Game Development Reference
In-Depth Information
Figure 11-5.
Variation of atmospheric density with altitude
It's apparent from Figure 11-5 that density changes quite significantly with increasing alti-
tude. The density at 80
km
is almost 100,000 times less than the density at sea level.
Another quantity needed to compute aerodynamic drag is the drag coefficient for the
rocket. The drag coefficient will be a function of Reynolds number, and there will be a spike
in drag coefficient if and when the rocket exceeds the speed of sound. Typically, values of
rocket drag coefficients range from 0.2 to 1.0. If you don't want to go through the trouble of
modeling drag coefficient more precisely for your game simulation, you can assume a constant
drag coefficient somewhere in the typical range.
It turns out that drag isn't such a big deal with large rockets, because the thrust generated
by the rocket engines tends to be much greater than the drag force. Furthermore, because the
density decreases by orders of magnitude as the altitude increases, the peak drag force level
occurs at relatively low altitudes and declines significantly after that point. Figure 11-6
presents the computed velocity profiles with and without drag effects for the Saturn 1B rocket
during a vertical ascent. A constant drag coefficient of 0.5 was used in the calculations.
The inclusion of drag effects has a small but noticeable effect on the velocity profile of the
Saturn 1B rocket. If drag is included in the calculation, the velocity of the rocket at 150 seconds
is equal to 1500
m/s
. If drag is not included, the velocity of the rocket at 150 seconds is equal to
1560
m/s
for a difference of about 4%.
