Game Development Reference
In-Depth Information
For the “ideal” impact shown in Figure 7-4, the line of action of the collision is along a
vector whose angle is equal to the loft of the club,
. The club head velocity along the line of
action,
v
cp
, is normal to the club head face and is therefore equal to the velocity in the x-direction
multiplied by the cosine of the loft angle.
α
vv a
=
cos
(7.1)
cp
cx
The component of initial club head velocity normal to the line of action,
v
cn
, which will be
important in determining the spin of the golf ball, can be found using the sine of the loft angle.
vv a
=
sin
(7.2)
cn
cx
The post-impact velocity of the golf ball can be determined from Equation (6.14a) developed
in Chapter 6. It is a function of the mass of the ball,
m
b
, the mass of the club head,
m
c
, the coef-
ficient of restitution,
e
, and the velocity component in the direction of the line of action of the
collision,
v
cp
.
(
)
(
)
1
+
em
1
+
em
′
c
c
v
=
v
=
v
cos
a
(7.3)
bp
cp
cx
mm
+
mm
+
b
c
b
c
Equation (7.3) represents the post-impact velocity of a golf ball after an “ideal” hit, but as
we all know in the real world, the “ideal” hit rarely ever occurs. The club face may not strike the
ball at the bottom of the swing, thereby changing the effective loft of the club. The club face
might also strike the ball at an angle, changing the line-of-action vector of the collision from
the x-z plane. We'll discuss how to deal with nonideal impacts in the “Impact Modeling Decisions”
section a little later in this chapter.
Friction Effects
When the club face strikes the ball, there will be friction between the two surfaces, and this fric-
tion effect is very important in golf simulations. It not only affects the initial velocity of the ball,
but is also responsible for the ball acquiring spin. For the purposes of developing some basic
relations in this section, we will assume an “idealized” impact where the line of action of the
collision is in the x-z plane and the spin axis of the golf ball is parallel to the y-axis.
As we saw in Figure 7-4, because the club is lofted when it impacts the ball, it will have
velocity components both normal to and parallel to the club face. At the moment of impact, the
ball starts to slide up the face of the club. The relative velocity between the ball club as the
sliding begins is equal to the velocity of the club normal to the line of action,
v
cn
. Because the
ball is sliding over the club face, a friction force is generated that resists this motion. The friction
force does two things: it reduces the relative velocity between the club and ball, and it generates a
torque on the ball that causes it to spin. The general situation is illustrated in Figure 7-5.
