Game Development Reference
in the technical literature (see the Bibliography for sources). Note that experimentally
determined friction coefficient data will vary, even for the same surface conditions,
depending on the specific condition of the material used in the experiments and the
execution of the experiment itself.
Fluid Dynamic Drag
Fluid dynamic drag forces oppose motion like friction. In fact, a major component of
fluid dynamic drag is friction that results from the relative flow of the fluid over (and
in contact with) the body's surface. Friction is not the only component of fluid dynamic
drag, though. Depending on the shape of the body, its speed, and the nature of the fluid,
fluid dynamic drag will have additional components due to pressure variations in the
fluid as it flows around the body. If the body is located at the interface between two fluids
(like a ship on the ocean where the two fluids are air and water), an additional compo‐
nent of drag will exist due to the wave generation.
In general, fluid dynamic drag is a complicated phenomenon that is a function of several
factors. We won't go into detail in this section on all these factors, since we'll revisit this
subject later. However, we do want to discuss how the viscous (frictional) component of
these drag forces is typically idealized.
Ideal viscous drag is a function of velocity and some experimentally determined drag
coefficient that's supposed to take into account the surface conditions of the body, the
fluid properties (density and viscosity), and the flow conditions. You'll typically see a
formula for viscous drag force in the form:
F v = -C f v
where C f is the drag coefficient, v is the body's speed, and the minus sign means that the
force opposes motion. This formula is valid for slow-moving objects in a viscous fluid.
“Slow moving” implies that the flow around the body is laminar , which means that the
flow streamlines are undisturbed and parallel.
For fast-moving objects, you'll use the formula for F v written as a function of speed
squared as follows:
F v = -C f v 2
“Fast moving” implies that the flow around the object is turbulent , which means that
the flow streamlines are no longer parallel and there is a sort of mixing effect in the flow
around the object. Note that the values of C f are generally not the same for these two
equations. In addition to the factors mentioned earlier, C f depends significantly on
whether the flow is laminar or turbulent.