Two hypotheses were tested: (a) stroke frequency is predictable from the amplitudes of bodyroll and the turning effect around the body's long-axis generated by the non-propulsive fluid forces (that is, the torque driving bodyroll), and (b) swimmers exhibit at least one alteration in the factors influencing the bodyroll cycle as they increase the stroke frequency for faster swimming, so that they can reduce the fluid forces "wasted" in non-propulsive directions. The mechanical formula that links stroke frequency and the kinetics of bodyroll was derived on the basis of Euler's equation of motion. Experimental data were collected from competitive swimmers to validate the derived mechanical relations and to examine the strategy that skilled swimmers would use to change the stroke frequency as they swam faster. A strong correlation (slow: r=0.70 and fast: r=0.85) and a non-significant difference between the observed stroke frequency and the formula-based estimates supported the first hypothesis. As the subjects increased stroke frequency (38%) for faster swimming, bodyroll decreased (19%) and the trunk twist increased (40%). The combined alterations resulted in a small reduction in the shoulder roll (12%), enabling the swimmers to gain the benefits associated with a large rolling action of the upper trunk, while limiting the amount of increase in the turning effect of fluid forces in non-propulsive directions (40%). The second hypothesis was, therefore, supported. The derived mechanical formula provides a theoretical basis to explore mechanisms underlying the interrelations among stroke frequency, stroke length and swimming speed, and sheds light on a possible reason that swimmers generally adopt six-beat kicks.
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