Game Development Reference
In-Depth Information
Figure 7-14.
A linear approximation to soccer drag coefficient data
Magnus Force
Just as it is with golf balls, the force due to spinning, or Magnus force, is very important in
modeling the flight of a soccer ball. Players use spin to bend the ball around defenders on
penalty or corner kicks. For soccer balls, we'll use the same expression for Magnus force that
we used for golf balls in which the magnitude of the force is a function of the density, velocity,
frontal area, and a lift coefficient.
1
2
2
FCv A
=
r
(7.55)
M
L
In order to evaluate the Magnus force experienced by a soccer ball, we need to calculate
the lift coefficient,
C
L
. Fortunately, there is some experimental data on which we can base our
estimation. Tests were conducted at the University of Sheffield in which a soccer ball was fired
at a constant velocity of 18
m/s
with varying spin rates.
5
The lift and drag coefficients experi-
enced by the ball were measured, and the results are shown in Figure 7-15.
To use this information in a soccer simulation, a function is defined, shown in Equation (7.56),
that approximates the lift coefficient experimental data. The results from Equation (7.56) are
included in Figure 7-15.
0.25
⎛⎞
r
C
=
0.385
(7.56)
⎜⎟
⎝⎠
L
v
Just as was the case with modeling golf balls, the expression for computing the lift coeffi-
cient of a soccer ball shown in Equation (7.56) is still a function of the rotational spin ratio, but
it is more accurate than the Bernoulli approximation of assuming that the lift coefficient is
equal to the rotational spin ratio.
