Biomechanics and Medicine in Swimming XI

To calculate the orientation of the both hands during underwater phase,
the visual markers were attached on the tip of the 1st , 3rd and 5th fingers
and the wrist of the swimmer. The swimming flume used in the experiment
has windows at the bottom and the left side of a swimmer. Four
synchronized cameras (TK-C1461, Victor, Japan) were set on to register
motion of the swimmer’s hands through the windows. Each visual
marker on the video was digitized manually at a frequency of 60 field/
second using a digitizing software (Video Annotator for Excel, JISS,
Japan) and the three dimensional coordinates were calculated using 3D-
DLT method using a computational software (Mathematica 7, Wolfram
Research, USA). The orientation of the hands was expressed as the normal
vector of the hand plane, which was calculated by the method of
least squares with the 3-D coordinates of the four markers on the hand.
One other visual marker, fixed on the umbilicus, was used as an alternative
point to the centre of gravity. The movement of the marker was
recorded by a high speed camera (Fastcam-pci, Photron, Japan) with
250 fps from the bottom view. The positions were digitized manually
and calibrated it along with swimming direction only using the referred
software (Video Annotator for Excel and Mathematica).
The component on the swimming direction of the hydrodynamic
force Fhand on each hand was calculated using the normal vector of the
hand. It was defined that the propulsive force Fp was the summation of
the components of the left and right hands. The swimming acceleration
a was calculated as the second-order derivative of the position of
the umbilicus with respect to time. The inertial term ma was defined as
the product of the swimming acceleration and the swimmer’s mass. The
estimation of the drag force Fd was based on the equation of motion
Eq.2, Biomechanics so the drag force and was Medicine obtained as XI the difference Chapter of the 2 inertial Biomechanics
term ma and the propulsive force Fp (Fig. 2). Note that the obtained
Fd in the present study was backward force and would be expressed as
negative value.
The coefficient of drag Cd was calculated in each trial using the following
equation,
as the difference of the inertial term ma and the propulsive force Fp (Fig. 2). Note that
the obtained Fd in the present study was backward force and would be expressed as
negative value.
The 2Fcoefficient
of drag Cd was calculated in each trial using the following equation,
RESULTS
The inertial term, propulsive and drag force during 5 seconds were obtained in each
subject (Fig. 3). The mean drag forces were 21.3 N in the competitive swimmer and
50.3 N in the triathlete, respectively. It was observed that the competitive swimmer had
phases of no propulsive force. On the other hand, the triathlete kept producing
146
chaPter2.Biomechanics
with high stroke frequency. To compare the drag estimated in the present
study with that of previous studies, the mean and absolute values of
Reynolds numbers and coefficient of drag were calculated and plotted
in same plane with the reported values (Takagi et al. 1998) in Fig. 4.
Figure 3. The inertial term, propulsive force and drag force during front
crawl swimming of the competitive swimmer (Left graphic) and the
triathlete (Right graphic).
Figure 4. The relationship between Reynolds number and coefficient
of active swimming drag reported by previous researches (Takagi et al.
d Cd
= Eq.4,
1998) and the mean and absolute values obtained by this study, which
2
rA
2Fd
wholev
is indicated by the plus “+” (the competitive swimmer) and the cross “x”
Cd
= Eq.4, 2
ρAwholev
(the triathlete) markers.
where where r was ρ density was of density water, and of v water, was the mean and v swimming was the velocity, mean swimming velocity, which was 1.3
which was 1.3 m/s. The Awhole was the swimmer’s surface area, which was dIscussIon
calculated m/s. The Awhole by the Shitara’s was formula the for swimmer’s Japanese male, surface area, which It was seemed calculated that it would by be difficult the Shitara’s for the triathlete to maintain the in-
formula for Japanese male,
structed swimming velocity, which was 1.3 m/s. The Fig. 3 demonstrated
0.
619 0.
460 4
Awhole = 105. 29 × ( H × 100)
× W / 10 Eq.5, the reason was the larger drag force. The drag force of the triathlete
reached 150 N. It must be noted that the drag force was expressed as
where H and W were the swimmer’s height and weight, respectively (Shitara et al.
where H and W were the swimmer’s height and weight, respectively negative value in the Fig. 3, although it was less than 100 N in the com-
(Shitara 2009). et al. 2009). To discuss To discuss validity of of the the drag drag force Fforce Fd obtained by our methodology, the
d obtained petitive swimmer. To overcome the larger drag force and to maintain the
by our coefficient methodology, of the drag coefficient Cd was of compared drag C with the reported values (Takagi et al. 1998).
d was compared with the velocity, the triathlete had to keep producing the propulsive force with
reported values (Takagi et al. 1998).
high stroke frequency without a break. As a result, the triathlete’s effectiveness
of swimming could be lower. It was not so large de-acceleration
of the competitive swimmer, although he had phases of no propulsive
force (Fig. 3). It was because the drag force was not so large in the phases.
The lower drag force would provide him effective swimming.
The validity of the obtained drag force in the methodology deserves
more discussion. The comparison of the coefficient of drag with the previous
researches in the Fig. 4 showed that the obtained values would be
Figure 2. A schematic view to quantify the drag force Fd during front lower in some degree. It was observed that the drag force was positive
crawl swimming. The drag force was obtained as the difference of the value in every in-sweep phases of the both subjects (Fig. 3), although the
inertial term ma and the propulsive force Fp along with swimming di- drag force should be negative value, which meant backward force, in the
rection.
definition of the Equation 2. In this study, the drag force was calculated
as the difference between the measured inertial term and propulsive
results Figure 2. A schematic view to quantify the drag force Fd force. during The positive front drag crawl force swimming.
resulted from the smaller propulsive force
The The inertial drag term, force propulsive was and obtained drag force as during the difference 5 seconds were of obthe
inertial than the term inertial ma term. and It was the assumed propulsive that the propulsive force was extained
in each subject (Fig. 3). The mean drag forces were 21.3 N in erted by the hands only and that the direction of the hydrodynamic force
force Fp along with swimming direction.
the competitive swimmer and 50.3 N in the triathlete, respectively. It on the hand was perpendicular to plane of the hands. However, there are
was observed that the competitive swimmer had phases of no propulsive possibilities that any segments additional to the hands, especially the
force. On the other hand, the triathlete kept producing propulsive force forearms, contribute to produce forward force. It seemed that the hy-
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