Game Development Reference
jectile. This was illustrated in the example program discussed in Chapter 4 . Recall that
the drag force is a vector just like any other force and that it acts on the line of action of
the velocity vector but in a direction opposing velocity. While those formulas work in
a game simulation, as we said before, they don't tell the whole story. While we can't treat
the subject of fluid dynamics in its entirety in this topic, we do want to give you a better
understanding of drag than just the simple idealized equation presented earlier.
Analytical methods can show that the drag on an object moving through a fluid is
proportional to its speed, size, shape, and the density and viscosity of the fluid through
which it is moving. You can also come to these conclusions by drawing on your own
real-life experience. For example, when waving your hand through the air, you feel very
little resistance; however, if you put your hand out of a car window traveling at 100 km/
h, then you feel much greater resistance (drag force) on your hand. This is because drag
is speed dependent. When you wave your hand underwater—say, in a swimming pool
—you'll feel a greater drag force on your hand than you do when waving it in the air.
This is because water is more dense and viscous than air. As you wave your hand un‐
derwater, you'll notice a significant difference in drag depending on the orientation of
your hand. If your palm is in line with the direction of motion—that is, you are leading
with your palm—then you'll feel a greater drag force than you would if your hand were
turned 90 degrees as though you were executing a karate chop through the water. This
tells you that drag is a function of the shape of the object. You get the idea.
To facilitate our discussion of fluid dynamic drag, let's look at the flow around a sphere
moving through a fluid such as air or water. If the sphere is moving slowly through the
fluid, the flow pattern around the sphere would look something like Figure 6-5 .
Figure 6-5. Flow pattern around slowly moving sphere
Bernoulli's equation , which relates pressure to velocity in fluid flow, says that as the fluid
moves around the sphere and speeds up, the pressure in the fluid (locally) will go down.
The equation, presented by Daniel Bernoulli in 1738, applies to frictionless incompres‐
sible fluid flow and looks like this: 1
P / γ + z + V 2 / (2g) = constant
1. In a real fluid with friction, this equation will have extra terms that account for energy losses due to friction.