Game Development Reference
In-Depth Information
Modeling the Impact of Ball and Foot
The initial phase of the flight of a soccer ball is conceptually similar to the flight of a golf ball. In
soccer, there is an initial impact of the player's foot with the ball, creating a force impulse along
the line of action of the collision. The ball will also be given a spin due to friction between the
foot and ball. However, modeling the collision between the foot and ball is complicated because
the shoe worn over the foot is not a simple shape. To properly determine the line of action of the
collision, it is necessary to know where on the foot and where on the ball the collision occurs.
Fortunately, for game programming purposes, there really is no reason to try to model
the impact between the foot and soccer ball. It is enough to simply specify the initial velocity
components, spin rate, and spin axis of the ball. A top-rate professional soccer player can kick
a soccer ball such that it has an initial velocity of 25-35
m/s
with an initial spin rate of 8-10
rev/s
. You
can use these values as upper limits in your game simulations.
Modeling the Soccer Ball in Flight
Just like a golf ball or a cannonball, once a soccer ball leaves the ground, it's a projectile and is
subject to the forces caused by gravity, aerodynamic drag, wind, and spin. The gravity force is
constant and acts in the vertical direction, as always. The force due to wind and spin can be
treated the same as we have done previously in this topic. The force due to aerodynamic drag,
however, is a bit more complicated for soccer balls, because the differences between laminar
and turbulent drag must be taken into account.
Laminar and Turbulent Drag
We learned in Chapter 5 that there are basically two ways that air can flow over an object.
Laminar flow is when the air flows smoothly over the object and generally speaking occurs at
low Reynolds number conditions. As the Reynolds number increases, a point is reached where
the flow no longer smoothly travels over the object but instead becomes chaotic. This condi-
tion is known as turbulent flow. The laminar/turbulent distinction has significance for computing
aerodynamic drag because the drag over an object is higher for laminar flow than it is for turbu-
lent flow.
As with all of the other projectiles we have studied, the force on soccer ball due to aerody-
namic drag is typically expressed as a function of the density of the air, the square of the
velocity of the ball, the frontal area of the ball, and a quantity known as the drag coefficient.
1
2
F
=
r
v AC
2
(7.51)
D
D
Researchers at the University of Sheffield
5
performed wind tunnel tests to determine the
drag coefficient of a nonspinning soccer ball as a function of Reynolds number. The results are
shown in Figure 7-13. At lower Reynolds numbers, the flow is laminar and the drag coefficient
value is about 0.47. When the Reynolds number reaches a value of approximately 100,000, the
flow begins to transition from laminar to turbulent flow and the drag coefficient decreases.
At a Reynolds number of 130,000-140,000 the flow around the soccer ball is fully turbulent, and
the drag coefficient levels off at a value of about 0.22.
