Game Development Reference
In-Depth Information
0.5
Experimental data
0.4
0.3
0.2
0.1
0
0
100000
200000
300000
Re
Figure 7-13.
Drag coefficient of a nonspinning soccer ball
The question now becomes which drag coefficient should be used—the laminar one or the
turbulent one? The answer is maybe one, maybe the other depending on the velocity of the
soccer ball. As we saw in Chapter 5, the Reynolds number is the ratio of the air density, object
velocity, and characteristic length divided by the air viscosity.
r
m
vL
Re
=
(7.52)
For soccer balls the characteristic length,
L
, is taken to be the diameter of the ball. The
viscosity of a fluid can be thought of as a measure of how easily an object can move through a
fluid. The viscosity of maple syrup, for instance, would be quite high. The viscosity of air at low-
to-moderate temperatures can be approximated using the relation shown in Equation (7.53).
1.5
T
kg
ms
m
=
1.458
e
−
6
(7.53)
T
+
110.4
−
Let's use Equations (7.52) and (7.53) to compute the Reynolds number of a soccer ball
flying through the air at various velocities at sea level where the temperature is 294
K
(70
o
F
).
The density of the air at is 1.2
kg/m
3
and the viscosity is 1.82e - 5
kg/m-s
. The Reynolds number
at these conditions for various velocities using the diameter of the ball as the characteristic
length is shown in Table 7-3.
