Game Development Reference

In-Depth Information

stability in your integration algorithms. We'll discuss these issues more when we show

you several simulation examples in
Chapter 7
through
Chapter 14
.

We've devoted this entire chapter to projectile motion because so many physical prob‐

lems that may find their way into your games fall in this category. Further, the forces

governing projectile motion affect many other systems that aren't necessarily projectiles

—for example, the drag force experienced by projectiles is similar to that experienced

by airplanes, cars, or any other object moving through a fluid such as air or water.

A projectile is an object that is placed in motion by a force acting over a very short period

of time, which, as you know from
Chapter 5
, is also called an impulse. After the projectile

is set in motion by the initial impulse during the launching phase, the projectile enters

into the projectile motion phase, where there is no longer a thrust or propulsive force

acting on it. As you know already from the examples presented in
Chapter 2
and
Chap‐

ter 4
, there are other forces that act on projectiles. (For the moment, we're not talking

about self-propelled “projectiles” such as rockets since, due to their propulsive force,

they don't follow “classical” projectile motion until after they've expended their fuel.)

In the simplest case, neglecting aerodynamic effects, the only force acting on a projectile

other than the initial impulsive force is gravitation. For situations where the projectile

is near the earth's surface, the problem reduces to a constant acceleration problem.

Assuming that the earth's surface is flat—that is, that its curvature is large compared to

the range of the projectile—the following statements describe projectile motion:

• The trajectory is parabolic.

• The maximum range, for a given launch velocity, occurs when the launch angle is

45°.

• The velocity at impact is equal to the launch velocity when the launch point and

impact point are at the same level.

• The vertical component of velocity is 0 at the apex of the trajectory.

• The time required to reach the apex is equal to the time required to descend from

the apex to the point of impact assuming that the launch point and impact point

are at the same level.

• The time required to descend from the apex to the point of impact equals the time

required for an object to fall the same vertical distance when dropped straight down

from a height equal to the height of the apex.

Simple Trajectories

There are four simple classes of projectile motion problems that we'll summarize:

• When the target and launch point are at the same level