Game Development Reference
In-Depth Information
The distance the ball will travel during its skid can be determined from Equation (7.37).
1
2
x
=
2.57 * 0.15
−
* 0.5*9.8* 0.15
=
0.33
m
(7.48)
2
The ball is now rolling, and the distance the ball will travel when it is rolling can be computed
from Equation (7.40). We'll assume a medium-hard green with a coefficient of rolling friction
of 0.065.
2
1
1.82
x
=
*
=
2.6
m
(7.49)
2
0.065*9.8
The final distance the putt will travel is the sum of the distances during the collision, skid,
and roll phases.
x
=++=
0.06
0.33
2.6
2.99
m
(7.50)
putt
Slope Effects
Up to now we have been considering the physics of putting on a flat surface. Most greens are
not flat, however, but have slopes, ridges, undulations, and other physical features. Accounting
for slope does add complexity to a putting simulation, but we have already covered all the
necessary elements. The line-of-action vector of the collision is measured relative to the vector
parallel to the slope in the direction the ball is struck. For example, if the ball is struck with a
3-degree lofted putter on a 5-degree upslope, the angle of the line of action will be 8 degrees.
If the golf is rolling on a slope, a moment is generated that causes an angular acceleration
of the ball. If the ball is hit on a downslope, the moment will cause the ball to roll farther than
it would on a flat green, and the opposite is true if the ball is hit on an upslope. If the geometry
of the green is complicated, the motion of the putted ball can be quite complicated as well,
since the axis of the moment due to slope may be different from the initial roll axis of the ball.
Soccer
Soccer, or football as it is known in most of the world, is probably the most widely played,
widely watched sport in the world. When the World Cup Championships are held every four
years, well over one billion people watch the competition on television. In this topic, the sport
will be referred to as soccer to differentiate it from American football, which will be discussed
later in this chapter.
People have been playing games involving kicking a ball around for over 2000 years. During
the Han Dynasty of China in 2nd-3rd century BC, men kicked a leather ball stuffed with
feathers and hair into a net attached to a bamboo cane as part of their military training. An
early brand of soccer (called football) was played in the British Isles during medieval times.
Modern soccer dates its origin to 1863 in England when a set of rules was set down to stan-
dardize the various incarnations of football that were being played at that time. The rules forbid
tripping, shin-kicking, and other acts of violence that had often been a part of early versions of
soccer. With some dissension, it was also agreed that players could not carry the ball. Those
who were unhappy with this rule split off to form the sport of rugby. The now mostly standardized
