Game Development Reference
Moving further aft along the sphere, the boundary layer grows in thickness and will not
be able to maintain its adherence to the sphere surface, and it will separate at some point.
Beyond this separation point , the flow will be turbulent, and this is called the turbulent
wake . In this region, the fluid pressure is lower than that at the front of the sphere. This
pressure differential gives rise to the pressure component of drag. Figure 6-7 shows how
the flow might look.
Figure 6-7. Flow pattern around sphere showing separation
For a slowly moving sphere, the separation point will be approximately 80° from the
Now, if you were to roughen the surface of the sphere, you'll affect the flow around it.
As you would expect, this roughened sphere will have a higher friction drag component.
However, more importantly, the flow will adhere to the sphere longer and the separation
point will be pushed further back to approximately 115°, as shown in Figure 6-8 .
Figure 6-8. Flow around a roughened sphere
This will reduce the size of the turbulent wake and the pressure differential, thus de‐
creasing the pressure drag. It's paradoxical but true that, all other things being equal, a
slightly roughened sphere will have less total drag than a smooth one. Ever wonder why
golf balls have dimples? If so, there's your answer.
The total drag on the sphere depends very much on the nature of the flow around the
sphere—that is, whether the flow is laminar or turbulent. This is best illustrated by
looking at some experimental data. Figure 6-9 shows a typical curve of the total drag
coefficient for a sphere plotted as a function of the Reynolds number .