What do we know about the formula for air drag force?

[victorhugo]

Is it the typical "get some results and stack the maths together and chuck in some constants to make it fit to get some approximation" or do we understand the rules behind it to derive the formula, such as how the molecules repel each other and how energy is transferred depending on temperature, velocity, etc

 

[rcgldr]

If you're considering speeds greater than Mach 0.3, it gets complicated. In order to use the simple formula where drag force = Cd v², Cd becomes a function of v, interpolated from measured or calculated values in a table. Wiki article, note table showing how drag coefficient varies with Mach (speed). In the wiki example, Cd is near constant until Mach 0.4 (it's also possible that when the table was generated, values of Cd for speed less than Mach 0.4 weren't important, so a constant Cd was chosen, not measured).

http://en.wikipedia.org/wiki/External_ballistics#Doppler_radar-measurements

 

[Delta Kilo]

Is it the typical "get some results and stack the maths together and chuck in some constants to make it fit to get some approximation" or do we understand the rules behind it to derive the formula, such as how the molecules repel each other and how energy is transferred depending on temperature, velocity, etc

It is both.
We do understand the rules quite well, see Navier-Stokes Equations, unfortunately most of the time they do not have analytic solutions (*) so it's either heavy-duty number crunching CFD or back to method #1.

(*) And we don't even know if solutions exist. It is quite literally a million-dollar question, see http://www.claymath.org/millennium-problems

 

[victorhugo]

(*) And we don't even know if solutions exist. It is quite literally a million-dollar question, see http://www.claymath.org/millennium-problems

So a Nobel prize awaits the answer?

 

[BvU]

Probably. Sure worth a try ... twice therefore !