How fins affect the economy and efficiency of human swimming
1 Dipartimento di Scienze e Tecnologie Biomediche, Universita' degli Studi
di Udine, Italy
2 Centre for Biophysical and Clinical Research into Human Movement,
Manchester Metropolitan University, Alsager, United Kingdom
3 Centre of Research and Education in Special Environments, State University
of New York at Buffalo, USA
* Author for correspondence at present address: Centre for Biophysical and Clinical Research into Human Movement, Manchester Metropolitan University, Hassall Road, Alsager, ST7 2HL, UK (e-mail: P.Zamparo{at}mmu.ac.uk PZamparo{at}makek.dstb.uniud.it)
Accepted 8 June 2002
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Summary |
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Key words: energetics, biomechanics, swimming, fin, human, energy, balance
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Introduction |
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Data on fin swimming are scarce and refer mainly to underwater (SCUBA
diving) experiments that focus on the differences in economy of swimming at
different depths (e.g. Morrison,
1973) or with different swim-fin designs (e.g.
Pendergast et al., 1996
). An
analysis of the mechanical determinants of the improved economy brought about
by the use of fins (in comparison to swimming without them) has never been
attempted because quantification of the mechanical work performed during
aquatic locomotion is not simple.
In the present study the energy cost, mechanical work and efficiency of swimming using the leg kick were measured/estimated with methodologies previously applied to human and fish locomotion. Using these data, we attempted to calculate a complete energy balance for swimming. The differences in economy and efficiency brought about by the use of fins allowed us to further investigate the relative importance of the mechanical determinants of aquatic locomotion in humans.
Approach to the problem
As is the case for human locomotion on land, the economy and efficiency of
locomotion in water depend on the mechanical work (Wtot)
that the muscles have to produce to sustain a given speed (see
Fig. 1). This work is generally
partitioned into two major components: (i) the work that has to be done to
overcome external forces (the external work, Wext) and
(ii) the work that has to be done in order to accelerate and decelerate the
limbs with respect to the centre of mass (the internal work,
Wint). The contribution of the elastic and viscous factors
to total work expenditure is thought to play a minor role in swimming and is
not considered here.
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The external work in aquatic locomotion is generally partitioned into two components: Wd, the work that is needed 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.
The resistance to motion (and hence Wd) in swimming can
be measured by towing the subjects (passive drag) or while the subjects are
actually swimming (active drag). Active drag is higher than passive drag, due
to changes in frontal surface area and fluid dynamics caused by arm/leg
movements and, as such, is a better estimate of the force opposing motion. In
contrast with passive drag, active drag is difficult to assess and is
generally obtained indirectly from measures of energy expenditure (e.g.
di Prampero et al., 1974;
Toussaint et al., 1988
).
The term Wk is a quantity even more difficult to
measure than Wd. The contribution of this factor was
estimated in swimming humans by Toussaint and coworkers
(1988). They compared the
difference in the energy consumed while swimming on the MAD (Measuring Active
Drag) system to the energy consumed while swimming freely. With this device
the subject swims by pushing off fixed pads positioned at the water surface
and hence does not waste any energy to give water momentum; in these
conditions his/her
O2 reflects the
energy expended to overcome drag only. However, only arm propulsion could be
investigated with that set-up, since the legs are fixed together and supported
by a small buoy.
An alternative way of obtaining an estimate of the term
Wk comes from studies of animal locomotion. As discussed
by Lighthill (1975), Alexander
(1977
) and Daniel et al.
(1992
), many animals (e.g.
eels) proceed in water with undulatory movements. Waves of bending, produced
by rhythmic muscular contractions, can be observed moving along the body in a
caudal direction, giving the water backward momentum from both sides of the
fish's body. At high Reynolds number (Re), thrust arises from the
lateral acceleration of the body segments. The viscous forces, which dominate
motion at low Re values, are negligible. Humans swim at Re
values of about 106, which are comparable to those of slender fish
(e.g. 105 for eels, as estimated by Alexander,
1977
).
During steady state aquatic locomotion, at high Re and for a given
(forward) speed v, the efficiency of the undulatory movement of a
slender fish is given by:
![]() | (1) |
F is also defined as:
![]() | (2) |
![]() | (3) |
Whereas arm propulsion (e.g. in the arm stroke) is more analogous to rowing
(the hands are used as oars which move water backwards), other swimming styles
(e.g. the butterfly or swimming with a monofin) resemble the undulating
movements of slender fish. Waves of bending similar to the ones described for
slender fish were reported for subjects swimming the butterfly stroke
(Ungerechts, 1983;
Sanders et al., 1995
). The leg
(flutter kick) is similar to the butterfly (dolphin) kick, but whereas in the
dolphin kick the legs are moved synchronously, in the flutter kick they are
moved alternatively, out of phase by half a cycle (see
Fig. 2A). Thus, waves of
bending can be expected also when swimming using the leg kick (with and
without fins); hence, an estimate of the Froude efficiency can be attempted as
well as an estimate of the contribution to propulsion by the use of fins.
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Finally, the internal work (Wint) can be measured from
kinematic analysis according to a method originally proposed by Cavagna and
Kaneko (1977). When swimming
using the leg kick, the internal work is likely to be similar to that of
walking, as in both cases the legs move with a sinusoid-like pattern, almost
symmetrically with respect to the centre of mass (see
Fig. 2A). A model equation,
derived from that proposed for walking by Minetti and Saibene
(1992
), is proposed in this
paper for the calculation of the internal work of the leg kick, based on the
values of kick frequency and kick depth.
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Materials and methods |
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Subjects
The experiments were performed on seven elite college swimmers who were
members of a Division I University men's swimming team (State University of
New York at Buffalo, NY, USA). Their average body mass was 71.6±7.2 kg,
their average stature 1.79±0.69 m and their average age 19.9±1.3
years. The subjects' maximal oxygen consumption
O2max was
measured in a separate session by increasing velocity in 0.1 m s-1
increments from 0.4 m s-1 up to a maximum of 1.3-1.4 m
s-1, and ranged from 2.74 to 3.861 O2 min-1
(3.15±0.381 O2 min-1, mean ± S.D.).
Fins
Apollo Bio-Fin Pro fins were used in this study. These fins were made of
rubber, small in size and highly flexible. This type of fin was shown to be
effective in increasing the economy of swimming compared with different types
of fins in previous underwater (SCUBA diving) experiments
(Pendergast et al., 1996). The
subjects used fins of two different sizes; their length, mass and surface area
are reported in Table 1. The
size of the fins was determined by the foot size of the subjects.
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Experimental protocol
The subjects swam (at the water surface) in an annular pool 2.5 m wide, 2.5
m deep and 60 m circumference above the swimmer's path and were paced by a
platform moving at constant speed approximately 60 cm above the water surface.
The speed of the swimmer was set by means of an impeller type flow meter (PT
301, Mead Inst. Corp., Riverdale, NY, USA) placed 1.5 m in front of
the swimmer and connected to a tachometer (F1-12 P Portable indicator, Mead
Inst. Corp., Riverdale, NY, USA). Subjects were requested to swim with the
arms hyper-extended over the head and the thumbs joined with the palms down.
The forward propulsion was attained by kicking the legs with (LF) or without
fins (L).
Active body drag was measured as described by di Prampero et al.
(1974). Known masses (0.5-4
kg) were attached to the swimmer's waist by means of a rope and a safety belt
that did not interfere with the swimming mechanics. The rope passed through a
system of pulleys fixed to the platform in front of the swimmer, thus allowing
the force to act horizontally along the direction of movement. This force,
defined by di Prampero et al.
(1974
) as `added drag'
(Da), leads to a reduction of the swimmer's active body
drag (Db); in our experimental conditions
Da could be better defined as an `added thrust', since it
acts by facilitating the swimmer's progression in water by pulling the subject
forward. At constant speed, the `added thrust' is associated with a consequent
reduction of
O2
and the energy required to overcome Db becomes zero when
Da and Db are equal and opposite. At
the beginning of the experimental session a load was applied to the pulley
system (its mass depending on the speed and/or condition) and the subject was
asked to attain the requested speed. After 3 min, once the steady state was
attained, expired gas was collected (for approximately 60 s) into an
aerostatic balloon through a waterproof inspiratory and expiratory
valve-and-hose system supported by the platform. After 1 min the expired gas
collection was terminated and the load on the pulley was diminished by
approximately 0.5 kg. This procedure was repeated until, in the last step, the
subject swam freely (without any added load). During each collection of
metabolic data the kick frequency (KF, Hz) was also
recorded.
O2
values were determined by means of the standard open circuit method: the gas
volume was determined by means of a dry gas meter (Harvard dry gas meter, USA)
and the O2 and CO2 fractions in the expired air were
determined using a previously calibrated gas spectrometer (MGA 1100, Perkin
Elmer, CA, USA). The
O2 values
obtained in the last step (without any `added thrust') were used in the
calculations of the energy cost of free swimming: net
O2 (above rest,
assumed to be 3.5 ml O2 min-1 kg-1) was
converted to watts W, assuming that 1 ml O2 consumed by the human
body yields 20.9 J (which is strictly true for a respiratory quotient of
0.96), and divided by the speed
to yield the energy cost of swimming per
unit of distance (C) in kJ m-1.
The swimmer's Db was estimated, at any given speed and
condition, by extrapolating the
O2 versus
Da relationship to resting
O2. The power
dissipated against drag was then calculated from the product of the active
body drag times the speed
(
d=Db
).
The experiments were carried out over a range of speeds (N=5) that could be accomplished aerobically. The range of speeds depended on the condition selected: 0.6-1.0 m s-1 (L), 0.7-1.1 m s-1 (LF). Each subject participated in several experimental sessions, each corresponding to 1-3 swims at a given speed and/or condition; the swims were separated by at least 15-20 min of rest.
Kinematic analysis
During the experiments, video recordings were taken at a sampling rate of
50 Hz (Handy Cam Vision, Sony, Japan) while the subjects passed in front of an
underwater window. Black tape markers were applied on selected anatomical
landmarks in order to facilitate the following video analysis. The distance
between the hip (great trochanter) and the knee (lateral epicondyle) was
measured and recorded for each subject and each experimental session and was
utilized as a calibration factor.
After the experiments, the data were downloaded to a PC and digitized using a commercial software package (Peak Motus, Co, USA). The 2-D coordinates of selected anatomical landmarks were utilized to calculate the trunk inclination, the kick depth, the Froude efficiency and the internal work. Only the data collected during steady state free swimming were analyzed.
Trunk inclination (TI, degrees) was measured with the leg proximal to the camera fully extended (see Fig. 2A), from the angle between the shoulder (acromion process) and the hip (great trochanter) segment and the horizontal. In the same frame, kick depth (KD, m) was measured from the vertical distance between the ankles (lateral malleolous). Finally, in this same frame the 2-D coordinates of the hip and the knee (lateral epicondyle) markers were recorded in order to obtain the calibration factor (for each subject, speed and condition). 1-3 passes of the swimmer were filmed for each condition and speed; data for TI and KD reported in the text are the mean of all the values measured in all the passes (in each subject and for each condition and speed).
The internal work (Wint)
The internal work of the leg kick, with and without fins, was computed from
video analysis during free swimming (without any added drag) on two subjects
according to the method originally proposed by Cavagna and Kaneko
(1977). To measure
Wint the locations of nine anatomical landmarks (wrist,
elbow, shoulder, neck, hip, knee, ankle, heel, toe tip) were digitized over
one complete swimming cycle. On the assumption that bilateral swimming
movements are symmetrical, the 2-D coordinates obtained from the body side
proximal to the camera were duplicated (shifted half a cycle) and the swimming
cycle was reconstructed for the whole body (see
Fig. 2A). The 3-D coordinates
obtained and standard anthropometric tables (Dempster, 1959) allowed us to
calculate the position and the linear and angular speed of each body segment,
from which the position of the body centre of mass was also derived. When
swimming with fins, the extra mass of the fins was taken into account in order
to compute the segment mass/total mass fraction of each body segment. The sum
of the increases, over 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 were then computed by a custom
software package (Minetti,
1998
) in order to calculate Wint.
As shown by Minetti and Saibene
(1992) the mechanical internal
work rate when walking
(
int, in W) could be
described by the following equation:
![]() | (4) |
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This model equation was utilized to estimate k (Systat 5, USA) in the two conditions (kL and kLF) by means of a multiple non-linear regression.
The Froude efficiency (F) and the kinetic energy
(Wk)
The Froude efficiency F of swimming with (LF) and without fins (L) was
calculated from the values of average forward speed (
) and from the
velocity of the backward wave (c) on the same two subjects.
c (m s-1) was measured as indicated by Ungerechts
(1983
) and Sanders et al.
(1995
) from the 2-D
coordinates of the hip, knee and ankle joints. As shown in
Fig. 2B, each coordinate
reaches its minimum/maximum displacement with a phase-shift represented by the
time lag (
t). The distance between the anatomical landmarks
lT (the thigh length) and
lS (the shank
length) divided by the corresponding time lag between the waves minima gives
the velocity of the wave along the body
(c=
lT/
tT and
c=
lS/
tS). From the
values of c, the Froude efficiency was calculated according to
Equation 1 and the term Wk was calculated according to
Equation 3.
Statistics
The regressions between
O2 and
Da for each condition were calculated by the sum of the
least-squares linear analysis model. The differences in the measured variables
(e.g. C, Db, Wint) as determined in
the L and LF conditions were compared by the paired Student's t-test
at matched speeds (from 0.7 to 1.0 m s-1 only, N=28).
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Results |
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The energy cost of the swimming leg kick is reported in Fig. 4 as a function of the speed for both L and LF conditions. At paired speeds, the energy cost when swimming with fins was 42±2 % lower than when swimming without (LFL=-4.5±2.5 J m-1 kg-1, P<0.001). When compared at the same metabolic power, the decrease of C brought about by the use of fins allowed an increase of progression speed of approximately 0.2 m s-1.
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Average values of kick depth, kick frequency, active body drag and trunk inclination are reported in Table 2. Fins only slightly decrease (14 %) the kick depth (at the ankle level) but cause a large reduction (43 %) in the kick frequency. No significant differences in active body drag and trunk inclination were observed between the two conditions at comparable speed.
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Froude efficiency (F), calculated by Equation 1 in two subjects, was
found to be 0.61±0.02 (N=39) when swimming with the legs only
and 0.69±0.02 (N=24) when swimming with fins. No differences
were found in the time lag (
t) between the data calculated
from the hip-knee or knee-ankle coordinates within both L and LF conditions.
As shown in Fig. 5, the wave
speed (c, m s-1) was found to increase linearly with the
kick frequency (KF, Hz). The strength of this relationship
(r2=0.911) suggests that
F can be accurately
estimated from individual values of kick frequency and speed assuming a
wavelength of 2.33 m. Using this simplified method the average values of
F (N=35) were found to be 0.61±0.01 when swimming with
the legs only and 0.70±0.04 when swimming with fins, i.e. a 16 %
increase at comparable speeds (see Table
3).
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From the individual data of
d (W)
(
d=Db
)
and
F, the term
k (W)
could be estimated using Equation 2.
k increased with swimming
speed in both conditions and was 32 % smaller in LF than in L at comparable
speeds (see Table 4).
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The internal work rate
(int, W kg-1),
as measured in two subjects during actual swimming, is reported in
Fig. 6 as a function of the
speed (
, m s-1).
int was found to increase
with the speed in both conditions. In these two subjects
int was found to range from
13 to 43 W in the L condition (N=10) and from 9 to 18 W in the LF
condition (N=10).
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The constant k, as obtained from the multiple non-linear regression, was
found to be 13.93 (kL, N=10, r2=0.976)
in the L condition and 25.55 (kLF, N=10,
r2=0.832) in the LF condition. The good coefficients of
determination suggest that
int can be accurately
estimated from individual values of kick frequency and depth and from the
estimated values of k (e.g. by applying Equation 5). The so-calculated average
values of
int
(N=35 in L and LF) are reported in
Table 4:
int increased with swimming
speed in both conditions and was 74 % smaller in LF than in L at comparable
speeds.
Along with the mean values of
int and
k the values of
d and
tot are also reported in
Table 4 as well as the values
of
(in kW, i.e. the net metabolic power).
tot increased with the
speed in both conditions and was significantly reduced (36 %) by the use of
fins at comparable speeds. The contribution of
k and
int to
tot were found to be
speed-independent within both conditions. The contribution of
k to
tot is approximately the
same in the L and LF condition (24±1 %, mean ± S.D. at all
speeds). On the contrary, whereas
int is a major determinant
of
tot in the L condition
(40±1 % of
tot,
average at all speeds), its contribution is reduced to a half in the LF
condition (18±13 % of
tot, average at all
speeds).
As shown in Fig. 7, at
comparable speeds fins reduce
k by 32 %,
int by 74 % and
tot by 36 % (whereas
d is unchanged). The
decrease in
brought about by the use of fins (42 %) is
proportional to the decrease in
tot (36 %), so that the
mechanical efficiency of swimming (
M:
tot/
) is
only slightly higher when swimming with fins: it ranges from 0.08 to 0.12 in
the L condition and from 0.11 to 0.17 in the LF condition. On average (all
subjects at comparable speeds), fins increase the mechanical efficiency of
swimming by about 10 % compared to use of legs alone (see
Table 3).
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Discussion |
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Substantial variation in the energy cost of swimming using the leg kick was
observed in the L condition (Fig.
4). The differences in economy of swimming in subjects of
comparable skill (assumed here) and at comparable speeds are attributed to the
anthropometric characteristics that determine the subject's position in water.
These differences can be quantified by measuring the underwater torque
(T', a measure of the tendency of the feet to sink) by means of an
underwater balance. T' was indeed found to be a major determinant of the
energy cost of swimming at low to moderate speeds (see
Pendergast et al., 1977). At
moderate speeds, T' (a static measure of the subject's position in
water) relates to the subject's dynamic position in water (e.g. the trunk
inclination, TI). Hence TI can also be
expected to be a determinant of C. When speed increases, hydrodynamic lift
acts on the body, which assumes a more streamlined position in the water and
the difference between static and dynamic position (T' and
TI) lessens.
C and TI were found to be linearly related (the larger TI, the larger C) in the L condition, with an average correlation coefficient (for the five speeds considered) of 0.759±0.082 (range: 0.710-0.881, N=7 for each regression, P<0.05 except for 0.7 ms-1). This suggests that part of the variability of C observed in the L condition is indeed attributable to differences in anthropometric characteristics of the subjects. In contrast, even if no differences in TI were found between the L and LF conditions, the relationships between C and TI were not significant in the LF condition, which indicates that other factors more strongly influence the energy cost of locomotion when fins are used.
Work components and efficiency of swimming
As previously discussed for land locomotion
(Minetti et al., 2001), an
improvement in economy does not imply, per se, a parallel improvement
in the efficiency of locomotion. The effects of the use of fins on the
efficiency of the leg kick can be investigated only by measuring all the
components of the total mechanical work.
As shown by the flow diagram in Fig.
1 (adapted from Daniel,
1991) the efficiency of aquatic locomotion is determined by three
factors. (1) The efficiency with which muscles use oxygen to generate work.
This efficiency is usually defined as mechanical or musculoskeletal
efficiency
(
M=
tot/
).
(2) The efficiency with which the work done by the muscles produces a useful
movement (i.e. that fraction of the work that gives kinetic energy to the
fluid). This component takes into consideration the fact that some of the
contractile energy `is lost' in accelerating the mass of the lower limbs, in
deforming parts involved in thrust production (e.g. the fin's blade) and in
overcoming viscous damping in the tissues; this efficiency is called hydraulic
efficiency (
H) (Alexander,
1983
). Whereas the contribution of the elastic and viscous factors
is difficult to assess, the contribution of the inertial factors can be
estimated by measuring the internal work of swimming
(Wint). Hydraulic efficiency is given by:
![]() | (7) |
![]() | (8) |
In the computation of
tot=
k+
d+
int,
the elastic and viscous terms were considered negligible and the terms
d and
int were directly measured.
The term
k was obtained
from the values of Froude efficiency.
In the following paragraphs the measured/calculated values of the above mentioned parameters will be discussed separately. The average values of all the efficiencies indicated in this figure are reported in Table 3.
The power needed to overcome drag
(d)
The term d was
calculated as proposed by di Prampero et al.
(1974
) and was found to be
unaffected by the use of fins, at comparable speeds.
It can be debated whether the decrease of
O2 observed as a
consequence of adding masses to the pulley system (Da, see
Fig. 2) is attributed to
changes in Wd only. We found that the added thrust
(Da) not only reduced the swimmer's active body drag (and
hence
d) but also affected
the frequency of the kick: the higher Da, the lower
KF. The observed reduction of
O2 for any given
Da has therefore to be attributed to a decrease in
int and
k (both proportional to
KF). Since the contribution of these factors to total
O2 is large at
Da=0 (during free swimming) but negligible at the highest
Da, it can be shown that these factors affect only the
slope of the relationship between Da and
O2 and not the
point at which the regression crosses the Da axis, thus
they do not affect the determination of Db.
Thus, even if the procedure to determine active body drag is based on several assumptions, this is still, in our opinion, the best method proposed so far to estimate resistive forces to aquatic locomotion in humans.
The internal work rate
(int)
To our knowledge, no data for
int have been reported
before (nor even considered as a source of energy expenditure) for swimming
humans. The internal work rate when swimming using the leg kick accounts for
approximately 40% of
tot in
the L condition and for about 20% of
tot in the LF condition
(its contribution to
tot
being almost independent of the speed). Hence, fins halve the contribution of
inertial factors to energy expenditure in aquatic locomotion. In absolute
terms,
int increases more
than threefold over the selected speed range in both conditions and can
account for up to 50 W at the higher KF observed. Not
considering this parameter could therefore lead to a severe underestimation of
the overall swimming efficiency.
In this paper the model equation proposed Minetti and Saibene
(1992) for walking was adapted
to describe the relationship between
int, kick frequency and
kick depth when swimming. The value of k, a constant which takes into account
the inertial parameters of the moving segments, turned out to be comparable to
that calculated by Minetti and Saibene
(1992
) for walking (k=21.64).
In the L condition, k was found to be half of that calculated for walking
(kL=13.93), in agreement with the fact that only the lower limbs
are moving and the oscillation amplitude is smaller. The larger value of k in
the LF condition (kLF=25.55) reflects the effect of the added fin
mass on the inertial parameters of the lower limbs.
KF was found to be the main determinant of
int in swimming. Indeed, as
shown in Table 2, values of
KD increase only slightly, whereas large variations in
KF are observed with speed in both conditions. Moreover,
fins only slightly decrease the amplitude of the kick but cause a large
reduction in the kick frequency. Hence, as a first approximation, the term
(2KD)2 in Equation 5 can be considered as
constant and
int can be
calculated from
int=kKF3.
When the
int data as
directly measured in the two subjects in both conditions were pooled, the
equation became
int=6.9KF3
(N=20, r2=0.789; where
int is in W and
KF in Hz). The coefficient of determination is only
slightly lower than the one obtained with the model equation
(r2=0.841, see above) suggesting that this approximate
version of the equation can be safely utilized to estimate
int when data for
KD are not available.
There is some debate about whether external and internal work have to be
separately calculated and summed in walking (assuming no energy transfer
between the two) or jointly computed, allowing for any possible transfer, but
in cycling (Minetti et al.,
2001) and swimming the lower limb movement minimally affects the
movement of the centre of mass. Moreover, in swimming, limb movement occurs in
an orthogonal axis with respect to progression and the vertical and horizontal
oscillations of the centre of mass are kept to a minimum.
The Froude efficiency (F)
In this paper the Froude efficiency was estimated by applying the equation
proposed by Lighthill (1975)
and Alexander (1977
) for animal
locomotion in water (Equation 1) to human swimming. This method is based on
the calculation of the speed of the bending waves that move along the body (of
the swimmer or the fish) in a caudal direction.
As shown in Fig. 5, wave
speed (c, ms-1) increased linearly with the kick frequency
(KF, Hz). Since kick frequency is the reciprocal of the
wave period (T, s), the slope of the above linear relationship is the
wavelength (, m). As shown by the high determination coefficient, the
wavelength was found to be quite constant for different subjects, speeds and
conditions (
=2.34±0.18 m, N=20) and similar to the
values measured by Sanders et al.
(1995
) in male swimmers using
the butterfly stroke (2.24±0.25 m). The good agreement between the
average values of wavelength measured in the different studies, the small
standard deviation and the high determination coefficient
(r2), suggest that the linear relationship between wave
speed and KF described above can be utilized to predict
the Froude efficiency of swimming using the leg kick from measurements of kick
frequency (KF) and average speed (
).
That c depends essentially on KF while the
wavelength of the propulsive wave () is almost constant at different
swimming speeds was also observed and reported by Webb for the rainbow trout
Salmo gairdneri
(1971a
). Fish with similar
body forms are characterized by similar specific wavelengths
(
/L, where L is the fish length). Depending on the
fish swimming type,
is larger (carangiform mode) or smaller
(angulliform mode) than L (Webb,
1971a
). The data reported above (
=2.3 m and hence
>body length) are compatible with the morphological observation
that humans are relatively thicker for their length and resemble, if we can
risk such a comparison, a trout rather than an eel.
The values of Froude efficiency measured in this study are not far from
those measured in the rainbow trout by Webb (according to the method proposed
by Lighthill), who reported a range of values for F of
0.61-0.81 at speeds between 0.1 and 0.52 ms-1
(Webb, 1971b
).
The kinetic work rate not useful for thrust production
(k)
The data for k were
obtained according to Equation 3 and using the measured/calculated values of
d and
F.
k data for swimming humans
are scarce; the only other values reported in the literature were obtained by
means of the MAD system. With this method
k is calculated as
k=
O2eqFREE
O2eqMAD)/
where
O2eqFREE
is the energy expended when swimming freely (expressed in W),
O2MAD
(W) is the energy expended when swimming on the MAD system and
is the
efficiency of swimming (as obtained by graphical analysis). In those
conditions (arm stroke only with the legs floating),
k was found to range from
16 to 64 W at speeds of 1.0-1.3 ms-1
(Toussaint et al., 1988
).
Since the values of
k
increase with speed, it is reasonable that the values found in the present
study (9-31 W in both conditions) are lower than those reported at higher
speeds using the arm stroke. The two sets of data are not, however, directly
comparable. In fact, the term
k as defined by Toussaint
et al. is given by the sum
k+
int
since it was obtained from values of
tot and
d only (indeed, they
correctly defined their efficiency as `propelling').
For values of Froude efficiency ranging from 0.50 to 0.75 (a reasonable
range for human locomotion in water), the power wasted when imparting kinetic
energy to the water (k) is
bound to range from
k=
d
(
F=0.5) to
k=1/3
d (
F=0.75).
Not taking into account this parameter can therefore lead to an
underestimation of the overall swimming efficiency, as discussed above for
int and previously
emphasized by Toussaint et al.
(1988
). Indeed
k accounts for
approximately 25% of
tot
(for both conditions and at all speeds).
Hydraulic efficiency (H) and the propelling
efficiency (
P)
From the data reported in Table
4, the hydraulic efficiency can be calculated as:
H=(
k+
d)/
tot);
H
was found to be 0.59 in L and 0.82 in LF conditions, corresponding to a 40%
difference at comparable speeds (see Table
3). As indicated by Alexander
(1983
) the efficiency of a
propeller is given by the product of
Hx
F
(or, in other terms,
P=
d/
tot).
The propelling efficiency turned out to be 0.36 in the L and 0.58 in the LF
condition, i.e. 62% larger in LF than L at comparable speeds (see
Table 3). In both cases the
LFL difference was found to be independent of the swimming speed.
Propelling efficiency has also been estimated, in competitive swimmers, by
means of the MAD system when swimming using the arm stroke, and it was found
to be comparable to that calculated in this study: 0.53
(Toussaint et al., 1988) and
0.56 (Berger et al., 1997
) at
speeds between 0.9 and 1.35 ms-1.
All these values can be compared to the values of propelling efficiency of
other locomotory devices for aquatic locomotion. As reported by Abbott et al.
(1995), human-powered vehicles
with drag-device propulsion (such as boats propelled by poles, oars and
paddles) are characterized by propelling efficiencies of about 0.65-0.75. Even
though these values are larger than those reported for swimming, about one
third of the subject's power output is bound to be wasted using these
locomotory devices. Human-powered propeller-driven boats, which can reach
greater propelling efficiencies, have been developed since the 1890s for
practical transportation purposes (Abbott
et al., 1995
). Their development almost completely ceased when
gasoline-driven outboard motors were introduced; propellers with efficiencies
exceeding 90% are currently in use on human-powered watercrafts of recent
development (e.g. the flying fish; Abbott
et al., 1995
).
The efficiency of a propeller is higher if a large mass of fluid is
accelerated to a low velocity than if a small mass is accelerated to a high
velocity (Alexander, 1977).
Since fins increase the propelling surface they would be expected also to
increase propelling efficiency (as experimentally determined). The increase in
P observed in this study (62%) can be compared to the increase
of propelling efficiency (7%) obtained by the use of hand paddles when
swimming the arm stroke (Toussaint et al.,
1991
). The increase in
P with fins compared to
without fins or between fins and hand paddles may be partially explained by
the higher propelling surface of fins compared to feet (fin/foot surface area:
3.5; see Table 1) and hand
paddles (hand paddles/hand surface area: 0.026/0.018 m2=1.45).
Mechanical efficiency (M)
The mechanical efficiency of swimming with and without fins, at a given
speed, was calculated from the ratio of total mechanical power
(tot=
k+
d+
int)
to total metabolic power (
). Mechanical efficiency ranged from
0.08 to 0.17 in both conditions and at all speeds (0.11 and 0.13 for L and LF,
respectively; mean for all subjects at comparable speeds). These values are
higher than those reported for swimming humans. In those studies, however, any
contributions of internal and/or kinetic work were neglected. When internal
and kinetic work are not accounted for, efficiency values
(
=
d/
)
range from 0.03 to 0.05 (in the L condition), which is comparable to that
reported by others for front crawl swimming 0.05-0.08
(Toussaint et al., 1988
),
0.03-0.09 (Pendergast et al.,
1977
) and 0.04-0.08 (Holmer,
1972
) and compatible with the fact that the leg kick is a less
effective way of moving in water than the arm stroke (e.g.
Adrian et al., 1966
).
Locomotory (mechanical) efficiency is generally investigated to get insight into how muscles (the actuators) work in situ. The challenge is to compute all the components of the external and internal work (as well as taking into account the contribution of elastic energy storage and release, viscous damping in the tissues and so on...) in order to obtain the best possible estimate of muscle efficiency.
By taking k and
int into consideration in
the computation of
, a better
estimate of
M in swimming humans was obtained than in previous studies.
The values are still lower than those expected from the thermodynamics of
muscle contraction (0.25-0.35 at optimal contraction speeds;
Woledge et al., 1985
),
however. The `gap' between the measured values of
M and the optimal
values of muscle efficiency could arise from an underestimation of
, from an
overestimation of
and (obviously
enough) from muscle inefficiency itself.
Among the factors that might contribute to an overestimation of
(the metabolic power above resting
conditions) is an underestimation of `basal metabolic rate' (which was not
measured in this study but assumed to be 3.5 ml min-1
kg-1), e.g. because a larger fraction of
is utilized for thermoregulation in
water in respect to land locomotion. Moreover, as previously pointed out by
Gaesser and Brooks (1975
) for
humans and Stevens and Dizon
(1982
) for warm-bodied fish,
basal metabolic rate increases with progression speed/work rate. If this can
be accounted for, higher values of
M would result mainly at the higher
investigated speeds.
Among the factors that can contribute to an underestimation of
(particularly in
the case of LF) is the work done in deforming parts involved in thrust
production. These are expected to be higher in LF (the fins' blade) than in L
(the foot's sole).
As far as muscle efficiency itself is concerned, inefficiency should arise when the muscles are not working in the optimal range of either their force/length and/or force/speed relationships.
The leg kick is quite an ineffective way of using the lower limb muscles.
The range of motion of the hip and knee joints is more restricted than in
walking and cycling (an appreciable bending is observed only in the recovery,
almost passive, phase of the cycle, see
Fig. 2A) so that the leg
extensors probably do not contract at their optimal length (maximal force of
the knee extensors occurs at a knee angle of about 110°; e.g.
Narici et al., 1988).
The other factor that is known to affect muscle efficiency (and hence
mechanical efficiency) is the contraction speed at which the muscles are
working. From studies of muscle physiology, it is known that only at a given
contraction velocity is the maximum efficiency reached
(Woledge et al., 1985). While
we did not directly measure the contraction speed of the lower limb extensor
muscles, it is reasonable to assume that the kick frequency is strongly
associated to it. Frequencies of about 1.0 Hz have been suggested as the
optimum one for Type I fibres (in cycling;
Sargeant and Jones, 1995
).
Fins decrease the kick frequency from 1.59±0.25 Hz in L to
1.02±0.25 Hz in LF conditions (average at all speeds and for all
subjects) and hence are expected to increase
M by allowing the muscles to
work more efficiently (as found in this study and for other locomotory tools
on land; see Minetti et al.,
2001
).
Performance efficiency ()
The rate of useful work production divided by total rate of energy
expenditure has been used as a measure of performance for many biological
systems (Daniel, 1991). In the
step diagram of Fig. 1,
performance efficiency is defined as the ratio of useful power (necessary to
generate thrust) to total energy expenditure
.
This concept is useful for briefly summarizing the results found in this
study.
Since fins do not affect
(at comparable
speeds), the increase in economy (42%) observed when fins are used must
produce an increase in performance; the ratio
is equal to 0.03-0.05 in L and 0.07-0.09 in LF and corresponds to a 77%
difference at comparable speeds. This increase is almost completely explicable
on the basis of the observed increase of propelling efficiency (66%). Of the
increase in
P, one third has to be attributed to an increase in
F
(13%) and two thirds to an increase of hydraulic efficiency (40%). The
increase in
P is obtained essentially through a 43% decrease in
KF (which leads to a 74% decrease of
) and through an
increase in the propelling surface (3.5 times higher with fins), which allows
for the acceleration of larger masses of fluid at lower speeds
(Alexander, 1977
).
Conclusions
A complete energy balance during swimming using the leg kick, with and
without fins, was attempted by combining methodologies previously applied to
human and fish swimming. From the combination of these techniques, the economy
(C), total mechanical work (Wtot), propelling efficiency
(F) and mechanical efficiency (
M) of swimming were computed. While
the breakdown of the individual components of performance efficiency helps in
understanding why swimming with fins represents an advancement in human
powered locomotion in water, the overall gain in propulsion is far from being
commensurate with what muscles are expected to produce based on their
performance in land locomotion. Despite the lowering of energy expenditure and
an increase of 0.2 ms-1 in swimming speed at equivalent metabolic
power, other solutions with different locomotory devices should be pursued to
increase Froude efficiency (e.g. to decrease
), hydraulic
efficiency (e.g. to decrease
) and muscle
efficiency in order to further improve swimming performance in humans.
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