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How fins affect the economy and efficiency of human swimming

P. Zamparo1,2,*, D. R. Pendergast3, B. Termin3 and A. E. Minetti2

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



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  		Fig. 1. A flow diagram of the steps of energy conversion in aquatic locomotion (adapted from Daniel, 1991Go). See text for abbreviations and Discussion for details.

 


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  		Fig. 2. (A) Schematic representation of the kinematics of the leg (flutter) kick. (B) Vertical displacement of the hip, knee and ankle as a function of time, obtained by video analysis. The kick frequency in A is about half of that shown in B. At variance with walking, where the displacements of these anatomical landmarks are in-phase with each other, when swimming using the leg kick each co-ordinate reaches its minimum/maximum at a phase-shift ({Delta}t) with respect to the others. The distance between the anatomical landmarks ({Delta}lT, the thigh length; {Delta}lS, the shank length) divided by the time lag (or phase shift, {Delta}t, in s) gives the velocity of the bending wave along the body (c={Delta}lT/{Delta}tT; c={Delta}lS/{Delta}tS).

 


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  		Fig. 3. The linear relationships between added drag (Da) and rate of oxygen consumption (O2) obtained from a subject swimming with fins at the indicated speeds. Active body drag Db was estimated, at each speed, by extrapolating the Da versus O2 relationship to O2rest (basal metabolic rate, BMR) as indicated by the dotted lines and the arrows pointing downwards. Da=0 corresponds to free swimming (see text for details).

 


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  		Fig. 4. Energy cost of swimming using the leg kick (C) as a function of the speed ({nu}), measured with fins (open circles) or without (closed circles). The descending curves represent iso-metabolic power hyperbolae (as calculated for a `standard' subject of 75 kg body mass) of 0.4, 0.6, 0.8 and 1.0 kW (from bottom to top). Fins decrease the energy cost of swimming by approximately 40 % at comparable speeds and, for any given metabolic power, fins increase the speed of progression by approximately 0.2 m s-1.

 


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  		Fig. 5. In some types of aquatic locomotion, bending waves can be observed moving along the body in a caudal direction (e.g. the ondulatory movements of slender fish). Similar waves were observed in this study in subjects swimming using the leg kick (see also Fig. 2). The velocity of the wave travelling along the body (wave speed: c, m s-1) increases linearly with the kick frequency (KF, Hz) with fins (LF, open circles) and without fins (L, closed circles). The relationship between c and KF is well described by c=2.33KF (r2=0.911, N=20), the slope of which is the wavelength ({lambda}, m).

 


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  		Fig. 6. Internal work rate (int, W kg-1), measured in two subjects as a function of the speed (v, m s-1). Wint increases with the speed in both conditions: with fins (FL, open circles) or without (L, closed circles). At paired speeds, int is larger when swimming without fins than when swimming with them. The differences in int are mainly attributable to differences in kick frequency (about 40 % lower when fins are used; see text for details).

 


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  		Fig. 7. Mean values of the power (W, left vertical axis) to impart `useless' kinetic energy to the water (k) and to overcome frictional (d) and inertial forces (int) as measured without fins (L) and with fins (LF) at a speed of 0.9 m s-1. The mean (± 1 S.D.) kick frequency at the same speed is also reported in the two conditions (KF, Hz, closed circles, right vertical axis).

 

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© The Company of Biologists Ltd 2002