Game Development Reference
In-Depth Information
The ratio in Equation (7.22) is also known as the
rotational spin ratio
. According to Bernoulli's
equation, the Magnus force lift coefficient is equal to the rotational spin ratio. But how good is
this approximation? The results from Equation (7.22) can be compared against experimental
measurements of the lifting force exerted on a spinning golf ball. Figure 7-7 displays the exper-
imental measurements of lift coefficient on a standard dimpled golf ball as a function of the
rotational spin ratio.
2
Also shown in Figure 7-7 is the lift coefficient predicted by Equation (7.22),
which is a straight line.
Figure 7-7.
Experimental and computed lift coefficients for a standard golf ball
In looking at Figure 7-7, we can see that the Bernoulli equation approximation for the lift
coefficient, shown in Equation (7.22), underpredicts the lift coefficient for rotational spin ratios
below 0.3 and overpredicts the lift coefficient for rotational spin ratios above 0.3. A more accu-
rate estimation of
C
L
can be obtained by using the expression shown in Equation (7.23), which
models the relationship between rotational spin ratio and
C
L
as a curve.
⎛⎞
r
C
=−
0.05
+
0.0025
+
0.36
(7.23)
⎜⎟
⎝⎠
L
v
The values from Equation (7.23) are also shown in Figure 7-7 and are closer to the experi-
mental values. One thing to keep in mind when using Equation (7.23) is that it is based on the
absolute magnitude of the angular and translational velocities. When you plug the value of the
rotational spin ratio into Equation (7.23), make sure the value is positive.
