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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 swimmingThe 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
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.
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 = C
D
1/2
ρ
A v
2
(1) L = C
L
1/2
ρ
A v
2
(2)In Equations 1 and 2, v is the ﬂuid velocity, C
D
and C
L
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 (C
D
) and lift (C
L
) coefﬁcients, using Equations 1 and 2.
Results
Figures 3 and 4 show the values of C
D
and C
L
, respec-tively, obtained for the hand model with different ﬁnger spreads.One can note that the C
D
presented the highest values for an attack angle of 90° in the three hand models (
≈
0.90 < C
D
< 1.10). In the three models, the C
D
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 C
D
when compared with the models with ﬁngers closed and with large ﬁnger spread. This last model presented the lowest values of C
D
. For attack angles of 0°, 15°, and 30°, the values of C
D
were very similar in the three models of the swimmer’s hand.The C
L
resembled a sinusoidal curve across the attack angle. Maximum values for any hand model occurred near 30°–45° (C
L
≈
0.60). Furthermore, the C
L
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).
90Figure 3
— Values of C
D
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 C
L
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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