Game Development Reference
In-Depth Information
Summary: Gravity-Only Projectile Trajectory Model
A very simple projectile model that we call the gravity-only model can be formulated if it is
assumed that the only net force on the projectile is due to gravity. Here are some of the key
outcomes of the gravity-only model:
•
The only force on the projectile is due to gravity, which acts in the vertical, or z-, direction.
The horizontal velocity components in the x- and y-directions will remain constant at
whatever the initial velocities in those directions are.
•
The motion in the three coordinate directions is independent. What happens in the
y-direction, for instance, has no effect on what happens in the x- or z-directions.
•
The projectile trajectory is independent of mass and projectile geometry.
•
The velocity in the x- and y-directions is constant over the entire trajectory and is equal
to the initial velocities in the x- and y-direction.
•
The shape of the projectile trajectory will be a parabola.
The advantage of the gravity only model is that it is easy to formulate and minimizes the
computer time required to solve the equations of motion. Closed-form expressions can be
obtained for the velocity and location of the projectile as a function of time. The disadvantage,
as you probably could guess, is that it ignores some potentially important effects, such as aero-
dynamic drag and wind effects. The gravity-only model cannot be applied to all projectile
trajectory problems, but it gives a reasonably accurate representation of projectile motion if
the projectile is not traveling too quickly, spinning too rapidly, or exposed to a strong wind.
A summary of the equations of motion for the gravity-only projectile trajectory model is
shown in Table 5-1.
Table 5-1.
Summary of Equations of Motion for the Gravity-Only Projectile Model
x-Direction
y-Direction
z-Direction
−
mg
Force
0
0
−
g
Acceleration
0
0
v
v
z
v t
−
Velocity
x
0
y
0
0
1
2
x
vt x
+
yvt
+
2
zvt
+−
t
Location
0
0
0
y
0
0
z
0
