the study of swimming propulsion using computational fluid dynamics

DANIEL ALMEIDA MARINHO

THE STUDY OF SWIMMING PROPULSION USING

COMPUTATIONAL FLUID DYNAMICS

A three-dimensional analysis of the

swimmer’s hand and forearm

Universidade de Trás-os-Montes e Alto Douro

Vila Real, Portugal, 2009

UNIVERSIDADE DE TRÁS-OS-MONTES E ALTO DOURO

DANIEL ALMEIDA MARINHO

THE STUDY OF SWIMMING PROPULSION USING

COMPUTATIONAL FLUID DYNAMICS

A three-dimensional analysis of the swimmer’s hand and forearm

PhD in Sport Sciences

Promoters: Professor António José Silva

Professor Abel Rouboa

Vila Real, Portugal, 2009

I

Este trabalho foi expressamente elaborado com vista à obtenção do grau de Doutor em

Ciências do Desporto, de acordo com o disposto no Decreto-lei n.º 216/92, de 13 de

Outubro.

II

This thesis was supported by the Portuguese Government by a grant of the Science and

Technology Foundation (SFRH/BD/25241/2005).

III

To Tia Belinha

IV

Acknowledgments

The present thesis was only possible to be developed with the important help of so

many people, who had a significant contribution to this final work. Many thanks to all

of them.

I would like to express my deepest appreciation to Professor António José Silva,

promoter of this thesis, for providing his scientific knowledge, for guiding this scientific

research, as well as for his encouragement during the whole project. To ToZé, my

gratitude for believing in me and in my work, for his support, help and friendship.

To Professor Abel Rouboa, promoter of this thesis, for his important contribution during

the whole project. My sincere appreciation for his friendship, for helping me with the

theoretical part of the CFD methodology and for the important collaboration in the

writing of the papers.

To Professor Victor Reis, for his important remarks and cooperation during all phases

of this project, especially reviewing all the papers and the final form of the thesis. To

Victor, I would also like to thank for helping me since the first meeting we had in Vila

Real and for his constant support and friendship.

To Professor João Paulo Vilas-Boas, Professor Francisco Alves, Professor Leandro

Machado and Professor Per-Ludvik Kjendlie, for their important remarks, corrections

and suggestions to improve this project.

To my friends Luciano Sousa and Luís Leal, for their cooperation and significant help

during the numerical simulation procedures.

To my colleagues and friends Mário Marques, Aldo Costa, Pedro Guedes de Carvalho,

Tiago Barbosa and Nuno Garrido, for their encouragement and support in everything I

V

needed. To Mário, special thanks for our discussions and valuable remarks during our

trips and for being always interested in the progress of this thesis.

Sincere thanks to all the swimming team of Clube Fluvial Vilacondense. Many thanks

to António Vasconcelos (Tonas), Daniel Novais and Catarina Figueiredo, for their

cooperation and interest and for allowing the necessary free time for developing this

thesis.

Sincere thanks to the swimmer Adriano Niz, for volunteering to participate in this work.

I would like to thank the staff of the Radiology Department of Hospital de São João,

Porto, and personally to the Department Director, Professor Isabel Ramos, for helping

with the computer tomography scans procedures, allowing to obtain the geometry of the

swimmer’s hand and forearm.

I would also like to express my gratitude to the Med Mat Innovation Company, Maia,

especially to Professor José Domingos Santos and to Engineer Bruno Sá, for their

contributes to the design of the digital model of the swimmer’s hand and forearm.

Many thanks to all my friends.

Finally, I wish to express my sincere gratitude to all my family, especially my parents

and my sisters, for encouraging and supporting me during all my life, for being present

when I needed them, for understanding and admiring my work; for everything!

VI

Abstract

The main purpose of the present thesis was to study the mechanism of swimming propulsion using

Computational Fluid Dynamics (CFD) through a three-dimensional analysis of the swimmer’s hand and

forearm.

CFD methodology is a branch of fluid mechanics that solves and analyses problems involving a fluid

flow by means of computer-based simulations. This methodology can be considered as an interesting

approach to use in swimming research, since it allows simulating the water flow around the human body

and thus, to analyse the propulsive forces produced by the swimmer.

The first part of this thesis was to be able to apply CFD using a three-dimensional model of the swimmer

body. After the propulsive force measurements using a true three-dimensional model of a human segment

have been demonstrated, it was possible to improve previous CFD analysis, including a more realistic

model of the swimmer hand and forearm. Additionally, the CFD methodology was applied to address

some practical concerns of swimmers and coaches, such as the finger’s relative position during the

underwater path of the stroke cycle.

The main conclusions of the present thesis were: (i) the drag coefficient was the main responsible for the

hand and forearm propulsion, with a maximum value of force corresponding to an angle of attack of 90º;

(ii) an important contribution of the lift force to the overall force generation by the hand/forearm in

swimming phases was observed at angles of attack of 30º, 45º and 60º, especially when the little finger

leads the motion; (iii) the hand model with the thumb adducted presented higher values of drag

coefficient compared with thumb abducted models. The model with the thumb fully abducted allowed

increasing the lift coefficient of the hand at angles of attack of 0º and 45º; (iv) the resultant force

coefficient showed that the hand model with the thumb fully abducted presented higher values than the

positions with the thumb partially abducted and adducted at angles of attack of 0º and 45º. At an angle of

attack of 90º, the model with the thumb adducted presented the highest value of resultant force

coefficient; (v) the hand model with little distance between fingers presented higher values of drag

coefficient than the models with fingers closed and fingers with large distance spread. The values for the

lift coefficient presented little differences between the models with different finger’s spreading and; (vi)

the results suggested that for hand positions in which the lift force can play an important role, the

abduction of the thumb may be better, whereas at higher angles of attack, in which the drag force is

dominant, the adduction of the thumb may be preferable. Furthermore, it is suggested that fingers slightly

spread could allow the hand to create more force during swimming.

VII

Resumo

O objectivo principal da presente dissertação foi estudar o mecanismo propulsivo em natação, utilizando a

Dinâmica Computacional de Fluidos (DCF) através de uma análise tridimensional da mão e antebraço do

nadador.

A metodologia de DCF baseia-se na simulação computacional do escoamento do fluido em torno de

estruturas físicas. Esta metodologia pode ser considerada como uma forma interessante para ser utilizada

na investigação em natação, tornando possível a simulação do escoamento da água em torno do nadador

e, desta forma, analisar as forças propulsivas produzidas pelo nadador.

A primeira parte desta dissertação foi dedicada à aplicação da DCF utilizando um modelo tridimensional

do corpo do nadador. Após ter sido demonstrada a possibilidade de se analisar as forças propulsivas

usando um modelo tridimensional de um segmento humano, foi possível melhorar as análises numéricas

anteriormente efectuadas, incluindo um modelo mais real da mão e antebraço do nadador. Para além

disso, a metodologia de DCF foi aplicada para tentar responder a algumas questões mais práticas de

nadadores e treinadores, tais como a posição relativa dos dedos durante o trajecto motor em natação.

As conclusões da presente dissertação foram as seguintes: (i) o coeficiente de arrasto foi o principal

responsável pela produção de força pela mão e antebraço, apresentando o valor mais elevado com um

ângulo de ataque de 90º; (ii) foi observada uma importante contribuição da força de sustentação para a

produção de força pela mão e antebraço, com ângulos de ataque de 30º, 45º e 60º, especialmente quando o

dedo mínimo actuava como bordo de ataque; (iii) o modelo da mão com o polegar em adução apresentou

valores superiores no coeficiente de arrasto do que os modelos com o polegar em abdução. O modelo com

o polegar totalmente em abdução permitiu aumentar o coeficiente de sustentação da mão, com ângulos de

ataque de 0º e 45º; (iv) o modelo da mão com o polegar totalmente em abdução apresentou valores

superiores no coeficiente de força resultante do que as posições com o polegar parcialmente em abdução e

em adução, com ângulos de ataque de 0º e 45º. Com um ângulo de ataque de 90º, o modelo com o polegar

em adução apresentou o valor do coeficiente de força resultante mais elevado; (v) o modelo da mão com

uma pequena distância entre os dedos apresentou valores do coeficiente de arrasto mais elevados do que

os modelos com os dedos juntos e com uma maior distância entre os dedos. Os valores do coeficiente de

sustentação apresentaram pequenas diferenças entre os modelos com diferente espaçamento entre os

dedos e; (vi) os resultados apresentados sugerem que, nas posições da mão nas quais a força de

sustentação pode desempenhar um importante papel, a abdução do polegar pode ser benéfica, enquanto

que, com ângulos de ataque mais elevados, nos quais a força de arrasto é dominante, a adução do polegar

parece ser preferível. Adicionalmente, foi também sugerido que um pequeno afastamento dos dedos pode

permitir à mão criar mais força durante o nado.

VIII

Table of contents

Acknowledgments...........................................................................................................V

Abstract ........................................................................................................................VII

Resumo ........................................................................................................................VIII

Table of contents........................................................................................................... IX

List of tables ....................................................................................................................X

List of figures ................................................................................................................ XI

General introduction .................................................................................................... 14

Study 1

The hydrodynamic drag during the gliding in swimming .......................................... 20

Study 2

The use of Computational Fluid Dynamics in swimming research............................ 31

Study 3

Design of a three-dimensional hand/forearm model to apply Computational Fluid

Dynamics .................................................................................................................... 40

Study 4

Computational analysis of the hand and forearm propulsion in swimming............... 50

Study 5

Hydrodynamic analysis of different thumb positions in swimming .......................... 64

Study 6

Swimming propulsion forces are enhanced by a small finger spread ........................ 83

Review

Swimming simulation: a new tool for swimming research and practical applications

.................................................................................................................................... 95

Main conclusions ........................................................................................................ 136

References ................................................................................................................... 139

Appendix .............................................................................................................CXLVIII

IX

List of tables

Study 1

Table 1: Drag coefficient values and contribution of pressure and skin friction drag for the total drag to

each velocity and for the two different gliding positions. .................................................................25

Study 2

Table 1: Values of CD and CL of the hand/forearm segment as a function of pitch angle. Sweep back angle

= 0º and flow velocity = 2.00 m/s. ....................................................................................................36

X

List of figures

Study 1

Figure 1: Swimmer’s model geometry with the surfaces meshed using Gambit. An example for the

position with the arms along the trunk is presented. .........................................................................22 Figure 2: Computational fluid dynamics model geometry with the swimmer with the arms extended at the

front. The water depth is 1.80 m, the width is 2.50 m and the length is 8.0 m. ................................24 Figure 3: Relationship between the drag coefficient and the velocity for the two different gliding

positions. The regression equations and the R2 values are also presented. .......................................26

Study 2

Figure 1: Hand and forearm model inside the domain with 3-D mesh of cells. .........................................34 Figure 2: Computational vision of the relative pressure contours on the hand/forearm surfaces. ..............35

Study 3

Figure 1: Computer tomography scans protocol. .......................................................................................44 Figure 2: Two different perspectives of the hand and forearm model produced by the image processing

techniques. ........................................................................................................................................45 Figure 3: Hand and forearm model inside the domain with three-dimensional mesh of cells....................47 Figure 4: Computational vision of the relative pressure contours on the hand/forearm surfaces. ..............48

Study 4

Figure 1: Three-dimensional reconstruction of the swimmer hand and forearm. The boundaries of the

human segments were obtained by the computer tomography scans................................................53 Figure 2: Hand and forearm model inside the three-dimensional domain. The whole domain was meshed

with 900 thousand cells.....................................................................................................................55 Figure 3: Progressive mesh of the hand and forearm model. Adaptive meshing was used to achieve

optimum mesh refinement. ...............................................................................................................55 Figure 4: Computational fluid dynamics oil-film plot shows the direction of the water flow in the wake of

the model. The flow path line at a 90º angle of attack of the hand and forearm segment is presented

(sweep back angle = 0º). ...................................................................................................................56 Figure 5: Drag and lift coefficients vs. flow velocity for each angle of attack. Sweep back angle = 0º.....57 Figure 6: Drag and lift coefficients vs. flow velocity for each angle of attack. Sweep back angle = 90º...57 Figure 7: Drag and lift coefficients vs. flow velocity for each angle of attack. Sweep back angle = 180º.58 Figure 8: Drag coefficient vs. angle of attack for each sweep back angle (SA). Flow velocity = 2.0 m/s. 59 Figure 9: Lift coefficient vs. angle of attack for each sweep back angle (SA). Flow velocity = 2.0 m/s. ..59

XI

Study 5

Figure 1: The models of the hand with the thumb in different positions: fully abducted, partially abducted

and adducted. ....................................................................................................................................68 Figure 2: The model of the hand with the thumb fully abducted inside the domain (Angle of attack = 0º,

Sweepback angle = 0º)......................................................................................................................70 Figure 3: The angle of attack (Schleihauf, 1979). The arrow represents the direction of the flow. ...........71 Figure 4: The sweep back angle (Schleihauf, 1979). The arrows represent the direction of the flow........71 Figure 5: Drag and lift coefficients vs. flow velocity for each angle of attack in the position with the

thumb fully abducted. .......................................................................................................................72 Figure 6: Drag and lift coefficients vs. flow velocity for each angle of attack in the position with the

thumb partially abducted...................................................................................................................73 Figure 7: Drag and lift coefficients vs. flow velocity for each angle of attack in the position with the

thumb adducted.................................................................................................................................73 Figure 8: Values of drag coefficient obtained for the different angles of attack and for the different thumb

positions. Sweepback angle = 0º and flow velocity = 2.0 m/s. .........................................................74 Figure 9: Values of lift coefficient obtained for the different angles of attack and for the different thumb

positions. Sweepback angle = 0º and flow velocity = 2.0 m/s. .........................................................75 Figure 10: Values of the resultant force coefficient obtained for the different angles of attack and for the

different thumb positions. Sweepback angle = 0º and flow velocity = 2.0 m/s. ...............................75

Study 6

Figure 1: Anthropometric characteristics of the swimmer hand. Hand length (1): 20.20 cm, index breadth

(2): 1.50 cm, index length (3): 8.10 cm, palm length (4): 9.50 cm, hand breadth (5): 8.90 cm. .......86 Figure 2: Computational fluid dynamics model geometry with the hand inside the domain (model with

fingers closed)...................................................................................................................................87 Figure 3: Values of CD obtained for the different attack angles and for the different finger spread.

Sweepback angle = 0º and flow velocity = 2.0 m/s. .........................................................................89 Figure 4: Values of CL obtained for the different attack angles and for the different finger spread.

Sweepback angle = 0º and flow velocity = 2.0 m/s. .........................................................................90

Review

Figure 1: Hydrodynamic drag force of the swimmer, the digital CFD model and the mannequin. Adapted

from Bixler et al. (2007). ................................................................................................................108 Figure 2: The angle of attack (Schleihauf, 1979). The arrow represents the direction of the flow. .........111 Figure 3: The sweep back angle (Schleihauf, 1979). The arrows represent the direction of the flow......111 Figure 4: Drag coefficient vs. angle of attack for the digital model of the hand, forearm and hand/forearm

(Sweep back angle = 0º). Adapted from Bixler and Riewald (2002). .............................................111 Figure 5: Lift coefficient vs. angle of attack for the digital model of the hand, forearm and hand/forearm

(Sweep back angle = 0º). Adapted from Bixler and Riewald (2002). .............................................112

XII

Figure 6: Drag and lift coefficient of the hand/forearm model for angles of attack of 0º, 45º and 90º (SA:

Sweep back angle). Flow velocity = 2.0 m/s. Adapted from Silva et al. (2008a). ..........................113 Figure 7: The hand and forearm model used by Silva et al. (2008a) inside the three-dimensional CFD

domain. ...........................................................................................................................................113 Figure 8: Comparison between steady and accelerated drag and lift coefficients for angles of attack of 0º,

90º and 180º (Sweep back angle = 0º). Adapted from Rouboa et al. (2006)...................................115 Figure 9: Drag coefficient for angles of attack of 0º, 45º and 90º for the different thumb positions (Sweep

back angle = 0º, Flow velocity = 2.0 m/s). Adapted from Marinho et al. (2008d). ........................118 Figure 10: Lift coefficient for angles of attack of 0º, 45º and 90º for the different thumb positions (Sweep

back angle = 0º, Flow velocity = 2.0 m/s). Adapted from Marinho et al. (2008d). ........................119 Figure 11: Drag coefficient for angles of attack of 0º, 15º, 30º, 45º, 60º, 75º and 90º for the different finger

spread positions (Sweep back angle = 0º, Flow velocity = 2.0 m/s). Adapted from Marinho et al.

(2008e)............................................................................................................................................120 Figure 12: Lift coefficient for angles of attack of 0º, 15º, 30º, 45º, 60º, 75º and 90º for the different finger

spread positions (Sweep back angle = 0º, Flow velocity = 2.0 m/s). Adapted from Marinho et al.

(2008e)............................................................................................................................................121 Figure 13: Momentum reduction in an average second of two types of kicking movements (large/slow vs.

small/fast). Adapted from Lyttle and Keys (2006). ........................................................................122 Figure 14: The model used by Marinho et al. (2008a) in a ventral position with the arms alongside the

trunk inside the CFD domain. .........................................................................................................123 Figure 15: The model used by Marinho et al. (2008a) in a ventral position with the arms extended at the

front, with the shoulders fully flexed, inside the CFD domain. ......................................................123 Figure 16: Two-dimensional model used by Silva et al. (2008b) to determine the effect of drafting

distances on hydrodynamic drag.....................................................................................................125 Figure 17: Relationship between total drag, skin-friction drag and pressure drag and the gliding velocity

for the positions with the arms alongside the trunk (AAT) and with the arms extended at the front

with the shoulders flexed (AEF). Adapted from Marinho et al. (2008a). .......................................127

XIII

General introduction

14

General introduction

Swimming is one of the major athletic sports. To swim faster, thrust should be

maximized and drag should be minimized. These aims are difficult to achieve because

swimmers surge, heave, roll and pitch during every stroke cycle. In addition,

determining the human forces is difficult due to the restrictions of the measuring

devices and the specificity of aquatic environment. Thus, human swimming evaluation

is one of the most complex but outstanding and interesting topics in sport biomechanics.

Over the past decades, research in swimming biomechanics has evolved from the study

of swimmer’s kinematics to a flow dynamics approach, following the line of research

from the experimental biology (Dickinson, 2000; Arellano et al., 2006). Significant

efforts have been made to understand swimming mechanics on a deeper basis. In the

past, most of the studies involved experimental data. However, nowadays the numerical

solutions can give new insights about swimming science. Computational fluid dynamics

(CFD) methodology is one of the different methods that have been applied in swimming

research to observe and understand water movements around the human body and its

application to improve swimming technique and/or swimming equipments and

therefore, swimming performance. CFD methodology consists of a mathematical model

that simulates the fluid flow around physical structures. Hence, the use of CFD can be

considered as a new step forward to the understanding of swimming mechanisms and

seems to be an interesting approach to use in swimming research. In this sense, the main

purpose of the present thesis was to study the mechanism of swimming propulsion using

CFD through a three-dimensional analysis of the swimmer’s hand and forearm.

After the introduction section, in which we establish the issue and the main purpose of

this work, we present six studies and a review work, each of them with a particular aim.

The first part of this thesis is to apply CFD in swimming using a three-dimensional

model of the swimmer body (Studies 1 and 2). Although the emergence of very

interesting works applying CFD in human swimming, the majority of the digital models

used in the numerical simulations applied two-dimensional models of the swimmer

body (Bixler and Schloder, 1996; Silva et al., 2005; Rouboa et al., 2006; Zaidi et al.,

2008). Thus, in study 1, The hydrodynamic drag during the gliding in swimming, we

15

applied CFD in swimming using a three-dimensional model of the swimmer body. This

approach allowed evaluating the drag force resisting forward motion during the

swimming gliding after starts and turns. This study was our first application of a three-

dimensional CFD analysis in swimming which was very important to improve our work

regarding swimming propulsion. In study 2, The use of Computational Fluid Dynamics

in swimming research, it was possible to investigate the hand and forearm propulsion in

steady flow conditions applying a three-dimensional CFD analysis. Despite the

contribution of this study to improve the CFD approach, the hand and forearm model

used in the study was still a poor representation of the swimmer hand and forearm. The

CFD analysis was performed using a three-dimensional model of the hand and forearm

with the fingers slightly flexed. These differences between digital models and true

human segments can lead to some misinterpretation of the biomechanical basis of

human swimming propulsion. Therefore, in study 3, Design of a three-dimensional

hand/forearm model to apply Computational Fluid Dynamics, a true three-dimensional

model of the human hand and forearm was developed through the transformation of

computer tomography scans into input data to apply CFD methodology. This study has

shown the great potential offered by reverse engineering procedures for developing true

digital models of the human body to improve the prediction of hydrodynamic forces in

swimming (Studies 4, 5 and 6). The purpose of study 4, CFD analysis of the hand and

forearm propulsion in swimming, was to analyze the propulsive force produced by a

swimmer hand/forearm three-dimensional segment using a steady state CFD analysis. In

this study we attempted to improve previous analysis including a more realistic model

of the swimmer hand and forearm and different orientation angles of the propelling

segments. In studies 5 and 6, Hydrodynamic analysis of different thumb positions in

swimming and Swimming propulsion forces are enhanced by a small finger spread, we

attempted to apply CFD to address some practical concerns of swimmers and coaches

that remain controversial, such as the finger’s relative position during the underwater

path of the stroke cycle. CFD was applied to study the hydrodynamic characteristics of

a true model of a swimmer hand with the thumb in different abduction/adduction

positions (Study 5) and with different finger spreading (Study 6). The last part (Review,

Swimming Simulation: a new tool for swimming research and practical applications) is

an overview of swimming simulation studies from a CFD perspective. This perspective

16

means emphasis on the fluid mechanics and CFD methodology applied in swimming

research. In this last work, we briefly explain the CFD methodology and report the

contribution of the different studies in swimming using CFD, including the studies of

this thesis. This fact is the main reason why this review is the last and not the first work

or even the introduction section. During this final part we discuss the main results of the

CFD research in swimming and present some future directions to improve CFD in

swimming investigations.

This work finishes with the main conclusions and with all the references used in this

thesis. As an appendix to this thesis, the letters of acceptance of the in press papers are

presented.

It seems important to underline that the studies presented in this thesis are a part of a

project involving the Department of Sport Sciences, Exercise and Health and the

Department of Engineering of the University of Trás-os-Montes and Alto Douro (Vila

Real, Portugal). This research project entitled Computational Fluid Dynamics: an

analytical tool for the 21st century swimming research was supported by the Portuguese

Government by a grant of the Science and Technology Foundation

(POCTI/DES/58872/2004). In the last four years several works have been presented in

International and National Scientific Meetings and others have been published in

Scientific Journals.

17

Study 1

Marinho, D.A., Reis, V.M., Alves, F.B., Vilas-Boas, J.P., Machado, L., Silva, A.J.,

Rouboa, A.I. (2008). The hydrodynamic drag during the gliding in swimming.

Journal of Applied Biomechanics (in press).

Study 2

Marinho, D.A., Reis, V.M., Alves, F.B., Vilas-Boas, J.P., Machado, L., Rouboa, A.I.,

Silva, A.J. (2008). The use of Computational Fluid Dynamics in swimming

research. International Journal for Computational Vision and Biomechanics (in

press).

Study 3

Marinho, D.A., Reis, V.M., Vilas-Boas, J.P., Alves, F.B., Machado, L., Rouboa, A.I.,

Silva, A.J. (2008). Design of a three-dimensional hand/forearm model to apply

Computational Fluid Dynamics. Brazilian Archives of Biology and Technology (in

press).

Study 4

Marinho, D.A., Vilas-Boas, J.P., Alves, F.B., Machado, L., Barbosa, T.M., Reis, V.M.,

Rouboa, A.I., Silva, A.J. (2008). Computational analysis of the hand and forearm

propulsion in swimming. International Journal of Sports Medicine (under

revision).

Study 5

Marinho, D.A., Rouboa, A.I., Alves, F.B., Vilas-Boas, J.P., Machado, L., Reis, V.M.,

Silva, A.J. (2008). Hydrodynamic analysis of different thumb positions in

swimming. Journal of Sports Science and Medicine (in press).

18

Study 6

Marinho, D.A., Barbosa, T.M., Reis, V.M., Kjendlie, P.L., Alves, F.B., Vilas-Boas, J.P.,

Machado, L., Silva, A.J., Rouboa, A.I. (2008). Swimming propulsion forces are

enhanced by a small finger spread. Journal of Applied Biomechanics (under

revision).

Review

Marinho, D.A., Barbosa, T.M., Kjendlie, P.L., Vilas-Boas, J.P., Alves, F.B., Rouboa,

A.I., Silva, A.J. (2009). Swimming simulation: a new tool for swimming research

and practical applications. In: M. Peters (Ed.), Lecture Notes in Computational

Science and Engineering – CFD and Sport Sciences. Berlin: Springer (in press).

19

Study 1

The hydrodynamic drag during the gliding in swimming

Marinho, D.A., Reis, V.M., Alves, F.B., Vilas-Boas, J.P., Machado, L., Silva, A.J., Rouboa, A.I. (2008).

The hydrodynamic drag during the gliding in swimming. Journal of Applied Biomechanics (in press).

20

The hydrodynamic drag during the gliding in swimming

Abstract

This study used computational fluid dynamics methodology to analyse the effect of body position on the

drag coefficient during submerged gliding in swimming. The k-epsilon turbulent model implemented in

the commercial code Fluent® and applied to the flow around a three-dimensional model of a male adult

swimmer was used. Two common gliding positions were investigated: a ventral position with the arms

extended at the front, and a ventral position with the arms placed along side the trunk. The simulations

were applied to flow velocities between 1.6 and 2.0 m/s, which are typical of elite swimmers when

gliding underwater at the start and in the turns. The gliding position with the arms extended at the front

produced lower drag coefficients than with the arms placed along the trunk. We therefore recommend that

swimmers adopt the arms in front position rather than the arms beside the trunk position during the

underwater gliding.

Introduction

The underwater phases of swimming after starts and turns are a large and important

component of the total event time in modern swimming. Accordingly, Guimarães and

Hay (1985) refer, for instance, that it is essential to minimize the hydrodynamic drag

during the gliding. Thus, the swimmer must adopt the most hydrodynamic position

possible. Race analysis has suggested that rather than the start position used by the

swimmer it is his body alignment under the water that mostly determines the success of

the start (Vilas-Boas et al., 2000; Cossor and Mason, 2001).

The passive drag of swimmers moving underwater in a streamlined position has been

measured experimentally (for example, Jiskoot and Clarys, 1975; Lyttle et al., 2000).

These studies revealed the difficulties involved in conducting such experimental

research. An alternative approach is to apply the numerical technique of computational

fluid dynamics to determine a swimmer’s passive drag.

The first application of computational fluid dynamics to swimming was conducted by

Bixler and Schloder (1996). They used a two-dimensional numerical analysis to

evaluate the effects of accelerating a hand-sized disc through the water. Additional

research using computational fluid dynamics techniques was performed by Rouboa et

21

al. (2006) to evaluate the steady and unsteady propulsive force of a swimmer’s hand and

arm. Their results suggested that a three-dimensional computational fluid dynamics

analysis of a human form could provide useful information about swimming. This was

already confirmed by Alves et al. (2007), in the upper arm propulsion, and by Bixler et

al. (2007), in the analysis of an entire swimmer’s body drag. Hence, the main aim of

this study was to analyse the effect in the drag coefficient of the use of two distinct

ventral positions during the underwater gliding in swimming, applying computational

fluid dynamics. A second aim was to study the relative contributions of the skin friction

drag and the pressure drag for the total drag during the gliding.

Methods

Three-dimensional model

To obtain the geometry of a human body, a model was created in CAD (Computer-

Aided Design), based on the anthropometrical characteristics of a group of elite national

level male swimmers. The surfaces of the swimmer were then developed using Gambit,

a geometry modelling program of Fluent (Fluent®, Inc. Hannover, USA), which

provides sophisticated computational fluid dynamics software. These surfaces were then

meshed, creating the volume mesh which has been imported into Fluent® computational

fluid dynamics program for analysis (Figure 1).

Figure 1: Swimmer’s model geometry with the surfaces meshed using Gambit. An example for the

position with the arms along the trunk is presented.

22

Computational fluid dynamics model

The swimmer was modelled as if he were gliding underwater in one of two distinct

ventral positions. The first position was a streamlined position, with the arms extended

at the front. This is the shape usually adopted after the start and after pushing off from

the wall after a turn. The second position was with the arms along the trunk. This is the

shape adopted by the swimmers during the second gliding phase after a turn in

breaststroke.

The computational fluid dynamics analyses were performed with the body in a

horizontal position with an attack angle of 0º. The attack angle was defined as the angle

between a horizontal line and a line drawn from the vertex to the ankle bone.

The swimmer’s model used for the analysis was 1.87 m tall with head, chest, waist and

hip circumferences of 0.57 m, 1.04 m, 0.85 m and 0.95 m, respectively. In the

streamlined position, the model had a finger to toe length of 2.37 m and in the position

with the arms along the trunk the distance from vertex to toe was 1.92 m.

The boundary conditions of the computational fluid dynamics model were designed to

represent the geometry and flow conditions of a part of a lane in a swimming pool. The

water depth of the model was 1.80 m with a 2.50 m width. The length was 8.0 m in the

streamlined position and 7.55 m in the position with the arms along the trunk, allowing

in both situations the same flow conditions behind and in front of the swimmer. In both

positions, the distance to the front surface was 2.0 m and to the back surface was 3.63

m. The swimmer model middle line was placed at a water depth of 0.90 m, equidistant

from the top and bottom surfaces (Figure 2).

The model’s body surface had roughness parameters of zero. The whole domain was

meshed with 900 million cells. The grid was a hybrid mesh composed of prisms and

pyramids. Significant efforts were conducted to ensure that the model would provide

accurate results, namely by decreasing the grid node separation in areas of high velocity

and pressure gradients.

23

Figure 2: Computational fluid dynamics model geometry with the swimmer with the arms extended at the

front. The water depth is 1.80 m, the width is 2.50 m and the length is 8.0 m.

Steady-state computational fluid dynamics analyses were performed using the Fluent®

code and the drag coefficient was calculated for velocities ranging from 1.60 to 2.0 m/s

in increments of 0.10 m/s. Flow velocities were chosen to be within the range of typical

underwater gliding velocities at the start and in the turns. The Fluent® code solves flow

problems by replacing the Navier-Stokes equations with discretized algebraic

expressions that can be solved by iterative computerized calculations. Fluent® uses the

finite volume approach, where the equations are integrated over each control volume.

We used the segregated solver with the standard k-epsilon turbulence model because

this turbulence model was shown to be accurate with measured values in a previous

research (Moreira et al., 2006).

All numerical computational schemes were second-order, which provides a more

accurate solution than first-order schemes. We used a turbulence intensity of 1.0% and a

turbulence scale of 0.10 m. The water temperature was 28º C with a density of 998.2

kg/m3 and a viscosity of 0.001 kg/mm/s. Incompressible flow was assumed.

In human swimming, the total drag is composed of the skin friction drag, pressure drag

and wave drag. Skin friction drag is attributed to the forces tending to slow the water

flowing along the surface of a swimmer's body. It depends on the velocity of the flow,

the surface area of the body and the characteristics of the surface. Pressure drag is

caused by the pressure differential between the front and the rear of the swimmer and it

is proportional to the square of swimming velocity, the density of water and the cross

sectional area of the swimmer. Finally, swimming at the water surface is constrained by

the formation of surface waves leading to wave drag. In this study we considered

24

hydrodynamic drag depending only on the skin friction and pressure drag since the

model was placed 0.90 m underwater. These two drag components were computed by

Fluent® software.

Statistical analyses

To analyse the relationship between the velocity and the drag coefficient, regression

lines between these parameters were computed. The regression equations were

calculated and the R2 value was used as a measure of the robustness of the model.

Results

Table 1 shows the drag coefficient values produced by both models: with the arms

along the trunk and with the arms extended at the front. The percentage and the absolute

values of total drag due to skin friction and pressure drag are also presented.

Table 1: Drag coefficient values and contribution of pressure and skin friction drag for the total drag to

each velocity and for the two different gliding positions.

Velocity Drag coefficient Drag coefficient

(m/s) (arms along the trunk) (arms extended at the front)

Total

drag

Pressure

drag

Friction

drag

Total

drag

Pressure

drag

Friction

drag

1.6 0.824 0.758 91.98% 0.066 8.02% 0.480 0.417 86.95% 0.063 13.05%

1.7 0.782 0.719 91.99% 0.063 8.01% 0.475 0.413 86.98% 0.062 13.02%

1.8 0.763 0.702 92.01% 0.061 7.99% 0.432 0.376 87.01% 0.056 12.99%

1.9 0.762 0.701 92.04% 0.061 7.96% 0.431 0.375 87.03% 0.056 12.97%

2.0 0.736 0.677 92.05% 0.059 7.95% 0.428 0.373 87.04% 0.055 12.96%

For all the velocities, the drag coefficient of the position with the arms extended at the

front was lower than the drag coefficient of the position with the arms along the trunk.

Moreover, the pressure drag was dominant, with a percentage of about 92% and 87% of

25

the total drag, in the position with the arms along the trunk and with the arms extended

at the front, respectively. The absolute values of skin friction drag were quite similar in

both positions.

On the other hand, in both positions, the drag coefficient of the model decreased with

the velocity (Table 1 and Figure 3).

Arms along the trunk0,90

y = -0,1975x + 1,1287R2 = 0,90

y = -0,148x + 0,7156R2 = 0,81

Veloci .s-1)

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0.90 Arms extended at the front

0.80 y = -0.1975x + 1.1287

0.70

Dra

g co

effic

ient

R2 = 0.90 0.60

0.50

0.40 y = -0.1480 156 x + 0.7R2 = 0.81 0.30

0.20 1,50 1,60 1,70 1,80 1,90 2,00 1.5 1.6 1.7 1.8 1.9 2.0

ty (mVelocity (m/s)

Figure 3: Relationship between the drag coefficient and the velocity for the two different gliding

positions. The regression equations and the R2 values are also presented.

Discussion

The main aim of this study was to analyse the drag coefficient arising from the use of

two different gliding positions in swimming, through computational fluid dynamics.

The drag coefficient changed slightly from 0.824 at 1.60 m/s to 0.736 at 2.00 m/s, in the

position with the arms along the trunk, and from 0.480 at 1.60 m/s to 0.428 at 2.00 m/s,

in the position with the arms extended at the front. The inverse relationship between the

drag coefficient and the velocity found in the present study seems to correspond to what

happens in experimental situations with the human body totally submersed (Jiskoot and

Clarys, 1975; Lyttle et al., 2000).

26

Moreover, the gliding position with the arms extended at the front presented lower drag

coefficient values than the position with the arms placed along the trunk. This body

position, with the arms at the front, is mostly accepted by the swimming technical and

scientific communities as the most hydrodynamic one, being called the streamlined

position (Guimarães and Hay, 1985). The position with the arms extended at the front

seems to be the one that allows a higher reduction of the negative hydrodynamic effects

of the human body morphology: a body with various pressure points due to the large

changes in its shape. This position seems to smooth the anatomical shape especially at

the head and shoulders. Considering the breaststroke turn, the first gliding, performed

with the arms at the front, must be emphasized in relation to the second gliding,

performed with the arms along the trunk.

Bixler et al. (2007) demonstrated the validity of computational fluid dynamics analysis

as a tool to examine the water flow around a submerged swimmer’s body. This form of

research has opened a new gate of analysis into the swimming hydrodynamics and has

been shown to hold promise as a way to assess the flow characteristics and associated

drag forces experienced by swimmers, for instance, in different gliding positions after

starts and turns.

Another aim of the present study was to analyze the influence of the skin friction drag

and the pressure drag in the total drag during the gliding. We choose a pool depth of

1.80 m, with the swimmer model placed at the midpoint between top and bottom, to

avoid significant wave drag, limiting our research to the influence of the pressure drag

and the skin friction drag in the total drag coefficient. Lyttle et al. (1999) concluded that

there is no significant wave drag when a typical adult swimmer is at least 0.6 m under

the water’s surface.

The computed drag forces components showed that for both gliding positions the

pressure drag was dominant. Nevertheless, skin friction drag was by no means

negligible, presenting an absolute value of about 0.06. This drag component represented

≈13% and ≈8% of total drag in the position with the arms extended at the front and with

the arms along the trunk, respectively. However, these values are based on the swimmer

model’s surface having a zero roughness. Therefore, the development of roughness

parameters for human skin would allow a more accurate computational fluid dynamics

27

model to be built in further studies. Since this task is still in development, we assumed

to conduct our simulations based upon the swimmer’s surface having a zero roughness.

We chose this value as a first step in the application of numerical simulation techniques

in swimming research, using a three-dimensional model of a whole human body. We

had to opt between a certain value and a zero value. Indeed, we simulated a situation as

the swimmer was shaved (smoothed), with roughness zero. In our opinion, the change

in the roughness parameter would affect each body position in approximately the same

way and our main finding would be the same. However, the contribution of each drag

component would possibly be a little different with the use of a roughness skin value.

Nevertheless, we are convinced that the pressure drag would be dominant and the skin

friction drag would be important as well. How this relative contribution would be

changed is a very interesting question, which could lead to further research. But one can

speculate about this. On one hand, if the surface roughness were increased in the model,

the skin friction drag would probably be higher. It is expected that the surface roughness

increase could lead to increase the turbulence around the surface, thus increasing skin

friction drag. On the other hand, if the surface roughness were increased the pressure

drag could be reduced. The boundary layer, which would be mainly laminar, would

change into a turbulent one (Massey, 1989). When the flow regime is laminar,

separation at the body surface starts almost as soon as the pressure gradient becomes

adverse and a larger wake forms while when the flow regime is turbulent, separation is

delayed and the corresponding wake is smaller, thus decreasing pressure drag. The

importance of keeping the boundary layer attached to the swimmer body surface is so

important that swimwear manufacturers sometimes purposely cause the boundary layer

to become turbulent (Polidori et al., 2006).

Moreover, since the absolute values of skin friction drag are about the same in the two

gliding positions, it is possible that the increase in this component would be

approximately the same. The main difference could occur at the pressure drag since the

position with the arms along the trunk presented higher absolute values. It is expected

that the drag force decrease in this body position would be more accentuated, thus

decreasing the differences between the two models. However, we think these changes

would not be sufficient to have an effect on our primary finding: the gliding position

28

with the arms extended at the front produced lower drag coefficients than with the arms

placed along the trunk.

Another different situation could happen if the swimmer were at the water’s surface.

The contribution of the skin friction drag would be reduced due to the reduction in the

wetted area and the generation of wave drag (Bixler et al., 2007).

Although limited to passive drag, this study allowed the evaluation of the effects of

different body positions on performance, being a first step towards the analysis of active

drag. On the other hand, computational fluid dynamics methods have provided a way to

estimate the relative contribution of each drag component to the total drag. Future

studies could improve this computational fluid dynamics results by analysing the

passive drag of a swimmer at the water’s surface and including wave drag in the

measurements. Moreover, the evaluation of the active drag while the swimmer is

kicking must also be attempted in the future.

References

Alves, F., Marinho, D., Leal, L., Rouboa, A., Silva, A. (2007). 3-D computational fluid dynamics of the

hand and forearm in swimming. Medicine and Science in Sports and Exercise, 39(Suppl. 1), S9.

Bixler, B.S., Schloder, M. (1996). Computational fluid dynamics: an analytical tool for the 21st century

swimming scientist. Journal of Swimming Research, 11, 4-22.

Bixler, B., Pease, D., Fairhurst, F. (2007). The accuracy of computational fluid dynamics analysis of the

passive drag of a male swimmer. Sports Biomechanics, 6, 81-98.

Cossor, J., Mason, B. (2001). Swim start performances at the Sydney 2000 Olympic Games. In: J.

Blackwell, R. Sanders (Eds.), Proceedings of Swim Sessions of the XIX Symposium on

Biomechanics in Sports, pp. 70-74. San Francisco: University of San Francisco.

Guimarães, A., Hay, J. (1985). A mechanical analysis of the grab starting technique in swimming.

International Journal of Sports Biomechanics, 1, 25-35.

Jiskoot, J., Clarys, J.P. (1975). Body resistance on and under the water surface. In: L. Lewillie, J.P. Clarys

(Eds.), Swimming II, pp. 105-109. Baltimore: University Park Press.

Lyttle, A.D., Blanksby, B.A., Elliott, B.C., Lloyd, D.G. (1999). Optimal depth for streamlined gliding. In:

K.L. Keskinen, P.V. Komi, A.P. Hollander (Eds.), Biomechanics and Medicine in Swimming VIII,

pp. 165-170. Jyvaskyla: Gummerus Printing.

29

Lyttle, A., Blanksby, B., Elliot, B., Lloyd, D. (2000). Net forces during tethered simulation of underwater

streamlined gliding and kicking technique of the freestyle turn. Journal of Sports Sciences, 18,

801-807.

Massey, B.S. (1989). Mechanics of Fluids. London: Chapman & Hall.

Moreira, A., Rouboa, A., Silva, A., Sousa, L., Marinho, D., Alves, F., Reis, V., Vilas-Boas, J.P., Carneiro,

A., Machado, L. (2006). Computational analysis of the turbulent flow around a cylinder.

Portuguese Journal of Sport Sciences, 6(Suppl. 1), 105.

Polidori, G., Taiar, R., Fohanno, S., Mai, T.H., Lodini, A. (2006). Skin-friction drag analysis from the

forced convection modeling in simplified underwater swimming. Journal of Biomechanics, 39,

2535-2541.

Rouboa, A., Silva, A., Leal, L., Rocha, J., Alves, F. (2006). The effect of swimmer’s hand/forearm

acceleration on propulsive forces generation using computational fluid dynamics. Journal of

Biomechanics, 39, 1239-1248.

Vilas-Boas, J.P., Cruz, M.J., Sousa, F., Conceição, F., Carvalho, J.M. (2000). Integrated kinematic and

dynamic analysis of two track-start techniques. In: R. Sanders, Y. Hong (Eds.), Proceedings of the

XVIII International Symposium on Biomechanics in Sports, Applied Program – Application of

Biomechanical Study in Swimming, pp. 113-117. Hong Kong: The Chinese University Press.

30

Study 2

The use of Computational Fluid Dynamics in swimming research

Marinho, D.A., Reis, V.M., Alves, F.B., Vilas-Boas, J.P., Machado, L., Rouboa, A.I., Silva, A.J. (2008).

The use of Computational Fluid Dynamics in swimming research. International Journal for

Computational Vision and Biomechanics (in press).

31

The use of Computational Fluid Dynamics in swimming research

Abstract

The aim of the present study was to apply Computational Fluid Dynamics to the study of the

hand/forearm forces in swimming using a three-dimensional model. Models used in the simulations were

created in CAD, based on real dimensions of a right adult human hand/forearm. The governing system of

equations considered was the incompressible Reynolds averaged Navier-Stokes equations implemented in

the Fluent® commercial code. The drag coefficient was the main responsible for propulsion, with a

maximum value of force propulsion corresponding to a pitch angle of 90º. The lift coefficient seemed to

play a less important role in the generation of propulsive force with pitch angles of 0º and 90º but it is

important with pitch angles of 30º, 45º and 60º.

Introduction

The creation of propulsive force in human swimming has been recently studied using

numerical simulation techniques with computational fluid dynamics (CFD) models

(Bixler and Schloder, 1996; Bixler and Riewald, 2002; Silva et al., 2005; Rouboa et al.,

2006; Gardano and Dabnichki, 2006).

Nevertheless, some limitations still persist, regarding the geometrical representation of

the human limbs. In the pioneer study of Bixler and Schloder (1996), these authors used

a disc with a similar area of a swimmer hand, while Gardano and Dabnichki (2006)

used standard geometric solids to represent the superior limb. Rouboa et al. (2006) tried

to correct and to complement the backward works using a two-dimensional (2-D) model

of a hand and a forearm of a swimmer, situation that seems to be an important step

forward in the application of CFD to the human propulsion. However, it seems it is

possible to go forward, reason why we propose to apply CFD to the studied of the hand

and forearm propulsion with three-dimensional (3-D) models, as it was already

experimented by Lyttle and Keys (2006) to analyse the dolphin kicking propulsion.

In this sense, with this work we want to continue using CFD as a new technology in the

swimming research, applying CFD to the 3-D study of the propulsion produced by the

swimmer hand and forearm. Therefore, the aim of the present study is twofold. First,

continuing to disseminate the use of CFD as a new tool in swimming research. Second,

32

to apply the method in the determination of the relative contribution of drag and lift

coefficients resulting from the numerical resolution equations of the flow around the

swimmers hand and forearm using 3-D models under the steady flow conditions.

Methods

Mathematical model

The dynamic fluid forces produced by the hand/forearm, drag (D) and lift (L), were

measured in this study. These forces are function of the fluid velocity and they were

measured by the application of the equations 1 and 2.

D = CD ½ ρ A V2 (1)

L = CL ½ ρ A V2 (2)

In equations 1 and 2, V is the fluid velocity, CD and CL are the drag and lift coefficients,

respectively, ρ is the fluid density and A is the projection area of the model for different

angles of pitch used in this study (0º, 30º, 45º, 60º, 90º).

CFD methodology consists of a mathematical model applied to the fluid flow in a given

domain that replaces the Navier-Stokes equations with discretized algebraic expressions

that can be solved by iterative computerized calculations. This domain consists of a

three-dimensional grid or mesh of cells that simulate the fluid flow (Figure 1). The fluid

mechanical properties, the flow characteristics along the outside grid boundaries and the

mathematical relationship to account the turbulence were considered.




33

Figure 1: Hand and forearm model inside the domain with 3-D mesh of cells.

Resolution method

The whole domain was meshed with 400000 elements. The grid was a hybrid mesh

composed of prisms and pyramids. The numerical method used by Fluent® is based on

the finite volume approach. The steady solutions of the governing system equations are

given in each square element of the discretized whole domain. In order to solve the

linear system, Fluent® code adopts an AMG (Algebraic Multi-Grid) solver. Velocity

components, pressure, turbulence kinetic energy and turbulence kinetic energy

dissipation rate are a degree of freedom for each element.

The convergence criteria of AMG are 10-3 for the velocity components, the pressure, the

turbulence kinetic energy and the turbulence kinetic energy dissipation ratio.

The numerical simulation was carried out in three-dimensions (3-D) for the

computational whole domain in steady regime.

Application

In order to make possible this study we analysed the numerical simulations of a 3-D

model of a swimmer hand and forearm. Models used in the simulations were created in

CAD, based on real dimensions of a right adult human hand/forearm.

Angles of pitch of hand/forearm model of 0º, 30º, 45º, 60º and 90º, with a sweep back

angle of 0º (thumb as the leading edge) were used for the calculations (Schleihauf,

1979).

34

On the left side of the domain access (figure 1), the x component of the velocity was

chosen to be within or near the range of typical hand velocities during freestyle

swimming underwater path: from 0.5 m/s to 4 m/s, with 0.5 m/s increments. The y and z

components of the velocity were assumed to be equal to zero. On the right side, the

pressure was equal to 1 atm, fundamental pre requisite for not allowing the reflection of

the flow.

Around the model, the three components of the velocity were considered as equal to

zero. This allows the adhesion of the fluid to the model.

It was also considered the action of the gravity force (g = 9.81 m/s2), as well as the

turbulence percentage of 1% with 0.1 m of length.

The considered fluid was water, incompressible with density (ρ = 996.6 x 10-9 kg/mm3)

and viscosity (μ = 8.571 x 10-7 kg/mm/s).

The measured forces on the hand/forearm model were decomposed into drag and lift

components. The combined hand and forearm drag (CD) and lift (CL) coefficients were

calculated, using equations 1 and 2. The independent variables were the angle of pitch

and fluid boundary velocity. The dependent variables were pressure and velocity of the

fluid within the dome. Post-processing of the results with Fluent® allowed the

calculation of component forces through integration of pressures on the hand/forearm

surfaces (Figure 2).

Figure 2: Computational vision of the relative pressure contours on the hand/forearm surfaces.

35

Results

In table 1 it is possible to observe the CD and CL values produced by the hand/forearm

segment as a function of pitch angle. It is presented the values found for a flow velocity

of 2.00 m/s with a sweep back angle of 0º.

Table 1: Values of CD and CL of the hand/forearm segment as a function of pitch angle. Sweep back angle

= 0º and flow velocity = 2.00 m/s.

Pitch angle CD CL

0º 0.35 0.18

30º 0.51 0.27

45º 0.63 0.32

60º 0.76 0.29

90º 1.10 0.05

The CD and CL values were almost constant for the whole range of velocities (for a

given pitch angle).

According to the obtained results, hand/forearm drag was the coefficient that accounts

more for propulsion, with a maximum value of 1.10 for the model with an angle of pitch

of 90º. The CD values increased with the angle of pitch. Moreover, CL seems to play a

residual influence in the generation of propulsive force by the hand/forearm segment at

angles of pitch of 0º and 90º, but it is important with angles of pitch of 30º, 45º and 60º.

Discussion

The aim of the present study was to apply Computational Fluid Dynamics to the study

of the hand/forearm forces in swimming using a 3-D model and to determine the

relative contribution of drag and lift coefficients to the overall propulsive force

production.

Computational Fluid Dynamics methodology was developed by engineers to solve

numerically complex problems of fluid flow using an iterative optimization approach.

The net effect is to allow the user to model computationally any flow field provided the

geometry of the object and some initial flow conditions are prescribed. This can provide

36

answers to problems which have been unobtainable using physical testing methods,

thereby bridging the gap between theoretical and experimental fluid dynamics. In this

research we tried to improve the previous studies that applied CFD to the analysis of

swimming propulsion, using a more realistic model of the swimmer hand and forearm

(3-D model). Thought, this model still needs to be improved, namely using a model in

which the fingers would be extended. This is an issue that should be addressed in future

studies.

We are very pleased with the results pointed out in the simulations of our study. CD was

the main responsible for propulsion, with the maximum value of force production

corresponding to an angle of pitch of 90º, as expected. The CD obtained the highest

value at an orientation of the hand/forearm plane where the model was directly

perpendicular to the direction of the flow. The same result was reported by Berger et al.

(1995), in which the drag force increases to a maximum where the plane was the same

as the presented in this work (angle of pitch = 90º).

CL has a residual influence in the generation of propulsive force by the hand/forearm

segment for angles of pitch of 0º and 90º, but it is important with angles of pitch of 30º,

45º and 60º. These data confirm recent studies reporting reduced contribution of lift

component to the overall propulsive force generation by the hand/forearm segment in

front crawl swimming, except for the insweep phase, when the angle of attack is within

30º-60º (Berger et al., 1995; Sanders, 1999; Bixler and Riewald, 2002; Rouboa et al.,

2006).

Although in this study we had only tested flow in steady regime and this situation does

not truly represent what happens during swimming, the present study allowed us to

apply CFD in the study of propulsive forces in swimming, using a three-dimensional

model of a human hand/forearm. By itself, this situation seems to be an important step

to the advancement of this technology in sports scope.

The results of the values of CD and CL are similar to the ones found in experimental

studies (Wood, 1977; Schleihauf, 1979; Berger et al., 1995; Sanders, 1999), important

fact to the methodological validation of CFD, giving as well conditions to the primary

acceptation to the analysis of hydrodynamic forces produced through unsteady flow

conditions and through different orientations of the propelling segments.

37

For the three different orientation models and for the whole studied velocity range, the

CD and CL remain constant. Similar results were observed as well in other studies using

CFD (Bixler and Riewald, 2002; Silva et al., 2005; Rouboa et al., 2006).

Conclusion

This study tried to apply CFD to the analysis of swimming propulsion. As conclusions

we can state that the computational data found seem to demonstrate an important role of

the drag force and a minor contribution of the lift force to the propulsive force

production by the swimmer hand/forearm segment.

On the other hand, it was demonstrated the utility of using CFD in the propulsive force

measurements, using a more realistic model (3-D) of a human segment. This situation is

an additional step forward to the necessary continuation to keep developing this

technology in sport studies, in general, and in swimming, as a particular case.

References

Berger, M.A., de Groot, G., Hollander, AP. (1995). Hydrodynamic drag and lift forces on human hand

arm models. Journal of Biomechanics, 28, 125-133.



Bixler, B.S., Riewald, S. (2002). Analysis of swimmer’s hand and arm in steady flow conditions using

computational fluid dynamics. Journal of Biomechanics, 35, 713-717.

Gardano, P., Dabnichki, P. (2006). On hydrodynamics of drag and lift of the human arm. Journal of


Lyttle, A., Keys, M. (2006). The application of computational fluid dynamics for technique prescription

in underwater kicking. Portuguese Journal of Sport Sciences, 6(Suppl. 2), 233-235.

Moreira, A., Rouboa, A., Silva, A.J., Sousa, L., Marinho, D., Alves, F., Reis, V., Vilas-Boas, J.P.,

Carneiro, A., Machado, L. (2006). Computational analysis of the turbulent flow around a cylinder.


Rouboa, A, Silva, A., Leal, L., Rocha, J., Alves, F. (2006). The effect of swimmer’s hand/forearm



38

Sanders, R.H. (1999). Hydrodynamic characteristics of a swimmer’s hand. Journal of Applied


Schleihauf, R.E. (1979). A hydrodynamic analysis of swimming propulsion. In: J. Terauds, E.W.

Bedingfield (Eds), Swimming III, pp. 70-109. Baltimore: University Park Press.

Silva, A., Rouboa, A., Leal, L., Rocha, J., Alves, F., Moreira, A., Reis, V., Vilas-Boas, J.P. (2005).

Measurement of swimmer's hand/forearm propulsive forces generation using computational fluid

dynamics. Portuguese Journal of Sport Sciences, 5, 288-297.

Wood, T.C. (1977). A fluid dynamic analysis of the propulsive potential of the hand and forearm in

swimming. Master of Science Thesis. Halifax, NS: Dalhouise University Press.

39

Study 3

Design of a three-dimensional hand/forearm model to apply

Computational Fluid Dynamics

Marinho, D.A., Reis, V.M., Vilas-Boas, J.P., Alves, F.B., Machado, L., Rouboa, A.I. and Silva, A.J.

(2008). Design of a three-dimensional hand/forearm model to apply Computational Fluid Dynamics.

Brazilian Archives of Biology and Technology (in press).

40

Design of a three-dimensional hand/forearm model to apply


Abstract

The purpose of this study was to develop a three-dimensional digital model of a human hand and forearm

to apply Computational Fluid Dynamics to propulsion analysis in swimming. Computer tomography

scans of the hand and forearm of an Olympic swimmer were applied. The data were converted, using

image processing techniques, into relevant coordinate input, which can be used in Computational Fluid

Dynamics software. From that analysis it was possible to verify an almost perfect agreement between the

true human segment and the digital model. This technique can be used as a means to overcome the

difficulties in developing a true three-dimensional model of a specific segment of the human body.

Additionally, it may be used to improve the use of Computational Fluid Dynamics generally in sports and

specifically in swimming studies, decreasing the gap between the experimental and the computational

data.

Introduction

The finite element method is currently one of the best established numerical tools in the

field of biomechanical engineering and has been used in the computational analysis of

the fluid flow around human structures. In the sports scope, it has been used in the study

of the propulsive forces produced by the hand and forearm in human swimming.

Despite the increasing amount of high quality research, a common weakness still

remains. Practically all the models have been developed based on approximate

analytical representations of the human structures and their geometrical accuracy has

never been discussed. This approach has been commonly adopted, for example, to

reduce the computational cost of memory requirements (Aritan et al., 1997). However,

one of the main reasons for such limitations is the difficulty to design a true digital

model of the human limbs.

In most cases, the authors used two-dimensional models (Bixler and Schloder, 1996;

Silva et al., 2005; Rouboa et al., 2006) and when three-dimensional models were used,

these were very simple and reductive representations of the human limbs (Gardano and

Dabnichki, 2006). These differences between true and computed models could lead to

less accurate numerical results (Candalai and Reddy, 1992). In an experimental

41

simulation of the effect of the ischial tuberosity’s geometry on the shear and

compressive stress in buttock tissue, Candalai and Reddy (1992) showed that the

influence of the geometry on the stress magnitude could be significant. In a numerical

simulation of this experimental work, a possible variation of more than 60% was found

in the shear stress.

Magnetic resonance imaging and computer tomography scans seem to be a good

approach for designing true human models. However, the use of these kinds of scans is

not a straightforward task and requires the implementation of image processing and

other numerical techniques, such as the conversion into relevant coordinate input. It

should be noted that mesh generation, the first step in finite element modeling, is a

tough procedure, especially when solving three-dimensional problems (Aritan et al.,

1997). Ideally, a mesh should allow modifications, usually by changing some

predefined parameters and it should be based on directly obtained anatomical data.

Thus, it is important to use the magnetic resonance imaging or the computer

tomography data to provide geometrical input for generation or modification of finite

element models. Most of the well established finite element software packages provide

special tools for parametric modification of an existing mesh. These tools help the user

to reduce the time and to increase the accuracy and reliability of model modifications.

Therefore, the aim of the present study was to develop a true three-dimensional model

of the human hand and forearm, through the transformation of computer tomography

scans into input data to apply Computational Fluid Dynamics to the propulsion analysis

in swimming.

Materials and Methods


Computational Fluid Dynamics methodology consists of a mathematical model applied

to the fluid flow in a given domain. This domain replaces the Navier-Stokes equations

with discretized algebraic expressions that can be solved by iterative calculations. This

domain consists of a three-dimensional grid or mesh of cells that simulates the fluid

flow around structures. The fluid mechanical properties, the flow characteristics along

42

the outside grid boundaries and the mathematical relationship to account the turbulence

were also considered:

0divV = (1)

( ) 0VVkcvpV.VtV t

2

=∇+∇⎟⎟⎠

⎞⎜⎜⎝

⎛ε

+∇±∇+∇±∂∂

μ

(2)

ρε

kkkkkkk kkk −+

∂

⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

∂+

∂

⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

∂+

∂

⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

∂=

∂∂

+∂

∂+

∂∂

+∂

∂ Φμz

zσμ

yyσ

μ

xxσ

μ

z)V(

y)V(

x)V(

t)(

t

ttt

zyx ρρρρ

(3)

k

ρε

k

ε

εεε

ερVερVερVρk εεε2

t

ttt

zyx

zz

yy

xx

z)(

y)(

x)(

t)(

2CΦ−μ+∂

⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

σμ

∂

+∂

⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

σμ

∂

+∂

⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

σμ

∂

=∂

∂+

∂

∂+

∂∂

+∂

∂

(4)

Where k is the turbulent kinetic energy and ε is the turbulent kinetic energy dissipation

ratio. Vx, Vy and Vz represent the x, y and z components of the velocity V. μt is the

turbulent viscosity and ρ represents the fluid density. υ is the kinematic viscosity, Ф is

the pressure strain, C2, Cμ, σε and σk are model constants, 1.92, 0.09, 1.30 and 1.00,

respectively.

In order to create the three-dimensional digital model we applied computer tomography

scans of a hand and forearm segments of an Olympic swimmer. With these data we

converted the values into a format that can be read in Gambit, Fluent® pre-processor.

Fluent® software is used to simulate the fluid flow around structures, allowing the

analysis of values of pressure and speed around (i.e. the hand and forearm of a

swimmer). With these values we can calculate force components through integration of

pressures on the hand/forearm surfaces, using a realistic model of these human

segments, thus decreasing the gap between the experimental and the computational data.

The numerical method used by Fluent® is based on the finite volume approach. The

solutions of the governing system equations are given in each square element of the

discretized whole domain. In order to solve the linear system, Fluent® code adopts an

Algebraic Multi-Grid (AMG) solver. Velocity components, pressure, turbulent kinetic

43

energy and turbulent kinetic energy dissipation ratio are degrees of freedom (DOF) for

each element.

Computer tomography scans

Eighteen cross-sectional scans of the right arm (hand and forearm) were obtained using

a Toshiba® Aquilion 4 computer tomography scanner. Computer tomography scans

were obtained with configuration of V2.04 ER001. A 2 mm slice thickness with a space

of 1 mm was used. The subject was an Olympic level swimmer, who participated in the

2004 Olympic Games in Athens. The subject was lying with his right arm extended

upwards and fully pronated. The thumb was adducted and the wrist was in a neutral

position (Figure 1). This protocol has been approved by the appropriate ethical

committee of the institution in which it was performed, and the subject consented to

participate in this work.

Figure 1: Computer tomography scans protocol.

Conversion into relevant coordinate input

The transformation of values from the computer tomography scans into nodal

coordinates in an appropriate coordinate system demands the use of image processing

44

techniques. The image processing program used in this study was the Anatomics Pro®.

This program allowed obtaining the boundaries of the human segments, creating a

three-dimensional reconstruction of the swimmer hand and forearm. This program uses

computational functions, graphics functions and mouse functions.

At first, before processing and converting procedures the data was prepared, namely by

observing the computer tomography data and erasing the non-relevant parts of the

anatomical model. For example, surfaces supporting the subject were also scanned,

reason why it had to be defined the relevant points and deleted the irrelevant ones. This

step was also conducted using the software FreeForm Sensable®. Finally, the data was

converted into an IGES format (*.igs), that could be read by Gambit/Fluent® to define

the finite elements approach through the three-dimensional surfaces.

Results and Discussion

In figure 2 it is possible to observe the hand and forearm model produced by the image

processing techniques. We can verify an almost perfect agreement with the true human

segment. This technique could lead to overcome the difficulty to develop a true three-

dimensional model of a specific segment of the human body.

Figure 2: Two different perspectives of the hand and forearm model produced by the image processing

techniques.

45

As it was referred, one of the main limitations of the application of numerical

techniques in swimming research is the quality of the models used to represent the

human limbs. Indeed, there are few studies applying this computational tool in the

analysis of human swimming propulsion and they used very simple representations of

the human body (Bixler and Schloder, 1996; Silva et al., 2005; Gardano and Dabnichki,

2006; Rouboa et al., 2006). Despite the important contributes of those studies, the

design and the use of a more realistic model is an essential feature to the development of

Computational Fluid Dynamics in swimming analysis (Gardano and Dabnichki, 2006).

The generation of a three-dimensional model from computer tomography scans of the

human limbs has been used in other fields, such as in biomedical and engineering

scopes (e.g. Tu et al., 1995; Aritan et al., 1997; Long et al., 1998). Prosthetic design and

analysis, for instance, require a correct description of the limb geometry, allowing the

output from the program to be used as a digital input for manufacturing prosthetics or

limb models. Moreover, the magnetic resonance imaging techniques could allow clear

separation of the skin, fat and muscle layers. Furthermore, the local compartment fat

content can be estimated with a high level of accuracy (Aritan et al., 1997). These

applications suggest that there is scope for some physiological applications such as

finding muscle cross-sections or volumes. However, in this study only the outer contour

of the hand and forearm were considered. The generation of the mesh of cells to define

the finite elements, allowing the analysis of the fluid flow takes place around those

segments. The mesh of the whole domain was defined in Gambit Module, a mesh tool

of the Fluent® software. The hand/forearm model was placed centred in the domain with

larger dimensions in order to determine the undisturbed boundary conditions. The

schematic design of the computational model is shown in figure 3. The whole domain

was meshed with a hybrid mesh composed of prisms and pyramids.

With this model it was possible to export the generated mesh to the Fluent® processor,

where we were able to define the conditions suitable to be computed. It was possible to

compute the force values produced by the hand and forearm model through the

integration of pressures on the hand/forearm surfaces (Figure 4). Fluent software allows

the analysis of the force components in the three directions of the space, with the model

with different orientations, as it occurs in swimming.

46

Figure 3: Hand and forearm model inside the domain with three-dimensional mesh of cells.

However, one should note that simulation or modelling of water flow conditions around

the hand and forearm when treated as one segment does not illustrate the complexity of

propulsion generating process. It is widely known that propulsion generated by the

upper extremity is a result of mutual displacement of each segment in three dimensions

(Toussaint et al., 2002). Moreover, the upper arm can provide effective propulsion

through most of the stroke (Gardano and Dabnichki, 2006). Thus, further research must

consider these concerns and the movement at the wrist, elbow, and shoulder joints must

be added in the modelling of the arm propulsion. The human model obtained with

computer tomography scans can be used to evaluate accurately various aspects of

unsteady motion, such as accelerations, decelerations, and multi-axis rotations of the

propelling segments. This aim could be achieved by performing transient time-

dependent numerical simulations including user-defined functions and moving meshes

allowing simulating the swimmer’s movements (Lyttle and Keys, 2006).

As a final remark, we could state that the computer tomography scans allowed the

creation of a complete and true digital anatomic model of a swimmer hand and forearm.

This fact will help us to improve the use of Computational Fluid Dynamics in

swimming studies, decreasing the gap between the experimental and the computational

data.

47

Figure 4: Computational vision of the relative pressure contours on the hand/forearm surfaces.

References

Aritan, S., Dabnichki, P., Bartlett, R. (1997). Program for generation of three-dimensional finite element

mesh form magnetic resonance imaging scans of human limbs. Medical Engineering and Physics,

19, 681-689.



Candalai, R.S., Reddy, N.P. (1992). Stress distribution in a physical buttock model: effect of simulated

bone geometry. Journal of Biomechanics, 15, 493-504.





Long, Q., Xu, X.Y., Collins, M.W., Griffith, T.M., Bourne, M. (1998). The combination of magnetic

resonance angiography and computational fluid dynamics: a critical review. Critical Reviews in

Biomedical Engineering, 26, 227-274.


acceleration on propulsive forces generation using Computational Fluid Dynamics. Journal of





Toussaint, H.M., Van Den Berg, C., Beek, W.J. (2002). “Pumped-up propulsion” during front crawl

swimming. Medicine and Science in Sports and Exercise, 34, 314-319.

48

Tu, H.K., Matheny, A., Goldgof, D.B., Bunke, H. (1995). Left ventricular boundary detection from

spatio-temporal volumetric computer tomography images. Computerized Medical Imaging and

Graphics, 19, 27-46.

49

Study 4

Computational analysis of the hand and forearm propulsion in

swimming

Marinho, D.A., Vilas-Boas, J.P., Alves, F.B., Machado, L., Barbosa, T.M., Reis, V.M., Rouboa, A.I.,

Silva, A.J. (2008). Computational analysis of the hand and forearm propulsion in swimming.

International Journal of Sports Medicine (under revision).

50

Computational analysis of the hand and forearm propulsion in

swimming

Abstract

The purpose of this study was to analyze the propulsive force in a swimmer’s hand/forearm using three-

dimensional computational fluid dynamics techniques. A three-dimensional domain was designed to

simulate the fluid flow around a swimmer hand and forearm model in different orientations (0º, 45º and

90º for the three axes Ox, Oy and Oz). The hand/forearm model was obtained through computerized

tomography scans. Steady-state analyses were performed using the commercial code Fluent®. The drag

coefficient was the main responsible for the hand and forearm propulsion, presenting higher values than

the lift coefficient for the entire model orientations. The drag coefficient of the hand/forearm model

increased with the angle of attack, with the maximum value of force production corresponding to an angle

of attack of 90º. The drag coefficient obtained the highest value at an orientation of the hand plane where

the model was directly perpendicular to the direction of the flow. Important contribution of the lift force

to the overall force generation by the hand/forearm in swimming phases was observed, when the angle of

attack near 45º.

Introduction

The performance of swimmers is limited by their ability to produce effective propulsive

force (the component of the total propulsive force acting in the direction of moving) and

to minimize the drag forces resisting forward motion (Chatard et al., 1990; Gardano and

Dabnichki, 2006). The measurement of the propulsive forces generated by a swimmer

has been of interest to sports biomechanics for many years. Despite the task of directly

measuring the propulsive forces acting on a freely swimming subject is practically

impossible, Hollander et al. (1986) developed a system for measuring active drag

(MAD system) by determining the propulsive force applied to underwater push-off pads

by a swimmer simulating the front crawl arm action only. However, the intrusive nature

of the device disables its use during competition and reduces its ecological validity

(Payton and Bartlett, 1995). A non-intrusive method of estimating propulsive hand

forces during free swimming was developed by Schleihauf (1979) and was the basis of

several studies (Berger et al., 1995; Sanders, 1999). In this method the instantaneous

propulsive forces are estimated according to vectorial analysis of forces combination’s

51

acting on model hands in an open-water channel and the recordings of underwater

pulling action of a swimmer. Although these experiments accounted for fixture drag, the

effects of interference drag at the wrist were not considered. These researchers revealed

the difficulties involved in conducting such studies experimentally. They had to choose

between unwanted wave and ventilation drag or inaccurate interference drag (Bixler and

Riewald, 2002).

An alternative approach to evaluate the arm and hand swimming propulsion is to apply

the numerical technique of computational fluid dynamics (CFD) instead of experimental

methods to calculate the solution. Moreover, to avoid wave, ventilation and interference

drag, CFD has the advantage of showing detailed characteristics of fluid flow around

the hand and arm.

The first application of CFD in swimming was conducted by Bixler and Schloder

(1996), when they used a CFD two-dimensional analysis to evaluate the effects of

accelerating a flat circular plate through water. Additional research using CFD

techniques was performed by Rouboa et al. (2006) to evaluate the steady and unsteady

propulsive force of a swimmer’s hand and arm. Their results suggested that a three-

dimensional CFD analysis of a human form could provide useful information about

swimming. This was already confirmed by Bixler et al. (2007), in the analysis of an

entire submerged swimmer’s body drag. The main implication of this study was to

demonstrate the validity and accuracy of the CFD analysis as a tool to examine the

water flow around human structures. Therefore, the purpose of this study was to analyze

the propulsive force produced by a swimmer hand/forearm three-dimensional segment

using steady-state computational fluid dynamics.

Materials and Methods

Digital model of the swimmer hand and forearm

A CFD model was created based upon an Olympic swimmer’s right forearm and hand.

The hand/arm boundary was located at the level of the styloid processes of the radius

and ulna. The model was created by computer tomography scans of a male swimmer

hand and forearm, allowing the acquisition of the boundaries of the human segments.

The subject was an Olympic level swimmer, who participated in the 2004 Olympic

52

Games, in Athens. This protocol has been approved by the appropriate ethical

committee of the institution in which it was performed, and the subject gave informed

consent to participate in this work.

Cross-sectional scans of the right hand and forearm were conducted using a Toshiba®

Aquilion 4 computer tomography scanner. The subject was lying with his right arm

extended upwards and fully pronated. The transformation of values from the computer

tomography scans into nodal coordinates in an appropriate coordinate system demands

the use of image processing techniques. The image processing programs used in this

study were the Anatomics Pro (Anatomics®, Kannapolis, Australia) and the software

FreeForm (Sensable Technologies®, Wobum, USA). These programs allowed obtaining

the boundaries of the human segments, creating a three-dimensional reconstruction of

the swimmer hand and forearm (Figure 1).

Figure 1: Three-dimensional reconstruction of the swimmer hand and forearm. The boundaries of the

human segments were obtained by the computer tomography scans.

Then, the data was converted into an IGES format (*.igs), that could be read by the grid

generator Gambit/Fluent (Fluent Inc®, Hanover, USA) to define the finite elements

approach through the three-dimensional surfaces. This geometry protruded into a dome-

shaped mesh of fluid cells from its base, which was in the plane of the dome base.

Mathematical model

The dynamic fluid forces produced by the hand and forearm segment, lift (L) and drag

(D), were measured in this study. Drag force is defined as the force acting parallel to the

flow direction and lift force lies perpendicular to the drag force. These forces were

computed by the application of the equations 1 and 2.

53

2

21 ρSVCD D=

(1)

2

21 ρSVCL L=

(2)

In equations 1 and 2, CD and CL represent the drag and lift coefficients, respectively, V

represents the water velocity, ρ represents the fluid density and S represents the

projection surface of the model for different angles of attack used in this study.

The numerical simulation techniques methodology consists of a mathematical model

applied to the fluid flow in a given domain that replaces the Navier-Stokes equations

with discretized algebraic expressions. These equations can be solved by iterative

computerised calculations. The Fluent CFD code (Fluent®, Inc. Hannover, USA), was

used to develop and solve these equations using the finite volume approach, where the

equations were integrated over each control volume. The domain consists of a three-

dimensional grid or mesh of cells that simulate the fluid flow around the human

segments.



research (Moreira et al., 2006). All numerical computational schemes were second-

order, which provides a more accurate solution than first-order schemes. The considered

fluid was water, with a turbulence intensity of 1.0% and a turbulence scale of 0.10 m.

The water density was 998.2 kg/m3 with a viscosity of 0.001 kg/mm/s.

Boundary conditions

The numerical simulations were carried out in three-dimensions for the computational

domain in steady flow. A three-dimensional domain was designed to simulate the fluid

flow around a swimmer hand and forearm model (Figure 2). The whole domain was

meshed with 900 thousand cells. The grid was a hybrid mesh composed of prisms and

pyramids. Significant efforts were conducted to ensure that the model would provide

accurate results, namely by decreasing the grid node separation in areas of high velocity

54

and pressure gradients. Adaptive meshing was used to achieve optimum mesh

refinement (Figure 3).

Figure 2: Hand and forearm model inside the three-dimensional domain. The whole domain was meshed

with 900 thousand cells.

Figure 3: Progressive mesh of the hand and forearm model. Adaptive meshing was used to achieve

optimum mesh refinement.

The angle between the hand/forearm and the flow direction is defined as being the angle

of attack and the leading edge of the hand relative to the fluid flow is called the sweep

back angle. Angles of attack of hand/forearm models of 0º, 45º and 90º, with sweep

back angles of 0º (thumb as the leading edge), 90º (top of the fingers as the leading

edge) and 180º (little finger as the leading edge) were used for the calculations

(Schleihauf, 1979).

Water velocity was prescribed to the inlet portion of the dome surface and was held

steady at values between 0.50 m/s and 4.00 m/s, with 0.50 m/s increments as reported

by experimental literature for swimmer’s upper limbs actions (Lauder et al., 2001). The

55

location of this surface and the direction of prescribed flow changed as the orientation

of the model varied.

The dome’s base was a plane of symmetry, requiring the flow there to remain in that

plane. Around the model, the velocity was considered as equal to zero. This allows the

adhesion of the fluid to the model.

The independent variables were the angle of attack, sweep back angle and fluid

boundary velocity. The dependent variables were pressure and velocity of the fluid

within the dome. Post-processing of the results with Fluent allowed the calculation of

component forces through integration of pressures on the hand/forearm surfaces. The

measured forces on the hand/forearm models were decomposed into drag (CD) and lift

(CL) coefficients, using equations 1 and 2.

Results

The path of the water moving near the hand and forearm surface can be revealed by a

CFD oil-film plot. In figure 4 the flow path line at a 90º angle of attack of the hand and

forearm segment is presented. One can observe the direction of the water flow in the

wake of the propelling segments.

Figure 4: Computational fluid dynamics oil-film plot shows the direction of the water flow in the wake of

the model. The flow path line at a 90º angle of attack of the hand and forearm segment is presented

(sweep back angle = 0º).

In figures 5, 6 and 7 the evolution of the values of CD and CL according to flow velocity

for each orientation of the hand/forearm model is presented. During the numerical

simulations, the fluid velocity, the angle of attack and the sweep back angle were

changed to analyze the CD and CL on the hand/forearm.

56

For the three sweep back angles, the CD and CL remained almost constant regarding the

different flow velocities. Nevertheless, we were able to note a slightly decrease in the

force coefficients, especially from 0.50 to 2.0 m/s. This situation occurred for a given

angle of attack and with the same tendency at sweep back angles of 0º, 90º and 180º.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

C D 0ºC L 0ºC D 45ºC L 45ºC D 90ºC L 90º

Forc

e co

effic

ient

s

Flow velocity (m/s)

Figure 5: Drag and lift coefficients vs. flow velocity for each angle of attack. Sweep back angle = 0º.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0


Forc

e co

effic

ient

s

Flow velocity (m/s)


57

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0


Forc

e co

effic

ient

s

Flow velocity (m/s)


Moreover the CD was the coefficient that accounts more for the hand and forearm

propulsion, presenting higher values than the CL for the entire model orientations. The

CD of the hand/forearm model increased with the angle of attack. The CD presented the

maximum values with an angle of attack of 90º for the three sweep back angles (CD ≈

0.90) and the minimum values with an angle of attack of 0º (CD ≈ 0.45, sweep back

angle = 0º, 180º; CD ≈ 0.20, sweep back angle = 90º). The CL of the model presented the

maximum values with an angle of attack of 45º (CL ≈ 0.50, sweep back angle = 180º; CL

≈ 0.30, sweep back angle = 0º, 90º). The values of CL were very similar for the angles of

attack of 0º and 90º. However, the minimum values were obtained with an angle of

attack of 90º (CL ≈ 0.15).

As we can observe in figures 8 and 9, the CD and CL of the hand/forearm model

followed the same tendency in relation with the angle of attack in the three sweep back

angles that were tested. However, it seems important to reinforce the great contribution

of the CL to the overall propulsive force production of the hand and forearm in

swimming technique at an angle of attack of 45º, especially when the little finger leads

the motion. Regarding CD, the major differences occurred as well with an angle of

attack of 45º, when the sweep back angle is 180º.

58

0.1

0.3

0.5

0.7

0.9

1.1

0 45 90

SA = 0º

SA = 90º

SA = 180º

Dra

g co

effic

ient

Angle of attack (degrees)

Figure 8: Drag coefficient vs. angle of attack for each sweep back angle (SA). Flow velocity = 2.0 m/s.

0.1

0.3

0.5

0.7

0.9

0 45 90

SA = 0º

SA = 90º

SA = 180º

Lift

coef

ficie

nt


Figure 9: Lift coefficient vs. angle of attack for each sweep back angle (SA). Flow velocity = 2.0 m/s.

Discussion

The aim of this study was to analyze the propulsive force in a swimmer’s hand/forearm

three-dimensional segment using CFD.

In the present study we tried to improve the previous CFD analysis, using a real model

of the swimmer hand and forearm. Furthermore, we used different orientation angles of

the hand and forearm segment. Changes in the sweep back angle were included in the

simulations trying to approach to different upper arm orientations often adopted during

59

real swimming. In addition, the use of a plane of symmetry in the dome’s base was

conducted to ensure that the flow remained in that plane. Although this is an

approximation to actually modeling an elbow and upper arm, it avoids the edge effects

that would have occurred if water were allowed to flow under the bottom of the arm, or

the wave and ventilation drag that would have occurred if the dome bottom were

modeled as a free water surface (Bixler et al., 2007).

For the three sweep back angles, the CD and CL remained almost constant throughout

the flow velocities tested. A similar situation was already reported in other numerical

studies (Bixler and Riewald, 2002; Silva et al., 2005; Rouboa et al., 2006; Alves et al.,

2007). Nevertheless, we were able to note a slightly decrease in the force coefficients,

especially from 0.50 to 2.0 m/s. Berger et al. (1995) in a towing tank and Bixler and

Riewald (2002) in a numerical study reported both a similar situation for lower

velocities. A little decrease in the force coefficients values occurred with the velocity

increase. However, from a practical standpoint, in both studies the coefficients were

considered independent of the flow velocity.

The CD was the main responsible for the hand and forearm propulsion, presenting

higher values than the CL for the entire model orientations. The CD of the hand/forearm

model increased with the angle of attack, with the maximum value of force production

corresponding to an angle of attack of 90º. The CD obtained the highest value at an

orientation of the hand plane where the model was directly perpendicular to the

direction of the flow. The same result was reported by other authors (Schleihauf, 1979;

Berger et al., 1995; Alves et al., 2007), in which the drag force increased to a maximum

where the plane was the same as the presented in this work (angle of attack = 90º).

The CL seemed to have a residual influence in the generation of propulsive force by the

hand and forearm segment for angles of attack of 0º and 90º, but played an important

role with an angle of attack of 45º, especially when the little finger leads the motion

(sweep back angle = 180º). This fact may be related to the differences in the flow

around the hand when the leading edge is the little finger. In this position it is possible

that a low-pressure area on the knuckle side of the hand is created, producing more lift

and a smoother flow around the hand. The hand seems to be the main contributor for

generating lift force (Berger et al., 1995; Bixler and Riewald, 2002). It is tempting to

60

compare the hand with a wing-shaped hydrofoil. For such profiles it is known that the

value of the CL is dependent on the angle of attack. It is not expected that hands have

the full characteristics of such lift force generators. However, hands can certainly

generate some lift force, depending on the hand orientation with respect to the flow.

Further research during actual swimming is necessary to establish the orientation and

movement of the hand in which the forward component of the sum of drag and lift

forces is maximal. Moreover, since distinct patterns of timing and sequence of body roll

on front crawl and backstroke are used by the swimmers (Lee et al., 2008) the effect of

this rotation on the propulsive force production should be simulated. Considering these

results, it seems essential to analyze a larger range of angles of attack, trying to clarify

the true importance of the lift force to the propulsive force production. The CD has its

maximum values if the flow vector is at right angles to the hand plane, whereas the CL

has its maximum values if the hand plane makes an angle with the flow vector. It seems

probable that the lift force plays an important role at other angles of attack rather than

the 45º, as it is suggested by Schleihauf (1979) at an attack angle of 15º.

In summary, the CD was the main responsible for the hand/forearm propulsion with a

maximum value at an angle of attack of 90º. The CL seems to play an important role at

an angle of attack of 45º, especially when the little finger leads the motion. These data

confirm recent studies reporting supremacy of drag component and an important

contribution of lift force to the overall propulsive force generation by the hand/forearm

in swimming phases, when the angle of attack nears 45º.

The results have demonstrated this numerical tool can effectively be used both to

improve the foundational knowledge of swimming hydrodynamics as well as to provide

useful practical information to coaches and swimmers. Ideally, with increases in the

database of information created by the CFD analysis, more conclusions could be

derived which could be applicable to larger swimming populations. Further studies

should include the unsteady effects of motion, such as accelerations, decelerations and

multi-axis rotations. This could be accomplished by performing transient time-

dependent analysis using user-defined functions and moving meshes (Lyttle and Keys,

2006). The ultimate goal should be to use this numerical technique to evaluate complete

arm and leg strokes and to prescribe the optimum pulling pattern.

61

References



Berger, M.A.M., de Groot, G., Hollander, P. (1995). Hydrodynamic drag and lift forces on human

hand/arm models. Journal of Biomechanics, 28, 125-133.

Bixler, B., Schloder, M. (1996). Computational fluid dynamics: an analytical tool for the 21st century


Bixler, B., Riewald, S. (2002). Analysis of swimmer’s hand and arm in steady flow conditions using




Chatard, J.C., Lavoie, J.M., Bourgoins, B., Lacour, J.R. (1990). The contribution of passive drag as a

determinant of swimming performance. International Journal of Sports Medicine, 11, 367-372.



Hollander, A.P., de Groot, G., Van Ingen Schenau, G.L., Toussaint, H.M., de Best, H., Peeters, W.,

Meulemans, A., Schreurs, A.W. (1986). Measurement of active drag during crawl arm stroke

swimming. Journal of Sports Sciences, 4, 21-30.

Lauder, M., Dabnichki, P., Bartlett, R. (2001). Improved accuracy and reliability of sweepback angle,

pitch angle and hand velocity calculations in swimming. Journal of Biomechanics, 34, 31-39.

Lee, J., Mellifont, R., Winstanley, J., Burkett, B. (2008). Body roll in simulated freestyle swimming.

International Journal of Sports Medicine, 29, 569-573.






Payton, C., Bartlett, R. (1995). Estimating propulsive forces in swimming from three-dimensional

kinematic data. Journal of Sports Sciences, 13, 447-454.




62




Bedingfield (Eds.), Swimming III, pp. 70-109. Baltimore: University Park Press.




63

Study 5

Hydrodynamic analysis of different thumb positions in swimming

Marinho, D.A., Rouboa, A.I., Alves, F.B., Vilas-Boas, J.P., Machado, L., Reis, V.M., Silva, A.J. (2008).

Hydrodynamic analysis of different thumb positions in swimming. Journal of Sports Science and

Medicine (in press).

64

Hydrodynamic analysis of different thumb positions in swimming

Abstract

The aim of the present study was to analyze the hydrodynamic characteristics of a true model of a

swimmer hand with the thumb in different positions using numerical simulation techniques. A three-

dimensional domain was created to simulate the fluid flow around three models of a swimmer hand, with

the thumb in different positions: thumb fully abducted, partially abducted, and adducted. These three hand

models were obtained through computerized tomography scans of an Olympic swimmer hand. Steady-

state computational fluid dynamics analyses were performed using the Fluent® code. The forces estimated

in each of the three hand models were decomposed into drag and lift coefficients. Angles of attack of

hand models of 0º, 45º and 90º, with a sweep back angle of 0º were used for the calculations. The results

showed that the position with the thumb adducted presented slightly higher values of drag coefficient

compared with thumb abducted positions. Moreover, the position with the thumb fully abducted allowed

increasing the lift coefficient of the hand at angles of attack of 0º and 45º. These results suggested that,

for hand models in which the lift force can play an important role, the abduction of the thumb may be

better, whereas at higher angles of attack, in which the drag force is dominant, the adduction of the thumb

may be preferable.

Introduction

The numerical simulation technique is currently one of the best established numerical

tools in the field of biomechanical engineering. This methodology has been used in the

computational analysis of the fluid flow in several research fields, such as medicine,

biology, industry and sports (e.g. Boulding et al., 2002; Marshall et al., 2004; Guerra et

al., 2007; Dabnichki and Avital, 2006). This numerical tool is a branch of fluid

mechanics that solves and analyses problems involving a fluid flow by means of

computer-based simulations. Thus, one of the major benefits is to quickly answer many

'what if?' questions. It is possible to test many variations to seek for an optimal result,

without human experimental testing. The user is able to computationally model any

flow field, provided the geometry of the object is known and some initial flow

conditions are prescribed. This can provide answers and insights into problems which

have been unavailable or obtainable with very expensive costs (using physical or

experimental testing techniques). As such, numerical simulation techniques can be seen

as bridging the gap between theoretical and experimental fluid dynamics.

65

In sports scope, the main results suggested that the numerical analysis could provide

useful information about performance. Indeed, the use of numerical simulation

techniques has produced significant improvements in equipment design and technique

prescription in areas such as sailing performance (Pallis et al., 2000), Formula 1 racing

(Kellar et al., 1999) and winter sports (Dabnichki and Avital, 2006). In swimming, this

methodology has been used to study the propulsive forces produced by the hand and

forearm in swimming (Bixler and Schloder, 1996; Silva et al., 2005; Gardano and

Dabnichki, 2006; Rouboa et al., 2006; Lecrivain et al., 2008) and the magnitude of drag

forces resisting forward motion (Marinho et al., 2008a; Silva et al., 2008; Zaidi et al.,

2008). However, a common weakness still remains: practically all the models that have

been developed are based on approximate analytical representations of the human

structures and their geometrical accuracy has never been discussed. This approach has

been commonly adopted, for example, to reduce the computational cost of memory

requirements (Aritan et al., 1997). One of the main reasons for such limitations is the

difficulty to design a true digital model of the human limbs. In most cases, the authors

used two-dimensional models (Bixler and Schloder, 1996; Silva et al., 2005; Rouboa et

al., 2006; Silva et al., 2008; Zaidi et al., 2008). When three-dimensional models were

used, these were very simple and reductive representations of the human limbs

(Gardano and Dabnichki, 2006). Gardano and Dabnickki (2006) used standard

geometrical solids to represent the upper limb, which leaded to significant differences

between the human limb and the digital model. These differences between true and

computed models could lead to less accurate numerical results (Candalai and Reddy,

1992). In fact, Candalai and Reddy (1992) conducted a simulation of the effect of the

ischial tuberosity’s geometry on the shear and compressive stress in buttock issue and

showed that the influence of the geometry on the stress magnitude could be significant.

A possible variation of more than 60% in the shear stress was found. Despite the

differences between the aims of the work of Candalai and Reddy (1992) and swimming

studies, one should be aware of the ecological validity of the data that is obtained,

stressing the relevance of the scanned models instead of analytical representations.

Moreover, it should be noted that mesh generation, the first step of numerical

simulations, is a tough procedure, especially when solving three-dimensional problems.

66

Thus, it should be based on directly obtained anatomical data (Aritan et al., 1997;

Lecrivain et al., 2008; Marinho et al., 2008b).

Magnetic resonance imaging, computer tomography scans and laser scans seem to be a

good approach to design true human models (Aritan et al., 1997; Marshall et al., 2004;

Lecrivain et al., 2008; Marinho et al., 2008b). The overall aim of this approach, also

called reverse engineering process, is to build a virtual model geometrically identical to

an existing object. Scanning and data manipulation are the two main parts in this

process. Briefly one needs to gather the requisite data from a three-dimensional object

and then to edit the data and translate it into more suitable formats such as surface

models (Lecrivain et al., 2008).

Using a true model of the human body it is possible to improve the quality of the

numerical simulations techniques and to provide insights into some questions that

remain unclear in swimming technique. The thumb’s relative position during the

underwater path of the stroke cycle is one of these questions. An inter-subject variety of

thumb position can be observed among elite swimmers. Some swimmers maintain the

thumb adducted, others maintain the thumb abducted and others maintain the thumb

partially abducted. In fact, there remains much to be learned on the effect of thumb

position and whereas similar results are obtained by different methods of testing

(Takagi et al., 2001). Schleihauf (1979) showed that a thumb partially abducted allows

higher propulsion. Berger et al. (1997) found that models with different thumb

abduction/adduction had very little effect on drag forces but an effect on lift forces.

Takagi et al. (2001) reported that adduction and abduction of the thumb influenced the

lift force. The thumb abducted seemed to be advantageous for generating lift force when

the thumb is the leading edge and the thumb adducted seemed to be advantageous when

the little finger leads the motion (Takagi et al., 2001). To our knowledge, there is no

research published using a numerical approach on the repercussion of thumb

abduction/adduction and with anthropometrical data of elite swimmers’ hand.

Therefore, the aim of the present study was to analyze the hydrodynamic characteristics

of a true model of a swimmer hand with the thumb in different positions using

numerical simulation techniques.

67

Methods


Scanning

Cross-sectional scans of the right hand were obtained using a Toshiba® Aquilion 4

computer tomography scanner, using a configuration of V2.04 ER001. The subject was

an Olympic level male swimmer, who participated in the 2004 Olympic Games in

Athens. The subject was lying with his right arm extended upwards and fully pronated

and with the thumb in three positions: fully abducted, partially abducted and adducted

(Figure 1). In the position with the thumb fully abducted the angle between the

forefinger and the thumb was 68º and in the position with the thumb partially abducted

the angle between these two fingers was 30º. The hand length, the palm length and the

hand breadth of the swimmer were 20.20 cm, 9.50 cm and 8.90 cm, respectively. This

protocol has been approved by the appropriate ethical committee of the institution in

which it was performed and the subject gave informed consent to participate in this

work.

Figure 1: The models of the hand with the thumb in different positions: fully abducted, partially abducted

and adducted.

Data manipulation

The transformation of the values from the computer tomography scans into nodal

coordinates in an appropriate coordinate system demands the use of image processing

techniques. The image processing program used in this study was the Anatomics Pro®,

which allowed obtaining the boundaries of the human segments, creating a three-

dimensional reconstruction of the swimmer hand.

68

At first, before processing and converting procedures the data was prepared, namely by

observing the computer tomography data and erasing the non-relevant parts of the

anatomical model. This step was also conducted using the software FreeForm

Sensable®. Finally, the data was converted into an IGES format (*.igs), that could be

read by Gambit/Fluent® to define the finite elements approach through the three-

dimensional surfaces (Figure 2).

Computational fluid dynamics

Most computational fluid dynamics procedures are divided into three successive stages:

pre-processing, simulation and post-processing. The pre-processing stage involves

creating a computational domain where the flow simulation occurs, bounding it with

external conditions and discretising it into an adequate mesh grid. The solution of the

flow problem is defined at nodes inside each cell. The accuracy of a solution and its cost

in terms of necessary computer memory and calculation time are dependent on the

quality of the grid. Optimal meshes are often non-uniform: finer in areas of high

pressure and velocity gradients and coarser in areas with relatively little change. The

simulation is performed through an iterative algorithm until convergence. The variables

of interest (for instance, the hydrodynamic forces) are then extracted from the computed

flow field (Lecrivain et al., 2008).

Pre-processing

The whole domain was meshed with 200.000 cells. The grid was a hybrid mesh

composed of prisms and pyramids. Adaptive meshing was used to achieve optimum

mesh refinement. Thus, significant efforts were conducted to ensure that the model

would provide accurate results by decreasing the grid node separation in areas of high

pressure and velocity gradients.

69

Figure 2: The model of the hand with the thumb fully abducted inside the domain (Angle of attack = 0º,

Sweepback angle = 0º).

Solving steady flow

The numerical simulations of a three-dimensional model of a swimmer hand were

analyzed under steady flow conditions using the Fluent® code. The hydrodynamic fluid

forces produced by the hand, lift (L) and drag (D), were computed in this study. These

forces are functions of the fluid velocity, being determined by the application of the

equations 1 and 2.

2D V.A..C.

21D ρ=

(1)

2L V.A..C.

21L ρ=

(2)

In equations 1 and 2, V is the water velocity, CD and CL are the drag and lift

coefficients, respectively, ρ is the fluid density and A is the projection area of the model

for different angles of attack used in this study. Drag force is defined as the force acting

parallel to the flow direction and lift force lies perpendicular to the drag force.

70

The angle between the hand and the flow direction is defined as the angle of attack

(Figure 3) and the leading edge of the hand relative to the flow is the sweep back angle

(Figure 4). Angles of attack of hand models of 0º, 45º and 90º, with a sweep back angle

of 0º (thumb as the leading edge) were used for the calculations (Schleihauf, 1979). The

measured forces on the hand models were decomposed into drag (CD) and lift (CL)

coefficients, using equations 1 and 2 and the resultant drag coefficient was calculated by

the sum of CD and CL, using the Pythagoras theorem.

Angle of attack

Figure 3: The angle of attack (Schleihauf, 1979). The arrow represents the direction of the flow.

90º

0º 180º

270º Figure 4: The sweep back angle (Schleihauf, 1979). The arrows represent the direction of the flow.

On the left side of the domain access (Figure 2), the x component of the velocity was

chosen to be within the range of typical hand velocities during front crawl swimming

underwater path: from 0.50 m/s to 4.00 m/s, with 0.50 m/s increments (Lauder et al.,

2001; Rouboa et al., 2006). The y and z components of the velocity were assumed to be

equal to zero. On the right side, the pressure was equal to 1 atm, a fundamental pre

requisite to prevent the reflection of the flow. Around the model, the three components

of the velocity were considered equal to zero to allow the adhesion of the fluid to the

71

model. It was also considered the action of the gravity force (g = 9.81 m/s2), as well as

the turbulence percentage of 1% with 0.10 m of length (Bixler and Riewald, 2002;

Marinho et al., 2008a). The considered fluid was water, incompressible with density (ρ

= 996.6 x 10-9 kg/mm3) and viscosity (μ = 8.571 x 10-7 kg/mm/s).

The incompressible Reynolds averaged Navier-Stokes equations with the standard k-

epsilon (k-ε) model was considered and implemented in the commercial code Fluent®,

as shown before (Moreira et al., 2006).

Results

In figures 5, 6 and 7 the evolution of the values of CD and CL according to flow velocity

and angle of attack for each thumb position are presented. For the three thumb

positions, CD and CL remained almost constant throughout the flow velocities tested

(0.50-4.0 m/s). However, it was possible to note a slightly decrease in the force

coefficients, especially from 0.50 to 1.50 m/s.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0


Thumb fully abducted

Dra

g an

d lif

t coe

ffic

ient

Velocity (m/s)

Figure 5: Drag and lift coefficients vs. flow velocity for each angle of attack in the position with the

thumb fully abducted.

72

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0


Thumb partially abducted

Dra

g an

d lif

t coe

ffic

ient


thumb partially abducted.

Velocity (m/s)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0


Thumb adducted

Dra

g an

d lif

t coe

ffic

ient

Velocity (m/s)


thumb adducted.

73

In figures 8 and 9 the values of CD and CL obtained for the different angles of attack and

for the different thumb positions are presented for a flow velocity of 2.0 m/s.

It is possible to notice that the values of the CD increased with the angle of attack.

Indeed, the maximum value of CD was produced at an angle of attack of 90º, presenting

a value of about 1.0 in the three models. Moreover, the values of CD were almost similar

in the three different thumb positions, although the position with the thumb adducted

presented slightly higher values at 0º, 45º and 90º.

The CL presented the maximum values at an angle of attack of 45º (CL ≈ 0.6). The

values of CL at angles of attack of 0º and 90º seemed to be identical (CL ≈ 0.15).

Further, the position with the thumb fully abducted and with the thumb partially

abducted presented higher values of CL when compared with the thumb adducted

position at angles of attack of 0º and 45º. Nevertheless, the position with the thumb fully

abducted presented higher values when compared with the thumb partially abducted

position at 0º and 45º. At an angle of attack of 90º the values of CL were identical

irrespective of the thumb position.

0.1

0.3

0.5

0.7

0.9

1.1

0 45

Dra

g co

effic

ient

90

Thumb abducted

Thumb partiallyabductedThumb adducted


Figure 8: Values of drag coefficient obtained for the different angles of attack and for the different thumb

positions. Sweepback angle = 0º and flow velocity = 2.0 m/s.

74

0.1

0.3

0.5

0.7

0.9

0 45 90

Thumb abducted


Lift

coef

ficie

nt


Figure 9: Values of lift coefficient obtained for the different angles of attack and for the different thumb

positions. Sweepback angle = 0º and flow velocity = 2.0 m/s.

When analyzing the resultant force coefficient (Figure 10), one can note that the

position with the thumb abducted presented higher values than the positions with the

thumb partially abducted and adducted at angles of attack of 0º and 45º. However, at an

angle of attack of 90º the position with the thumb adducted presented the highest value

of resultant force coefficient.

0.3

0.5

0.7

0.9

1.1

0 45

Res

ulta

nt fo

rce

coef

ficie

nt

90

Thumb abducted



Figure 10: Values of the resultant force coefficient obtained for the different angles of attack and for the

different thumb positions. Sweepback angle = 0º and flow velocity = 2.0 m/s.

75

Discussion

The aim of the present study was to analyze the hydrodynamic characteristics of a true

model of a swimmer hand with the thumb in different positions using numerical

simulation techniques.

In this research we tried to improve the previous studies that applied the numerical

techniques to the analysis of swimming propulsion, using a more realistic model of the

swimmer hand. Indeed, the computer tomography scans allowed the creation of a

complete and true digital anatomic model of a swimmer hand (Aritan et al., 1997).

One of the major benefits of the numerical simulation procedures is that it allows the

user to modify the inputs into the model to determine how its changes affect the

resultant flow conditions. Regarding swimming, changes in technique can be examined

using the model, rather than the “trial and error” approach that typically is used. In this

work we have analysed the hydrodynamic forces produced by the swimmer hand with

the thumb in different positions as used by high level swimmers.

For the three thumb positions, the CD and CL remained almost constant throughout the

flow velocities that were tested. A similar observation was already reported in other

numerical studies (Bixler and Riewald, 2002; Silva et al., 2005; Rouboa et al., 2006;

Alves et al., 2007). However, in the present study, a slightly decrease in the CD and CL

were noted, especially from 0.50 to 1.50 m/s. Berger et al. (1995) and Bixler and

Riewald (2002) observed a similar tendency for lower velocities, in a towing tank

experiment and using numerical techniques, respectively. For lower velocities, a very

small decrease in the force coefficients values occurred with the velocity increase.

However, from a practical standpoint, the coefficients were considered constant since

the forces at these velocities are relatively small (Bixler and Riewald, 2002).

The values of CD produced by the swimmer hand were very similar concerning the three

thumb positions. However, the position with the thumb adducted presented slightly

higher values at the angles of attack tested in this study. Moreover, the values of CL

changed with the thumb position at angles of attack of 0º and 45º, although at an angle

of attack of 90º the values of the different thumb positions were identical. At 0º and 45º,

the position with the thumb fully abducted presented the highest values of CL.

76

Schleihauf (1979) studied the changes in the values of CL as a function of the thumb

position (thumb 100% abducted, 75% abducted and 50% abducted). However the

authors did not study the CD nor the position with the thumb adducted. In the study of

Schleihauf (1979), the position with the thumb fully abducted showed a maximum CL at

an acute angle of attack of 15º, whereas the models with partial thumb abduction

showed a maximum value of CL at higher angles of attack (45º-60º). In these angles of

attack the position with the thumb partially abducted presented higher values when

compared with the thumb fully abducted. Berger et al. (1997) reported that the thumb

position determined lift forces, although the drag forces were not influenced by thumb

abduction/adduction. Moreover, Takagi et al. (2001) estimated the drag and lift forces

from direct measurement of pressure differences between the front and back of the hand

in a resin model with the thumb abducted and adducted. The experimental results

revealed that the thumb position influenced the fluid force over the entire hand,

especially in the lift force. For a sweep back angle of 0º (as used in the present study),

the model with abducted thumb seemed to be advantageous for generating lift force,

whereas for a sweep back angle of 180º (the little finger as the leading edge), the

adducted thumb seemed preferable. However, in the study of Takagi et al. (2001), the

CD presented similar values in the two thumb position for a sweep back angle of 0º. For

a sweep back angle of 180º, the position with the thumb adducted presented higher

values.

Although some differences in the results of different studies, it seems that when the

thumb leads the motion (sweep back angle of 0º) a hand position with the thumb

abducted into the plane of the hand would be preferable to an adducted thumb position.

In this case, it is possible to suggest that during the insweep phase of the underwater

path in butterfly, breaststroke and front crawl techniques and in the upsweep phase of

backstroke technique the position with the thumb abducted could be gainful for

swimmers. On the other hand, based only on the study of Takagi et al. (2001), when the

little finger leads the motion (sweep back angle of 180º), during the outsweep phase of

butterfly and breaststroke, and some parts of the downsweep phase in backstroke and

upsweep in front crawl, the position with the thumb adducted seemed preferable. A

possible explanation may be related to the change in the flow around the hand due to the

77

thumb position: the lift force is enhanced by a pressure increase on the palm and a

pressure decrease on the back of the hand (Colwin, 1992; Takagi et al., 2001).

In the present study only the sweep back angle of 0º was analyzed. Thus these technical

implications must be taken with serious concerns. In fact, further studies are warranted

to analyze the thumb position with different sweep back angles and for a higher range of

angles of attack. In addition, one should be careful to generalize these results since each

swimmer has a different hand shape and the main findings could vary between different

subjects. However, it seems that the thumb position may play an important role in

optimizing swimming technique. When analyzing the resultant force coefficient, we

found that the position with the thumb abducted presented higher values than the

positions with the thumb partially abducted and adducted at angles of attack of 0º and

45º. At an angle of attack of 90º the position with the thumb adducted presented the

highest value of resultant force coefficient. These data seem to corroborate previous

findings abovementioned. For hand positions in which the lift force can play an

important role (Figures 5, 6 and 7) the abduction of the thumb may be benefic for

swimmers. In addition, at higher angles of attack, in which the drag force is dominant,

the adduction of the thumb may be preferable. The resultant force coefficient data

showed that the largest values were produced when the angle of attack was 90º. Sanders

(1997) found that the largest resultant forces were produced when the hand had around

90º of attack regardless of sweep back angle. These results are interesting in light of

observations that swimmers use sculling motions rather than pulling the hand directly

opposite the desired direction of motion with angles of attack near 90º to improve the

movement efficiency (Sanders, 1999). On the other hand, it remains the question

whereas this resultant force can be used to propel into the desired direction. Thus, in the

future it seems important to analyze the effective propulsive force produced by the

swimmer hand during the underwater path.

In all the thumb positions the CD obtained the highest value at an angle of attack of 90º,

i.e., where the hand plane was directly perpendicular to the direction of the flow. The

same result was reported by others using experimental (Berger et al., 1995; Sanders,

1999) and numerical approaches (Rouboa et al., 2006; Alves et al., 2007), indicating the

contribution of the hand surface area to the CD increase.

78

The CL seemed to have a residual influence in the generation of propulsive force by the

hand for angles of attack of 0º and 90º, but it is important at an angle of attack of 45º.

These findings are similar to those found in experimental (Wood, 1977; Schleihauf,

1979; Berger et al., 1995; Sanders, 1999) and numerical studies (Bixler and Riewald,

2002; Alves et al., 2007), reporting the important role of lift force to the overall

propulsive force production by the hand in underwater phases of swimming strokes

when the angle of attack nears 45º (e.g. insweep phase). In fact, although the CD and CL

were very similar in the three thumb positions at angles of attack of 0º and 45º, it was

possible to observe that for the positions with the thumb fully abducted and partially

abducted the CL presented higher values than CD at an angle of attack of 45º. Thus, it

seems essential to reinforce the need to analyze a larger range of angles of attack and

sweep back angles, trying to clarify the true importance of the lift force to the

propulsive force production. Lift force plays an important role at other angles of attack

rather than the 45º, as reported by Schleihauf (1979) at an angle of attack of 15º and by

Sanders (1999) at sweep back angles rather than 0º.

In the present study, despite the fact that only the drag and lift coefficients under steady

flow conditions were modelled, we do consider that the numerical approach that was

conducted is highly satisfactory. Firstly, the use of a true three-dimensional model of a

swimmer hand seemed to be an important step to the convergence between the

experimental and the computational data. Secondly, it was possible to vary the thumb

position and to investigate the effect on the CD and CL produced by the swimmer hand.

Nevertheless, this line of research must be improved considering the unsteady effects of

motion, such as accelerations, decelerations and rotation of the propelling segments.

Indeed, Sanders (1996), Berger et al. (1999) and Rouboa et al. (2006) showed that

unsteady and steady motion can lead to different results, concluding that the unsteady

effects should be considered when seeking accurate estimates of forces in swimming.

Hence, the effect of the thumb position on the hydrodynamic characteristics of the

swimmer hand must be further investigated performing time-dependent numerical

analysis with user-defined functions and moving meshes.

79

Conclusion

The position with the thumb adducted presented slightly higher values of drag

coefficient when compared with the positions with the thumb abducted (although values

were very similar). Moreover, the position with the thumb fully abducted allowed

increasing the lift coefficient of the hand at angles of attack of 0º and 45º. At an angle of

attack of 90º the values of lift coefficient were identical irrespective of the thumb

position.

The combination of drag and lift coefficient (resultant force coefficient) showed that the

position with the thumb fully abducted presented higher values than the positions with

the thumb partially abducted and adducted at angles of attack of 0º and 45º. However, at

an angle of attack of 90º the position with the thumb adducted presented the highest

value of resultant force coefficient. These results suggested that for hand positions in

which the lift force can play an important role the abduction of the thumb may be

benefic whereas at higher angles of attack, in which the drag force is dominant, the

adduction of the thumb may be preferable for swimmers.

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Design of a three-dimensional hand/forearm model to apply Computational Fluid Dynamics.


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82

Study 6

Swimming propulsion forces are enhanced by a small finger spread

Marinho, D.A., Barbosa, T.M., Reis, V.M., Kjendlie, P.L., Alves, F.B., Vilas-Boas, J.P., Machado, L.,

Silva, A.J., Rouboa, A.I. (2008). Swimming propulsion forces are enhanced by a small finger spread.

Journal of Applied Biomechanics (under revision).

83

Swimming propulsion forces are enhanced by a small finger spread

Abstract

The main aim of this study was to investigate the effect of finger spread on the propulsive force

production in swimming using computational fluid dynamics. Computer tomography scans of an Olympic

swimmer hand were conducted. This procedure allowed obtaining three models of the hand with different

finger spread: fingers close together, fingers with little distance spread (0.32 cm) and fingers with large

distance spread (0.64 cm). Steady-state computational fluid dynamics analyses were performed using the

Fluent® code. The measured forces on the hand models were decomposed into drag and lift coefficients.

Angles of attack of hand models of 0º, 15º, 30º, 45º, 60º, 75º and 90º, with a sweep back angle of 0º were

used for the calculations. The results showed that the model with little distance between fingers presented

higher values of drag coefficient than the models with fingers closed and fingers with large distance

spread. One can note that the drag coefficient presented the highest values for an attack angle of 90º in the

three hand models. The lift coefficient resembled a sinusoidal curve across the attack angle. The values

for the lift coefficient presented little differences between the three models, for a given attack angle.

These results suggested that fingers slightly spread could allow the hand to create more propulsive force

during swimming.

Introduction

The study of human swimming propulsion is one of the most complex areas of interest

in sport biomechanics (Payton et al., 2002). Over the past decades, research in

swimming biomechanics has evolved from the observation subject’s kinematics to a

basic flow dynamics approach, following the line of the scientists working on this

subject in experimental biology (Dickinson, 2000; Arellano et al., 2006).

Computational fluid dynamics (CFD) is one of the recent methodologies used to

achieve this goal. This methodology allows to analyze the water flow around the human

body, to understand the magnitude of drag forces resisting forward motion (Marinho et

al., 2008; Silva et al., 2008) and to compute the propulsive forces produced by the

propelling segments (Bixler and Riewald, 2002; Lecrivain et al., 2008).

CFD could help coaches in the short term on technique prescription. Moreover, this

methodology could provide answers to some practical issues that remain controversial.

The finger’s relative position during the underwater path of the stroke cycle is one of

84

these cases. A large inter-subject variety of fingers relative position can be observed

during training and competition. Some swimmers: (i) maintain the fingers close

together; (ii) others have a small distance between fingers and; (iii) others have a large

distance between fingers. Indeed, the propulsive repercussions of those three

possibilities are not a clear topic for swimming coaches and scientists. There is a lack of

research on this issue, conducting to some ideas among the swimming community with

little empirical (experimental or numerical data) support. Experimental data are

controversial: Schleihauf (1979) showed that finger closed together and thumb partially

abducted allow higher propulsion; Berger (1996) concluded that finger spreading do not

influence propulsion, but a rather more recent paper suggests that fingers close together

induces less propulsion than fingers spread (Sidelnik and Young, 2006). To our

knowledge, there is no research published using a numerical approach on the effect of

finger spreading and with anthropometrical data of elite swimmers hands.

Therefore, the main aim of this study was to investigate the effect of finger spread on

the propulsive force production in swimming using computational fluid dynamics.

Methods


Scanning

To obtain the geometry of the hand, cross-sectional scans of the right hand of an elite

swimmer (Figure 1) were conducted using a Toshiba® Aquilion 4 computer tomography

scanner. Computer tomography scans were obtained with configuration of V2.04

ER001. The subject was an Olympic level swimmer, who participated in the 2004

Olympic Games in Athens. The subject was lying prone, with his right arm extended

ahead and fully pronated. This procedure was conducted with different finger spreads:

fingers close together, fingers with little distance spread (a intra-finger distance of 0.32

cm, from tip to tip) and fingers with large distance spread (0.64 cm, from tip to tip)

(Schleihauf, 1979). This protocol has been approved by the appropriate ethical

committee of the institution in which it was performed and the subject gave informed

consent to participate in this work.

85

Figure 1: Anthropometric characteristics of the swimmer hand. Hand length (1): 20.20 cm, index breadth

(2): 1.50 cm, index length (3): 8.10 cm, palm length (4): 9.50 cm, hand breadth (5): 8.90 cm.

Data manipulation

The transformation of values from the computer tomography scans into nodal

coordinates in an appropriate coordinate system warrants the use of image processing

techniques. The image processing program used in this study was the Anatomics Pro

(Anatomics®, Kannapolis, Australia). This program allowed obtaining the boundaries of

the human segments, creating a three-dimensional reconstruction of the hand. At first,

before processing and converting procedures, the data was prepared by observing the

computer tomography data and erasing the non-relevant parts of the anatomical model.

This step was also conducted using the software FreeForm (Sensable Technologies®,

Wobum, USA). Finally, the data was converted into an IGES format (*.igs), that could

be read by Gambit/Fluent software (Fluent Inc®, Hanover, USA) to define the finite

elements approach through the three-dimensional surfaces (Figure 2).

CFD study

The Fluent® code solves flow problems by replacing the Navier-Stokes equations with

discretized algebraic expressions that can be solved by iterative computerized

86

calculations. Fluent® uses the finite volume approach, where the equations are

integrated over each control volume.

The dynamic fluid forces produced by the hand, lift (L) and drag (D), were measured in

this study. These forces are functions of the fluid velocity and they were measured by

the application of the equations 1 and 2, respectively:

D = CD ½ ρ A v2 (1)

L = CL ½ ρ A v2 (2)

In equations 1 and 2, v is the fluid velocity, CD and CL are the drag and lift coefficients,

respectively, ρ is the fluid density and A is the projection area of the model for different

angles of attack used in this study.

Figure 2: Computational fluid dynamics model geometry with the hand inside the domain (model with

fingers closed).

Pre-processing

The whole domain was meshed with a hybrid mesh composed of prisms and pyramids.

Significant efforts were conducted to ensure that the model would provide accurate

87

results by decreasing the grid node separation in areas of high velocity and pressure

gradients.

Solving steady flow

Angles of attack of hand models of 0º, 15º, 30º, 45º, 60º, 75º and 90º, with a sweep back

angle of 0º (thumb as the leading edge) were used for the calculations (Schleihauf,

1979).

Steady-state CFD analyses were performed using the Fluent® code and the drag and lift

coefficients were calculated for a flow velocity of 2.0 m.s-1 (Lauder et al., 2001; Rouboa

et al., 2006).




All numerical computational schemes were second-order, which provides a more

accurate solution than first-order schemes. We used a turbulence intensity of 1.0% and a

turbulence scale of 0.10 m. The water temperature was 28º C with a density of 998.2

kg/m3 and a viscosity of 0.001 kg/mm/s. Incompressible flow was assumed. The

measured forces on the hand models were decomposed into drag (CD) and lift (CL)

coefficients, using equations 1 and 2.

Results

Figures 3 and 4 show the values of CD and CL, respectively, obtained for the hand

model with different finger spread.

One can note that the CD presented the highest values for an attack angle of 90º in the

three hand models (≈0.90 < CD < 1.10). In the three models the CD increased with the

attack angle. Moreover, it was possible to observe that for attack angles higher than 30º,

the model with little distance between fingers presented higher values of CD when

compared with the models with fingers closed and with large finger spread. This last

88

model presented the lowest values of CD. For attack angles of 0º, 15º and 30º, the values

of CD were very similar in the three models of the swimmer’s hand.

0,1

0,3

0,5

0,7

0,9

1,1

0 15 30 45 60 75 90

Fingers

0.64 cm spread

0.32 cm spread

closed

Figure 3: Values of CD obtained for the different attack angles and for the different finger spread.

Sweepback angle = 0º and flow velocity = 2.0 m/s.

On the other hand, the CL resembled a sinusoidal curve across the attack angle.

Maximum values for any hand model occurred near 30º-45º (CL≈0.60). Furthermore,

the CL seemed to be independent of the finger spreading, presenting little differences

between the three models. However, it was possible to note slightly lower values for the

position with a larger distance between fingers, especially for attack angles ranging

from 15º to 60º.

Dra

g co

effic

ient

1.10

0.90

0.70

0.50

0.30

0.10

Attack angle (degrees)

89

0,1

3

5

7

0 15 30 45 60 75 90

0,

0,

0,

0.64 cm spread

0.32 cm spread

closed

Figure 4: Values of CL obtained for the different attack angles and for the different finger spread.

Sweepback angle = 0º and flow velocity = 2.0 m/s.

Discussion

The main aim of this study was to analyse the effect of finger spread in the swimming

propulsive force production, through CFD. Results suggested that fingers slightly

spread could allow the hand to create more propulsive force during swimming.

In this study we tried to clarify one technical concern of the swimming community:

which should be the best finger position to improve force production by the hand during

swimming? Therefore, three models with different finger spread were chosen for the

analysis, addressed to characterize different swimming strategies. In addition, the option

to analyze one position with fingers closed, one with little distance between fingers and

another with a larger distance between fingers, was based on the pioneer study of

Schleihauf (1979). Despite some theoretical assumptions and expert opinions (e.g.

Counsilman, 1968; Colwin, 1992; Maglischo, 2003), there are few experimental studies

to clarify this issue (Schleihauf, 1979; Takagi et al., 2001; Berger, 1996; Sidelnik and

Young, 2006). Rather than an experimental analysis, the present study applied the

Fingers

Attack angle (degrees)

Lift

coef

ficie

nt

0.70

0.50

0.30

0.10

90

numerical techniques of CFD to compute the forces produced by the model of the

swimmer’s hand. Bixler et al. (2007) has already demonstrated the validity of CFD

analysis as a tool to examine the water flow around the swimmer body. Nevertheless, it

is very important that the digital model corresponds to a truthful representation of the

human segment to ensure accurate numerical results (Candalai and Reddy, 1992;

Lecrivain et al., 2008). Indeed, the computer tomography scans allowed the creation of

a true digital model of the swimmer’s hand (Aritan et al., 1997). Moreover, precise

images of complex three-dimensional shape bodies, as human hand’s, obtained by

imagiography is becoming widely used in reverse engineering (Lecrivain et al., 2008).

The main finding of the present research was that the model with little distance between

fingers presented higher values of CD than the models with fingers close together and

with fingers widely spread. Furthermore, the CL seemed to be independent of the finger

spread, presenting little differences between the three models. These results suggest that

the use of a position with little distance between fingers seems to be gainful for

swimmers.

The hand position with little distance between fingers seemed to increase the projection

area of the hand, thus increasing force production. The distance between fingers seemed

not enough to allow the water to flow freely. Indeed, a turbulent flow between the

fingers may be formed, creating some kind of barrier. Nevertheless, regarding the CL,

the values for the position with little finger spread and for the position with fingers

closed were very similar. For attack angles lower than 90º, the flow above the dorsal

surface of the hand, flowing at high velocities, could prevent the flow between fingers.

In this condition, assuming the higher velocity difference between the two surfaces of

the swimmers’ hand will occur at the attack angle corresponding to the higher CL (in

this case, between 30º and 45º), it will be expectable, then, that the so called “barrier”

will be stronger at that CL values. As it can be seen from the figures 3 and 4, at an attack

angle of 45º it is perceptible a relative grow of the CD value considering the curve

tendency, corresponding to the maximal CL value obtained for the slight spreading

condition, and for all studied conditions, which is, for the higher flow velocity

difference between both faces of the hand. Concerning this topic, Ungerechts and

Klauck (2006) did suggest fingers slightly spread to induce flow around the hand at the

beginning of the arm cycle.

91

However, this gain did not occur when we analyzed larger distances between fingers. In

both CD and CL coefficients, for the position with large finger spread, the values were

lower when compared to the positions with fingers closed and slightly spread. For the

CD and for attack angles higher than 30º, the position with more distance between

fingers presented lower values. This position presented also lower values in CL. It seems

that there is a critical distance between fingers beyond which the force production

became compromised.

Schleihauf (1979) has already reported an identical situation. The CD for both fingers

closed and slightly spread positions presented higher values than the large spread

position. On the other hand, the values of CL increased in indirect proportion to finger

spread for attack angles ranging between 0º and 60º. Berger (1996) reported that

spreading the finger did not influence propulsive force. Moreover, lift force at attack

angles between 60º-80º was higher when spreading the fingers (Berger, 1996). In a

recent experimental study, Sidelnik and Young (2006) determined that a hand with 10º

of separation between fingers created more stroke force than a fingers-together

configuration, across all attack angles tested.

Furthermore, CD presented the highest values for an attack angle of 90º in the three hand

models (≈0.90<CD<1.10) whereas CL resembled a sinusoidal curve across the attack

angle (CL≈0.60). These results are quite similar to the ones already described with

experimental methodologies (e.g., Schleihauf, 1979; Berger et al., 1995; Takagi et al.,

2001).

In summary, this study showed that CFD methodology can be an important tool for

coaches and swimmers to improve performance. However, the present results were

obtained using steady flow simulations. Further studies should include the unsteady

effects of motion, such as accelerations, decelerations and rotations (Sanders, 1999). It

seems interesting to observe if the results would be the same as suggested by

Ungerechts and Klauck (2006). These authors proposed the use of fingers slightly

spread to induce flow around the hand at the beginning of the arm cycle and to create

unsteady flow to allow a marked increase of propelling momentum.

Although the results of the present numerical research showed that fingers slightly

spread created more force, this is a comparison of only three hand positions. In the

92

future, there are many hand shape parameters that could be included by varying for

instance wrist angle, thumb abduction and hand configuration (flat vs. cupped palm and

flexed vs. extended interphalangeal joints).

References

Arellano, R., Nicoli-Terrés, J.M., Redondo, J.M. (2006). Fundamental hydrodynamics of swimming

propulsion. Portuguese Journal of Sport Sciences, 6(Suppl. 2), 15-20.



19, 681-689.

Berger, M. (1996). Force generation and efficiency in front crawl swimming. PhD Thesis. Amsterdam:

Faculty of Human Movement Sciences, Vrije Universiteit.

Berger, M., de Groot, G., Hollander, A.P. (1995). Hydrodynamic drag and lift forces on human/arm

models. Journal of Biomechanics, 28, 125-133







Colwin, C. (1992). Swimming into the 21th Century. Champaign, Illinois: Leisure Press.

Counsilman, J. (1968). The Science of Swimming. Englewood Cliffs: Prenctice-Hall Inc.

Dickinson, M.H. (2000). How animals move: an integrative view. Science, 288, 100-106.






Maglischo, E.W. (2003). Swimming Fastest. The essential reference on training, technique and program

design. Champaign, Illinois: Human Kinetics.



93




Payton, C., Baltzopoulos, V., Bartlett, R. (2002). Contributions of rotations of the trunk and upper

extremity to hand velocity during front crawl swimming. Journal of Applied Biomechanics, 18,

243.








Sidelnik, N.O., Young, B.W. (2006). Optimising the freestyle swimming stroke: the effect of finger

spread. Sports Engineering, 9, 129-135.

Silva, A.J., Rouboa, A., Moreira, A., Reis, V., Alves, F., Vilas-Boas, J.P., Marinho, D. (2008). Analysis

of drafting effects in swimming using computational fluid dynamics. Journal of Sports Science

and Medicine, 7(1), 60-66.





Ungerechts, B., Klauck, J. (2006). Consequences of unsteady flow effects for functional attribution of

swimming strokes. Portuguese Journal of Sport Sciences, 6(Suppl. 2), 109-111.

94

Review

Swimming simulation: a new tool for swimming research and practical

applications

Marinho, D.A., Barbosa, T.M., Kjendlie, P.L., Vilas-Boas, J.P., Alves, F.B., Rouboa, A.I., Silva, A.J.

(2009). Swimming simulation: a new tool for swimming research and practical applications. In: M. Peters

(Ed.), Lecture Notes in Computational Science and Engineering – CFD and Sport Sciences. Berlin:

Springer (in press).

95

Swimming simulation: a new tool for swimming research and practical

implications

Abstract

This chapter covers topics in swimming simulation from a computational fluid dynamics perspective.

This perspective means emphasis on the fluid mechanics and CFD methodology applied in swimming

research. We concentrated on numerical simulation results, considering the scientific simulation point-of-

view and especially the practical implications with swimmers.

1. Introduction

Swimming is one of the major athletic sports and many efforts are being made to

establish new records in all events. To swim faster, thrust should be maximized and

drag should be minimized. These aims are difficult to achieve because swimmers surge,

heave, roll and pitch during every stroke cycle. In addition, measurements of human

forces and mechanical power are difficult due to the restrictions of measuring devices

and the specificity of aquatic environment. Thus, human swimming evaluation is one of

the most complex but outstanding and interesting topics in sport biomechanics. Over the

past decades, research in swimming biomechanics has evolved from the study of

swimmer’s kinematics to a flow dynamics approach, following the line of research from

the experimental biology (Dickinson, 2000; Arellano et al., 2006). Significant efforts

have been made to understand swimming mechanics on a deeper basis. In the past, most

of the studied involved experimental data, nowadays the numerical solutions can give

new insights about swimming science. Computational fluid dynamics (CFD)

methodology is one of the different methods that have been applied in swimming

research to observe and understand water movements around the human body and its

application to improve swimming technique and/or swimming equipments and

therefore, swimming performance. One recent example is the cooperation between

Speedo® swimwear manufacturer and Fluent® CFD software provider, in the process of

improving the swimwear’s hydrodynamic characteristics. The CFD software was

incorporated into Speedo’s design process to evaluate the drag and fluid flow

characteristics around the male and female swimmers for various flow conditions. This

96

work allowed Speedo® to simulate the flow around the virtual swimmer body, thus

making the swimsuits as hydrodynamic as possible (Fluent, 2004). Fastskin FSII® and

recently the LZR® suits are the most visible examples of the application of CFD in

swimming research and its influence in the swimming performance. However, other

issues related to swimming science, besides the swimwear, were and are also being

solved with this methodology.

Therefore, the use of CFD can be considered as a new step forward to the understanding

of swimming mechanisms and seems to be an interesting approach to the swimming

research. In this sense, the main purpose of this book chapter is to present the basis of

this methodology and its applications in swimming research.

This chapter is divided in seven parts. In the first part, we introduce the issue and the

main aims of the paper. In the second, we briefly explain the CFD methodology and its

basic steps. In the third part, we show some applications of CFD in biological systems.

In the fourth part, some applications of CFD to human beings are presented. In the fifth

part, it can be observed the contribution of the different studies in swimming using

CFD, where we can analyse some practical application of the CFD technology in

swimming research. In the final parts, we present some ideas to future studies in

swimming using CFD and the main conclusions.

2. Fluid mechanics and CFD methodology

2.1. Background

CFD is a branch of fluid mechanics that solves and analyses problems involving a fluid

flow by means of computer-based simulations. CFD methodology consists of a

mathematical model that replaces the Navier-Stokes equations with discretized

algebraic expressions that can be solved by iterative computerized calculations. The

Navier–Stokes equations describe the motion of viscous non-compressible fluid

substances. These equations arise from applying Newton's second law to fluid motion,

together with the assumption that the fluid stress is the sum of a diffusing viscous term

(proportional to the gradient of velocity), plus a pressure term. A solution of the

Navier–Stokes equations is called a velocity field or flow field, which is a description of

the velocity of the fluid at a given point in space and time. CFD methodology is based

97

on the finite volume approach. In this approach the equations are integrated over each

control volume. It is required to discretize the spatial domain into small cells to form a

volume mesh or grid, and then apply a suitable algorithm to solve the equations of

motion. In addition, CFD analyses complements testing and experimentation, reducing

the total effort required in the experimental design and data acquisition.

In the beginning of its application CFD was quite difficult to use. It was applied only in

a few companies of high technological level, namely in the Aerospatiale Engineering or

in some specific scientific research areas. It became obvious that its application had to

assume a user friendly interface and to progress from a heavy and difficult computation

to practical, flexible, intuitive and quick software. Therefore, the following step was to

transform CFD in a new set of commercial software to be used in different applications

and to help the connection between the user and the computer.

Presently, this tool is used in the resolution of complex engineering problems involving

fluid dynamics and it is also being extended to the study of complex flow regimes that

define the forces generated by species in self propulsion.

The basic steps of CFD analysis are:

1. Problem identification and pre-processing: (i) define the modelling goals, (ii) identify

the domain that wants to model, (iii) design and create the grid.

2. Solver execution: (i) set up the numerical model, (ii) compute and monitor the

solution.

3. Post-Processing: (i) examine the results; (ii) consider revisions to the model.

2.2. Advantages and limitations

CFD can be used to predict fluid flow, heat and mass transfer, chemical reactions and

related phenomena by solving the set of governing mathematical equations. The results

of CFD analyses can be relevant in conceptual studies of new designs, detailed product

development, troubleshooting and redesign.

Lyttle and Keys (2006) referred that CFD can provide the answers into many complex

problems which have been unobtainable using physical testing techniques. One of the

98

major benefits is to quickly answer many “what if” type questions. It is possible to test

many variations until one arrives at an optimal result, without physical/experimental

testing. CFD could be seen as bridging the gap between theoretical and experimental

fluid dynamics. For example, with this methodology it is possible to study the

aerodynamic of a race car before being constructed or to study the air flow inside the

ventilation system of a park station, to simulate situations where a fire takes place, to

analyse the ventilation and the acclimatisation of a specific building, such as an hospital

where the quality of the air is quite important.

CFD was developed to model any flow filed provided the geometry of the object is

known and some initial flow conditions are prescribed. CFD is based on the use of

computers to solve mathematical equation systems. However, it is essential to apply the

specific data to characterize the study conditions. Therefore, in the CFD studies the

subject who analyzes the problem must be considered. The scientific knowledge, the

computational program which solves the equations system representing the problem, the

kind of computer that executes the defined calculations in the numerical program and

the person who verifies and analyses the obtained results must also be taken in account.

In this sense, one must consider that the CFD analyses can have some inaccurate results

if there is not thorough study of the specific situation. The inserted data should not have

wide-ranging estimation. On the other hand, the available computational resources can

be insufficient to obtain results with the necessary precision. Previous to any simulation,

the flow situation must be very well analysed and understood, as well as of the obtained

results.

2.3. Validity, reliability, accuracy

CFD studies are becoming more and more popular. However, a main concern still

persists. Can the numerical data be comparable with experimental research? Are the

numerical results accurate enough to be meaningful and therefore have ecological

validity? For sport scientists who work in close connection with coaches and athletes

this question is important in order to give good, appropriate and individual feed-backs

for practitioners.

99

Several studies within different scopes attempted to verify the validity and accuracy of

CFD. This numerical tool has been validated as being feasible in modelling complicated

biological fluid dynamics, through a series of stepwise baseline benchmark tests and

applications for realistic modelling of different scopes for hydro and aerodynamics of

locomotion (Liu, 2002).

In bioscience, Yim et al. (2005) described in detail critical aspects of this methodology

including surface reconstruction, construction of the volumetric mesh, imposition of

boundary conditions and solution of the finite element model. Yim et al. (2005) showed

the validity of the methodology in vitro and in vivo for experimental biology. Barsky et

al. (2004) have also demonstrated good agreement between the numerical and

experimental data on tethered DNA in flow. Moreover, Gage et al. (2002) reported that

computational techniques coupled with experimental verification can offer insight into

model validity and showed promise for the development of accurate three-dimensional

simulations of medical procedures.

In engineering, Venetsanos et al. (2003) illustrated an application of CFD methods for

the simulation of an actual hydrogen explosion occurred in a built up area of central

Stockholm Sweden in 1983. The subsequent simulation of the combustion adopted

initial conditions for mean flow and turbulence from the dispersion simulations, and

calculated the development of a fireball. This data provided physical values that were

used as a comparison with the known accident details to give an indication of the

validity of the models. The simulation results were consistent with both the reported

near-field damage to buildings and persons and with the far-field damage to windows.

In sports some trials have been carried-out to compare the numerical results with

experimental results also. A combined CFD and experimental study on the influence of

the crew position on the bobsleigh aerodynamics was conducted by Dabnichki and

Avital (2006). The experimental results obtained in a wind tunnel suggested that the

adopted computational method is appropriate and yields valid results. In what concerns

to aquatic sports there is a lack of studies comparing experimental and CFD data.

However, CFD was developed to be valid and accurate in a large scope of fluid

environments, bodies and tasks, including sports. So, it is assumed that CFD have

ecological validity even for swimming research.

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Another important concern is related with CFD reliability. In experimental tests, the

input data are not always the same and thus the outputs will vary. However, the

numerical simulations allow having always the same input conditions and therefore the

same outputs.

2.4. Areas of application

CFD has a wide field of applications, being used in biomechanical studies applied to

several research fields, such as industry, biology, medicine and sports (e.g. Boulding et

al., 2002; Marshall et al., 2004; Dabnichki and Avital, 2006; Guerra et al., 2007).

The broad physical modelling capabilities of CFD have been applied to industrial

applications ranging from air flow over an aircraft wing to combustion in a furnace,

from bubble columns to glass production, from blood flow to semiconductor

manufacturing, from clean room design to wastewater treatment plants. The ability of

the software to model in-cylinder engines, aeroacoustics, turbomachinery, and

multiphase systems has served to broaden its reach. Today, thousands of companies

throughout the world benefit from this important engineering design and analysis tool.

Its extensive range of multiphysics capabilities makes it an important and interesting

tool in engineering studies.

Recently, medical applications were also described by this method (e.g. Berthier et al.,

2002; Ruiz et al., 2005). Berthier et al. (2002) analyzed the blood flow patterns in a

coronary vessel digital model whereas Ruiz et al. (2005) simulated the complex three-

dimensional airflow pattern in the human nasal passageways.

In biology, the CFD models started to be used in the middle of the 90s in the flying

study of insects as well as in the inquiring of the aerodynamic and hydrodynamic forces

involved in the propulsion and energy conservation through the generation of organized

vortex systems in animals displacing by body undulation (Liu et al., 1996; Liu et al.,

1997; Liu et al., 1998).

In sports scope, the main results suggested that a CFD analysis could provide useful

information about performance. Indeed, this methodology has produced significant

improvements in equipment design and technique prescription in areas such as sailing

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performance (Pallis et al., 2000), Formula 1 racing (Kellar et al., 1999) and winter

sports (Dabnichki and Avital, 2006). CFD has been applied to swimming in order to

understand its relationships with performance mainly by three research groups. One

coordinated by Barry Bixler from Honeywell Aerospace (USA), another coordinated by

António José Silva from the Research Centre in Sport, Health and Human Development

(Portugal), and another coordinated by Bruce Mason from the Australian Institute of

Sport (Australia).

The numerical techniques have been applied to the analysis of the propulsive forces

generated by the propelling segments (Bixler and Schloder, 1996; Rouboa et al., 2006)

and to the analysis of the hydrodynamic drag forces resisting forward motion (Lyttle

and Keys, 2006; Marinho et al., 2008a).

3. CFD applied to biological systems

Fluid dynamic phenomena in animal locomotion are complicated because biological

fluid dynamics involves the interaction of elastic or even flexible living issues with

surrounding viscous fluid (Liu, 2002). The biological fluid dynamic phenomena are, in

general, characterized by large-scale vortex structure due to the highly unsteady motions

and the complex and variable geometry of the object in swimming and flying.

3.1. CFD overview in birds/insects

The flight of insects has fascinated physicists and biologists for many years. On one

hand, insects owe much of their amazing evolutionary success to flight. One the other,

their flight seems improbable using standard aerodynamic theory (Sane, 2003). The

small size, high stroke frequency and peculiar reciprocal flapping motion of insects

have combined to prevent simple explanations of flight aerodynamics. Nevertheless,

recent developments in high-speed videography and tools for computational and

mechanical modelling have allowed researchers to make progresses in the

understanding of insect flight. These CFD models, combined with modern flow

visualization techniques, have revealed that the fluid dynamic phenomena underlying

flapping flight are different from those of non-flapping, two-dimensional wings on

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which most models are based (Sane, 2003). In fact, even at high angles of attack, a

prominent leading edge vortex remains stably attached on the insect wing and does not

shed into an unsteady wake thus enhances the forces generated by the wing, enabling

insects to hover and maneuver.

With recent advances in computational methods, many researchers have begun

exploring numerical methods to resolve the insect flight problem (Ellington et al., 1996;

Liu and Kawachi, 1998; Liu et al., 1998; Dickinson et al., 1999; Wang, 2000; Hamdani

and Sun, 2001). Although ultimately these techniques are more rigorous than simplified

analytical solutions, they require large computational resources and are not as easily

applied to large comparative data sets (Sane, 2003). Moreover, CFD simulations rely

critically on empirical data both for validation and relevant kinematic input. However,

several studies have recently emerged that have led to some important CFD models of

insect flight.

Liu and co-workers (Liu and Kawachi, 1998; Liu et al., 1998) using the hawkmoth

Manduca as a model, were the first to attempt a full Navier-Stokes simulation by a

finite volume approach. In addition to confirm the smoke streak patterns observed on

both real and dynamically scaled model insects (Ellington et al., 1996), this study added

finer detail to the flow structure and predicted the time course of the aerodynamic forces

resulting from these flow patterns. Furthermore, Dickinson et al. (1999) used a

computational approach to model Drosophila Melanogaster flight for which force

records exist based on a dynamically scaled model. Although roughly matching

experimental results, these methods have added a wealth of qualitative detail to the

empirical measurements (Ramamurti and Sandberg, 2002), and even provided

alternative explanations for experimental results (Sun and Tang, 2002). Despite the

importance of considering the three-dimensional effects, comparisons of experiments

and simulations in two-dimensions have also provided important insight. For instance,

the simulations of Hamdani and Sun (2001) matched complex features of prior

experimental results with two-dimensional airflows at low Reynolds number (Dickinson

and Gotz, 1993). In fact, two-dimensional CFD models have also been used to address

feasibility issues (Sane, 2003). Wang (2000) reported that the force dynamics of two-

dimensional wings, although not stabilized by three-dimensional effects, might still be

sufficient to explain the enhanced lift coefficient measured in insects.

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Interestingly some swimming researchers suggest a link between swimmers propulsion

actions and insects or birds wings actions (Colwin, 1984; Toussaint et al., 2002).

Colwin (1984) firstly introduced the concept of propulsion through vortex generation in

human swimming, based upon the mechanism of flapping wings fly, and Toussaint et

al. (2002) suggested that, as insects and birds wing’s do, swimmers also use arm

rotation that could lead to the establishment of a proximal-distal pressure gradient,

which would induce significant axial flow along the arm toward the hand. It was

observed that: (i) the flow during insweep and part of the outsweep was highly

unsteady; (ii) the arm movements were largely rotational; (iii) a clear axial flow

component, not in the direction of the arm movement, was observed during insweep and

outsweep and; (iv) both the V-shaped "contracting" arrangement of the tufts during the

outsweep, and pressure recordings, point to a pressure gradient along the direction of

the arm during the outsweep, as predicted on theoretical grounds (Toussaint et al.,

2002).

3.2. CFD overview in fishes

Most aquatic animals use the jet-stream propulsion in a form of propagating a transverse

wave along the body from head to tail (Liu, 2002). Physics of fluids around fishes

swimming is often of a dynamic vortex structure as their fins usually perform

periodically oscillating motions.

Liu et al. (1996) studied the hydrodynamics and undulating propulsion of tadpoles using

a two-dimensional CFD modelling method. The CFD analysis showed that the

kinematics of tadpoles is specifically matched to their special shape and produces a jet-

stream propulsion with high propulsive efficiency, as high as that achieved by teleost

fishes. The authors reported as well that the shapes and kinematics of tadpoles appeared

to be specially adapted to the requirement of these organisms to transform into frogs.

Liu et al. (1997) extended their two-dimensional modelling of tadpole swimming to

more realistic three-dimensional situation. Essentially they asked how the three-

dimensional effects of unsteady undulatory hydrodynamics by swimming tadpoles

affected their locomotion performance. Within this study the unsteady flow generated

by an undulating vertebrate has been modelled in three dimensions for the first time.

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This study demonstrated the feasibility of using three-dimensional CFD methods to

model the locomotion of undulatory organisms. Tadpoles are unusual among vertebrates

in having a globose body with a laterally compressed tail abruptly appended to it.

Compared with most teleost fishes, tadpoles swim awkwardly, with waves of relatively

high amplitude at both the snout and tail tip. The authors confirmed results from the

previous two-dimensional study, which suggested that the characteristic shape of

tadpoles was closely matched to their unusual kinematics. Specifically, the three-

dimensional results revealed that the shape and kinematics of tadpoles collectively

produce a small 'dead water' zone between the head-body and tail during swimming

precisely where tadpoles can and do grow hind limbs without those limbs obstructing

flow. In addition, Liu et al. (1997) showed that three-dimensional hydrodynamic effects

(cross flows) were largely constrained to a small region along the edge of the tail fin.

Although this three-dimensional study confirmed most of the results of the two-

dimensional study, it showed that propulsive efficiency for tadpoles was lower than

predicted from a two-dimensional analysis. This low efficiency was not, however, a

result of the high-amplitude undulations of the tadpole. This was demonstrated by

forcing the 'virtual' tadpole to swim with fish-like kinematics, i.e. with lower-amplitude

propulsive waves. That particular simulation yielded a much lower efficiency,

confirming that the large-amplitude lateral oscillations of the tadpole provide positive

thrust.

Fishes CFD data, as reported for the insects and birds condition, can give in a near

future some insights or raise questions about propulsive and drag phenomena during

non-steady flow with human locomotion in aquatic environment. Especially topics such

as the undulatory motion and its relationship with human body undulatory motion in

some swim strokes, such as Butterfly stroke, as well as to the kick action in Front

Crawl, Backstroke and Butterfly stroke.

4. CFD applied to human beings

4.1. Terrestrial locomotion

In the literature there are not many works that applied CFD to human terrestrial

locomotion. However, CFD has been recently used in high-performance sports, such as

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car racing and motorcycling (Hannah, 2002). One of the reasons for the relatively slow

start of the application of CFD in this scope is the enormous complexity of the flow

conditions – non-stationary flows, high level of turbulence and complex body shapes,

requiring the use of very powerful computational facilities and advanced CFD codes

(Dabnichki and Avital, 2006).

Dabnichki and Avital (2006) focused on the influence of the position of crew members

on aerodynamics performance of two-man bobsleigh. The authors studied female crews

because they used sleds built for males and thus there is a bigger gap between the crew

and the side walls. The position of the brakewoman’s body in terms of upper body

inclination and the distance between the cavity and the athlete were studied through

computational means. Dabnichki and Avital (2006) showed that crew members did

influence the drag level significantly and suggested that internal modifications can be

introduced to reduce the overall resistance drag.

Nevertheless, some experience and background knowledge of human terrestrial

locomotion can be useful in a near future for aquatic locomotion. In both environments,

powerful computational facilities and advanced CFD codes will be useful for a better

understanding of human locomotion for a wide variety of tasks.

4.2. Aquatic locomotion

Regarding aquatic locomotion, CFD has been applied in swimming attempting to

understand deeply the biomechanical basis underlying swimming locomotion. Several

studies have been conducted willing to analyze the propulsive forces produced by the

propelling segments (e.g. Bixler and Riewald, 2002; Rouboa et al., 2006) and the drag

force resisting forward motion (e.g. Bixler et al., 2007; Marinho et al., 2008a). To our

knowledge, the application of CFD methodology in aquatic and nautical activities is

restricted to swimming. However, it would be interesting to apply this methodology in

other fields such sailing, windsurfing, surfing, canoeing and rowing, not only in the

analysis of equipment design (Pallis et al., 2000) but also to relate different displacing

strategies with performance. In the same way, CFD can also provide new highlights

about aquatic activities related to health (e.g. head-out aquatic exercises or water-

aerobics) and muscle-skeletal injuries rehabilitation in water (e.g., hydrotherapy).

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In the following chapter, the application of CFD into competitive swimming will be

discussed deeply.

5. CFD applied to competitive swimming

5.1. Experimental vs. numerical data

CFD analysis in swimming has addressed to understand two main topics of interest: (i)

the propulsive force generated by the propelling segments and; (ii) the drag forces

resisting forward motion, since the interaction between both forces will influence the

swimmer’s speed.

Some authors attempted to compare the numerical data with experimental data available

in previous researches about propulsion and drag. However, not always this is an easy

goal because the models included in the CFD simulations are not the same as used in

experimental measurements.

Bixler et al. (2007) tried to overcome this problem and studied the accuracy of CFD

analysis of the passive drag of a male swimmer. The aim of this study was to build an

accurate computer-based model to study the water flow and drag force characteristics

around and acting on the human body while in a submerged streamlined position.

Comparisons of total drag force were performed between a real swimmer, a digital CFD

model of this same swimmer and a real mannequin based on the digital model. Drag

forces were determined for velocities representative of the ones presented in elite

competition during the underwater gliding (i.e., between 1.50 and 2.25 m/s). Bixler et

al. (2007) found drag forces determined from the digital model using the CFD approach

to be within 4% of the values assessed experimentally for the mannequin, although the

mannequin drag was found to be 18% less than the real swimmer drag (Figure 1). In

fact, the Bixler et al. (2007) study has reinforced the idea of the validity and accuracy of

CFD in swimming research. This study also showed that the drag of the real swimmer is

quite high compared to the model due to little body movements during the gliding

position. Another difference between the swimmer and the model is that the swimmer’s

skin is flexible while the mannequin’s skin is rigid.

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20

30

40

50

60

70

80

90

1.50 1.75 2.00 2.25

CFD

Mannequin

Swimmer

Dra

g fo

rce

(N)

Velocity (m/s)

Figure 1: Hydrodynamic drag force of the swimmer, the digital CFD model and the mannequin. Adapted

from Bixler et al. (2007).

Other authors used CFD in swimming research, and compared their results with

experimental data available in the literature. Bixler and Riewald (2002) and Silva et al.

(2005) analysed the swimmer’s hand and arm in steady flow conditions using CFD.

Drag and lift coefficients computed for the hand and arm fitted well with steady-state

coefficients determined experimentally by other researchers (Wood, 1977; Schleihauf,

1979; Berger et al., 1995; Sanders, 1999). For instance, Wood (1977) found drag

coefficient (CD) values of 0.30 and 1.10 and lift coefficient (CL) values of 0.10 and 0.15;

while Silva et al. (2005) found CD values of 0.27 and 1.16 and CL values of 0.15 and

0.02 at angles of attack of 0º and 90º, respectively. Although the comparison is

satisfactory, the differences between experimental and numerical data could be the

result of wave and ventilation drag caused by the arm piercing the free water surface in

the towing tank experiments (Berger et al., 1995; Bixler and Riewald, 2002).

Lyttle and Keys (2006) aimed to compare two different dynamic kicking techniques

using CFD and needed to validate the model to show the compatibility with actual

testing results. Due to the unavailability of empirical testing to accurately measure

active drag throughout an underwater kick cycle, the model was validated using steady-

state tests. Repeated streamlined glide towing trials showed that the CFD model results

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were within two standard deviations of the mean empirical passive drag for the subject,

thus indicating that CFD predicted results were of sufficient accuracy.

Gardano and Dabnichki (2006) showed close correspondence between the CFD trends

and experimental data measured in a low speed wind tunnel in quasi-static approach

using a three-dimensional model of a swimmer arm.

Vilas-Boas et al. (2008) compared the passive drag values in the two gliding positions

assumed during breaststroke starts and turns, calculated through inverse dynamics based

upon the velocity to time gliding curve and the swimmers’ inertia, and similar results

obtained through CFD. Authors found out very similar and coherent results, allowing

them to sustain the validity of the CFD approach.

Although the emergence of very interesting works applying CFD in human swimming,

some limitations still remains. The majority of the digital models have been developed

based on approximate analytical representations of the human structures. In most cases,

the authors used two-dimensional models (Bixler and Schloder, 1996; Silva et al., 2005;

Rouboa et al., 2006; Zaidi et al., 2008) and when the authors used three-dimensional

models, sometimes these were very simple and reductive representations of the human

limbs (Gardano and Dabnichki, 2006; Marinho et al., 2008b). Gardano and Dabnichki

(2006) used standard geometric solids to represent the human arm; while Marinho et al.

(2008b) used a three-dimensional model of the hand and forearm with the fingers

slightly flexed. These differences between digital models and the real human segments

can lead to some misinterpretation of the biomechanical basis of human swimming

propulsion. This fact is one of the causes for the improvement of CFD studies in

swimming, developing the models through engineering procedures (Lyttle and Keys,

2006; Bixler et al., 2007; Lecrivain et al., 2008; Marinho et al., 2008c).

Lyttle and Keys (2006), Bixler et al. (2007) and Lecrivain et al. (2008) applied the so-

called “reverse engineering process” to build a virtual model geometrically identical to

the swimmer body, carrying-out a three-dimensional mapping using a whole body laser

scanner. Marinho et al. (2008c) developed a true three-dimensional model of the human

hand and forearm, through the transformation of computer tomography scans into input

data to apply CFD methodology. In a general way, the reverse engineering process

involves the capture of the point cloud of the real object, editing the point cloud,

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creating the mesh from the point cloud for viewing and editing, creating smooth

surfaces over the mesh, and creating a solid model from the smooth surfaces (Lecrivain

et al., 2008). These studies have shown the great potential offered by reverse

engineering procedures for developing true digital models of the human body to

improve the prediction of hydrodynamic forces in swimming.

5.2. Segmental propulsion

5.2.1. Variation of drag and lift according to angle of attack

As stated by Lyttle and Keys (2006) one major advantage of CFD procedures is the

possibility to assess how the variance of the inputs affects the resultant flow conditions.

Hence, CFD has been used to analyze some concerns arising from empirical data.

One of the major themes is related to the relative importance of drag and lift forces to

the overall propulsive force production in swimming. Several studies were carried-out

using digital models of the human hand and/or forearm and/or upper arms.

Bixler and Riewald (2002) evaluated the steady flow around a swimmer’s hand and

forearm at various angles of attack (Figures 2) and sweep back angles (Figure 3). The

CFD model was created based upon an adult male’s right forearm and hand with the

forearm fully pronated. Force coefficients measured as a function of angle of attack

showed that forearm drag was essentially constant (CD ≈ 0.65) and forearm lift was

almost zero (Figures 4 and 5). Moreover, hand drag presented the minimum value near

angles of attack of 0º and 180º and the maximum value was obtained near 90º (CD ≈

1.15), when the model is nearly perpendicular to the flow. Hand lift was almost null at

95º and peaked near 60º and 150º (CL ≈ 0.60). Axial coefficients were large for the

forearm at all angles of attack and for the hand near 90º. Thus, Bixler and Riewald

(2002) suggested the employ of three-dimensional lift coefficient incorporating forces

acting along the two axis perpendicular to the flow direction.

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Angle of attack

Figure 2: The angle of attack (Schleihauf, 1979). The arrow represents the direction of the flow.

90º

180º 0º

Figure 3: The sweep back angle (Schleihauf, 1979). The arrows represent the direction of the flow. 270º

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 30 60 90 120 150 180

Hand

Forearm

Hand/Forearm

Dra

g co

effic

ient

Angle of attack (degrees) Figure 4: Drag coefficient vs. angle of attack for the digital model of the hand, forearm and hand/forearm

(Sweep back angle = 0º). Adapted from Bixler and Riewald (2002).

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0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 30 60 90 120 150 180

HandForearm

Hand/Forearm

Lift

coef

ficie

nt


Figure 5: Lift coefficient vs. angle of attack for the digital model of the hand, forearm and hand/forearm

(Sweep back angle = 0º). Adapted from Bixler and Riewald (2002).

5.2.2. Relative contribution of drag and lift to propulsion

The relative contribution of drag and lift forces to overall propulsion is one of the most

discussed issues. It was found that more lift force is generated when the little finger

leads the motion than when the thumb leads (Bixler and Riewald, 2002; Silva et al.,

2008a). Silva et al. (2008a), using a real digital model of a swimmer hand and forearm,

confirmed the supremacy of the drag component. They also revealed an important

contribution of lift force to the overall propulsive force production by the hand/forearm

in swimming phases, when the angle of attack is close to 45º (Figure 6).

The drag coefficient presented higher values than the lift coefficient for all angles of

attack. In fact, the drag coefficient increased with the angle of attack showing the

maximum values with an angle of attack of 90º (CD ≈ 90º) and the minimum values with

an angle of attack of 0º (CD ≈ 0.45). The lift coefficient of the model presented the

maximum values with an angle of 45º (CL ≈ 0.50). Silva et al. (2008a) obtained values

of lift coefficient very similar for the angles of attack of 0º and 90º, although the

minimum values were obtained with an angle of attack of 90º (CL ≈ 0.15). In this study

the hand and forearm force coefficients were not analyzed independently but a

combined analysis was performed (Figure 7).

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0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 45 90

CD SA = 0 º

CD SA = 180 º

CL SA = 0 º

CL SA = 180 º

Dra

g an

d lif

t coe

ffic

ient


Figure 6: Drag and lift coefficient of the hand/forearm model for angles of attack of 0º, 45º and 90º (SA:

Sweep back angle). Flow velocity = 2.0 m/s. Adapted from Silva et al. (2008a).

Figure 7: The hand and forearm model used by Silva et al. (2008a) inside the three-dimensional CFD

domain.

Sato and Hito (2002) aimed to estimate thrust of a swimmer’s hand and to explore ways

to increase it. The computed drag and lift coefficients at each angle of attack showed

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values of drag coefficient higher than lift coefficient at all angles of attack. From the

results of CFD simulations the authors turned out that the resultant force was maximal

with an angle of attack of 105º and the direction of the resultant force in that situation

was -13º. Based on this analysis, the authors suggested stroke backward and with a

little-finger-ward, out sweep motion, as the best stroke motion to produce the maximum

thrust during underwater path.

5.2.3. Studies with unsteady flows

The studies above mentioned were conducted using steady state CFD analysis. Aiming

to approach to more similar real swimming conditions, some authors (Bixler and

Riewald, 2002; Sato and Hino, 2003; Rouboa et al., 2006) stated the contribution of

including the unsteady effects of motion into the numerical simulations.

The pioneer study of Bixler and Schloder (1996) was conducted both in steady and

unsteady state flow conditions. These authors analyzed the flow around a disc with a

similar area of a swimmer hand. Different simulations with different initial velocity and

acceleration were conducted to model identical real swimming conditions, especially

during insweep and upsweep phases of the front crawl stroke. According to the obtain

results the authors reported that the hand acceleration can increase the propulsive force

by around 24% compared with the steady flow condition. Thus, the drag and lift forces

produced by the swimmers’ hand in a determined time are dependent not only on the

surface area, the shape and the velocity of the segment but also on the acceleration of

the propulsive segment.

Sato and Hino (2003) showed a numerical method of unsteady CFD simulation to

predict swimmer’s propulsive force. The results of the simulations agreed well with the

data measured experimentally. The hydrodynamic forces acting on the accelerating

hand was much higher than with a steady flow situation and these forces amplifies as

acceleration increase.

Rouboa et al. (2006) analyzed the effect of swimmer’s hand/forearm acceleration on

propulsive forces generation using CFD. A two-dimensional model of a right male

hand/forearm was studied with angles of attack of 0º, 90º and 180º. The main results

reported that under the steady flow condition the drag coefficient was the one that

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contributes more for propulsion with a maximum of 1.16, when the orientation of the

hand/forearm is plane and the model is perpendicular to the direction of the flow. Under

the hand/forearm acceleration condition, the measured values for propulsive forces were

approximately 22.5% higher than the forces produced under the steady flow condition

(Figure 8).

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

0.50 1.50 2.50

0 º Steady 0 º Accelerated

90 º Steady 90 º Accelerated180 º Steady 180 º Accelerated

Dra

g an

d lif

t coe

ffic

ient

Velocity (m/s)

Figure 8: Comparison between steady and accelerated drag and lift coefficients for angles of attack of 0º,

90º and 180º (Sweep back angle = 0º). Adapted from Rouboa et al. (2006).

Analyzing this data, one is tempted to suggest that coaches must advise their swimmers

to accelerate their hands during the propulsive movement. However, one should be

careful with the practical considerations of this conclusion. There are factors other than

instantaneous force to be considered. For instance, Rouboa et al. (2006) referred that the

gain produced by increase in force magnitude is offset by a decrease in duration of force

application. Thus, in the future it could be interesting to calculate the impulse and to

compare a lower force applied for longer time to a higher force applied for shorter time.

These studies confirm that unsteady mechanisms are present in swimming propulsion.

However, both Sato and Hino (2003) and Rouboa et al. (2006) did not consider

direction changes or acceleration in directions other than the hand/forearm velocity

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direction. Swimmers do not move their hands and arms in a steady velocity or linear

direction. The swimmer’s hand/forearm motion is a combination of movements in

horizontal (forward-backward), lateral (inward-outward) and vertical (upward-

downward) directions. Therefore, it seems essential to include other aspects of unsteady

motions, namely the multi-axis rotations, with the rotation of the mesh relative to the

flow. Regarding this issue, Lecrivain et al. (2008) used unsteady CFD procedures to

analyze the performance of a lower arm amputee swimmer.

5.2.4. Contribution of arm’s action to propulsion

Lecrivain et al. (2008) used a complex CFD mesh model, representing the swimmer

body and its upper arm. The model, including the arm rotation relative to the body and a

body roll movement relative to the water, interacted dynamically with the fluid flow.

The unsteady evolution of the interaction was achieved through dynamic

moving/deforming meshes for the particular body parts which have a relative motion

with full computation of the interaction carried out at each successive time step. In

further research, the authors intend to analyze the effect of different arm rotations and

body roll movements in the arm propulsive force production. Lecrivain et al. (2008)

were also able to note that the arm provided effective propulsion through most of the

stroke, and this must be considered when studying the arm propulsion. In fact, Gardano

and Dabnichki (2006) underlined the importance of the analysis of the entire arm rather

than different parts of it. Thus, the authors concluded that drag profiles differed

substantially with the elbow flexion angle, as the maximum value could vary by as

much as 40%. In addition, Gardano and Dabnichki (2006) stated that maximum drag

force was achieved by 160º of elbow angle. A prolonged plateau between 50º and 140º

indicated greater momentum generated at 160º in comparison with the other

configurations. This fact suggests a strong possibility for the existence of an optimal

elbow angle for the generation of a maximum propulsive force. However, these findings

are only possible to confirm if an entire model of the swimmer’s arm, its movement

relative to the body and the body’s movement relative to the water is computed with

CFD. This concern seems an interesting topic to address in further studies.

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5.2.5. Contribution of leg’s action and kicking to propulsion

The majority of the CFD studies regarding swimming propulsion are based on arm

analyses, since this is the most relevant segment producing propulsion. Nevertheless,

kicking has a lower but also relevant role in overall propulsion. So, it is important to

describe a pioneer study about the propulsion generated during underwater dolphin

kicking.

Based on video images of an elite swimmer, Lyttle and Keys (2006) performed a three-

dimensional CFD analysis, modelling the swimmer performing two kinds of underwater

dolphin kick: (i) high amplitude and low frequency dolphin kick and; (ii) low amplitude

and high frequency dolphin kick. This model included the addition of user defined

functions and re-meshing to provide limb movement. The results demonstrated an

advantage of using the large slow kick, over the small fast kick, concerning the velocity

range that underwater dolphin kicks are used. In addition, changes were also made into

the input kinematics (ankle plantar flexion angle) to demonstrate the practical

applicability of the CFD model. While the swimmer was gliding at 2.18 m/s, a 10º

increase in ankle plantar flexion created greater propulsive force during the kick cycle.

These results demonstrated that increasing angle flexibility will increase the stroke

efficiency for the subject that was modelled.

Even if most of propulsion (85 to 90%) is generated by the arm’s actions in front crawl

(Hollander et al., 1988; Deschodt, 1999) leg’s propulsion should not be disregarded. In

this sense, CFD massive studies about kicking action should also be implemented.

5.2.6. Finger’s positions

Understanding the basis of the propulsive force production can play an important role in

the swimmers’ technical training and performance. So, CFD can supply information to

coaches on technique prescription, providing answers to some practical issues that

remain unclear. The finger’s relative position during the underwater path of the stroke

cycle is one of these cases. A large inter-subject range of fingers relative position can be

observed during training and competition, regarding thumb position and finger

spreading. Concerning thumb position, some swimmers maintain the thumb adducted,

others have small thumb abduction, and others have the thumb totally abducted.

117

Concerning finger spreading, some swimmers maintain the fingers close together,

others have small distance between fingers, and others present a large distance between

fingers.

Marinho et al. (2008d) analyzed the hydrodynamic characteristics of a true model of a

swimmer hand with the thumb in different positions using CFD. The authors analyzed

angles of attack of 0º, 45º and 90º with a sweep back angle of 0º (the thumb as the

leading edge). These authors showed that the position with the thumb adducted

presented slightly higher values of drag coefficient compared with thumb abducted

positions. Further, the position with the thumb fully abducted allowed increasing the lift

coefficient of the hand at angles of attack of 0º and 45º (Figures 9 and 10).

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1.10

0 45

Dra

g co

effic

ient

90

Thumb abducted



Figure 9: Drag coefficient for angles of attack of 0º, 45º and 90º for the different thumb positions (Sweep

back angle = 0º, Flow velocity = 2.0 m/s). Adapted from Marinho et al. (2008d).

118

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0 45

Lift

coef

ficie

nt

90

Thumb abducted



Figure 10: Lift coefficient for angles of attack of 0º, 45º and 90º for the different thumb positions (Sweep

back angle = 0º, Flow velocity = 2.0 m/s). Adapted from Marinho et al. (2008d).

These findings seemed similar to the ones found by Schleihauf (1979) with

experimental research. In the study of Schleihauf (1979) the position with the thumb

fully abducted showed a maximum lift coefficient at an acute angle of attack of 15º,

whereas the models with partial thumb abduction showed a maximum value of lift

coefficient at higher angles of attack (45º-60º). In these orientations, the position with

the thumb partially abducted presented higher values than with the thumb fully

abducted. Moreover, Takagi et al. (2001) using experimental measurements revealed

that the thumb position influenced the lift force. For a sweep back angle of 0º (as used

in the study of Marinho et al., 2008d) the model with abducted thumb presented higher

values of lift force, whereas for a sweep back angle of 180º (the little finger as the

leading edge), the adducted thumb model presented higher values of lift force. In

addition, the drag coefficient presented similar values in the two thumb positions for a

sweep back angle of 0º and higher values in the thumb adducted position for a sweep

back angle of 180º. Although some differences in the results of different studies, CFD

data seemed to indicate that when the thumb leads the motion (sweep back angle of 0º)

a hand position with the thumb abducted would be preferable to an adducted thumb

119

position. In addition, when analyzing the resultant force coefficient, Marinho et al.

(2008d) found that the position with the thumb abducted presented higher values than

the positions with the thumb partially abducted and adducted at angles of attack of 0º

and 45º. At an angle of attack of 90º, the position with the thumb adducted presented the

highest value of resultant force coefficient.

Marinho et al. (2008e) aimed to study the effect of finger spread on the propulsive force

production in swimming using CFD. The authors studied the hand with different finger

spreads: fingers close together, fingers with little distance spread (a mean intra finger

distance of 0.32 cm, tip to tip), and fingers with large distance spread (0.64 cm, tip to

tip), similar to the procedure used by Schleihauf (1979). Marinho et al. (2008e) found

that for attack angles higher than 30º, the model with little distance between fingers

presented higher values of drag coefficient when compared with the models with fingers

closed and with large finger spread. For attack angles of 0º, 15º and 30º, the values of

drag coefficient were very similar in the three models of the swimmer’s hand. In

addition, the lift coefficient seemed to be independent of the finger spreading,

presenting little differences between the three models (Figures 11 and 12). Nevertheless,

Marinho et al. (2008e) were able to note slightly lower values of lift coefficient for the

position with larger distance between fingers. These results suggested that fingers

slightly spread can be used by swimmers to create more propulsive force.

0.10

0.30

0.50

0.70

0.90

1.10

0 15 30 45 60 75 90

Large distancespreadLittle distancespreadFingers closetogether

Dra

g co

effic

ient


Figure 11: Drag coefficient for angles of attack of 0º, 15º, 30º, 45º, 60º, 75º and 90º for the different finger

spread positions (Sweep back angle = 0º, Flow velocity = 2.0 m/s). Adapted from Marinho et al. (2008e).

120

0.10

0.20

0.30

0.40

0.50

0.60

0 15 30 45 60 75 90

Large distancespreadLittle distancespreadFingers closetogether

Lift

coef

ficie

nt


Figure 12: Lift coefficient for angles of attack of 0º, 15º, 30º, 45º, 60º, 75º and 90º for the different finger

spread positions (Sweep back angle = 0º, Flow velocity = 2.0 m/s). Adapted from Marinho et al. (2008e).

However, one should be careful transferring these findings to swimming, because the

above mentioned studies were conducted only under steady state flow conditions. It is

interesting to know if the results would be similar if unsteady conditions were included

during the numerical simulations.

5.3. Drag

In addition to the analysis of the propulsive forces generation, CFD methodology can be

used to understand the intensity of drag forces resisting forward motion and its effects

over swimming performance (Lyttle and Keys, 2006; Bixler et al., 2007; Marinho et al.,

2008a; Silva et al., 2008b; Zaidi et al., 2008).

5.3.1. Kicking after start and turn

Lyttle and Keys (2006) sought to discriminate between active drag and propulsion

produced in underwater dolphin kicking aiming to optimize the underwater phase in

121

swim starts and turns. As mentioned before, using a three-dimensional model of a male

swimmer performing two types of dolphin kicking movements (large/slow, small/fast),

the authors found that both kick techniques have a similar effect at 2.40 m/s. It seemed

that for velocities higher than 2.40 m/s there is a trend for the small kick to become

more effective whereas for velocities lower than 2.40 m/s the large kick appeared to be

more effective (Figure 13).

20.0

40.0

60.0

80.0

100.0

120.0

1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20 2.30 2.40

Large/Slow kick

Small/Fast kick

Mom

entu

m re

duct

ion

(Ns)

Velocity (m/s)

Figure 13: Momentum reduction in an average second of two types of kicking movements (large/slow vs.

small/fast). Adapted from Lyttle and Keys (2006).

Lyttle and Keys (2006) compared the dynamic underwater kicking data with the results

of experimental studies (Lyttle et al., 2000), and suggested that velocities around 2.40

m/s represent a cross-over point, whereby at higher velocities it seemed more efficient

to the swimmer to maintain a streamlined position than to initiate underwater kicking.

The authors stated that this situation is due to the swimmer creating more active drag

than propulsion while kicking compared to remaining in a streamlined position, thus

leading to a negative acceleration of the swimmer. Although it appeared that the

swimmer would benefit from a smaller kick at higher velocities, it seemed better to

maintain a streamlined position.

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5.3.2. Gliding positions

Regarding the analysis of the underwater gliding in swimming, Marinho et al. (2008a)

investigated two common gliding positions: a ventral position with the arms placed

alongside the trunk, and a ventral position with the arms extended at the front with the

shoulders fully flexed (Figures 14 and 15). A three-dimensional model of a male adult

swimmer was used and the simulations were applied to flow velocities between 1.60

and 2.00 m/s.

Figure 14: The model used by Marinho et al. (2008a) in a ventral position with the arms alongside the

trunk inside the CFD domain.

Figure 15: The model used by Marinho et al. (2008a) in a ventral position with the arms extended at the

front, with the shoulders fully flexed, inside the CFD domain.

123

The gliding position with the arms extended at the front, with the shoulders flexed,

presented lower drag coefficient (CD ≈ 0.4) values than the position with the arms

placed along the trunk (CD ≈ 0.7). Regarding the position with the arms extended at the

front of the swimmer with the shoulders flexed, the values are very similar to the ones

found by Bixler et al. (2007), using a CFD approach, as well, and to the ones found by

Vilas-Boas et al. (2008), through experimental inverse dynamics. Considering the

breaststroke turn, Marinho et al. (2008a) suggested that the first gliding, performed with

the arms at the front, should be emphasized in relation to the second gliding, performed

with the arms along the trunk.

Zaidi et al. (2008) numerically analyzed the effect of the position of the swimmer’s

head on the underwater hydrodynamics performances in swimming. The obtained

numerical results revealed that the position of the head had a noticeable effect on the

hydrodynamic performances, strongly modifying the wake around the swimmer. The

position with the head aligned with the body seemed to allow the swimmer to carry out

the best water penetration during the underwater swimming phases, comparing with a

lower and a higher head position. The head aligned with the axis of the body induces a

decrease in the drag from 17% to 21%, for a range velocity from 2.20 m/s to 3.10 m/s.

For lower velocities (i.e., 1.40 m/s), the drag is only slightly affected by the change in

the head position. However, it should be kept in mind that Zaidi et al. (2008) used a

two-dimensional steady flow model to simulate a really unsteady three-dimensional

flow.

5.3.3. Drafting

Silva et al. (2008b) aimed to investigate the effect of drafting on the hydrodynamic

drag, using a two-dimensional model. The purpose of this study was to determine the

effect of drafting distance on the drag coefficient in swimming. Numerical simulations

were conducted for various distances between swimmers (0.5–8.0 m) and swimming

velocities (1.6–2.0 m/s) and the drag coefficient was computed for each one of the

distances and velocities (Figure 16).

124

Figure 16: Two-dimensional model used by Silva et al. (2008b) to determine the effect of drafting

distances on hydrodynamic drag.

Silva et al. (2008b) found that the relative drag coefficient of the trailing swimmer was

lower (about 56% of the leading swimmer) for the smallest inter-swimmer distance (0.5

m). This value increased progressively until the distance between swimmers reached 6.0

m, where the relative drag coefficient of the trailing swimmer was about 84% of the

leading swimmer. The results indicated that the drag coefficient of the trailing swimmer

was equal to that of the leading swimmer at distances ranging from 6.45 to 8.90 m. The

authors concluded that these distances allow the swimmers to be in the same

hydrodynamic conditions during training and competitions. As a suggestion to specific

swimming training sets, Silva et al. (2008b) stated that a swimmer must start swimming

at least when the leading swimmer reaches a 10 m distance from the starting wall, rather

than the 5 m distance commonly used in training. Nevertheless, concerning open water

competitions, the athletes could take important advantages of swimming in a drafting

situation. However, these conclusions must be read carefully because this study was

conducted using a two-dimensional model of the human body and only the passive drag

was computed. Moreover, the simulations were applied with the swimmers under the

water and not swimming at the water surface. Therefore, as suggested by the authors,

further researches should apply the modelling of bodies on/at the water surface, taking

into account the above and underwater body volumes and fluid characteristics.

125

5.3.4. Relative contribution of drag components to total drag

In addition to the analysis of the hydrodynamic drag under different body positions,

some authors attempted to investigate the contribution of skin-friction drag, pressure

drag and wave drag to the total drag (Bixler et al., 2007; Marinho et al., 2008a; Zaidi et

al., 2008). In human swimming, the total drag is composed of the skin-friction drag,

pressure drag and wave drag. Skin-friction drag is attributed to the forces tending to

slow the water flowing along the body surface of the swimmer. It depends on the

velocity of the flow, the surface area of the body and the characteristics of the surface.

Pressure drag is caused by the pressure differential between the front and the rear of the

swimmer and it is proportional to the square of swimming velocity, the density of water

and the cross sectional are of the swimmer. Finally, swimming at the water surface is

constrained by the formation of surface waves leading to wave drag. However, the three

mentioned studies only considered hydrodynamic drag depending on the skin-friction

drag and pressure drag since the model was placed underwater. In the study of Bixler et

al. (2007) the swimmer model was placed at a water depth of 0.75 m. In the study of

Zaidi et al. (2008) the swimmer was positioned 1.50 m below the water surface while

Marinho et al. (2008a) used a swimmer model placed at a water depth of 0.90 m. This

assumption was proven to be correct using experimental tests (Lyttle et al., 1999;

Vennell et al., 2006). Lyttle et al. (1999) concluded that there is no significant wave

drag when a typical adult swimmer is at least 0.60 m under the water’s surface. More

recently, Vennell et al. (2006) found that at 0.75 m below the water surface was below

the location where “surface effects” begin to influence significantly the drag force.

Indeed, the authors showed that to avoid significant wave drag a swimmer must be

deeper than 1.8 chest depths and 2.8 chest depths below the water surface for velocities

of 0.9 and 2.0 m/s, respectively. It seems interesting attempting to conduct similar

studies with a CFD approach, requiring the simulation of the interface between air and

water.

Bixler et al. (2007) showed that pressure drag represented around 75% of the total

hydrodynamic drag. Although pressure drag was dominant, skin-friction drag was by no

means insignificant, representing 27% and 25% of total drag for gliding velocities of

1.50 and 2.25 m/s, respectively. The significantly higher percentage of pressure drag

was as well found by Marinho et al. (2008a) and Zaidi et al. (2008). Zaidi et al. (2008)

126

found for the position with the head aligned with the body that pressure drag

represented around 80% of the total drag whereas Marinho et al. (2008a) found a

percentage of around 87% and 92% for this drag component in the position with the

arms extended at the front with the shoulders flexed, and in the position with the arms

along the trunk, respectively (Figure 17). However, the absolute values of skin-friction

drag were about the same in the two gliding positions, being the main differences

attributable mainly to the pressure drag component. It is important to reinforce that

these values for the drag components were computed for underwater gliding. If the

model were at the water’s surface these percentages would be somewhat different due to

the decreasing in wetted area and the generation of wave drag.

0.00

0.20

0.40

0.60

0.80

1.00

1.60 1.80 2.00

AAT Total CD AEF Total CD

AAT Skin-friction CD AEF Skin-friction CD

AAT Pressure drag CD AEF Pressure drag CD

Dra

g co

effic

ient

Velocity (m/s)

Figure 17: Relationship between total drag, skin-friction drag and pressure drag and the gliding velocity

for the positions with the arms alongside the trunk (AAT) and with the arms extended at the front with the

shoulders flexed (AEF). Adapted from Marinho et al. (2008a).

Moreover, both Bixler et al. (2007) and Marinho et al. (2008a) studies were based on

the swimmer model’s surface having a zero roughness. Therefore, the development of

roughness parameters for human skin would allow a more accurate CFD model to be

built in further studies. It seems possible that if the surface roughness were increased in

the models the skin-friction drag would probably be higher, due to increased turbulence

127

around the surface (Bixler et al., 2007). On the other hand, if the surface roughness were

increased the pressure drag could be reduced. Massey (1989) stated that the boundary

layer, which would be mainly laminar, would change into a turbulent one. When the

flow is laminar, separation of the boundary layer at the body surface starts almost as

soon as the pressure gradient becomes adverse, and a larger wake forms. However,

when the flow is turbulent, separation is delayed and the corresponding wake is smaller,

thus decreasing pressure drag (Polidori et al., 2006; Marinho et al., 2008a).

5.3.5. Swimsuits and training equipments

The study of the effects of different swimsuits on the hydrodynamic drag was one of the

first applications of CFD in swimming (Fluent, 2004). As stated in the introduction

section, the cooperation between Speedo® and Fluent® allowed developing some well-

known swimsuits, as FastSkin® and LZR® suits. However, Speedo® is not the only

manufacture using numerical solutions to enhance the swimsuits. Arena® in straight

cooperation with the Mox Institute at Politecnico de Milano (Milan, Italy) developed

mathematical models and simulations to measure the water flow around the swimmer

using the PowerSkin® new generation swimsuits. With CFD methodology it is possible

to analyze the velocity and the direction of the water flow around the body, thus

allowing evaluating the different paths due to different suit tissues and body

compressive effects. However, the major research conducted in this field is performed

with great secrets. To our knowledge, there is no study published about this issue.

Therefore, new lines of research concerning the effects of different swimsuits on

performance should be attempted in the future. For instance, it seems important to

evaluate the use of different suit tissues, different ways to sew the tissue pieces,

different suit types and sizes, and the effect of swim suits upon wobbling body masses,

and full body (and body parts) compression during different swimming phases.

Based on these assumptions, it seems CFD can also be an interesting tool to help

developing training equipments. For example, different paddles, fins, kickboards, pull-

buoys, cups, swim goggles and training aids used by the swimmers can be evaluated

using numerical simulation techniques. The effect of different lane lines in the

swimmer’s performance can also be analysed with a CFD approach.

128

6. CFD methods contribution for near future development of swimming science

As one can note, CFD can be a good approach to study swimming hydrodynamics and

can contribute to the development of swimming science. However, despite the

important steps forward in the application of CFD in swimming, there are several

aspects that can be improved.

The concern of Gardano and Dabnichki (2006) and Lecrivain et al. (2008) of taking into

account the entire arm when studying the arm propulsion should be considered. In

addition, the effect of whole body movements on the arm propulsive force production

must also be attempted in the future. Moreover, the analysis of hydrodynamic forces

must be conducted with the body at the water surface, taking into account the interface

between air and water. This fact will require the simulation of two different fluids

around the swimmer body, allowing including wave drag in the evaluations. The

modelling of whole body swimming movements seems to be the next step in swimming

research applying CFD methodology.

Furthermore, the development of roughness parameters for human skin would allow a

more accurate CFD model to be built in future studies, to more accurately understand

the relative contribution of skin-friction drag to the total hydrodynamic drag. As stated

by Bixler et al. (2007), as CFD methods continue to develop, it will be possible to

evaluate the effects of different techniques, body positions, and swimwear on

performance, thus optimizing swimmers’ performance.

Therefore, with these assumptions we can state some ideas and some purposes for other

studies following and complementing the ones we have presented during this chapter:

1. Propulsive forces studies:

(i) The computation of the ideal shape for a swimmers hand, arm, foot, or other body

segment;

(ii) The computation of the effects of acceleration (positive and negative), and multi-

axis rotations on lift and drag;

129

(iii) The computation of the added mass of water as an inertial effect to the body

displacement during the stroke cycle;

(iv) The computation of the effect of different stroke patterns on propulsion in front

crawl, backstroke, butterfly and breaststroke.

2. Drag forces studies:

(i) The computation of total drag force on a swimmer moving through the water, and the

relative contribution of pressure drag, skin-friction drag and wave production drag for

the total drag;

(ii) The effect of different forms of streamlining on the hydrodynamic drag;

(iii) The computation of the effect of underwater turbulence and waves on a swimmers

motion;

(iv) The effect on hydrodynamic drag of “dragging” off a swimmer, either in an

adjacent lane and/or behind;

(v) The evaluation of the effects of different swimming suits and other equipments on

hydrodynamic drag;

(vi) The computations of the ideal body shape and size to minimise drag;

(vii) Eventually, to calculate active drag, using moving meshes would be an important

task.

7. Conclusion

In summary we can state that the recent evidence strongly suggests that CFD technique

can be considered as an interesting new approach for evaluation of swimming

hydrodynamic forces. In the near future, as in the present, CFD will provide valorous

arguments for defining new swimming techniques or equipments.

Therefore, within this chapter we attempted to present the already applied CFD

techniques and to propose new procedures that may be used by the research community

130

in further studies under similar research topics in order to improve swimming

performance.

On the other hand, we tried to make some contribution to the dissemination of the main

results, not only stimulating young researchers in the fulfilment of the existent gap

between the sports sciences and other sciences (hydrodynamics in the present case) but

also to the spreading of the use of this recent technique (in sports context) by the ones

that are really interested in the development of new concepts and applications.

We also aimed to contribute to the application of the knowledge gathered into practical

situations, trying to introduce some new insights in the designing of new propulsive

techniques in swimming, new ways of streamlining the body during the displacement or

even the development of new materials (suits and others) helping the swimmer moving

faster.

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135

Main conclusions

136

Main conclusions

The main aim of the present thesis was to study the mechanism of swimming propulsion

using CFD through a three-dimensional analysis of the swimmer’s hand and forearm.

Hence, the main purpose of our first studies was to be able to apply the numerical

simulation techniques using a three-dimensional model of the swimmer body. After the

propulsive force measurements using a true three-dimensional model of a human

segment have been demonstrated, it was possible to improve previous CFD analysis,

including a more realistic model of the swimmer hand and forearm. Additionally, the

CFD methodology was applied to address some practical concerns of swimmers and

coaches, such as the finger’s relative position during the underwater path of the stroke

cycle.

Nevertheless, there are several further CFD procedures that must be accomplished to

understand deeply the generation of propulsive force in swimming. The applied

numerical simulations were still only an approximation to actually model a swimmer’s

arm. As stated during this thesis, one should note that the simulation of water flow

conditions around the hand and forearm when treated as one segment do not illustrate

the complexity of propulsion generating process. Moreover, the CFD analyses were

carried-out under steady flow conditions. One should be aware that these conditions do

not truly represent the swimmer’s movements. Therefore, further research should

consider the movement at the wrist, elbow, and shoulder joints and the aspects of

unsteady motion, such as accelerations and multi-axis rotations of the propelling

segments, must be added to the modelling of the arm propulsion. However, taking into

account the above considerations, we can state the main conclusions of the present

thesis:

1. The drag coefficient was the main responsible for the hand and forearm propulsion,

with a maximum value of force corresponding to an angle of attack of 90º.

2. An important contribution of the lift force to the overall force generation by the

hand/forearm in swimming phases was observed with angles of attack of 30º, 45º and

60º, especially when the little finger leads the motion.

137

3. The hand model with the thumb adducted presented higher values of drag coefficient

compared with thumb abducted models. The model with the thumb fully abducted

allowed increasing the lift coefficient of the hand at angles of attack of 0º and 45º.

4. The resultant force coefficient showed that the hand model with the thumb fully

abducted presented higher values than the positions with the thumb partially abducted

and adducted at angles of attack of 0º and 45º. At an angle of attack of 90º, the model

with the thumb adducted presented the highest value of resultant force coefficient.

5. The hand model with little distance between fingers presented higher values of drag

coefficient than the models with fingers closed and fingers with large distance spread.

The values for the lift coefficient presented little differences between the models with

different finger’s spreading.

6. The results suggested that for hand positions in which the lift force can play an

important role, the abduction of the thumb may be better, whereas at higher angles of

attack, in which the drag force is dominant, the adduction of the thumb may be

preferable. Furthermore, it is suggested that fingers slightly spread could allow the hand

to create more force during swimming.

138

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139

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1350-1358.

Study 1


The hydrodynamic drag during the gliding in swimming. Journal of Applied Biomechanics (in

press).

Study 2




Study 3




Study 4

Marinho, D.A., Vilas-Boas, J.P., Alves, F.B., Machado, L., Barbosa, T.M., Reis, V.M., Rouboa, A.I.,

Silva, A.J. (2008). Computational analysis of the hand and forearm propulsion in swimming.

International Journal of Sports Medicine (under revision).

Study 5




Study 6


Silva, A.J., Rouboa, A.I. (2008). Swimming propulsion forces are enhanced by a small finger


146

Review


(2009). Swimming simulation: a new tool for swimming research and practical applications. In: M.

Peters (Ed.), Lecture Notes in Computational Science and Engineering – CFD and Sport Sciences.

Berlin: Springer (in press).

147

Appendix

CXLVIII

Appendix

Letters of acceptance of the in press papers:

Study 1


The hydrodynamic drag during the gliding in swimming. Journal of Applied Biomechanics (in

press).

Study 2




Study 3




Study 5




Review


(2009). Swimming simulation: a new tool for swimming research and practical applications. In: M.

Peters (Ed.), Lecture Notes in Computational Science and Engineering – CFD and Sport Sciences.

Berlin: Springer (in press).

CXLIX

Date: Wed, 31 Aug 2008 16:43:10 -0400 (EDT)

From: [email protected]

Reply-To: [email protected]

Subject: Journal of Applied Biomechanics - Decision on Manuscript ID JAB-2007-

0223.R1

To: [email protected], [email protected], [email protected]

Cc: [email protected]

31-Aug-2008

Dear Prof.:

It is a pleasure to accept your manuscript entitled "The hydrodynamic drag during the

gliding in swimming" in its current form for publication in the Journal of Applied

Biomechanics.

Manuscripts are published in the order of acceptance, so please await further

instructions from our managing editor, Mr. Leon Jeter. He will contact you when the

time approaches for final preparation of your article.

Thank you for your fine contribution. On behalf of the Editors of the Journal of

Applied Biomechanics, we look forward to your continued contributions to the Journal.

Sincerely,

Prof. Thomas Buchanan

Editor-in-Chief, Journal of Applied Biomechanics

[email protected]

João Manuel R. S. Tavares <[email protected]> Thu, Dec 20, 2007 at 7:12 PM

To: Daniel Marinho <[email protected]>

Cc: [email protected]

Dear Daniel Marinho,

The review procedure of your manuscript (IJCV&B_12_11_07) entitled “The use of

Computational Fluid Dynamics in swimming research” has been completed.

The referees have recommended its publication. Some minor revisions are suggested

and I would be glad if you would consider them for the final version of your

manuscript.

Please review the attached documents listing the requirements for your revision.

Please note that the final version of your manuscript should be send to us in a pdf file

and also in an editable file (like Microsoft Word or latex file – including all necessary

sources files).

If you have any question, please do not hesitate to contact me.

Thank you very much for your interest in IJCV&B.

Kind regards,

João Tavares

Remetente: "DEXT BABT" <[email protected]>

Data: 27/10/2008 11:45

Assunto: Brazilian Archives of Biology and Technology

Para: [email protected]

Of.0727/08 - BABT

Brazilian Archives of Biology and Technology

Curitiba, October 17th, 2008

Dear Author,

We inform that your article: "Design of a three-dimensional hand/forearm model to

apply Computational Fluid Dynamics", after been submitted to judgment, it was

aproved, however with some comments.

We would like to remind you that the copy to be sent must be in accordance with the

norms for publication (http://www.tecpar.br), you can consult the latest volumes of the

Brazilian Archives of Biology and Technology. We request the devolution of your work

be in the maximum of 20 (twenty) days period.

Yours truly,

Prof. Dr. Carlos Ricardo Soccol

Editor

JOURNAL OF SPORTS SCIENCE & MEDICINE ELECTRONIC JOURNAL (ISSN 1303-2968)

http://www.jssm.org

EDITORIAL OFFICE Hakan Gür, MD, PhD, Journal of Sports Science and Medicine,

Department of Sports Medicine, Medical Faculty of Uludag University, 16059 Bursa, Turkey Phone: +90 (532) 326 82 26 Fax: +90 (224) 442 87 27 E-mail: [email protected]

December 04, 2008 Daniel A. Marinho Universidade da Beira Interior, Departamento de Ciências do Desporto. Rua Marquês d'Ávila e Bolama. 6201-001 Covilhã, Portugal Manuscript: #1036-2008/JSSM TITLE: “HYDRODYNAMIC ANALYSIS OF DIFFERENT THUMB POSITIONS IN SWIMMING” Dear Dr. Marinho, I am glad to inform you that your revised manuscript is accepted for publication in the Journal of Sports Science and Medicine and it will be published in March 2009 issue of JSSM. The manuscript will now be edited for style and format. Please do not hesitate to contact me if you have any questions. Thank you for giving the JSSM the opportunity to publish your work Sincerely, Hakan Gür, MD, PhD Editor-in-Chief

Editor-in-Chief Hakan Gür, TUR Associate Editors-in-Chief Mustafa Atalay, FIN Andrew Lane, UK Roger Ramsbottom, UK Section Editors Aging Michael E. Rogers, USA Children and Exercise Craig A. Williams, UK Computer, Mathematics and Statistics in Sports John Hammond, AU Laboratory Techniques in Exercise Physiology Itzik Weinstein, ISR Metabolism/Endocrinology Allan H.Goldfarb, USA Molecular aspects Mustafa Atalay, FIN Resistance/Strength Training Nicholas A. Ratamess, USA Testing, Performance Roger Ramsbottom, UK Psychology Andrew Lane, UK Respiration J. Richard Coast, USA Sport Supplementation and Drug R. Jay Hoffman, USA Sports Traumatology Nicola Maffulli, UK Combat Sports Special Edition Editors Andrew Lane, UK Marcus Smith, UK Editorial Board Tiago Barbosa, POR Cem S. Bediz, TUR Lee E. Brown, USA Wojtek J.Chodzko-Zajko, USA Jole T. Cramer, USA M.Nedim Doral, TUR Emin Ergen, TUR James Paul Finn, AU Peter Hofmann, AUS Frank I. Katch, USA Justin Keogh, NZ Sadi Kurdak, TUR Erdem Kasikcioglu, TUR Eleftherios Kellis, GRE William J. Kraemer, USA Max J. Kurz, USA Willem van Mechelen, NL Erich Müller, AUS Ken Noakas, AU Tim Noakes, ZA Fadıl Ozyener,TUR Stephane Perrey, FRA Danny M. Pincivero, USA Scott K. Powers, USA Zsolt Radak, HUN Michael Sagiv, ISR Stephen Seiler, NOR Chandan Sen, USA Antonio Spataro, ITA Esma Sürmen-Gür, TUR Peter Tiidus, CAN Kate Webster, AU Darryn S. Willoughby,USA Indexed in SCI Expanded, Focus On: Sports Sci & Med, ISI J Master List, SciSearch, SPORTDiscus, J-Gate, DOAJ, Index Copernicus, SPONET, GEOBASE, EMBASE, EMNursing, ScholarGoogle, Compendex, Scopus

2007 Impact Factor: 0.290

Per-Ludvik Kjendlie <[email protected]> Sun, Sep 14, 2008 at 10:44 PM

To: Daniel Marinho <[email protected]>

Cc: antonio silva <[email protected]>, João Paulo Vilas-Boas <[email protected]>,

[email protected]

Dear Daniel,

I trust that you and Antonio have discussed about the CFD chapter. He proposed you as

the new first author, of whom I believe is an excellent choice. Attached in this mail you

will have the correspondence I have had with the editor of this book. Below is also two

emails (one containing 'guidelines for authors')

Please read it. Please keep it for future needs. Please also respond to the following:

1. Before I write to the editor, I must be sure that you can devote the time needed for

this, and that you agree to be the first author (which you should…). Please bear in mind

that the deadline is 31. December. 08.

2. Please send me your CV (short form) and full contact information. Also the postal

address, I will send you a book as an example of the book-series, there you can see the

lay-out style etc.

Please keep in touch soon. I must contact the editor in a few days.

Best regards

Per-Ludvik

*********************************************

* Per-Ludvik Kjendlie, PhD *

* Associate Professor *

* Department of Physical Performance *

* Norwegian School of Sport Sciences *

* PO box 4014 Ullevaal Stadion *

* N- 0840 OSLO NORWAY *

* Phone +47 2326 2355 / Fax: +47 2223 4220 *

* Cellphone +47 90650249 *

*********************************************

---

Copy of 2 important emails:

-----

email 1. from : Peters, Martin, Springer DE [[email protected]]

Dear Per-Ludvik,

As I mentioned a while ago we are planning to publish a book in the LNCSE series

devoted to CSE topics with applications to sport. We looked through many potential

topics -- everything took longer than expected -- and then it turned out that it makes

sense with the first book of this kind to focus on CFD related topics. This was agreed

with the LNCSE series editors last week. Cf http://www.springer.com/series/3527 for

info on the series and its editors.

You can see a list of the envisaged contributions in the enclosed memo

<<LNCSE_sport_summary_for_authors_11032008.pdf>> . Other topics are sailing,

soccer, Australian football, and ski jumping. For another future book potential topics are

nutrition, metabolism of athletes, biomechanics, other biomedical topics, materials,

other technology-dependent issues.

This brings me now to my question: Would you like, possibly together with scientists of

SINTEF MARINTEK and the Portuguese CFD group mentioned in

http://www.forskning.no/Artikler/2007/desember/1198928487.74 write a contribution

of about 30 pages for the book on your swimming simulation project?

Here are a few additional remarks:

i) It seems to me that teaming up with such an outstanding institute as MARINTEK and

the CFD experts you would be in a very good position to get interesting results, both

from the scientific simulation point-of view and the practical implementation with

swimmers.

ii) You see from the outline of the book that there is another swimming simulation team

in Australia. If you like and think this is useful, you might consider collaborating with

them -- independently of whether this would be reflected in the book contribution.

iii) Here is another option you might like to explore: We have been in touch with Marco

Pilloud, a former professional swimmer, who now has a company in Switzerland for

teaching of swimming. I believe that you could benefit by collaborating with him, since

he could provide very good examples of stroke technique issues which could be good

research problems for your investigations. Have a look at Marco's self-description in the

appendix to this message.

I hope that you like the idea and will join. Swimming simulation is a very challenging

problem, and hence the perfect topic for the planned book. Simultaneously with this

message, I am writing to all authors -- with all of them we have had preliminary

discussion about the book project.

The following info might be useful for you: I shall visit Oslo in April to meet scientists

at SIMULA and the University. I could insert a visit to NIH, too, and this would be

possible in the mornings of either 8th or 9th April.

With best regards,

Martin

Dr Martin Peters

Executive Editor

Mathematics, Computational Science and Engineering

Mathematics Editorial IV

Springer-Verlag

Tiergartenstr. 17

69121 Heidelberg

Germany

Email 2. from editorial assistant at Springer.

Dear Professor Kjendlie,

On request of Dr. Peters I would like to let you know that he would like to suggest

December 31st, 2008, as date of delivery for your contribution to the planned LNCSE

sports volume. The approximate length of your contribution should be 30 pages

(although there is certainly some flexibility).

We would like to take this opportunity to draw your attention to our TEX macro

packages. The easiest way for you to get hold of our TEX macros is to follow the link

"For Authors" at http://www.springer.com and then the link "Author guidelines for book

authors" or to look directly at

http://www.springer.com/authors/book+authors?SGWID=0-154102-12-417900-0

(please make sure to enter the complete URL into your browser field) where you can

find all Springer macro packages. Please pick up the LaTEX 2e macro package

designed for contributed books. Thank you very much in advance.

If you have any additional question, please do not hesitate to get in touch with us again.

Looking forward to hearing from you again,

With kind regards,

Ruth Allewelt

________________________________________

[email protected]

Just click on www.springer.com

for easy and fast access to all Springer publications - and big online savings, too!

Ruth Allewelt

Assistant to Dr. Peters

Mathematics Editorial IV Phone: 06221 487 8409

Springer Fax: 06221 487 68355

Tiergartenstr. 17

69121 Heidelberg

Germany

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