1 TÜRKİYE PROFESYONEL LİGLERİNDE GÖREV ... - Spor Bilim

y
b
m m
g
a 1
a 2
z x
shoulder
elbow
wrist
front view left side view
Figure 1. The model
The velocity of an infinitesimal arm segment dr in the direction perpendicular to the axis of
the arm segment, shown in Figure 2, can be written as
Va t b
= V -V
sinq
, (1)
where V t is the tangential component of the velocity of the arm segment relative to the
shoulder joint which is equal to 2p fr'
, b V is the velocity of the body in x direction, q is the
angle between the projection of the arm axis on x-y plane and x direction, f is the stroke rate
and r ' is the projection on x-y plane of the length from the shoulder joint to the infinitesimal
arm segment. We also note that r ' is the perpendicular distance from z-axis to the
infinitesimal arm segment. The propulsive force of the infinitesimal element, dF p , can be
written as
dF
p
2
= k DV dr . (2)
a
a
Here, k a is the drag coefficient and D is the diameter of the arm. These basic relations will
be used in the derivation of the propulsive force expression for each separate part of the arm.
x
90-q
V t
Figure 2. Infinitesimal element on the arm
V b
V a
r'
q
y
q
a 2
a 1
y