An energy balance of front crawl
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- Zamparo, P., Pendergast, D.R., Mollendorf, J. et al. Eur J Appl Physiol (2005) 94: 134. doi:10.1007/s00421-004-1281-4
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With the aim of computing a complete energy balance of front crawl, the energy cost per unit distance (C= Ėv−1, where Ė is the metabolic power and v is the speed) and the overall efficiency (ηo=Wtot/C, where Wtot is the mechanical work per unit distance) were calculated for subjects swimming with and without fins. In aquatic locomotion Wtot is given by the sum of: (1) Wint, the internal work, which was calculated from video analysis, (2) Wd, the work to overcome hydrodynamic resistance, which was calculated from measures of active drag, and (3) Wk, calculated from measures of Froude efficiency (ηF). In turn, ηF=Wd/(Wd+Wk) and was calculated by modelling the arm movement as that of a paddle wheel. When swimming at speeds from 1.0 to 1.4 m s−1, ηF is about 0.5, power to overcome water resistance (active body drag × v) and power to give water kinetic energy increase from 50 to 100 W, and internal mechanical power from 10 to 30 W. In the same range of speeds Ė increases from 600 to 1,200 W and C from 600 to 800 J m−1. The use of fins decreases total mechanical power and C by the same amount (10–15%) so that ηo (overall efficiency) is the same when swimming with or without fins [0.20 (0.03)]. The values of ηo are higher than previously reported for the front crawl, essentially because of the larger values of Wtot calculated in this study. This is so because the contribution of Wint to Wtot was taken into account, and because ηF was computed by also taking into account the contribution of the legs to forward propulsion.
To compute a complete energy balance of front crawl, two parameters must be known: the energy expended to cover one unit distance and the efficiency with which this energy is transformed into mechanical work.
The energy cost per unit distance (C) is defined as: Ė v−1, where Ė is the net metabolic power expenditure, and v is the speed of progression.
The mechanical (overall) efficiency (ηO) is defined as: ηO=Wtot C−1, where Wtot is the total mechanical work per unit distance.
In aquatic locomotion, Wtot is the sum of two terms: the work needed to accelerate and decelerate the limbs with respect to the centre of mass (the internal work, Wint) and the work needed to overcome external forces (the external work). The latter, in turn, can be further partitioned into: Wd, the work to overcome drag that contributes to useful thrust, and Wk, the work that does not contribute to thrust (both types of work give water kinetic energy, but only Wd effectively contributes to propulsion) (Alexander 1983; Daniel et al. 1992).
Of the three components of Wtot, only the term Wd can be “easily” quantified by using the standard methods to assess active or passive drag reported in the literature. On the other hand, the term Wk is a quantity quite difficult to assess, and we are not aware of methods for calculating Wint when swimming the front crawl.
To this aim: (1) we measured Wd and C, (2) we developed a new method to calculate Wint based on a three-dimensional (3D) kinematic analysis of the swimming movements, and (3) we revisited a simple model to calculate the ηP of the arm stroke. In this paper we also indicate a simple way to take into account the contribution of the legs to forward propulsion. Thus, we propose here a method to estimate the propelling efficiency of the front crawl as a whole, a parameter that, to our knowledge, has not been computed before.
Those calculations were applied to data collected in subjects swimming the front crawl with and without fins in order to investigate the effects of this locomotory tool on the propelling and overall efficiency of the front crawl and, last but not least, in order to test the sensitivity of our model to different experimental conditions.
The experiments were performed on six elite college swimmers who were members of a Division I University men’s swim team (State University of New York at Buffalo, N.Y.). Their average body mass was 71.1 (7.9) kg, their average stature 1.79 (0.08) m, and their average age 20.0 (1.3) years. The experimental protocol was approved by the Institutional Review Board, and the subjects were informed about the methods and aims of the study and gave their written informed consent to participate.
The subjects were asked to swim the front crawl with (ALF) and without fins (AL); the experiments were carried out over a range of speeds (at 1.0, 1.1, 1.2, 1.3 and 1.4 m s−1) that could be accomplished aerobically. Apollo Bio-Fin Pro fins were used in this study. Their characteristics are described in detail elsewhere (Zamparo et al. 2002).
The work to overcome water resistance
The active body drag (Db) was measured as described in detail elsewhere (di Prampero et al. 1974; Zamparo et al. 2002). Briefly, the subjects swam in an annular pool, and were paced by a platform moving at constant speed above the swimmer’s path. Known masses were attached to the swimmer by means of a rope which passed through a system of pulleys fixed to the platform in front of him, thus allowing the force to act horizontally along the direction of movement. This force (Da) facilitates the swimmer’s progression in water by pulling the subject forward and, at constant speed, it is associated with a consequent reduction in rate of oxygen uptake (V̇O2) The energy required to overcome Db becomes zero when Da and Db are equal and opposite. The swimmer’s Db was estimated, at any given speed and condition, by back-extrapolating the V̇O2 versus Da relationship to resting V̇O2. The power dissipated against drag was calculated from the product of the active body drag times the speed (Ẇd=Db v).
During the metabolic data collection (e.g. when the subject was swimming freely, without any added load) the kick frequency (KF, kicks per second, hertz) and the stroke frequency (SF, strokes per second, hertz) were also recorded.
The energy cost of swimming
The energy expenditure was calculated by measuring the steady-state V̇O2 (litres per minute), by a standard open-circuit method when swimming at constant speed (without any added load, Da=0). Net V̇O2 (above resting values, assumed to be equal to 3.5 ml min−1 kg−1) was converted to watts assuming that 1 ml O2 consumed by the human body yields 20.9 J (which is strictly true for a respiratory ratio of 0.96) and divided by the speed to yield the net energy cost of swimming per unit of distance (C) in kilojoules per minute (di Prampero 1986).
The internal work
Wint was estimated, in a separate series of experiments, by simulating the swimming movements outside water. In these experiments, the motion of the limbs was “decomposed” into two sub-movements: the leg kick and the arm stroke. The subjects were asked to lie on a swimming bench, to hyper-extend the arms over the head (the hands holding onto a support) and to simulate the leg kick by moving the legs at different frequencies (imposed by means of a metronome) that were selected to match the range of those utilized during actual swimming. A system of pulleys supported the legs via ankle straps in order to simulate the unloading conditions of underwater kicking. Alternatively, the legs (still supported by the pulleys) were fixed together and the subjects were asked to move only the upper limbs in such a way as to simulate the pattern of movement of the arm stroke they would have use during free swimming. Also in this case, the experiments were repeated at different frequencies to match the range of those utilized during actual swimming.
Eighteen reflective markers were put on relevant joints on the subject (nine per side), and a session of video sampling (100 Hz) was recorded at each frequency and condition by a 4-camera motion analysis system (ELITE, BTS, Italy). The 3D coordinates obtained were utilized to calculate the sum of the increases, in the time course, of absolute rotational kinetic energy and of relative (with respect to the body centre of mass) linear kinetic energy of adjacent segments over one cycle (Wint) by means of a custom software package (Minetti 1998).
The calculations of internal mechanical power (Ẇint) are based on the computation of the kinetic energy changes of the body segments with respect to the body centre of mass. The rationale for calculating Ẇint resides in the Koenig principle which states that, in a multi-segment system, the total kinetic energy is given by the sum of: (1) the kinetic energy of a point moving with the velocity of the centre of mass, and (2) the kinetic energy associated with the velocity of the particles relative to the centre of mass. It follows that the computation of the internal work is meaningful only if the movement of the two limbs is reciprocal (i.e. if it does not induce a change in the position of the centre of mass). Whereas in the leg kick the movement of the limbs is indeed reciprocal, this is not necessarily true for the arm stroke. Especially at low stroking frequencies, some of the subjects maintained one arm hyper-extended to the front while stroking with the contra-lateral (and vice versa), thus affecting the centre of mass position over time, and increasing the speed oscillations at each stroke.
The variation in the position of the centre of mass over time was therefore computed for both the arm stroke and the leg kick. In the leg kick the centre of mass was found to “move” in a 3D space of less than 1 cm3, (indicating that this kind of movement is reciprocal, as expected), whereas in the arm stroke, variations in the centre of mass position of as much as 50 cm3 were observed (mainly due to displacements on the z axis). In this study, the data in which the centre of mass position varied more than 5 cm3 were discarded in the computation of Ẇint. The discarded data corresponded mainly to low frequencies of movement, the arm stroke becoming more and more reciprocal as the speed (and hence the SF) increases. Hence, if any, care should be taken in calculating Ẇint based on measures of SF at slow stroke frequencies, a condition in which Ẇint is negligible in any case (see Results and Discussion).
From the relationship between Ẇint and KF and between Ẇint and SF experimentally determined, the internal work rate during actual swimming was computed based on the values of KF and SF actually measured during free swimming. The data of Ẇint due to the movements of the arms and the legs were finally summed together to calculate the internal work rate when swimming the front crawl.
The propelling and the Froude efficiency
In Eq. 2a, v is the average forward speed of the swimmer, ηFA is the Froude efficiency (defined below) of the arm stroke, and the term l is the average shoulder to hand distance. The term l was calculated by assuming: (1) an average upper limb length of 0.575 m (as proposed by Martin et al. 1981), (2) an average elbow angle during the in-sweep of 130° (as reported by Payton et al. 1999), and (3) an equal arm and forearm length. From these calculations l=0.52 m.
It is therefore apparent from Eqs. 3, 4 and 5 that the product of hydraulic and Froude efficiency yields the propelling efficiency (ηH ηF=ηP), and hence that the propelling efficiency will be equal to the Froude efficiency only in the case that ηH=1 (e.g. Wint=0). It also follows that a decrease in ηH (e.g. an increase in Wint) is necessarily associated with a decrease in ηP for any given ηF.
where ηFA is the efficiency of the arm stroke (calculated according to Eq. 2b), and ηFL is the efficiency of swimming by using the leg kick only. The Froude efficiency of the leg kick (ηFL) was measured in a previous study (Zamparo et al. 2002) and found to be 0.60 when swimming without fins and 0.71 when swimming with fins, and to be unaffected by the speed (from 0.6 to 1.0 m s−1). It is assumed here that these values still apply at the speeds investigated in this study (from 1.0 to 1.4 m s−1).
The propelling efficiency, the total work and the mechanical efficiency
Once the terms ηF and Wd for the front crawl are known (for any given speed) it is easy to calculate Wk (rearranging Eq. 3). Once the term Wk for the front crawl is obtained, it can be added to the terms Wint and Wd to calculate Wtot for any given speed. Once the term Wtot is calculated, the propelling and hydraulic efficiencies can be computed (see Eqs. 4 and 5), and the mechanical efficiency of swimming the front crawl can finally be obtained.
The regressions between V̇O2 and Da for each condition were calculated by the sum of the least square linear analysis model. The differences in the measured variables (e. g. C, Db, Wint...), as determined in the AL and ALF conditions at comparable speeds, were compared by the paired Student’s t-test at matched speeds (n=30 throughout). Values given are means (SD).
Values of kick (KF) and stroke frequency (SF) at the investigated speeds (v) when swimming the front crawl with (ALF) and without fins (AL). The values of Ẇint for the arm stroke (ẆintA) and the leg kick (ẆintL) were calculated as indicated in the text. The values of Ẇint for the front crawl (Ẇint AL) are the sum of ẆintL and ẆintA
v (m s−1)
Values of Froude efficiency for the arm stroke (ηFA), the leg kick (ηFL) and the front crawl (ηFAL) at the investigated speeds while swimming with (ALF) and without (AL). See text for details. SF Stroke frequency, SL Stroke length (or distance per stroke), v average speed
v (m s−1)
Average values of the power needed to overcome frictional forces (Ẇd), to impart “unuseful” kinetic energy to the water (Ẇk) and to overcome inertial forces (Ẇint) when swimming ALF and AL at the indicated speeds (v). Data of total mechanical power (Ẇtot), net metabolic expenditure (Ė) and net energy expenditure per unit distance (C) are also reported. The last row reports the percentage differences between the AL and ALF condition
v (m s−1)
Ẇ k (W)
C (J m−1)
Average values (all subjects and all speeds) of the efficiencies measured in this study when swimming the front crawl with (ALF) and without (AL) fins. The last row reports the percentage difference between the AL and ALF conditions. ηO overall efficiency, ηP propelling efficiency, ηH hydraulic efficiency, ηF Froude efficiency
The term Wd was calculated by measures of active body drag instead of passive drag
For the first time the contribution of the internal work was taken into consideration in the computation of Wtot
The contribution of the leg kick to forward propulsion was also taken into account
The work to overcome drag resistance
The values of hydrodynamic resistance reported in this paper are larger than those reported in the literature and obtained by using different methods. The drag forces created when the swimmer is moving through water are higher than those that can be measured in a static position (as shown by Thayer, as reported by Maglischo 2003, by using an hand–arm model) and this could explain the difference between these values and passive drag measurements. Active drag can be measured by means of the measure active drag (MAD) system (e.g. Toussaint 1990; Toussaint et al. 1990) from measures of the force exerted by the swimmer on instrumented fixed pads positioned at the water surface. In the MAD set up, however, the legs are supported by a pull buoy and fixed together, thus reducing the frontal area of the swimmer, and reducing the effect of the movements of the lower limbs to the overall hydrodynamic resistance. This could explain why the values reported here are higher than those measured by means of the MAD system.
However, the method utilized in this paper is not free of criticism due to the fact that: (1) the subjects are swimming in an annular pool (and not in a straight line), and (2) the values of active body drag are obtained indirectly by measures of V̇O2.
(1) The annular pool has a radius of 9.55 m at the swimmer’s path. For a subject of 70 kg body mass, the centripetal force will range from 7.3 N at 1 m s−1 to 14.4 N at 1.4 m s−1, i.e. about 17% of the active body drag at the same speed (50.1 N and 75.4 N, respectively, see Table 3). Centrifugal force points outward in the same plane as the drag force vector and is perpendicular to it. The resulting, overall force can be calculated to range from 50.6 N at 1 m s−1 to 76.8 N at 1.4 m s−1 i.e. about 1.5% larger than the drag force. Thus the difference between swimming in an annular pool or swimming in a straight line is indeed rather small.
(2) It can be debated whether the decrease of V̇O2 observed as a consequence of adding masses to the pulley system has to be attributed to changes in Ẇd only. We found that the added thrust (Da) not only reduced the swimmer’s active body drag (and hence Ẇd), but also affected the KF and SF: the higher Da, the lower KF and SF. The observed reduction of V̇O2 for any given Da has therefore to be also attributed to a decrease in Ẇint and Ẇk (both proportional to KF and SF). Since the contribution of these factors to total V̇O2 is large at Da=0 (during free swimming) and smaller at the highest Da, it can be shown that these factors affect only the slope of the relationship between Da and V̇O2 and not the point at which the regression crosses the Da axis, thus not affecting the determination of Db.
It must be pointed out that the high values of mechanical efficiency calculated in this study strongly depend on the correct determination of Db (ceteris paribus, a decrease of Ẇd of 50% leads to a decrease of ηO of the same amount). Therefore, until a more precise method to measure the active drag in aquatic locomotion is developed, the exact determination of the overall efficiency in water remains an open question.
The internal work rate
In a previous paper (Zamparo et al. 2002), the internal work rate of the leg kick was described by a model equation of the form: Ẇint=k(2KD)2 KF3 (where KD is the kick depth and k is a value related to the inertia parameters of the moving body segments). In that previous study, a two-dimensional kinematic analysis was carried out to determine KD for each subject, speed and condition. The data analysis was simple and straightforward since the leg kick is a movement carried out essentially on the sagittal plane. Video data were also collected in this study, but, when swimming the front crawl, the subjects rolled so much that it was not possible to measure KD (a 3D kinematic analysis should have been done instead). In the previous study, it was however shown that, for practical purposes, a simpler equation of the form Ẇint=k KF3 (where k=6.9, Ẇint is in watts and KF in hertz) was accurate enough to calculate Ẇint at different speeds and in different conditions (with and without fins) because KD is almost unaffected by the speed (it can be included in the constant k), and the increase in speed is obtained essentially by an increase in KF. This relationship between Ẇint and KF3 is indicated in Fig. 3 by the continuous line, while the diamonds represent the values of Ẇint as measured in this study by means of the ELITE system. This figure indicates that the experiments outside water reproduce the actual swimming condition well enough, at least for the leg kick. In the same figure the data obtained when simulating the arm stroke outside water are also reported, the dashed line interpolating the data is well described by an equation of the form: Ẇint=k SF3 (where k=38.2, Ẇint is in watts and SF in hertz). The pattern of movement in the arm stroke is similar, if any, to the circular motion of cycling, a case in which Ẇint is indeed related to f3 (the cube of the cycling frequency) (Minetti et al. 2001).
The data of Ẇint reported in this study indicate the following. (1) The contribution of the internal work to Ẇtot due to the arm stroke is rather small (in the range of speeds investigated in this study). (2) The contribution of the internal work to Ẇtot due to the leg kick cannot be neglected, and it is responsible for the differences between Froude and propelling efficiency calculated in this study for the front crawl.
Hence, the kicking of the legs is the major determinant of the “un-optimal” hydraulic efficiency of the front crawl (ηH is about 0.9 when swimming with or without fins, see Table 4). This observation gives a quantitative explanation of the general understanding in swimming practice that it is better to use the leg kick as little as possible, i.e. for stabilizing the body and improving the propulsion of the upper limbs, rather than for obtaining an increase in propulsion directly from the action of the legs. The last statement obviously applies to “non-sprint” swimming races, where the efficiency of locomotion, rather than the power output, is the parameter to be maximized.
The propelling efficiency of the front crawl
All the methods proposed so far to measure ηP measured indeed the efficiency of the arm stroke. Toussaint and coworkers (1990, 1991, 1992) report values of propelling efficiency in the 0.45–0.75 range, not far from the (corresponding) values of ηFA reported here, i.e. 0.42–0.55 when swimming the front crawl with or without fins (see Table 2). In contrast, the values of efficiency reported by Martin and co-workers (1981) are much lower (about 0.20) than those reported here. This could be attributed to the fact that in their paper they did not take into account the average elbow angle during the in-sweep phase, but (implicitly) assumed a constant elbow angle of 180°. In this paper, we assumed an average elbow angle during the in-sweep of 130° (as reported by Payton et al. 1999), and hence we calculated an l value smaller that that reported by Martin and co-workers (1981). As indicated by Eq. 2a and 2b, lower values of l necessarily mean higher values of efficiency.
In the model presented in this paper, the forward speed of the swimmer is assumed to be constant, and the arm is assumed to move with a constant angular speed about the shoulder. Over a stroke cycle, propulsion and drag are unsteady and this obviously affects the Froude efficiency in different phases of the arm stroke. An analysis of the variations in drag and propelling efficiency during a stroke cycle was not included in the aims of this paper, and we preferred to use a steady-state approach by taking into account the net effect of these factors on the propelling efficiency of the front crawl, i.e. by utilizing the average values of v and SF over several cycles in the computation of ηF. Moreover, in the front crawl, the stroke is more symmetrical and the intra-cyclic variations in speed are rather small compared to other strokes (Craig and Pendergast 1979).
Eq. 2a and 2b indicates that an increase in propelling efficiency is associated with an increase in the distance per stroke. The notion that better swimmers distinguish themselves from the poorer ones by a greater distance per stroke (by a lower stroke frequency for a given speed) has been suggested and discussed by several authors (Craig and Pendergast 1979; Craig et al. 1985; Toussaint and Beek 1992). Both the model presented in this study and the model proposed by Martin and coworkers (1981) (which is based on the same theory of swimming propulsion) have the advantage of pointing out at the direct relationship between these two parameters.
The effect of using fins when swimming the front crawl
The results of this study confirm data and conclusions previously reported regarding the effects of passive locomotory tools in human locomotion (Minetti et al. 2001; Zamparo et al. 2002). For the same “gait” (e.g. bicycling, swimming the leg kick, swimming the front crawl), the improvement in the economy of locomotion due to the use of “tools” is not due to an increase in the (overall) efficiency of locomotion. It depends, rather, on a reduction of the overall work performed per unit distance. Indeed, the reduction in the energy demands due to the use of fins (Ė, about 10%) is brought about by a proportional reduction in Ẇtot, (about 15%) (see Table 3 and Eq. 1) so that the overall efficiency (ηO=Ẇtot/Ė) is the same when swimming with or without them.
Thus, fins reduce the energy requirements of swimming the front crawl mainly because they reduce the total mechanical work in water locomotion (internal and kinetic, the work against drag being unaffected by the use of fins). The use of fins is indeed associated with a slight increase in the hydraulic efficiency (about 5%, from 0.87 to 0.92, without and with fins, respectively), which is brought about by a 40% decrease in Ẇint when fins are used. Using fins also reduces the term Ẇk by about 20%, a reduction that is brought about by an equal increase in propelling efficiency.
It is interesting to note that the use of fins in the front crawl induces not only a decrease in the kick frequency, but also a decrease in the stroke frequency. The decrease in SF due to the use of fins is a necessary consequence of the fact that in the front crawl SF and KF are coupled (about 3:1 in these subjects). This indicates that this locomotory tool not only improves the propulsion efficiency of the lower limbs (Zamparo et al. 2002) but also influences, to some extent, the propulsion efficiency of the arms. As indicated in Table 4, when fins are used the propelling efficiency of the front crawl increases of about 20%, e.g. about twice the increase in efficiency that can be obtained by using hand paddles (Toussaint et al. 1991).
The effect of leg action in enhancing the overall propulsive force by improving the propulsive action of the arms has also been suggested by others. As an example, Deschodt and co-workers (1999) showed that not only the leg kick (in the full stroke) allows for a 10% increase in maximal speed in a 25 m sprint (in comparison with swimming with arms alone), but also that the leg kick directly influences the kinematics of the arm stroke modifying the wrist trajectory and increasing the stroke length (as found in this study).
The overall efficiency of swimming
Data presented in this study show: (1) that the front crawl (with or without fins) is indeed a more efficient way of moving in water than the leg kick (with or without fins) as indicated by other studies (Adrian et al 1966; Pendergast et al. 2003), (2) that the overall efficiency of the front crawl can be substantially higher than previously reported (di Prampero et al. 1974; Toussaint 1990; Toussaint et al. 1990), but (3) that it does not reach an optimum since ηO increases almost continuously from the slower speeds attainable with the leg kick to those attainable in the front crawl (see Fig. 4). As shown by Pendergast and coworkers (2003), the overall efficiency in water locomotion can reach optimal values (0.25–0.35) only at the speeds and loads attainable with hulls and boats.
The higher mechanical efficiency in the front crawl, with respect to the leg kick, is essentially attributable to a larger total mechanical output for an almost identical energy input (ηO=Ẇtot/Ė). Indeed Ė ranges from 0.3 to 1.0 kW in both cases, whereas Ẇtot ranges from 30 to 100 W in the leg kick (Zamparo et al. 2002), and is about two times larger, at any given speed, in the front crawl (present study). Due to the higher speeds attainable with the front crawl, similar values of Ė implies lower values of the energy expended to cover one unit distance (C=Ė/v) with respect to the leg kick. Hence the economy of the front crawl is higher than that of the leg kick. In addition, in the front crawl, this energy is more effectively transformed into work per unit distance because higher loads can be produced and sustained. Hence the efficiency of the front crawl is higher that that of the leg kick. These data confirm previous hypotheses that the efficiency in swimming it is limited by the amount of force that can be applied to the water (Pendergast et al. 2003; Zamparo et al. 2002).
In this paper we proposed an energy balance for front crawl by considering the contribution of both the upper and lower limbs to forward propulsion. The larger values of ηO obtained in this study with respect to previous studies are to be attributed to the three factors: (1) the term Wd was calculated by measures of active body drag, (2) the contribution of Wint was taken into consideration in the computation of Wtot, (3) the contribution of the leg kick to forward propulsion was taken into account.
The model of arm propulsion proposed in this study is based on the Newtonian principle of action–reaction, and is a simplified version of that proposed by Martin and coworkers (1981). Even if this model can be considered too simple for describing the complex pattern of movement of the arm stroke, it gives values of propelling efficiency comparable to those reported in the literature, and obtained with far more complex calculations and set ups. Moreover, it has the advantage of pointing out at the direct relationship between the propelling efficiency and the ratio v/SF (i.e. the distance per stroke), a parameter that is largely utilized in common practice to assess swimming performance.
The technical assistance of Dean Marky, Frank Modlich and Chris Eisenhardt is gratefully acknowledged, as well as the patience and kind co-operation of the swimmers. This research has been partially supported by the US Navy, NAVSEA, Navy Experimental Unit, contract N61 33199C0028.