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Fig. 3. Efficiency cascade for the leg kick in swimming, with and without fins
(adapted from Zamparo et al.,
2002 ). This example illustrates all the possible mechanical works
(expressed as costs) to be done: WD against water drag
(which generates propulsion), WK to uselessly accelerate
water, WINT to accelerate limbs,
WOTHER to deform propulsive structures (fins). The sum of
WD + WK is called
WFLUID, the sum of WINT +
WOTHER is WPROPULSOR and the total
mechanical work is WTOT (the sum of
WFLUID + WPROPULSOR). E
represents the metabolic cost for swimming the leg kick and, depending on the
muscle efficiency value, is transformed into different proportions of work and
heat. For each bifurcation (proceeding left to right and bottom to top) there
is a desired transformation, marked by the blue arrow, and a side effect,
marked by the yellow arrow. Thus we could say that most of
WTOT should be WFLUID and most of
WFLUID should be WD, mainly because
WD is the only indispensable work to secure propulsion
(given that body shape and limbs movement). The overall efficiency, here
called Performance efficiency (EfPE), which is the ratio
between WD (the unavoidable work) and E, can be
considered as the product of other efficiencies relating to the use (or
misuse) of mechanical work along the chain. From top to bottom, the Froude
efficiency (EfFR) is the ratio between useful work for
propulsion and the total work needed to accelerate the fluid, thus it is low
when more water is uselessly accelerated. The ratio between
WFLUID and WTOT is the Hydraulic
efficiency (EfHY), and is low when a lot of work is done
because of dissipations or wastes in the propulsive machinery (limbs and
fins). The Transmission efficiency (EfTR, in swimming it
should be called Propelling efficiency) is the ratio between the indispensable
WD and WTOT (thus it is the product of
EfHY and EfFR) and accounts for all
the energy degradation `outside' the involved muscles. The Muscle efficiency
(EfMU) is the ratio between the mechanical work and the
metabolic energy expenditure (= work + heat) and accounts for the optimality
of the operative range (contraction length and speed) and for the presence of
co-contractions (resulting in heat with no work). As anticipated,
EfPE=EfMUxEfTR=EfMUxEfHYxEfFR.
This analysis is crucially important, not just to better understand the energy
flow in swimming, but also to appreciate the effects of passive tools, as
fins, in enhancing this locomotion. While in the quoted study
WOTHER was not measured, the experimental
WD, WK, WINT
values have been collected and the efficiency computed both for non-fins and
fins conditions. The changes introduced by those passive tools have been
marked with green (equal and down arrow) signs, while the change in
efficiencies is numerically indicated in the schema. Finally, despite the
unquestionable advantage of introducing fins in swimming the leg kick, a lot
can still be done (maybe by considering a radically different design of the
passive tool) to increase the efficiency and the economy of this
locomotion.
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10 min). For a mathematical discussion of estimation of their
speed values, see Appendix.