Effect of imposing changes in kick frequency on kinematics during undulatory underwater swimming at maximal effort in male swimmers

Human Movement Science 38 (2014) 94–105

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Effect of imposing changes in kick frequency on kinematics during undulatory underwater swimming at maximal effort in male swimmers Hirofumi Shimojo a,⇑, Yasuo Sengoku b, Tasuku Miyoshi c, Shozo Tsubakimoto b, Hideki Takagi b a

Graduate School of Comprehensive Human Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8574, Japan Faculty of Health and Sport Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8574, Japan c Graduate School of Engineering, Iwate University, 3-18-8 Ueda, Morioka, Iwate 020-8550, Japan b

a r t i c l e

i n f o

Article history:

PsycINFO classification: 3720 Keywords: Dolphin kick Swimming velocity Strouhal number Froude efficiency

a b s t r a c t Undulatory underwater swimming (UUS) is an important swimming technique after a start and after turns. It was considered that a higher swimming velocity (U) resulted from a higher kick frequency (f), and greater propelling efficiency, i.e., Strouhal number (St) and Froude efficiency (gF), resulted from a lower f. The aim of this study was to investigate whether changing f affected U and St, gF plus other kinematics of UUS. Ten national-level male swimmers participated in the study. First, the swimmers performed maximal UUS (Pre; this f was defined as 100% F). Second, the swimmers synchronized their f with the sound of a metronome and with six frequencies (85% F, 90% F, 95% F, 105% F, 110% F, and 115% F) randomly presented. During the higher f sessions, kick amplitude (A) significantly decreased from Pre (115% F: 10.8%, p < .05); however, U was unchanged. In contrast, in lower f sessions, St and gF were unchanged, but the wavelength per body length (kBL), which indicates UUS mode, significantly decreased (90% F: 1.3%, p < .05). In conclusion, these results suggest that increasing f for UUS would not affect U, but a decrease in f may be suitable for human undulation training. Ó 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author at: Faculty of Health and Sport Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 3058574, Japan. Tel.: +81 29 853 6330. E-mail addresses: [email protected], [email protected] (H. Shimojo), sengoku@taiiku. tsukuba.ac.jp (Y. Sengoku), [email protected] (T. Miyoshi), [email protected] (S. Tsubakimoto), takagi@taiiku. tsukuba.ac.jp (H. Takagi). http://dx.doi.org/10.1016/j.humov.2014.09.001 0167-9457/Ó 2014 Elsevier B.V. All rights reserved.

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1. Introduction Human undulatory underwater swimming (UUS) was first performed during the Moscow Olympic Games in 1980 (Counsilman & Counsilman, 1994). Some participants in backstroke events covered nearly 25 m using UUS after performing the starting motion. UUS is a technique used by swimmers to propel themselves underwater after the starting motion and during the turn phase. Once UUS was introduced, it began to spread through competitive swimming as several swimmers began using the technique, including participants in butterfly and freestyle events. Several swimmers believe that UUS is important for decreasing their race times, and several studies on UUS have been published (Arellano, Pardillo, & Gavilán, 2002, 2003; Atkison, Dickey, Dragunas, & Nolte, 2013; Connaboy, Coleman, Moir, & Sanders, 2010; Connaboy, Coleman, & Sanders, 2009; Connaboy et al., 2007; Hochstein & Blickhan, 2011; Lyttle, Blanksby, Elliott, & Lloyd, 2000). Lighthill (1975) stated that UUS performance was primarily determined by the shape, i.e., the frequency, amplitude, and temporal coupling of the UUS movements. Horizontal swimming velocity (U) of UUS, and in general the speed in all cyclic forms of locomotion (on land and in water), is given by the product of cycle frequency (f) and cycle amplitude (A): ms1 = cycles1  mcycle1. Thus changes in one of these parameters have an influence on the other two. This applies also for human UUS, as discussed by Connaboy et al. (2009). Arellano et al. (2002, 2003) investigated UUS kinematics by comparing international junior and senior swimmers with national age groups and observed no differences A but, they reported significant differences in f and the average horizontal velocity of the center of mass (CM). The authors concluded that an increase in the swimming velocity of human UUS seem to be caused by an increase in f. Therefore, f is considered to be the most important factor for increasing UUS velocity. The relationship between f and U in UUS has traditionally been determined by observing f over a range of U, either in flow tanks and pools. However, this limited approach does not completely describe the extent of the relationship between f and U beyond an optimal/critical value of f, a further increase in frequency would not increase U (Connaboy et al., 2009). The relationship between f and U was firstly described by Craig and Pendergast (1979) in the four swimming strokes. The curve relating these two parameters showed that an increase in frequency brought about an increase in speed up to a point after which further increases in f do not allow for a further increase in U. In free swimming, these experiments were performed well before the study of Connaboy et al. (2009) and this approach applies also for UUS. To clarify this relationship in UUS, Cohen, Cleary, and Mason (2012) used a simulation to investigate whether increasing f during dynamic UUS affected the net streamwise forces of an elite swimmer. Their simulation indicated that the mean net streamwise forces were linearly related to f. In addition, the findings from a computational fluid dynamics study suggested that a more efficient UUS performance resulted from the larger A/lower f than the smaller A/faster f kick (Lyttle & Keys, 2004). Nevertheless, whether changes in f affect UUS performance has not been investigated in a real swimmer. If a swimmer was required to modulate f alone while performing UUS at maximal effort, we expect the streamwise/resistive force of the swimmer and the propelling efficiency would change. This imposed change could be estimated using U and the propelling efficiency. In USS, such as that of a fish, the propelling efficiency can indicate two kinematic variables: (1) the Strouhal number calculated from U, f, and A (Arellano et al., 2003) and (2) the Froude efficiency calculated from U and the body wave velocity of undulatory motion (Lighthill, 1975). The aim of this study was to investigate whether changing the kick frequency while maintaining UUS at maximal effort would change the other UUS kinematics, such as swimming velocity and propelling efficiency, in well-trained male swimmers. 2. Methods 2.1. Participants Ten national level male swimmers (mean age, 21.3 ± 0.9 years; mean body weight, 71.3 ± 4.8 kg; mean height (L), 175.5 ± 5.4 cm; and mean whole body length (BL), 225.1 ± 7.6 cm) voluntarily partic-

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ipated in this study. All swimmers had >10 years of competitive experience. This study was approved by the ethics committee of the author’s university, and informed consent was obtained from the swimmers. 2.2. Experimental settings The experiments were performed in an indoor pool (50 m  7 lanes, 1.35–1.80 m depth, 28 °C). The experimental task consisted of basic prone UUS, which the swimmers performed 0.5–1.0 m under the water surface so that wave drag was negligible (Lyttle & Blanksby, 2000). Twelve points were marked with LEDs on the swimmers’ right side to record the swimmers’ joint positions during swimming. The twelve anatomical landmarks were as follows: ear-hole, superior margin of the sternum, lateral epicondyle of the femur (knee), lateral malleolus (ankle), calcaneus (foot), tuberositas ossis metatarsalis quinti (toe), acromion (shoulder), lateral condyle of the humerus (elbow), styloid process (wrist), fifth distal phalanx (finger), greater trochanter (hip), and the lower end of the tenth rib (rib). Length between the head vortex and ear was measured in a previous experiment; the head position was estimated from the ear-hole position because the head is generally hidden by the arms during UUS. The body segment parameters (BSP) for Japanese athletes (Ae, Tang, & Yokoi, 1992) were used to calculate each swimmer’s CM. Each swimmer’s motion was recorded with two video cameras (High speed 1394 Camera, DKH Inc., Japan) that were positioned laterally to the swimmer at an underwater window. The sampling rate for motion capture was 100 Hz. 2.3. Swimming sessions The swimmers performed a normal 400-m warm-up swim and were familiarized with the experiment. The swimmers performed UUS at maximal effort with a push-off start until they were recorded for at least 15 m while performing at the preferred f (Pre). The toe position was digitized immediately after the Pre session using motion analysis software (Tracker, open source physics). The digitized data was processed in MATLAB (Mathworks, USA) to calculate f (Hz), which was the duration between consecutive points at which the vertical toe position was at its lowest value. We defined f at maximal effort as 100% kick frequency (100% F), and calculated f at 85%, 90%, 95%, 105%, 110%, and 115% of the standard kick frequency. Six-level metronome sounds corresponding to the frequencies were played through an underwater speaker (MT-70 Toyo Onkyo Corp., Tokyo, Japan), and the swimmers synchronized their movement cycle with the metronome sound while performing at maximal UUS. The swimmers rested for at least 5 min between sessions, and the sessions were performed in a randomly determined order (% frequency; 85% F, 90% F, 95% F, 105% F, 110% F, 115% F). The swimmers were asked to maximize their swimming velocity in each kick frequency session. After the performing the kick frequency sessions, the swimmers again performed maximal UUS with the preferred f (Post) to determine whether the swimmers were fatigued. 2.4. Data procedure Coordinates of the 12 markers were recorded during UUS using the 2-dimensional direct linear transformation (2D-DLT) method in Tracker. The 2D coordinates were filtered in MATLAB with a low-pass Butterworth filter and a 6-Hz net cut-off frequency. After the 2D coordinates were converted into global coordinates, the instant abrupt movement of the global mass points was observed when the 2D coordinate field changed from first camera to the subsequent camera. This phenomenon was caused by an optical axis shift, which called as aberration, and particularly occurred at the field edge when filming through the underwater window. Thus, the global coordinates were again filtered with a low-pass Butterworth filter and 6-Hz net cut-off frequency over a 20-frame window (i.e., 0.02 s) centered on the instant the abruptly moving mass appeared.

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2.5. Kinematic variables A one-kick cycle began at the lowest peak for the toe position and ended at the next lowest peak. All variables were obtained during three cycles and an additional 15 frames that immediately preceded and followed the three cycles. Three complete values were obtained for all variables and the mean of these values was used for in analysis (Connaboy et al., 2010). The f (Hz) and kick amplitude Atoe (m) were calculated from the toe coordinates. f was the duration of one-kick cycle, whereas Atoe was the vertical displacement of the toe coordinates between the peak and trough of one-kick cycle. The non-dimensional kick amplitude (A) was calculated by dividing Atoe by body height (L). The average swimming velocity U (m s1) was the average horizontal CM velocity during one-kick cycle. The horizontal distance per kick Dc (m) was calculated with following equation:

Dc ¼ U  f

1

;

ð1Þ

where U is the average horizontal CM velocity, and f is the kick frequency. The value of Dc indicates horizontal distance covered during a kick. The Strouhal number, St, was calculated with the following equation:

St ¼ f  Atoe  U 1 ;

ð2Þ

where St is a dimensionless number that describes the kick amplitude normalized to the progression given by the swimming velocity and kick frequency ratio. Using the propelling efficiency calculation method for elongated-body theory (Lighthill, 1975), Zamparo, Pendergast, Termin, and Minetti (2002) obtained the Froude efficiency, gF, from the velocity of the progressing undulatory wave (ms1) in the lower leg and U during the flutter kick. Waves of bending similar to those described for slender fish have been described in butterfly (Ungerechts, Daly, & Zhu, 1998) and monofin swimming (Nicolas, Bideau, Colobert, & Berton, 2007). The gF was calculated using the following equation:

gF ¼ ðc þ UÞ=2c;

ð3Þ

–1

where c (ms ) is the whole body wave velocity and U is the average swimming velocity. Body wave velocity was calculated from the 2D joint coordinates (Hochstein & Blickhan, 2011; Nicolas et al., 2007; Zamparo et al., 2002), and each coordinate reached its maximum displacement with a phase shift represented by a time lag (Fig. 1). Distance between the anatomical landmarks divided by the corresponding time lag between the waves minima gives the velocity of the wave along the body. The whole body wave velocity, c, was obtained from the slope of regression for the shift in the minimum along the body axis (i.e., each landmark) depending on time (Hochstein & Blickhan, 2011). If the average swimming velocity is higher than the whole body wave velocity (U > c), the wave decelerates the body. Thus, gF is in the range 0.5–1.0, and a value of gF = 1 (i.e., U = c) implies that the total power is equal to thrust power, whereas power is partially lost when gF < 1 (i.e., c > U). The body wavelength k (m) was calculated by dividing the whole body wave velocity, c, by f. Connaboy et al. (2007) calculated k using equation of physics as follows:

k¼cf

1

;

kBL ¼ k  BL1 ;

ð4Þ ð5Þ

where c and f are the whole body wave velocity and kick frequency, respectively. The body wavelength per body length kBL was calculated by dividing k by the whole body length (BL), which indicates the mode of undulatory locomotion, such as anguilliform and sub-carangiform (Connaboy et al., 2009). We divided one-kick cycle into the following three phases: (1) first upward kick, Up1st; (2) second upward kick, Up2nd; (3) downward kick, Dw. The difference between the first and second kick phase was that the toe trajectory abruptly changes from a vertical direction to a horizontal direction (Arellano et al., 2002). We first determined the time of the direction change between Up1st and Up2nd according to the velocity vector for the toe trajectory, separated the vector’s horizontal and vertical

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Fig. 1. Typical model of human UUS in waves traveling from wrist to toe. U, center of mass of swimming velocity; c, traveling wave velocity.

components, and determined the time of direction changing from the instant when the horizontal component was greater than the vertical component during upward kicking. The kick frequency (f), non-dimensional kick amplitude (A), average swimming velocity (U), Horizontal distance per kick (Dc), Strouhal number (St), whole body wave velocity (c), Froude efficiency (gF), wavelength (k), wavelength per body length (kBL), and three kick phase duration (Up1st, Up2nd, and Dw) were all considered kinematic variables for observation.

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2.6. Statistical analysis All values are presented as the mean and standard deviation (SD). After performing a normality analysis with the Shapiro–Wilk test, we compared the kinematic variables recorded in the Pre and Post sessions using a repeated t-test. Subsequently, the variables were compared in each kick frequency condition (seven levels, including Pre) using a repeated one-way ANOVA, followed by Sidak’s multiple comparison. A p value <.05 was considered statistically significant. Statistical analyses were conducted with SPSS 19.0 for Windows (Chicago, IL, USA). 3. Results Mean values for the kinematic variables are presented in Table 1. We identified significant differences for both c and gF between the Pre and Post sessions (p < .05). The ratio of f to Pre in each session was slightly lower than the targeted f, which was predetermined and fluctuated (Table 1). According to the repeated one-way ANOVA, a significant main effect of f was observed for A, U, Dc, c, k, kBL, Up2nd, and Dw (p < .05) but not for St and Up1st. Fig. 2 presents representative stick images fixed at CM for each session; the toe coordinate path in each session is superimposed in Fig. 3. We observed a decrement of Atoe that corresponded to an increase in f. 4. Discussion 4.1. Effect of UUS kinematics The aim of this study was to investigate whether variations in the kinematics of UUS, such as swimming velocity and propelling efficiency, were affected by kick frequency during maximal UUS in male swimmers. We identified two main findings in this study. First, U significantly decreased when f was decreased, but showed no significant change when f was increased. Second, St and gF showed no significant change when f was decreased, however gF significantly decreased and St remained unchanged when f was increased. U showed no significant difference between the Pre and Post sessions. Thus, we assumed the swimmers were not fatigued after performing repeated UUS trials. 4.1.1. Swimming velocity and kick amplitude The U value did not change with an increased f (Table 1). In general, U was affected by a combination of A and f of end-effector movement in UUS (Connaboy et al., 2009), and it was considered that human UUS was accomplished by producing a large propulsive force by increasing the momentum of water with up-and-down movement of the feet (Hochstein & Blickhan, 2011; Miwa, Matsuuchi, Shintani, Kamata, & Nomura, 2006). If the swimmers wish to increase f beyond the maximal voluntary f, which means requiring more internal work of locomotion for the swimmers (Zamparo et al., 2002), they must generate larger torque power than it at maximal effort UUS. Therefore, the swimmers could not maintain A during higher f sessions due to the reduction of torque power. Thus, U was not increased during higher f sessions, which indicates the total momentum of water that swimmers generated was constant, regardless of the higher f and smaller A. If swimmers want to increase their speed, U, they should train by increasing f without decreasing A during maximal UUS. Konstantaki and Winter (2009) investigated the effect of six week leg kicking training for competitive male swimmers (an experiment group conducted a kicking training session equivalent to 20% of total training per a week, while a control group was equivalent to 4%) with randomized control design. The authors reported that 200-m kicking time of the training group was shorter (6%) than the control group, and concluded leg-kicking swimming training could enhance exercise efficiency and improve leg endurance. Based on this idea, UUS training should be included in daily training and it could enhance swimming economy of swimmers. When we focused on individual swimmers, some increased their U at 105% F (one swimmer; +1%), at 110% F (three swimmers; average increasing value was +4.6%), at 115% F (three swimmers; average

Variable

The ratio of value to Pre (%) Kick frequency Non-dimensional kick amplitude Swimming velocity Horizontal distance per kick Strouhal number Wave velocity Wave length Wave length per body length Froude efficiency First upward phase Second upward phase Downward phase  

Significant differences from Pre. p < .05. ** p < .01. *

90% F

95% F

100% F (Pre) 105% F

1.83 ± 0.13  1.93 ± 0.16  2.00 ± 0.16  2.26 ± 0.16 2.31 ± 0.20 31.56 ± 3.75  30.65 ± 3.55  29.22 ± 2.83 28.34 ± 2.57 26.50 ± 3.34

110% F

115% F

Post

t-value (Pre vs. Post)

2.33 ± 0.18 26.81 ± 3.48

2.46 ± 0.21  2.28 ± 0.15 1.19 25.31 ± 3.26  27.72 ± 2.80 2.01

F-value (85% F–115% F) 119.86** 28.76**

1.48 ± 0.09  0.81 ± 0.07 

1.49 ± 0.11  0.78 ± 0.06 

1.50 ± 0.09 0.75 ± 0.05

1.60 ± 0.12 0.71 ± 0.06

1.53 ± 0.11 0.67 ± 0.07 

1.58 ± 0.13 0.68 ± 0.06 

1.55 ± 0.14 0.64 ± 0.07 

1.58 ± 0.10 0.70 ± 0.07

0.70 ± 0.09 3.08 ± 0.09  1.95 ± 0.05 0.86 ± 0.01

0.69 ± 0.07 3.18 ± 0.14 1.95 ± 0.05 0.87 ± 0.01 

0.69 ± 0.07 3.21 ± 0.14 1.95 ± 0.06 0.87 ± 0.02

0.70 ± 0.06 3.40 ± 0.16 1.98 ± 0.06 0.88 ± 0.02

0.70 ± 0.07 3.52 ± 0.12 1.96 ± 0.06 0.87 ± 0.01

0.69 ± 0.06 3.59 ± 0.19 1.97 ± 0.07 0.87 ± 0.01

0.70 ± 0.07 3.68 ± 0.14  1.97 ± 0.05 0.88 ± 0.01

0.70 ± 0.08 0.11 3.50 ± 0.19 2.30* 1.96 ± 0.07 1.36 0.87 ± 0.01 1.68

0.37 39.04** 3.09* 6.83**

0.74 ± 0.02 37.2 ± 2.5 17.5 ± 1.4

0.74 ± 0.02 36.8 ± 1.9 17.5 ± 1.1

0.74 ± 0.02 36.6 ± 2.2 17.3 ± 1.6

0.74 ± 0.01 36.8 ± 0.8 17.0 ± 1.3

0.72 ± 0.02  36.5 ± 1.3 16.7 ± 1.0

0.72 ± 0.02  36.5 ± 1.0 16.8 ± 0.9

0.71 ± 0.02  37.0 ± 1.1 16.1 ± 1.1

0.73 ± 0.02 2.62* 36.1 ± 1.1 1.64 17.0 ± 0.9 0.14

18.41** 0.42 3.55**

45.3 ± 2.1

45.7 ± 1.5

46.1 ± 1.7

46.2 ± 1.4

46.8 ± 1.0

46.7 ± 1.4

46.9 ± 1.3

46.9 ± 1.2

83.5 ± 3.1 111.2 ± 5.6

87.6 ± 3.2 108.1 ± 6.0

91.3 ± 5.3 103.2 ± 5.1

104.9 ± 3.9 93.3 ± 5.2

106.2 ± 5.2 94.5 ± 7.0

111.8 ± 4.9 89.2 ± 6.4

101.4 ± 3.5 97.8 ± 3.5

92.3 ± 4.9 113.7 ± 7.1 99.4 ± 5.3 90.9 ± 5.0 98.8 ± 2.1 98.4 ± 1.3 100.6 ± 1.7 101.2 ± 7.2 103.3 ± 5.7 98.0 ± 5.9

93.4 ± 4.5 109.3 ± 2.5 98.9 ± 4.9 93.8 ± 5.2 98.4 ± 1.3 98.7 ± 1.0 100.0 ± 1.4 99.9 ± 4.0 103.4 ± 6.2 98.9 ± 2.4

94.0 ± 4.6 105.8 ± 5.3 98.0 ± 3.4 94.7 ± 4.8 98.4 ± 1.4 98.9 ± 1.3 99.8 ± 1.1 99.5 ± 5.3 102.3 ± 9.0 99.6 ± 3.6

95.7 ± 3.4 93.6 ± 3.3 100.3 ± 4.7 103.6 ± 5.8 98.9 ± 2.0 99.4 ± 0.8 97.6 ± 1.5 99.1 ± 4.3 98.9 ± 7.8 101.3 ± 2.9

98.6 ± 5.0 95.4 ± 3.4 99.2 ± 7.2 105.8 ± 6.3 99.4 ± 0.8 99.4 ± 1.1 97.7 ± 1.3 99.1 ± 2.8 99.6 ± 4.9 100.9 ± 2.0

97.0 ± 5.4 89.1 ± 4.6 100.0 ± 6.9 108.3 ± 4.4 99.5 ± 1.0 99.8 ± 0.6 96.6 ± 1.3 100.5 ± 2.5 95.1 ± 5.1 101.5 ± 2.8

98.8 ± 4.3 97.6 ± 4.8 99.7 ± 5.6 103.0 ± 4.2 99.2 ± 1.7 99.6 ± 0.8 98.7 ± 1.5 98.1 ± 3.7 100.7 ± 7.4 101.5 ± 2.7

1.01 1.61

1.73

9.45** 68.15**

2.79*

H. Shimojo et al. / Human Movement Science 38 (2014) 94–105

Actual value Kick frequency f (Hz) Non-dimensional kick amplitude A (%) Swimming velocity U (ms1) Horizontal distance per kick Dc (m) Strouhal number St (fAU1) Wave velocity c (ms1) Wave length k (m) Wave length per body length kBL Froude efficiency gF First upward phase Up1st (%) Second upward phase Up2nd (%) Downward phase Dw (%)

85% F

100

Table 1 Kinematic values and the ratio to Pre for each session. t-value, and F-value (including Pre).

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Fig. 2. Representative stick images and toe coordinate path during one-kick cycle fixed on the center of gravity at (a) 85% F, (b) 90% F, (c) 95% F, (d) 105% F, (e) 110% F, and (f) 115% F. f, kick frequency; Atoe, kick amplitude; U, center of mass of swimming velocity; c, traveling wave velocity.

Fig. 3. Typical toe coordinate path during a one-kick cycle fixed at the lowest vertical position and mean horizontal position of zero in each session.

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increasing value was +3.4%), thus there were some swimmers who could increase their U by increasing f. This result means many swimmer chose their ‘preferred’ f but the frequency did not replace ‘optimal’ f for some swimmers. Thus, there is a possibility that the optimal value existed near the preferred f and A combination that swimmers chose during UUS (Boitel et al., 2010). During lower f sessions, U values linearly decreased by decreasing f (Table 1). If the swimmers tried to increase U with a lower f, they would need a greater propulsive force during the one-kick cycle, implying that the swimmer’s A should increase (Fig. 3). It seems the swimmers adapted to keep their U at maximal effort. However, this adaptation with a larger A (i.e., lower f) led to a greater resistive force acting on the swimmer due to an increment of cross-sectional area (Cohen et al., 2012); thus, U decreased in this study. Several studies on walking and running provide convincing evidence that most individuals selfoptimize walking and running cadences and suggest that minimizing energy cost may be an important factor contributing to cadence determination (Martin, Sanderson, & Umberger, 2000). In a previous study, the authors stated the possibility that cyclic activities are organized to minimize the demands placed on the neuromusculoskeletal system (e.g., minimizing energy cost, muscle activation, or muscle stress; or maximizing mechanical efficiency). Therefore, it seems that the swimmers naturally chose an optimal f and A to balance the propulsive force to a maximum and the resistive force to a minimum during maximal UUS. However, this speculation did not apply for all swimmers because some swimmers could not determine an optimal f and A combination in this study. Cohen et al. (2012) indicated a faster f becomes net streamwise force and swimming velocity increases, even beyond f for maximal UUS in the simulation study. However, Nakashima (2009) described results from a simulation that did not always apply to actual swimmers, which was confirmed by our results. Connaboy et al. (2009) concluded that there was a lack of empirical research directly examining the effects of changes in end-effector movement frequency on human maximal UUS by reviewing a hundred hydrodynamic UUS studies. Therefore, our findings were important for human UUS study. Further research is expected to investigate the training effect of kick frequency when it is changed during maximal UUS. 4.1.2. Propelling efficiencies The parameter of f, A and Dc have physiological and anatomical constrains, but for swimming more efficiently, it is better to reduce the f and to increase the Dc, as much as possible. This consideration derives from the observation that propelling efficiency of leg-kicking swimming is proportional to the distance covered per stroke for a given speed (Zamparo, Pendergast, Termin, & Minetti, 2006). When f was reduced (85% F, 90% F), A and Dc was actually lager than at Pre but increasing Dc did not compensate for the decrease in f so that the U was also reduced (U = f  Dc). We used St and gF as an index of propelling efficiency, however, propelling efficiency was not improved when decreasing f (Table 1). Similar results, i.e., the change of St and gF were little at different velocity in leg-kicking swimming were reported (Zamparo et al., 2002). Hence, the propelling efficiency seems to be unchangeable when immediate f decreased. The St was defined as the ability to create vortices (Triantafyllou, Triantafyllou, & Grosenbaugh, 1993). In contrast, measures of slip have been used to assess the effectiveness and efficiency of UUS performance in aquatic animals and referred to as gF (Lighthill, 1975). If gF is small, unnecessary energy is lost as excessive amounts of water are accelerated along the body and at the wake (Connaboy et al., 2009), and it reflects that an ability of the swimming body to impart useful kinetic energy to the water is lower (Zamparo et al., 2002). Therefore, the result of gF shows that greater slip occurred during f increased at maximal UUS (Table 1), which suggest the propelling efficiency will be wasted when immediate f increased. More interestingly, when f was increased, A and Dc tended to decrease too. These changes (i.e., stroke length decreasing) were observed also the four swimming strokes (Craig & Pendergast, 1979), which means at maximal velocity a further increase in f is detrimental for performance. By integrating Eqs. (1) and (2), St can be expressed as following equation:

St ¼ Dc1  Atoe ;

ð6Þ

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where Dc and Atoe is horizontal and vertical distance covered during a kick respectively. The equation shows St is unaffected by f, and if St is kept constant, the decrease in Dc is compensated by the decrease in Atoe. At this moment, the cause of these phenomena is not clear yet. According to a previous study (Godoy-Diana, Aider, & Wesfreid, 2008) which investigated wake pattern behind flapping foil by using particle image velocimetry (PIV) method, it revealed that a transition from the typical vortex street (called von-Kármán vortex) to the reverse vortex street happened when the frequency or the amplitude increased beyond an optimal point. Additionally, they presented the dynamical features that was the symmetry breaking of this reverse vortex pattern giving rise to an asymmetric wake at amplitude increased. Thus, we expect the propelling efficiency in UUS might be affected by vortex manner. Most of these fluid mechanics related to propelling efficiency (i.e., slip and creating vortices) are invisible under normal conditions. To clarify the mechanism of propelling efficiency during UUS, future studies are required that combine measurement of vortices around a swimmer, which is referred to as PIV (Hochstein & Blickhan, 2011; Miwa et al., 2006) and measurement of total mechanical and metabolic energy expenditure during UUS (Zamparo et al., 2002). 4.1.3. Body waves and kick phases Linear relationship between c and f in the human flutter kick-swimming was also reported (Zamparo et al., 2002). Similar result was observed in this study (see Table 1, relationship f and c). To control f, joints throughout the swimmer body were oscillated and undulated quickly or slowly (Fig. 2), which could explain swimmers’ adaptation as changing f strategy. kBL represents the undulatory mode (Connaboy et al., 2007), and the undulatory mode of human UUS are similar to the sub-carangiform mode (between 0.5 and 1 kBL; e.g., trout), which means small amplitude of undulation is observed in the anterior aspects of the swimmer’s body (Connaboy et al., 2009). Nakashima (2009) recommend this smaller amplitude of upper-body UUS for actual swimmers because it prevents flow separation around the upper limbs (which leads more resist force). In this study, the swimmers’ kBL were significantly lower during f decreasing sessions (see Table 1, kBL in 90% F), in addition, gF were steady. It seems that a more effective UUS may be achieved during decreasing f sessions than increasing f sessions because the undulatory mode was more effective without sacrificing propelling efficiency. Cohen et al. (2012) investigated net streamwise force history during human dynamic UUS and reported that a peak in thrust generation was observed in near the end of the upward kick, that is, Up2nd and Dw are concerned in thrust force. Therefore, changes in f affect not only kick cycle time but also Up2nd and Dw duration (see Table 1, result of ANOVA in Up2nd and Dw), implying that the thrust force pattern also would be affected. Atkison, Dickey, Dragunas, and Nolte (2013) investigated human UUS performance by considering the two phases as separate. Three phase separations, which was firstly reported by Arellano et al. (2002), may be better for comparing phases within one-kick cycles and for quantifying thrust force deceleration. 4.2. Implications for training The swimmers oscillated each joint to a different amplitude according to the change in f (Figs. 2 and 3). These adaptations could be helpful for coaches to predict how swimmers select their strategy under different task constraints. Although U was not decreased in Post, c and gF were significantly changed at Post. This result indicates varied f affected the swimmer’s undulatory mode, in other words, training over 15 m with UUS for several trials will cause swimmers adaptation. However, we could not determine whether the effect of increasing or decrease f in this study; further studies should investigate this training effect. 4.3. Limitation During movement synchronized with auditory cue (e.g., tapping), the person must intend to move and coordinate the movement with an external referent in real-time (Repp, 2005). Our task constraints imposed different f (which might be ‘not preferred’ for the swimmers) and to listen to the sound, furthermore, to maximize U for the swimmers. Therefore, there might be complexity for

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performing the task constraints. However, to control f during UUS imposingly, our methodology was limited. In an actual race, if coaches want to immediately change a swimmer’s f (or stroke frequency), the swimmer must reproduce their stroke or kick cycle depending on a memorized rhythm. To resolve methodological limitation, reproduced UUS after swimmers memorize a given stroke or kick frequency should be further investigated. 5. Conclusion Increasing kick frequency did not affect average swimming velocity, but decreasing kick frequency significantly decreased the average swimming velocity. Depending on the swimmer, it was expected that incremental changes in kick frequency may increase the average swimming velocity, in fact there were three swimmers whose average swimming velocity was improved. Decreasing kick frequency had no effect on either Froude efficiency or Strouhal number; however, increasing kick frequency had a negative effect on Froude efficiency. 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