Game Development Reference
In-Depth Information
This definition is equal to the previous one without the gravitational acceleration scaling.
The units for the specific impulse as defined in Equation (11.11) are typically expressed in
terms of
(N-s)/kg
, which is equivalent to
m/s
. You can use either definition for
I
sp
in your game
programming; just make sure that the units of the
I
sp
value that you are using match the defi-
nition of
I
sp
.
Altitude Effects
Looking at Equation (11.3), one of the contributions to engine thrust is the pressure thrust
caused by the difference between the nozzle exit pressure and the surrounding atmospheric
pressure. As altitude increases, the atmospheric pressure decreases, so the thrust generated
by the engine will increase. For example, the F-1 rocket engine used with the Saturn 5 rocket
generates a specific impulse of 260
s
at sea level and 304
s
in a vacuum. The corresponding sea-
level thrust for the F-1 engine is 6.67
e
+ 6
N
, and the vacuum thrust is 7.86
e
+ 6
N
.
One way to model altitude effects on thrust is to simply vary the thrust from the sea-level
to vacuum values using the pressure ratio as the scale factor.
p
(
)
FF
=
−
F
−
F
(11.12)
T
T vacuum
,
T vacuum
,
T SL
,
p
0
In Equation (11.12), the quantity
p
is the atmospheric pressure at the current altitude and
p
0
is the pressure at sea level. The quantity
F
T,SL
is the sea-level thrust and
F
T,vacuum
is the
vacuum thrust.
It turns out that pressure decreases quite rapidly with altitude, so that the pressure ratio
gets small when the rocket is still at a relatively low altitude. Table 11-2 lists the pressure and
pressure ratio over a range of altitudes. Also shown in Table 11-2 is the thrust produced by an
F-1 engine according to Equation (11.12). At 10
km
, the pressure ratio is down to 0.262 and the
engine thrust is 96% of the vacuum thrust value of 7.86
e
+ 6
N
. At 30
km
, the pressure ratio has
dropped to about 0.011.
Table 11-2.
Pressure and Pressure Ratio As a Function of Altitude
Pressure (
N/m
2
)
Altitude (
km
)
Pressure Ratio
F-1 Engine Thrust (
N
)
0
101,325
1.0
6.672
e
+ 6
5
54,054
0.533
7.276
e
+ 6
10
26,506
0.262
7.549
e
+ 6
20
5531
0.055
7.795
e
+ 6
30
1198
0.011
7.847
e
+ 6
40
287
0.003
7.856
e
+ 6
For game programming purposes, one way to incorporate altitude effects on thrust would
be to compute the thrust according to Equation (11.12) up to an altitude of 40-50
km
and just
use the vacuum thrust value at higher altitudes.
