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The issue of yaw stability in planes is solved by having the center of mass in front of the center of pressure .
Additionaly the the pitch stability is solved by the center of gravity beeing ahead of the center of lift of the airfoil and the elevator creating downforce.
This also works in simmilar ways for ground effect vehicles, but here the ground effect adds some additional altitude stability.
In cars that still touch the ground you wouldn't be able to do that as any lift on the front axle causes the front axle to move up and generate more lift.
Eventualy leading to the entire car taking off uncontrolled when it spirals out of controll.
There are cars with the center of gravity behind the center of drag.
These cars can get aerodynamicly unstable at high speed.
If you've ever driven an MR2 at 200 km/h or more without the spare tire in place, you'll know what I'm talking about.
The opposite case can be found in front engine frront wheel drive wagons with their center of gravity beeing far ahead of the center of drag, wich makes them realy stable at topspeed.
To move the center of drag (or rather pressure) rear, you want vertical finns on the rear of your car.
A big issue with rear end lift is that it creates oversteer, wich can be dangerous at high speed.
A big issue with front end lift is that it can get out of controll and make the car take off entirely.
In passenger cars this is not at all a good idea.
Before going into such marginal gains with as high of a risk as that, there are other things to optimize.
Such as variable cooling systems, better undertrays and ending the SUV-craze.
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