Game Development Reference
In-Depth Information
reasonable to assume that the drag coefficient for a projectile is constant. You could also take
the more rigorous approach and build a variable drag coefficient into your projectile model. As
a game programmer, you will have to decide whether it is necessary to add this extra complexity
to your simulation.
Altitude Effects on Density
It would simplify the drag model even further if the drag force could be considered to be a function
of velocity only—that is to say, if density could be considered to be constant as well as the drag
coefficient. The density of air is a function of altitude, but unless the altitude changes by several
miles over the course of the trajectory, it is reasonable to assume that density is constant during
the flight of the projectile. That being said, there will be altitude effects on the trajectory of a
projectile. Drag effects will be less at Denver, Colorado, than they will be at sea level because
the atmospheric density will be lower in Denver. While assuming that density is constant over
the course of a projectile trajectory is probably okay, the density value should be adjusted
according to the local altitude. Table 5-4 shows the value of air density at several altitudes in
both SI and English units.
Table 5-4.
Values of Air Density As a Function of Altitude
Density (
kg/m
3
)
Density (
slug/ft
3
)
Altitude (
m
)
Altitude (
ft
)
0.0
0.0
1.225
0.00238
305
1000
1.189
0.00231
610
2000
1.154
0.00224
914
3000
1.121
0.00218
1219
4000
1.088
0.00211
1524
5000
1.055
0.00205
2134
7000
0.992
0.00192
3048
10,000
0.905
0.00176
A situation where the assumption of density would not be valid would be in modeling the
trajectory of a rocket or missile because the air density at the upper extent of the earth's atmo-
sphere is orders of magnitude less than at sea level. We'll look into modeling rocket and missile
trajectories in Chapter 11.
Laminar and Turbulent Flow
So far in this chapter, we have discussed the physics of a projectile flying through a fluid such
as air. In the previous section, we introduced the concept of drag as the resistance a fluid exerts
on an object traveling through it. It turns out there are two general ways that air or any other
fluid can travel over an object. The fluid can travel smoothly and steadily over the object. This
is known as
laminar
flow. Typically, low Reynolds number flows will be laminar. As the Reynolds
