Biomechanics and Medicine in Swimming XI

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¾
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Fig. 2. Correction of head inclination.
When calculating the EE j , the dimensions of the each component must
to be equivalent to the mechanical power, and a window of data was
set at 5 sec (= Δt) for the purpose of including one cycle during WW
(Kaneda et al., 2009b). Therefore, the EE j was calculated as follows:
EE j = (Az' 2 +Ay' 2 t +∆t
∫ ) /∆tdt × weight(kg) × v(m /min)/weight(kg) (6)
t
where v is the walking speed measured by stopwatch.
The EEwd was regarded as the anterior-posterior acceleration ( Aap). From the equation (4) and (5), the Aap is expressed as (Figure 2):
Aap = Az'sinϑ + Ay'cosϑ
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(7)
Therefore, the EEwd was calculated as follows:
t +∆t
2
EEwd = ∫ Aap /∆tdt × weight(kg) × v(m /min)/weight(kg) (8)
t
The acceleration data was averaged in the last 20 sec of the each trial
to develop the estimation equation for the EE. The data of the each
component was Z-scored.
The results of this estimation equation for the males and females showed
in Table 2 and Figure 3, and Figure 4 showed the results of the residual
analysis. The correlation coefficients were high in both males (r = 0.79)
and females (r = 0.77).
Table 2. Coefficients of the each component and correlation coefficients
in each sex.
Sex α 0 α 1 α 2 α 3 adj r 2 r
Male 0.06206 -0.00044 0.02202 0.00773 0.630 0.794
Female 0.06928 0.00071 0.02042 -0.00639 0.598 0.773 ¾
Fig. 3. Comparison between the estimated and measured EE.
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chaPter6.medicineandwatersafety
Fig. 4. Relative error of the estimated EE from measured EE.
dIscussIon
This study conducted water walking (WW) with wide range of Japanese
males and females. Energy expenditure were measured and threedimensional
accelerations with a triaxial accelerometer to develop an
estimation equation for energy expenditure (EE) during WW by using
acceleration data. For the purpose to adopt wide range of subjects, and
with the EE influenced by the walking speed rather than the body size
and sex (Kaneda et al., 2009a), the swimming pool depth of the WW
(1.1m) was selected as general.
There are many studies estimating EE during land walking, jogging
and other life style activities (Kumahara et al., 2004; Scott et al., 2006;
Tanaka et al., 2007), in which the r 2 values reported by Scott et al. (2006)
were from 0.436 to 0.719. The r 2 values in the present study were 0.630
for the males and 0.598 for the females. It was considered that we could
develop the estimation equation for the WW as a good manner. In this
study, the estimation equation was composed three items that were resting
metabolic rate (RMR), internal energy expenditure for moving his/
her body (joint energy expenditure: EE j ) and energy expenditure against
for water drag force (EE wd ). This estimation equation is original because
we have to consider water drag force for water exercise that ordinary
need not to consider in land exercise. In the WW, the EE is influenced
by dominantly the walking speed rather than the body size and sex
(Kaneda et al., 2009a), and the gravitational stress at the lower extremity
joint was reduced and greater exert force required for moving (Miyoshi
et al., 2005). Those studies would indicate that we have to consider the
effect of water drag force rather than the gravity stress for the EE in the
WW. Indeed, approximately 65% to 70% of the body weight was offset
in the subjects of this study. Even if we consider about gravity effect, we
cannot estimate and measure buoyancy correctly because it is continuously
changing.
The EE in this study was per unit time. In the view point of mechanics,
the EE per unit time can be said as the mechanical power. The
mechanical power (P) is expressed as follows:
P = Fv (9)
where F is mechanical force and v is velocity. The mechanical force is
expressed as follows:
F = ma (10)
∴ P = mav (11)
where m is mass of the object and a is acceleration. Therefore, we multiplied
the body weight and the measured walking speed to the acceleration.
And finally, the values were divided by body weight for eliminating
the effect of the weight bearing. Until now, we could not find out
any previous study adopting such a theoretical estimation method even
in land activities. Though the correlation coefficients of the developed
equation in this study were high (males: r = 0.79, females: r = 0.77),
residual analysis showed large estimation errors, over 30%. We have to
continue considering about much reliable method for estimating EE
during WW. Moreover, future study about estimation of EE in various
water exercise form will be useful for health promotion water exercise.
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