Game Development Reference
In-Depth Information
Table 7-3.
Reynolds Number for a Typical Soccer Ball
Velocity (
m/s
)
Reynolds Number
3.0
45300
5.0
75500
7.0
105700
9.0
136000
10.0
151000
15.0
226500
20.0
302000
In comparing the values shown in Table 7-3 with the drag coefficient data shown in
Figure 7-11, it is clear that at ball velocities of greater than 9.0
m/s
the flow around the ball will
be fully turbulent, and the lower drag coefficient value of approximately 0.22 can be applied.
At velocities between 9.0 and 7.0
m/s
, the flow is transitioning from turbulent to laminar flow,
and the drag coefficient will be between 0.22 and 0.47. At velocities below 7.0
m/s
, the flow
around the ball is fully laminar, and the drag coefficient will be about 0.47.
Now it is perfectly conceivable for a soccer ball to start its flight at a velocity faster than 9
m/s
and slow down during its flight to a velocity of less than 7
m/s
. When this happens, the ball
experiences all three flight regimes during its flight—turbulent, transitional, and laminar—and
the drag characteristics of the ball will change dramatically as well. Some of the most dramatic
shots in soccer history where the ball seemed to change course in midair were made possible
by the transition from turbulent to laminar flow.
Building this type of drag coefficient behavior into a soccer simulation is quite easy. The
Reynolds number is computed and a simple “if” test is used to determine the drag coefficient
value. When the flow is transitioning between laminar and turbulent flow, the drag coefficient
can be assumed to vary linearly between 0.47 and 0.22.
(7.54a)
C
=
0.47
for
Re
<
100000
D
Re
−
100000
(7.54b)
C
=−
0.47
0.25 *
for
100000
<<
Re
135000
D
35000
(7.54c)
C
=
0.22
Re
>
135000
for
D
Figure 7-14 shows the linear approximation curves on top of the experimental data. As you can
see, the three straight lines do a pretty good job of modeling the soccer ball drag coefficient data.
