Biomechanics and Medicine in Swimming XI

developed to measure pressure on the hand and to predict hydrodynamic
forces acting on the hand during swimming. The data logger was attached
on the back of the swimmer, and twelve pressure sensors were
attached on the swimmer’s hand according to Kudo et al. (2008). An
underwater motion capture system using eight cameras (Qualisys, Sweden)
was used to acquire kinematic data of the hand during swimming.
Three reflective markers were attached on the right hand, the third fingertip,
trapezium and pisiform bone. The data logger and the motion
capture system were synchronized, and the signals were recorded at 100
Hz. The signals of data logger and motion capture system for a right
hand stoke were smoothed using a fourth order, zero lag, low-pass Butterworth
filter (Winter, 1990). Static pressures due to the hand depth
during swimming were taken into account based on the marker data so
as to predict hydrodynamic forces (drag and lift forces) acting on the
hand by the pressure method (Kudo et al., 2008)
The present study constructed a new best-fit equation using a dependent
value which hydrodynamic forces acting on the hand model
divided by the size of the hand model used in the previous study (Kudo
et al., 2008), taking into consideration the hand size of a swimmer. Thus,
the magnitude of hydrodynamic forces acting on the swimmer’s hand
was predicted by multiplying the predicted values from the best-fit
equations by the hand size of a swimmer (Loetz et al., 1988; Takagi and
Wilson, 1999). For constructing the best-fit equations in the present
study, hydrodynamic forces were decomposed into the three directions
in the local reference hand-centric system; a direction parallel to the
longitudinal axis of the hand (z-axis), a direction perpendicular to the
plane of hand motion in the two consecutive frames (x-axis), a direction
perpendicular to the z- and x-axes (y-axis). Using kinematic data from
the motion capture system the directions of drag and lift forces, the
angle of attack (AP) and sweepback angle (SB) were computed. Propulsive
forces exerted by the hand during swimming were computed using
the hand kinematics and hydrodynamic forces on the swimmer’s hand.
The best-fit equations used to predict hydrodynamic forces acting on
the hand model by the pressure method in the previous study consisted
of 12 regression coefficients and higher order polynomials. The number
of regression coefficients was up to 36. Therefore, there might be a
considerable effect of multicollinearity on the prediction (Kutner et al.,
2004). Different order of best-fit equations, including the order of bestfit
equation from the pressure method in the previous study (B-Eq1)
and the first order of best-fit equations (B-Eq2), were used to predict
hydrodynamic forces acting on the swimmer’s hand to check the effect
of multicollinearity on the prediction. In addition, the variance inflation
factor (VIF) was computed to quantify the effect of multicollinearity.
results
Mean propulsive forces exerted by the hand predicted by B-Eq1 over a
stroke was 15 ± 11 N. Mean propulsive forces exerted by the hand predicted
by B-Eq2 over a stroke was 33 ± 24 N, and the maximum value
of propulsive force was 77 N (Figure 1). The contribution of drag and lift
forces to propulsive force predicted by B-Eq2 was 55% and 45%, respectively.
Mean hand speed over a stroke was 2.3 ± 0.3 ms -1 and maximum
hand speed was 2.7 ms -1 . The angle of attack (AP) changed from 24˚ to
85˚, and the sweepback angle (SB) changed from 73˚ to 254˚ over a stroke.
Mean values of VIF were 12.86 ± 7.05 for the first-order polynomial
equations with the 12 sets of pressure, 39.28 ± 32.50 for the secondorder
polynomial equations with the pressure sets, and 196.10 ± 298.10
for the third-order polynomial equations with the pressure sets.
contribution of drag and lift forces to propulsive force predicted by B-Eq2 was 55% and
45%, respectively. Mean hand speed over a stroke was 2.3 ± 0.3 ms
chaPter2.Biomechanics
-1 and maximum
hand speed was 2.7 ms -1 . The angle of attack (AP) changed from 24� to 85�, and the
sweepback angle (SB) changed from 73� to 254� over a stroke.
Mean values of VIF were 12.86 ± 7.05 for the first-order polynomial equations with
the 12 sets of pressure, 39.28 ± 32.50 for the second-order polynomial equations with
the pressure sets, and 196.10 ± 298.10 for the third-order polynomial equations with the
pressure sets.
Force (N)
Propulsion
Propulsion from drag force
Propulsion from lift force
Frame
Figure 1 Propulsive force exerted by the swimmer’s hand
Figure 1 Propulsive force exerted by the swimmer’s hand
DISCUSSION
This study developed a method to predict propulsive forces exerted by the hand in
swimming. Feedback on propulsive forces exerted by the hand predicted can be
provided to the swimmer and coach within a few hours by combining the pressure
method with kinematic data from the motion capture system. Additionally, the
contribution of drag and lift forces to propulsion by the hand can be provided to help
swimmers and coaches in the analysis of stroke technique to improve swimming
performance.
The mean of hydrodynamic forces acting on the hand predicted by the best-fit
equation in the previous study (B-Eq1) was different from that by B-Eq2. The mean of
VIF changed considerably among the three different orders of best-fit question. The
results mean that multicollinearity might affect the predicted values. A maximum VIF
value in excess of 10 indicates that multicollinearity may influence the least square
dIscussIon
This study developed a method to predict propulsive forces exerted by
the hand in swimming. Feedback on propulsive forces exerted by the
hand predicted can be provided to the swimmer and coach within a
few hours by combining the pressure method with kinematic data from
the motion capture system. Additionally, the contribution of drag and
lift forces to propulsion by the hand can be provided to help swimmers
and coaches in the analysis of stroke technique to improve swimming
performance.
The mean of hydrodynamic forces acting on the hand predicted by
the best-fit equation in the previous study (B-Eq1) was different from
that by B-Eq2. The mean of VIF changed considerably among the three
different orders of best-fit question. The results mean that multicollinearity
might affect the predicted values. A maximum VIF value in excess
of 10 indicates that multicollinearity may influence the least square
estimates of regression coefficients (Kutner et al., 2004). The values of
correlation coefficient were 0.69 in propulsions predicted by B-Eq1 and
B-Eq2, 0.79 in propulsions from drag forces predicted by the two bestfit
equations, and 0.88 in propulsions from lift forces predicted by the
two best-fit equations. The results indicate that the trend of the prediction
is similar in the two equations. Based on the VIF values B-Eq2
may be better to predict hydrodynamic forces acting on the hand during
swimming. The erroneous effect on the prediction of hydrodynamic
forces acting on the hand during swimming can be detected using the
information on the magnitude of hydrodynamic forces acting on the
hand, kinematics of hand, as well as AP and SB. Further study is necessary
to validate the pressure method to predict propulsive forces exerted
by the hand during swimming especially for the magnitude of hydrodynamic
force predicted.
The present study showed that a swimmer is able to generate propulsive
forces by the hand in the down-sweep phase between 20 and 40
frames (Figures 1 and 2). The majority of propulsion resulted from lift
forces. During the down-sweep phase, drag force by the hand did not
have substantial contribution to propulsive force because the hand was
still moving forward. The swimmer in this study did not incorporate
sideway sweep of the hand in the inward sweep phase between 40 and
60 frames (Figure 2). Thus, the contribution of lift forces to propulsive
forces was small (Figure 1). Propulsive forces from lift forces exerted by
the swimmer’s hand can be increased if the swimmer performed further
inward sweep. The gaps of the hand trajectories in the xy-plane between
40 and 60 frames were large and the trajectories moved backwards, indicating
that the hand moved backwards with large velocities (Figure
2). Therefore, propulsive forces from drag forces reached the maximum
value (69 N) between 40 and 60 frames that is 90% of propulsive forces
by the hand (Figure 1). Berger et al. (1999) reported mean propulsive
forces exerted by the hand in the front crawl stroke of 21 N among nine
swimmers at a mean swimming velocity of 1.15 ms-1 . Berger et al. (1999)
and Schleihauf et al. (1983) showed that a swimmer attained maximum
propulsion of approximately 100 N by the hand. The propulsive forces in
this study were not considerably different from the two previous studies.
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