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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: W_D against water drag (which generates propulsion), W_K to uselessly accelerate water, W_INT to accelerate limbs, W_OTHER to deform propulsive structures (fins). The sum of W_D + W_K is called W_FLUID, the sum of W_INT + W_OTHER is W_PROPULSOR and the total mechanical work is W_TOT (the sum of W_FLUID + W_PROPULSOR). 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 W_TOT should be W_FLUID and most of W_FLUID should be W_D, mainly because W_D is the only indispensable work to secure propulsion (given that body shape and limbs movement). The overall efficiency, here called Performance efficiency (Ef_PE), which is the ratio between W_D (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 (Ef_FR) 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 W_FLUID and W_TOT is the Hydraulic efficiency (Ef_HY), 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 (Ef_TR, in swimming it should be called Propelling efficiency) is the ratio between the indispensable W_D and W_TOT (thus it is the product of Ef_HY and Ef_FR) and accounts for all the energy degradation `outside' the involved muscles. The Muscle efficiency (Ef_MU) 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, Ef_PE=Ef_MUxEf_TR=Ef_MUxEf_HYxEf_FR. 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 W_OTHER was not measured, the experimental W_D, W_K, W_INT 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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