On the other hand, I read somewhere else that with increasing speed, the effective center of pressure moves forward, to actually well in front of the vehicle. Any thoughts, Porkpie?
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Center of gravity and center of pressure - all this is important - YES.
But what helps if they looks on the right place, when the aerodynamic is wrong.
Exactly this creates the effect you request. If the aerodynamic, especially on the front end, is wrong, the pressure increase "uncontrolled" - with result that the center of pressure moves.
The center of pressure moves always...depends on the speed - more worse the aerodynamic is, so more he moves - but not always forward, he can move also backwards. If this happens your front end start to be weak.
If you got a clean aerodynamic with the right airflow along the car and rip off on the rear end the moving is so small that there is no effect on the balance of the car.