ESTABLISHING COMPUTATIONAL FLUID DYNAMICS MODELS FOR SWIMMING TECHNIQUE ASSESSMENT

Transcription

1 ESTABLISHING COMPUTATIONAL FLUID DYNAMICS MODELS FOR SWIMMING TECHNIQUE ASSESSMENT Matt Keys BEng (Hons) School of Civil and Resource Engineering / School of Sports Science, Exercise and Health The University of Western Australia This Thesis is presented for the degree of Doctor of Philosophy At The University of Western Australia. April 2010

2 Abstract This thesis set out to create a three dimensional active computational fluid dynamics model capable of assessing swimming techniques and enhancing an understanding of the assessment capabilities of the model in practice. Over the past century, numerous studies have measured the passive and active drag of swimmers. Passive drag usually refers to the combination of pressure and viscous forces on a rigid body moving at a constant velocity through water. Active drag is usually described as the combined pressure and viscous forces acting on a swimming body travelling at constant or varying velocities through water. Due to the complexities in measuring active drag, the range of techniques used have not provided any definitive conclusions regarding the accuracy of any single measurement technique over another. More recently, an increased use of mathematical modelling has sought to improve estimates and understanding of active drag. One such method is to use Computational Fluid Dynamics (CFD), but to date simulations mostly have considered passive drag and quasi-static studies using isolated segments. This project focused on extending the technology by providing a full CFD simulation of the entire human body during a normal swimming stroke. It was completed via the following steps: 1. Setting up and validating a passive drag simulation of an elite swimmer. 2. Developing a mathematical algorithm for controlling the movements of the three dimensional model within the CFD environment. 3. Subsequently, using the above models to simulate increasingly complex movements in the sequence of: Dolphin kick underwater. Freestyle kick underwater. Freestyle kick near the water surface. Breaststroke kick underwater. Full freestyle stroke. -ii-

3 Abstract A CFD model capable of all these steps was developed and the model validations revealed sufficient accuracies when analysing changes in active drag during swimming. Hence, the study has advanced the quantitative understanding of how: The influence of segmental contribution to total drag and propulsion, while underwater kicking and freestyle swimming; particularly the effects of ankle flexibility and knee depth. The stroke symmetry in swimmers is related to the total stroke efficiency. The effects of different kicking techniques at the air-water interface to maximise propulsion. Wave effects change the distribution of drag over the body by increasing the drag to the upper sections of the body and decreasing it to the lower sections. The effect of segmental acceleration can act as a mechanism for developing propulsive forces in different movement patterns. Specific propulsion mechanisms in the freestyle arm-stroke rely on underwater pressure variations that are a result of precursor movements and the formation of a wave around the body. The CFD modelling procedure has the ability to allow for changes in the input variables and successfully trial different scenarios. This research used a case study approach with a small group of elite swimmers. With further advancements in kinematic data collection and a greater number of CFD simulations, the amount of new information to be obtained can expand greatly. -iii-

4 TABLE OF CONTENTS Abstract...ii TABLE OF CONTENTS...iv LIST OF TABLES...viii LIST OF FIGURES...x Acknowledgments...xiv Statement of Candidate Contribution...xv Chapter 1 Introduction... 1 Background...1 Statement of the Problem...3 Limitations...4 Delimitations...4 Thesis Structure...5 Chapter 2 Literature Review... 6 Introduction...6 Overview of Competitive Swimming Technique...6 Kinematic Measurement...9 Swimming Fluid Dynamic Theory (Hydrodynamics)...11 Passive versus Active Drag...19 CFD Theory...30 CFD in Sport...34 Swimming CFD Studies...34 Summary...38 Chapter 3 Study 1- CFD Model Methodology and Passive Drag Validation Introduction...39 Methodology...41 Laser Imaging of a Swimmer...41 CFD Methodology...43 CFD Model...46 Boundary Layer Modelling...48 Calibration/Validation of CFD Model...48 Field Trials to Establish Swimmer s Kinematics...53 CFD User Defined Functions iv-

5 Contents Shoulder Joint...73 Flexible Joints...74 Summary...75 Chapter 4 Study 2 - Dolphin Kick Underwater Introduction...77 Methodology...79 Results...80 Discussion...83 Ankle Flexibility Effect on Propulsion...85 Conclusion...88 Chapter 5 Study 3 - Freestyle Kick Underwater Introduction...89 Methodology...90 Results...92 Discussion...96 Overall Freestyle Kick Review...96 Left and Right Side Comparison...97 Comparison Between Freestyle and Dolphin Kicks...99 Conclusion Chapter 6 Study 4 - Freestyle Kick at Water Surface Introduction Methodology Results Discussion Passive Drag Comparisons Overall Comparisons of Active Drag Left Side Segment Comparison Left versus Right Side Comparison Conclusions Chapter 7 Study 5 - Breaststroke Kick Underwater Introduction Methodology Kinematic Data CFD Variables Results v-

6 Contents Discussion Video Comparisons Overall Active Drag Body Component Forces CFD Parameter Sensitivity Conclusion Chapter 8 Study 6 - Full Freestyle Stroke at Water Surface Introduction Methodology Kinematic Data Collection Kinematic Data to Virtual Skeletal Movement Equations Average Velocity Estimation Temporal Data CFD Mesh Sensitivity Results Discussion Overall Drag and Propulsion Feet Force Profile Trunk Force Profile Arms Force Profile Wave Influence CFD Sensitivity Conclusion Chapter 9 Conclusions, Summary and Future Research Directions Summary Study Study Study Study Study Study Conclusions Study Study Study vi-

7 Contents Study Study Study Future Research Direction Study Study Study Study Study Study References Appendices Appendix A - Propulsion and Drag Plots Dolphin Kick Comparison Appendix B - Graphic Plots Dolphin Kick Underwater Freestyle Kick Freestyle Kick Near Water Surface Breaststroke Kick Full Freestyle Stroke vii-

8 LIST OF TABLES Table 3-1 Steady glide drag results and test data. 50 Table 3-2 Steady glide results with boundary layer mesh included. 50 Table 3-3 Comparison of passive drag values from Bixler et al. (2007) study. 52 Table 3-4 Digitised points and corresponding initial coordinates on scanned model. 63 Table 3-5 Joint centres and calculated initial coordinates from scanned model. 64 Table 3-6 Rigid segment lengths from scanned model. 65 Table 4-1 Kinematic data for dolphin kick techniques. 79 Table 4-2 Average momentum (Ns) reduction in swimmer through 1 s of swimming. 80 Table 5-1 Descriptive kinematic variables for the freestyle kick. 90 Table 5-2 Temporal phases of the freestyle (flutter) kick. 90 Table 5-3 Comparisons between total and segment momentum changes for the underwater dolphin kick and freestyle kick at 2.18 m/s. 92 Table 5-4 Average momentum (Ns) change in swimmer through 1s of kicking. 95 Table 5-5 Average momentum (Ns) change in swimmer through 1s of kicking. 95 Table 5-6 Total & segment momentum changes for left & right kick cycles at 2.18 m/s. 98 Table 6-1 Points of interest in the freestyle (flutter) kick. 104 Table 6-2 Differences in passive drag on body components when fully submerged compared to near-surface. 105 Table 6-3 Differences in momentum per second (Ns/s) created for fully submerged and near-surface simulations. 106 Table 6-4 Passive drag on swimmers at various depths - extracted from a towing study by Lyttle (1999). 109 Table 6-5 Velocity and acceleration variations at critical points in a wave cycle. 111 Table 7-1 Critical temporal points throughout the breaststroke kick. 120 Table 7-2 Length error from VICON data (cm). 121 Table 7-3 Alternative turbulence and discretisation models trialled. 122 Table 7-4 Momentum change during the breaststroke kick cycle. 123 Table 7-5 Comparison of underwater breaststroke kick with underwater freestyle and dolphin kick simulations at 1.5m/s. 123 Table 8-1 Critical temporal points through a full freestyle stroke cycle viii-

9 Tables Table 8-2 The momentum (Ns) changes in the swimmer from the full freestyle stroke simulation over one full stroke cycle. 137 Table 8-3 Timing for the temporal phases of the left and right arms through the freestyle stroke ix-

10 LIST OF FIGURES Figure Flow chart detailing the stages of model development. 41 Figure Laser scanned images of the subject for passive drag and lower body motion simulations. 42 Figure Laser scanned images of the subject for full stroke simulations. 43 Figure Overview of the fully submerged streamlined glide model. 44 Figure Overview of the surface model simulations. 45 Figure The triangulated mesh surrounding the head. 47 Figure The triangulated mesh surrounding the hands. 47 Figure Towing testing set-up used for the passive drag measurement (Lyttle, 1999). 50 Figure Sample kinematics from underwater dolphin kicking trial. 54 Figure Sample kinematics from full freestyle stroke trial. 55 Figure Measurement points used to collect freestyle kinematic data. 56 Figure The joints used and the fixed lengths maintained for the 2D trial. 58 Figure Breakdown of each limb into a rigid body rotating around joint centres. 59 Figure From the field trials at each point in time; x, y, z co-ordinates are recorded for each monitoring point. From these, the joining vector and amount of twist in the segment can be determined. 60 Figure Details how co-ordinates are then transferred into a set of polar rotational angles with time. 60 Figure Comparisons of measured and calculated coordinates for the right ankle. 66 Figure Comparisons of measured and calculated coordinates for the right wrist. 66 Figure Average length to measured digitised length for the right forearm. 67 Figure Average length to measured digitised length for the right calf. 67 Figure Comparison of mathematical fitted curve with actual measured θxz angle for the left calf. 68 Figure Comparison of mathematical fitted curve with actual measured θy angle for the left calf. 68 Figure Each node point is referenced back to the predecessor joint to identify its motion. 72 Figure The double ball and socket joint arrangement for the shoulder. 74 -x-

11 Figures Figure Angle of rotation measurement positions. 80 Figure Combined pressure and viscous drag forces over entire body for one full cycle. 81 Figure Combined pressure and viscous drag forces at the knees for one full cycle. 81 Figure Sample pressure plot output of the CFD model. 82 Figure Velocity changes through kicking cycle. 83 Figure Net thrust graph highlighting effects of ankle flexibility on propulsion. 86 Figure Net thrust graph highlighting effects of ankle flexibility on propulsion created by the feet. 87 Figure Net thrust graph highlighting effects of ankle flexibility on the propulsion created by the total body. 87 Figure Total force curve for all body parts combined. 93 Figure Force curves for left and right leg components separately. 93 Figure Force curves for the left and right feet. 94 Figure Feet and knee drag/propulsion curves for the freestyle kick cycle. 94 Figure Sample picture displaying levels of flow velocity and their vector directions. 95 Figure Velocity comparison for freestyle kick kinematic data. 96 Figure Graph of the cumulative momentum loss for each kicking scenario at a velocity of 2.18m/s. 99 Figure Example of output from the CFD simulation detailing the surface deviation over the body as well as velocity vectors. 105 Figure Comparison of the total net force on the swimmer for submerged and nearsurface simulations. 106 Figure Comparison of the left foot net force on the swimmer during submerged and near-surface simulations. 107 Figure Comparison of the left calf net force on the swimmer during submerged and near-surface simulations. 107 Figure Comparison of the right foot net force on the swimmer during submerged and near-surface simulations. 108 Figure Comparison of the right calf net force on the swimmer during submerged and near-surface simulations. 108 Figure The wave profile around the swimmer at 2m/s xi-

12 Figures Figure Critical points through the wave cycle (Barltrop & Adams, 1991). 111 Figure Detailing the wave profile length during the freestyle kick. 113 Figure Left foot rising above the water surface at 0.35s. 116 Figure Right foot emerging from the water at the top of the cycle at 0.21s. 117 Figure Comparisons of calf lengths calculated from the VICON kinematics throughout the stroke. 121 Figure Comparisons of the breaststroke 3D simulation and actual underwater footage of the kicking pattern used by the tested subject. 124 Figure Cumulative momentum loss throughout the breaststroke kick cycle. 125 Figure Total body force throughout the breaststroke kick cycle. 125 Figure Forces on the upper body and hip segments throughout the breaststroke kick cycle. 126 Figure Forces on the thigh and knee segments throughout the breaststroke kick cycle. 126 Figure Forces on the calf, ankle and feet segments throughout the breaststroke kick cycle. 127 Figure Comparisons between various turbulence and discretisation parameters from 1.9 to 2.5s. 127 Figure Displacement, velocity and acceleration data for the left ankle. 129 Figure The air bubbles surrounding a swimmer at the start of a 50m event. 133 Figure Velocity of the centre between the left and right iliac crests through the freestyle stroke. 135 Figure The overall forces on the swimmer throughout the freestyle stroke. 138 Figure The forces on the right and left legs throughout the freestyle stroke. 138 Figure The forces on the trunk, right and left arms throughout the freestyle stroke. 139 Figure Pressure contours when maximum net force occurs during a stroke. 139 Figure Comparison of left leg foot positions with propulsive forces. 140 Figure The left foot coming out of the water during motion analysis testing. 141 Figure The left foot coming out of the water during the simulations. 141 Figure Comparison of left and right ankle joint plantar/dorsiflexion angles throughout the freestyle stroke cycle (using a 6 beat kicking pattern). 144 Figure Angle of the upper trunk to the horizontal throughout the stroke. 146 Figure Static pressure contours showing the wave shape around the swimmer.149 -xii-

13 Figures Figure Pressure below the body at various times along the length of the body. 151 Figure Comparisons of coarse and fine mesh simulations. 153 Figure Comparisons of time averaged coarse and fine mesh simulations. 153 Figure A-1 - Comparison of drag forces on the body during dolphin kick. 178 Figure A-2 - Comparison of drag forces on the hips during dolphin kick. 178 Figure A-3 - Comparison of drag forces on the thighs during dolphin kick. 179 Figure A-4 - Comparison of drag forces on the knees during dolphin kick. 179 Figure A-5 - Comparison of drag forces on the calves during dolphin kick. 180 Figure A-6 - Comparison of drag forces on the ankles during dolphin kick. 180 Figure A-7 - Comparison of drag forces on the feet during dolphin kick xiii-

14 Acknowledgments The author is most appreciative of Dr Andrew Lyttle who spent many late nights digitising the kinematic data, organising the swimmers and sharing all his extensive knowledge of biomechanics needed to complete this project. He was also the driving force behind the Western Australian Institute of Sport (WAIS) becoming involved in this area of study and providing the necessary funding for its completion. Thanks also must go to Martin Fitzsimons and Steve Lawrence from WAIS for continually supporting and resourcing this project. I am also fortunate to have benefited from Prof Liang Cheng s knowledge and understanding of Computational Fluid Dynamics, and for gaining the support of the Civil Engineering department for the study. Thanks too, to Prof Emeritus Brian Blanksby for all his advice and wisdom that enabled the study to be trouble free, combined with the best lesson in English I have ever received. To Jay Davies, the person who originally convinced both myself and Andrew Lyttle that this study could be possible, and was an area of research that should be developed. To the swimmers who provided kinematic data and 3D digital scans, thankyou sincerely. -xiv-

15 Statement of Candidate Contribution I certify that, except where references are made in the text to the work of others, the contents of this thesis and the development of the computation fluid dynamics models are original and have not been submitted to any other university. The thesis is the result of my own work. Matt Keys April, xv-

16 Chapter 1 Introduction Background The aim of the study was to develop and validate three dimensional active motion Computational Fluid Dynamics (CFD) models of a swimmer during a full stroke to understand better the fluid flow around the body, and to calculate the active drag and propulsion forces. Elite level swimming techniques at present generally are derived from a mix of natural genetics, feel for the water, knowledge from experienced coaches, and trial and error methods. Although these techniques are considered to be highly efficient, little is known from a hydrodynamic view point as to what makes any one technique faster than another. Another unknown factor is the percentage of propulsion or drag that is created by each of the body segments at various stages throughout a swimming stroke. Current research in this area has incorporated either one, or a combination of, the following methods to estimate the drag/propulsion effects and flow patterns: Physical testing using force plates, drag lines or towing devices. Analysis and numerical modelling of recorded flow lines and vortex patterns measured by injecting dye or Particle Image Velocimetry (PIV) methods, based on swimmers in a test pool or swimming flume. Entirely numerical modelling using estimations of drag and inertia effects on shapes similar to those of human limbs. -1-

17 Chapter 1 - Introduction Each of these systems has provided valuable information and partially provided some empirical data concerning some of the many questions raised. However, due to their inherent limitations and the highly complex fluid flows around the irregularly shaped human form that is always changing shape and position, none of these techniques have been able to provide a full understanding of what is actually occurring throughout a full swimming stroke cycle. CFD is the science of predicting fluid flow, heat and mass transfer, chemical reactions, and related phenomena by numerically solving the set of governing mathematical equations based on conservation of mass, momentum, energy, turbulence and species. The field of Engineering has used CFD to analyse fluid flow around and through objects to optimise design and performance. Together with the advancement of computer speed over the past decade, it has enabled CFD to model increasingly complex systems. Of the CFD methods that have been developed, this study utilised the finite volume method (FVM) in which the domain is discretised into a finite set of control volumes or cells. A commercial suite of CFD software (FLUENT, Fluent Inc., Lebanon, NH) was used as a basis from which to develop the CFD models. Further complexity was added by developing User Defined Functions (UDFs) to move and re-mesh the cells to represent the movements of the swimmer during stroking. Validation of any numerical modelling is important. When features are continuously added to a CFD model, it is necessary to quantify the accuracy of each parameter in relation to the resultant output. As outlined above, the capability to empirically measure the active drag and propulsive effects on each segment of a swimmer s body while in full stroke is not currently possible. Modern assessment procedures such as PIV can provide some degree of validation due to the location and size of vortices that may be created, although PIV usually provides only a 2D output. The best current method available for validating active drag models is to initially validate the passive drag model. In addition, the forces generated throughout the stroke were compared with the acceleration and deceleration of the body from the actual kinematic data. It was not the intention of this study to provide an exact simulation of a given swimmer during full swimming but to provide the backbone methodology to eventually reach this goal. With the improvement in three dimensional kinematic data collection, increased -2-

18 Chapter 1 - Introduction knowledge of surface roughness, and as more advanced fluid dynamics turbulence and boundary models become available, this initial foray into developing a CFD methodology for swimming can be updated to provide greater accuracy in assessing the actual drag and propulsion. Hence, this study aimed to develop a reasonably accurate CFD model, to provide significant and additional foundational knowledge about swimming technique, that would not be substantially affected by any relatively minor current limitations. Most research to date has listed drag as a positive value. However, throughout this report, any force in the direction of body travel is referred to as propulsion and given a positive value. Any force that is opposite to the direction of travel is referred to as drag, and given a negative value. This allows conventions to be maintained within the same reference frame, similar to the way displacement and velocity are measured. Statement of the Problem The major purpose of this thesis was to develop a three dimensional CFD model utilising the commercial CFD software, FLUENT, in order to estimate the active drag and propulsion on a swimmer throughout an entire stroke; and evaluate the accuracy of the model by validating it against known measured data. More specifically, the studies sought to investigate the use of the tool in the following areas: 1 - Passive drag on a streamlined swimmer. 2 - Active drag/propulsion generated by a swimmer conducting a dolphin kick underwater. 3- Active drag/propulsion generated by a swimmer conducting a freestyle kick underwater. 4 - Active drag/propulsion generated by a swimmer conducting a freestyle kick at the surface of the water. 5 - Active drag/propulsion generated by a swimmer conducting a breaststroke kick underwater. 6 - Active drag/propulsion generated by a swimmer conducting a full freestyle stroke at the surface of the water. -3-

19 Chapter 1 - Introduction Limitations Analysis in the aquatic environment is more complex than on land. Kinematic motion analysis in water is a problematic area. The data obtained from measuring 2D movement patterns with a swimmer completely submerged is less error-prone than the 3D kinematics of a swimmer at the surface. The small difficulties in deriving this data would affect the absolute values of the model output but would have little impact on the creation of a methodology for measuring active drag and propulsion. With the improved measures of 3D kinematics, the accuracy of the computer simulated models would continue to improve. Computational Fluid Dynamics is a developing area and is becoming more accurate and understood with time, and increased computing processing power. Results emanating from these simulations are not exact replications of the real world, but are the most accurate currently available. Best practice from industries such as aeronautical, automotive and the offshore industry would be followed to ensure that these errors are minimised. Delimitations This project was delimited to the set swimming skills listed above under the aims of research, for individuals of similar body shape and technique styles as used by the test swimmer in each study. This was performed in an attempt to control the related influences of active drag that differences in kinathropometry, gender and swimming technique may produce. -4-

20 Chapter 1 - Introduction Thesis Structure This thesis is organised as follows: Chapter 1 introduces the background to the thesis indicating the aims and general understanding behind the study. Chapter 2 reviews the many ways active and passive drag are currently measured during the swimming stroke and an introduction to current status of CFD research in the area. Chapter 3 outlines the methodology used in setting up the CFD models and a basis for validating the initial model against known passive drag test results. An understanding of the principles involved in setting up the motion algorithm for two dimensional and three dimensional motions is also outlined. Chapters 4 to 8 detail the use of the CFD methodology outlined in Chapter 3 on various swimming skills or combination of skills, with the analysis degree of complexity increasing with each chapter. Chapter 9 summarises the thesis, indicates the advantages and disadvantages of using this approach, lists the initial results from the swimming techniques that were analysed as well as future research to further advance the level of knowledge in this area. -5-

21 Chapter 2 Literature Review Introduction A complex interaction of forces exist as swimmers move through the water. To date, understanding the exact mechanisms surrounding the creation of propulsion and minimising active drag during swimming is unresolved. The three options by which to increase swimming velocity are: to increase the total propulsive forces; minimise the total resistive forces; or a combination both. For coaches and sports scientists to effectively apply technique changes via these options; a thorough knowledge of the mechanisms for propulsion generation and drag force development is essential. Overview of Competitive Swimming Technique Components of the race Competitive swimming events at Olympic level are restricted to the four strokes of freestyle (alternatively known as front crawl), butterfly, backstroke and breaststroke. The indoor events range from 50m to 1500m which are all conducted in a standard 50m long pool. Freestyle, Breaststroke and Butterfly races all start from a standing position on a starting block located at the edge of the pool. After diving into the pool to start the race, the swimmer holds a streamlined position under the water. This position is characterised by fully extended legs, feet flexed, arms fully extended overhead with hands overlapping, and the head between the arms. In freestyle and butterfly, swimmers can then perform a number of dolphin kicks or freestyle kicks while moving to break out at the surface of the water whereupon they begin the full stroke. Breaststroke -6-

22 Chapter 2 - Literature Review swimmers are permitted to utilise a single dolphin kick followed by an underwater breaststroke arm stroke and kick during the underwater phase. Footage of the 2008 Australian Olympic Trials shows that the winner of the 50m freestyle spent the first 1.12 s getting the entire body off the starting block and into the water, then completed four dolphin kicks over 1.16 s before the break out to start swimming. The first full arm stroke was completed after a total of 2.72 s in a race completed in less than 22 s. The entire glide time without any kicking was less than 0.2 s and the total amount of glide plus kicking time was 1.16 s. Therefore, these sections of the event make up 0.9% and 5.2% of the race, and the swimming component made up over 87%. The remainder of the time was spent in the air or during the breakout stroke. These ratios would vary between the different strokes, event length and experience levels. A full description and variations in kick patterns can be found in Maglischo (2003) but a brief summary is given below of the three main styles of kick and the freestyle stroke. Underwater kicking- dolphin, freestyle, breaststroke Three main kicking techniques are used in competitive swimming. Traditionally, the freestyle kick is used during freestyle and backstroke events, the dolphin kick is used during butterfly events and the breaststroke kick is used during the breaststroke events. There have been occasional attempts, even at the Olympic Games, to use a dolphin kick near the end of a freestyle event to help maintain momentum and timing. The dolphin kick commonly is used in both the freestyle and backstroke events after the start and turns while the swimmer is fully submerged and in a streamlined position. Freestyle kick The freestyle kick consists of alternating diagonal sweeps of the legs with the downbeat of one taking place during the upbeat of the other. The primary directions of the kicks are up and down. The downbeat is a movement that begins with the flexion at the hip, followed by extension at the knee. The swimmer flexes the leg slightly at the knee and pushes down with the thigh at the hip. At this point the foot reaches the top of its path and its maximum plantar flexion. In a wave-like-motion, the thigh moves down first, followed by the calf and then the foot trailing until the leg straightens out below the line of the body with the ankle flexion decreasing. The upbeat overlaps the end of the downbeat as the thigh begins its path upwards by creating slight hyper-flexion in the -7-

23 Chapter 2 - Literature Review knee. The calf and foot then follow the thigh in an upward path until the thigh is approximately horizontal; the calf and foot continue to move upwards until returning to the top of the swept path. During sprinting, swimmers usually perform six kicks (three left and three right) for each complete arm cycle. During longer events, swimmers may reduce the number of kicks per cycle to four or two, to try and save energy and improve efficiency. Dolphin kick During the dolphin kick, the legs move synchronously through an upbeat and downbeat similar to those of the freestyle kick. A major difference between the dolphin and freestyle kicks is the ability of the pelvic region to be included in the wave-like-motion. The downbeat begins with a downward press of the pelvic region initially followed by the thighs, calves and feet. This additional body component allows greater force and motion of the lower limbs which some consider enables them to generate greater propulsive force. Breaststroke kick The breaststroke kick is very different from the freestyle and dolphin kicks. The phases of the kick are the recovery, the out-sweep, the catch, the in-sweep, and the lift and glide. The kick cycle begins with the feet and lower legs recovering forward from a fully extended position. As they are flexed towards the buttocks, the feet are dorsiflexed and swept outwards as well as forward until they are outside the shoulders and facing back. This is where the catch takes place, a position where a swimmer begins to apply propulsive force in the initial stages of the cycle. From the catch, swimmers sweep the legs outwards and back inwards in a circular motion by extending the thighs and calves simultaneously, until they are completely extended at the knees, and together. From there, the legs are fully extended in alignment with the body and are held in a streamlined position until the next kick begins. Freestyle stroke overview One stroke cycle of freestyle (alternatively known as front crawl) consists of right and left arm-strokes, and a varying number of kicks as mentioned above. The underwater section of the arm-stroke can be divided into five distinct phases: the entry and stretch, -8-

24 Chapter 2 - Literature Review down-sweep, catch, in-sweep and up-sweep followed by an above-water arm recovery. The hand entry and stretch of one arm increases the streamlining of the body during the final propulsive phases of the opposite arm. This occurs when the arm is extended above and in front of the head, and does not generate propulsion. The down-sweep is usually also non-propulsive as it occurs when the hand and forearm move down to a sufficiently deep position in the water with the undersides of the upper arm, forearm and palm of the hand facing backwards to begin the catch. The catch is the phase when the hand moves backwards and slightly outwards away from the body applying propulsive force. The in-sweep then follows with the hand continuing to move backwards relative to the body, and also inwards until the forearm and hand are below the body of the swimmer. From there, the up-sweep begins with the swimmer continuing to move the arm and hand, backwards and upwards towards the thigh before exiting the water. There are also a number of differences in the arm recoveries of swimmers which do not create propulsion but is thought to improve balance, timing and better body positioning for the next arm stroke. Kinematic Measurement Traditional motion analysis in sports biomechanics has involved the use of video based (2D and 3D) motion analysis, and 3D opto-reflective (both passive and active) systems (such as Vicon, Motion Analysis, etc.). The opto-reflective systems are regarded as the gold standard in biomechanical motion analysis. Typically, the video based systems have been used in field settings for deriving kinematics, while the more complex and expensive opto-reflective systems tend to be laboratory based. Richards (1999) reported a root mean square error of between 0.1 and 0.2cm in opto-reflective systems when predicting a 50cm distance. More recently, Elliott, Alderson & Denver (2006) showed that video systems produced larger errors in measuring a known elbow flexion/extension angle when compared with opto-reflective systems. The accuracy of video based analysis is heavily influenced by factors such as the number of cameras used, positioning of the cameras, the type of movement patterns analysed, the size and quality of the image space to be calibrated, and methods of calibration. Hence, reported video based errors in these comparison studies are likely to be minimised when compared with typical field-based situations in which manual digitising of video is used. -9-

25 Chapter 2 - Literature Review Advances such as the advent of micro-electro-mechanical (MEMS) technology, there has also been a proliferation of small, highly accurate and low drift inertial sensors. The potential for of this newer motion analysis technology has attracted a large amount of interest and its use has become increasingly widespread in biomechanics and biomedical community (Giansanti, 2003; Ohgi, Ichikawa, Homma & Miyaji, 2003; Cutti, Giovanardi, Rocchi & Davalli, 2006; Godwin et al., 2006; Cutti et al., 2008). The use of 3D accelerometers in technique analysis have been applied in swimming for single or dual segment analysis, and achieved good correlations with video-derived data (Ohgi et al., 2003; Ichikawa, Ohgi, Miyaji & Takeo, 2006). However, the constrained nature of these types of movement patterns allows the accelerometer output to be optimised based on expected paths of motions. Unfortunately, the use of accelerometers alone for the reconstruction of full body joint kinematics has been found to be insufficient (Giansanti, 2003). Independent analyses of the static and dynamic errors for complete inertial units have displayed results that are within the manufacturer s specifications (RMS error of 2-3, depending on the inertial sensor), with lower errors being recorded at lower movement speeds (Cutti et al., 2006; Godwin et al., 2006). These errors are larger than those typically reported for optical movement analysis systems based on infrared cameras (eg. VICON) (Cutti et al., 2006). However, the results are likely to be comparable to field testing 3D video motion analysis using manual digitising methods. Cutti et al. (2008) further determined that the inertial sensor units reported similar results to a concurrent Vicon analysis when using the same upper body anatomical calibration protocol. Motion analysis in the aquatic environment is especially challenging and the use of opto-reflective motion analysis in the pool is not feasible. Likewise, there are significant technical hurdles to overcome prior to incorporating a full body inertial sensor system as a non-invasive method of obtaining accurate kinematic information. This also would require the ability to transfer the output of the inertial sensor results to an anatomically based kinematic model. Even manual video based motion analysis is complicated by the swimmer moving through two different mediums of air and water; refraction considerations in the underwater footage and surface turbulence obscuring body landmarks. -10-

26 Chapter 2 - Literature Review Swimming Fluid Dynamic Theory (Hydrodynamics) The two main effects governing the force of a fluid at any point on an object are pressure, which acts perpendicular to the surface; and shear stress, which acts parallel to the surface at the point (Gerhart, Gross & Hochstein, 1992). It is the integral of these pressures over an entire object that culminates in the overall force on an object: r F = pnda ˆ + τ tda w ˆ where n and t are unit vectors, perpendicular and tangential to the surface at each location; and p and τ w are the pressure and shear stress, respectively. Determining the pressure and shear stress at each point over an entire body is not a simple procedure. Hence, simplified methods have been established to enable a quicker, but not always accurate, estimation of the total force on an object. Fluid force equation The force in each direction on a body with respect to time is best described using Morrison s equation (Barltrop & Adams, 1991; Techet, 2004), which is a combination of inertial and drag terms: 1 F( t) = ρ C VU& m + ρcd AU U 2 inertial term drag term where ρ is the density of the fluid, U is the velocity of the object relative to the fluid, U. U is utilised to maintain the direction of velocity, A is the area of the object in the direction of the force, V is the volume of the object, and C m and C d are the inertial and drag coefficients, respectively. This equation also can be adapted for rotation by substituting rotational variables for the translational variables. -11-

27 Chapter 2 - Literature Review Coefficient of drag and inertia Morrison s equation is highly dependent on the two coefficients that are used, namely C d and C m. Any error in these values would directly translate into an error in the overall forces on an object. For many common shapes, values for these coefficients have been calculated through experimental testing. The drag coefficient has been found to vary significantly, depending on the velocity and density of the fluid that surrounds it, and both coefficients vary with the size and shape of the object. In swimming, C d has been reported to be between 0.65 and 0.75 for a swimmer in the most streamlined position at the surface (Havriluk, 2005), and the drag coefficient of a submerged human body was estimated to be ~0.30 (Bixler, Pease & Fairhurst, 2007). Recently, Vennell, Pease & Wilson (2006) confirmed that the drag coefficient varies with velocity for the human body. This relationship is not traditionally considered in swimming research, but fluid mechanics commonly refers to the drag coefficient varying with shape, surface roughness, velocity, and viscosity. The two distinct conditions of flow around a body are referred to as laminar and turbulent. Laminar flow is characterised by smooth motion of fluid in layers. Turbulent flow is characterised by the random three-dimensional motion of the fluid particles superimposed on the mean motion (Gerhart et al., 1992). For the same ratio of velocity, density, size and viscosity of an object in a fluid, it was found that the drag coefficient and whether flow is laminar and/or turbulent were similar. The Reynolds number was developed to assist with these comparisons. Reynolds number The Reynolds number which defines the magnitude of the inertial to the viscous forces on the flow particles acting on a body can be calculated by Re = ρul µ where, ρ is the fluid density, U is the body s velocity; L is the characteristic length of the object in the direction of the flow and µ represents a constant known as viscosity (Gerhart et al., 1992). -12-

28 Chapter 2 - Literature Review Laminar versus turbulent flow in swimming For a smooth, flat plate with no surface irregularities, the transition from a laminar to a turbulent flow occurs at Reynolds numbers of Therefore, at a velocity of about 2.5 m/s, which is common during the streamline phase of starts and turns, only about 20cm of the body length (i.e. only the hands) remains in a laminar flow. That is assuming that this transition occurs at the same Reynolds number, if not lower, for the human body in a streamlined position. Skin roughness, which depends on the height and shape of irregularities on the surface, influences the amount of random motion of fluid particles and causes the transition to occur even earlier under real conditions. Transition also occurs at even lower Reynolds numbers in decelerating flow, as is the case for gliding bodies, than for bodies moving with a constant velocity (Gerhart et al., 1992). Thus, it can be concluded that, for the ranges of Reynolds number corresponding to when the human body is gliding in competitive swimming, turbulent flow is dominant along almost the whole length of the swimmer. During active swimming, the majority of the body is accelerating and decelerating in a turbulent flow. Thus, any conventional simplifications of fluid forces on a body need to be treated with caution. Components of drag used in swimming Traditionally, swimming research has adapted these concepts by separating the forces on a body into the three categories of friction, pressure and wave effects (Karpovich, 1933). Alternative terms are skin drag, form drag and wave drag, respectively. Friction (or skin drag) Frictional resistance or skin drag is the contribution to the drag that exists due to the presence of the shear stress applied by the fluid. Decreasing roughness to create a smoother surface decreases the amount of the frictional resistance for a body. Shaving hair off the body and legs, but not the forearms where drag is beneficial for propulsion, can reduce frictional drag. Previous studies have reported between 21% and 23% reduction in the physiological cost at maximal swimming velocities when -13-

29 Chapter 2 - Literature Review compared to an unshaven condition (Sharp, Hackney, Cain & Ness, 1988). Wearing a latex cap, and tight swim suits made of a sheer fabric with minimal seams and edges, have been suggested as other methods of reducing frictional drag (Rushall, Holt, Sprigings & Cappaert, 1994). Previous studies have estimated that a typical female competitive swimming suit worn in the 1970s adds approximately 9% to the total body drag, as calculated from towing trials with and without a swimming suit (Van Manen & Rijken, 1975). Quantifying the contribution of the frictional drag to total drag has been extremely difficult. Using CFD analyses, Bixler et al. (2007; explained later in this chapter) attempted to differentiate between total drag and frictional drag, but many assumptions were still made. Generally in water, friction drag is influenced by surface roughness and the velocity of the object relative to the fluid, as well as any changes to body position (e.g. streamline configuration). Pressure (or form drag) Pressure forces (not including inertial pressure forces which are detailed later) result from differences between pressure at the leading and trailing edges of the body. Moving along the body, the fluid particles near the surface are slowed down by the wall shear stress as a result of the fluid moving along the object. When the momentum of faster moving fluid near the body surface is insufficient, the flow cannot follow the curve of the body and separates from the surface. Boundary separation results in the formation of a relatively low-pressure region behind the body (Gerhart et al., 1992). This region, which is deficient in momentum (i.e. a lower relative velocity in the direction of flow), is called wake although wake is not necessarily the product of separation (Hoerner, 1965). Separation of the flow from the body leads to the formation of large and small eddies at the downstream part of the body, and results in changes to the pressure drag (Gerhart et al., 1992). The total pressure force is equal to the amount of pressure difference between the front and rear of the swimmer, integrated over the area to which the pressure is applied. Numerous studies have revealed that certain actions such as having the head above the water, turning the head to breathe, lowering the legs, having legs and arms abducted, -14-

30 Chapter 2 - Literature Review and body rolling during the streamlined glide on the surface would increase the total forces mainly due to an increase in the projected area (Counsilman, 1955). During these actions, parts of the body protrude beyond the maximum cross-sectional area of the chest, increasing the projected area and, consequently the pressure forces. The importance of form drag was demonstrated by swimmers of similar body size (height and mass) recording very different active drag values (Kolmogorov & Duplishcheva, 1992). Body inclination also is important in passive drag studies because it increases the frontal surface area (Alley, 1952; Clarys, Jiskoot & Lewillie, 1973). An increase in the angle of attack, or the angle of the body to the direction of flow, can also increase the projected area (Bixler et al., 2007). Because of the effect of chest cross-sectional area on the pressure drag, some anthropometric parameters of chest girth, depth and breadth were significantly correlated with drag force values (Chartard, Lavoie & Bourgoin, 1990; Lyttle, Blanksby, Elliott & Lloyd, 1998). In addition to the anthropometric parameters, the shape and the contour of the body also affect the pressure forces because they determine how the flow moves over the body. Counter-intuitively, turbulence can be produced deliberately to delay separation and reduce drag, such as dimples on a golf ball. The dimples produce turbulence in the layer closest to the ball. By slowing down the fluid closest to the surface it reduces the momentum and delays the onset of separation. Recently turbulators and turbulence amplifiers have been designed by some swim suit manufacturers to increase the turbulence near the surface to delay or minimise separation to reduce drag. Despite these claims by the manufacturers, no empirical research has been released by these companies. As with frictional resistance, pressure resistance is hard to quantify experimentally because the overall force on a body is all that can be detected. The overall force is a combination of both pressure and shear stress. However, as with frictional drag, changes in velocity and surface roughness are likely to affect pressure forces on an object of the same size and body position in water. Wave forces As a body moves through the water, it dissipates energy into the water. When the body is completely submerged and not near the surface, this energy is dissipated through turbulent eddies that transfer it into heat through friction. When the body is near the -15-

31 Chapter 2 - Literature Review surface, part of the energy from the moving body is used to lift the water against gravity and forms waves on the surface (Vorontsov & Rumyantsev, 2000). Vorontsov & Rumyantsev, (2000) suggested that wave drag is related to the Froude number (Fr), which determines the ratio of inertial to gravitational forces applied to fluid particles. This dimensionless ratio can be quantified as: Fr = V c V gl where v is the velocity of the moving body, c is the velocity of the wave generated, L is the length of the body in direction of flow and g is the gravitational acceleration constant. It is believed that the wave drag increases with the Froude number although this is dependent on the shape of the object. Extending the arms forward increases the body length, thereby reducing the Froude number which reduces the wave drag when compared to a posture with the arms by the sides of the body. For example, it was reported that having arms by the sides results in 21.5% more passive drag when compared with the streamlined position. However, increasing the length also increases the Reynolds number which can reduce the drag coefficient. Hence, the force changes can not solely be a result of changes to wave effects. The Froude number has been used to indicate a limiting velocity for a swimmer gliding on the surface. It was suggested that, at the Froude number of 0.45, where the swimmer with an extended height of 2.5 m reaches a speed of 2.23 m/s, the wave length is equal to the extended height of the swimmer, and this would be the maximum velocity a swimmer could achieve (Vennell et al., 2006). Nothing stops the swimmer having a shorter length than the length of a wave. However, it may change the distribution of wave forces that then require a greater increase in propulsive forces to increase velocity. This would not result in a maximum potential speed while swimming. The effects of wave forces on the body are also dependent on the depth at which the body travels (Barltrop & Adams, 1991). At a depth of three times the body thickness, the forces thought to be associated with wave effects are reported to become negligible. Its maximum value is when submerged just beneath the surface. Recently, Lyttle et al. (1998) and Vennell et al. (2006) established that the wave forces are negligible at a -16-

32 Chapter 2 - Literature Review depth of about 0.6 m underwater. It was found that, at a velocity of 2.5 m/s on the surface, the wave drag contributes to at least 40% of the total resistance in a streamlined glide position; while at 2 m/s and depth of 0.4 m, the wave drag corresponds to only 15 % of the total drag (Vennell et al., 2006). This is contradictory to traditional wave theory which claims that a wave created at these swimming velocities (Barltrop & Adams, 1991) would have an effect up to 2m below the surface. In this case, it is not the wave drag that is reduced, but the ratio of energy that is transferred to the water in the form of sub-surface turbulence or wave effects. Perhaps the amount of energy transferred into wave energy is reduced when gliding at these depths. But this does not discount the effect of a wave when a swimmer pushes off after a turn into a wave created by themselves, or a swimmer travelling in the other direction. Separating the effects of wave drag from those of surface friction and pressure effects is a difficult proposition, and any of these results should be treated with caution. However, factors that will affect the wave force on a body would be the velocity of the body relative to the water, and the depth of the body below the surface. Inertial forces A common reference in swimming and fluid dynamics literature is for inertial forces to be listed as added mass. The added water mass concept has become recognised as a potential contributing factor in the total resistance to motion in the water (Ungerechts, 1983; Pai & Hay, 1988; Coleman, Persyn & Ungerechts, 1998; Klauck, 1998; Ungerechts, Daly & Zhu, 1998). As mentioned previously, the forces on the body are the result of only two effects, the pressure perpendicular to the surface and the shear stress parallel to the surface. When a fluid accelerates, it is the result of a pressure differential in the fluid (Gerhart et al., 1992). When a body accelerates through water it imposes a force on the fluid which results in a distributed pressure near to where the body is moving. This increased pressure then provides the necessary influence to accelerate the fluid. This increased pressure, either from the fluid accelerating or a body accelerating in water, then creates a localised pressure which imposes a force on the object. The sum of this pressure over the surface of the body creates the forces associated with inertia. Calculating this pressure at each point is difficult and simplifications have been made such as Morrison s equation referred to above. An -17-

33 Chapter 2 - Literature Review adaptation, of the inertial component of the equation for the commonly used term added mass would be: F inertia = ρ C U& = ( ρ + C ) U& m am where C am is just the added mass, whereas C m is the inertial (or added mass) coefficient. However, the formula is essentially the same, with the coefficients being strongly related to the force. Therefore, any error in the coefficient would be passed on directly to the force. In principle, every fluid particle would accelerate to some extent as the body moves, and the added mass is the weighted integration of this entire mass (Barltrop & Adams, 1991). Another simplifying assumption is that a fraction of the boundary layer moves with the same speed as the body and the remaining part stays still. The thickness of that layer is another way of determining a coefficient to be used generally for different shapes and sizes of swimmers or objects. Generic values for these coefficients could be obtained experimentally but would differ from one swimmer to the next. Hence, the error within calculations would be as large as the variation in the sizes and shapes of the swimmers tested. As with the drag coefficient, the inertial coefficient or added mass coefficient decreases with improvement in streamlining. For a porpoise, the added mass coefficient is about (Lang & Daybell, 1963). Klauck (1998) quantified the added mass of 18 swimmers during time dependent acceleration. Swimmers were accelerated from rest using a semi-tethered towing device. The time dependent velocity curves were separated into the velocity and acceleration dependent components of the water resistance to yield the added mass for each swimmer. Results showed that the added water mass were in the order of 30-70kg, and varied substantially between individuals. This added mass would equate to a coefficient of between 0.3 and 0.8, significantly greater than that of the porpoise. The more streamlined a body, together with less capture water mass zones, the less the added mass. By adopting a streamlined position, the swimmer decreases the size of the wake, and the amount of inertial drag or added mass moving with the swimmer. -18-

34 Chapter 2 - Literature Review For a body accelerating in water, the normal inertial coefficient is listed as C m -1 (Techet, 2004) and assumes that the object has a zero internal mass. With humans having a density very close to that of water, using the same C m value for water acceleration as body acceleration would take into account the additional force associated with the movement of the mass of the body itself. Differentiating these inertial forces from the wave, pressure and shear stress/friction effects, also would be a difficult task and the overall force should be regarded as the best measure. However, it can be seen that changes to the acceleration of an object relative to the surrounding water would be the predominant factor in changes to inertial forces. Improvements in the streamline position can reduce inertial drag but correct form during the propulsion phase of the stroke can positively increase the inertial forces generated by the arms and legs. Total force Total force is regarded as the combination of the friction, pressure, wave and inertial effects, and is the easiest force to measure as it represents the overall effect on the swimmer. It is this total force that is used to estimate the passive and active drag for different streamline positions and strokes. For each swimmer, changing surface roughness, velocity, acceleration, depth below the water and body positioning all change the total force on the body. Passive versus Active Drag Considerable research exists in both passive and active drag when swimming (Counsilman, 1955; Clarys, 1978; Kolmogorov & Duplishcheva, 1992; Toussaint and Hollander, 1994; Arellano, Terres-Nicoli & Redondo, 2006). Passive drag usually refers to the combination of both pressure and shear stress effects on a rigid body moving at a constant velocity through the water. Active drag usually describes the combined pressure and shear stress effects acting on a moving body travelling at a constant or varying velocity through water. There are also several reviews of the different research methodologies to measure active and passive drag, along with a critique of the inherent problems and benefits of each (Lyttle, 1999; Wilson & Thorp, 2002). Estimations of -19-

35 Chapter 2 - Literature Review active drag appear to have the greatest degree of uncertainty, although steady progress has been made towards more advanced methods of refining these measurements. Passive drag studies Early experimental research into passive drag involved towing swimmers behind a rowboat and measuring the resistance with a dynamometer (DuBois-Reymond, 1905, cited in Karpovich, 1933) and towing swimmers by means of a windlass on shore (Liljestrand & Stenstrom, 1919, cited in Karpovich, 1933). In 1933, Karpovich provided a more controlled examination of passive drag in swimming. An electric motor was used to tow the swimmers along the length of a pool with the tension of the towing line and the velocity of the swimmer being recorded graphically on a resistograph. It is unclear whether the towing rope was inelastic with increases in tension, or whether the velocity of the swimmer could be accurately and consistently controlled. Eleven adult male and three adult female swimmers were towed at the surface in the prone glide position, at velocities of 0.47 and 0.97 m/s; and the supine glide position at velocities of 0.73, 0.81 and 1.18 m/s. Although the velocities were not matched for the prone and supine streamline positions, resistance was higher over the velocity range when the swimmer was supine. Extra trials also were performed with balsa wood secured between the legs in order to counteract the feet sinking at the lower velocities. However, insufficient methodological details were published to determine the exact research design used by Karpovich (1933) and the analysis appeared to use a case study approach. No indication of the level of expertise of the swimmers was provided. This may have introduced variance into the passive drag data, given that the experience level could influence streamlining proficiency (Chatard et al., 1990). Passive drag forces were only reported for velocities between 0.47 and 1.48 m/s, despite references within the discussion to towing swimmers at velocities greater than 1.5 m/s. The effects on passive drag of lifting the head, breathing, accelerating and wearing a bathing suit also were examined by Karpovich (1933), although full data were not reported. Raising the head from a horizontal position, until the eyes were just above the water level, did not increase the water resistance appreciably. Turning the head to the side to breathe, resulted in approximately 7 N of extra drag force at a velocity of 1.5 m/s -20-

36 Chapter 2 - Literature Review compared with prone, streamlined gliding. Resistance also increased when accelerating to a given velocity than when the swimmer was towed at a uniform rate, although this change was not quantified. Researchers also concluded that the fit of the bathing suit was more important than the material of which it was composed when comparing glides in the nude, silk suits and woollen suits. Alley (1952) provided a more extensive analysis of the passive drag experienced by a single elite level male swimmer to eliminate the introduction of extraneous factors such as body shape, body density and skill level. To measure the passive drag forces, Alley (1952) suspended a platform over the water by cables. An electric winch towed the swimmer at the water surface toward the apparatus in a prone streamline position, with the subject s head slightly inclined. A spring scale was attached to the platform and to the side of the pool to measure the forces exerted on the platform by the swimmer. Alley (1952) recognised that using a spring scale permitted too much swinging motion of the apparatus and suggested that, in future, a more stable apparatus be used. Towing velocities between 0.34 m/s and 1.94 m/s were used. Trials at the three slowest velocities of 0.34, 0.45 & 0.63 m/s were repeated, with and without balsa wood floats around the legs (Alley, 1952). Since then, the most common method used for studying passive drag forces in human swimming has been to tow subjects at various velocities, depths or body positions using electro-mechanical motors or weights and pulley systems to more accurately control towing velocities (Counsilman, 1955; Kent & Atha, 1971; Clarys et al., 1973; di Prampero et al., 1974; Clarys et al., 1974; Clarys & Jiskoot, 1975; Jiskoot & Clarys, 1975; Van Manen & Rijken, 1975; Miyashita & Tsunoda, 1978; Clarys, 1979; Clarys, 1985; Ria, Bernard, Falgairette & Roddier, 1987; Chatard et al., 1990a & 1990b; Kolmogorov & Duplishcheva, 1992; Kolmogorov et al., 1997; Maiello et al., 1998, cited in Lyttle, 1999). Small errors have existed with this method in terms of verifying the error in the testing equipment due to sensor drag effects and friction through the equipment (Bixler et al., 2007). A previous study on the intra-day reliability of passive drag when using a towing system revealed a coefficient of variation values of between %, at two different depths and two different velocities. A coefficient of multiple determination (R2) value of 0.998, indicated high intra-day reliability (Lyttle, Elliott, Blanksby & Lloyd, 1999). Inter-day reliability, as assessed by retesting a -21-

37 Chapter 2 - Literature Review swimmer on multiple days, also showed a strong correlation (R2=0.89) and no significant differences (p=0.15) between testing sessions (Lyttle et al., 1999). As these towing methods quantify the total drag force, it is difficult to differentiate between what proportion of the total force is composed of frictional drag, pressure drag and wave drag. Estimations of the contribution of wave drag to the total drag force at different depths have been investigated by Jiskoot and Clarys (1975); Lyttle et al. (1998) and Vennell et al. (2006). The results of Jiskoot and Clary (1975) were contrary to the other two studies, with higher passive drag values being recorded at 0.6m underwater than recorded at the surface. This is likely a result of the towing device used by Jiskoot and Clarys, which possibly allowed the swimmers to be towed in a partially submerged position. This is not applicable to human swimming given the inability of humans to hydroplane across the water surface. Lyttle et al. (1998) and Vennell et al. (2006) found that wave drag was not significant at a depth of 0.6m underwater, and that this has implications for optimal gliding depths during the underwater phases of swimming. However, these results do not take into account the effects of incoming wave fronts occurring during swim turns as a result of the inbound swimming, which could conceivably increase the depth at which wave drag becomes negligible. Active drag studies One of the first methods of measuring active drag was to use a fixed line method of tethered swimming. The swimmer swam against a line connected to a set of weights or a tension sensor device and the direct maximum force was measured (Counsilman, 1955). The main problem with this technique was that, due to the swimmer being stationary, the different stroke technique produced drag and inertial forces results that could not be related directly to typical swimming. The expected benefits of keeping a streamline shape and efficient stroke technique would be ignored as well as any effect wave creation on performance. As previously mentioned, a common technique for measuring passive drag was to tow a swimmer through the pool at a fixed velocity with the tension force recorded via a towline. A variation of this technique was also used to measure the net force while swimming with a vertical rod attached from the waist to a towing carriage moving along -22-

38 Chapter 2 - Literature Review at a set speed with the swimmer (Clarys et al., 1973; Clarys, 1978; Clarys, 1985). Subjects were tested at six to ten velocities (based on individual maximum free swimming velocity) while performing the freestyle stroke. Recording a positive force indicated that the swimmer created higher active drag forces than the propulsive forces produced while swimming at a given velocity. A negative recorded force indicated that the swimmer produced greater propulsion while swimming than the active drag force created. At a zero force level, the swimmer was maintaining the speed of the towing carriage, which indicated that the propulsive force equalled the resistive force. A curve was fitted to the forces recorded at each of the velocities and extrapolated to zero velocity. The extrapolated force at zero velocity was added to the original curve to obtain the swimmer s active drag. When extrapolating the drag-velocity curve to zero velocity, one assumes that the propulsive forces are constant at all velocities. However, with the forces on body components being a combination of velocity drag (pressure and frictional), wave drag and inertial forces, any assumptions made during extrapolation can influence the result greatly. Decreasing the velocity of the system to reduce the extrapolation then brings the system back to the original tethered swimming approach that was used, with its own problems as discussed above. A similar method was used by Glazkov and Dementyev (1977) and Takagi et al. (1997) to calculate active drag in the freestyle (front crawl) stroke. In a progression from the towing approach, a technique was developed where an object with a known hydrodynamic drag was towed behind the swimmer (Kolomogorov & Duplishcheva, 1992). The swimmer swam normally without the towed object, and again with the towed object. Assuming equal power output between the two trials, the difference in swimming speeds was used as a basis for calculating the active drag. One of the main problems was the reliance on the swimmer to duplicate the same technique at the same energy level for both swims. These towing and pulling systems also slightly change the balance of the swimmer in the water by applying additional force to the midsection of the swimmer. Even if the swimmer was able to repeat the same technique without being influenced by the towed object, the known hydrodynamic properties would vary in a similar way to the changes in forces on a swimmer (i.e. frictional drag, pressure drag, wave drag and inertial drag). As the object is behind the swimmer, the velocity at which the swimmer travels would govern the amount of disturbed water or waves through which the object is pulled. Assuming the object is always submerged in a -23-

39 Chapter 2 - Literature Review constant velocity laminar stream, which is an idealisation, would create inaccuracies in estimations. Also, determining the disturbed water and wave properties on the object would almost be as difficult as determining them on a swimmer. An alternative to the line tension systems was the Measure Active Drag (MAD) technique (Hollander et al., 1986; Toussaint et al., 1988). Swimmers push off a number of force panels spaced along the base of the pool while using an arms only stroke. Provided the swimmer used only the force when pushing against the force plates for propulsion, the average force measurement could be used to estimate the drag on the swimmer s body without using any towlines. Comparison of the MAD results with the tow line showed the method produced a lower average value of active drag (Wilson & Thorp, 2002). Rushall et al. (1994) analysed the lift and drag forces on the forearm and hand, at various angles and speeds. They found that the hand contributed twice the force of the forearm at 1m/s, but the forearm contributed 15% greater force than the hand at 2m/s. These results show the potential errors with the technique used in the MAD system. Depending on the speed of the swimmer, less than half the actual propulsive force would be measured as there is no way to discount the fluid forces on the forearm or hand before striking the plates. This may be the reason that lower average propulsive forces are reported for the MAD tests than found with the tethered approaches (Wilson and Thorp, 2002). An alternative method could be to use pressure sensors connected to the hand and forearm as a method for measuring the change in pressure force with time. From these pressure readings, together with approximations of area, forces are derived. This has the added benefit of measuring the pressure and force throughout the stroke (which the MAD system did not). However, the cumbersome wire set-up and pressure panels could alter the flow paths and pressure forces which could also lead to different results. No published research has used this approach but attempted trials have shown that, to estimate the total force on a limb when only the pressure at a single point is obtained, could again lead to large extrapolation errors. In addition to attempts at empirical measurement of physical forces from a swimmer while swimming, a number of researchers are using non-restrictive mathematical methods to estimate the amount of active drag (Toussaint 2006; Ungerechts, Persyn & -24-

40 Chapter 2 - Literature Review Colman, 1999). A swimmer moves through the water by transferring energy into the water. This energy becomes visible in the water in the form of waves and turbulence. In combination with some of the direct measurement techniques (such as the MAD system), the size of the wave produced is also measured to determine the transfer of energy to wave energy (Toussaint, 2006). While this method can reasonably measure the energy in the wave area that has moved away from the swimmer, generally there are many other areas where the wave is created and then disturbed by another part of the body. As these disturbed waves cannot easily be measured, one can only account for a percentage of the forces. In addition, the amount of energy transferred into turbulence cannot be measured using this technique. The energy transferred into waves is a combination of all the forces (frictional, pressure, inertial and wave) and cannot be identified solely as the wave drag. Another method that fluids use to dissipate energy is through turbulence. Turbulence is unsteady, irregular motion in which transported quantities (e.g. mass, momentum) fluctuate in time and space. It is identifiable by swirling patterns, characterised by turbulent eddies or vortices. A recently popular technique titled Two Component Particle Image Velocimetry (2C PIV) has attempted to measure the size and rotational velocities of the larger vortices in two dimensions (Ungerechts et al., 1999). The amount of energy that is in the water is then estimated via mathematical models and can then be transferred back to an active drag or propulsive force. This technique has since been trialled by visualising the vortices generated from the movement of a hand and forearm in a swimming flume (Kamata et al., 2006). A single male subject was used in a 4.6m x 2.0m x 1.5m swimming flume. The research shows the development of the vortices, and the speed and circulation values but fails to transfer these into any drag effects. Further studies have attempted to measure the unsteady flow in the dolphin kicking wake (Miwa et al., 2006), around a monofin (Matsuuchi et al., 2006) and the hand motion by both a male and female swimmer (Yamada et al., 2006) using the same set-up as the Kamata trials. These studies were able to measure vortex rings during swimming but did not report on any associated propulsive forces that were generated. Further advances in technology, and the capability to measure waves and vortices in three dimensions, would improve this method for estimating active drag in isolated situations. However, this methodology would still only provide a proportion of -25-

41 Chapter 2 - Literature Review the total drag created by the body throughout the stroke as some of the vortices and waves generated would not be visible. Also, as the technique measures post-force effects of the body moving through the water, it cannot pinpoint the exact times at which these forces occur, or on which part of the body. The overall drag on a swimmer might eventually be calculated using this technique but assumptions would remain regarding the exact movement of a body component which generated the propulsive effects. One benefit of the PIV technology may be to identify where the stroke vortices are formed. That would allow identification of how the energy that is held within them could be utilised as propulsion in another section of the stroke. The results by Yamada et al. (2006) suggested a vortex pair with peak velocities of 1m/s at a diameter of 0.12m. This suggests a localised acceleration of 16m/s 2 within the vortex which would be a significantly high pressure to push against to generate propulsion. The diameter of these may be restrictive in that they are similar to the size of human limbs. Thus, any movement near them would probably destroy the vortex before any benefit was retrieved. Further research in this area could locate additional vortices with sufficient energy which could be reused by a swimmer. However, this does not help to determine the active drag and propulsion throughout the entire stroke. Active drag is a difficult parameter to determine because when swimming at constant velocity, the forces on the body change throughout the stroke. But, overall, there is a zero net force on the water. To create a force that could be measured, a change in the person s velocity or technique is required. The equation below demonstrates the forces that are typically referred to in swimming research (Rushall et al., 1994). At a constant velocity, the total force is zero, and studies have tried to determine the amount of propulsive and drag components that make up this total force. This is the same as trying to determine how much of the total force on a body results from friction, pressure, wave and inertial forces:- Force Total = Force propulsion Force drag The basis upon which one tries to differentiate between propulsion and drag forces is that, if a swimmer is able to decrease active drag by holding a better streamline position, -26-

42 Chapter 2 - Literature Review and maintain the same propulsive forces, the net force would be greater than zero. The body accelerates until the increased velocity brings the active drag back to equal the propulsive force. A recent review study by Wilson & Thorp (2002) summarised 23 different active drag studies and found the ranges for drag varied from -35N +/- 20N at 1 m/s, to -140N +/- 70N at 1.9m/s. There has been difficulty in reaching agreement concerning active drag and different studies have shown that it may be greater than or less than passive drag. The main body parts predominantly producing drag are the head; upper, mid and lower torso; with the arms and legs occasionally producing drag but mostly producing propulsion. A very different active drag value can be obtained if the drag forces are only recorded on the segments continually producing drag. This is especially the case when compared with a value that accounts for the drag when a body component produces drag, but excludes drag when the limb is producing propulsion. Results would be even more extreme if the sum of all pressure and shear stress effects in the positive direction were classed as propulsion, and all those in the negative direction were classed as drag, as performed in a recent study (Von Loebbecke, Mittal, Mark & Hahn, 2009). Although this approach would provide the upper bound for active drag, it might not be a useful number in aiding technique improvement. Using this technique for a 10cm x 10cm flat plate sitting vertically 1m below the water surface, the pressure would be 10kPa. although the plate is not moving, this approach suggests that there was an active drag force of 100N and a propulsive force of 100N. The correct amount of negative forces to use as active drag will be debated for some time. A more accurate and useful reference to active drag would be the total force on the body at any point in time throughout the stroke. A positive value would suggest propulsive forces, with the body accelerating; and a negative value would suggest drag forces dominating, and the body decelerating. Efforts then to increase maximum propulsive forces throughout the stroke and decrease maximum drag forces would be a way to improve techniques. Energy used by the swimmer is also an important variable. di Prampero, Pendergast, Wilson & Rennie (1974) were the first to describe the total active drag during the freestyle (front crawl) stroke and their methods have been used by Holmer & Haglund (1978) and Niklas et al. (1993). This method involved adding known extra drag loads to swimmers moving at a constant velocity and calculating this as a function of oxygen (O 2 ) consumption. The propulsive and resistive forces produced simultaneously by the -27-

43 Chapter 2 - Literature Review swimmer per cycle were either increased or decreased according to the direction of the extra drag load. The relationship between the net O 2 uptake equals the force of the extra drag load. This relationship was expressed in a regression equation and extrapolated to the baseline of resting O 2 uptake to give the active drag force. However, this procedure is complicated and must be repeated in its entirety for each recording point as the velocity is increased. Energy absorbed by the swimmer would not necessarily relate to stroke efficiency because a variation in efficiency would exist between the start and end of a testing session, and across athletes. The inability to accurately measure active drag has led to entirely mathematical models of swimming to try and predict it as well as the drag created by each segment of the body (Moghadam, Mehrvar & Pazouki, 1996; Ito & Okuno 2002; Nakashima, 2006). Using the standard Morrison s equations for inertial and velocity forces on a moving body in a fluid, researchers have been estimating forces on each body segment during a swimming stroke. Morrison s equations rely heavily on the coefficients that convert the known volume, area, velocity, acceleration and density into an equivalent force. These coefficients are dependent on the shape and Reynolds number, which would change from swimmer to swimmer, and throughout the swimming stroke. Sugimoto et al. (2006) used a model similar to that developed by Nakashima (2006). The body was divided into 21 elliptical cylinders in order to estimate the propulsion and drag effects during underwater dolphin kick. One trial was run at a fast (2.32Hz) kicking cycle and another at a slow (1.2Hz) kicking cycle. The fast cycle produced a maximum propulsive force for the entire body of 665N, with a maximum drag of -247N. The slow cycle produced a maximum propulsive force of 371N, with a maximum drag of -163N. These forces were mostly generated by the feet and are relatively high considering the amount of ankle strength it would require. However, a good correlation was found with velocity. Further developments to refine the coefficients would eventually result in better estimations of the true forces created. The major benefit of the Sugimoto et al. (2006) technique is that it provides a quick turn-around of results. However, this technique is unable to predict the flow pattern changes created by the upper parts of the body, and -28-

44 Chapter 2 - Literature Review the effect they would cause downstream. The impact of waves on a swimmer s body also is ignored when using this technique. Propulsive theory Reducing the active drag component of the total force equation has been one focus of research, while another has attempted to increase the propulsive forces while swimming (Counsilman, 1968; Silvia, 1970; Counsilman, 1970; Rushall et al, 1994). These studies outlined the theories used to understand how propulsive/drag forces could occur. Initially, Counsilman (1968) and Silvia (1970) used a similar approach by claiming that major propulsive contributions resulted from moving fluid backwards in order to generate forward movement of the body. This was explained in line with Newton s third Law of Motion which indicated that, for every action there was an equal and opposite reaction, and has been termed the action/reaction or drag/propulsion method. Later, Counsilman (1970) proposed that Bernoulli s principle of lift was the main driver associated with propulsion. The reasoning provided at the time was the S-shaped hand path profile throughout the stroke rather than purely a linear path that would optimise the action/reaction mechanism. Movement perpendicular to the direction of travel resulted in the hypotheses that lift forces similar to that of an aerofoil was providing the greatest proportion of propulsion. The use of Bernoulli s principle to explain the hand path is flawed when considering that the hand and arm are not a streamlined shaped airfoil and that lift is ideally created in situations of high velocity and low acceleration, which is the opposite to that occurring in swimming. In the aviation industry, there has also been a strong movement away from Bernoulli s principle when describing the theory of lift and more focus is now on the Coanda effect as the predominant force. The Coanda effect (named after Romanian born aeronautical engineer Henri Coanda) is the phenomenon in which the flow attaches itself to a nearby surface and remains attached even when the surface curves away from the initial flow direction. It is the suction force required to pull the fluid down around the curve that creates the lift in an aerofoil and has also been shown to be the dominant force in many areas where Bernoulli s principle was previously suggested. -29-

45 Chapter 2 - Literature Review As with the aviation industry, swimming has tended to move away from Bernoulli s principle and back to the transfer of fluid being the dominant theory (Rushall et al., 1994). There has been a growing trend for investigations into potential unsteady methods of propulsion to explain optimal hand paths and kick techniques (Maglischo, 2003). These have included potential energy returns from the formations of vortices (Ungerechts et al., 1999) and accelerated flow along limbs (Toussaint, 2006). As only the resultant force is able to be quantified, there are similar problems, when separating predominant forces generating drag, and also the active drag from propulsion. Assumptions have been made that can show any of the theories to be correct, assuming the assumptions are correct. It is difficult to measure the differential pressure across the body at any point in time. This has led to assumptions being made, which would inevitably mean different conclusions will be reached, depending on the dominant theory of the day. This is a typical problem in most fluid dynamic areas, and has driven to the rise of Computational Fluid Dynamics (CFD) as a tool to estimate the true pressure and shear stress effects of the fluid on an object. CFD Theory CFD is based on the fundamental governing equations of fluid dynamics the continuity, momentum, and energy equations. The actual equations are selected with due regard for the flow regime of the simulation (e.g. Navier-Stokes for viscous, Euler for inviscid, etc.). A full description of the terms and different methods used in CFD are provided by Versteeg & Malalasekera (1995) and summarised below. The most prevalent are the Finite Difference method (FDM), the Finite Element method (FEM), and the Finite Volume method (FVM). All methods are variations on dividing an overall larger domain into smaller discretised elements where the fluid dynamics can be better predicted. The layout, or combination of nodes and elements that join them together, is termed the mesh or grid. The FDM is the oldest technique and easier to implement than the FEM and the FVM. The FDM approximates the derivatives of the solution at a set of mesh points within the computational domain using the finite difference quotients in order to transform the boundary-value problem to a system of algebraic equations. Although this method is simple, it usually requires that the grid cells and nodes follow the direction of flow or is -30-

46 Chapter 2 - Literature Review structured, although this is mainly for convenience. Consequently, coordinate-mapping techniques or adaptive meshing algorithms are needed to solve problems with complicated geometries. In addition, there is no straight-forward way to test the accuracy of a solution, and the scheme is prone to certain types of numerical instability requiring artificial correction. The FEM works by using various geometrical elements to discretise the whole computational domain. Then the weakened governing equations are transformed into a set of algebraic equations with enforced boundary conditions and, finally, the resulting algebraic system of equations are solved. The attractive feature of the FEM is its ability to handle complex geometries with relative ease. Furthermore, the coefficient matrix of the global algebraic equation is usually sparse, banded, symmetric and positive definite. This is of great benefit in improving the computational efficiency and reducing memory requirements. The FVM is similar to the FEM and is the standard approach used in most commercial CFD codes. The governing Navier-Stokes or Eulerian equations are solved on discrete control volumes. In the FVM, volume integrals in a partial differential equation that contain a divergence term, are converted to surface integrals. By using the divergence theorem, these terms are then evaluated as fluxes at the surfaces of each finite volume. Because the flux entering a given volume is identical to that leaving the adjacent volume, these methods are conservative. Another advantage of the FVM is that it is easily formulated to allow for unstructured meshes. This is the method in the commercial code FLUENT which has been used in previous swimming studies. The area of CFD is constantly evolving with new proposed methods of modelling fluid flow. One such technique is Smoothed Particle Hydrodynamics (SPH), which is a new branch of CFD. Instead of a mesh, moving fluid particles are used to define the fluid. Values and gradients of physical quantities at a point are obtained from particles in a smoothed neighbourhood of that point. Meshing is not needed, even with moving boundaries or interfaces. This method is still under intensive development and a recently published book (Liu & Liu, 2003, p30) comments that There is still a long way for the method to become extensively applicable, practically useful and robust as the traditional grid-based methods such as FEM and FDM. This is because much work -31-

47 Chapter 2 - Literature Review needs to be done to consolidate the theoretical foundations of the SPH method, and to remedy its inherent numerical drawbacks. Further advances continue in the area of FVM computational fluid dynamics. FLUENT's main turbulence models have traditionally been Reynolds-Averaged Navier- Stokes (RANS) based such as the k-epsilon (Launder & Spalding, 1972) and k-omega (Menter, Kuntz & Langtry, 2003) models. Recent advances in computing processor capabilities have enabled the software to increase the capability to utilise Large Eddy Simulation (LES) models (FLUENT, 2007). Here, large eddies are explicitly resolved in an unsteady solution using filtered Navier-Stokes equations. The rationale behind LES is that, by modelling less turbulence (and resolving more), the error introduced by turbulence modelling can be reduced. The LES capability is claimed to be more accurate in areas where a wide range of turbulence scales occur (Kim, 2005). Although not used in the following studies, this capability may have the potential to be used in swimming simulation in order to gain additional information above that which the standard RANS models produce. The use of second order discretisation schemes are now common in CFD modelling. Here, quantities at cell faces are computed using a multi-dimensional linear reconstruction approach to obtain a second order accuracy, and this process has been followed in previous swimming research (Bixler et al., 2007). For both the calculation of velocity derivatives and construction of scalar values at cell faces, gradients are used. Typically, these are cell based gradients determined from the value at the centre of each adjacent cell. However, the unstructured tetrahedral meshes used in swimming simulations, due to their complex shapes, may need an alternative method such as recommended by Rauch, Natira & Yang (1991). These researchers reconstruct exact values from the weighted average of the cells surrounding a node. This preserves a second order accuracy and has been found to be more accurate than cell based gradients for these mesh configurations. Sensitivities of this approach across a variety of examples would need to be trialled for greater clarification. -32-

48 Chapter 2 - Literature Review Near-wall treatments Turbulent flows are significantly affected by the presence of walls (FLUENT, 2007). The mean velocity field is affected through the no-slip condition that has to be satisfied at the wall. However, the turbulence is also changed considerably by the presence of the wall. Very close to the wall, viscous damping reduces the tangential velocity fluctuations, and kinematic blocking reduces the normal fluctuations. However, towards the outer area of the near-wall region, the turbulence is augmented rapidly by the production of turbulence kinetic energy due to the large gradients in mean velocity. The near-wall modelling significantly impacts the fidelity of numerical solutions as walls are the main source of mean vorticity and turbulence. In the near-wall region, the solution variables have large gradients, and the momentum and other scalar transports occur most vigorously. Therefore, accurate representation of the flow in the near-wall region is required to determine successful predictions of wall-bounded turbulent flows (Launder & Spalding, 1972). Several studies have shown that the near-wall region largely can be subdivided into three layers (Launder & Spalding, 1972). In the innermost layer, called the viscous sublayer, the flow is almost laminar, and the (molecular) viscosity plays a dominant role in momentum and heat, or mass transfer. In the outer layer, called the fully-turbulent layer, turbulence plays a major role. Finally, there is an interim region between the viscous sub-layer and the fully turbulent layer, where the effects of molecular viscosity and turbulence are equally important. In CFD, various turbulence models are primarily valid for turbulent core flows (such as the k-epsilon turbulence models). Therefore, these models need to be made suitable for near-wall flows and two options exist for modelling near-wall flow. Accurate results can be obtained by employing high density grids near the wall via no-slip boundary conditions, together with better turbulence models for predicting this region (such as the k-omega turbulence models). This is very computationally expensive. Depending on the turbulence model selected, another option is to include wall functions. Wall functions are a compromise between accuracy and computational costs. Use of wall functions relaxes the demand for a high density grid near the wall at the price of accuracy. It is -33-

49 Chapter 2 - Literature Review known that wall functions do not work well for flow separations or flow with reverse pressure gradients (Launder & Spalding, 1972). As a result, wall functions need to be used with care when simulating swimming to ensure inaccuracies are minimised. CFD in Sport Computational Fluid Dynamics (CFD) has been used in a number of sporting areas to optimise performance (Hanna, 2002). Sports such as Formula 1 motor racing (Makowski et al., 2001), America s Cup Sailing (Pallis, Banks & Okamoto, 2000), soccer (Haake, Goodwill & Carr, 2006) as well as the Olympic sports of cycling (Haake & Bramall, 2004), ski jumping (Meile, Mayar & Muller, 2006) and bobsled (Montellebi, Avital & Dabnichki, 2002) have all used CFD as a means to optimise or understand better the effects of fluid flow and pressure forces in their sports. All the research for these sports was completed using the Finite Volume Method available in FLUENT s CFD code. However, they have generally focused on static geometric forms rather than the increased complexities afforded by dynamically changing shapes. With fluid effects being the major contributing factor to swimming performance, it has been a natural progression for swimming to use the same technology. Swimming CFD Studies Initial investigations involving CFD and swimming used a disk of the same size as a human hand to estimate the forces on the hand throughout the freestyle swimming stroke (Bixler & Schloder, 1996). With improved technology, this was adjusted to create a model of the hand and forearm which optimised pitch angle of the hand in the water (Bixler & Riewald, 2001). These studies utilised the growing capabilities of the commercial software FLUENT to estimate the effects. In these FLUENT simulations, the fluid was treated as incompressible, all numerical schemes were of a second order, and non-equilibrium wall functions were chosen to handle the near-wall flow. The standard k-epsilon turbulence model was applied for a turbulence intensity of 1% and turbulence length of 0.1m. Validation of FLUENT for measuring active drag on the hand segment was carried out. This was done by comparing the outcome of the simulations with physical quasi-static testing at varying pitch angles for a model of a hand in a wave tank. The geometry to obtain the required validation resulted in an adapted mesh of approximately 200,000 cells. -34-

50 Chapter 2 - Literature Review Sato & Hino (2002), used a similar technique at the Japanese National Maritime Research Institute s Centre for CFD research using their in-house software (SURF). They compared two elite freestyle swimmers arm stroke patterns to determine the efficiency of each swimmer s stroke. The study did not declare whether a full set of Navier-Stokes equations was used to model the turbulence, or the Reynolds Averaged Navier-Stokes models as per the FLUENT software. Although both freestyle techniques produced similar propulsion for the entire stroke, the benefits were in different parts of the arm sweep. These would not be detectable in traditional active drag estimations. There was no indication of how the kinematic movement of the swimmer s hand or accuracy of this motion was determined. Improvements in body scanning technology, together with advancements in FLUENT s commercial software, led to swimsuit manufacturer, Speedo, scanning one male and one female elite swimmer to estimate the passive drag effects of their Fastskin suits. Despite the launch of these suits in 2004 prior to the Athens Olympics, the results of this study (Bixler et al., 2007) have been released only recently. A model of 2.6 million cells was used for speeds between 1.5m/s and 2.25m/s, utilising the standard k-epsilon turbulence models and second order discretisation schemes. The study compared the results of the CFD simulations with those of the swimmer and an equivalent smooth skin mannequin. The mannequin was tested with and without the swimsuit. The comparison between the CFD results and the swimmer showed a difference of up to 38N, or 35%, at the higher speeds. However, when removing the drag associated with the variables of the towing device, the smoothness of skin (replacing the swimmer with a smooth skinned rigid mannequin of the same shape and size without swimwear) reduced this difference to 2.6N or 3.6%. This variation in forces provides useful insights into the error margins that could be expected by comparing passive drag forces with smooth walled CFD results. The George Washington University, together with USA Swimming, have used the software VICAR3D to estimate propulsive and drag forces on the different underwater dolphin kick styles used by USA team swimmers. A recent report (Von Loebbecke et al., 2009) detailed a number of these results by using a similar approach as studies 1 and -35-

51 Chapter 2 - Literature Review 2 of this thesis. The underwater dolphin kick was modelled for one male and one female elite swimmer. The swimmers body form was scanned using a 3D scanning technique and imported into FLUENT's pre-processor, GAMBIT, before being transferred to VICAR3D. There was a dearth of information provided on the construct of the CFD model except that it contained 4.2 million cells and utilised the Navier-Stokes equations with second order dicretisation schemes. The validation of the passive drag simulations were conducted only against results from previous studies by Lyttle, Blanksby, Elliott & Lloyd (1999 & 2000) and Bixler et al. (2007), where different swimmers were used. Hence, it is unclear as to the error margin involved in the simulations. The speed used in the model was also 1m/s, which is significantly slower than when underwater dolphin kicks are used in elite swimming competitions. The attempt to measure active drag was then taken to the next level. Any pressure and shear stress effects that were associated with propulsion were separated from those involved with drag, and the total drag effects were integrated to produce an overall active drag. This produces a higher active drag than the passive measurement which utilised the integral of all positives and negative pressures. Had the same methodology been used for both simulations, a different result could have emerged. It appears that, with each different measure for active drag, a different number will be obtained. A more efficient method for conducting the analysis would be to compare peak drag and peak propulsion throughout the stroke as mentioned previously in this chapter. The Australian Institute of Sport (AIS), together with Monash University and the Commonwealth Scientific and Industrial Research Organisation (CSIRO), have embarked on a program to trial a CFD technique detailed previously, and called Smoothed Particle Hydrodynamics (SPH). Here, a meshless method for simulating swimming techniques is used but it may take considerable time to develop even before swimming strokes can begin to be analysed. Also, a number of smaller CFD studies have used FLUENT in a two dimensional situation to look at head positioning and drafting distances (Zaidi, Taiar, Fohanno & Polidori, 2008; Silva et al., 2008). Using two dimensional models adds problems with eliminating three dimensional effects. This changes flow around the body as it assumes -36-

52 Chapter 2 - Literature Review infinite width and all the flow is required to go above or below the swimmer, greatly increasing the drag. Validating these models is very difficult and, as a result, previously used methodology of Bixler & Riewald (2001) was adopted. These studies have the potential for large error values due to both the 2D effect and the inability to validate results. However, this does show that the use of commercial CFD codes to predict swimming performance is increasing, and as these models are fine tuned to actual swimming, a greater increase in the foundational knowledge of swimming would become available. These previous studies (Bixler et al., 2007; Von Loebbecke et al., 2009; Zaidi et al., 2008; Silva et al., 2008) replicated the CFD methodology of an earlier study by Bixler & Schloder (1996). They suggested the standard k-epsilon model was the best turbulence model to examine passive and active drag in swimming. This was mainly because it provided the closest estimation to actual measured results. These had been identified to vary greatly rather than an understanding of the turbulence model itself. The standard k-epsilon model is the most widely used turbulence model since being proposed by Launder and Spalding (1972). However, there are some inherent limitations with this model. More recent advances in this area have resulted in better performance in flows involving rotation, boundary layers under strong adverse pressure gradients and separation. It has been recommended that the realisable k-epsilon model (Shih et al., 1995; FLUENT, 2007) may provide better turbulence results. More research and validation is required to optimise and validate the simulations, but using current "best practice" should provide some insight into swimming techniques. The other possible alternative for this application is the Shear-Stress Transport (SST) k- omega turbulence models developed by Menter, Kuntz & Langtry (2003). This combines the accuracy of modelling the near-wall region by utilising the standard k- omega model (Wilcox, 1998) and blending it with the free stream independence of the k-epsilon models (Launder & Spalding, 1972). This method requires a high resolution of the near-wall mesh and greatly increases computational times. The CFD studies have begun to fill a gap not obtainable by testing, and have improved on the mathematical modelling that has been the primary way to determine the passive drag, active drag, frictional forces, pressure forces, wave forces and inertial forces. -37-

53 Chapter 2 - Literature Review Greater understanding of the flow field and pressures around different components of the body would continue to provide additional knowledge that could not be obtained previously. Summary As can be seen above, there have been many efforts in swimming to estimate active drag as a single value. The rationale for this is that it can be used as a reference for comparing different stroke techniques and body shapes. Differentiating between the proportion of forces on the body that relate to frictional drag, pressure force, wave effects and inertial movement; as well as between active drag and active propulsion, remains a difficult proposition. Variations in techniques and body sizes in swimming have been studied for decades (Thrall, 1960; Clarys 1978, 1979, 1986; Bideau et al., 2002). There are many possible comparisons between body form (e.g. small versus large feet), experience level (e.g. novice versus elite) and technique factors (e.g. different hand catch positions) that would provide meaningful practical information to swim coaches for refining their swimming knowledge. The inability of previous measurement techniques to differentiate the drag forces into separate forces for each body part, has led to drawing only broad, and sometimes questionable, conclusions. The mathematical approaches, and more recently, the CFD simulations, have provided greater insight into both the steady and unsteady forces acting on a body, and the variation of those forces throughout a swimming cycle. However, currently, this has been restricted mostly to lower body movement. With a fully validated CFD model, previous findings could be re-evaluated to provide a greater level of understanding into the mechanisms involved. These, in turn, could lead to different or stronger conclusions. It is expected that, through a full CFD simulation of swimming strokes, there would be an increase in the fundamental knowledge of how propulsion and drag are created throughout the body. This information could be applied to swimming strokes and, potentially, lead to more efficient swimming techniques. -38-

54 Chapter 3 Study 1- CFD Model Methodology and Passive Drag Validation Introduction Before any assessment of stroke performance can be established, the computational fluid dynamics (CFD) model needs to be set up and validated. Many steps have been followed in order to develop a fully dynamic model such as outlined in this chapter. The first step involved finding appropriately skilled athletes who were willing to take part in the trial. The volunteers were elite Australian swimmers capable of times < 24s for 50m butterfly, < 22s for 50m freestyle and < 29s for 50m breaststroke. These criteria place the subjects at, or among, the top level of world swimming and represent an array of techniques capable of producing fast swimming speeds. The next step was to create a virtual three-dimensional model of the swimmers by using a full size laser imaging scanning system. These virtual models were then imported into the CFD software to set up the appropriate conditions and constraints based on values for previous passive drag testing (Lyttle, 1999). The base models were then compared in a passive drag situation against actual towing drag test results to ensure the model set-up -39-

55 Chapter 3 - CFD model methodology and passive drag validation utilised the most effective mesh, domain and turbulence settings. These results were also compared with a similar study of the accuracy of passive drag measurement using CFD (Bixler et al., 2007). The final step was to develop a method for simulating the active motion of the swimmers through the water. This involved measuring the kinematics of the subjects while swimming at speed, translating these kinematics into the two-dimensional motion of the virtual models and, subsequently, into three-dimensional motion. The comparisons of the active propulsion and drag, with actual swimming performances, are reviewed in later chapters. This study aimed to determine the optimal development of these virtual models. With incomplete input data available for surface roughness, kinematics and skeletal movement, as well as no accurate method for measuring active forces, validating the active simulations is not currently possible. As a result, a best practice approach was used based on validated passive drag simulations and utilising CFD methodology from areas where full validation was possible (such as aeronautical and automotive industries). The passive drag validation should also provide a level of accuracy that can be expected from the results. -40-

56 Chapter 3 - CFD model methodology and passive drag validation Methodology Figure 3-1 shows the stages that this thesis followed to develop the final goal of a full freestyle CFD simulation. This chapter focuses on the development of the best practice methodology developed during stage 1 that is utilised in stages 2 and 3. Figure Flow chart detailing the stages of model development. Laser Imaging of a Swimmer The 3D mapping of swimmers was performed using a Cyberware WBX whole body laser scanner with a density of one point every 4mm by Headus, an animation company based in Perth, Australia. All scans were performed with the swimmers wearing fulllength competition swimsuits. This laser scan procedure created a 3D superficial model -41-

57 Chapter 3 - CFD model methodology and passive drag validation of a swimmer within the order of a million surface points. Higher resolution scans were also conducted of the hands and feet using casts of these limbs (density of one point every 0.66mm), as well as a high resolution scan of the head using a scanning device with density of one point every 0.66mm. The higher resolutions were performed due to the importance of these areas in setting the initial flow conditions and in developing thrust (in the case of the feet and hands). The higher resolution scans were then aligned and merged seamlessly into the full body scan to provide more accuracy at these locations. The 3D model was then processed to extract 288 non-uniform rational b- splines (NURBS) curved surfaces forming a 3D solid model of the swimmers. Figure Laser scanned images of the subject for passive drag and lower body motion simulations. There was a slight difference in the scanned body position between the initial experimental studies and the final full body stroking study due to the complex nature of the dynamic mesh properties available within the CFD software. The scans used for the passive drag and lower-limb-only motion were performed with the swimmer assuming a streamlined glide position. This involved the subject in a fully extended position with the hands overlapping overhead, feet plantar-flexed and the arms pressed tightly against the head (see Figure 3-2). For the full stroke simulation, the body position was similar except that the fingers and hands were separated from each other, the arms were away from the head with the legs separated, and the feet were plantar-flexed (see Figure 3-3). -42-

58 Chapter 3 - CFD model methodology and passive drag validation Figure Laser scanned images of the subject for full stroke simulations. CFD Methodology CFD is based on the fundamental governing equations of fluid dynamics the continuity, momentum and energy equations. The actual equations applied are selected with due regard for the flow regime of the simulation (eg. Navier-Stokes for viscous, Euler for inviscid, etc.). The computer simulation was performed using the CFD software package FLUENT version (for the initial passive drag and lower limb simulations) and version (for the full body active drag simulations). In brief, the CFD finite volume technique involves creating a domain, inside which the flow simulation occurs; bounding the domain with appropriate external conditions, and breaking the domain up into a finite number of volumes or cells. The governing equations of fluid flow are then integrated over the control volumes of the solution domain. Finite difference approximations are substituted for the terms in the integrated equations representing the -43-

59 Chapter 3 - CFD model methodology and passive drag validation flow processes. This converts the integral equations into a system of algebraic equations that are solved using iterative methods. Before creating the CFD model, a number of assumptions are made. This allows the model to be solved in a reasonable time frame while still maintaining the salient characteristics of the flow. The assumptions and simplifications made in the validation of passive drag, and all fully submerged simulations, are listed below: The models are generally established using the realisable k-epsilon turbulence model together with second order discretisation. This is recommended as best practice for this type of simulation (Shih et al., 1995; FLUENT, 2004) although variations are trialled throughout the studies to provide a sensitivity of CFD variables. The model is single phase with no air/water interface. The 0.5m depth of the swimmer during the kicking kinematic measurement trials were increased to 1.5m to reduce any confinement effects on the flow due to this assumption. The width of the pool included in the model was 3m and the pool floor is modelled 1.5m below the centre of the swimmer. A 5m length of pool was modelled to provide sufficient distance past the swimmer to allow convergence of the model and not affect results. Domain independence checks were completed with all boundaries moving further away from the swimmer with insignificant change in flow profiles and drag forces. 3m Outflow Inlet 3m Moving walls Figure Overview of the fully submerged streamlined glide model. -44-

60 Chapter 3 - CFD model methodology and passive drag validation The domain is assumed to be moved at the average speed of the swimmer s centre of gravity so that the swimmer remains relatively stationary. This is achieved via an upstream inlet, a downstream outlet, symmetry sides, and moving top and bottom walls. The purpose of the first stage (Figure 3-1) was to allow benchmarking of swimmer s CFD model drag forces with both previously reported experimental passive drag results (Lyttle, 1999); and the experimentally derived passive drag results for the swimmer used in the kicking studies (Chapter 3). In stage two, the same model was then used in further studies (Chapters 4-7) with the addition of user defined functions (UDF) and remeshing to provide limb movement. For stage three, a third model (Chapter 8) was then developed by using the same CFD methodology as stage two; but with an alternative swimmer geometry, where the arms and hands are separated rather than in the streamline position. In this stage, the upper body movement was also included in the model. Two other alterations were made in the third stage model. The depth was increased to 4.5m to equate with the standard FINA water depth of 3m, together with 1.5m of air space above the water. A multi-phase flow model allowed the calculation of the wave effect as well as allowing arm recovery above the water without influencing the results. 1.5m 3.0m Figure Overview of the surface model simulations. The stage 1 analysis was steady state, and stages 2 and 3, unsteady (time dependent). The stage 2 and 3 analyses were completed by breaking the limb movements down into -45-

61 Chapter 3 - CFD model methodology and passive drag validation discrete time steps. The package then solved the unsteady flow field for that position before moving on to the next position. The volume mesh was also updated at each time step. CFD Model The CFD process requires geometric construction of the simulation to define the extent of the domain to be investigated. This was achieved by subtracting the swimmer (3D solid model generated from the laser scan) from the 3D volume representing the section of pool being simulated at each point in time. The domain surfaces were comprised of varying mesh densities to define the detail around highly curved areas while still maintaining a workable mesh size. Between the different models, the surface mesh on the swimmer varies between 60,000 for stage 1 and 2, and 100,000 triangular surface elements for stage 3, and the total simulation comprises between 2 and 5 million cells. Figure 3-6 presents the surface mesh around the head of the swimmer used in the kicking studies and Figure 3-7 details the concentration of mesh around the hands used in the full body stroking model. Mesh independence checks were made by increasing the number of cells used around critical areas and ensuring no changes to the flow dynamics with refined accuracy occurs. These were run for both the passive and active drag cases to ensure that an optimal number of cells were used for both computational run times and accuracy of results. -46-

62 Chapter 3 - CFD model methodology and passive drag validation Figure The triangulated mesh surrounding the head. Figure The triangulated mesh surrounding the hands. -47-

63 Chapter 3 - CFD model methodology and passive drag validation Boundary Layer Modelling CFD allows a number of different approaches to modelling the transition boundary layer in turbulent flows. The simplest approach uses standard wall functions to simulate the boundary layer combined with the use of tetrahedral cells. This is the most computationally efficient way to represent the boundary layer. A potentially more accurate boundary layer can be obtained by using a structured boundary layer mesh in conjunction with the standard wall functions. In this case, prism cells of increasing thickness away from the boundary are used, which then transition into tetrahedral cells in the main fluid region. The logarithmic law for mean velocity, which is applied in the standard wall functions used, requires the dimensionless y+ value (a comparative measurement of velocity across the wall region) to be between 30 and 60, but can be up to 300 in order for it to be considered valid (Launder & Spalding, 1972). A comparison between the sensitivity of this change in boundary mesh configuration is required because the moving analysis requires regular remeshing between time steps. Due to small gaps between body parts during the stroke, the dynamic model requires variations ranging from no boundary layer mesh on a small amount of the body, to the majority having between three and five boundary layer cells where possible. This is a combination of the first two approaches and is the method used for the simulations in Chapters 4 to 8. The third approach could have been to model a very fine mesh with a high number of prism elements within the boundary layer and utilise the full turbulence equations rather than a wall function. This would require cell sizes <0.1mm near the wall boundary. For a rigid object, this can provide a better estimation of wall effects and separation but, in the case of a human body with varying roughness throughout, it was decided that this level of detail was computationally intensive and would not create a significant advantage in the current studies. Calibration/Validation of CFD Model Although the basis for the CFD model study was to compare different swimming techniques, the model needs to be calibrated to show the degree of compatibility with -48-

64 Chapter 3 - CFD model methodology and passive drag validation empirical test results. Due to the unavailability of a method to accurately measure active drag throughout a swimming cycle, the model was calibrated by using steady state tests. Two initial trials for the CFD model were arranged, in both cases using wall functions at the near-wall region. The first used tetrahedral cells for the boundary, and the second, the five prism layer boundary mesh. Both these models kept the y+ values for the boundary layer between 28 and 76, which were within the limits recommended by Launder & Spalding (1972). The results (Tables 3-1, 3-2) indicated a slightly closer passive drag force to the measured results for the prism boundary layer arrangement in the prone swimmer when compared with the tetrahedral boundary cell analysis. The difference between the two examples was less than 9N for the 2.2m/s velocity case. This was smaller than the difference when some surface roughness was taken into account, but should be considered when reviewing the results of the various models. A sensitivity study was undertaken to compare the various turbulence models and discretisation schemes, with most variants producing similar (within 4%) total passive drag values. Utilising the node based gradient option recommended by Rauch et al. (1991), the simulation with tetrahedral boundary layer mesh showed a smooth wall combined drag of 71.7N which was similar to that with the prism boundary mesh. Such a result suggested this could be a better alternative than the prism boundary layer models as it provided a similar result but enable the flexibility of the deforming mesh close to the surface. A combination of the two was probably the most practical outcome. The basis for this study was not to accurately calibrate the results to measured data, due to the inaccuracies that can occur during the empirical tests (Bixler et al., 2007), but to achieve close calibration for the technique comparison simulations. It was expected that the variation in drag forces throughout the active stroking would greatly outweigh the small differences found during the static drag validation. Initially, the CFD results were compared with the steady state drag results from a previous study (Lyttle, 1999) which measured the passive drag by towing 40 experienced adult male swimmers at a variety of speeds and depths. The passive forces for the range of towing velocities at the 0.5m depth from Lyttle (1999) were used in the comparisons to the static CFD output. The comparison of the CFD results with the empirical passive drag test data showed that the CFD results were, for an average skin -49-

65 Chapter 3 - CFD model methodology and passive drag validation roughness of 1mm, one standard deviation below the mean. For a smooth skin (i.e. zero surface roughness), this equated to approximately three standard deviations below the mean (Tables 3-1 and 3-2). Table 3-1 Steady glide drag results and test data. Smooth walls 1mm roughness Test Results Velocity Pressure Viscous Combined Pressure Viscous Combined Mean Combined (m/s) (N) (N) (N) (N) (N) (N) (N) Standard Deviation Table 3-2 Steady glide results with boundary layer mesh included. Smooth walls 1mm roughness Test Results Velocity Pressure Viscous Combined Pressure Viscous Combined (m/s) (N) (N) (N) (N) (N) (N) (N) Mean Combined Standard Deviation Figure Towing testing set-up used for the passive drag measurement (Lyttle, 1999). -50-

66 Chapter 3 - CFD model methodology and passive drag validation On closer examination of the test subjects used in the initial study, the scanned swimmer was of similar anthropometric profile to those at the lower end of the drag spectrum. Further towing tests were completed by using the same testing set-up as the previous steady glide testing (Lyttle, 1999, see Figure 3-8) and the same swimmer as the scanned data. At 2.2m/s, the passive drag force acting on the swimmer was 88N +/- 3.5N, which compares within the two standard deviations demonstrated by the CFD model. This indicates that the predicted results of the steady state CFD model were reasonably accurate, depending on the level of surface roughness used. A previous study found that the variation between passive drag recorded when using a smooth skinned mannequin, and a swimmer of exactly the same shape, could be up to 35% (see Table 3-3) (Bixler et al., 2007). This was associated with the influence of the towing device, the briefs worn by the swimmer and the reduction in surface roughness of the skin. When validating the CFD results of static drag against the measured data, the influence of these testing variables should be considered. At these speeds, Lyttle (1999) identified that the drag resulting from the test equipment was negligible. However, in a similar study by Bixler et al. (2007), the equipment drag at these speeds could account for up to 20N of drag. The skin roughness was able to account for up to 10N and the swimwear a further 6N. A further study investigated the influence of swimwear on passive drag and reported that 1970 s swimwear for women increased the passive drag on a swimmer by approximately 9% (Van Manen & Rijken, 1975). This result was higher than that found for the mannequin tests with modern briefs swimwear in the Bixler et al., (2007) study, of around 6-7%. The variations found for these measurements have the potential to influence the validation of the results presented. It is therefore reiterated that this study focused on the active portion of the stroke and took great care to consider the influence of these possible errors when interpreting and discussing findings herein. Given the major complexities involved in quantifying fluid effects on such a complicated shape as the human body, precise absolute propulsion and drag forces are currently unattainable, and impossible to validate in an active swimming situation. A major benefit of utilising CFD technology lies in comparing techniques using the same CFD model. Comparisons between different CFD scenarios using the model, results in the substantial reduction of -51-

67 Chapter 3 - CFD model methodology and passive drag validation any possible errors due to any inaccuracies or assumption in the CFD model are the same in both simulations. Table 3-3 Comparison of passive drag values from Bixler et al. (2007) study. Velocity (ms -1 ) CFD Results (N) Mannequin without Swimwear (N) Mannequin with Swimwear (N) Swimmer with support drag removed (N) Swimmer including support (N) The ratio of viscous drag to total drag (i.e. viscous and pressure drag) in this study was similar to previous CFD studies (Bixler et al., 2007; Von Loebbecke et al., 2009). In the simulations, the viscous drag to total drag ratio was 22.8% for the case with prism boundary mesh, and 28.6% for the case with tetrahedral boundary mesh. Bixler et al. (2007) reported a range of 25 to 28% while Von Loebbecke et al. (2009) reported values closer to 30%. However, Von Loebbecke s (2009) simulations were at a velocity of 1m/s and it appears viscous drag has a higher percentage at lower velocities (Bixler et al., 2007). Additionally, this ratio can be heavily influenced by the shape of the swimmer, which prevents precise comparisons between models. This project sought to provide a working model that demonstrates similar results for peaks of propulsion and drag which is reflective of that achieved throughout the stroke of an active swimmer. Passive drag is highly dependent upon separation of water flow from the body and this can vary with slight changes in body position. In contrast, the active drag is not as dependent on these factors for its maximum and minimum peaks as it is more dependent upon the high variation in forces on each body part throughout the stroke cycle. These validation results showed that a surface roughness over the entire body of 0.63 mm allows for the required frictional drag associated with skin roughness and bathers. Tests conducted by Bixler et al. (2007) suggested a value closer to 0.3mm based on the -52-

68 Chapter 3 - CFD model methodology and passive drag validation comparison between the forces obtained from the CFD sensitivity analysis, and the trials with the mannequin and the swimmer. Non-swimming based research suggested a value of perfectly smooth skin was closer to 0.05mm when not accounting for hair and any other skin imperfections (Wilhelm, 1997; McCornick-Stager & Tanner, 2005). This variation in roughness was used in a sensitivity analysis for a sample of the dynamic runs in later Chapters to ascertain effect of surface roughness on active swimming drag and propulsion. The distribution of this surface roughness would also make a difference to the distribution of forces and presents an opportunity for further refinement of the CFD model in the future when the ability to accurately measure surface roughness over different parts of the body can be incorporated. Field Trials to Establish Swimmer s Kinematics Measuring kinematics for swimmers is difficult due to the large ranges of motion of the human body parts. This makes the simpler techniques time consuming and inaccurate as well as the aquatic environment which makes many conventional kinematic motion analyses more problematic. Recent advances in motion analysis techniques have involved the applications of different sensor technology, including magnetic and inertial sensors. These sensor devices are not yet fully validated and significant technical developmental work is still required prior to being used in water. The best approach was determined to be manual video digitising for both the underwater testing and the full freestyle stroke at the surface. As a comparison, the breaststroke kick was recorded using the VICON motion sensor system in a dry-land laboratory setting. Hence the kinematics for the breaststroke would be subject to the differences between the true breaststroke kick and it s replication in a lab-based environment. Comparisons of the 3D swimmer animation with actual video footage for all kinematic data was completed after each trial to note any visible discrepancies between the derived kinematic data and the actual swimming technique. Underwater kicking 2D kinematic measurement The elite national level butterfly swimmer was filmed underwater from the side. The camera axis was horizontal to capture motion in the vertical plane during underwater dolphin and freestyle kicks at near-maximal effort. The swimmer performed separate -53-

69 Chapter 3 - CFD model methodology and passive drag validation trials using the following underwater kicking techniques: high amplitude, low frequency dolphin kicks; low amplitude, high frequency dolphin kicks; and the typical underwater freestyle (flutter) kick that competitive swimmers typically adopted in competition. A full 2D kinematic analysis using manual digitising was performed for the three selected conditions. This allowed the 2D segment kinematics to be defined for the foot, calf, thigh, pelvis, trunk, upper arm, forearm and hand, as well as the calculation of the swimmer s centre of gravity (CG) (see Figure 3-9). To obtain the swimmers centre of gravity the motion analysis system used for the manual digitising (APAS-Ariel Performance Analysis System) adopted Dempster's (1955) cadaver data to determine the centre of mass of the segments. While symmetry was assumed between the left and right limbs for the dolphin kicks, the left and right side variances were measured for the freestyle kick. In all trials, the swimmer was able to push off the wall with the kinematics recorded approximately 5m from the wall. This resulted in a deceleration of the swimmer throughout the kick cycle as reflected by an overall net resistive force. This is similar to what occurs during the underwater kicking phases of swimming events where kicking is used to provide a lower deceleration rate than experienced by gliding alone. This is a result of the higher relative velocity of the underwater phase compared to that occurring when stroking at the surface. Figure Sample kinematics from underwater dolphin kicking trial. Freestyle surface 3D kinematic measurement The elite freestyle swimmer was filmed swimming at the water surface from four camera angles. A separate above and below water camera were used on each side of the swimmer with each camera orientated at between to the horizontal plane. The -54-

70 Chapter 3 - CFD model methodology and passive drag validation swimmer performed his regular freestyle technique and a full 3D kinematic analysis was performed using manual video digitising, based on the collective data obtained from the four different cameras (see Figure 3-10). The segments defined were in accordance with the joints and anatomical landmarks listed in detail later in this chapter (Table 3-4 and Figure 3-11). Swimmers were marked up by a level 3 accredited kinanthropometrist. Each individual segment was recorded to enable bilateral differences to be explored. For each segment, medial and lateral anatomical landmarks were digitised at the distal and proximal ends of the segments to allow rotations to be described. For these swimming trials, the subject started from 10m behind the measurement area, and swam from a water start at near-maximal effort to assist with the maintenance of a constant velocity through the measurement area. Figure Sample kinematics from full freestyle stroke trial. -55-

71 Chapter 3 - CFD model methodology and passive drag validation Figure Measurement points used to collect freestyle kinematic data. -56-

72 Chapter 3 - CFD model methodology and passive drag validation CFD User Defined Functions User defined functions (UDFs) were utilised within FLUENT to convert the kinematic data from the kinematic analysis into relative motion of the segments within the 3D animated model. The method of transformation of the kinematics was similar for both the 2D and 3D cases. 2D motion UDF In order to use UDFs to control movements of the body parts and dynamic meshing to maintain the required mesh quality, the body was broken into four rigid (body including arms, thighs, calves, feet) and three flexible (hips, knees, ankles) sections. Based on measured kinematic data of the swimmer, a mathematical curve was fitted to the rotational movements of the three main joints, with the global horizontal and vertical movement of the hip joint also modelled. As the swimmer was expected to be holding a constant velocity, no slope was used in the equations for the hip joint movement. The UDFs were written to preserve the joint offsets (i.e. length of each limb) along the length of the swimmer (Figure 3-12). For all joint rotations, an eight coefficient Fourier series function, together with a calculated average, were used to convert the raw data into a smooth profile for integration into the CFD model. A variation in the number of coefficients used showed that the eight coefficients provided the best fit to the joint rotational data. In the 2D case, the equations of motion could be used to control the rotational velocity through the Rigid-body UDF within FLUENT. The horizontal and vertical co-ordinates of the knee joint were then determined by the fixed length of the thigh segment and the hip angle of rotation. The ankle joint was then determined using similar means as with the knee joint. The toes and tips of the fingers are similarly determined from the ankle and hip joints, respectively. This process resulted in sagittal plane flexion-extension angles about the moving joints. A comparison between the FLUENT software and the kinematic data showed that at the extreme points of the hands and toes the swimmer was always within 5mm of the actual measured position of the swimmer within the 2 dimensional planes. -57-

73 Chapter 3 - CFD model methodology and passive drag validation Ankle Rotation Angle Knee Rotation Angle Hip Rotation Angle Figure The joints used and the fixed lengths maintained for the 2D trial. For the underwater dolphin kick simulations, the number of rigid segments was constrained to four, as both the left and right sides were assumed to be moving symmetrically. For the underwater and surface freestyle kick simulations, the number of rigid body joints is increased to seven, with the leg sections separated bilaterally into their left and right sides. In both cases the upper trunk, head and arms were simulated as a rigid segment that moved together. 3D motion UDF The 3D motion of the segments was required for the breaststroke kick and the full simulation of the freestyle stroke. The breaststroke kick required the same seven components as the freestyle kick simulations. However, the full simulation resulted in 21 rigid segments, with 27 joints being tracked which together form the virtual skeleton. Tables 3-5 and 3-6 contain the list of joints and rigid segments used, with the initial coordinates of those video digitised data points located on the scanned swimmer. Also contained within these tables are the locations of the joint centres used for the simulations, and the rigid lengths between joints that were maintained. The methodology behind the conversion between the 3D kinematics and the 3D animated motion is significantly more complex than for the 2D case. Similar to the 2D situation, each limb is treated as a rigid segment of a fixed length, with the joint centres and their associated axis of rotation used to define the rotation of each segment. Figure 3-13 provides a representative schematic sketch of how each segment is linked; points 2-A, 2-B and 2-C are determined by the rotations of the entire segment around point 1- C. Points 3-A, 3-B and 3-C are then determined from the location of 2-C and the rotations of the segment, and the fixed length of the segment. -58-

74 Chapter 3 - CFD model methodology and passive drag validation Points A and B were obtained from the digitised data with point C calculated as the mid point between them. At each time step, a Cartesian (i.e. x, y and z) co-ordinate is determined for the joint centre. From these joint centre co-ordinates, the polar angles θy, θxz and θt were then determined. These polar co-ordinates were then used as the basis for the movements of the body. The polar co-ordinates provide a number of advantages over the Cartesian system. The polar system ensures the integrity of the segment lengths are maintained throughout the swimmer. The polar system also enables variations is flexibility of joints to be adjusted easily without compromising on the integrity of the model. Twisting of segments is also possible using the polar system with only 1 extra variable, the Cartesian system would require 2 additional points with 3 variables each resulting in a substantial increased in calculations. When comparing kinematic data from swimmers of different height and limb length the polar system enables direct comparison of the angles the limbs form with each other. This property also enables the kinematics of one swimmer to be placed on another by just varying the segment lengths in the CFD simulation. This would enable swimmers to identify whether a certain technique would suit their body profiles before spending weeks and months practising it in the pool. 3-A 3-C 1-C 1-A 2-C 2-A 3-B 1-B 2-B Figure Breakdown of each limb into a rigid body rotating around joint centres. -59-

75 Chapter 3 - CFD model methodology and passive drag validation y y x x z z Figure From the field trials at each point in time; x, y, z co-ordinates are recorded for each monitoring point. From these, the joining vector and amount of twist in the segment can be determined. y θy Length θt θxz Figure Details how co-ordinates are then transferred into a set of polar rotational angles with time. The mid iliac crest, which is defined as the mid-point between the left and right iliac crests (see Figure 3-11) acts as the root segment for the animated model and is used as the basis of all movement. The horizontal and vertical displacement of this point controls the movement of all other joints. Table 3-5 shows the hierarchy of joints used. Therefore, the formula for each joint motion is: -60-

76 Chapter 3 - CFD model methodology and passive drag validation x y z n n n = x = y = z n 1 n 1 n 1 + Segment _ Length *cos( θ ) *cos( θ ) + Segment _ Length *sin( θ Segment _ Length *cos( θ ) *sin( θ ) xz xz xz ) y y with n referring to the current joint, and n-1 referring to the predecessor joint detailed in Table 3-5. Using this methodology, the calculated joint centres are computed relative to the mid iliac crest motion and could be compared to the actual measured values from the digitised video data. The largest error was expected to lie in the joints furthest away from the mid iliac crest, such as the ankles and wrists. Figures 3-16 and 3-17 graphically represents the variation in x (horizontal) and y (vertical) position between the calculated and measured values for the right ankle and right wrist joints. There was considerable difference between the two values at certain points in the stroke. The right ankle revealed a discrepancy range of between -6 cm and +2cm in the y direction, and - 7cm to +2cm in the x direction during parts of the kicking motion. Likewise for the right wrist, the average error was 6 and 9cm for the x and y directions. Similar errors were also obtained in the z direction. Although the exact error involved in calculating the coordinates of the joint centres in the CFD model could not be determined, it is likely that a considerable amount of the discrepancies are as a result of digitised data error. To highlight this, the segment length was calculated between the right wrist and right elbow for the digitised data throughout the stroke and compared with that of the fixed measured segment length of the swimmer s forearm from the 3D scan (see Figure 3-18). A similar comparison was performed for the distance between the knee and the ankle (Figure 3-19). The actual fixed length of the limb was 27.3cm (refer Table 3-16) with the average variation in length 3.1cm. The right calf fixed length was 45.1cm with an average error of 2.5cm. The average variation of 10% and 5%, together with the continual variation in the error, compound the differences in the wrist and ankle locations. The variations in length from the digitised data during parts of the stroke for each segment were common. Redigitisation of these segments over periods of high variation (such as found for the forearm during the in-sweep of the arm stroke) resulted in similar digitised outputs, -61-

77 Chapter 3 - CFD model methodology and passive drag validation indicating that digitising reliability is not the main cause of the variation. In which case, it may be possible that there were inherent errors that may have occurred in some movement planes when resolving the transformations during the digitising process. This is possibly either through a non-optimal placement of the cameras during filming, errors in calibrating the control frame or an insensitivity of the direct linear transformation process for movement in some planes using the current camera set-up. A second source of the differences could be found in poor estimations of joint angles. Figures 3-20 and 3-21 show the θxz and θy angles calculated from the measured data for the left calf, and the eight coefficient Fourier series used to estimate the change of angle throughout the stroke. The coefficients are optimised for the least Σr 2 between the measured and calculated angles. The measured data demonstrates that there are abrupt changes in the angles. These are considered to be errors in the data and are smoothed out with the approximated curve. The fit between the calculated and measured angles is better for the θxz angle due mainly to the better camera angles available when measuring this plane. A third source of error could relate to difficulties in predicting the true joint centre of rotation that are extremely complex to model for all joints in the human body. The shoulder joint in particular is problematic, with the estimated centre of the joint moving dynamically within the joint structure depending on the type of upper arm movement (de Groot & Brand, 2001). The simplification of the shoulder joint centre location for this joint is outlined later in this section. Because measuring of kinematic movement in water is still in its developmental stages, some visual comparisons were made between actual video footage of the swimmer and the generated computer images of the models for a final comparison. In regions where there were significant potential digitising errors, small changes were then made to the 3D animated model to reflect the actual position of all joints, as seen in the video. This was done to try and remove as much error as possible from the kinematic data and motion approximations. -62-

78 Chapter 3 - CFD model methodology and passive drag validation Table 3-4 Digitised points and corresponding initial coordinates on scanned model. Position Number Position Name Abbreviation X Y Z 1 Left Metacarpal 1 LM Left Metacarpal 5 LM Left Radial Notch LRN Left Ulna Notch LUN Left Elbow Medial Epicondyle LME 6 Left Elbow Lateral Epicondyle LLE 7 Left AC Joint LAC 8 Left Shoulder Joint Centre LSJ 9 Left Ear LE Right Ear RE Right Shoulder Joint Centre RSJ 12 Right AC Joint RAC 13 Right Elbow Medial Epicondyle RME 14 Right Elbow Lateral Epicondyle RLE 15 Right Radial Notch RRN Left Ulna Notch LUN Right Metacarpal 1 RM Right Metacarpal 5 RM C7 Vertebrae C7V Left Lateral Thoracic 8 vertebra LLT 21 Right Lateral Thoracic 8 vertebra RLT 22 Left Lateral Lumbar 1 LLL 23 Right Lateral Lumbar 1 RLL 24 Left Iliac Crest LIC 25 Right Iliac Crest RIC 26 Left Knee Lateral Condyle LKL Left Knee Medial Condyle LKM Left Ankle Medial Malleolus LAM Left Ankle Lateral Malleolus LAL Left Mid Heel LMH 31 Left Metatarsal 1 LM Left Metatarsal 5 LM Right Knee Lateral Condyle RKL Right Knee Medial Condyle RKM Right Ankle Medial Malleolus RAM Right Ankle Lateral Malleolus RAL Right Mid Heel RMH 38 Right Metatarsal 1 RM Right Metatarsal 5 RM

79 Chapter 3 - CFD model methodology and passive drag validation Table 3-5 Joint centres and calculated initial coordinates from scanned model. Joint Centres Number Segment/Joint Name Abbreviation X Y Z 101 Left Hand LH LW 102 Left Wrist LW LE 103 Left Elbow LE LS2 104 Left Shoulder LS MB 105 Left Shoulder LS LS1 106 Right Hand RH RW 107 Right Wrist RW RE 108 Right Elbow RE RS2 109 Right Shoulder 1 RS MB 110 Right Shoulder 2 RS RS1 Preceeding Joint 111 Mid Head MH C7V 112 C7 Vertebra C7V MB 113 Mid Shoulders MS MB 114 Mid Back MB TP 115 Lower Back LB TP 116 Mid Iliac Crest TP Control 117 Pelvis Mid MP TP 118 Pelvis Left LP TP 119 Pelvis Right RP TP 120 Left Knee LK LP 121 Left Ankle LA LK 122 Left Mid Foot LMF LA 123 Left Toes LT LT 124 Right Knee RK RP 125 Right Ankle RA RK 126 Right Mid Foot RMF RA 127 Right Toes RT RMF -64-

80 Chapter 3 - CFD model methodology and passive drag validation Table 3-6 Rigid segment lengths from scanned model. Rigid Body Length Number Limb Name Abbreviation Length (cm) 1 Left Hand LH Left Forearm LFA Left Upper Arm1 LUA Left Upper Arm2 LUA Right Hand RH Right Forearm RFA Right Upper Arm1 RUA Right Upper Arm2 RUA Head HD Upper Body UB Mid Body MB Lower Body LB Pelvis P Left Thigh LTH Left Calf LC Left Foot LF Left Toes LTS Right Thigh RT Right Calf RC Right Foot RF Right Toes RTS

81 Chapter 3 - CFD model methodology and passive drag validation 10 Right Ankle - Model to measured comparison Y value (cm) X-Value (cm) -40 Time (sec) CFD Model Y Coord Digitised Y-Coord CFD Model X-Coord Digitised X-Coord -350 Figure Comparisons of measured and calculated coordinates for the right ankle Right Wrist - Modelled to measured comparison Y-value (cm) X-value (cm) Time (sec) CFD Model Y Coord Digitised Y Coord CFD model X Coord Digitised X Coord Figure Comparisons of measured and calculated coordinates for the right wrist. -66-

82 Chapter 3 - CFD model methodology and passive drag validation 45 Right Forearm Length from Digitisation Length (cm) Time (sec) Figure Average length to measured digitised length for the right forearm. NB: pink dotted line is the segment length of the right forearm from the 3D scanned image. Right Calf Length from Digitisation Length (cm) Time (sec) Figure Average length to measured digitised length for the right calf. NB: pink dotted line is the segment length of the right forearm from the 3D scanned image. -67-

83 Chapter 3 - CFD model methodology and passive drag validation 0.8 Angle comparison between measured and model Angle (rad) Time (sec) Digitised Angle(xz) CFD model Angle(xz) Figure Comparison of mathematical fitted curve with actual measured θxz angle for the left calf. Angle comparison between measured and model Angle (rad) Time (sec) Digitised Angle(y) CFD model Angle(y) Figure Comparison of mathematical fitted curve with actual measured θy angle for the left calf. -68-

84 Chapter 3 - CFD model methodology and passive drag validation The validation of joint movements is critical when developing a precise simulation model but that was beyond expectation of the intended final outcome of this thesis. Further developments in measuring 3D kinematics in the aquatic environment through improvements in measurement technology would improve the overall accuracy of the CFD model. This thesis aimed to develop a means for measuring the amount of propulsion and drag throughout the stroke based on current kinematic measurement capability. Variations of the stroke technique were trialled throughout this project to ascertain the effects that certain changes in technique have on the individual drag/propulsion relationship on different parts of the body and on the overall stroke efficiency. The next phase of the model development to assist with this endeavour was the movement of the mesh that surrounds the virtual skeleton outlined earlier in this chapter. As detailed for the 2D motion, the standard UDF in FLUENT for rigid-body motion is only capable of rotating mesh using a Cartesian coordinates system and does not allow for polar angles of rotation. A UDF was written to define the movement of each surface mesh point associated with the rigid section forming each limb. This same UDF was then used to transform each mesh point associated with the boundary prisms and additional boundary layer mesh to enable a consistent mesh surrounding the object throughout the swimming stroke. To achieve this capability, each group of nodes was collated into zones that defined the movement. Within each zone a limited number of points need to move in the three rotational polar angles and translate in the three Cartesian directions between time steps. -69-

85 Chapter 3 - CFD model methodology and passive drag validation -70- The basis for this formulation was as follows: Each joint centre point is identified: x-joint coordinate = x n y-joint coordinate = y n z-joint coordinate = z n Each node point is defined by: x-node coordinate = x i y-node coordinate = y i z-node coordinate = z i A vector was then defined, derived from the three vectors for which the polar moments are based: [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] ) ( ) ( ) ( 2 ) ( ) ( ) ( 1 ) ( ) ( ) ( ) cos( ) sin( 0 n n n n n n n n t n n n n n n n n t n n n n n n n n t y y y yprev xz xz yprev xz z z y y x x z z V z z y y x x y y V z z y y x x x x V V V V V V V + = + = + = = = = = = = ϑ ϑ

86 Chapter 3 - CFD model methodology and passive drag validation -71- A rotational matrix around each vector is then defined [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] t y xz i V V V V V V V V V V V V V V V V V V V V V V V V M i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i,, ) cos( )) cos( *(1 2 * 2 ) *sin( 0 )) cos( *(1 2 * 1 ) *sin( 1 )) cos( *(1 2 * 0 ) *sin( 0 )) cos( *(1 2 * 1 ) cos( )) cos( *(1 1 * 1 ) *sin( 2 )) cos( *(1 1 * 0 ) *sin( 1 )) cos( *(1 2 * 0 ) *sin( 2 )) cos( *(1 1 * 0 ) cos( )) cos( *(1 0 * 0 = = ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ ϑ The location of the new mesh point was then defined by the multiplication of the original co-ordinates minus the predecessor joint s previous location by the three rotational matrices, and then the new predecessor s location was added. [ ] [ ] [ ] + = ) ( ) ( ) ( 1) ( 1) ( 1) ( 1) ( 1) ( 1) ( ) ( ) ( ) ( * * * t n t n t n t n t i t n t i t n t i xz y t t i t i t i z y x z z y y x x M M M z y x

87 Chapter 3 - CFD model methodology and passive drag validation This calculation was repeated for each node associated with the rigid zone and for each time step. For limbs such as the forearm and calf, where the majority of the rotation occurs in the limb rather than at the joint, an additional complexity of the torsional rotation was included. The torsional rotation of each member was set as constantly increasing along the length of the segment rather than completely at the joint. Mesh Node Figure Each node point is referenced back to the predecessor joint to identify its motion. -72-

88 Chapter 3 - CFD model methodology and passive drag validation Shoulder Joint At this point in time, complete and accurate method for describing shoulder joint motion, inclusive of all its degrees of freedom and incorporating the role of the scapular motion currently eludes the biomechanics fraternity (de Groot & Brand, 2001; Borstad & Ludewig, 2002). As better models for this combined motion are developed and the measurement of the motion via more advanced kinematic data collection, the CFD model can be upgraded to incorporate these changes. In the initial results of the CFD analyses it was expected that the minor differences in shoulder positioning would be minimal compared to the increase in foundational knowledge derived for the motion of the segments through the water. Hence, the shoulder joint was treated as a simplified double ball and socket joint (Figure 3-23) which provided an extra three angles to those from the other joints in the body (all other joints treated as single ball and socket joint). As the kinematic data measured here could only record two points for the shoulder (the gleno-humeral joint centre and the acromio-clavicular (AC) joint), an approximation of the distribution of rotation into the modelled joint was required. Previous research of the shoulder joint (de Groot & Brand, 2001; Borstad & Ludewig, 2002) provided estimations of the scapular motion in relation to the upper arm angle. The ratio of rotation of the scapula joint was estimated as 44% of the shoulder joint in elevation (or the θy angle). There is limited research investigating the movement ratio of the horizontal adduction/abduction contributed by the scapula joint relative to the upper arm and hence this needed to be approximated. This movement is likely to be highly individualised when considering the specialised sub-set of the population who were subjects in these studies. Various ratios were examined with 10%, 20%, 30% and 40% all trialled on a subjective visual basis. Examining the visual outputs from the model showed that a adduction/abduction rotational percentage of 10% appeared to be the most realistic when compared to that of the freestyle swimmer performing the stroke. This 10% ratio refers to the segment L3 (Figure 3-23) taking 90% of the rotation of L2, and 10% of the rotation of L

89 Chapter 3 - CFD model methodology and passive drag validation It was also assumed that there was no torsional rotation of the scapular joint at any time and that any torsional rotation in the shoulder was performed by the shoulder joint itself. θt L4 θy L3 Rigid L2 L2 Flexible Flexible Figure The double ball and socket joint arrangement for the shoulder. Flexible Joints The flexible joints used in the CFD simulation were from specialised UDFs written in collaboration with CFD Boost Pty Ltd. These UDFs are the property of CFD Boost Pty. Ltd. and the details of how they maintain the integrity of the joints cannot be detailed in this thesis. The benefits of these UDFs can be seen in the output graphics (Appendix A). These animation plots highlight the ability of these UDFs in the maintenance of joint integrity to allow for the realistic motion of the swimmer to be preserved. -74-

90 Chapter 3 - CFD model methodology and passive drag validation Summary This study has achieved the following outcomes that are critical to evaluating swimming techniques via a Computation Fluid Dynamic simulation using the commercial code FLUENT. Finding athletes capable of producing elite level times in the butterfly, breaststroke and freestyle strokes. Then, 3D geometric models of these swimmers were developed and the kinematic data recorded of common swimming skills. Errors in the derived kinematic data indicated that further research is required in this area to improve the overall accuracy and applicability of the CFD results. A best practice methodology for determining the correct mesh sizing, boundary layer feature and domain boundaries together with using alternative industry best practice turbulence models of the realisable k-epsilon model with near-wall functions and second order discretisation schemes enabled validating the CFD models against physical trials of the same swimmers in a passive drag simulation. The study created a means to convert digitised kinematic data into a connected virtual skeleton of rigid members and joints that can describe the movement of any part of the swimmer through a series of equations. Although the differences between digitised and calculated coordinates were higher than expected, this new methodology of relating joint movements has advanced current knowledge and would lead to improved measurements. New UDFs were developed that enable moving the mesh nodes and surfaces required to replicate the movement of the swimmer in a simulation. Through review of past research and visual optimisation, the rotational ratios of the scapula and shoulder joints are suggested with a 44%, 10% and 0% ratio used for the elevation, adduction/abduction and torsional motions of the upper arm, respectively. -75-

91 Chapter 3 - CFD model methodology and passive drag validation There are considerable difficulties in predicting errors that may be evident in the final CFD simulations. These are due to the accuracy of kinematic data, human body surface roughness, towing passive drag test data, as well as the inability to fine tune the CFD variables as a confirmed measured value to compare the results against was not available. However, best practice is used in all situations and it is expected that the macro findings revealed from the CFD simulations would not be significantly affected by these errors. As technology and research in these areas improve, the developments in this study can refine and better predict the micro actions within an active swimming simulation. -76-

92 Chapter 4 Study 2 - Dolphin Kick Underwater Introduction The next logical step was for the theories and methodologies developed in the preceding chapter to be applied to a practical swimming skill. Initially an application with limited complex components, such as air/water interface effects and 3D swimmer kinematics, was selected to enable a proof-of-concept validation of the CFD model. The dolphin (or butterfly) kick is used by many swimmers in an underwater phase of up to 15m after the start of a race, and after each turn. Currently a variety of underwater kicking techniques are used by competitive swimmers with their selection usually based on little scientific rationale. Previous empirical studies have been unable to differentiate between the active drag and propulsion created during the underwater dolphin kick, and they have not examined how variations in the frequency and magnitude of the kicks affect the resultant effectiveness of the kicks (Lyttle et al., 2000). This study examined two dolphin kick patterns on the same body shape in the same upper body streamlined position. This was conducted to establish if it is possible to determine how and where different underwater dolphin kick patterns produced drag and propulsive forces. The kick patterns include one of a high amplitude/low frequency, and -77-

93 Chapter 4 - Dolphin kick underwater one of a low amplitude/high frequency kick technique. Both of these examples were reflective of kicking patterns used in high level competitive swimming. An elite level butterfly swimmer capable of swimming 50 m butterfly times in less than 24 s was selected to provide the 3D body scans and kinematics of the two techniques. The dolphin kick was also the simplest kicking technique for analysis because it can be assumed that the movement is mainly in a two dimensional plane. With the upper body held as rigid as possible, it limits the number of rigid links to four. -78-

94 Chapter 4 - Dolphin kick underwater Methodology Summary input data resulting from the kinematic analysis are listed below (see Table 4-1, Table 4-2 and Figure 4-2) for both of the underwater kicking conditions and are compared with data from international swimmers (Arellano, Pardillo & Gavilan, 2002). A comparison of the Strouhal number, an estimation of kicking efficiency (Arellano et al., 2002), can be misleading given the overall deceleration throughout the kick cycle in the current study. However this deceleration is reflective of what occurs during the underwater phases of competitive swimming races. The results in the table below demonstrate clear differences in the kick amplitudes and frequencies between the two types of underwater dolphin kicks. A comparison of dolphin kick frequencies used following a dive entry in the 100m and 200m men s freestyle finals at the Sydney Olympics demonstrate similar kick frequency values to the current study (Ian Thorpe produced ~2.30Hz in the 200m and Michael Klim produced ~2.56Hz in the 100m final). The features of the two techniques are listed in Table 4-1 below. Table 4-1 Kinematic data for dolphin kick techniques. (NB: rotational values are based on the direction of angles shown in Figure angles >180º referred to as hyperextension) Large Kick Small Kick Amplitude (m) Frequency (Hz) Maximum Hip Rotation (deg) Minimum Hip Rotation (deg) Maximum Knee Rotation (deg) Minimum Knee Rotation (deg) Maximum Ankle Rotation (deg) Minimum Ankle Rotation (deg)

95 Chapter 4 - Dolphin kick underwater Ankle Rotation Angle Knee Rotation Angle Hip Rotation Angle Figure Angle of rotation measurement positions. Results An output of combined pressure and viscous drag forces were calculated at each time step through the analysis. The best measurement of technique effectiveness is to integrate the force-time curve to determine the momentum created or removed from the swimmer per cycle. The change in momentum would be equivalent to the impulse subjected on the body by the water. This momentum can then be converted to a value per second so as to compare different techniques. Table 4-2 details the momentum removed from the swimmer for the analysis runs completed. Figure 4-2 shows the full output of force versus time for all analysis runs, with the graphs altered to show a full cycle of each comparison. To do this, the small kick plots were extrapolated to plot over a 0.43 s interval. Further plots of the individual body part momentum curves are shown in Appendix A. Table 4-2 Average momentum (Ns) reduction in swimmer through 1 s of swimming. Large Kick Small Kick 2.4m/s 2.18m/s 1.5m/s 2.4m/s 2.18m/s 1.5m/s Total per cycle Total per second Body per second Hips per second Thighs per second Knees per second Calves per second Ankles per second Feet per second

96 Chapter 4 - Dolphin kick underwater 100 Total Drag Force (N) Time (sec) Large 2.4m/s Large 2.18m/s Large 1.5m/s Small 2.4m/s Small 2.18m/s Small 1.5m/s Figure Combined pressure and viscous drag forces over entire body for one full cycle. (NB: Small kick results are stretched to plot over 0.43 s interval). 40 Knees Drag Force (N) Large 2.4m/s Large 2.18m/s Large 1.5m/s Small 2.4m/s Small 2.18m/s Small 1.5m/s Figure Combined pressure and viscous drag forces at the knees for one full cycle. (NB: Small kick results are stretched to plot over 0.43 s interval). -81-

97 Chapter 4 - Dolphin kick underwater The temporal sequences of the kick cycle are listed below Time Description 0.07 to 0.12 s Lifting the feet on the upswing of the kick 0.12 to 0.30 s The feet accelerating downward in the down phase of the kick 0.30 to 0.40 s The feet are below the body and decelerating to end the down-sweep 0.40 to 0.50 s The feet are accelerating upwards in the up-sweep again. Figure Sample pressure plot output of the CFD model. -82-

98 Chapter 4 - Dolphin kick underwater Discussion At all speeds modelled, both of the underwater dolphin kicking scenarios revealed that the kick still created a net drag effect, and indicated that the swimmer was not able to maintain any of these kicking speeds. From closer inspection of the velocity of the hips calculated from the kinematic data (Figure 4-5), it can be seen that, rather than holding a constant speed, the swimmer is decelerating, which is in agreement with the CFD results. Both the CFD results and the kinematic analysis are comparable with a previous study (Lyttle et al., 2000) that showed a net drag effect in both underwater freestyle and dolphin kick techniques at speeds between 1.6m/s and 3.1m/s,. This deceleration represents the realistic effects that occur during underwater kicking in competition. Given that the role of the underwater kick is to minimise the deceleration rate throughout the underwater phase prior to stroke resumption. 300 Velocity of Large Kick over 1 second 250 Velocity (cm/sec) y = x Time (s) Figure Velocity changes through kicking cycle. The results demonstrated that both kick techniques have a similar effect at 2.40 m/s. However, although the values were not quantified, it appears that for speeds of greater than 2.40 m/s, there may be a trend for the small/fast kick to become more efficient. It was found in this study that for speeds <2.40 m/s, the large/slow kick is more effective. The momentum change results showed a 4% difference in favour of the large/slow kick at 2.18 m/s and 18% at 1.50 m/s. However, this translates to a much smaller 1.7% and -83-

99 Chapter 4 - Dolphin kick underwater 2.2% improvement in the predicted distance swum in the subsequent second of kicking (based on a 90kg swimmer). These velocities can be compared with data from elite swimmers who typically enter the water from a dive start at between 4.50 and 5.50 m/s (Benjanuvatra, Lyttle, Blanksby & Larkin, 2004) and push off the wall after turning at between 2.60 and 3.20 m/s (Lyttle et al., 1999). Free swimming velocity (which represents the velocity at which swimmers should initiate stroking) ranges from 1.60 and 2.20 m/s, depending on the stroke, distance and their levels of performance. When comparing the dynamic underwater kicking data with steady-state results, it can be seen that velocities around 2.40 m/s may represent a cross-over point. That is, at higher velocities it is more efficient for the swimmer to maintain a streamlined position than to perform an underwater kick. This is due to the swimmer creating more active drag than propulsion while kicking than occurs when remaining in a streamlined position, leading to wasted energy and/or a greater degree of swimmer deceleration. Hence, although it appears that swimmers have the potential to benefit from a small/fast kick pattern at higher velocities compared with a large/slow kick, results indicated that it would be even more beneficial to just maintain a streamline position. However, direct comparisons between dynamic analysis and steady-state analysis should be made with a degree of caution, and need further investigation for more definitive findings. The main benefit of the large kick is the acceleration that is created on both the upsweep and the down-sweep. The larger kick can create up to 50N more propulsive force in these acceleration phases whereas they only create 25N more drag in the nonacceleration phase. The main benefit of the propulsion does not come from the feet where the propulsive forces are only marginally greater for the large kick than the small kick. The main benefit comes from the thighs and calves where much greater propulsion is generated in the large kick as opposed to the small kick. These results differ from a later study (Von Loebbecke et al., 2009) that detailed peak forces in a female swimmer of approximately 350N and a male swimmer of 650N. These propulsive force values appear to be high as they suggest the equivalent of lifting 66kg by using a dolphin kick for a male swimmer, rather than the more reasonable peak of 5kg as found in the current study. There is insufficient detail in the Von Loebbecke et al. (2009) report to determine why the differences occurred. -84-

100 Chapter 4 - Dolphin kick underwater A major component of drag in the large kick is when the knees drop, prior to the main down-sweep, due to the increased frontal surface area and flow changes. This dropping of the knees creates up to 20N more drag for the large kick model (Figure 4-3) during the 0.08 s of the cycle. Movement of the upper body during the large kick also generates significantly more drag in phases of the large kick cycle than that of the small kick. However, in the up-sweep of the feet, the body maintains sufficient momentum to offset some of the loss imposed by the high amplitude kick. Ankle Flexibility Effect on Propulsion The relative importance of a flexible ankle joint has never been quantified. This is despite that, anecdotally, more effective underwater kickers tend to have better flexibility through a range of joints, particularly the ankle and knee. To illustrate the capabilities of the CFD modelling technologies, various scenarios were modelled by varying ankle movements in order to examine the effects on a swimmer s net thrust during underwater dolphin kicks. In this case study example, three scenarios were examined, with results in Figure 4-6: The full range of ankle plantar flexion/dorsi-flexion of the test subject (pink curve). A 10 shift in the ankle flexibility referring to 10 less maximum plantar flexion and 10 greater maximum dorsi-flexion angle (green curve). A 10 decrease only in maximum plantar flexion angle (blue curve). -85-

101 Chapter 4 - Dolphin kick underwater Max = 41.2N Max = 24.8N Feet Component Drag Force (N) Time (s) -70 Min = -68.8N -110 Min = N Original 10deg shift 10deg less plantar flexion Figure Net thrust graph highlighting effects of ankle flexibility on propulsion. The results in Figure 4-6 demonstrate that, while the swimmer is travelling at 2.18m/s, a 10 increase in ankle plantar flexion will create a greater peak propulsive force of 16.4N during the kick cycle. However, with 10 more dorsi-flexion, the peak drag will increase by 31.4N. When focusing on only increased plantar flexion during the downsweep, which occurs between s (Figures 4-7 & 4-8), it represents approximately 3.7 times greater momentum contribution by the feet over the whole of the down-sweep. To put this in perspective, it equates to an extra ~21% of total momentum created by the entire body during the down-sweep (due to the contribution of other segments in creating the propulsion) and ~6.3% over the full kick cycle. The relative contribution of the increased flexibility would change at different kicking velocities throughout the underwater phase but the general trend of the benefits would be the same. This provides important information to coaches on the effects of flexibility on the generation of propulsion while kicking. -86-

102 Chapter 4 - Dolphin kick underwater 60 Force on Feet with Different Ankle Flexibility Force (N) Original Flexibility Time (s) 10 Degrees Less Flexibility Figure Net thrust graph highlighting effects of ankle flexibility on propulsion created by the feet. 50 Total Force with Different Ankle Flexibility Force (N) Original Flexibility Time (s) 10 Degrees Less Flexibility Figure Net thrust graph highlighting effects of ankle flexibility on the propulsion created by the total body. -87-

103 Chapter 4 - Dolphin kick underwater Conclusion The results of this case study found the large/slow underwater dolphin kick was the more effective of the two analysed underwater dolphin kicking techniques at speeds where kicking produced less drag than the streamlined glide. This result was based solely on the two kicking patterns analysed and cannot be generalised to the large number of possible kicking patterns used by elite swimmers. However, this case study highlights the value of CFD in optimising swimming techniques. Two main areas of technique improvement that were discovered were the impact that ankle flexibility had on propulsion and the effect of excess body movement patterns on the production of drag forces. Greater flexibility throughout the ankle joint was found to result in greater net propulsion being produced. Dropping the knees too far below the horizontal line of the body during the dolphin kick was also demonstrated to lead to a significant increase in drag and slow the swimmer s velocity. -88-

104 Chapter 5 Study 3 - Freestyle Kick Underwater Introduction Swimmers competing within the freestyle and backstroke events have the choice of using either a freestyle kick or a dolphin (butterfly) kick during the underwater phase following a start, or after each turn. For elite competition in these events, there exist swimmers who use either of these techniques exclusively or a combination of both during underwater kicking. It is not known why one technique may be preferable or beneficial than another for individual swimmers, or at which time it is best to transition between these techniques if using a combination of the styles. There is also a paucity of information as to whether these kicking techniques are dependent on factors such as body shape, streamline position, joint flexibility and/or strength of the swimmer. To advance to the next phase of CFD models, the methodology was applied to the freestyle kick which increased the number of rigid limbs in the CFD animation from four to seven segments. In order to generate comparative results between the dolphin and freestyle kicks, the same scanned swimmer performed both kicking techniques. -89-

105 Chapter 5 - Freestyle kick underwater Methodology Following the methodology detailed in Chapter 3, 2D kinematics were extracted for the elite butterfly swimmer while performing an underwater freestyle kick. Kinematics were obtained for both the left and right legs with the details shown in Tables 5-1 and 5-2. This additional leg independence required the CFD model to be increased from four rigid segments to seven, and a more detailed hip joint to account for the 3D joint rotation. The results of these simulations were compared with the results from Study 2 to see which kicking style produced the best results. Table 5-1 Descriptive kinematic variables for the freestyle kick. Derived Kinematic Variables Left Leg Right Leg Kick Amplitude (vertical displacement of toe) (m) Average Horizontal CM Velocity (m/s) Kick Frequency (Hz) Minimum Hip Rotation (deg) Maximum Hip Rotation (deg) Minimum Knee Rotation (deg) Maximum Knee Rotation (deg) Minimum Ankle Rotation (deg) Maximum Ankle Rotation (deg) Table 5-2 Temporal phases of the freestyle (flutter) kick. Time Description 0.16 s Right foot at the highest point and left foot at its lowest 0.26 s Right knee at its lowest point, left and right feet cross over 0.36 s Left foot at the highest point and right foot at its lowest 0.46 s Left knee at its lowest point, left and right feet cross over. -90-

106 Chapter 5 - Freestyle kick underwater A major benefit of the CFD modelling procedure is that the user can modify inputs into the model to determine how variances in the input parameters affect the resultant flow conditions. Similar to the underwater dolphin kick study, the CFD models were re-run over a range of velocities to ascertain any differences in drag and propulsion at various kicking velocities. -91-

107 Chapter 5 - Freestyle kick underwater Results An output of combined pressure and viscous drag was calculated at each time step through the analysis runs. The variation of this combined force over time can be seen in Figures 5-1, 5-2, 5-3 and 5-4 for the overall body; the left and right legs separately; the feet; and the knees. As outlined in Study 2, the best measurement of technique effectiveness is the momentum created or removed from the swimmer per cycle. The momentum can then be converted to a per-second measurement to compare different techniques. An overall summary of these combined momentum changes, and comparison with the equivalent for the dolphin kicks found in Study 2, are shown in Table 5-3. Any momentum changes can then be extrapolated to a distance travelled in the next second of kicking based on these results to provide a more practical comparison (Table 5-4 and 5-5). A large amount of data was produced from each simulation. Figure 5-5 displays a sample fluid flow velocity plot that can be derived from the CFD model, and animated to graphically depict where high water velocities and vortices are generated throughout the kick cycle. More outputs through the entire cycle can be found in Appendix A. Table 5-3 Comparisons between total and segment momentum changes for the underwater dolphin kick and freestyle kick at 2.18 m/s. Dolphin Large/Slow Kick Dolphin Small/Fast Kick Freestyle Kick Total per cycle (Ns) Total per second (Ns) Body per second (Ns) Hips per second (Ns) Thighs per second (Ns) Knees per second (Ns) Calves per second (Ns) Ankles per second (Ns) Feet per second (Ns)

108 Chapter 5 - Freestyle kick underwater 50 Total Drag/Propulsion Force - Freestyle Kick Force (N) Figure Total force curve for all body parts combined. 100 Drag/Propulsion force Left/Right Leg During Freestyle Force (N) Left Leg Right Leg Figure Force curves for left and right leg components separately. -93-

109 Chapter 5 - Freestyle kick underwater 50 Drag/Propulsion force Left/Right Feet During Freestyle Force (N) Time (sec) foot-left foot-right Figure Force curves for the left and right feet. 30 Drag/Propulsion force Left/Right Knee During Freestyle Force (N) Time (sec) knee-left knee-right Figure Feet and knee drag/propulsion curves for the freestyle kick cycle. -94-

110 Chapter 5 - Freestyle kick underwater Table 5-4 Average momentum (Ns) change in swimmer through 1s of kicking. Large/Slow Dolphin kick Small/Fast Dolphin Kick Freestyle Kick Modelled Velocity (m/s) Total per second (Ns) Distance next second (m) Table 5-5 Average momentum (Ns) change in swimmer through 1s of kicking. Large/Slow Dolphin kick Small/Fast Dolphin Kick Freestyle Kick Modelled Velocity (m/s) Total per second (Ns) Distance next second (m) Modelled Velocity (m/s) Total per second (Ns) Distance next second (m) Figure Sample picture displaying levels of flow velocity and their vector directions. -95-

111 Chapter 5 - Freestyle kick underwater Discussion Overall Freestyle Kick Review Tables 5-4 and 5-5 detail the overall momentum change throughout the freestyle kick at velocities of 1.5m/s, 2.18m/s and 2.4m/s. When these are compared to the passive drag values listed in Study 1, it can be seen that the amounts of drag at 2.4m/s are almost similar, with the underwater freestyle kick showing increased benefits as the velocity of the swimmer slows. This comparison is made by comparing the total momentum change (Ns) per average second of the kick cycle (Ns/s which is equivalent to N). At 1.5m/s, the improvement when using the freestyle kick is just over 40%, when compared to no kick at all. This correlates well with a study by Lyttle et al. (2000) that showed an average difference in net force of 46% at 1.6m/s for the 16 experienced swimmers tested. However, the negative net momentum in this study demonstrate that, even at these slower speeds, the freestyle kick still cannot maintain this velocity. Reviewing the kinematic data validates this finding, showing a steady decline in velocity throughout the kicking period. 300 Velocity of Iliac Crests 250 Velocity (cm/s) Time (s) Left iliac crest Right iliac crest Linear (Left iliac crest) Figure Velocity comparison for freestyle kick kinematic data. The velocity profile in Figure 5-6 partially validates the overall force profile. It shows two distinctive peaks in each 0.39 s cycle, and these occur with a longer lasting velocity -96-

112 Chapter 5 - Freestyle kick underwater peak at around 0.45 s. This higher peak occurs after the longer peak force period (Figure 5-1) even though the force peak is not as high as the force at 0.2 s. This comparison is valid as a higher propulsive force translates into greater acceleration of the swimmer. The acceleration then has a lag effect to create a faster velocity. The analysis revealed that an equal amount of the propulsive force that is generated is coming from the motion of the calves and the thighs. This is different from conventional coaching theory that proposes that the power in the freestyle kick is generated by the motion of the feet (Maglischo, 2003). The feet also record a higher drag force than the calf and thighs, which could be related to the projection area of the feet that are orientated towards the rear and is therefore subject to form drag suction pressure. Reasoning behind the calves and thighs producing higher than expected propulsion values could be due to the greater volume associated with these components. As mentioned in the Literature Review, the forces on objects in the water can be estimated by using Morrison s equation (Gerhart et al., 1992). With the feet and legs accelerating at similar rates, the greater volume associated with the calves and thighs would equate to a higher propulsive force for these regions. Left and Right Side Comparisons A major advantage of the CFD technique is that it can differentiate what parts of the swimmer s body is creating the active drag and propulsion throughout the cycle. This allows a more effective mechanism for identifying areas of inefficiency that can be targeted when prescribing technique modifications. The underwater freestyle kick data showed a number of differences between the left and right leg movements during the freestyle kick. The flexibility in the right ankle was less than that for the left ankle, with the range of movement for the right ankle being 27 as opposed to 52 for the left ankle. The swimmer appeared to counteract this by increasing the knee bend in the right leg. The right leg knee range of movement was 56, compared with only 42 in the left leg. The results of the CFD analysis (Figure 5-2) indicate that the right leg created more peak propulsion during the start of its down-sweep but also created a greater drag near the end of the down-sweep when the feet drag below the projected line of the body. -97-

113 Chapter 5 - Freestyle kick underwater Table 5-6 shows this additional drag had a greater impact on the effectiveness of the right leg, with the left leg creating almost 6.5Ns greater propulsion for each cycle (16.6Ns for each second). This resulted mainly from the differences in net force between the left and right legs, at the feet and knees. This could have resulted from the reduced flexibility of the right ankle, and the impact that it appeared to have on the amplitude of the movement of the entire right leg. Table 5-6 Total and segment momentum changes for left and right kick cycles at 2.18 m/s. Left Leg Right Leg Total per cycle (Ns) Total per second (Ns) Hips per second (Ns) Thighs per second (Ns) Knees per second (Ns) Calves per second (Ns) Ankles per second (Ns) Feet per second (Ns) The peak propulsion force by the right foot was 17N (Figure 5-3), was greater than that of the left at 9.7N, and most likely was due to the higher angle of the calf at this time. The peak drag of the right foot was 48.9N and 30.9N by the left foot, and was due to dropping the right leg further below the line of the body. This occurs also when comparing the knee forces with the right knee dropping earlier in the cycle and further below the line of the body. Hence, a peak drag of 19.1N was created whereas the peak drag of the left knee was 7.6N (Figure 5-4). From this simple comparison it could be concluded that improved flexibility of the right ankle may improve the swimmer s freestyle kick performance by 4-5%. -98-

114 Chapter 5 - Freestyle kick underwater Comparison Between Freestyle and Dolphin Kicks Figure 5-7 outlines the differences in kicking techniques between the underwater freestyle kick and the low and high amplitude dolphin kicks. The underwater freestyle kick had a much smaller cumulative momentum loss over time, when compared to either of the underwater dolphin techniques. 40 Cumulative Momentum Loss for Each of the Three Kicking Scenarios 35 Momentum Loss (Ns) Time (s) Freestyle Kick Small/Fast Dolphin Kick Large/Slow Dolphin Kick Figure Graph of the cumulative momentum loss for each kicking scenario at a velocity of 2.18m/s. At the modelled velocity of 2.18 m/s, the underwater freestyle kick provided the least amount of momentum loss and a greater predicted distance travelled over the subsequent second of kicking (based on a 90kg swimmer), than either of the two underwater dolphin kicks (see Tables 5.4 & 5.5). The 90kg weight is the approximate dry weight of the swimmer used in the study. However, to get the true distance travelled, the dry weight plus any additional added water mass that the body carries around it should also be included. This amount is unknown but previous studies (Klauck, 1998) have estimated it to be between 30 and 70kg, depending on the shape and streamlined technique of the swimmer. Simulations at 1.5m/s and 2.4m/s (Table 5-5) showed a similar 30% reduction in momentum loss of the freestyle kicks over both dolphin kicks. -99-

115 Chapter 5 - Freestyle kick underwater It cannot be implied automatically that the freestyle kick is more efficient than the dolphin kick for all circumstances. Other factors, such as the potential energy cost differences in applying the different techniques should also be considered. More importantly, it does allow the interrogation of these three techniques to establish where the differences in drag and propulsion are, and if they can be modified to produce a more efficient kicking technique. Complementary testing of the energy costs for each kicking technique, such as lactate and oxygen uptake tests, also would be required before any recommendations of appropriate kicking styles can be applied. Freestyle and dolphin kicks are similar in nature in that they both take place mainly in a two dimensional plane. However, because the legs move alternately in the freestyle kick, it requires a significantly different pelvic and hip movement than for the dolphin kick. Thus, in order to simulate the freestyle kick correctly this required a slight adjustment to the models used for the dolphin kick around the hip and pelvis area. Due to the slightly different models being used for the dolphin and freestyle kicks as the CFD animation model evolved, the area of the body associated with each part is slightly different. Hence, comparing each individual part may lead to misleading results. However, if only the knees, calves, ankles and feet are compared, which were of the same area, a base comparison should give an overall picture. The underwater dolphin kick is usually considered by most elite swimmers as subjectively feeling stronger in the water than the underwater freestyle kick. The results showed that peak feet propulsion and the overall propulsion of the dolphin kick were substantially greater than in the freestyle kick. In this case study, the dolphin kick produced peak feet propulsion of 41N for the large kick, and 35N for the small dolphin kick, compared with 29N for the freestyle kick. The overall benefit of the feet in the dolphin kick also was 14Ns (average of large and small amplitudes) greater throughout the cycle. However, these benefits were quickly eroded by the influence of the knees, calves and ankles which, due to the high amplitude and extra knee bend of the dolphin kick, produced an average 27Ns of momentum loss per second. This is clearly seen in the knees with a drag peak of 48N and 68N for the dolphin kicks, and only 24N for the freestyle kick

116 Chapter 5 - Freestyle kick underwater Conclusion This study recorded broad ranging findings as to whether the underwater dolphin kick was the more effective kicking technique during the underwater phase after a start or turn. It could be that this is not always correct. Indeed, for the current swimmer, the underwater freestyle kick recorded substantially lower momentum losses than either of the two underwater dolphin kicking techniques. The breakdown of the forces demonstrated that the net effects of the propulsion produced and the drag experienced by the swimmer can vary. It is dependent on the timing and magnitude of the movements by each segment throughout the technique. This study also revealed that asymmetries in the flexibility of a swimmer between the left and right sides can largely affect the drag experienced, or the propulsion created by the swimmer, through the kicking cycle. Again, it is reiterated that these are case study analyses only, and definitive findings regarding the best technique were beyond the expectations of this study. The macro outcomes from this study do show that: There can be a substantial difference between the propulsion generated by the left and right sides of the body. Small changes to a swimmer s technique to modify asymmetries could improve swimming speed. During the freestyle kick, the contribution by the calves and thighs may be substantially greater than shown by previous research (Von Loebbecke et al., 2009)

117 Chapter 6 Study 4 - Freestyle Kick at Water Surface Introduction A number of studies have tried to estimate wave drag (Lyttle, 1999; Toussaint et al., 1988) created by a swimmer, and the differences between the forces acting on a swimmer at depth and one close to the surface. Most have developed ways to estimate the overall drag on a swimmer s body but, due to the unavailability of empirical testing technology, it could not be determined as to the parts of the body with which the additional drag (if any) was associated. The CFD model can predict the propulsion or drag created by each body segment throughout the stroke by combining this with a multi-phase model. Therefore, the differences between the forces on the body components when at depth, and at the surface, can be determined. Usually, discussions on drag centre around either passive or active drag; or frictional, form and wave drag. These are sometimes treated as different entities. However, in practice, they are all comprised of different ratios of pressure and wall shear forces on -102-

118 Chapter 6 - Freestyle kick at water surface the body. These two forces determine the amount of drag and propulsion a swimmer generates throughout the stroke cycle. This study aimed to validate the use of the FLUENT CFD software in predicting the change in drag for a swimmer kicking at or near the water surface. This was then compared with a completely submerged swimmer to gain some insights into how and where the differences occur. Methodology The methodology used in setting up the simulations and the kinematic measurements can be found in Chapter 3. To provide an initial insight into the capabilities of a simulation to determine the differences between a submerged freestyle kick and one closer to the surface, a standard case study format was used. Previous studies have examined the differences in passive drag by comparing a swimmer near the surface and at various depths below (Lyttle, 1999). It was found that most swimmers produced greater passive drag when near the surface. To create a bench mark for the CFD models, a similar passive drag study was completed. At a velocity of 2 m/s two simulations were compared: A fully submerged set-up as per Study 1. A near-surface model with the mid iliac crest located 0.1m below the free surface. This benchmarking provided an initial indication of the differences created by changes in trailing vortices. While under water, the trailing vortices form a three dimensional vortex in any direction. However, at the water surface, the vortices will not form across phases (i.e the air/water interface) and a surface wave results. The difference in forces on each body component can then be compared before active drag is introduced. Using the same freestyle kicking pattern outlined in Study 3, two examples were then analysed: A fully submerged set-up as per Study 3 at a speed of 1.5m/s created in an entire water domain

119 Chapter 6 - Freestyle kick at water surface A multi-phase domain with the mid iliac crest of the swimmer situated 0.1m below the air-water interface at the same speed of 1.5m/s The rationale behind using 1.5m/s for kick comparisons was because elite swimmers complete 50m of freestyle kick in approximately s. When the wall push-off is ignored, the average speed would be around 1.5m/s. Selecting a 2m/s kick would potentially be too fast considering that speed approximates the maximum swimming speed for elite sprinters. The kinematics were the same as for Study 3 and the notable temporal points throughout the kick cycle are shown again in Table 6-1. Table 6-1 Points of interest in the freestyle (flutter) kick. Time Description 0.16 s Right foot at the highest point and left foot at its lowest 0.26 s Right knee at its lowest point, left and right feet cross over 0.36 s Left foot at the highest point and right foot at its lowest 0.46 s Left knee at its lowest point, left and right feet cross over. Results The following tables and figures represent the analysis results simulating the freestyle kick near the surface of the water. As with studies 1-3, the output is broken down into the drag and propulsion created by each individual component. Table 6-2 represents the passive drag force comparison in Newtons with Table 6-3 displaying the culmination of momentum throughout the kick cycle and then averaged to a per/second value. This provides a Ns/s value which can be compared to the force value of the passive drag simulation

120 Chapter 6 - Freestyle kick at water surface Figure Example of output from the CFD simulation detailing the surface deviation over the body as well as velocity vectors. Table 6-2 Differences in passive drag on body components when fully submerged compared to near-surface. Freestyle Kick Submerged Freestyle Kick- Velocity 2 m/s 2 m/s Near-Surface Change % Change Total (N) % Hands (N) % Arms (N) % Head (N) % Upper Body (N) % Total-Body (N) % Hips (N) % Thighs (N) % Knees (N) % Calves (N) % Ankles (N) % Feet (N) % -105-

121 Chapter 6 - Freestyle kick at water surface Table 6-3 Differences in momentum per second (Ns/s) created for fully submerged and near-surface simulations. Freestyle Kick Submerged Freestyle Kick Near-Surface Velocity 1.5m/s 1.5m/s Change % Change Total per cycle (Ns) % Total per second (Ns) % Body per second (Ns) % Hips per second (Ns) % Thighs per second (Ns) % Knees per second (Ns) % Calves per second (Ns) % Ankles per second (Ns) % Feet per second (Ns) % Drag/Propulsion Comparison - Total Force (N) Time (sec) Total - Near Surface Total - Fully Submerged Figure Comparison of the total net force on the swimmer for submerged and near-surface simulations

122 Chapter 6 - Freestyle kick at water surface Drag/Propulsion Comparison Left Foot Force (N) Time (sec) Left Foot - Near Surface Left Foot - Fully Submerged Figure Comparison of the left foot net force on the swimmer during submerged and nearsurface simulations. Drag/Propulsion Comparison Left Calf Force (N) Time (sec) Left Calf - Near Surface Left Calf - Fully Submerged Figure Comparison of the left calf net force on the swimmer during submerged and nearsurface simulations

123 Chapter 6 - Freestyle kick at water surface Drag/Propulsion Comparison Right Foot Force (N) Time (sec) Right Foot - Near Surface Right Foot - Fully Submerged Figure Comparison of the right foot net force on the swimmer during submerged and nearsurface simulations. Drag/Propulsion Comparison Right Calf Force (N) Time (sec) Right Calf - Near Surface Right Calf - Fully Submerged Figure Comparison of the right calf net force on the swimmer during submerged and nearsurface simulations

124 Chapter 6 - Freestyle kick at water surface Discussion Passive Drag Comparisons The differences between the fully submerged and near-surface passive models showed an overall difference in average drag of 11.3N at 2m/s, or the equivalent of an 18.2% decrease when fully submerged. This correlates reasonably well with Lyttle (1999) who studied a group of experienced swimmers. He found a decrease in passive drag at 1.9m/s and 2.2m/s of 13.7% and 19.2%, respectively; with the overall differences in drag being 12.8N and 26.0N. As detailed in Study 1, there are a several possible reasons for recording lower passive drag values in the CFD models when compared with the average of a number of swimmers. One primary discriminator could relate to the shape and streamlined position of the swimmer used in this case study. This also demonstrates the benefits and accuracy available when comparing CFD models as any errors would be similar in both the simulations. Table 6-4 Passive drag on swimmers at various depths - extracted from a towing study by Lyttle (1999). NB: drag is listed as positive in this table

125 Chapter 6 - Freestyle kick at water surface It is well documented (Hertel, 1966; Barltrop & Adams, 1991) that the differences between drag below the surface and near the surface are primarily due to related increases in wave drag. However, previously it has been unclear as to how changes in depth affect where the drag forces change on the body. This is required in order to give an insight into optimal body types for reducing this difference. Although the overall change between the submerged and near-surface trials was 18.2%, there were significant differences in the body segments where those changes occurred. The head and arms generated the largest increase in drag with 44% and 50.2% increase contribution to the near-surface overall drag. The overall section of the body above the waist resulted in a 121.7% increase but these increases were counteracted by the lower body components. The thighs, knees, calves and feet all recorded considerable reductions in drag; and the feet changed from an area of drag to a component propelling the body forward. The total change for the lower body components was a 103.5% reduction in drag when compared with the overall submerged segment results. Variations in where the actual drag is concentrated can greatly influence changes in understanding the way propulsion is generated while someone is swimming. The reasoning behind such changes can be explained by examining the surface profile of the water surrounding the body when it is near the surface. Part of the energy dissipated through the water can be seen to form waves on the surface of the water over the body. This wave has a crest in front of the head region, centred around the forearms and forms a trough just below the hips. Due to the forces associated with this type of wave, assuming it has a formation similar to that of linear (Airey) wave theory (Barltrop & Adams, 1991), the peaks in the static pressure indicate that the wave length was around 2.7m (see Figure 6-7); which would imply a period of 1.28 s for the wave. This also aligns itself with the speed of the wave which would be moving with the swimmer at 2m/s. Throughout a wave, the acceleration and velocity of the water varies greatly. Figure 6-8 and Table 6-5 show where these variations occur and these can have an impact on the forces of the body components in those regions

126 Chapter 6 - Freestyle kick at water surface 2.7m Figure The wave profile around the swimmer at 2m/s. Figure Critical points through the wave cycle (Barltrop & Adams, 1991). Table 6-5 Velocity and acceleration variations at critical points in a wave cycle. Location Horizontal Velocity Horizontal Acceleration 1 Maximum (positive) Zero 2 Zero Minimum (negative) 3 Minimum (negative) Zero 4 Zero Maximum (positive) -111-

127 Chapter 6 - Freestyle kick at water surface A wave with these characteristics, at a depth of 0.1m, has associated acceleration and velocity ranges (Barltrop & Adams, 1991): Velocity Range => to 0.31 m/s Acceleration Range => to 1.54 m/s 2 The changes in force can then be associated with two factors: 1 - The reduction or increase of the surrounding velocity. 2 - The added inertial forces based on the accelerating water. Force surface = Force submerged 0.5* C d * Area* density* V 2 wave C m * Vol * density* A wave The values for drag coefficient C d and inertial coefficient C m (otherwise known as an added mass coefficient) then determine how much force on the body part changes. For example, the thigh force changed by 39.77N which may be associated with the following situation: Assuming a thigh area of 0.03m 2 and a volume of 0.016m 3 ; With a water density of 1000 kg/m 3 ; A peak acceleration of 1.5m/s 2 and a velocity of -0.2m/s = * C = * C d d *0.03*1000 *( 0.2) * abs( 0.2) C 24 * C m m *0.016 *1000 *1.5 Possible values may be C d = 0.5 and C m = 1.66 which are in line with values that are used for a cylinder. These values would equate to the acceleration of the water contributing most of the difference. It is not recommended to use these coefficients as more research is required to determine how the increased force associated with wave drag varies with different body shapes. However, it does show that the acceleration and volume of the limbs play the most important roles in the impact of the wave drag on a body. It suggests that swimmers with greater volume body components in the lower half of their bodies actually receive an increased benefit from wave drag than those with greater volume in the upper sections of the body

128 Chapter 6 - Freestyle kick at water surface Due to this acceleration phenomenon within the wave, it is suggested that any section of the body within the zone 4 area of the wave (Figure 6-8 and 6-9) that is removed from the water during the swimming stroke, has the potential to greatly impact on the performance. Hence, if a section of the upper body is raised out of the water (such as increased head height), the wave drag would decrease and could improve the performance of the swimmer. Any section of the lower body that is raised out of the water (such as the feet during the kick) would actually increase the overall drag on the body and decrease performance. This is assuming no other reactional changes in body position occur in these examples. One example could be that lifting the head may reduce the wave drag, but also drop the hips and knees lower into the water which would counteract any benefit. Overall Comparisons of Active Drag The velocities of the active simulations were different and so the wave effect also would be expected to be different. However, the active drag has shown similar changes in distribution of forces when compared with passive cases. Figure 6-9 shows that the length of the wave was marginally shorter than occurred for the passive case and was 1.7m long. This suggests a 1.04 s period and a velocity of 1.63m/s m Figure Detailing the wave profile length during the freestyle kick

129 Chapter 6 - Freestyle kick at water surface In accordance with linear wave theory, the point when maximum and minimum velocities and accelerations occur is detailed in Figure 6-8 and Table 6-5. A wave with these characteristics at a depth of 0.075m has associated acceleration and velocity ranges: Velocity Range => to 0.32 m/s Acceleration Range => to 1.95 m/s 2 Using the critical points of a wave detailed in Figure 6-8: Point 1 is closest to the forearms and would have a minimal change in force. Point 2 would surround the upper body and head regions, and have a large negative impact due to the high volume in the area as well. Point 3 around the hip area would have a minimal impact. Point 4 around the thighs, knees and calves should show the highest increase in propulsive force. These observations appear to correlate well with the changes in forces noted from the simulations. The differences between the total changes in force on the body were higher due to higher acceleration and higher volume, because the peak acceleration point was located closer to the main upper body with its additional volume. These results could explain partially the findings of two studies (Toussaint et al., 1989; Lowensteyn, Signorile & Glitz, 1994) regarding the effects of buoyancy. Lowensteyn et al. (1994) found that artificially increasing the buoyancy of a swimmer by placing latex pads in the abdomen, hip, thigh, chest, back and buttocks resulted in significantly slower swimming times. This contradicted an earlier study (Toussaint et al., 1989) which improved buoyancy by adding a wetsuit with overall buoyancy distribution and produced a 12-16% speed increase. If the latex pads had been distributed differently, such as more being located towards the calves and thighs, rather than the upper body, it would have enhanced buoyancy without increasing the volume in an area where wave drag has a detrimental effect. The change in force on the body as a whole does not remain constant throughout the kick cycle (Figure 6-2). The maximum propulsive peak in the fully submerged -114-

130 Chapter 6 - Freestyle kick at water surface simulation occurred at just after 0.2 s. However, in the near-surface simulation, it does not appear to go through as rapid an increase as the submerged trial and peaks later, at closer to 0.25 s. This coincides with the right foot commencing its downward acceleration phase at the top of the up-sweep. However, the second peak coincides with the left foot going through the same phase as occurred in the submerged trial and reaches its second peak force at a similar time of 0.37 s. To understand this result, the individual segments are reviewed below. Left Side Segment Comparison Comparing the force output data for the left foot and left calf over time, revealed a very similar offset between the two graphs for about 60% of the time, with the near-surface simulation increased in both cases. However, between 0.3 and 0.4 s this offset changed such that the fully submerged case increased the propulsion rate faster, and actually produced more propulsion, than the near-surface model. Reviewing the surface level at this time (Figure 6-10) indicates that the left foot was out of the water at 0.35 s. That appears on the graph as a region where the forces level out around zero and no propulsion is generated. It represents a major loss in swimming propulsion as this point is the start of the acceleration phase of the foot and also the maximum point of acceleration of the water within the wave. A similar effect was noted with the left calf at 0.35 s, as the submerged simulation rose to a peak height at around this time. However, for the near-surface simulation, a peak force did not occur on the left calf until around 0.38 s which is when the calf was fully submerged again. Due to elevating the left leg out of the water, the total force difference during this phase was 0.796N, which equated to a momentum loss in force-seconds per cycle of 2.04Ns. Based on an average drag force of 40N at 1.5m/s, this would equate to a speed increase of ~2.5% by just keeping the left foot below the surface, provided this change does not lead to losses elsewhere

131 Chapter 6 - Freestyle kick at water surface Figure Left foot rising above the water surface at 0.35s. Left versus Right Side Comparison A similar effect was found for the right side of the body where the swimmer s right leg completed a slightly greater up-sweep, such that the right foot and calf came higher out of the water (Figure 6-11). When this occurs at 0.21 s, the fully submerged simulation again creates greater propulsion than the near-surface simulation. The right leg during this phase loses 1.64Ns/cycle or 5.08Ns/s of the stroke. This equates to about a 6.5% increase in speed if the right foot was keep submerged at all times and all other factors remained equal. It should be remembered that lowering the ranges of the feet up-sweeps to avoid breaking contact with the water changes the kick technique. Therefore, the two cannot be compared directly. Despite this, it would be expected that an improvement would still be possible

132 Chapter 6 - Freestyle kick at water surface Figure Right foot emerging from the water at the top of the cycle at 0.21s. Conclusions This study has shown that the multiphase flow capabilities provided in the FLUENT CFD software can predict the difference in forces associated with a swimmer at depth and a swimmer located near the surface. It was found that the build up of a surface wave over the body correlates well with the speed associated with a linear wave in water of that depth. It was also demonstrated that forces on the various body components can change dramatically from when the body is fully submerged to when the body is near the surface. A higher drag force was found to be associated with the upper body and a lower drag force was associated with the lower limbs. The maximum height the feet reached during the kicking cycle had considerable impact on the active drag when near the surface. With the feet in this case study breaching the surface, a considerable loss of momentum was created that can have a negative influence on the speed of the swimmer by as much as 5%

133 Chapter 7 Study 5 - Breaststroke Kick Underwater Introduction The capabilities of the methodology detailed in Chapter 3 did enable valuable insight into how different kick techniques generate propulsion in Studies 2-4. These studies mostly used two dimensional kicking motions where a low error was expected for the kinematic results. To reach the ultimate goal of simulating full active swimmer motion, the kinematics requires three dimensional movement patterns. With investigations of alternative technology for measuring 3D kinematics at the airwater interface ongoing, a means to advance the CFD simulations was required. This study used current 'best practice' dry land kinematics measurement technology via the VICON 12D system to analyse a swimmer completing the breaststroke kick. The breaststroke kick was selected because it is the slowest of the kicking techniques and involved the largest range of movement. Validation of the simulation was not possible but it enabled reaching an intermediate step along the way to simulating the full stroke. Also, some insights as to how the breaststroke kick may generate propulsion were made

134 Chapter 7 - Breaststroke kick underwater Methodology The subject used in this study was an elite breaststroker from the Western Australian Institute of Sport. Given the expenses involved in performing 3D scans of swimmers, the 3D body scan of the subject used in studies 1-4 was again used in this study. The kinematics from the dry-land trials were then overlaid on to this 3D body scan. This has the potential to present some minor variances than may have been experienced if the 3D body shape of the tested subject was utilised. Given the nature of this study as a development step of the CFD model rather than a breaststroke kick optimisation, this was not considered a major limitation. The kinematics for the breaststroke kick were taken from the VICON 12D motion measurement system and adjusted to suit 2nd order smoothness on a joint angle basis as detailed in Chapter 3. The swimmer was in prone lying on a bench with his lower trunk, hips and legs extending off the rear of the bench in free space. A twelve camera VICON MX motion analysis system (Oxford Metrics Group, Oxford) was utilised to acquire 3D kinematics during a breaststroke kick. The standard VICON static and dynamic camera calibrations were performed with the cameras set to operate at 250Hz. The average residual error for each of the cameras following calibration was expected to be 0.5mm. The lower limb marker set was fixed to specific anatomical landmarks on the participant with double sided low allergenic tape. Prior to dynamic trial data collection, three subject calibration trials were collected. First was a static trial with the participant standing on a specially designed foot rig to determine the natural foot position (Besier, Sturnieks, Alderson & Lloyd, 2003). The ankle joint centres were then calculated from this trial data, at the mid-point between two markers on the medial and lateral ankle malleolus. The calculations of the knee and hip joint centres used a functional technique which necessitated two further trials and has previously been described in detail (Besier et al., 2003). The kinematic data were then overlaid onto the scanned model of the butterfly swimmer used in studies 1-4. As a final check, the motion of the model was compared with video footage of the breaststroke swimmer to visually ensure the simulations, which were -119-

135 Chapter 7 - Breaststroke kick underwater based on the dry land laboratory movements,approximated the in-water swimming technique of the same swimmer. All the models were run at velocities of 1.5m/s with movement from the hips downwards only. This speed was selected to approximate the elite breaststroker s 200m breaststroke swimming speed (derived from current race analyses of the national level breaststroker). Being only a case study, the same kinematics were used for the left and right legs. The simulation was treated as being fully submerged in order to keep the variables to a minimum. This was reflective of the underwater breaststroke kick that is performed by swimmers in the underwater phase following the dive start and each turn. Kinematic Data Table 7-1 Critical temporal points throughout the breaststroke kick. Time Description 0.40 s Knees bent, feet straight, half way point on legs coming forward 0.52 s Knees at lowest point and start to move outwards 0.92 s Knees reaches widest point and feet start to rotate out (everting) 1.08 s Feet fully rotated outwards, ankles start to push outwards as knees begin coming in 1.34 s Feet are perpendicular to the body and coming up to the midpoint of the return cycle 1.51 s Knees are almost together, feet start slowing down as they begin coming together 1.90 s Feet reach the end of kick and are close together 2.01 s Feet begin to lift on retraction 2.20 s Knees begin to drop The VICON kinematic data are currently regarded as the 'best practice' approach for dry land kinematics and uses 12 opto-electric cameras to detect movements. Two advantages of the VICON system over the manual video digitising are, firstly there was a significant improvement, as the maximum error for the calf length was restricted to -120-

136 Chapter 7 - Breaststroke kick underwater 2.4cm, or 5.5% of the true length, with the average error less than 1cm (Figure 7-1). This is based on the segment length calculated from the data and compared to the average length due to the different subject used for the data collection to the simulation model. This has proved to be up to 2.5 times more accurate than the video digitised method, detailed in Chapter 3 (Figures 3-19), which recorded average error of 2.5cm for the calf lengths and a maximum error of 4 times greater at transient points through some movement planes. Secondly, due to the automatic measurement of the VICON system the number of data points measured was 4 times greater per second than the manual video digitising. This enabled a smoother acceleration profile which is important when converting to a swimming simulation. Table 7-2 Length error from VICON data (cm). Segment Maximum (cm) Minimum (cm) Average (cm) Error (cm) Left Thigh /-1.64 Right Thigh /-1.04 Left Calf /-2.08 Right Calf / Calf Segment Length during stroke Length (cm) Time (sec) Left Calf Average Right Calf Average Left Calf Right Calf Figure Comparisons of calf lengths calculated from the VICON kinematics throughout the stroke

137 Chapter 7 - Breaststroke kick underwater CFD Variables All the results listed are based on the third trial (Table 7-3). However, as a comparison between CFD variables, both the standard and realisable k-epsilon turbulence models were compared together with 1st and 2nd order discretisation schemes. Due to the tetrahedral meshing, the PISO velocity-pressure coupling was used in all cases. Table 7-3 Alternative turbulence and discretisation models trialled. Trial Number of cells Surface Cells Turbulence model Discretisation 1 2,893,000 78,527 Standard k-epsilon 1st order 2 2,893,000 78,527 Realisable k-epsilon 1st order 3 2,893,000 78,527 Realisable k-epsilon 2nd order -122-

138 Chapter 7 - Breaststroke kick underwater Results The CFD simulation was run for the breaststroke kick. The figures and tables below detail the results of this simulation. The forces were broken down into a per segment length contribution to enable an understanding of which components generated the propulsion and drag throughout the stroke. Summaries of the total momentum change throughout a cycle and a per second average are then used for comparison with other swimming techniques. The breaststroke kick cycle lasted 2 s with comparison of the momentum change over the stroke listed below and the video comparison with the simulation shown in Figure 7-2. Table 7-4 Momentum change during the breaststroke kick cycle. Component Momentum Change (Ns) Total per cycle (Ns) Total per second (Ns) Body per second (Ns) Hips per second (Ns) -8.0 Thighs per second (Ns) -2.6 Knees per second (Ns) -7.3 Calves per second (Ns) Ankles per second (Ns) -1.6 Feet per second (Ns) Table 7-5 Comparison of underwater breaststroke kick with underwater freestyle and dolphin kick simulations at 1.5m/s. Technique Momentum Change (Ns) Large amplitude dolphin kick Small amplitude dolphin kick Freestyle Kick Breaststroke Kick Ns Ns Ns Ns -123-

139 Chapter 7 - Breaststroke kick underwater Figure Comparisons of the breaststroke 3D simulation and actual underwater footage of the kicking pattern used by the tested subject

140 Chapter 7 - Breaststroke kick underwater 200 Cumulative Momentum Loss for the Breaststroke Kick Momentum Loss (Ns) Time (s) Figure Cumulative momentum loss throughout the breaststroke kick cycle. 40 Drag/Propulsion Force of the Breastroke Kick Force (N) Time (s) Overall Body Figure Total body force throughout the breaststroke kick cycle

141 Chapter 7 - Breaststroke kick underwater 20 Drag/Propulsion Force of the Breastroke Kick Force (N) Time (s) Upper Body and Arms Hips Figure Forces on the upper body and hip segments throughout the breaststroke kick cycle. 20 Drag/Propulsion Force of the Breastroke Kick Force (N) Time (s) Thighs Knees Figure Forces on the thigh and knee segments throughout the breaststroke kick cycle

142 Chapter 7 - Breaststroke kick underwater 20 Drag/Propulsion Force of the Breastroke Kick Force (N) Time (s) Calves Ankles Feet Figure Forces on the calf, ankle and feet segments throughout the breaststroke kick cycle. 100 Comparisons Beweeen Turbulence and Discretisation Variables Force (N) 50 Time (s) Trial 1- Standard / 1st order Trial 2 - Realisable / 1st order Trial 3 - Realisable / 2nd order Figure Comparisons between various turbulence and discretisation parameters from 1.9 to 2.5s

143 Chapter 7 - Breaststroke kick underwater Discussion Video Comparisons Comparing the video and simulation showed that the swimming movements during the testing presented a similar pattern to that shown in water. It should be noted that the kinematics were based on the swimmer attempting to replicate his normal in-water kick pattern on dry land in a laboratory and some differences might be expected. The main differences were the external rotation angle that the feet retained throughout the kick being slightly less in the video than via the kinematics, as displayed in the simulation. This presents a possible need for further research to examine this angle and ascertain how it can influence the propulsion generated. As the kinematics were recorded from a dry land trial, it is expected that these results would be fine tuned further once in-water kinematics can be recorded more accurately. Hence, the main findings from this study serve to increase foundational knowledge, rather than defining an optimal kick pattern. Overall Active Drag The underwater breaststroke kick created more drag than the underwater freestyle and dolphin kicks. This was expected, considering the speeds at which both techniques are usually used. A fully submerged breaststroke kick only occurs once throughout each length of the pool, namely, just prior to the swimmer breaking the surface off the dive and after each turn. When combined with the upper body movements and wave effects as detailed in chapter 6, the overall body drag during a breaststroke kick would decrease. It was expected that a similar peak force would occur during the main swimming section of the race, provided that the feet did not breach the surface as was the case in Study 4 and not accounting for wave influence. Therefore, these results should provide a good basis for determining the relative parts of the kick cycle during which maximum propulsion and drag occur. There appear to be four major points of interest in the overall drag/propulsion curve. The first is at 0.52 s which shows drag approaching -180N. As expected, this corresponds with the legs retracting towards the body. In a normal stroke, this is -128-

144 Chapter 7 - Breaststroke kick underwater compensated by the upper body pulling backwards at the same time. Such backward acceleration of the upper body would create propulsion and counteract some of the drag created by the legs. The second point of interest was a short, peak propulsive force that occurred at 0.91s. It coincided with the feet turning out (everting) and beginning the outwards push that occurs at the beginning of the return portion of the kick. The third point of interest was the highest peak propulsion which occurred at 1.35 s and coincides with the maximum acceleration of the feet backwards (Figure 7-9). The fourth point coincided almost with the end of the acceleration of the feet at 1.92 s and was also where the ankles and feet are close to maximum velocity. This point represents the end of the kick propulsion phase and is the point at which the drag on the entire swimmer begins to increase. This shows that, throughout the breaststroke kick, the propulsion is almost always driven by points of high acceleration rather than high velocity, although the two are interrelated Displacement, Velocity and Acceleration Data for the left Ankle in the x-direction Disp (mm) / vel (mm/s) / Accl'n (mm/s 2 ) Time (s) Displacement Velocity Acceleration Figure Displacement, velocity and acceleration data for the left ankle

145 Chapter 7 - Breaststroke kick underwater Body Component Forces Figures 7-5 & 7-7 reveal that force changes throughout the kick cycle vary slightly from body part to body part. The upper body and arms are kept entirely rigid in this example but the force can be seen to vary by around 5N throughout the cycle. This effect appears to be due to the swimmer s frontal surface area increasing as the legs come closer to the trunk as it results in a slightly less streamlined position overall. Thus, the pressure at the front of the swimmer is increased which, in turn, increases the force on the arms and upper body. The thighs showed a high peak at around 1.3 s which would be a direct translation to the knees coming together earlier than when the feet begin the main propulsion phase. The lower legs, ankles and feet all recorded similar patterns with peaks at around 1.35 s. That corresponded to the body s overall peak, and tied in well with the peak acceleration of the ankles. It should also be noted that the calves generated as much propulsion as the feet. This is useful information for both coaches and swimmers who could try to ensure that their feet and calves are positioned carefully throughout the stroke. In addition, it is important to note that it is the initial acceleration of the kick which dictates the greatest contribution to propulsion. Hence, a technique where the feet and ankles have a faster acceleration rather than just a higher overall velocity could probably result in quicker swimming speeds. This finding indicates that development of explosive power through the movement range is important. CFD Parameter Sensitivity Comparisons of discretisation and turbulence models demonstrated that the overall trend was similar for all three trials (see Figure 7-8). Therefore, regardless of the exact CFD variables selected, the peak propulsion and peak drag forces occur at a similar time. The difficulties arise when examining the overall momentum change throughout the cycle. The 2nd order realisable model revealed an overall difference of 12Ns/s compared with the 1st order standard k-epsilon turbulence model. The reason for the simulation tests was to gauge the percentage of error in overall estimations that may occur in these simulations. Therefore,validation was important. All similar studies (Bixler et al., 2007; Von Loebbecke et al, 2009; Zaidi et al., 2008; Silva et al., 2008) have followed the lead from an initial study (Bixler & Schloder, 1996) that suggested the standard k-epsilon -130-

146 Chapter 7 - Breaststroke kick underwater turbulence model was the best to use when studying passive and active drag in swimming. The standard k-epsilon model is the one most widely used since it was proposed by Launder and Spalding (1972). However, it has some limitations and advances in this area have gained greater accuracy with flows involving rotation, boundary layers under strong adverse pressure gradients and separation. Hence, it has been recommended that the realisable k-epsilon model (Shih et al., 1995; FLUENT, 2007) could be the preferred model to use. More research and validation is required to fully optimise and validate the simulations. However, using current "best practice" provides introductory in-roads and greater insight into the swimming technique analyses. Conclusion This study completed a successful 3D analysis of a swimmer throughout the breaststroke kick cycle, and provided an increase in foundational knowledge which may be exploited by coaches for improving breaststroke kick technique. It was found that the ranges of movement which were recorded could be translated to the simulation within visual tolerances. Therefore, this also validated the approach of using the simplified joint centre and fixed segment approach detailed in Chapter 3, especially if, and when, more accurate kinematic data can be recorded. Another finding was that the greatest contribution to the propulsion generated within the breaststroke kick was from the acceleration phase. This occurred when the feet begin to move away from the body via the lower and upper leg extension and rotation. Improving the acceleration during this phase is likely to improve the overall propulsive benefits of the kick

147 Chapter 8 Study 6 - Full Freestyle Stroke at Water Surface Introduction The literature review reported numerous studies that have tried to predict the effectiveness of one freestyle technique over another. To date, CFD predictions of forces acting on a swimmer have been limited to passive drag studies (Bixler et al., 2007), hand motion through the water (Bixler & Riewald, 2001; Sato & Hino 2002), underwater dolphin kick (Von Loebbecke et al., 2009) and the previous studies in this thesis on dolphin, freestyle and breaststroke kicks. All of these studies have limited their focus to the section of the race immediately after the start and the turning wall that accounts for a small proportion of the total race time. Footage of the 2008 Australian Olympic Trials shows that the winner of the 50m freestyle spent the first 1.12 s getting the entire body off the starting block and into the water, then completed four dolphin kicks over a further 1.16 s before the break out and the start of free swimming. The first full arm stroke was completed after a total of 2.72 s in a race completed in less than 22 s. The entire glide time without any kicking was less than 0.2 s and the total amount of glide plus kicking time was 1.16 s. Therefore, these sections of the event make up 0.9% and 5.2% of the race, and the swimming component make up over 87%. The remainder of the time was spent in the air or during the breakout stroke. It should also be noted that, for the majority of the -132-

148 Chapter 8 - Full freestyle stroke at water surface underwater phase, the swimmer is surrounded by air bubbles (Figure 8-1) which would alter greatly the flow dynamics around the body. The major advantages to be gained in swimming will come from improving the techniques used during the stroking phases. Therefore, this study aimed to provide initial steps towards advancing the understanding of where the major propulsive and drag forces are created within a full freestyle stroke. This study set out to: Use the methodology detailed in Chapter 3 to simulate the full swimming technique. Validate this model against swimming speed by measuring the overall drag throughout the stroke and ensuring that the stroke is capable of producing zero net drag at that speed. Use the results to discover where the major drag and propulsive phases occur for this specific freestyle stroking pattern. Figure The air bubbles surrounding a swimmer at the start of a 50m event

149 Chapter 8 - Full freestyle stroke at water surface Methodology The subject used in this study was a swimmer at the Western Australian Institute of Sport who, shortly after the time of the kinematic data collection, became the world record holder for the 50m and 100m freestyle events. As such, the base freestyle stroke technique used by this swimmer can be considered to be highly evolved. A full 3D scan of this swimmer was used for the CFD simulation. For the purposes of this study, one full, non-breathing stroke was analysed using the CFD model. Kinematic Data Collection Current motion analysis techniques have limited use in a pool based setting. The kinematic data were collected using manual video digitising from four cameras views. The procedures and accuracy of this type of data collection are detailed in Chapter 3. The duration of the stroke cycle analysed was 1.04 s with the time frame used in the simulation the same as the time captured from the kinematic data. Kinematic Data to Virtual Skeletal Movement Equations The 3D Kinematic data were transformed from Cartesian co-ordinates into a series of polar rotational equations for each limb. The procedure and expected accuracy for this is detailed in Chapter 3. It should be noted that there are limitations in the derived kinematics because of the inherent inaccuracies associated with this measurement technique in an aquatic setting. The main problems are changes in body shape covering visual joint location points, water clarity due to bubbles, light reflection near the surface and standard camera difficulties of parallax error, distorted lenses and set-up calibration issues. The redigitisation of segments during areas of the stroke that recorded high errors (such as the forearm during the in-sweep phase) with similar co-ordinate outputs also indicates that there were movement planes that were sensitive to errors in the transformation process. Despite these potential errors, the current 3D animated motion records the best possible data available for full body kinematics of all body segments and provides a good basis for the developmental analyses of free swimming stroking patterns. A subjective comparison between the animated simulation and competitive and training video footage from different angles, revealed very similar movement patterns throughout the stroke

150 Chapter 8 - Full freestyle stroke at water surface Average Velocity Estimation From the kinematic data, the average digitised velocity of the mid iliac crests (mid point between the left and right iliac crests, Figure 3-10) was used to determine the average velocity of the water for the CFD simulation. Although the velocities ranged was between 1.9m/s and 2.3m/s, the average over this time was 2.08m/s. Variation and errors stated in Study 1 for the kinematic data, meant that the mid iliac crest velocity was modelled as constant, rather than accelerating and decelerating as per the dolphin kick simulations in Study 2. The acceleration and deceleration of the mid iliac crest was only small and ignoring this is not expected to influence any results. However, for swimmers with higher inter-cyclic variation this can be modelled in future studies to determine the impact of this effect. 250 Velocity Comparison of Water to Mid Iliac Crest 200 Velcoity (cm/sec) Time (sec) Velocity of mid iliac crest Water Velocity Figure Velocity of the centre between the left and right iliac crests through the freestyle stroke

151 Chapter 8 - Full freestyle stroke at water surface Temporal Data The table below (see Table 8.1) outlines the temporal time periods for key events throughout the stroke cycle. Table 8-1 Critical temporal points through a full freestyle stroke cycle. Time Description 0.19 s Left foot reaches top as right foot reaches bottom of sweep 0.20 s Right hand exits the water 0.37 s Left foot reaches bottom as right foot reaches top of sweep 0.44 s Left hand reaches the deepest point 0.56 s Left foot reaches top as right foot reaches bottom of sweep 0.58 s Right hand enters the water 0.64 s Left forearm at closest point to vertical 0.70 s Left hand exits the water 0.73 s Left foot reaches bottom as right foot reaches top of sweep 0.90 s Left foot reaches top as right foot reaches bottom of sweep 0.98 s Right hand at deepest point 1.04 s Right forearm at closest point to vertical 1.06 s Left foot reaches bottom as right foot reaches top of sweep 1.08 s Left hand enters the water CFD Mesh Sensitivity The final results also included a sensitivity review on the mesh density. Due to the long computational times required for these simulations, a lower number of cells are sometimes warranted for efficiency reasons. These reductions could make significant improvement in the analysis time and reduced labour, if high power computer processors are not available. If the accuracy of the lower cell count can be determined it may also be used as an initial screening check of a technique without spending to much time. To find the differences resulting from a smaller mesh count, two trials were conducted using the standard fine mesh of almost five million cells, and a coarse version with only 2 million cells

152 Chapter 8 - Full freestyle stroke at water surface Results The results listed below detail the force on the individual body segments throughout the full freestyle stroke. A summary momentum change of the segments is also listed in Table 8-2. The full freestyle stroke analysed has a cycle time of 1.04s, the momentum changes were then averaged to a per/second value to enable comparison with previous studies. Table 8-2 The momentum (Ns) changes in the swimmer from the full freestyle stroke simulation over one full stroke cycle. Left Side Right Side Total Velocity 2.08m/s 2.08m/s 2.08m/s Total per cycle (Ns) Total per second (Ns) Hand per second (Ns) Wrist per second (Ns) Forearm per second (Ns) Elbow per second (Ns) Upper Arm per second (Ns) Shoulder per second (Ns) Head per second (Ns) Neck Per Second (Ns) Upper Trunk per second (Ns) Mid Trunk per second (Ns) Pelvis per second (Ns) 3.18 Hips per second (Ns) Thighs per second (Ns) Knees per second (Ns) Calves per second (Ns) Ankles per second (Ns) Feet per second (Ns) Combined Arms per second (Ns) Combined Legs per second (Ns) Trunk and Head per second (Ns)

153 Chapter 8 - Full freestyle stroke at water surface Overall Propulsion/Drag on Freestlye Swimmer Force (N) Time (sec) Figure The overall forces on the swimmer throughout the freestyle stroke. Drag/Propulsion for Body Parts Force (N) Time (sec) Right Leg Left Leg Figure The forces on the right and left legs throughout the freestyle stroke

154 Chapter 8 - Full freestyle stroke at water surface Drag/Propulsion for Body Parts Force (N) Time (sec) Right Arm Left Arm Head and Body Figure The forces on the trunk, right and left arms throughout the freestyle stroke. Figure Pressure contours when maximum net force occurs during a stroke

155 Chapter 8 - Full freestyle stroke at water surface Force component for Left Leg Force (N) Time (sec) Left Calf Left Foot Total Left Leg Figure Comparison of left leg foot positions with propulsive forces

156 Chapter 8 - Full freestyle stroke at water surface Figure The left foot coming out of the water during motion analysis testing. Figure The left foot coming out of the water during the simulations

157 Chapter 8 - Full freestyle stroke at water surface Discussion Overall Drag and Propulsion The overall positive change in momentum throughout the cycle did not correlate exactly with expected results of a zero momentum change due to the swimmer maintaining constant velocity. This could be due to several factors, but there are potentially two main reasons. Firstly, the differences between the completely smoothed wall CFD simulations and the true drag are influenced by roughness of the swimmer s body and the quality of swimwear used. As detailed in previous research (Bixler et al., 2007), this may account for up to an 18N error at these velocities. Also, the accuracy of the kinematic data outlined in Chapter 3 contains inherent errors associated with manual three-dimensional digitisation. This can lead to differences in the location of the body components which are coupled with errors in translating the digitised coordinates into a linked polar coordinate set of equations. The previous studies 2-5 have found the amount of propulsive force is governed strongly by the acceleration of the body components. Hence, small errors in positional data are amplified when the acceleration data are calculated. These, in turn, influence the overall average drag/propulsion values. However, the important points related to the timing and causes of peak propulsion would be maintained as the variation of forces throughout the stroke is greater than the overall errors. It can be seen from the breakdown of the distribution of forces that the arms and legs create significant amounts of propulsion, with the trunk contributing the majority of the drag. The hands provided a total propulsive momentum of 23.8Ns while the combined contribution of the wrist, forearm and elbow was 27.6Ns. This highlights that the forearm position during the underwater arm stroke is as critical as that of the hands. The head contributes less drag than the upper and lower trunk components. That could be related to both the fact that it is occasionally positioned in only a semi-submerged state and also has less volume which influences the potential amount of wave drag experienced (refer Study 4). The thighs, knees and calves also contributed a greater percentage of the propulsion than the feet. That also reinforces the importance of entire leg movements and positioning rather than just focusing on the feet positioning. However, this may result from the feet coming out of the water regularly, and wave assistance, as discussed later in this chapter

158 Chapter 8 - Full freestyle stroke at water surface The overall changes in force throughout the stroke (Figure 8-3) were as expected. There were six clear cycles throughout the stroke containing four small peaks and two large peaks. These peaks represent the six beat kick that is adopted with the two large peaks correlating with the peak propulsion of the left arm at just after 0.56s, and the right arm at 1.07s, occurring at the same time as two of the kick cycles. The two larger propulsive peaks are validated by the overall velocity of the mid iliac crest. The two highest velocity peaks (see Figure 8-2) occurred just after the occurrences of the peak propulsive forces, namely at 0.64s and 1.14s, where the swimmer s velocity surged to around 2.3m/s. The smaller propulsive force peaks also have a small influence on the velocity. A comparison with the iliac crest was made due to it being a fixed point, instead of a calculated centre of mass..any estimate of the centre of mass requires an approximation of added water mass as well as body component densities, and these could lead to further discrepancies in comparisons. An additional validation of the model occurs when comparing events just before the main two peaks. Here, the overall propulsion at around 0.4s is considerably higher than that at around 1s. This can be seen when translated onto the velocity profile with a velocity above average at around 0.48s, but only an average velocity at 1.08s. A previous study into intra-cyclic velocity fluctuations (Buckwitz, Bahr & Ungerechts, 2002) reviewed the variation in velocities of all four strokes. The freestyle stroke was examined at a velocity of 1.2m/s for a stroke cycle time of 1.8s. In this case the velocity peak occurred within 0.3s of the hands entering the water and suggested that the second velocity peak might be smaller at slower swimming speeds, and the initial catch could be the biggest driver. There was not sufficient detail to show if the peak in their study coincided with a peak in velocity, or acceleration of the hand and forearm. Feet Force Profile The six cycles of the six beat kick easily can be seen when analysing only the contribution of each leg throughout the cycle (Figure 8-4). The correlation of these peaks showed a similar pattern to that found in studies 2-4 of this thesis, with the maximum propulsive peaks starting when the feet approach the top and bottom of their sweep

159 Chapter 8 - Full freestyle stroke at water surface Comparing left and right leg motions showed a similar asymmetry to that of Study 4 where a different swimmer was used. However, the magnitude of the change in the current study was not as large as exhibited by the subject in the freestyle kick example. The range of ankle movement in the earlier study showed a total range of 55.3º for the left ankle as compared with 29.0º for the right ankle. The kinematics for this swimmer revealed a 42.1º variation in the left ankle compared to a 35.3 degree variation in the right ankle (Figure 8-10). The better ankle flexibility on the left side can be seen to provide slightly better propulsion with the left leg contributing Ns compared with Ns for the right side. 200 Joint Angle Comparison for the Ankles Angle (deg) Time (sec) Right Ankle Left Ankle Figure Comparison of left and right ankle joint plantar/dorsiflexion angles throughout the freestyle stroke cycle (using a 6 beat kicking pattern). The other notable difference was the variation in ankle flexibility throughout the stroke, with the peak plantar-flexion angle on some kicks varying by as much as 20º. This difference can be seen in Figure 8-10 which highlights the different plantar-flexion angles of the left foot at the top of various kicks. These inter-cycle variations in flexibility were renewed with regard to the findings of the resultant effects of ankle flexibility as part of Study 2. Based on these earlier results, it was expected that the peak left foot propulsion would occur at 0.26s with a large -144-

160 Chapter 8 - Full freestyle stroke at water surface drop-off to the peak occurring at 0.58s. The force results in the current study demonstrate that the opposite appears to be the case (Figure 8-4). Closer inspection of the models in studies 2 and 4 shows that the results found in Study 4 for the nearsurface modelling of the freestyle kick may have a greater impact than the variation in ankle flexibility on the resultant force output. In the current study, the high ankle flexibility that occurs at 0.26s is counteracted by the foot coming out of the water. This reduces the amount of volume that is able to benefit from both the wave water acceleration and the foot s initial acceleration into the down-sweep, which occurs when it is in air rather than water. Due to the differences in fluid density between air and water, the force would decrease by around 800 times for any body part out of the water. Using this theory of foot positioning in relation to water surface level, the comparisons of leg propulsion in each cycle have greater correlations. When comparing the foot position (Figure 8-7), it can be seen that the foot is clearly out of the water at 0.22s and again at 0.92s. At 0.56s, the foot is still mainly surrounded by water. Hence, the force peak at 0.56s is up to twice that of the other occurrences, even though the ankle flexibility was not nearly as effective. If the feet were kept lower in the water for all three kicks, it would be expected that an additional 60N of propulsion could have been generated for up to 0.06s on each of the two out-of-water kicks. This would enable a potential difference in a kick cycle of 6.92Ns per second on the left leg only. This difference at a swimming velocity of 2.08m/s could make up to a 3.5% difference in the overall swimming speed and time, which is clearly of practical significance in competitive swimming. A similar effect of reduced magnitude is seen with the right leg which has the potential to influence times even further by staying in the water. The concept of keeping the feet submerged at all times is not a common coaching instruction and, as can be seen here, does not always occur in some elite swimmers. However, it is not a new concept. The author corresponded with Tom Jager (USA), who held the world record of 21.81s for the 50m freestyle for more than 10 years, wearing only a traditional pair of lycra briefs. He mentioned that one of his main focus areas was ensuring that his kick was strong, and the feet were submerged at all times (personal correspondence, Jager, 1999)

161 Chapter 8 - Full freestyle stroke at water surface Trunk Force Profile In comparison with the legs and arms, the variation in drag on the trunk is relatively constant. This would be expected due to the small range of movement of these parts. The largest moving component in this group is the upper trunk which also has the highest volume. As the upper trunk twists to almost 42º with the motion of the arms it has a slight variation in force which makes up greater than 90% of the variation in the force generated by the trunk. This is due also to the differences in wetted area to which the upper trunk is exposed, as well as the frontal surface area. The upper trunk moves through a range of ~12º degrees about the transverse plane (see Figure 8-11), with the steepest angles occurring when the arms are leaving the water to commence recovery. The small accelerations and decelerations of the trunk can create surges in the force but most of these are counteracted as the overall body moves in the other direction. This also can be seen when the trunk force over time is reviewed (Figure 8-5). The average force on the trunk is approximately 70N and varies by around +/- 40N as it accelerates and decelerates with the movement of the arms. There is no clear evidence to determine the best body positioning from a single case study. But, with the possibilities of sensitivity simulations in the future, parameters such as most efficient body angles can be investigated to a greater degree. Angle of the Upper Body to the Horizontal Angle (deg) Time (sec) Figure Angle of the upper trunk to the horizontal throughout the stroke

162 Chapter 8 - Full freestyle stroke at water surface Arms Force Profile The initial review of the individual arm force profiles confirm the observations detailed in the overall drag and propulsion review. There is a definite peak associated with the left and right arms as they move through the cycle. The left arm peak occurs at 0.55s and the right at 1.07s. There is a secondary lower peak that occurs prior to these at 0.33s for the left, and 0.89s for the right. For both arms, there is a section of almost no force for almost 0.4s prior to an initial drag on the arm, before a small, then large, peak. This common series of events will be reviewed as they appear to provide the links to the arm motions. Table 8-3 Timing for the temporal phases of the left and right arms through the freestyle stroke. Phase Left Hand (s) Right Hand Initial hand entry and outstretching of the arm Acceleration at the start of the stroke pushing outwards The change of direction from pushing outwards to bringing the arm back in towards the centre of the body The main propulsion phase along the base of the body when the forearm is close to perpendicular to the direction of travel (s) The exit of the hand from the water The recovery of the arm The first phase with the arm out in front of the head appears to create an equal amount of drag for both arms of around -34N to -38N, and lasts for between 0.09 and 0.11s. This is due to the drag resulting from placing the arm in a zone of high moving water, and also potentially due to the wave drag which will be discussed later. The hand is seen as the first point to start accelerating out of this extended position when it begins to move at around 0.18s. Then comes the initial acceleration phase where the swimmer pushes out laterally from the body and rapidly accelerates the hands and forearms; with a peak force in this phase of between 50N and 100N. The force is governed initially by accelerating the forearm and hand, and then slowly transitions towards being more velocity related. The right -147-

163 Chapter 8 - Full freestyle stroke at water surface hand has a 15% greater acceleration and velocity, which partially explains the slightly greater forces generated at this time. The third phase appears to be a transition between when the swimmer is pushing outwards by using mostly the lateral muscles, and then changes to pulling inwards towards the midline of the body. The simulation shows considerable deceleration at this point by the forearm and hands, and is probably the reason for the drop in propulsion. It is expected that this effect might not be as dramatic as these results show given the acceleration drop in the simulation also occurs at a point where some of the kinematic data reaches the outer limits of its accuracy as mentioned in Study 1. Hence, the resultant deceleration of the forearm and hands are higher in the model than in the actual coordinates measured. However, the results do show that keeping this section of the pull-through at high acceleration and high velocity helps to improve the overall stroke technique. The fourth phase is the main power pulling section of the stroke with peak propulsive forces reaching between 260N to 340N. This peak force can be equated to the strength required in each arm, with 340N equivalent to holding ~34kg on an outstretched arm. This is indicative of the considerable strength required by the swimmer. It should be noted that this peak force does not occur at either the peak acceleration or velocity of the hand or forearm. It also appears to occur just after the swimmer has the best angle of the hand and forearm exposed at 90º to the direction of travel. The observation of the swimmers peak intra-cyclic velocity occurring just after this was made in the discussions of the overall drag and propulsion force. It appears to support that this force is, in fact, a true peak, although the exact cause is still unclear. It can only be estimated that it is a combination of: A relatively high velocity of the hand and forearm at this point. A high angle of the hand and forearm exposed at 90º to the direction of travel. The arm moving backwards in the wave profile and out of the zone which creates a negative acceleration in the direction of travel. The possibility of the wave moving backwards along the body as this is also the point at which the centre of gravity of the volume in the water is at the -148-

164 Chapter 8 - Full freestyle stroke at water surface furthest point back. This is due to the contra-lateral hand not entering the water until almost the exact point this peak begins to deteriorate. The fifth phase is the section where the arm exits the water and this is almost a point where drag forces quickly overtake the propulsive forces. This may be a result of the arm decelerating as it approaches the end of the stroke, but also may be due to some of the wave effects. The sixth phase is the recovery where each arm in turn, is out of the water. As expected during this phase, the forces on the arms are almost zero due to the density of air having very little impact on any resistive drag forces at this speed. The forces discussed are only the fluid interaction effects on the body and do not include acceleration of the body mass. Wave Influence The theory of wave formation around the body has been mentioned in Study 4 and a similar pattern can be seen here. A swimming speed of 2.08m/s would, under linear wave theory, imply a similar wave speed and a wavelength of 2.76m for a period of 1.33 s. The wave in this model appears to be a lot more dynamic, but there is an underlying wave of this length evident (see Figure 8-12). 2.7m Figure Static pressure contours showing the wave shape around the swimmer

165 Chapter 8 - Full freestyle stroke at water surface The wave in this model appears to change with the change in length of the swimmer as he moves his arms from the front to the back of the body on each side. This changing wave formulation may be an explanation for part of the reason that the peak force is generated at this time. Figure 8-13 shows the change in pressure at a depth of 300mm below the body or 550mm below the surface of the water. The general wave profile can be seen with a higher pressure closer to the front of the body, and dropping down around the pelvis area, before increasing again towards the rear of the swimmer. Through the time from 0.45s to 0.74s there is a considerable change in the profile underneath the body. The profile at 0.74s is the normal wave profile seen with the steep gradient near the thighs that increases the propulsive force in this area as detailed in Study 4. However, at 0.45s this steep gradient disappears and appears to move backwards, which is coincident with the length of the overall swimmer shortening. At around 0.54s, a second wave forms around the mid-section of the body. This is also the point where the left arm is passing through. As the right hand enters the water again, balance appears to restore itself back to the traditional wave formation. Further understanding of this situation is required to determine what is exactly causing this scenario and how it may benefit a swimmer. The pressure wave at 0.3m is the location where the forearm and hand pass through, so it also could be a contributing factor for the peak force occurring later in the stroke than indicated by the acceleration and velocity profiles of the swimmer s arms. It appears that this short wave that is created has a high acceleration component, similar to two waves joining, which may in turn create a short surge in the direction of swimming. Keeping the velocity high, and the forearm and hand perpendicular to the direction of flow to ensure maximum volume and added mass capacity at this point, can potentially make for a higher efficiency of the stroke

166 Chapter 8 - Full freestyle stroke at water surface 6500 Pressure at 300mm Below the Body Along its Length 6000 Pressure (Pa) Distance (m) 0.45s 0.54s 0.63s 0.69s 0.74s Figure Pressure below the body at various times along the length of the body. NB: 0m represents the hip location, 1.2m is the point where the hands enter the water. CFD Sensitivity Mesh concentration sensitivity As a test of mesh concentration sensitivity prior to the final simulation, coarse and fine mesh simulations were completed to compare the difference in results. The two following situations were trialled: Mesh Concentration Number of Cells Surface Mesh Cells Coarse mesh 2,007,850 40,868 Fine Mesh 4,939,950 98,880 When compared with other CFD studies, Bixler et al. (2007) started with 1.3 million cells and was required to increase the number to 2.6 million before mesh independence was established in a passive drag situation. Von Loebbecke et al. (2009) used 4.2 million cells when analysing the dolphin kick, although only required 19,156 and 26,428 surface mesh cells, for the female and male model, respectively. This would appear to be a relatively low resolution compare with the number of cells utilised

167 Chapter 8 - Full freestyle stroke at water surface A mesh sensitivity study is used to determine the optimum number of cells to use for an analysis. The more cells used, the longer the computational time, less cells results in a lower accuracy and less reliable output. Finding the optimum mesh density is important but may vary depending on what is required from the analysis. Coarse mesh simulations are usually run as a first pass to gain an understanding of the fluid flow and the overall system before refining the mesh to gain more accurate results. Figure 8-14 shows that the coarse mesh results were more erratic than the fine mesh. Upon further inspection of the models, it was found that the dynamic mesh functionality created a number of highly skewed cells in the coarse mesh and temporarily caused a high or low pressure on one to two cells for a single body component. The algorithms for the dynamic mesh are able to detect these highly skewed cells and remesh the zone by the next time step. These minor errors cause the erratic movement of the freestyle force output for coarse mesh simulation. Although, the overall trend of the coarse mesh results still appear to follow the trend of the fine mesh. Figure 8-15 shows a 0.1 sec moving time average of the coarse mesh which removed excessive outliers and smooths the forces over numerous time steps. It can be seen with this filtering of the coarse mesh example, that the total force on the body in both simulations became closer aligned. It is recommended that the finer mesh is used when calculating the actual drag on a swimmer. However, due to the high processor power required to run these simulations in a reasonable time period, and with reasonable smoothing, a partially accurate coarse mesh model may be able to provide some initial insights into the stroke effectiveness. For the final simulation of the freestyle study the finer mesh was used

168 Chapter 8 - Full freestyle stroke at water surface Comparison of Coarse Vs Fine Mesh Force (N) Coarse Mesh Fine Mesh Figure Comparisons of coarse and fine mesh simulations. Comparison of Coarse Vs Fine Mesh Force (N) Coarse Mesh Time Avergaed Fine Mesh Figure Comparisons of moving time averaged coarse and fine mesh simulations

169 Chapter 8 - Full freestyle stroke at water surface Conclusion There is considerably more data to be analysed and detailed from these results but this study set out only to examine whether the CFD simulations could be used for such an application, and provide some initial insights into how propulsion and drag are generated throughout a stroke cycle. This study demonstrated that additional research is required to refine 3D kinematics. Only then would the accelerations and velocities of each section of the body be accurately predicted utilising the polar angle algorithm for body movement detailed in Chapter 3. With further refinement of these kinematic results, the best CFD variables can then be selected to correctly validate the CFD models against the swimmer s speed. There have also been some practical points derived from this study that provide knowledge of how the propulsion and drag within a single case study can be used to improve swimming speed. These are: Keeping the feet submerged at all times. Maximising the acceleration at the beginning of the arm stroke and leg kick. Gaining the closest perpendicular angle to the direction of travel for the hands and forearm at all times; this is sometimes termed as 'getting over the stroke'. Keeping a perpendicular forearm for the change in wave motion near the end of the stroke. Removing the arm from the water as soon as the wave moves through. Limiting the glide time the arm is extended at the front of the stroke

170 Chapter 9 Conclusions, Summary and Future Research Directions Summary It is acknowledged this thesis involves a number of case study approaches in the development of the CFD methodology as it applies to swimming. While generic principles found in these studies can be extrapolated to general swimming foundational knowledge, specific technical details are applicable to the swimmers used in the study. The following are a summary of conclusions resulting from the individual studies: Study 1 Validated the passive CFD model and found similar differences between actual measured drag and CFD results of previous studies. Explanations for these differences include skin and swimwear roughness factors, towing device interference and variations in Reynolds numbers as water flows around the body

171 Chapter 9 - Conclusions The suggested methodology for transforming kinematic data into a polar angle algorithm for motion of the body highlighted the errors inherent in 3D kinematic data. Due to fewer variables, the 2D kinematic data, as expected, had a reduced error, but 2D analyses are limited due to mainly 3D movement used in swimming. An idealised simulation of the shoulder joint was proposed with a 10% adduction/abduction rotation and a 44% elevation rotation for the shoulder-toscapular movement ratios. This ratio appeared to provide a more realistic shoulder movement pattern that may be applied to the increased joint movement range exhibited by elite swimmers. Study 2 Dolphin kick analyses showed the larger amplitude kick produced better results of the two kicking patterns at 1.50m/s and 2.18 m/s. Although this is based on only two kick patterns studied and cannot be generalised. However, this case study highlighted how CFD can be a powerful tool in optimising swimming techniques. Two areas for technique improvement were the impacts of ankle flexibility and associated depth below the body reached by the knees in propulsion. During kicking, swimmers reach their maximum plantar-flexion on the down-sweep of the kick cycle. The results showed greater plantar-flexion flexibility produced greater propulsion. Technique inefficiencies such as excessive knee drop during the down-sweep were found to produce considerable increase in drag and slow the swimmer s velocity. Study 3 The freestyle kick analysis indicated that coaches opinions that the dolphin kick is a more efficient kicking technique during the underwater phases after starts and turns might not always be correct. Benefits can vary depending on the amount of movement of each segment throughout the cycle

172 Chapter 9 - Conclusions This study also revealed that asymmetries in the flexibility of a swimmer between the left and right sides can also have a large effect on minimising drag or creating propulsion through the kicking cycle. Excessive knee bend can greatly impact on drag when it interferes with the main flow of water below the body. Flexibility of the ankle joint appeared to considerably impact on the ability of the swimmer to generate peak propulsion and also to position the other limbs to compensate for that difference. Study 4 Simulating freestyle kick near the water surface has shown that the multiphase flow capabilities provided via the FLUENT CFD software are capable of predicting the differences in forces associated with a swimmer at depth and a swimmer located near the surface. It was found that the build up of a surface wave over the body correlated well with the associated linear wave speed in water of that depth. It was shown that the forces on the body components change dramatically between when the body is fully submerged and when the body is near the surface; with a higher drag force associated with the upper body and a lower drag force associated with the lower limbs when near the surface. The height that the feet reach during the kicking cycle also had a considerable impact on the active drag and propulsion when near the surface. With the feet in this case study breaching the surface, a significant loss to momentum is created that can reduce the speed of the swimmer by as much as 5%

173 Chapter 9 - Conclusions Study 5 By using a breaststroke kick example, it was found that the range of movement recorded could be translated to the simulation using the CFD methodology procedures within visual tolerances. The greatest proportion of propulsion generated within the breaststroke kick came from the acceleration phase when the feet are in a everted position and begin to move away from the body. Improving this acceleration would most likely improve the overall propulsion benefits of the kick without too many other movements affected. Study 6 Applying all the knowledge learnt from the initial studies, it was found that predicting the overall drag throughout a full swimming stroke was possible using the commercial CFD code FLUENT. Keeping the feet fully submerged at all times could improve swimming speed. Maximising the acceleration at the beginning of the stroke for the arms and the down-sweep for the legs can improve swimming speed. Ensuring as close to a perpendicular angle to the direction of travel for the hands and forearm at all times, or 'getting over the stroke', can improve swimming speed. Keeping a perpendicular forearm to the direction of travel for the potential change in wave motion at the end of the stroke can result in a large propulsive increase for the swimmer. Removing the arm from the water as soon as the wave moves through can reduce the drag on the swimmer and improve swimming speed

174 Chapter 9 - Conclusions Limiting the time that the arm is extended at the front of the stroke and gliding can reduce the drag on the body overall, and increase swimming speed. Conclusions On the basis of the findings in the above studies, it can be concluded that: Study 1 Errors inherent in 3D kinematic data caption require considerable improvements in accuracy, especially in the aquatic medium. The 2D kinematic data were more accurate than 3D but such analyses are limited due to the 3D movements in swimming. Validation of the passive CFD model demonstrated similar differences between actual measured drag, CFD results and previous studies. Increased shoulder joint flexibility of this specialised subject population (ie. elite swimmers) require an increased awareness of the mechanisms for modelling movement about this joint. Study 2 The large/slow underwater dolphin kick was more efficient than the lesser amplitude kicking style. This case study highlighted the value of CFD in optimising swimming techniques. Greater ankle flexibility during the dolphin kick has the potential to provide greater propulsion. Dropping the knees too far during the dolphin kick can produce a significant increase in drag and slow the swimmer s velocity

175 Chapter 9 - Conclusions Study 3 Universal acceptance by coaches that the dolphin kick is always more efficient during the first phase after a start or turn might not always be correct. The swimmer in this case study recorded substantially lower momentum losses when using the underwater freestyle kick than either dolphin kicking techniques. The breakdown of the forces demonstrated that the balance between the amount of propulsion produced, and the drag experienced by the swimmer, can vary depending on the timing and magnitude of the movements by each segment throughout the technique. Asymmetries in flexibility between the left and right sides also can influence the drag experienced by the swimmer, or the propulsion created, when kicking. There can be substantial differences between the propulsion generated by the left and right sides of the body. During the freestyle kick, the contribution by the calves may be substantially greater than shown by previous research (Von Loebbecke et al., 2009). Study 4 The multiphase flow capabilities in the FLUENT CFD software can predict differences in forces associated with a swimmer at depth and near the surface. The build up of a surface wave over the body correlated well with the speed associated with a linear wave in water of that depth. Forces on body components are quite different when the body is fully submerged from when the body is near the surface. A higher drag force was associated with the upper body and a lower drag force was associated with the lower limbs

176 Chapter 9 - Conclusions The maximum height the feet reached during the kicking cycle impacted on the active drag when near the surface. Considerable loss of momentum occurred in this case study by the feet breaching the surface; and can influence swimmer speed by up to ±5%. Study 5 A successful 3D analysis of a swimmer performing a breaststroke kick cycle could be completed using CFD. The ranges of movement which were recorded could be translated to the simulation within visual tolerances. The analysis validated the use of a simplified joint centre and fixed segment approach detailed in Chapter 3 - when accurate kinematic data can be recorded. The majority of propulsion in the breaststroke kick was generated from the acceleration phase when the feet begin to move away from the body via calf and thigh extension, and rotation. Improving leg acceleration is likely to improve the overall kick propulsion. Study 6 These studies achieved their aims of indicating whether CFD simulations could be used for swimming applications, and gain some initial insight into how propulsion and drag are generated throughout a full swimming stroke. Additional research is required to refine 3D kinematics because, only then, can the accelerations and velocities of each section of the body be accurately predicted utilising the polar angle algorithm for body movement detailed in Chapter

177 Chapter 9 - Conclusions Practical points gathered have provided knowledge of how increasing propulsion and decreasing drag in a single case study can improve swimming speed by: - Keeping the feet submerged at all times. - Maximising the acceleration at the beginning of the arm stroke and leg kick. - Gaining the closest perpendicular angle to the direction of travel for the hands and forearm at all times; or, 'getting over the stroke'. - Keeping a perpendicular forearm to the direction of travel for the change in wave motion at the end of the stroke. - Removing the arm from the water as soon as the wave moves through. - Limiting the time the arm is extended at the front of the stroke

178 Chapter 9 - Conclusions Future Research Direction Study 1 1. The optimisation of kinematic data for a 3D water environment together with using a polar coordinate methodology for the range of motion of each limb would provide a more applicable CFD results and enable less error in the kinematic data when transferred into the simulation. This may involve looking at more high resolution cameras in clearer pools together with adjusted digitising software that is able to maintain distances between joint centres; alternatively it may be using inertial sensors attached to the swimmer. Advancing this area to ensure quick feedback to swimmers on peak acceleration of the limbs and angles of the arm to the direction of propulsion may reduce the time in perfecting techniques as well as aiding in the improvement of the CFD simulations. 2. A study into the understanding of roughness coefficient on an actual swimmer including the best method for representing skin, swimwear and hair factors would provide better representation of swimming forces throughout the stroke. 3. Looking into alternate turbulence models on a passive drag situation such as the Large Eddy Simulation models may also provide a better CFD simulation that more accurately predicts trailing vortices as well and boundary separation. Study 2 4. The models used in the initial dolphin kick simulations only used the four rigid segments when simulating the motion of the swimmer, this could be increased to take into account the additional upper body movement as well as the asymmetry behaviour that was shown to be evident in the freestyle kick. 5. Together with advancements in 3D kinematics, including the slight variations in movement of the feet, calves and thighs in the third dimension may show some additional vortex formation that is not picked up in the 2D kinematics

179 Chapter 9 - Conclusions 6. Tracking the comparison of iliac crest movement with overall force and added mass calculations would be a good way of validating results that may led to better selection of the turbulence models and boundary layer details to use in the simulation. Study 3 7. Simulating a range of freestyle kicks to understand the full range of motion that various swimmers can go through to determine the most optimal underwater kicking techniques. 8. Reviewing the longitudinal twisting of the body that occurs slightly in reaction to the freestyle kick to see if the twist has any impact on the streamlining of the upper body. Study 4 9. Expanding this area of research to simulate the number of studies that have been completed on measuring the best depth to push off after a turn or off the dive. The amount of wave drag that was shown in this study would mean a review of the various swimmer body shapes to determine if larger leg size when compared to the upper body has an impact on the difference in drag when submerged and at depth. This may set up an anthropometric identification criteria for the actual swimmers shape rather than general approaches currently used. Study With the improvement of 3D kinematics a full model can be created of the breaststroke technique. This would include an accurate measurement of the upper body movement of the swimmer in order to get the best representation of a swimmer through the majority of the racing stroke. The simulation of this technique would show what effects the wave drag and the upper body motion have on the propulsive phases of the kick

180 Chapter 9 - Conclusions Study Kinematic data collection is the first area that would increase the effectiveness of the CFD simulations. Once an accurate representation of the swimming stroke is established, the simulations can then be put through a number of sensitivity checks to ensure the best turbulence models and discretisation schemes are being used for analysing swimming. 12. A review of kinematics for a number of different freestyle techniques as well as a number of different swimming speeds, would demonstrate if the double wave effect suggested in this study occurs only at this speed or if it is common at all speeds. The additional kinematic data for other freestyle techniques would provide a range of motions that are used in freestyle. These would then be able to be used as bounds in optimising the stroke in a CFD area before transferring it to the swimmer. 13. A review of shape and size would also provide very interesting insight into techniques. By trialling the same kinematics of the freestyle stroke onto a second scanned image of a different body type would show the relative contribution of the technique and body shape. 14. Expand the strokes analysed to include butterfly and backstroke to see if any distinctive effects such as the double wave effect occur within these strokes. Expanding this to include different body shapes would also begin to provide an insight into whether body shape would dictate which stroke the swimmer could be more innately competitive in

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193 Appendices Appendix A - Propulsion and Drag Plots Dolphin Kick Comparison 40 Body Drag Force (N) Large 2.4m/s Large 2.18m/s Large 1.5m/s Small 2.4m/s Small 2.18m/s Small 1.5m/s Figure A-1 - Comparison of drag forces on the body during dolphin kick. 20 Hips Drag Force (N) Large 2.4m/s Large 2.18m/s Large 1.5m/s Small 2.4m/s Small 2.18m/s Small 1.5m/s Figure A-2 - Comparison of drag forces on the hips during dolphin kick

194 Appendix 50 Thighs Drag Force (N) Large 2.4m/s Large 2.18m/s Large 1.5m/s Small 2.4m/s Small 2.18m/s Small 1.5m/s Figure A-3 - Comparison of drag forces on the thighs during dolphin kick. 40 Knees Drag Force (N) Large 2.4m/s Large 2.18m/s Large 1.5m/s Small 2.4m/s Small 2.18m/s Small 1.5m/s Figure A-4 - Comparison of drag forces on the knees during dolphin kick

195 Appendix 40 Calves Drag Force (N) Large 2.4m/s Large 2.18m/s Large 1.5m/s Small 2.4m/s Small 2.18m/s Small 1.5m/s Figure A-5 - Comparison of drag forces on the calves during dolphin kick. 30 Ankle Drag Force (N) Large 2.4m/s Large 2.18m/s Large 1.5m/s Small 2.4m/s Small 2.18m/s Small 1.5m/s Figure A-6 - Comparison of drag forces on the ankles during dolphin kick

196 Appendix Feet Drag Force (N) Large 2.4m/s Large 2.18m/s Large 1.5m/s Small 2.4m/s Small 2.18m/s Small 1.5m/s Figure A-7 - Comparison of drag forces on the feet during dolphin kick

197 Appendix Appendix B - Graphic Plots Dolphin Kick Underwater Figure B-1 - Integrity of the model during the upswing of the dolphin kick. Figure B-2 - Typical velocity plot during the dolphin kick

198 Appendix Figure B-3 - Typical vector profile during the dolphin kick

199 Appendix Freestyle Kick Figure B-4(a),(b)- Sample picture displaying the flexibility differences between left and right ankles during the respective down-sweeps

200 Appendix Figure B-5 - Sample picture displaying pressure levels on the body during the right leg down-sweep and the left leg up-sweep. Figure B-6 - Sample picture of displaying flow velocity and their vector directions near the end of the right leg down-sweep

201 Appendix Freestyle Kick Near Water Surface Figure B-7 - Near-surface freestyle (flutter) kick at 0.1s. Figure B-8 - Near-surface freestyle (flutter) kick at 0.2s

202 Appendix Figure B-9 - Near-surface freestyle (flutter) kick at 0.3s. Figure B-10 - Near-surface freestyle (flutter) kick at 0.4s

203 Appendix Breaststroke Kick Figure B-11 - Velocity vectors at 0.41s in the breaststroke kick cycle. Figure B-12 - Velocity vectors at 0.91s in the breaststroke kick cycle

204 Appendix Figure B-13 - Velocity vectors at 1.41s in the breaststroke kick cycle. Figure B-14 - Velocity vectors at 1.91s in the breaststroke kick cycle

205 Appendix Figure B-15 - Pressure contours at 0.41s in the breaststroke kick cycle. Figure B-16 - Pressure contours at 0.91s in the breaststroke kick cycle

206 Appendix Figure B-17 - Pressure contours at 1.41s in the breaststroke kick cycle. Figure B-18 - Pressure contours at 1.91s in the breaststroke kick cycle

207 Appendix Full Freestyle Stroke Figure B-19 - Surface profile during right arm stroke at 0.16s. Figure B-20 - Surface profile during right arm stroke at 0.29s

208 Appendix Figure B-21 - Surface profile during right arm stroke at 0.46s. Figure B-22 - Surface profile during right arm stroke at 0.61s