Seventy-five young boys between 11 and 13 years-old in Tanner stages 1–2 by self-report were recruited. The sample included swimmers with a broad range of performances. All participants were enrolled in development swimming programs at local clubs or national teams and engaged in competitive swimming for at least 2 years. Participants were ranked based on their personal best time in the men’s 100 m freestyle event and then split-up into three tiers (Tier-1, i.e., top-tier, best performers; Tier-2, mid-tier; Tier-3, lower-tier; personal best: Tier-1 = 1.75 ± 0.07 m/s, Tier-2 = 1.53 ± 0.11 m/s, Tier-3 = 1.38 ± 0.13 m/s) of 25 swimmers each. Tier-1 swimmers were at that time age-group national champions, national record holders and/or enrolled in a talent ID program. Tier-2 swimmers were swimmers racing at national competitions. Tier-3 swimmers raced mostly at local and regional competitions.

Written informed consent was provided by both parents or guardians and the swimmers to be participate in this study. Verbal consent was also provided by coaches. All procedures were in accordance to the Helsinki Declaration regarding Human research. The University Ethics Board approved the research design.

Height (H, in m) was measured by a stadiometer (SECA, 242, Hamburg, Germany) and body mass (BM, in kg) on a weighting scale (Tanita, BC-545, Tokyo, Japan). Both measures were taken standing in the upright position, barefoot, and swimwear. Arm span (AS, in m) was measured with swimmers in the upright position, arms and fingers fully extended in lateral abduction at 90° to torso. The distance between fingertips of the 3rd fingers was measured with an anthropometric tape (RossCraft, Canada) (ICC = 0.99).

The trunk transverse surface area (TTSA) was assessed by a photogrammetric technique (Morais et al., 2011). Swimmers were photographed by a digital camera (Nikon, s9600, Tokyo, Japan) in the transverse plane (downward view). Subjects stood in the upright and streamlined position in swimwear, cap, and goggles. A calibration pole (0.945 m) was aside the swimmers’ shoulders. The TTSA was measured by an area measuring software (Udruler V3.0.1211, AVPSoft, United States) (ICC = 0.98).

Swimmers were invited to undergo three all-out trials of 25 m at front-crawl and push-off start (at least 30 min of rest). A Speedo-meter string (Swim Speedo-meter, Swimsportec, Hildesheim, Germany) was attached to the swimmers’ hip (Barbosa et al., 2013). The Speedo-meter was set on the forehead-wall of the swimming pool, about 0.2 m above water surface. An in-house built software (LabVIEW^®, v. 2010) was used to acquire (f = 50 Hz) and display speed-time data over each trial. Data was transferred from the Speedo-meter to interface by a 12-bit resolution acquisition card (USB-6008, National Instruments, Austin, TX, United States). Then, it was imported into a signal processing software (AcqKnowledge v. 3.9.0, Biopac Systems, Santa Barbara, CA, United States). Signal was handled with Butterworth 4th order low-pass filter (cut-off: 5Hz, based on the analysis of the residual error vs. cut-off frequency output).

Mean swim velocity over the trial (between about the 11th and 24th meters mark) was measured. Each time the swimmer began a new stroke cycle the researcher would insert a mark on the speed-time curve being displayed on the screen. These events were then used to calculate the stroke frequency (SF = 1/P, where P is the Period). The SL was calculated from the v and stroke frequency (SF) collected by the Speedo-meter:

Where SL (in m) is the stroke length, v is the swimming velocity (in m/s) and SF is the stroke frequency (in Hz). The SL was also normalized to the arm span (SL / AS, dimensionless).

A set of three parameters was used to assess the swim efficiency. The stroke index, as an overall swimming efficiency estimator (Costill et al., 1985):

Where SI (in m²/s) is the stroke index, SL (in m) is the stroke length and v (in m/s) is the swimming velocity. Another parameter was the intra-cyclic variation of the horizontal velocity of the hip (Barbosa et al., 2013):

Where dv (dimensionless) is the intra-cyclic variation of the horizontal velocity of the hip, v the mean swimming velocity, v_i the instant swimming velocity, F_i the acquisition frequency and n the number of data points. The dv mean value of three consecutive stroke cycles between the 11th and 24th mark was used for further analysis (ICC = 0.99). The last parameter selected was the Froude efficiency (Zamparo, 2006):

Where η_F (dimensionless) is the Froude efficiency, v (in m/s) the swimming velocity, SF (in Hz) the stroke frequency and l (in m) the shoulder to hand average distance. The l was measured between the acromion and tip of the third finger, on dry-land, with swimmer simulating a stroke cycle, with a measuring tape (RossCraft, Canada; ICC = 0.99 for absolute agreement).

The velocity perturbation method (VPM) was selected to estimate the active drag (Kolmogorov and Duplischeva, 1992). Active drag was calculated from the difference between the maximal swimming velocities at front-crawl in two all-out trials (with and without towing a perturbation buoy after push-off start). Swimming velocity was measured after clocking the all-out trials between the 11th and 24th meters of the starting wall with stopwatches (Golfinho Sports MC 822, Aveiro, Portugal) by two expert evaluators (ICC = 0.98) and the mean value was used for further analysis (Marinho et al., 2010). Active drag (D_a) was calculated as (Kolmogorov and Duplischeva, 1992):

where D_a (in N) is the active drag at maximal velocity, D_b the resistance of the perturbation buoy provided by the manufacturer and, v_b and v (in m/s) are the swimming velocities with and without the perturbation device, respectively. Active Drag coefficient was calculated after re-arranging equation 9:

Where C_Da (dimensionless) is the active drag coefficient, ρ the density of the water (being 1000 kg/m³), D_a the active drag (in N), v the swimming velocity (in m/s) and S the swimmer’s projected frontal surface area (or TTSA collected with the photogrammetric technique, in m²).

The Froude number is deemed as a good proxy of wave-making drag (Kjendlie and Stallman, 2008):

Where Fr (dimensionless) is the Froude number, v (in m/s) the swimming velocity, g the gravitational acceleration (being 9.81 m/s²), and H (in m) the swimmer’s height. Hull velocity, i.e., the speed at Fr = 0.42 (Vogel, 1994) was also selected:

Where v_h (dimensionless) is the hull velocity, g the gravitational acceleration (being 9.81 m/s²) and H (in m) the height. The Reynolds number was used to assess the water flow status around the swimmer:

Where Re (dimensionless) is the Reynolds number, v (in m/s) the swimming velocity, H (in m) the height, and υ the water kinematic viscosity (being 8.97 × 10^-7 m²/s at 26°C).

It was estimated the ẇ_ext, ẇ_d and ẇ_k as measures of power output. The ẇ_d was computed as:

Where ẇ_d (in W) is the power to overcome drag force, D_a (in N) the active drag and v (in m/s) the swimming velocity. The ẇ_ext was computed having as known variables the ẇ_d and η_F (Barbosa et al., 2015a):

Where ẇ_ext (in W) is the external mechanical power, ẇ_d (in W) the power to overcome drag force and η_F (dimensionless) the Froude efficiency. Thereafter, ẇ_k was obtained subtracting ẇ_d to ẇ_ext:

Where ẇ_k is the mechanical power to transfer kinetic energy to water, ẇ_ext the external mechanical power, ẇ_d the power to overcome drag force. The total power input is estimated as (Pendergast et al., 2015):

Where Ė_tot (in W) is the total power input, ẇ_d the power to overcome drag, η_F (dimensionless) the Froude efficiency and η_m the mechanical efficiency. It was assumed an average η_m of 0.2 as reported in experimental studies assessing the full stroke (i.e., arm pull plus flutter kicking) (Pendergast et al., 2003; Zamparo et al., 2005). Experimental studies where participants performed the arm-pull with no kicking and/or researchers did not measure/estimated the ẇ_int noted lower η_m (Toussaint et al., 1990; Cappaert et al., 1992). Hence, these lower values might be partly due to incomplete computation of all mechanical factors that determine ẇ_tot (Zamparo and Swaine, 2012).

Sample power was computed having as inputs an error probability of 0.05, f effect size of 0.40 and a power of 0.85 to run ANOVAs 1-way (3 groups). These yielded a total sample size of at least 72 subjects (G^∗Power, v.3.1.9.2, University of Kiel, Germany). Mean ± one standard deviation and 95% confidence intervals are reported for all dependent variables.

Data variation across tiers was analyzed by ANOVA 1-way, followed-up by Bonferroni post hoc test (p ≤ 0.05). Partial eta-squared (ηp2) was selected as variance effect size index and deemed to be with: (i) small if ηp2 < 0.01; (ii) medium 0.01 < ηp2 < 0.06 and; (iv) large ηp2 > 0.06. Cohen’s d was also selected but as standardized effect size of mean comparisons: (i) | d|< 0.2 trivial; (ii) 0.2 < | d|≤ 0.5 medium; (iii) | d| > 0.5 large.

Tier-1 and Tier-2 swimmers were significantly taller, heavier and with longer limbs than Tier-3 swimmers; albeit, there were no differences between Tier-1 and Tier-2 participants (Table 1).

As expected, there were variations in speed across all groups, being Tier-1 cohort significantly fastest (Table 2). Tier-1 and Tier-2 swimmers denoted the same long SL, with no-significant differences; conversely, Tier-2 and Tier-3 swimmers had the same slow SF, also with no-significant differences. Therefore, Tier-1 swimmers performed a longer SL and faster SF than all other swimmers under analysis. Tier-2 swimmers were able to deliver the same SL as Tier-1 but the SF was similar to Tier-3 counterparts.

As far as efficiency is concerned, SI was significantly different across all groups and better in Tier-1 swimmers (Table 3). η_F yielded mixed results, yet mean values were significantly higher in Tier-1 than Tier-3. The dv was significantly higher in low-tier swimmers than the other two groups. Altogether, Tier-3 swimmers were less efficient that their counterparts.

Comparing the hydrodynamics, parameters that are strongly dependent on speed showed the highest values in Tier-1 swimmers (Table 4). For instance, this was the case of D_a or Re that were significantly higher in top-tier swimmers. Conversely, parameters that are also anthropometrics-dependent, such as Fr and v_h Top-tier swimmers exhibited the best scores. There was no significant variation across groups in the C_Da.

Regarding mechanical power, Tier-1 swimmer showed significantly higher values than other two groups in all selected parameters (Table 5). There was no significant differences between the two other groups. Tier-1 swimmers delivered more power to overcome drag, transferring kinetic energy to water, and therefore more external power and power input.

Literature is consistent reporting that the best age-group swimmers are prone to be taller, heavier and having long limbs (Morais et al., 2012; Barbosa et al., 2015a). For instance, after a summer break of 10-weeks, swimmers grew-up, lengthen the arm span, had larger hands and feet, increased SL, SI, η_F, and delivered better performance than before (Moreira et al., 2014). When 94 young swimmers were followed-up over 3 years, arm span (as a proxy of anthropometrics) was retained in the output of a hierarchical linear model predicting swimming performance (Morais et al., 2017). Hence, regardless of the training or detraining program young swimmers are under, they are prone to improve their performances due to growth and maturation. The rate of growth and maturation is genetically determined, having each child different rates and, spurs happening in different moments of their development. Therefore, swimming fraternity involved in age-group swim should be aware of this phenomenon as there is very high between-subjects variability, leading to a significant amount of shifts in tier membership over time (Morais et al., 2015).

Being swimming a periodic motion, average velocity depends on the SL and SF (v = SL SF). As happened in Tier-1 swimmers, a long SL concurrent to a fast SF elicits a faster speed. Conversely, short SL and slow SF leads to slow speed as happened in Tier-3 swimmers. Tier-2 had long SL but slow SF. Nevertheless, different SL-SF combinations enable one to reach a given speed. Therefore, the question to be raised is if, at a given velocity, the best option is to increase the SF or SL. Analytical models have proposed a relationship between swim efficiency and SL (Toussaint and Hollander, 1994):

Where SL is the stroke length, η_p the propelling efficiency, w the mechanical work per stroke cycle, D the drag force and SF the stroke frequency. A longer SL would be related to better efficiency and higher mechanical work per stroke. Experimental studies recruiting adult swimmers have failed to confirm clearly this argument (Pendergast et al., 2003; Zamparo et al., 2005; Barbosa et al., 2008). Nonetheless, research on age-group swimmers has pointed out for the importance of a long SL. Structure equation modeling retained SL as a factor determining SI (Morais et al., 2012). Multifactorial models pointed out for same trend of SL being a strong predictor of performance (Saavedra et al., 2010). Surprisingly, following-up over 3 years young swimmers, SL was a strong negative predictor of performance when analyzed by hierarchical linear modeling (Morais et al., 2017). The explanation furnished in this latter research was that swimmers could be transitioning from prepubertal to peripubertal maturational stages at some point, affecting their motor control patterns. Coordination patters emerge from the continuous interaction of the constraints acting on the individual. So, there is the need of individual adaptations to interacting constraints (environmental, organismic and task constraints) (Seifert et al., 2014). Constraints acting on performance and training behaviors are more often temporary than permanent, and their influence can be strengthened or reduced according to different time scales (Harbourne and Stergiou, 2009). As such, Tier-2 swimmers are constraining their SL-SF combination with the understanding that increasing SL it will make them reach a faster speed as efficiently as possible.

Tier-3 swimmers were less efficient than the other two tiers. There was no difference between Tier-1 and Tier-2. Again, structural equation modeling has already proposed that swim efficiency is a performance-determinant in age-group swimming (Barbosa et al., 2010; Morais et al., 2012). Average and range values of dv (Barbosa et al., 2013), η_F (Zamparo, 2006; Morais et al., 2017) and SI (de Mello Vitor and Böhme, 2010; Morais et al., 2015) are within what is reported in the literature for this age bracket. A high dv is reported as related to poor time trials and more energy cost of swimming (Barbosa et al., 2010). Swimming, acceleration is the net balance between thrust and resistance. Deriving the Newton’s second law:

Where a is the swimmer’s acceleration, Pr the thrust, D the drag force, BM the swimmer’s body mass and m_a the added water mass. Such accelerations over the cycle, lead to:

Where v is the swimmer’s mean velocity, v₀ the swimmer’s velocity at the beginning of the stroke cycle, Δv the variation of the swimming velocity throughout the stroke cycle and t the time. Hence, swimmers are not able to keep an uniform motion (i.e., Δv = 0 m/s). Instead, they denote an intra-cyclic variation of the velocity (i.e., Δv ≠ 0 m/s). In the event of a higher dv (i.e., Δv in equation 19) for same average velocity, more work is needed to overcome inertia and drag:

Where w is the mechanical work, K drag factor, v swimming velocity and T duration of a stroke cycle.

η_p is the ratio of total work or power to overcome drag force and displace in water, whereas η_F is the ratio of external work or power to overcome this same force. Indeed, we did not account for ẇ_int. There are a few challenges to measure ẇ_int in water. A main concern is the shift of the center of mass over the stroke cycle which is deemed to potentially violating König’s theorem. By König’s second theorem, the kinetic energy is the sum of the kinetic energy of the center of mass and kinetic energy of moving parts of the body having as reference the center of mass (Rao, 2005):

Where, Ek is the energetic kinetic, N the reference frame, m the mass, v velocity of the center of mass, H angular momentum, ω angular velocity of rigid body R. Total kinetic energy must be greater or equal to kinetic energy of the center of mass. In swimming, the center of mass denotes a quite large volume of displacement leading to substantial inaccuracies measuring the ẇ_int.

An interesting note is that η_F ranged overall 21–30% for pooled sample. Humans walking on soft and slippery surface (i.e., sand) were reported as having a gait efficiency of 30–60% between 0.5 and 2.5 m/s (Lejeune et al., 1998). In this same study, walking at about 1.25 and 1.50 m/s the efficiency was approximately 44 and 50%, respectively. Adult competitive swimmers have a η_F of 50–60% (Pendergast et al., 2003). I.e. skilful young humans displacing in water can be almost as efficient as adults walking on soft sand. Overall, swim efficiency can be deemed as an important factor to reach better performances in age-group swimmers.

Hydrodynamics is arguably the domain where is less easy to find a clear trend. Parameters that are speed-dependent, such as D_a, turned out to be a disadvantage to better swimmers. Re-arranging equation 9, becomes clear the key-role played by the velocity term in the magnitude of the drag force:

Active drag depends on the square of the velocity. Tier-1 swimmers because swam faster the time trials, the drag to be overcome was likewise larger than their counterparts. Conversely, there was no significant variation across groups in the C_Da. Benchmarking with literature, C_Da of these participants is smaller. For pooled sample, the 95CI was 0.30–0.47. Over 2.5 years, the C_Da assessed by MAD system, decreased from a 95CI of 0.60–0.68 to 0.49–0.59 (Toussaint et al., 1990). In a research that young swimmers were monitor in three different moments of a season by VPM, the 95CI brackets were 0.41–0.55, 0.55–0.97, and 0.33–0.47 (Barbosa et al., 2015b). The 95CI of present research seems to overlap the data reported by the end of the season in the latter paper.

Typically, it is deemed a turbulent flow when Re > 5 × 10⁵. The lower limit of the 95CI in Tier-3 was 2.04 × 10⁶. This suggests that regardless of the tier, young swimmers are under turbulent conditions. Re was different across all tiers and higher in Tier-1. The difference in Re across tiers is explained by swim velocity each tier is able to reach and also the anthropometrics as discussed previously.

Other parameters that are anthropometric-depended, such as Fr and v_h, Tier-1 swimmers showed better scores. Both variables provide insight on wave-making resistance. Literature reports that swimmers with longer bodies (i.e., taller) benefit in decreasing the wave drag (Kjendlie and Stallman, 2008). This reasoning comes from naval engineering where ships with long hulls are under less wave drag. The 95CI of the v_h in our three tier was 1.61–1.64, 1.58–1.61, and 1.57–1.60 m/s. Their 95CI of the swim velocity was 1.48–1.53, 1.33–1.38 and 1.17–1.22 m/s. Hence, swim velocity falls within the v_h, suggesting that swimmers were displacing within wake wavelength. Moreover, there is room to increase the swim velocity by about 0.11–0.12, 0.23–0.25, and 0.38–0.40 m/s with negligible change in the wave drag.

Tier-1 swimmers delivered more mechanical power. In another research recruiting swimmers of the same age-group, percentile 10–90 for ẇ_D, ẇ_k, and ẇ_ext was 38–137, 96–282 and 135–329 W, respectively (Barbosa et al., 2015a). At 1.25 m/s the ẇ_D on MAD system was noted increasing from 52 ± 11.58 W to 77.2 ± 14.81W over a 2.5 years period in 13 young swimmers (Toussaint et al., 1990). In another study, at 1.2–1.4 m/s ẇ_D, ẇ_k and ẇ_ext were 74–97, 81–112 and 179–245, respectively (Zamparo et al., 2005). These values fall within the 95CI of our results. Tier-1 swimmers, as adult counterparts, use a much higher proportion of their ẇ_ext to overcome drag (Toussaint, 1990). This can be the result of a more efficient swim technique as discussed early on and, highest levels of dry-land strength and power being transferred into the swim stroke (Morais et al., 2018). High levels of dry-land strength that are transferred to in-water thrust elicit the swimmer to reach faster speeds (Morouço et al., 2011).

The power input was also higher in Tier-1 swimmers. This can be explained by their larger surface areas and speeds, as well as, having to overcome a higher drag force in comparison to counterparts. The mean values of each group are within what is reported in the literature selecting experimental techniques. For instance, the mean Ė_tot was for Tier-1, -2, and -3 2080 ± 929 W at 1.51 ± 0.06 m/s, 1216 ± 489 W at 1.35 ± 0.04 m/s, and 1177 ± 692 W at 1.19 ± 0.08 m/s, respectively. In Tier-1 was noted a large SD, that is almost the double of remaining groups. In Tier-1 four swimmers seem to be extreme cases (Ė_tot > 3 kW) due to large trunk transverse surface areas. Removing these 4 extreme cases, the mean Ė_tot would be 1742 ± 484 W. Zamparo et al. (2005) reported Ė_tot of 857 W at 1.2 m/s and 1126 W at 1.4 m/s. Pendergast et al. (2003) proposed that the Ė_tot –speed at 1.1–1.3 m/s should be around 1.0–1.4 kW. In a 200 m time trial, at 1.42 ± 0.05 m/s the Ė_tot was 2.23 ± 0.23 kW (Figueiredo et al., 2011). Hence, the Ė_tot derived in this research seems to be a fair approximation of what is reported by experimental studies. This analytical procedure can have good traction in settings where experimental testing is not feasible. For instance, events at official competitions, assessing large sample sizes, and facing time-constrains to monitor swimmers, equipment available does not fit the participant’s size (e.g., equipment is too large for small children). That said, to minimize the source of variability, it is advised to select always the same procedure and input the same assumptions running within- and between-subjects comparisons.

Benchmarking the strongest and weakest domains of each tier it is possible to have insight on the determinant factors explaining their performance (Table 6). Anthropometrics (to be taller, having longer limbs and heavier) is an advantage for Tier-1 swimmers. Anthropometric features are quite similar between Tier-2 and Tier-3. Tier-1 had long SL and high SF leading to a fast speed. Tier-3 on the other hand had short SL and slow SF. Conversely, Tier-2 was in the middle ground, having high SL but slow SF. As far as swim efficiency is concerned, Tier-3 swimmers were less efficient than the other two tiers. Hydrodynamics is arguably the domain where is less easy to find a clear trend. There was no significant variation across groups in the C_Da. But, parameters that are speed-dependent turned out to be a disadvantage for better swimmers, whereas, parameters that are anthropometric-depended they showed better scores. Tier-1 swimmers yielded larger external power and power input, which might be related to faster speeds, anthropometric features and swim technique. No differences were noted between the other two groups under comparison. As such, adding to the nature-nurture debate, one can argue that both are useful to excel at such early ages. The combination of nature (having here the anthropometrics as proxy) and nurture (swimming biomechanics and energetics) is the optimal solution. Mid-tier swimmers seems to be those that despite the anthropometrics is not yet on their favor, nurture has help them in some way to reach good performances. Low-tier swimmers are those lacking both “nature” and “nurture” features.

It can be addressed as limitations of this research: (i) this is a cross-sectional research. As such, data may vary along the season depending on training regime and individual rates of growth and development; (ii) one should exercise care extrapolating these findings to other cohorts of swimmers. Findings can vary in other age-groups and in girls; (iii) mechanical power output and power input were derived from a set of analytical formulae albeit, experimental procedures are also a potential alternative; (iv) all measurements were took considering a non-competitive distance. The shortest competitive distances in swimming are the 50 m and 50 y (approximately 45 m) events. 25 m trials were selected because it is very convenient. In a short and quick trial, it is possible to collect a comprehensive number of valid parameters. Moreover, there was a strong association (R = 0.79) in the speed over the 25 m bout and the 100 m race speed by our participants.