What's the optimal air density for lap times?

[DiogoBrand]

Whenever the Mexico Grand Prix is on, air density and how it affects the cars is always a big talking point, so that led me to a question:
What would be the best fluid density for cars to achieve the best lap times possible?
Higher densities have a positive effect on downforce, while creating more drag, also I guess the cars would perform better at Mexico if they were entirely developed with that air density in mind, but if you think about it:
If cars raced in a 0 gas density environment, a.k.a. a vacuum (not taking in consideration that there would be no air for the engine, radiators, or driver), they'd have no drag, but also no downforce.
While on the other hand if cars raced on a very dense environment, a.k.a. a liquid (not taking in consideration the lubrication and loss of temperatures of the tyres, and the viscosity), it would have massive downforce, but would also be impossible to get high speeds on the straights.

So considering only drag and downforce, is there an optimal gas, or fluid density for cars to race on and is there a way to find out what it is?

[flynfrog]

I don't have the answer Diogo, I find it a great question. Just as a thought experiment I would think the denser the better at least in the real world IE sea level. My reasoning is that the denser the air the more power the engine will make, the better the wings work, and the better the heat exchangers work to cool the car (you could close up openings). The only downside would be drag but I would guess that the more power and more DF would counter act the drag. This all goes out the window when we say get a few more BAR of pressure on the car. I think a few members have lap time simulators that might be able to punch in the change of power and df vs drag.

[Steven]

I don't really have the answer either

To add some info, here's a clip of McLaren explaining the aero impact of the altitude:

[SectorOne]

I´m guessing it won´t matter too much unless you´re at the very end of the spectrums i.e. dont have more downforce to slap on or can´t take off any more downforce.
Seems like if you´re right in the middle of the spectrum you could simply balance the aero to get the same outcome?
say SPA, medium DF. If you increase air density you can take off wing and still generate the same DF/Drag as before?

I´ve ignored engine, brake temps for simplicity in my ramblings above.

[Vyssion]

I would think that the main issue you would run into would be engine stoichiometry rather than aero... lower density would negatively affect the engine performance obviously.

But we are talking air density fluctuations somewhere in the region of <10% variance, ignoring other factors such as relative humidity and particulate content etc...

In terms of the theoretical equations that apply, both the drag and downforce equations vary proportionally with density. There is one way that you would swing the equations to imply a lower density is better though... There is a lot of confusion regarding whether to use planform or frontal area for force calculations. In aerospace, planform is used for lift whilst in racing what is typically done, is to use frontal area for both. In some racing teams (including F1 from my experience) uses a "fixed" area constant value to calculate them; this is due to the fact that with aerofoil pitch and rake angle changes, along with others, the actual frontal area changes and it is simpler to say that "this tweak gives x-many points of additional downforce" and ignore the area all together than to recalculate everything.

By this logic, if you were to swap to using frontal area for drag and planform area for lift, given that planform is usually much larger than the frontal area, you could argue that a lower density air would be better for aerodynamic efficiency (L/D) than a higher one, excluding all other factors. Whether this solution actually occurs in reality, I can't say off the top of my head... Within CFD, forces are typically calculated by summation of all of the pressure vectors on a surface and then the components in line with the specified coordinate system correspond to the lift and drag figures... i.e. the two figures for lift and drag are generated from one "magnitude" of pressure which is calculated using either coupled or uncoupled equations for velocity, pressure and density (or energy) and "not" area... specifically

[Nickel]

Surely this, as most things, would be track specific? Monaco would favor very dense air while Monza would favor low density air?