If the tyre friction coefficient..

[Tam Lin]

..goes down as the tyre load increases, how does downforce work?

I am trying to understand the basics of the theory of car suspensions, and all I get is a headache.

Is the graph of friction vs. load linear?

Why do light cars handle better, if we add "weight" using aero? I just don't get it.

[HiRich]

Lateral force available = "Grip" = coefficient of friction ("u&quot x Vertical Reactive Force (Fr)
G = u x Fr
Adding downforce increases the grip available

Also
Fc=m v2 /r
Fc= Centripetal Force = Sum of the four Grip Forces from the four tyres = G1+G2+G3+G4
m = mass of vehicle
v = velocity
r = radius of corner.
m and r are fixed for the experiment.

Downforce has no part in this equation, only the mass of the vehicle
Fc has increased, m and r are unchanged, so v can increase.

If we add 1g of downforce, the grip available broadly doubles.
Fc broadly doubles.
mv2/r therefore broadly doubles.
r is fixed, and crucially m also remains the same.
Therefore v (speed of cornering) can increase by a factor of square root of 2, approx. 1.4

Answering the other questions:
The reduction in the coefficient of friction is likely to be much less than the increase in vertical force. Understanding in detail how grip is being generated is very complicated, requiring you to consider each square millimetre of the contact patch separately. It is possible to create a situation where the coefficient of friction drops rapidly (though more likely it's a case of the rubber failing), but in principle changes in CoF will usually be smaller than the increase in reactive force.
The coefficient of friction may be broadly linear in small sections, but is generally non-linear.
You should also remember that if you are using significant amounts of downforce, you will use a tyre (and suspension set-up) suited to the conditions it will be used in.

[GreenV8S]

If you were to plot vertical load against grip you would find that at low load levels they were almost exactly proportional to each other - double the load produces double the grip etc. At higher load levels this linear relationship changes and instead of double the grip, you get a bit less than double the grip. The amount of grip is still increasing, but the grip coefficient (grip divided by vertical load) is gradually reducing as the load increases.

[Tam Lin]

Thanks to both. Understood, in effect I was getting confused between "grip" and the coefficient "of grip"