When does air resistance transition from linear to quadratic velocity dependence?

[Steven_Scott]

In lower-division physics classes, air resistance is usually ignored to make the mathematics of projectile motion easier to understand.

When air resistance is included, it's often stated that at lower velocities, air resistance is proportional to the velocity of the object,

F_air ∝ kv

At higher speeds, air resistance becomes proportional to the square of the velocity,

F_air ∝ kv²

What I'm wanting to know is, how do we know at what speed air resistance is simply proportional to velocity and when does it become proportional to the square of the velocity?

Is there an easier way to determine when this "transition" takes place or does it depend on the geometry of the object you're working with?

 

[Orodruin]

This depends on the nature of the air flow around the object and therefore also on its geometry.

 

[jrmichler]

Some good search terms are exterior ballistics, external ballistics, drag coefficient vs Reynolds number. Lots of good information, although most of it would make more sense if you had taken a class in fluid dynamics. The Reynolds number is a non-dimensional number that incorporates fluid density, fluid viscosity, object size, and object velocity. At higher velocities, the Mach number becomes important.