Game Development Reference
In-Depth Information
Single-stage rockets have a difficult time reaching Earth's orbit. The solution to this problem is
what is known as a
multistage
rocket.
Multistage Rockets
A multistage rocket is two or more rockets, called
stages
, that are piggybacked on top of one
another to create a single launch system. The Saturn V rocket, shown in Figure 11-9, consists of
three stages that are stacked one on top of the other. The advantage of using a multistage rocket
is that the velocity gains from each stage are cumulative. One stage fires its engines, resulting
in a given final velocity after the engine burn. When the next stage fires its engines, it starts
(approximately) from the final velocity of the previous stage.
Figure 11-9.
The three-stage Saturn V rocket (Photo courtesy of NASA)
As an example of the advantages of multistaging, let's analyze the three stages of the
Saturn 5 rocket using the rocket equation. For this approximate analysis, we'll assume that the
rocket is ascending vertically and that gravitational acceleration is constant. We'll ignore drag
effects and use the vacuum thrust effective exhaust velocity in the computations. To calculate
the change in velocity from each stage, we'll make use of the “delta-V” form of the rocket equation.
⎛
⎞
m
Δ= − =
vvv v
ln
0
−
t
⎜
⎟
(11.22)
0
e
⎜
⎟
m
⎝
⎠
f
Typical stage data for the Saturn 5 is shown in Table 11-4.
4, 5
The initial and final masses
for each stage include any higher stages that are part of the stack. In other words, the stage 1
masses include the mass of the second and third stages that sit on top of stage 1. When a stage
has finished firing its engine, it separates from the stack, and the structural weight of the stage
is no longer included in the rocket mass estimation. Stage 3 of the Saturn 5 normally performs
two engine burns, but we'll use the total burn time here in our calculations.
