[Tesla]

I stumbled across some threads questioning the benefits of excluding underflow air on these types of vehicles and have been trying to get a better picture of what is going on there.

As far as I can see the air dam is a "dirty fix" for a "dirty problem", that being primarily the "Aero torture chamber" of mechanical parts as Aerohead describes it.
So if we clean this up a bit, with some underbody panelling,belly pans, then I imagine this would be superior to an air dam.

It seems more and more car makers are shifting to this solution rather than ground hugging air dams, even on std road vehicles there is a gently downward inclined undertray starting from the front bumper to front axle assembly or further.

I also read that there is a fringe area between 9-14" ground clearance where it is questionable whether air should be excluded or allowed to flow under the vehicle. In my case I have 12" clearance under the bottom of the axles, the only things lower are the pumpkins (diff housing's) and the more I look at it the less sense keeping the air out makes, even with all the mechanicals. The only way would be to increase frontal area with a low air dam and full side skirts and that doesn't really make sense.

Information around this seems to be pretty scant, firstly most aero information is tainted with "top speed performance" concepts, and then most of it is in relation to regular road vehicles. I tried looking at the trucking industry and again, they have different goals and constaraints, although they are taller wheel vehicles, because of their load bearing nature the axle/suspension structures are so bulky that they have less under axle clearance than I do.

So I imagine this problem needs to be considered in the form of duct modeling.
I have 12" ground clearance at 54" wide, considering the mirror effect of the ground, this would represent a duct 24" high and 54" wide.
For a regular car, the same width but only 6" clearance would be 12" high x 54" wide.

Now I really don't know that much about airflow in ducts, but I do know that Volume (V) : Surface Area (SA) ratio is an important factor and the higher vehicle has nearly twice the volume for only a small increase in SA, 8.3:1 vs 4.9:1.
In addition to that we know boundary layer gets thicker as we go down the length of the vehicle, As an arbitary figure, assume it gets to 1" at the rear outflow, the numbers then become 22"x52" and 10"x52", that brings us to 7.9:1 vs 4.2:1 ratios, both got worse, but the lower vehicle dropped 14% while the higher vehicle dropped less, only 6%.

Now ignoring wheels and their turbulance for this exercise, airflow through the taller duct would be twice as good at the very least than that in the lower duct.

So if we think of the 3d model, body of rotation etc. with fixed external dimensions and we put a small hole in the middle and go through the stages of making the hole bigger, there must be a point where drag begins to fall as the hole gets bigger. until it becomes less than baseline eg:

No hole = Baseline
Small hole = Baseline +1 drag
Hole +1 = Baseline +2 drag
Hole +2 = Baseline +3 drag
Hole +3 = Baseline +2 drag
Hole +4 = Baseline +1 drag
Hole +5 = Baseline drag
Hole +6 = Baseline -1 drag
Hole +7 = Baseline -2 drag

So what are these numbers and at what point is it better to let air go under freely than try to restrict it?