1 TÜRKİYE PROFESYONEL LİGLERİNDE GÖREV ... - Spor Bilim

4 2 2 3 2 2 2 2
m &Vb
= k[ D a ( fpL1 s - i gn 1 a 2 f aLp V s
1 b+ iqn as i gn 1 bL
Vqs i n )
3
4 2 2 3 2 2 2 2 2 2 2 2 2
+ ka D ( pf 2L s ib+ n
2 a 4 fpL 2 aL sbi+ n
1 a s gi n a4 fp L- 1 aL sg i n
2 a 2pf L
2 bVbs
i n qs
i n
3
2 2 2 2
2
- 4pf L L Vgs+ i n sqi n L + Vqs i n ) kp A + ( 4 f g( L s+ ibn L s i ( n L n sbi) / ) 2
a1 a 2 b a 2 b h1 h 2 a a h
2 2 2
- 4f(LsinLsinLsin)/2)VsinVsin)sinkV
p g + b ( + b q + q - q
a1 2 a h b b b b
The equation of motion (19) is solved using the fourth-order Runge-Kutta method. A
constant stroke frequency is assumed and the rotation of the arm inside the water is divided
into 180 steps. Each step is taken as an increment of one degree in the angle θ.
Results
In the comparisons, the drag coefficient k a for the propulsive drag force of the arm segments
is taken as 400 kg/m³ and the drag coefficient for the hand is taken as 600 kg/m³. These are
the experimental values obtained by Martin et al. [4]. In addition, the drag coefficient of the
body k b is taken as 30 kg/m from Karpovich [6]. In order to check the performance of the
present model, two different comparisons are made. The results of the two sets of experiments
obtained by the authors are compared with the numerical results obtained by the model. The
following anatomical data which belongs to the male swimmer took part in the experiments, is
considered:
Diameter of upper arm...................... D
Length of upper arm.......................... L
Diameter of forearm......................... D
Length of forearm............................. L
Area of hand...................................... A
1
a1
2
a2
h
= 0.083m
= 0.340m
= 0.054m
= 0.300m
=
0.019m 2
Length of hand................................... L h = 0.190m
Mass of the swimmer……............…. m = 75kg In fully tethered swimming, the velocity of the swimmer is equal to zero and for a steady
state swimming period the force balance becomes
F D - F = 0 , (20)
t + p
where F t is the tether force. In Figures 5 and 6, the comparison of the tether force which is
obtained by the mathematical model and the tethered swimming experiments are given for the
stroke rates 0.33 sec-1 and 0.36 sec-1, respectively. It is seen that the tether force versus time
graphs of the proposed model and the experimental work are in good agreement.
The numerical and experimental results for the free crawl stroke swimming experiments
are shown in Figure 7. Using k b = 30 kg/m , the slope of the mean velocity versus the stroke
rate graph for the mathematical model is obtained as 1.716 (m/sec)sec. For the experimental
results, the slope of the best fit straight line calculated using least squares technique is
]
(19)