Game Development Reference
In-Depth Information
v
cn
ω
r
z
μF
N
x
Figure 7-5.
Friction between the ball and club face causes the ball to spin.
When analyzing the friction effects on a golf ball, there are two questions to answer: what
is the resulting velocity of the golf ball parallel to the club face, and what is the spin rate that is
imparted to the golf ball? Both questions can be answered by analyzing the frictional impulse
that is generated between the golf ball and club face, a concept that was introduced in Chapter 6.
If the ball is assumed to roll without slipping at the end of the frictional impulse, the post-collision
velocity normal to the line of action,
v
′
bc
, and the post-collision angular velocity of the ball,
w
,
can be computed from Equations (6.40) and (6.41).
5
v
5
v
sin
a
w
=
cn
= −
cx
(7.4)
b
7
r
7
r
b
b
5
5
′
v
=
v
= −
v
sin
a
(7.5)
bc
cn
cx
7
7
As we saw in Chapter 6, the post-collision normal velocity component and angular velocity
are independent of the coefficient of friction between the ball and club face. The spin rate only
depends on the initial club velocity,
v
cx
, and ball radius,
r
b
.
The collision between the ball and club face will change the velocity
of both the ball and
club head. The post-velocity component in Equation (7.5) is designated as
v
′
bc
because it
represents the post-collision velocity of the ball relative to the club face. It is equal to the differ-
ence between the post-collision velocities of the ball,
v
′
bn
, and club head,
v
′
cn
.
5
vvv
′
=−=−
′
′
v a
sin
(7.6)
bc
cn
bn
cx
7
What we really want is the post-collision velocity of the ball in the direction normal to the
line of action. To obtain this quantity, we can assume that there is conservation of momentum
in the normal direction.
′
′
mv
+
mv
=
mv
(7.7)
bbn
ccn
ccn
