In this study, active drag values calculated based on full and semi-tethered swimming tests (“residual thrust method”) were compared with i) passive drag values, as measured during passive towing trials, and ii) active drag values, as calculated by means of the “planimetric method”. Passive drag was significantly lower than active drag (measured by any method) and no differences were detected between speed-specific active drag values (kaST, kaSTfit and kaPL). We can thus conclude that, since these two approaches (“planimetric method” and “residual thrust method”) lead to similar results, they probably measure the same quantity. Dp values reported in this study are consistent with those reported in the literature, for a review, see (Gatta et al., 2015; Narita et al., 2017; Gatta et al., 2016). Regarding Da, while some studies report active drag equal or even lower than passive drag (Kolmogorov and Duplishcheva, 1992; Toussaint et al., 1988), others indicate that the former is larger than the latter (Formosa et al., 2012; Gatta et al., 2015; Hazrati et al., 2016; Narita et al., 2017; Shimonagata et al., 1999; Takagi et al., 1999). Given the large variability in the active drag estimates reported in the literature, the observation that two independent methods give comparable results constitutes a step forward in our understanding of the forces that resist motion in swimming. DaST and DaSTfit data reported in this study are consistent with data obtained by others (Narita et al., 2017; Shimonagata et al., 1999; Takagi et al, 1999) that applied the “residual thrust method”, although some differences in the Da/Dp ratio could be observed among studies (Da/Dp >1.5 in our study); this could be attributed to differences in the experimental protocol but also to differences among the participants. Indeed, as schematically represented in Figure 1, the partitioning between FST and FD could also depend on the capability of a swimmer to minimize the latter. In general terms, inter-subject differences in FD could be expected based on differences in the anthropometric characteristics (that influence passive drag) and in technical skill (that influences active drag). Indeed. swimmers with good technical skills have a lower active drag than less proficient ones (Pendergast et al., 2005). This suggests that the Da/Dp ratio can be expected to depend on the technical skills of a swimmer and to decrease with training. Then, a swimmer able to minimize FD could maximize the force exerted on the tether (FST) at a given external load. FST will thus depend on the muscle force the swimmers can generate (FTOT), on their propelling efficiency (FP / FTOT) but also on the partitioning between FST and FD. Thus, data reported in this study not only point out at the differences that can be expected between active and passive drag in general terms but also indicate that care should be taken when discussing data derived from semi-tethered tests (because the force balance depends also on propelling efficiency, and hence on the swimmer’s technical skills). Indeed, it was recently suggested that the capability of a swimmer to exert force during a semi-tethered trial depends (among the others) on the propulsive force necessary to overcome drag during these tests. Soncin et al. (2021) indeed observed that the correlation between semi-tethered force and swimming performance is higher when the effect of drag forces is accounted for. Unfortunately, in their paper only correlational parameters are reported (no actual data of semi-tethered force or drag force) and thus further comparisons with data reported in this study are not possible. The main limitation of the active drag estimation based on full and semi-tethered trials is strongly inherent to the assumption of steady-state swimming conditions, but the cyclic actions of swimming create a complexity of unsteady flow mechanics that affect hydrodynamic resistance. However, currently its effects on Da seem impossible to measure directly (Takagi et al., 2021). Furthermore, this method does not clarify the impact of the intra-cyclic variation of drag because the effect of the force variation around the mean was not considered and appears difficult to evaluate due to the connection between the tether and the swimmer. The “residual trust method” proposed in this study is based on the assumption that a swimmer can deliver an equal force during either full towing, free swimming or swimming against an external load. For this assumption to be true FTOT and FP must be the same in all conditions (see Figure 1); in other words, FP is assumed to be constant as well as propelling efficiency (FP/FTOT). In this study, no differences were detected between (measured) FT and the values of FP estimated by the model and no differences in SF were observed across load conditions, comforting the assumption of constant FP. In addition, FT is close to the (active) drag force that can be calculated from the DaPL vs. v relationship at maximal swimming speed (DaST = 0%, see Figure 2) as observed in a previous study (Gatta et al., 2016) and similar values of propelling efficiency (FP/FTOT = 0.4) were reported in full tethered swimming and in free swimming (Gatta et al., 2018). It is, thus, fair to assume that this state of affairs does not change in the case of semi-tethered swimming tests, thus supporting the assumption that both FP and propelling efficiency (FP/FTOT) remain constant. The observed lack of differences in SF among conditions is relevant also because, as suggested in the literature (Narita et al., 2017, Takagi et al., 1999), the assumption that a swimmer adopts the same technique, body position and kinematics in different experimental conditions is considered to be valid when the stroke rate is maintained constant. Thus, as our swimmers maintained their stroke rate, it is likely that they managed to maintain the same propulsive force. The individual coefficient of variation in the SF values was 2% on the average (60.2 ± 1.2 cycles.min-1); thus, it could be tentatively suggested that a difference in SF lower than 2 cycles.min-1 between trials could be considered acceptable. The assumption of a constant force is also supported by data of Samson et al. (2018) who demonstrated that the (estimated) propulsive forces generated by the hand in tethered and free-swimming are similar (except at sprint pace). A final consideration regards the highest applied load in semi-tethered swimming tests (85% of FT) where kaST is significantly lower than at the other loads (see Table 1). When average kaST is calculated over the entire load range (0-85%) it amounts to 37.7 kg.m-1 but when the highest load is excluded (0-75%) kaST amounts to 39.4 kg.m-1, a value even closer to kaSTfit (e.g. 40.3 kg.m-1). Whatever the reason for this difference, these findings indicate that care should be taken when attempting to assess active drag based on the “residual thrust method” when the applied load is too high. This observation is in agreement with recent data that indicate that with the velocity perturbation method (a semi-tethered test) active drag is probably underestimated when utilizing large external loads (Gonjo and Olstad, 2022). Last but not least, a lack of practice with resistive swimming tests could be a reason why swimmers could not produce the same power output between swimming conditions, since the error in the measurement of the swim and tow velocities can vary depending upon the level of the swimmers (Hazrati et al., 2016, Hazrati et al., 2018). We recruited top sprinters for this study, and they were familiar with the experimental procedures, but care should be taken when applying the “residual thrust method” in less proficient swimmers. In this case, care should be taken also to increase the recovery time between trials, because differences in propulsive force (and hence in SF) among conditions could occur because of fatigue. In conclusion, the present study demonstrates that active drag (front crawl swimming) is about 1.5 times larger than passive drag. The “residual thrust method” and the “planimetric method” led to similar results in the active drag quantification. Thus, the active drag estimation using an easy-to-use protocol based on full and semi-tethered swimming tests appears to provide reasonable results. Future studies should investigate whether this set of calculations could also be applied to the other strokes, for which the relationship between kp and ka is known (Gatta et al., 2015). |