Game Development Reference
In-Depth Information
The Impact Phase
The impact of the putter and golf ball can be modeled in exactly the same way as the impact of
the ball and any other club. For the time being, we will assume that the green is horizontal and
at the point of impact the head of the putter is in the x-direction. The line of action for the colli-
sion will be equal to the loft angle of the putter. The post-impact velocity normal and parallel
to the line of action can be determined from Equations (7.3) and (7.8). As before, the velocities
are a function of the mass of the putter head and ball, the impact velocity, the coefficient of
restitution, and the loft of the putter.
(
)
1
+
em
′
c
v
=
v
mm
cos
a
(7.28)
bp
cx
+
b
c
2
7(
mv
sin
a
v
′
=−
ccx
(7.29)
bn
mm
+
)
c
b
If the putter has a nonzero loft angle, the ball will be given a small spin rate due to the colli-
sion. The spin rate is a function of the impact velocity, loft angle, and ball radius, and can be
calculated from Equation (7.4).
5
7
v
sin
a
w
=−
cx
(7.30)
b
0
r
b
′
bn
, is usually small enough compared to the parallel
component that it can be ignored. The post-collision velocity of the ball in the x-direction can
be assumed to be equal to the post-collision velocity along the line of action.
The normal component of velocity,
v
′
′
vv
=
(7.31)
bx
bp
If the putter is lofted, the ball will initially take a small hop. The distance of the hop could
be determined from Equations (7.28) and (7.29), and the basic projectile relations presented in
Chapter 5, but the final equations become pretty complicated, with lots of sine and cosine
terms. The bottom line is this: depending on the putter loft angle and the speed of impact, a
golf ball will usually hop between 0.04 and 0.08
m
. For game programming purposes, you can
assume a middle range value for the hop, say 0.06
m
, and proceed to the skid phase
calculations.
The Skid Phase
After the collision with the putter face and the initial hop, the ball skids along the green for a
certain distance. As computed during the collision phase, the translational velocity at the start
of the skid is equal to and an angular velocity equal to . When the ball skids along the
putting green, a friction force develops between the ball and the ground in the direction opposite
to the motion of the ball. The magnitude of the friction force is equal to the normal force exerted by
the ball multiplied by the coefficient of friction. A schematic of the forces and velocities of the
ball at the start of the skid is shown in Figure 7-10.
v
′
w
bx
b
0
