Game Development Reference

In-Depth Information

Both of these equations are very simplified and inadequate for practical analysis of fluid

flow problems. However, they do offer certain advantages in computer game simula‐

tions. Most obviously, these formulas are easy to implement—you need only know the

velocity of the body under consideration, which you get from your kinematic equations,

and an assumed value for the drag coefficient. This is convenient, as your game world

will typically have many different types of objects of all sizes and shapes that would make

rigorous analysis of each of their drag properties impractical. If the illusion of realism

is all you need, not real-life accuracy, then these formulas may be sufficient.

Another advantage of using these idealized formulas is that you can tweak the drag

coefficients as you see fit to help reduce numerical instabilities when solving the equa‐

tions of motion, while maintaining the illusion of realistic behavior. If real-life accuracy

is what you're going for, then you'll have no choice but to consider a more involved

(read: complicated) approach for determining fluid dynamic drag. We'll talk more about

drag in
Chapter 6
through
Chapter 10
.

Pressure

Many people confuse pressure with force. You have probably heard people say, when

explaining a phenomenon, something like, “It pushed with a force of 100 pounds per

square inch.” While you understand what they mean, they are technically referring to

pressure, not force. Pressure is force per unit area, thus the units
pounds per square

inch
(psi) or
pounds per square foot
(psf ) and so on. Given the pressure, you'll need to

know the total area acted on by this pressure in order to determine the resultant force.

Force equals pressure times area:

F = PA

This formula tells you that for constant pressure, the greater the area acted upon, the

greater the resultant force. If you rearrange this equation solving for pressure, you'll see

that pressure is inversely proportional to area—that is, the greater the area for a given

applied force, the smaller the resulting pressure and vice versa.

P = F/A

An important characteristic of pressure is that it always acts normally (perpendicularly)

to the surface of the body or object it is acting on. This fact gives you a clue as to the

direction of the resultant force vector.

We wanted to mention pressure here because you'll be working with it to calculate forces

when you get to the chapters in this topic that cover the mechanics of ships, boats, and

hovercraft. There, the pressures that you'll consider are hydrostatic pressure (buoyancy)

and aerostatic lift. We'll take a brief look at buoyancy next.