Game Development Reference
In-Depth Information
reduction in drag. This is a result of the flow becoming fully turbulent with a corre‐
sponding reduction in pressure drag.
In the Cannon2 example in Chapter 4 , we implemented the ideal formula for air drag on
the projectile. In that case we used a constant value of drag coefficient that was arbitrarily
defined. As we said earlier, it would be better to use the formula presented in this chapter
for total drag along with the total drag coefficient data shown in Figure 6-9 to estimate
the drag on the projectile. While this is more “accurate,” it does complicate matters for
you. Specifically, the drag coefficient is now a function of the Reynolds number, which
is a function of velocity. You'll have to set up a table of drag coefficients versus the
Reynolds number and interpolate this table given the Reynolds number calculated at
each time step. As an alternative, you can fit the drag coefficient data to a curve to derive
a formula that you can use instead; however, the drag coefficient data may be such that
you'll have to use a piecewise approach and derive curve fits for each segment of the
drag coefficient curve. The sphere data presented herein is one such case. The data does
not lend itself nicely to a single polynomial curve fit over the full range of the Reynolds
number. In such cases, you'll end up with a handful of formulas for drag coefficient,
with each formula valid over a limited range of Reynolds numbers.
While the Cannon2 example does have its limitations, it is useful to see the effects of drag
on the trajectory of the projectile. The obvious effect is that the trajectory is no longer
parabolic. You can see in Figure 6-10 that the trajectory appears to drop off much more
sharply when the projectile is making its descent after reaching its apex height.
Figure 6-10. Cannon2 example, trajectories
Another important effect of drag on trajectory (this applies to objects in free fall as well)
is the fact that drag will limit the maximum vertical velocity attainable. This limit is the
so-called terminal velocity . Consider an object in free fall for a moment. As the object
accelerates toward the earth at the gravitation acceleration, its velocity increases. As