Game Development Reference
In-Depth Information
Equation (11.8) is called the
rocket equation
and was first presented by Tsiolkovskii in
1903. It states that in the absence of any external forces, the velocity of a rocket at any point
in time is a function of the original mass and velocity of the rocket,
m
0
and
v
0
, the effective
exhaust velocity of the combustion gases,
v
e
, and the current mass of the rocket,
m(t)
. Since
propellant is being burned and expelled during the flight of the rocket, the mass at time
t
will
be less than the original mass.
The rocket equation as shown in Equation (11.8) is not applicable to all rocket problems
because it does not include the effects of drag or gravity. If a rocket was flying through the
atmosphere, Equation (11.8) would overpredict the velocity. The rocket equation as shown in
Equation (11.8) would be able to predict the velocity of a rocket that was traveling in outer space.
Specific Impulse
Rocket engines are often characterized by a quantity known as the
specific impulse
,
I
sp
, defined
as the thrust produced by the engine divided by the mass flow rate and the gravitational
acceleration.
F
I
=
T
sp
dm
(11.9)
g
dt
Specific impulse has units of seconds and can also be expressed in terms of the effective
exhaust velocity.
v
I
=
e
(11.10)
sp
g
In looking at Equation (11.9), we can see that a rocket engine with a higher specific impulse
will deliver more thrust for a given mass flow rate than will an engine with a lower specific impulse.
Table 11-1 shows typical specific impulse values for some general types of rocket engines.
1, 2
Table 11-1.
Specific Impulse for Some Rocket Engine Types
Rocket Engine Type
Specific Impulse (
s
)
Liquid oxygen—liquid hydrogen
425-460
Liquid oxygen—kerosene
260-330
Hypergolic
260-290
Nuclear
825-925
Antimatter
10
7
The specific impulse for the antimatter is a rough estimate, of course. Specific impulse is
sometimes defined as being equal to the effective exhaust velocity of the engine.
I
=
v
(11.11)
sp
e
