Kick Amplitude Research Articles

Variability in depth for national-level swimmers’ freestyle dive starts, push starts and tumble turns

The dive start and tumble turn are key skills in freestyle swimming and are the fastest part of a race (Higgs, Pease & Sanders, 2016, J Sports Sci, 35, 995-1003). Consistency in performing them, to a high-level, is crucial when races can be won by <0.1s. Many studies have investigated dives, tumble turns and underwater undulatory swimming performance, however, very few have examined the effect of depth (West et al., 2022, Sports Med Open, 8). Swimming depth will affect wave drag, total distance travelled underwater and, possibly, kick amplitude. Collectively, these will impact dive and tumble turn performance. The current project aims to quantify the variability of a swimmer’s freely chosen depth when performing a freestyle dive start, push start and turn. Ethics approval for this study was provided by the School of Medicine’s Research ethics board. We aim to recruit 14 participants (7=male, 7=female), over the age of 16 and currently competing at a national level in freestyle events. After a 10-min self-determined warm-up, participants are asked to perform three freestyle dives, push starts, and tumble turns in a randomised order. There are three minutes rest between each task and five minutes between three tasks. Each of the nine tasks will be recorded using a custom-built CONTEMPLAS camera system, using 12 cameras filming at 100Hz. Participants are provided with 5-min to complete a self-determined cool-down. Video recordings will be analysed using SIMI Motion capture to perform manual digitisation. A coefficient of variance analysis and a repeated measures Anova and intraclass correlation to quantify the variability in depth within the dives, push starts and the turns at both an individual and group level. As part of this study, we are also assessing the reliability and validity of an automated digitising software package. The validity and reliability of the automatic digitisation method versus the manual digitisation method was analysed via a Bland Altman analysis to obtain the limits of agreement between the two methodologies. The results are pending, although they will be used to assign individual swimmers with target depth ranges for subsequent experiments that aim to identify the optimum depth for these skills.

Effects of paddles and fins on front crawl kinematics, arm stroke efficiency, coordination, and estimated energy cost.

Paddles and fins are used in swimmers training with different objectives (e.g., increase propulsive areas of hands and feet, improve the feeling of water flow). These artificial modifications of the stroke might be viewed as external constraints of the stroke task, both will either disturb or facilitate swimming modalities, so the coaches should manipulate its use to extract benefits for performance. This study seeks to investigate the precise effects of wearing either paddles (PAD) or fins (FINS) vs. a no-equipment (NE) trial in three all-out front crawl exercises on swimmer kinematics, arm stroke efficiency (), upper-limbs coordination patterns (Index of Coordination, IdC), and estimated energy cost (C). Eleven regional to national-level male swimmers participated in the study (age: 25.8 ± 5.5years, body mass: 75.2 ± 5.5kg, height: 177 ± 6.5cm) and were recorded from both sides of the swimming pool to collect all variables. Repeated measures ANOVA and Bonferroni post hoc were used to compare the variables. Effects sizes were calculated. Time to cover the distance and velocity were higher in FINS swimming, with larger values of stroke length (SL) and lower kick amplitude in comparison to the other trials (PAD and NE). The use of FINS also modified the stroke phases durations by presenting significant lower propulsion time during the stroke in comparison to PAD or NE. Values of IdC were lower (IdC < -1%, so catch-up pattern of coordination) for FINS in comparison to NE. In terms of , using PAD or FINS demonstrate higher arm stroke efficiency than swimming without equipment. Finally, C was significantly higher in FINS swimming in comparison to NE and PAD. From the present results, it should be noted that the use of equipment such as fins deeply modify the structure of the swimming stroke (from the performance-related parameters through the kinematics of both upper and lower limbs to the stroke efficiency and coordination pattern). So, using equipment should be appropriately scaled by the coaches to the objectives of the training session in swimming, and in emergent sports such as "SwimRun", paddles and fins must be viewed as tools to achieve higher velocities to cover a given distance.

Case study on the usefulness of an instrumented constant brake for the evaluation of the propulsive force of the fins in lifesavers.

Background: Assessing physical performance is essential to improve planning and training processes. This assessment is essential in lifesaving, both in its sporting and professional aspects.&#x0D; Objectives: The objective of this study is to explore the suitability of a propulsive force measurement test battery and the usefulness of an experimental power test in lifesaving that yields data on force, power and technique.&#x0D; Method: A world-class athlete has participated in this project. The same battery of tests has been carried out at three times of the season. The tests correspond to the maximum propulsive force test, the average propulsive force test and the experimental power test.&#x0D; Results: The maximum propulsive force (299.75 N - 332.13 N) has improved throughout the season, as well as the mean propulsive force (94.26 N - 94.96 N) and power (25.21 - 37 .59w). Also other parameters such as kick amplitude (164.66 N ± 29.31 - 228.10 N ± 20.07) have increased, while frequency (1.6 Hz - 1.2 Hz) has decreased throughout the season.&#x0D; Conclusions: The tests carried out provide relevant information and they are correlated with each other. The maximum propulsive force test and the experimental power test could provide the most relevant information to prescribe subsequent training.

Changes in Kinematics and Muscle Activity With Increasing Velocity During Underwater Undulatory Swimming.

This study aimed to investigate the changes in kinematics and muscle activity with increasing swimming velocity during underwater undulatory swimming (UUS). In a water flume, 8 male national-level swimmers performed three UUS trials at 70, 80, and 90% of their maximum swimming velocity (70, 80, and 90%V, respectively). A motion capture system was used for three-dimensional kinematic analysis, and surface electromyography (EMG) data were collected from eight muscles in the gluteal region and lower limbs. The results indicated that kick frequency, vertical toe velocity, and angular velocity increased with increasing UUS velocity, whereas kick length and kick amplitude decreased. Furthermore, the symmetry of the peak toe velocity improved at 90%V. The integrated EMG values of the rectus femoris, biceps femoris, gluteus maximus, gluteus medius, tibialis anterior, and gastrocnemius were higher at 90%V than at the lower flow speeds, and the sum of integrated EMGs increased with increasing UUS velocity. These results suggest that an increase in the intensity of muscle activity in the lower limbs contributed to an increase in kick frequency. Furthermore, muscle activity of the biceps femoris and gastrocnemius commenced slightly earlier with increasing UUS velocity, which may be related to improving kick symmetry. In conclusion, this study suggests the following main findings: 1) changes in not only kick frequency but also in kicking velocity are important for increasing UUS velocity, 2) the intensity of specific muscle activity increases with increasing UUS velocity, and 3) kick symmetry is related to changes in UUS velocity, and improvements in kick symmetry may be caused by changes in the muscle activity patterns.

Protected quantum coherence by gain and loss in a noisy quantum kicked rotor

We study the effects of non-Hermiticity on quantum coherence via a noisy quantum kicked rotor (NQKR). The random noise comes from the fluctuations in kick amplitude at each time. The non-Hermitian driving indicates the imaginary kicking potential, representing the environment-induced atom gain and loss. In the absence of gain and loss, the random noise destroys quantum coherence manifesting dynamical localization, which leads to classical diffusion. Interestingly, in the presence of non-Hermitian kicking potential, the occurrence of dynamical localization is highly sensitive to the gain and loss, manifesting the restoration of quantum coherence. Using the inverse participation ratio arguments, we numerically obtain a phase diagram of the classical diffusion and dynamical localization on the parameter plane of noise amplitude and non-Hermitian driving strength. With the help of analysis on the corresponding quasieigenstates, we achieve insight into dynamical localization, and uncover that the origin of the localization is interference between multiple quasi-eigenstates of the quantum kicked rotor. We further propose an experimental scheme to realize the NQKR in a dissipative cold atomic gas, which paves the way for future experimental investigation of an NQKR and its anomalous non-Hermitian properties.

Lower lung-volume level induces lower vertical center of mass position and alters swimming kinematics during front-crawl swimming

We examined the impact of lung-volume levels on the vertical center of mass (CoM) position and kinematics during submaximal front-crawl swimming at constant velocity. Thirteen well-trained male swimmers (21.2 ± 2.0 years) swam the front-crawl for 15 m at a target velocity of 1.20 m s−1 while holding one of three lung-volume levels: maximal inspiration (MAX), maximal expiration (MIN), and intermediate between these (MID). The three-dimensional positions of 25 reflective markers attached to each participant’s body were recorded using an underwater motion capture system and then used to estimate the body’s CoM. The swimming velocity and the vertical CoM position relative to the water’s surface were calculated and averaged for one stroke cycle. Stroke rate, stroke length, kick rate, kick amplitude, kick velocity, and trunk inclination were also calculated for one stroke cycle. Swimming velocity was statistically comparable among the three different lung-volume levels (ICC [2,3] = 0.875). The vertical CoM position was significantly decreased with the lower lung-volume level (MAX: −0.152 ± 0.009 m, MID: −0.163 ± 0.009 m, MIN: −0.199 ± 0.007 m, P < 0.001). Stroke rate, kick rate, kick amplitude, kick velocity, and trunk inclination were significantly higher in MIN than in MAX and MID, whereas the stroke length was significantly lower (all P < 0.05). These results indicate that a lower lung-volume level during submaximal front-crawl swimming induces a lower vertical CoM position that is accompanied by a modulation of the swimming kinematics to overcome the increased drag arising from a larger projected frontal area.

Muscle Synergy of the Underwater Undulatory Swimming in Elite Male Swimmers.

Improving the performance of underwater undulatory swimming (UUS) improves swimming time, so it is important to identify the pattern of muscle coordination in swimmers with fast UUS. This study aimed to identify muscular coordination in the trunk and lower limb during UUS in elite swimmers. Nine swimmers (aged 20 ± 2 years; height, 1.74 ± 0.03 m; weight, 73.0 ± 4.4 kg) participated in this study. Measurements were taken by electromyography of eight muscles: rectus abdominis (RA), internal abdominal muscle (IO), rectus femoris (RF), erector spinae (ES), multifidus (MF), tibialis anterior (TA), and thigh biceps (BF), and gastrocnemius (GS). For evaluation of muscle coordination, “muscle synergy” and “activation coefficient” were calculated using non-negative matrix factorization from electromyographic data. Kick frequency, kick amplitude, swim velocity, and kinematics of the pelvis were also calculated. Kick cycle was divided into two kick phases: downward kick (from the highest toe vertical coordinate to the lowest point) and upward kick (from the lowest point to the highest point). Kick frequency, kick amplitude, and swimming velocity were 1.9 ± 0.3 Hz, 0.45 ± 0.6 m, and 1.8 ± 0.2 m·s −1, respectively. The maximum backward pelvic tilt was 94.4 ± 4.5° and the minimum (forward) was 90.8 ± 5.7°. Three muscle synergy values were extracted from each swimmer during UUS: those involved in the transition from upward kick to downward kick (Synergy 1), downward kick (Synergy 2), and upward kick (Synergy 3). Synergy 1 involved mainly the RF, IO, and RA, which were activated during the turn from the upward to the downward phase. Synergy 2 involved mainly the MF, ES, and TA in the downward kick. Synergy 3 corresponded to the coordination of the BF and GS, which were active in the upward kick. In UUS by elite swimmers, both the upward kick and downward kick followed the trunk muscles involved in the pelvic forward–backward tilt movement, and lower limb muscles were activated. Muscle coordination based on pelvic forward-backward tilt during UUS is expected to contribute to the coaching field for elite swimmer development.

Overall indexes of coordination in front crawl swimming

ABSTRACTThe aim of this study was to propose a group of parameters able to quantify not only arm coordination but also inter limb coordination. These include the well know index of coordination with the relative duration of the stroke phases and two new parameters: the Index of synchronization (Ids) between arms and legs actions; and the Index of inter limb coordination (IdIC) calculated as the relative foot position during successive arm stroke phases. These parameters were compared between experts and amateur swimmers in a maximal front crawl sprint. The influence of arm stroke in leg kick parameters was also assessed, comparing the full stroke condition with a condition without arms actions. Sixty-five per cent of expert swimmers used synchronized limb actions while 95% of amateur swimmers used non-synchronized limb motions. These synchronized expert swimmers also converged towards a specific coordination pattern between foot position and arm stroke phases. In the condition without arms, both groups changed kick rate and amplitude. The present study reveals the interdependency of arms and legs actions and the importance of coordination and synchronization between limbs. Therefore, the proposed group of overall indexes of coordination provides a more complete marker for the analysis of swimming technique.

Incommensurate standard map.

We introduce and study the extension of the Chirikov standard map when the kick potential has two and three incommensurate spatial harmonics. This system is called the incommensurate standard map. At small kick amplitudes, the dynamics is bounded by the isolating Kolmogorov-Arnold-Moser surfaces, whereas above a certain kick strength, it becomes unbounded and diffusive. The quantum evolution at small quantum kick amplitudes is somewhat similar to the case of the Aubru-André model studied in mathematics and experiments with cold atoms in a static incommensurate potential. We show that for the quantum map there is also a metal-insulator transition in space whereas in momentum we have localization similar to the case of two-dimensional Anderson localization. In the case of three incommensurate frequencies of the space potential, the quantum evolution is characterized by the Anderson transition similar to the three-dimensional case of the disordered potential. We discuss possible physical systems with such a map description including dynamics of comets and dark matter in planetary systems.

Nonlinear theory of transverse beam echoes

Transverse beam echoes can be excited with a single dipole kick followed by a single quadrupole kick. They have been used to measure diffusion in hadron beams and have other diagnostic capabilities. Here we develop theories of the transverse echo nonlinear in both the dipole and quadrupole kick strengths. The theories predict the maximum echo amplitudes and the optimum strength parameters. We find that the echo amplitude increases with smaller beam emittance and the asymptotic echo amplitude can exceed half the initial dipole kick amplitude. We show that multiple echoes can be observed provided the dipole kick is large enough. The spectrum of the echo pulse can be used to determine the nonlinear detuning parameter with small amplitude dipole kicks. Simulations are performed to check the theoretical predictions. In the useful ranges of dipole and quadrupole strengths, they are shown to be in reasonable agreement.

Dynamical localization and the effects of aperiodicity in Floquet systems

We study the localization aspects of a kicked non-interacting one-dimensional (1D) quantum system subject to either time-periodic or non-periodic pulses. These are reflected as sudden changes of the onsite energies in the lattice with different modulations in real space. When the modulation of the kick is incommensurate with the lattice spacing, and the kicks are periodic, a well known dynamical localization in real space is recovered for large kick amplitudes and frequencies. We explore the universality class of this transition and also test the robustness of localization under deviations from the perfect periodic case. We show that delocalization ultimately sets in and a diffusive spreading of an initial wave packet is obtained when the aperiodicity of the driving is introduced.

Distribution of joint local and total size and of extension for avalanches in the Brownian force model.

The Brownian force model is a mean-field model for local velocities during avalanches in elastic interfaces of internal space dimension d, driven in a random medium. It is exactly solvable via a nonlinear differential equation. We study avalanches following a kick, i.e., a step in the driving force. We first recall the calculation of the distributions of the global size (total swept area) and of the local jump size for an arbitrary kick amplitude. We extend this calculation to the joint density of local and global sizes within a single avalanche in the limit of an infinitesimal kick. When the interface is driven by a single point, we find new exponents τ_{0}=5/3 and τ=7/4, depending on whether the force or the displacement is imposed. We show that the extension of a "single avalanche" along one internal direction (i.e., the total length in d=1) is finite, and we calculate its distribution following either a local or a global kick. In all cases, it exhibits a divergence P(ℓ)∼ℓ^{-3} at small ℓ. Most of our results are tested in a numerical simulation in dimension d=1.

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

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 (ηF), resulted from a lower f. The aim of this study was to investigate whether changing f affected U and St, ηF 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 ηF were unchanged, but the wavelength per body length (λBL), 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.

Influence of Angles of Attack, Frequency and Kick Amplitude on Swimmer’s Horizontal Velocity During Underwater Phase of a Grab Start

The underwater phase of starts represents an important part of the performance in sprint swimming's events. Kinematics variables that swimmers have to take into account to improve their underwater phase of starts are unknown. The aim of this study was to determine the kinematics variables that improve performance during the underwater phase of grab starts. A three-dimensional analysis of the underwater phase of ten swimmers of national level was conducted. Stepwise multiple linear regressions identified the main kinematics variables that influence the horizontal velocity of the swimmer each 0.5 m in the range of 5 to 7.5 m. The results show that the kinematics parameters change during the range of 5 to 7.5 m of the underwater phase of the starts. For this population of swimmers, the results enable proposals of four principles to improve the underwater phase: i) to be streamlined at the beginning of the underwater gliding phase, ii) to start the dolphin kicking after 6 m, iii) to generate propulsive forces using only feet and legs during underwater undulatory swimming, iv) to improve the frequency of underwater undulatory swimming.

Optimizing kick rate and amplitude for Paralympic swimmers via net force measures

Kicking is a key component of freestyle swimming yet the optimum combination of kick rate and kick amplitude remains unknown. For Paralympic swimmers, with upper and lower limb disabilities, the influence of the kick plays an important role in net force production. To determine optimum kick characteristics, 12 Paralympic swimmers aged 19.8 ± 2.9 years (mean ± s) were towed at their individual peak freestyle speed. The experimental conditions were (i) a prone streamline glide for passive trials and (ii) maximal freestyle kicking in a prone streamline for active trials at different speeds and kick amplitudes. Kick rate was quantified using inertial sensor technology. Towing speed was assessed using a novel and validated dynamometer, and net force was assessed using a Kistler force-platform system. When peak speed was increased by 5%, the active force increased 24.2 ± 5.3% (90% confidence limits), while kick rate remained at ∼150 kicks per minute. Larger amplitude kicking increased the net active force by 25.1 ± 10.6%, although kick rate decreased substantially by 13.6 ± 5.1%. Based on the current kick rate and amplitude profile adopted by Paralympic swimmers, these characteristics are appropriate for optimizing net force.

Pulsar spin-velocity alignment from single and binary neutron star progenitors

The role of binary progenitors of neutron stars (NSs) in the apparent distribution of space velocities and spin-velocity alignment observed in young pulsars is studied. We performed a Monte Carlo synthesis of pulsar populations originated from single and binary stars with different assumptions about the NS natal kick (kick―spin alignment, kick amplitude and kick reduction in electron-capture supernovae in binary progenitors with initial main-sequence masses from the range 8-11 M ⊙ which experienced mass exchange due to Roche lobe overflow). The calculated spin-velocity alignment in pulsars is compared with data inferred from radio polarization measurements. The observed space velocity of pulsars is found to be mostly affected by the natal kick velocity form and its amplitude; the fraction of binaries is not important here for reasonably large kicks. The natal kick―spin alignment is found to strongly affect the spin-velocity correlation of pulsars. Comparison with the observed pulsar spin―velocity angles favours a sizeable fraction of binary progenitors and kick-spin angles ∼5°―20°.

A comparison of the kinematics of the dolphin kick in humans and cetaceans

Prerecorded video footage of 9 female and 13 male Olympic level athletes swimming underwater by using the dolphin kick was analyzed and comparisons of the stroke kinematics were made with a previous analysis of cetacean swimming conducted by Rohr and Fish (Rohr, J. J., & Fish, F. E. (2004). Strouhal numbers and optimization of swimming by odontocete cetaceans. The Journal of Experimental Biology, 207, 1633–1642). The velocities of the swimmers ranged from 1.12m/s to 1.85m/s which corresponded to a range of effort levels. While some swimmers performed the dolphin kick on their backs (dorsal), others employed the prone (ventral) or the side (lateral) position and no distinctions were made between these positions when considering the results. The raw quantities measured were body length L (from the fingertips of the outstretched arms to the tips of the toes), time TL taken by the swimmer to traverse a body length, kick amplitude A at the toes, and the number of video frames per kick. These allowed us to determine the average velocity U of the swimmer, the kick frequency f, the reduced or length-specific velocity U/L (body lengths traversed per second), and the non-dimensional quantities kick amplitude A/L, the Strouhal number fA/U (ratio of tip or toe speed to forward speed) and the quantity fL/U (kicks per body length traversed). Trends of these dimensional and non-dimensional quantities were examined for the swimmers and compared to the cetaceans. Results showed that humans and cetaceans have comparable non-dimensional kick amplitudes, but kick frequency in humans was greater than for cetaceans swimming at equivalent speeds. Human swimmers required up to five kicks per body length traveled, while cetaceans require only 1.3. Length-specific velocities reached a maximum of 0.81 for humans and this was about half that of cetaceans. Human swimmers had a mean Strouhal number of 0.80, which was above the range considered optimal for underwater undulatory propulsion.

PECULIARITIES OF SCALING IN MODELS OF DUFFING OSCILLATOR UNDER ACTION OF KICKS WITH RANDOM MODULATION OF PARAMETERS

We study noise influence on universal properties of period-doubling cascade in a well-defined model of periodically kicked nonlinear dissipative oscillator. Two approaches of noise adding are considered: (i) modulation of kick's amplitude and (ii) modulation of the interval between kicks. We then derive corresponding stochastic discrete one- and two-dimensional maps and provide a detailed study of the noise scaling properties of the Feigenbaum scenario and of the non-Feigenbaum tricritical case. Illustrations of bifurcations trees and Lyapunov exponent charts are given.

Neutron star spin–kick velocity correlation effect on binary neutron star coalescence rates and spin–orbit misalignment of the components

We study the effect of the neutron star spin-kick velocity alignment observed in young radio pulsars on the coalescence rate of binary neutron stars. Two scenarios are considered for neutron star formation: when the kick is always present, and when it is small or absent if a neutron star is formed in a binary system as a result of electron-capture degenerate core collapse. The effect is shown to be especially strong for large kick amplitudes and tight alignments, reducing the expected galactic rate of binary neutron star coalescence compared to calculations with randomly directed kicks. The spin-kick correlation also leads to a much narrower neutron star spin-orbit misalignment.

Sticky orbits in a kicked-oscillator model

We study a four-fold symmetric kicked-oscillator map with sawtooth kick function. For the values of the kick amplitude λ =2 cos (2π p/q) with rational p / q, the dynamics is known to be pseudochaotic, with no stochastic web of non-zero Lebesgue measure. We show that this system can be represented as a piecewise affine map of the unit square—the so-called local map—driving a lattice map. We develop a framework for the study of long-time behaviour of the orbits, in the case in which the local map features exact scaling. We apply this method to several quadratic irrational values of λ, for which the local map possesses a full Legesgue measure of periodic orbits; these are promoted to either periodic orbits or accelerator modes of the kicked-oscillator map. By constrast, the aperiodic orbits of the local map can generate various asymptotic behaviours. For some parameter values the orbits remain bounded, while others have excursions which grow logarithmically or as a power of the time. In the power-law case, we derive rigorous criteria for asymptotic scaling, governed by the largest eigenvalue of a recursion matrix. We illustrate the various behaviours by performing exact calculations with algebraic numbers; the hierarchical nature of the symbolic dynamics allows us to sample extremely long orbits with high efficiency, i.e. uniformly on a logarithmic time scale.