is a measure of the efficiency with which the energy is transformed into useful work (the thrust) for progression in water.
The overall efficiency (total work performed/total energy expended) of locomotion can be easily computed once the propelling efficiency (e.g. the efficiency with which the total work production is transformed in useful thrust) of each form of locomotion is known (ηο=ηd/ηP).
As pointed out at the beginning of the Discussion, the values of ηP utilized in this study are not meant to define unequivocally a form of locomotion but rather to be indicative of the ratio of power "wasted" to total power production in this broad range of aquatic activities. Whereas several authors report a value of ηP of about 0.7 for boat locomotion and the propelling efficiency for leg kicking with and without fins was experimentally determined, there is no general agreement on the value of ηP for the front crawl (see also Table 1). Hence the calculated value of ηο for this form of locomotion in water is less certain than in the other cases. As shown by Fig. 5, disregarding the data points referring to the front crawl, the ηo vs. speed relationship could be described by two separate functions: ηo=0.14·v0.80, n=15, r2=0.824 for the leg kick (L and UWF) and ηο=0.21·v0.28, n=30, r2=0.994 for boat locomotion (R and K) with the calculated data of ηο for the front crawl lying between the two.
In turn, the reported values of ηo for rowing and kayaking are close to the values estimated by using rowing ergometers or by indirect calculations of mechanical power during actual competitions for these forms of locomotion (about 0.2–0.3, for a review see Hagerman 2000).
From Fig. 5 it is also possible to see that, as a general rule, the overall efficiency of aquatic locomotion increases from the slow speeds (and loads) associated with human swimming without aids to the high speeds (and loads) attainable with hulls and boats. In the latter case the overall efficiency attains values (0.25–0.35) similar to those observed for land locomotion at optimal contraction speeds (Woledge et al. 1985; Sargeant and Jones 1995; Minetti et al. 2001).
This message is also apparent by inspection of Table 2 which shows that, at variance with locomotion on land, the decrease in the energy requirements of water locomotion is associated with an increase, rather than a decrease, in the mechanical power output which is offset by an even larger increase in efficiency.
These data suggest that propulsion in water is limited by the amount of force that can be applied to the water. The reason of the "sub-optimal" values of overall efficiency in swimming (below 0.22 in "non" boat locomotion) could therefore be attributed to the fact that, in water, the muscles are forced to work far from the optimum in their force/length–force/speed relationship.
A further interesting outcome of the "global" analysis of aquatic locomotion proposed in this study can be derived by inspection of Figs. 6 and 7. At least in the range of speeds considered here (aerobic), the increase in speed is obtained by an increase in the frequency of the movement of the "propeller" and by maintaining the same distance per stroke (with the exception of kayaking). Hence, each form of locomotion in water can be almost univocally described by the distance the body/hull covers per cycle (dc, m·cycle−1) which, in turn, is related to the efficiency of locomotion: the higher dc the higher the propelling and overall efficiencies.
This finding is quite interesting since the link between dc and efficiency has been suggested and discussed previously by several authors. Particularly in the case of the front crawl, the distance the subject travels per stroke was proposed as an index of the propelling efficiency of the swimmer (e.g. Craig and Pendergast 1979): the higher the distance per stroke for any given speed the more efficient the propulsion in water (see, for a brief review, also Toussaint and Beek 1992). As shown in the literature (e.g. swimming: Termin and Pendergast 2001) subjects could indeed be trained to increase the distance per stroke (at a given set of speeds). It was also shown that the obtained increase in dc was associated with a decrease in the energy expenditure (when swimming/paddling) at the same speed or over the same distance. This indeed is the case when the efficiency of propulsion in water is improved.