ESTABLISHING COMPUTATIONAL FLUID DYNAMICS …ESTABLISHING COMPUTATIONAL FLUID DYNAMICS MODELS FOR SWIMMING TECHNIQUE ASSESSMENT Matt Keys BEng (Hons) School of Civil and Resource Engineering

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

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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.

Abstract

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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.

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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........................................................................................... 39

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 ..................................................................................57

Contents

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Shoulder Joint..........................................................................................................73

Flexible Joints..........................................................................................................74

Summary................................................................................................................75

Chapter 4 Study 2 - Dolphin Kick Underwater ............................... 77

Introduction............................................................................................................77

Methodology..........................................................................................................79

Results ...................................................................................................................80

Discussion..............................................................................................................83

Ankle Flexibility Effect on Propulsion....................................................................85

Conclusion .............................................................................................................88

Chapter 5 Study 3 - Freestyle Kick Underwater.............................. 89

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 ...........................................................................................................101

Chapter 6 Study 4 - Freestyle Kick at Water Surface................... 102

Introduction..........................................................................................................102

Methodology........................................................................................................103

Results .................................................................................................................104

Discussion............................................................................................................109

Passive Drag Comparisons....................................................................................109

Overall Comparisons of Active Drag ....................................................................113

Left Side Segment Comparison.............................................................................115

Left versus Right Side Comparison.......................................................................116

Conclusions .........................................................................................................117

Chapter 7 Study 5 - Breaststroke Kick Underwater ..................... 118

Introduction..........................................................................................................118

Methodology........................................................................................................119

Kinematic Data......................................................................................................120

CFD Variables.......................................................................................................122

Results .................................................................................................................123

Contents

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Discussion............................................................................................................128

Video Comparisons ...............................................................................................128

Overall Active Drag ..............................................................................................128

Body Component Forces .......................................................................................130

CFD Parameter Sensitivity ....................................................................................130

Conclusion ...........................................................................................................131

Chapter 8 Study 6 - Full Freestyle Stroke at Water Surface........ 132

Introduction..........................................................................................................132

Methodology........................................................................................................134

Kinematic Data Collection ....................................................................................134

Kinematic Data to Virtual Skeletal Movement Equations ....................................134

Average Velocity Estimation ................................................................................135

Temporal Data.......................................................................................................136

CFD Mesh Sensitivity ...........................................................................................136

Results .................................................................................................................137

Discussion............................................................................................................142

Overall Drag and Propulsion .................................................................................142

Feet Force Profile ..................................................................................................143

Trunk Force Profile ...............................................................................................146

Arms Force Profile ................................................................................................147

Wave Influence......................................................................................................149

CFD Sensitivity .....................................................................................................151

Conclusion ...........................................................................................................154

Chapter 9 Conclusions, Summary and Future Research

Directions ......................................................................................... 155

Summary..............................................................................................................155

Study 1...................................................................................................................155

Study 2...................................................................................................................156

Study 3...................................................................................................................156

Study 4...................................................................................................................157

Study 5...................................................................................................................158

Study 6...................................................................................................................158

Conclusions .........................................................................................................159

Study 1...................................................................................................................159

Study 2...................................................................................................................159

Study 3...................................................................................................................160

Contents

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Study 4...................................................................................................................160

Study 5...................................................................................................................161

Study 6...................................................................................................................161

Future Research Direction ...................................................................................163

Study 1...................................................................................................................163

Study 2...................................................................................................................163

Study 3...................................................................................................................164

Study 4...................................................................................................................164

Study 5...................................................................................................................164

Study 6...................................................................................................................165

References............................................................................................................166

Appendices ..........................................................................................................178

Appendix A - Propulsion and Drag Plots ............................................................178

Dolphin Kick Comparison.....................................................................................178

Appendix B - Graphic Plots.................................................................................182

Dolphin Kick Underwater .....................................................................................182

Freestyle Kick........................................................................................................184

Freestyle Kick Near Water Surface.......................................................................186

Breaststroke Kick ..................................................................................................188

Full Freestyle Stroke .............................................................................................192

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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. 136

Tables

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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. 147

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LIST OF FIGURES

Figure 3-1 - Flow chart detailing the stages of model development. 41

Figure 3-2 - Laser scanned images of the subject for passive drag and lower body

motion simulations. 42

Figure 3-3 - Laser scanned images of the subject for full stroke simulations. 43

Figure 3-4 - Overview of the fully submerged streamlined glide model. 44

Figure 3-5 - Overview of the surface model simulations. 45

Figure 3-6 - The triangulated mesh surrounding the head. 47

Figure 3-7 - The triangulated mesh surrounding the hands. 47

Figure 3-8 - Towing testing set-up used for the passive drag measurement (Lyttle,

1999). 50

Figure 3-9 - Sample kinematics from underwater dolphin kicking trial. 54

Figure 3-10 - Sample kinematics from full freestyle stroke trial. 55

Figure 3-11 - Measurement points used to collect freestyle kinematic data. 56

Figure 3-12 - The joints used and the fixed lengths maintained for the 2D trial. 58

Figure 3-13 - Breakdown of each limb into a rigid body rotating around joint centres. 59

Figure 3-14 - 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 3-15 - Details how co-ordinates are then transferred into a set of polar rotational

angles with time. 60

Figure 3-16 - Comparisons of measured and calculated coordinates for the right ankle.

66

Figure 3-17 - Comparisons of measured and calculated coordinates for the right wrist.

66

Figure 3-18 - Average length to measured digitised length for the right forearm. 67

Figure 3-19 - Average length to measured digitised length for the right calf. 67

Figure 3-20 - Comparison of mathematical fitted curve with actual measured θxz angle

for the left calf. 68

Figure 3-21 - Comparison of mathematical fitted curve with actual measured θy angle

for the left calf. 68

Figure 3-22 - Each node point is referenced back to the predecessor joint to identify its

motion. 72

Figure 3-23 - The double ball and socket joint arrangement for the shoulder. 74

Figures

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Figure 4-1 - Angle of rotation measurement positions. 80

Figure 4-2 - Combined pressure and viscous drag forces over entire body for one full

cycle. 81

Figure 4-3 - Combined pressure and viscous drag forces at the knees for one full cycle.

81

Figure 4-4 - Sample pressure plot output of the CFD model. 82

Figure 4-5 - Velocity changes through kicking cycle. 83

Figure 4-6 - Net thrust graph highlighting effects of ankle flexibility on propulsion. 86

Figure 4-7 - Net thrust graph highlighting effects of ankle flexibility on propulsion

created by the feet. 87

Figure 4-8 - Net thrust graph highlighting effects of ankle flexibility on the propulsion

created by the total body. 87

Figure 5-1 - Total force curve for all body parts combined. 93

Figure 5-2 - Force curves for left and right leg components separately. 93

Figure 5-3 - Force curves for the left and right feet. 94

Figure 5-4 - Feet and knee drag/propulsion curves for the freestyle kick cycle. 94

Figure 5-5 - Sample picture displaying levels of flow velocity and their vector

directions. 95

Figure 5-6 - Velocity comparison for freestyle kick kinematic data. 96

Figure 5-7 - Graph of the cumulative momentum loss for each kicking scenario at a

velocity of 2.18m/s. 99

Figure 6-1 - Example of output from the CFD simulation detailing the surface deviation

over the body as well as velocity vectors. 105

Figure 6-2 - Comparison of the total net force on the swimmer for submerged and near-

surface simulations. 106

Figure 6-3 - Comparison of the left foot net force on the swimmer during submerged

and near-surface simulations. 107

Figure 6-4 - Comparison of the left calf net force on the swimmer during submerged


Figure 6-5 - Comparison of the right foot net force on the swimmer during submerged


Figure 6-6 - Comparison of the right calf net force on the swimmer during submerged


Figure 6-7 - The wave profile around the swimmer at 2m/s. 111

Figures

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Figure 6-8 - Critical points through the wave cycle (Barltrop & Adams, 1991). 111

Figure 6-9 - Detailing the wave profile length during the freestyle kick. 113

Figure 6-10 - Left foot rising above the water surface at 0.35s. 116

Figure 6-11 - Right foot emerging from the water at the top of the cycle at 0.21s. 117

Figure 7-1 - Comparisons of calf lengths calculated from the VICON kinematics

throughout the stroke. 121

Figure 7-2 - Comparisons of the breaststroke 3D simulation and actual underwater

footage of the kicking pattern used by the tested subject. 124

Figure 7-3 - Cumulative momentum loss throughout the breaststroke kick cycle. 125

Figure 7-4 - Total body force throughout the breaststroke kick cycle. 125

Figure 7-5 - Forces on the upper body and hip segments throughout the breaststroke

kick cycle. 126

Figure 7-6 - Forces on the thigh and knee segments throughout the breaststroke kick

cycle. 126

Figure 7-7 - Forces on the calf, ankle and feet segments throughout the breaststroke

kick cycle. 127

Figure 7-8 - Comparisons between various turbulence and discretisation parameters

from 1.9 to 2.5s. 127

Figure 7-9 - Displacement, velocity and acceleration data for the left ankle. 129

Figure 8-1 - The air bubbles surrounding a swimmer at the start of a 50m event. 133

Figure 8-2 - Velocity of the centre between the left and right iliac crests through the

freestyle stroke. 135

Figure 8-3 - The overall forces on the swimmer throughout the freestyle stroke. 138

Figure 8-4 - The forces on the right and left legs throughout the freestyle stroke. 138

Figure 8-5 - The forces on the trunk, right and left arms throughout the freestyle stroke.

139

Figure 8-6 - Pressure contours when maximum net force occurs during a stroke. 139

Figure 8-7 - Comparison of left leg foot positions with propulsive forces. 140

Figure 8-8 - The left foot coming out of the water during motion analysis testing. 141

Figure 8-9 - The left foot coming out of the water during the simulations. 141

Figure 8-10 - Comparison of left and right ankle joint plantar/dorsiflexion angles

throughout the freestyle stroke cycle (using a 6 beat kicking pattern). 144

Figure 8-11 - Angle of the upper trunk to the horizontal throughout the stroke. 146

Figure 8-12 - Static pressure contours showing the wave shape around the swimmer.149

Figures

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Figure 8-13- Pressure below the body at various times along the length of the body. 151

Figure 8-14 - Comparisons of coarse and fine mesh simulations. 153

Figure 8-15 - 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. 181

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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.

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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, 2010

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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.

Chapter 1 - Introduction

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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


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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.


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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.


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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.

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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

Chapter 2 - Literature Review

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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


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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 dorsi-

flexed 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,


-9-

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.


-10-

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.


-11-

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:

∫ ∫+−= dAtdAnpF wˆˆ τ

r

where n and t are unit vectors, perpendicular and tangential to the surface at each

location; and p and τw 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:

||2

1)( UAUCUVCtF dm ρρ += &

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 Cm and Cd are the inertial and

drag coefficients, respectively. This equation also can be adapted for rotation by

substituting rotational variables for the translational variables.


-12-

Coefficient of drag and inertia

Morrison’s equation is highly dependent on the two coefficients that are used, namely

Cd and Cm. 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, Cd 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

µ

ρUL=Re

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).


-13-

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 5×105. 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


-14-

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,


-15-

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


-16-

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:

gL

V

c

VFr ≈=

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


-17-

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


-18-

adaptation, of the inertial component of the equation for the commonly used term

‘added mass’ would be:

UCUCF amminertia&& )( +∀=∀= ρρ

where Cam is just the added mass, whereas Cm 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

0.045 (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.


-19-

For a body accelerating in water, the normal inertial coefficient is listed as Cm-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 Cm 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


-20-

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


-21-

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

1.1 – 2.7%, 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


-22-

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


-23-

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 mid-

section 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


-24-

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 &


-25-

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


-26-

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/s2 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:-

dragpropulsionTotal ForceForceForce −=

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,


-27-

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

(O2) consumption. The propulsive and resistive forces produced simultaneously by the


-28-

swimmer per cycle were either increased or decreased according to the direction of the

extra drag load. The relationship between the net O2 uptake equals the force of the extra

drag load. This relationship was expressed in a regression equation and extrapolated to

the baseline of resting O2 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


-29-

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.


-30-

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


-31-

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


-32-

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.


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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 sub-

layer, 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


-34-

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.


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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


-36-

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


-37-

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.


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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.

-39-

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

Chapter 3 - CFD model methodology and passive drag validation

-40-

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.


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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 3-1 - 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 full-

length competition swimsuits. This laser scan procedure created a 3D superficial model


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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 3-2 - 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).


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Figure 3-3 - 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 6.1.22 (for the initial passive drag and lower limb simulations) and version

6.3.26 (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


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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

3m

Inlet

Outflow

Moving walls

Figure 3-4 - Overview of the fully submerged streamlined glide model.


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• 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 re-

meshing 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.

Figure 3-5 - 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

1.5m

3.0m


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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.


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Figure 3-6 - The triangulated mesh surrounding the head.

Figure 3-7 - The triangulated mesh surrounding the hands.


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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


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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


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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

Standard

Deviation

(m/s) (N) (N) (N) (N) (N) (N) (N)

1.6 -23.9 -10.1 -34.0 -26.6 -23.6 -50.2 -58.1 9.3

1.9 -32.5 -13.1 -45.6 -35.6 -31.3 -66.9 -80.4 10.0

2.2 -45.2 -18.1 -63.3 -50.3 -43.9 -94.2 -109.4 11.1

2.5 -58.4 -23.0 -81.3 -64.9 -56.3 -121.1 -140.5 14.4

2.8 -73.2 -27.3 -100.5 -77.2 -68.0 -145.2 -169.7 16.1

3.1 -89.7 -34.3 -124.0 -99.4 -85.7 -185.1 -204.1 19.2

Table 3-2 –

Steady glide results with boundary layer mesh included.

Smooth walls 1mm roughness Test Results

Velocity Pressure Viscous Combined Pressure Viscous Combined

Mean

Combined

Standard

Deviation

(m/s) (N) (N) (N) (N) (N) (N) (N)

2.2 -55.9 -16.6 -72.5 -72.0 -30.2 -102.2 -109.4 11.1

Figure 3-8 - Towing testing set-up used for the passive drag measurement (Lyttle, 1999).


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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


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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)

1.5 31.5 30.2 32.1 37.2 44.9

1.75 42.7 42.5 45.9 51.7 63.9

2 55.5 57.8 62.7 70 86.6

2.25 70.1 72.7 78.11 88.1 108.1

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


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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


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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 3-9 - 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 45-60° to the horizontal plane. The


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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 3-10 - Sample kinematics from full freestyle stroke trial.


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Figure 3-11 - Measurement points used to collect freestyle kinematic data.


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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.


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Ankle

Rotation Angle

Hip

Rotation Angle

Knee Rotation

Angle

Figure 3-12 - 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 co-

ordinates 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.


-59-

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.

1-C

1-B

2-A1-A

3-A

3-C

2-C

3-B

2-B

Figure 3-13 - Breakdown of each limb into a rigid body rotating around joint centres.


-60-

y

z

x

y

z

x

Figure 3-14 - 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.

Length

y

θy

θxz

θt

Figure 3-15 - 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:


-61-

)sin(*)cos(*_

)sin(*_

)cos(*)cos(*_

1

1

1

yxznn

xznn

yxznn

LengthSegmentzz

LengthSegmentyy

LengthSegmentxx

θθ

θ

θθ

−=

+=

+=

−

−

−

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,


-62-

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 Σr2 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.


-63-

Table 3-4 –

Digitised points and corresponding initial coordinates on scanned model.

Position

Number Position Name

Abbre-

viation X Y Z

1 Left Metacarpal 1 LM1 108.973 -2.397 -25.143

2 Left Metacarpal 5 LM5 107.433 -1.317 -16.093

3 Left Radial Notch LRN 99.380 -2.445 -21.705

4 Left Ulna Notch LUN 101.833 -2.830 -27.385

5 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 72.381 1.101 -7.406

10 Right Ear RE 71.703 1.067 7.934

11 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 99.044 -3.263 20.686

16 Left Ulna Notch LUN 103.044 -1.763 25.686

17 Right Metacarpal 1 RM1 109.554 -2.205 21.629

18 Right Metacarpal 5 RM5 106.062 -3.237 13.099

19 C7 Vertebrae C7V 61.801 3.581 0.163

20 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 -46.054 5.031 -20.782

27 Left Knee Medial Condyle LKM -48.201 5.074 -9.399

28 Left Ankle Medial Malleolus LAM -91.922 3.026 -20.158

29 Left Ankle Lateral Malleolus LAL -92.612 4.613 -26.305

30 Left Mid Heel LMH

31 Left Metatarsal 1 LM1 -105.847 -4.375 -21.665

32 Left Metatarsal 5 LM5 -104.777 -0.769 -30.224

33 Right Knee Lateral Condyle RKL -47.379 3.959 21.416

34 Right Knee Medial Condyle RKM -49.129 2.758 8.905

35 Right Ankle Medial Malleolus RAM -92.375 2.002 19.250

36 Right Ankle Lateral Malleolus RAL -93.033 2.237 26.349

37 Right Mid Heel RMH

38 Right Metatarsal 1 RM1 -106.146 -6.183 19.976

39 Right Metatarsal 5 RM5 -104.790 -3.333 29.145


-64-

Table 3-5 –

Joint centres and calculated initial coordinates from scanned model.

Joint Centres

Number

Segment/Joint

Name

Abbre-

viation X Y Z

Preceeding

Joint

101 Left Hand LH 108.203 -1.857 -20.618 LW

102 Left Wrist LW 100.606 -2.638 -24.545 LE

103 Left Elbow LE 76.443 1.535 -37.614 LS2

104 Left Shoulder LS1 53.683 4.300 -13.416 MB

105 Left Shoulder LS2 58.794 4.300 -22.628 LS1

106 Right Hand RH 107.808 -2.721 17.364 RW

107 Right Wrist RW 101.044 -1.800 23.186 RE

108 Right Elbow RE 77.898 1.000 37.512 RS2

109 Right Shoulder 1 RS1 55.103 5.000 12.708 MB

110 Right Shoulder 2 RS2 59.985 5.000 21.373 RS1

111 Mid Head MH 72.042 1.084 0.264 C7V

112 C7 Vertebra C7V 60.936 3.572 0.132 MB

113 Mid Shoulders MS 54.393 6.050 0.000 MB

114 Mid Back MB 22.460 1.000 0.000 TP

115 Lower Back LB 7.000 0.000 0.000 TP

116 Mid Iliac Crest TP 1.500 0.000 0.000 Control

117 Pelvis Mid MP -8.500 0.000 0.000 TP

118 Pelvis Left LP -8.500 0.000 -10.440 TP

119 Pelvis Right RP -8.500 0.000 10.440 TP

120 Left Knee LK -47.128 5.053 -15.091 LP

121 Left Ankle LA -92.267 3.819 -23.231 LK

122 Left Mid Foot LMF -98.190 0.624 -24.588 LA

123 Left Toes LT -105.312 -2.572 -25.944 LT

124 Right Knee RK -48.254 3.358 15.160 RP

125 Right Ankle RA -92.704 2.119 22.799 RK

126 Right Mid Foot RMF -99.086 -1.319 23.680 RA

127 Right Toes RT -105.468 -4.758 24.561 RMF


-65-

Table 3-6 –

Rigid segment lengths from scanned model.

Rigid Body

Length

Number Limb Name Abbreviation Length (cm)

1 Left Hand LH 8.587

2 Left Forearm LFA 27.786

3 Left Upper Arm1 LUA1 10.535

4 Left Upper Arm2 LUA2 23.318

5 Right Hand RH 8.972

6 Right Forearm RFA 27.364

7 Right Upper Arm1 RUA1 9.946

8 Right Upper Arm2 RUA2 24.441

9 Head HD 11.383

10 Upper Body UB 32.329

11 Mid Body MB 15.493

12 Lower Body LB 5.500

13 Pelvis P 10.000

14 Left Thigh LTH 39.233

15 Left Calf LC 45.884

16 Left Foot LF 14.778

17 Left Toes LTS 7.923

18 Right Thigh RT 40.174

19 Right Calf RC 45.118

20 Right Foot RF 14.605

21 Right Toes RTS 7.303


-66-

Right Ankle - Model to measured comparison

-40

-35

-30

-25

-20

-15

-10

-5

0

5

10

0.5 0.7 0.9 1.1 1.3 1.5

Time (sec)

Y v

alu

e (

cm

)

-350

-300

-250

-200

-150

-100

-50

0

50

X-V

alu

e (

cm

)

CFD Model Y Coord Digitised Y-Coord CFD Model X-Coord Digitised X-Coord

Figure 3-16 - Comparisons of measured and calculated coordinates for the right ankle.

Right Wrist - Modelled to measured comparison

-80

-60

-40

-20

0

20

40

60

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Time (sec)

Y-v

alu

e (

cm

)

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

X-v

alu

e (

cm

)

CFD Model Y Coord Digitised Y Coord CFD model X Coord Digitised X Coord

Figure 3-17 - Comparisons of measured and calculated coordinates for the right wrist.


-67-

Right Forearm Length from Digitisation

0

5

10

15

20

25

30

35

40

45

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Time (sec)

Len

gth

(cm

)

Figure 3-18 - 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

15

20

25

30

35

40

45

50

55

60

0.4 0.6 0.8 1 1.2 1.4 1.6

Time (sec)

Len

gth

(cm

)

Figure 3-19 - 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.


-68-

Angle comparison between measured and model

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0.6 0.8 1 1.2 1.4 1.6Time (sec)

An

gle

(ra

d)

Digitised Angle(xz) CFD model Angle(xz)

Figure 3-20 - Comparison of mathematical fitted curve with actual measured θxz angle for the left

calf.

Angle comparison between measured and model

-4

-3.8

-3.6

-3.4

-3.2

-3

-2.8

-2.6

-2.4

-2.2

-2

0.6 0.8 1 1.2 1.4 1.6

Time (sec)

An

gle

(ra

d)

Digitised Angle(y) CFD model Angle(y)

Figure 3-21 - Comparison of mathematical fitted curve with actual measured θy angle for the left

calf.


-69-

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.


-70-

The basis for this formulation was as follows:

Each joint centre point is identified:

x-joint coordinate = xn

y-joint coordinate = yn

z-joint coordinate = zn

Each node point is defined by:

x-node coordinate = xi

y-node coordinate = yi

z-node coordinate = zi

A vector was then defined, derived from the three vectors for which the polar moments

are based:

[ ]

[ ][ ]

[ ]

[ ]

[ ]

[ ]

[ ]

[ ]2

1

2

1

2

1

1

2

1

2

1

2

1

1

2

1

2

1

2

1

1

)()()(2

)()()(1

)()()(0

02

11

00

)cos(2

01

)sin(0

nnnnnn

nn

t

nnnnnn

nn

t

nnnnnn

nn

t

y

y

y

yprevxz

xz

yprevxz

zzyyxx

zzV

zzyyxx

yyV

zzyyxx

xxV

V

V

V

V

V

V

−−+−

−=

−−+−

−=

−−+−

−=

=

=

=

=

=

=

+++

+

+++

+

+++

+

ϑ

ϑ


-71-

A rotational matrix around each vector is then defined

[ ][ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]

[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ][ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]

tyxzi

VVVVVVVV

VVVVVVVV

VVVVVVVV

M

iiiiiiiiiiiiii

iiiiiiiiiiiiii

iiiiiiiiiiiiii

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

=

+−+−−−

−−+−+−

+−−−+−

=

ϑϑϑϑϑϑ

ϑϑϑϑϑϑ

ϑϑϑϑϑϑ

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(

)(

)(

)(

***

tn

tn

tn

tnti

tnti

tnti

xzyt

ti

ti

ti

z

y

x

zz

yy

xx

MMM

z

y

x


-72-

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 3-22 - Each node point is referenced back to the predecessor joint to identify its motion.


-73-

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 L4.


-74-

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.

θy

L3

L2

L4

L2

Flexible

Flexible

Rigid

θt

θy

L3

L2

L4

L2

Flexible

Flexible

Rigid

θt

Figure 3-23 - 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.


-75-

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.


-76-

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.

-77-

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

Chapter 4 - Dolphin kick underwater

-78-

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.


-79-

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 4-1 - angles >180º

referred to as hyperextension)

Large Kick Small Kick

Amplitude (m) 0.64 0.52

Frequency (Hz) 2.33 2.72

Maximum Hip Rotation (deg) 154.7 169.4

Minimum Hip Rotation (deg) 195.2 195.3

Maximum Knee Rotation (deg) 124.8 139.5

Minimum Knee Rotation (deg) 191.1 192.1

Maximum Ankle Rotation (deg) 136.8 134.8

Minimum Ankle Rotation (deg) 170.4 177.2


-80-

Figure 4-1 - 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 -44.40 -35.04 -9.59 -38.03 -31.24 -9.74

Total per second -103.46 -81.65 -22.34 -103.45 -84.98 -26.48

Body per second -59.94 -48.15 -17.95 -59.09 -48.42 -18.60

Hips per second -3.16 -2.24 1.53 -1.35 -0.98 1.62

Thighs per second -9.56 -6.37 0.60 -17.03 -13.85 -3.16

Knees per second -21.31 -19.75 -13.61 -16.00 -14.21 -9.63

Calves per second -2.61 -1.92 -0.61 -1.67 -2.01 -1.32

Ankles per second 3.50 4.78 8.49 0.33 1.37 5.05

Feet per second -10.37 -8.01 -0.79 -8.64 -6.87 -0.43

Ankle

Rotation

Angle

Hip

Rotation

Angle

Knee

Rotation

Angle


-81-

Total Drag Force (N)

-250

-200

-150

-100

-50

0

50

100

0.0700 0.1200 0.1700 0.2200 0.2700 0.3200 0.3700 0.4200 0.4700

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 4-2 - 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).

Knees Drag Force (N)

-80

-60

-40

-20

0

20

40

0.0700 0.1200 0.1700 0.2200 0.2700 0.3200 0.3700 0.4200 0.4700

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 4-3 - 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).


-82-

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 4-4 - Sample pressure plot output of the CFD model.


-83-

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.

Velocity of Large Kick over 1 second

y = -25.958x + 231.88

0

50

100

150

200

250

300

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time (s)

Velo

cit

y (

cm

/sec)

Figure 4-5 - 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


-84-

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 up-

sweep 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 non-

acceleration 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.


-85-

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).


-86-

Feet Component Drag Force (N)

-110

-70

-30

10

50

0.0700 0.1200 0.1700 0.2200 0.2700 0.3200 0.3700 0.4200 0.4700

Time (s)

Original 10deg shift 10deg less plantar flexion

Figure 4-6 - 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 down-

sweep, which occurs between 0.22-0.35s (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.

Max = 24.8N

Max = 41.2N

Min = -68.8N

Min = -100.2N


-87-

Force on Feet with Different Ankle Flexibility

-80

-60

-40

-20

0

20

40

60

0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4

Time (s)

Fo

rce (

N)

Original Flexibility 10 Degrees Less Flexibility

Figure 4-7 - Net thrust graph highlighting effects of ankle flexibility on propulsion created by the

feet.

Total Force with Different Ankle Flexibility

-200

-150

-100

-50

0

50

0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4

Time (s)

Fo

rce (

N)

Original Flexibility 10 Degrees Less Flexibility

Figure 4-8 - Net thrust graph highlighting effects of ankle flexibility on the propulsion created by

the total body.


-88-

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.

-89-

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.

Chapter 5 - Freestyle kick underwater

-90-

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) 0.57 0.53

Average Horizontal CM Velocity (m/s) 1.80 1.80

Kick Frequency (Hz) 2.56 2.56

Minimum Hip Rotation (deg) 169.4 169.8

Maximum Hip Rotation (deg) 185.1 187.0

Minimum Knee Rotation (deg) 147.0 140.2

Maximum Knee Rotation (deg) 189.2 196.4

Minimum Ankle Rotation (deg) 123.8 121.7

Maximum Ankle Rotation (deg) 179.1 150.7

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.


-91-

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.


-92-

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) -35.04 -31.24 -22.85

Total per second (Ns) -81.65 -84.98 -58.59

Body per second (Ns) -48.15 -48.42 -42.44

Hips per second (Ns) -2.24 -0.98 -5.46

Thighs per second (Ns) -6.37 -13.85 -0.71

Knees per second (Ns) -19.75 -14.21 -9.19

Calves per second (Ns) -1.92 -2.01 10.26

Ankles per second (Ns) 4.78 1.37 10.78

Feet per second (Ns) -8.01 -6.87 -21.83


-93-

Total Drag/Propulsion Force - Freestyle Kick

-200

-150

-100

-50

0

50

0.12 0.17 0.22 0.27 0.32 0.37 0.42 0.47 0.52

Fo

rce

(N

)

Figure 5-1 - Total force curve for all body parts combined.

Drag/Propulsion force Left/Right Leg During Freestyle

-100

-80

-60

-40

-20

0

20

40

60

80

100

0.12 0.17 0.22 0.27 0.32 0.37 0.42 0.47 0.52Fo

rce

(N

)

Left Leg Right Leg

Figure 5-2 - Force curves for left and right leg components separately.


-94-

Drag/Propulsion force Left/Right Feet During Freestyle

-50

-40

-30

-20

-10

0

10

20

30

40

50

0.12 0.17 0.22 0.27 0.32 0.37 0.42 0.47 0.52

Time (sec)

Forc

e (

N)

foot-left foot-right

Figure 5-3 - Force curves for the left and right feet.

Drag/Propulsion force Left/Right Knee During Freestyle

-30

-20

-10

0

10

20

30

0.12 0.17 0.22 0.27 0.32 0.37 0.42 0.47 0.52

Time (sec)

Fo

rce

(N

)

knee-left knee-right

Figure 5-4 - Feet and knee drag/propulsion curves for the freestyle kick cycle.


-95-

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) 2.18 2.18 2.18


Distance – next second (m) 1.73 1.71 1.87

Table 5-5 –

Average momentum (Ns) change in swimmer through 1s of kicking.

Large/Slow

Dolphin kick

Small/Fast

Dolphin Kick

Freestyle Kick







Figure 5-5 - Sample picture displaying levels of flow velocity and their vector directions.


-96-

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.

Velocity of Iliac Crests

0

50

100

150

200

250

300

0 0.2 0.4 0.6 0.8 1 1.2

Time (s)

Velo

cit

y (

cm

/s)

Left iliac crest Right iliac crest Linear (Left iliac crest)

Figure 5-6 - 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


-97-

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.


-98-

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) -1.89 -4.41

Total per second (Ns) -4.84 -11.31

Hips per second (Ns) -2.78 -2.68

Thighs per second (Ns) -0.49 -0.22

Knees per second (Ns) -3.17 -6.03

Calves per second (Ns) 4.40 5.86

Ankles per second (Ns) 5.20 5.58

Feet per second (Ns) -8.01 -13.82

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%.


-99-

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.

Cumulative Momentum Loss for Each of the Three Kicking Scenarios

0

5

10

15

20

25

30

35

40

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Time (s)

Mo

me

ntu

m L

os

s (

Ns

)

Freestyle Kick Small/Fast Dolphin Kick Large/Slow Dolphin Kick

Figure 5-7 - 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.


-100-

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.


-101-

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).

-102-

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

Chapter 6 - Freestyle kick at water surface

-103-

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.


-104-

• 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 30-34 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.


-105-

Figure 6-1 - 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-

Near-Surface Change % Change

Velocity 2 m/s 2 m/s

Total (N) -50.64 -61.94 -11.30 -18.2%

Hands (N) -5.13 -5.48 -0.35 -0.6%

Arms (N) -22.68 -53.79 -31.11 -50.2%

Head (N) -10.01 -37.27 -27.26 -44.0%

Upper Body (N) -6.14 -22.82 -16.68 -26.9%

Total-Body (N) -43.96 -119.37 -75.40 -121.7%

Hips (N) -2.63 -3.47 -0.84 -1.4%

Thighs (N) 3.13 42.90 39.77 64.2%

Knees (N) 2.06 12.72 10.67 17.2%

Calves (N) 1.97 6.10 4.13 6.7%

Ankles (N) -4.47 -11.97 -7.49 -12.1%

Feet (N) -6.73 11.14 17.87 28.9%


-106-

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

Change %

Change

Velocity 1.5m/s 1.5m/s

Total per cycle (Ns) -6.95 -18.15 -11.20 -61.7%

Total per second (Ns) -17.81 -46.53 -28.72 -61.7%

Body per second (Ns) -21.35 -137.53 -116.18 -249.7%

Hips per second (Ns) -1.21 -4.26 -3.05 -6.6%

Thighs per second (Ns) 1.75 33.13 31.38 67.4%

Knees per second (Ns) -4.30 19.96 24.26 52.1%

Calves per second (Ns) 9.63 27.07 17.44 37.5%

Ankles per second (Ns) 13.64 3.73 -9.91 -21.3%

Feet per second (Ns) -14.63 14.34 28.97 62.3%

Drag/Propulsion Comparison - Total

-100

-80

-60

-40

-20

0

20

40

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Time (sec)

Forc

e (

N)

Total - Near Surface Total - Fully Submerged

Figure 6-2 - Comparison of the total net force on the swimmer for submerged and near-surface

simulations.


-107-

Drag/Propulsion Comparison Left Foot

-60

-40

-20

0

20

40

60

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Time (sec)

Forc

e (

N)

Left Foot - Near Surface Left Foot - Fully Submerged

Figure 6-3 - Comparison of the left foot net force on the swimmer during submerged and near-

surface simulations.

Drag/Propulsion Comparison Left Calf

-60

-40

-20

0

20

40

60

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Time (sec)

Forc

e (

N)

Left Calf - Near Surface Left Calf - Fully Submerged

Figure 6-4 - Comparison of the left calf net force on the swimmer during submerged and near-



-108-

Drag/Propulsion Comparison Right Foot

-60

-40

-20

0

20

40

60

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Time (sec)

Forc

e (

N)

Right Foot - Near Surface Right Foot - Fully Submerged

Figure 6-5 - Comparison of the right foot net force on the swimmer during submerged and near-


Drag/Propulsion Comparison Right Calf

-60

-40

-20

0

20

40

60

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Time (sec)

Forc

e (

N)

Right Calf - Near Surface Right Calf - Fully Submerged

Figure 6-6 - Comparison of the right calf net force on the swimmer during submerged and near-



-109-

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.


-110-

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.


-111-

Figure 6-7 - The wave profile around the swimmer at 2m/s.

Figure 6-8 - 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)

2.7m


-112-

A wave with these characteristics, at a depth of 0.1m, has associated acceleration and

velocity ranges (Barltrop & Adams, 1991):

Velocity Range => -0.31 to 0.31 m/s

Acceleration Range => -1.54 to 1.54 m/s2

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.

wavemwavedsubmergedsurface AdensityVolCVdensityAreaCForceForce *******5.0 2 −−=

The values for drag coefficient Cd and inertial coefficient Cm (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 0.03m2 and a volume of 0.016m

3;

With a water density of 1000 kg/m3;

A peak acceleration of 1.5m/s2 and a velocity of -0.2m/s.

md

md

CC

CabsC

*24*3.013.390.42

5.1*1000*016.0*)2.0(*)2.0(*1000*03.0**5.013.390.42

−+−=−

−−−−−=−

Possible values may be Cd = 0.5 and Cm = 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.


-113-

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.

Figure 6-9 - Detailing the wave profile length during the freestyle kick.

1.7m

2 3

4


-114-

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 => -0.32 to 0.32 m/s

Acceleration Range => -1.95 to 1.95 m/s2

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


-115-

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.


-116-

Figure 6-10 - 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.


-117-

Figure 6-11 - 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%.

-118-

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 air-

water 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.

Chapter 7 - Breaststroke kick underwater

-119-

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


-120-

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 mid-

point 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


-121-

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 55.3 52.6 54.2 +/-1.64

Right Thigh 54.0 52.1 53.1 +/-1.04

Left Calf 45.9 42.6 43.8 +/-2.08

Right Calf 46.7 42.7 44.3 +/-2.44

Calf Segment Length during stroke

40

41

42

43

44

45

46

47

48

49

50

0 1 2 3 4 5 6 7Time (sec)

Len

gth

(cm

)

Left Calf Average Right Calf Average Left Calf Right Calf

Figure 7-1 - Comparisons of calf lengths calculated from the VICON kinematics throughout the

stroke.


-122-

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


-123-

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) -136.8

Total per second (Ns) -68.4

Body per second (Ns) -22.4

Hips per second (Ns) -8.0

Thighs per second (Ns) -2.6

Knees per second (Ns) -7.3

Calves per second (Ns) -13.2

Ankles per second (Ns) -1.6

Feet per second (Ns) -13.1

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 -22.34 Ns

Small amplitude dolphin kick -26.48 Ns

Freestyle Kick -17.81 Ns

Breaststroke Kick -68.4 Ns


-124-

Figure 7-2 - Comparisons of the breaststroke 3D simulation and actual underwater footage of the

kicking pattern used by the tested subject.


-125-

Cumulative Momentum Loss for the Breaststroke Kick

0

20

40

60

80

100

120

140

160

180

200

0 0.5 1 1.5 2 2.5 3

Time (s)

Mo

me

ntu

m L

oss (

Ns)

Figure 7-3 - Cumulative momentum loss throughout the breaststroke kick cycle.

Drag/Propulsion Force of the Breastroke Kick

-200

-160

-120

-80

-40

0

40

0.4 0.9 1.4 1.9 2.4

Time (s)

Fo

rce

(N

)

Overall Body

Figure 7-4 - Total body force throughout the breaststroke kick cycle.


-126-


-60

-40

-20

0

20

0.4 0.9 1.4 1.9 2.4

Time (s)

Fo

rce

(N

)

Upper Body and Arms Hips

Figure 7-5 - Forces on the upper body and hip segments throughout the breaststroke kick cycle.


-60

-40

-20

0

20

0.4 0.9 1.4 1.9 2.4

Time (s)

Fo

rce

(N

)

Thighs Knees

Figure 7-6 - Forces on the thigh and knee segments throughout the breaststroke kick cycle.


-127-


-60

-40

-20

0

20

0.4 0.9 1.4 1.9 2.4

Time (s)

Fo

rce

(N

)

Calves Ankles Feet

Figure 7-7 - Forces on the calf, ankle and feet segments throughout the breaststroke kick cycle.

Comparisons Beweeen Turbulence and Discretisation Variables

-250

-200

-150

-100

-50

0

50

100

1.9 2 2.1 2.2 2.3 2.4 2.5

Time (s)

Fo

rce

(N

)

Trial 1- Standard / 1st order Trial 2 - Realisable / 1st order Trial 3 - Realisable / 2nd order

Figure 7-8 - Comparisons between various turbulence and discretisation parameters from 1.9 to

2.5s.


-128-

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


-129-

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

-10000

-8000

-6000

-4000

-2000

0

2000

4000

6000

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

Time (s)

Dis

p (

mm

) /

ve

l (m

m/s

) /

Ac

cl'n

(m

m/s

2)

Displacement Velocity Acceleration

Figure 7-9 - Displacement, velocity and acceleration data for the left ankle.


-130-

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


-131-

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.

-132-

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

Chapter 8 - Full freestyle stroke at water surface

-133-

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 8-1 - The air bubbles surrounding a swimmer at the start of a 50m event.


-134-

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.


-135-

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.

Velocity Comparison of Water to Mid Iliac Crest

0

50

100

150

200

250

0.13 0.33 0.53 0.73 0.93 1.13Time (sec)

Velc

oity (

cm

/sec)

Velocity of mid iliac crest Water Velocity

Figure 8-2 - Velocity of the centre between the left and right iliac crests through the freestyle

stroke.


-136-

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


0.58 s Right hand enters the water

0.64 s Left forearm at closest point to vertical

0.70 s Left hand exits the water



0.98 s Right hand at deepest point

1.04 s Right forearm at closest point to vertical


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.


-137-

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) 31.23

Total per second (Ns) 30.03

Hand per second (Ns) 12.21 11.59 23.80

Wrist per second (Ns) 4.65 6.47 11.12

Forearm per second (Ns) 3.89 6.03 9.92

Elbow per second (Ns) 2.35 4.21 6.56

Upper Arm per second (Ns) -0.50 0.27 -0.23

Shoulder per second (Ns) -9.17 -8.02 -17.20

Head per second (Ns) -10.18

Neck Per Second (Ns) -0.37

Upper Trunk per second (Ns) -37.94

Mid Trunk per second (Ns) -24.74

Pelvis per second (Ns) 3.18

Hips per second (Ns) -4.55 -2.85 -7.41

Thighs per second (Ns) 9.46 8.82 18.28

Knees per second (Ns) 4.18 5.23 9.41

Calves per second (Ns) 14.81 12.57 27.39

Ankles per second (Ns) 0.38 -2.29 -1.91

Feet per second (Ns) 10.67 9.67 20.34

Combined Arms per second (Ns) 13.44 20.54 33.98

Combined Legs per second (Ns) 34.95 31.16 66.10

Trunk and Head per second (Ns) -70.05


-138-

Overall Propulsion/Drag on Freestlye Swimmer

-200

-100

0

100

200

300

400

500

0.13 0.33 0.53 0.73 0.93 1.13

Time (sec)

Fo

rce (

N)

Figure 8-3 - The overall forces on the swimmer throughout the freestyle stroke.

Drag/Propulsion for Body Parts

-60

-40

-20

0

20

40

60

80

100

120

140

0.13 0.33 0.53 0.73 0.93 1.13

Time (sec)

Fo

rce (

N)

Right Leg Left Leg

Figure 8-4 - The forces on the right and left legs throughout the freestyle stroke.


-139-

Drag/Propulsion for Body Parts

-200

-100

0

100

200

300

400

0.13 0.33 0.53 0.73 0.93 1.13

Time (sec)

Fo

rce (

N)

Right Arm Left Arm Head and Body

Figure 8-5 - The forces on the trunk, right and left arms throughout the freestyle stroke.

Figure 8-6 - Pressure contours when maximum net force occurs during a stroke.


-140-

Force component for Left Leg

-50

0

50

100

150

200

0 0.2 0.4 0.6 0.8 1 1.2

Time (sec)

Fo

rce (

N)

Left Calf Left Foot Total Left Leg


-50

0

50

100

150

200

0 0.2 0.4 0.6 0.8 1 1.2

Time (sec)

Fo

rce (

N)



-50

0

50

100

150

200

0 0.2 0.4 0.6 0.8 1 1.2

Time (sec)

Fo

rce (

N)


Figure 8-7 - Comparison of left leg foot positions with propulsive forces.


-141-

Figure 8-8 - The left foot coming out of the water during motion analysis testing.

Figure 8-9 - The left foot coming out of the water during the simulations.


-142-

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.


-143-

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.


-144-

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 34.95 Ns compared with

31.16 Ns for the right side.

Joint Angle Comparison for the Ankles

140

150

160

170

180

190

200

0.13 0.33 0.53 0.73 0.93 1.13Time (sec)

An

gle

(d

eg

)

Right Ankle Left Ankle

Figure 8-10 - 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


-145-

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 near-

surface 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).


-146-

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

0

5

10

15

20

25

30

35

0.13 0.33 0.53 0.73 0.93 1.13

Time (sec)

An

gle

(d

eg

)

Figure 8-11 - Angle of the upper trunk to the horizontal throughout the stroke.


-147-

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

(s)

Initial hand entry and outstretching of the arm 0.09-0.21 0.61-0.70

Acceleration at the start of the stroke pushing outwards 0.21-0.38 0.70-0.91

The change of direction from pushing outwards to

bringing the arm back in towards the centre of the body

0.38-0.45 0.92-0.98

The main propulsion phase along the base of the body

when the forearm is close to perpendicular to the

direction of travel

0.45-0.59 0.98-1.14

The exit of the hand from the water 0.59-0.67 0.10-0.24

The recovery of the arm 0.67-1.13 0.24-0.61

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


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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


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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).

Figure 8-12 - Static pressure contours showing the wave shape around the swimmer.

2.7m


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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.


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Pressure at 300mm Below the Body Along its Length

4000

4500

5000

5500

6000

6500

-0.5 -0.3 -0.1 0.1 0.3 0.5 0.7 0.9 1.1 1.3

Distance (m)

Pre

ssu

re (

Pa)

0.45s 0.54s 0.63s 0.69s 0.74s

Figure 8-13- 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.


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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.


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Comparison of Coarse Vs Fine Mesh

-400

-300

-200

-100

0

100

200

300

400

0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4

Fo

rce (

N)

Coarse Mesh Fine Mesh

Figure 8-14 - Comparisons of coarse and fine mesh simulations.

Comparison of Coarse Vs Fine Mesh

-400

-300

-200

-100

0

100

200

300

400

0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4Fo

rce (

N)

Coarse Mesh Time Avergaed Fine Mesh

Figure 8-15 - Comparisons of moving time averaged coarse and fine mesh simulations.


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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.

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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.

Chapter 9 - Conclusions

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• 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-to-

scapular 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.


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• 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%.


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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.


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• 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.


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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.


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• 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 3.


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• 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.


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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.


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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 5

10. 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.


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Study 6

11. 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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Appendices

Appendix A - Propulsion and Drag Plots

Dolphin Kick Comparison

Body Drag Force (N)

-120

-100

-80

-60

-40

-20

0

20

40

0.0700 0.1200 0.1700 0.2200 0.2700 0.3200 0.3700 0.4200 0.4700



Figure A-1 - Comparison of drag forces on the body during dolphin kick.

Hips Drag Force (N)

-20

-15

-10

-5

0

5

10

15

20

0.0700 0.1200 0.1700 0.2200 0.2700 0.3200 0.3700 0.4200 0.4700



Figure A-2 - Comparison of drag forces on the hips during dolphin kick.

Appendix

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Thighs Drag Force (N)

-50

-40

-30

-20

-10

0

10

20

30

40

50

0.0700 0.1200 0.1700 0.2200 0.2700 0.3200 0.3700 0.4200 0.4700



Figure A-3 - Comparison of drag forces on the thighs during dolphin kick.

Knees Drag Force (N)

-80

-60

-40

-20

0

20

40

0.0700 0.1200 0.1700 0.2200 0.2700 0.3200 0.3700 0.4200 0.4700



Figure A-4 - Comparison of drag forces on the knees during dolphin kick.

Appendix

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Calves Drag Force (N)

-40

-30

-20

-10

0

10

20

30

40

0.0700 0.1200 0.1700 0.2200 0.2700 0.3200 0.3700 0.4200 0.4700



Figure A-5 - Comparison of drag forces on the calves during dolphin kick.

Ankle Drag Force (N)

-15

-10

-5

0

5

10

15

20

25

30

0.0700 0.1200 0.1700 0.2200 0.2700 0.3200 0.3700 0.4200 0.4700



Figure A-6 - Comparison of drag forces on the ankles during dolphin kick.

Appendix

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Feet Drag Force (N)

-80

-60

-40

-20

0

20

40

0.0700 0.1200 0.1700 0.2200 0.2700 0.3200 0.3700 0.4200 0.4700



Figure A-7 - Comparison of drag forces on the feet during dolphin kick.

Appendix

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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.

Appendix

-183-

Figure B-3 - Typical vector profile during the dolphin kick.

Appendix

-184-

Freestyle Kick

Figure B-4(a),(b)- Sample picture displaying the flexibility differences between left and right ankles

during the respective down-sweeps.

Appendix

-185-

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.

Appendix

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Freestyle Kick Near Water Surface

Figure B-7 - Near-surface freestyle (flutter) kick at 0.1s.


Appendix

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Appendix

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Breaststroke Kick

Figure B-11 - Velocity vectors at 0.41s in the breaststroke kick cycle.


Appendix

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Appendix

-190-

Figure B-15 - Pressure contours at 0.41s in the breaststroke kick cycle.


Appendix

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Appendix

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Full Freestyle Stroke

Figure B-19 - Surface profile during right arm stroke at 0.16s.


Appendix

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ESTABLISHING COMPUTATIONAL FLUID DYNAMICS …ESTABLISHING COMPUTATIONAL FLUID DYNAMICS MODELS FOR SWIMMING TECHNIQUE ASSESSMENT Matt Keys BEng (Hons) School of Civil and Resource Engineering