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.
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
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.
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).
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
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,
D = CD 1/2 ρ A v2
L = CL 1/2 ρ A v2
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
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.
Figures 3 and 4 show the values of CD and CL, respec-
tively, obtained for the hand model with different finger
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).
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.
Propulsion Forces and Finger Spread 91
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).
92 Marinho et al.
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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