Game Development Reference

In-Depth Information

diameter. A more useful application of this scaling technique is estimating the viscous

drag on ship or airplane appendages based on model test data obtained from wind tunnel

or tow tank experiments.

The Reynolds number is used as an indicator of the nature of fluid flow. A low Reynolds

number generally indicates laminar flow, while a high Reynolds number generally in‐

dicates turbulent flow. Somewhere in between, there is a transition range where the flow

makes the transition from laminar to turbulent flow. For carefully controlled experi‐

ments, this transition (
critical
) Reynolds number can consistently be determined. How‐

ever, in general the ambient flow field around an object—that is, whether it has low or

high turbulence—will affect when this transition occurs. Further, the transition Rey‐

nolds number is specific to the type of problem being investigated (for example, whether

you're looking at flow within pipes, the flow around a ship, or the flow around an air‐

plane, etc.).

We calculate the total drag coefficient,
C
d
, by measuring the total resistance,
R
t
, from

tests and using the following formula:

C
d
= R
t
/ (0.5 ρ v
2
A)

where
A
is a characteristic area that depends on the object being studied. For a sphere,

A
is typically the projected frontal area of the sphere, which is equal to the area of a

circle of diameter equal to that of the sphere. By comparison, for ship hulls,
A
is typically

taken as the underwater surface area of the hull. If you work out the units on the right‐

hand side of this equation, you'll see that the drag coefficient is nondimensional (i.e., it

has no units).

Given the total drag coefficient, you can estimate the total resistance (drag) using the

following formula:

R
t
= (0.5 ρ v
2
A) C
d

This is a better equation to use than the ones given in
Chapter 3
, assuming you have

sufficient information available—namely, the total drag coefficient, density, velocity,

and area. Note the dependence of total resistance on velocity squared. To get
R
t
in units

of newtons (N), you must have velocity in m/s, area in m
2
, and density in kg/m
3
(re‐

member C
d
is dimensionless).

Turning back now to
Figure 6-9
, you can make a couple of observations. First, you can

see that the total drag coefficient decreases as the Reynolds number increases. This is

due to the formation of the separation point and its subsequent move aft on the sphere

as the Reynolds number increases and the relative reduction in pressure drag, as dis‐

cussed previously. At a Reynolds number of approximately 250,000, there is a dramatic