Game Development Reference
In-Depth Information
General Force Diagram
The forces that act upon a rocket during ascent are shown in Figure 11-3. By this time in the
topic, it probably comes as no shock to you that a rocket is acted upon by the forces of thrust,
drag, lift, and gravity. The thrust force is generated by the rocket engines. Drag, as always, acts
in the opposite direction of the velocity vector of the rocket. If the longitudinal axis of the
rocket is at an angle of attack relative to the flight path, a lift force will be generated. Gravity acts
in the vertical direction.
Figure 11-3.
A rocket during ascent experiences thrust, drag, lift, and gravity forces.
The angle
q
is called the pitch angle of the rocket. Most rockets lift off vertically, so the
pitch angle at liftoff will be 90
o
. The rocket force diagram shown in Figure 11-3 is very similar to
the airplane force diagram, Figure 10-20, that was presented towards the end of Chapter 10.
The net vertical force,
F
v
, and horizontal force,
F
h
, are functions of the thrust force,
F
T
, drag
force,
F
D
, lift force,
F
L
, and the pitch angle,
q
.
(
)
FFF
=−
cos
q
−
F
sin
q
(11.1)
h
T
D
L
(
)
FFF
=−
sin
q
+
F
cos
q
−
g
(11.2)
v
T
D
L
In this topic, we are using the convention that the vertical axis is in the z-direction. The
horizontal force component could be divided into x- and y-direction components depending
on the heading angle of the rocket.
Now that we have seen what the basic forces that act upon a rocket are, let's look at the
four forces in a bit more detail starting with the engine thrust.
Thrust
When the fuel and oxidizer are burned in the combustion chamber, the resulting high-
temperature, high-pressure gases are used to generate thrust. The thrust generated by a rocket
engine comes from two sources—the change in momentum imparted to the exhaust gases and
from the pressure difference at the exit plane of the nozzle.
dm
(
)
Fv
=
l
+
ppA
−
(11.3)
T
ex
e
a
e
dt
