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87

Journal of Applied Biomechanics, 2010, 26, 87-92

© 2010 Human Kinetics, Inc.

Marinho is with the Department of Sport Sciences, University

of Beira Interior, Covilhã, Portugal, and the Centre of Research

in Sports, Health, and Human Development, Vila Real, Portugal.

Barbosa is with the Centre of Research in Sports, Health, and

Human Development, Vila Real, Portugal, and the Polytechnic

Institute of Bragança, Bragança, Portugal. Reis is with the

Centre of Research in Sports, Health, and Human Development,

Vila Real, Portugal, and the University of Trás-os-Montes and

Alto Douro, Vila Real, Portugal. Kjendlie is with the Norwegian

School of Sport Sciences, Oslo, Norway. Alves is with the Fac-

ulty of Human Kinetics, Technical University of Lisbon, Lisbon,

Portugal. Vilas-Boas is with the Faculty of Sport, University of

Porto, Porto, Portugal. Machado is with the Faculty of Sport,

University of Porto, Porto, Portugal. Silva is with the Centre

of Research in Sports, Health, and Human Development, Vila

Real, Portugal, and the University of Trás-os-Montes and Alto

Douro, Vila Real, Portugal. Rouboa is with the University of

Trás-os-Montes and Alto Douro, Vila Real, Portugal, and the

Department of Mechanical Engineering and Applied Mechan-

ics, University of Pennsylvania, Philadelphia, PA.

Technical noTes

Swimming Propulsion Forces Are Enhanced

by a Small Finger Spread

Daniel A. Marinho, Tiago M. Barbosa, Victor M. Reis, Per L. Kjendlie, Francisco B. Alves,

João P. Vilas-Boas, Leandro Machado, António J. Silva, and Abel I. Rouboa

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 involved three models of the hand with differing finger spreads: fingers

closed together (no spread), fingers with a small (0.32 cm) spread, and fingers with large (0.64 cm) spread.

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. For hand models, angles of attack

of 0°, 15°, 30°, 45°, 60°, 75°, and 90°, with a sweep back angle of 0°, were used for the calculations. The

results showed that the model with a small spread between fingers presented higher values of drag coefficient

than did the models with fingers closed and fingers with a large spread. One can note that the drag coefficient

presented the highest values for an attack angle of 90° in the three hand models. The lift coefficient resembled

a sinusoidal curve across the attack angle. The values for the lift coefficient presented few differences among

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.

Keywords: hand shape, numerical simulations, computational fluid dynamics, forces, competitive swimming

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 observa-

tion of a 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 us to analyze the water flow

around the human body, to understand the magnitude of

drag forces resisting forward motion (Silva et al., 2008;

Marinho et al., 2009), and to compute the propulsive

forces produced by the propelling segments (Bixler &

Riewald, 2002; Lecrivain et al., 2008).

Computational fluid dynamics could help coaches,

in the short term, with technique prescription. Moreover,

this methodology could provide answers to some practi-

cal issues that remain controversial. The finger’s relative

position during the underwater path of the stroke cycle is

one of these cases. A large intersubject variety of relative

finger positioning can be observed during training and

competition. Some swimmers (i) maintain the fingers

closed together (not spread apart), (ii) others have a

small distance between fingers, and (iii) still others have

a large distance between fingers. Indeed, the propulsive

repercussions of those three possibilities remain unclear

for swimming coaches and scientists. There is a lack of

research on this issue, and some ideas are passed among

members of the swimming community with little empiri-

cal (experimental or numerical data) support. Experi-

mental data are controversial: for example, Schleihauf

(1979) showed that the fingers closed together and the

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88 Marinho et al.

thumb partially abducted allow higher propulsion and

Berger (1996) concluded that finger spreading does not

influence propulsion. But a more recent paper suggests

that fingers closed together induces less propulsion than

fingers spread (Sidelnik & Young, 2006). To our knowl-

edge, 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 inves-

tigate the effect of finger spread on propulsive force

production in swimming using CFD.

Methods

Three-Dimensional Model

Scanning. To obtain the geometry of the hand, eight

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. A 2-mm-slice thickness with a space

of 1 mm was used. The subject was an Olympics-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 closed

together, fingers with a small spread (an intrafinger

distance of 0.32 cm, from fingertip to fingertip), and

fingers with a large spread (0.64 cm, from fingertip to

fingertip) (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.

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, Saint Kilda, VIC, Australia). This program

allowed us to obtain the boundaries of the human

segments, creating a three-dimensional reconstruction

of the hand. At first, before processing and converting

procedures, the data were prepared by observing the

computer tomography data and erasing the irrelevant parts

of the anatomical model. This step was also conducted

using the software FreeForm (SensAble Technologies,

Woburn, MA, USA). Finally, the data were converted

into an IGES format (*.igs), which could be read by

Gambit/Fluent software (Fluent Inc, Lebanon, NH, 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

Figure 1 — Anthropometric characteristics of the swimmer’s 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, and hand breadth (5): 8.90 cm.

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Propulsion Forces and Finger Spread 89

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 1/2 ρ A v2

(1)

L = CL 1/2 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 the

angles of attack used in this study.

Preprocessing. 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 results by decreasing

the grid node separation in areas of high velocity and

pressure gradients.

Solving Steady Flow. For the calculations, hand model

angles of attack of 0°, 15°, 30°, 45°, 60°, 75°, and 90°,

with a sweep back angle of 0° (thumb as the leading edge)

were used (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). 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 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 28 °C with a density of 998.2 kg·m–3 and a viscosity

of 0.001 kg·(m·s)–1. Incompressible flow was assumed.

The measured forces on the hand models were decom-

posed into drag (CD) and lift (CL) coefficients, using

Equations 1 and 2.

Results

Figures 3 and 4 show the values of CD and CL, respec-

tively, obtained for the hand model with different finger

spreads.

One can note that the CD presented the highest values

for an attack angle of 90° 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 greater than 30°, the model with the

small distance between fingers presented higher values of

CD when compared with the models with fingers closed

and with large finger spread. This last model presented

the lowest values of CD. For attack angles of 0°, 15°,

and 30°, the values of CD were very similar in the three

models of the swimmer’s hand.

The CL resembled a sinusoidal curve across the attack

angle. Maximum values for any hand model occurred

near 30°–45° (CL ≈ 0.60). Furthermore, the CL seemed

to be independent of the finger spreading, thus presenting

little differences among 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 15° to 60°.

Figure 2 — Computational fluid dynamics model geometry with the hand inside the domain (the model with fingers closed).

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90

Figure 3 — Values of CD obtained for the different attack angles and for the different finger spreads. Sweepback angle = 0° and

flow velocity = 2.0 m/s.

Figure 4 — Values of CL obtained for the different attack angles and for the different finger spreads. Sweepback angle = 0° and

flow velocity = 2.0 m/s.

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Propulsion Forces and Finger Spread 91

Discussion

The main aim of this study was to analyze the effect of

finger spread in the swimming propulsive force produc-

tion, 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 differing

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 a small distance between fingers, and another

with a large distance between fingers was based on the

pioneering study of Schleihauf (1979). Despite some

theoretical assumptions and expert opinions (e.g., Coun-

silman, 1968; Colwin, 1992; Maglischo, 2003), there are

few experimental studies to clarify this issue (Schleihauf,

1979; Takagi et al., 2001; Berger, 1996; Sidelnik &

Young, 2006). Rather than an experimental analysis, the

current study applied the numerical techniques of CFD to

compute the forces produced by the model of the swim-

mer’s hand. Bixler et al. (2007) has already demonstrated

the validity of CFD analysis as a tool to examine the

water flow around a swimmer’s 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 & 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 3-D shapes, such as a human hand,

obtained by imagiography are becoming widely used in

reverse engineering (Lecrivain et al., 2008).

The main finding of the present research was that the

model with the small distance between fingers presented

higher values of CD than the models with fingers closed

together and with fingers spread widely. Furthermore,

the CL seemed to be independent of the finger spread,

presenting few differences among the three models. These

results suggest that the use of a position with a small dis-

tance between fingers seems to be gainful for swimmers.

The hand position with the small 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 the small

finger spread and for the position with fingers closed

were very similar. For attack angles lower than 90°, the

flow above the dorsal surface of the hand, flowing at high

velocities, could prevent the flow between fingers. In this

condition, assuming that 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 30° and 45°), it will thus be

expected that the so-called barrier will be stronger at

those CL values. As can be seen from Figures 3 and 4, at

α = 45° a relative increase of the CD value is perceptible.

This curve tendency corresponds to the maximal CL value

obtained for the slight spreading condition, and for all

studied conditions, indicating the higher flow velocity

difference between both faces of the hand. Concerning

this, Ungerechts & Klauck (2006) did suggest having

fingers slightly spread to induce flow around the hand at

the beginning of the arm cycle.

However, this gain did not occur when we analyzed

the greater distance between fingers. In both CD and CL

coefficients, for the position with large finger spread, the

values were lower when compared with the positions of

fingers closed and slightly spread. For the CD and for

attack angles higher than 30°, 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 identi-

cal situation. The CD for the fingers closed and slightly

spread positions presented higher values than the large

spread position. In contrast, the values of CL increased

in indirect proportion to finger spread for attack angles

ranging between 0° and 60°. Berger (1996) reported that

spreading the fingers did not influence propulsive force.

Moreover, lift force at attack angles between 60° and 80°

was higher when spreading the fingers (Berger, 1996).

In a recent experimental study, Sidelnik & Young (2006)

determined that a hand with 10° 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 90° 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 methodol-

ogy 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 (Sand-

ers, 1999). It would be interesting to observe whether the

results would be the same as suggested by Ungerechts

& 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 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).

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92 Marinho et al.

Acknowledgments

This work was supported by the Portuguese Government by

a grant of the Science and Technology Foundation (SFRH/

BD/25241/2005; PTDC/DES/098532/2008). We would like to

acknowledge the staff of the Radiology Department of Hospital

de São João, in Porto, Portugal, and personally to the depart-

ment director, Isabel Ramos. We would also like to express

our gratitude to the Med Mat Innovation Company, in Maia,

Portugal, and especially to José Domingos Santos and Bruno

Sá for their contributions.

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