Game Development Reference
In-Depth Information
Table 11-4.
Stage Data for the Saturn 5 Rocket
Quantity
Stage 1
Stage 2
Stage 3
Initial mass (
kg
)
2.85
e
+ 6
5.93
e
+ 5
1.19
e
+ 5
Final mass (
kg
)
8.85
e
+ 5
1.54
e
+ 5
1.54
e
+ 4
Isp (
s
)
304
418
418
Exhaust velocity, (
m/s
)
2980
4096
4096
Burn time, (
s
)
150
359
480
The change in velocity for each stage can be computed from Equation (11.22).
m
s
2.85
e
e
+
6
⎛
⎞
Δ=
v
2980 ln
−
150 *9.8
=
2015
(11.23a)
⎜
⎟
1
8.85
+
5
⎝
⎠
5.93
e
e
+
5
m
s
⎛
⎞
Δ=
v
4096 ln
−
359 *9.8
=
2004
(11.23b)
⎜
⎟
2
1.54
+
5
⎝
⎠
m
s
⎛
1.19
e
e
+
5
⎞
Δ=
v
4096 ln
−
480 *9.8
=
3671
(11.23c)
⎜
⎟
3
1.54
+
4
⎝
⎠
The total change in velocity for the rocket is the sum of the velocity changes for each stage.
m
s
Δ=Δ
v
v
Δ
v
Δ=
v
7957.7
(11.24)
total
1
2
3
v
result to the value that would be obtained if the first
stage of the Saturn 5 were flown by itself. In this situation, the initial mass of Stage 1 would
be 2.18
e
+ 6
kg
and the final mass would be 2.13
e
+ 5
kg
. If the engines were fired for 150 seconds,
the change in velocity according to the rocket equation would be the following:
Δ
Let's compare the multistage
m
s
⎛
2.18
e
e
+
6
⎞
Δ=
v
2980 ln
−
150 *9.81
=
5461
(11.25)
⎜
⎟
1
2.13
+
5
⎝
⎠
The advantages of staging are pretty clear. In this example, going with a multistage rocket
increased the potential
Dv
of the rocket by over 40%.
Incorporating a multistage rocket into a rocket simulation is pretty straightforward. When
a stage finishes its burn time, it is separated from the rest of the stack. The mass of the rocket
would be adjusted for structural weight of the stage that was jettisoned. There will typically be
a several-second delay between stage separation and when the engines of the next stage will
ignite. The general equations for thrust, drag, and gravity that we developed in this chapter are
equally applicable to multistage rockets.
