Game Development Reference
In-Depth Information
The coefficient of rolling friction,
m
r
, depends on the height of the grass, the type of grass,
and the relative dampness of the green. Typically, the value of
m
r
might range from 0.05 to
0.075.
4
A dry, tightly mowed green is considered “hard” and would have a lower coefficient of
rolling friction, whereas a damp green with longer grass would be considered “soft” and would
have a higher coefficient.
Sample Problem: Compute the distance of a putt
Let's take what we have learned about putting and compute how far a typical putted ball will
travel. We'll assume that the putting surface is flat. We'll also assume that the putter has a loft
of 3 degrees, the mass of the putter head is 0.33
kg
, and the coefficient of restitution is 0.78. The
impact velocity will be taken to be 1.65
m/s
.
We'll start by modeling the collision between the putter and the ball. The post-collision
velocity of the ball can be found from Equation (7.3).
(
)
1
+
0.78 0.33
3
p
⎛
⎞
m
s
v
′
=
1.65 cos
=
2.57
(7.41)
⎜
⎟
bp
0.0459
+
0.33
180
⎝
⎠
Because the putter loft angle is small, the post-collision velocity in the x-direction will be
assumed to be the same as the post-collision normal velocity.
m
s
(7.42)
′
==
vv
2.57
bx
bp
The initial spin rate of the ball is determined from Equation (7.4).
3
p
⎛
⎞
1.65sin
⎜
⎟
5
rad
s
(7.43)
180
⎝
⎠
w
=−
*
=−
2.89
b
0
7
0.02135
We won't go to the trouble to compute the distance that the ball will hop but will assume
it is 0.06
m
.
x
=
0.06
(7.44)
Now, we'll move on to the skid phase. The angular and x-direction velocities at the end of
the skid phase when the ball is in a pure-rolling motion can be computed from Equations (7.35)
and (7.36).
5
2
m
s
v
=
* 2.57
−
* 0.02135* 2.89
=
1.82
(7.45)
br
7
7
v
r
1.82
rad
s
w
==
br
=
85.2
(7.46)
br
0.02135
The elapsed time during which the ball will be skidding can be found from Equation (7.34).
We'll assume that the coefficient of sliding friction between the ball and green is 0.5.
(
)
2 2.57
+
0.02135* 2.89
t
=
=
0.15
s
(7.47)
7 * 0.5*9.8
