Aerodynamics

[luncheonticket]

Almost all production vehicles have some degree of aerodynamic lift at high speeds, except for maybe some of the fastest and most expensive exotics. The manufacturers usually tend to err on the side of low drag instead of low lift when choosing a compromise since it's more advantageous (high lift is only bad for high-speed handling while high drag is bad for top speed, fuel efficiency and emissions).

However, they are making great advances nowadays, achieving low drag figures while keeping lift to a bare minimum (or as I said, even managing to create some downforce).

@Killrob True, but that is true for most cars. However, lift is higher!

[aknot]

I happen to know a little about aerodynamics and feel I might help a little out, hoping you guys can use these formulas...
First of all: I'm going to leave out friction of airflow along the side of the car, since it only matters for long things like trains, not for cars. I won't be looking at turbulences, since barely possible to calculate. This can be assumed, as long as the rear of the car has a perfect edge and the scurface of the car is perfectly even. I'd guess we get around 10%-20% less than what we should.

Edit: First I had it totally wrong, everything was crap, so now I hope I finally have it right...

Lets get started:

At the front of the car air particles/molecules collide with the car's body. They then fly on in a different angle, roughly in the direction of the next convex edge. The change in momentum of those air particles are equal to the change in momentum of the car, which equals drag force and downforce/lift combined.

I will need the hight difference to the next convex edge, and I call it h. I will also need the lengthy distance from nosetip to said edge and call it x.

For dF i got:

dF = * h * rho * dA * ds/dt * v / ( cos(alpha)*x + sin(alpha)*h) = rho*dA*v^2 * h/(cos(alpha)*x+sin(alpha)*h)

horizontal component
dF_h=sin(alpha)*dF
and vertical: dF_v=cos(alpha)*dF

Where alpha is the angle of the outline of the car (so the angle counts, not so much its gradient!! Though that causes turbulences, as do concave edges...)

dF_h can be calculated for all heights and widths and added up to total drag.
dF_v will add up to total downforce/lift

But we are only half way through, since we need to have a look at the rear too.
Here we get a drag force because of an area of underpressure behind the car.
I took a few more minutes to work out the underpressure from the euler-equations. Since that was somewhat more complicated than the above I leave the mathematical details out and present my solution:

delta_p = p_0 * (rho * (v * sin(alpha) )^2) / (2*p_0 + rho * (v * sin(alpha) )^2)

where p_0 is enviromental pressure (100kPa), rho the density of air (1.29 kg/m^3) and v the velocity.

The actual drag force is the area of the plane we are looking at times the underpressure...
F=A*delta_p and has the direction of the normal onto said plane, therefore:
drag = -sin(alpha)*F
lift = cos(alpha)*F

I think I got it right; I usually do...

To implement this I'd simply divide the front area into lets say at least 1000 little squares, calculate front and rear drag influencies and add all of them up (as if you'd calculate with 1000 molecules)...
If you have any questions or need further explanations ask me, if I don't answer fast enough you can bug me by writing to aknot@mailfish.de
Greets

[aknot]

sorry folks, have to add something:

If you have a rear part like the Nissan or the Mercedes (coupés and notchbacks) and your speed is not too high then the air beeing sucked down along the rear window (generating lift through underpressure) hits that rear end and generates downforce again. The faster you are, the lower the air pressure behind the rear window, the fewer air flows onto the trunk and the rear spoiler, and guess what, the less downforce and the more lift you have.

[Killrob]

Hey aknot, this is really good stuff I mean I'm a PhD in physics, but don't know nearly as much about this so I just want to say well done, it makes sense! You've been studying some fluid dynamics I take? I guess I'll have to kidnap you if I run into problems with the aerodynamics calculations in my own game. What I find especially interesting is your lift/downforce considerations. So that's why the Audi TT had such big problems keeping its ass on the road when going 200+ km/h haha.

One area where "sides" or "flat" areas matter is the underworks, although they are poorly developed for most "normal" cars, but they definitely contribute to the drag through friction and causing turbulence.

Another question: turbulence... would you say that when it kicks in it behaves more like v^(2+x) where x is a positive number, or still just as v^2? For now I've settled for something around v^3 which seems to give reasonable results... but I'm a nub, so no telling if it actually makes sense, chaos is hard to calculate xD