Forces involved

Looking at the front view, the vertical forces acting on the vehicle are the weight (W = mg), pushing the vehicle down on the tires, and the aerodynamic lift (F_L = 0.5ρC_LAv²), lifting up the vehicle. Both are assumed to be equally distributed between the left and right tires and are acting one against each other.

Traction limit

The maximum inertia force (ma_Lmax) that can be apply before the vehicle begins sliding sideways will depend on the friction force.

The resulting vertical force (F_v) acting on all tires is:

The resulting friction force (F_f) from all tires will be:

That friction force will be the only force acting against the inertia of the vehicle, hence:

Rewriting:

Rollover limit

Because the friction force acts at ground level and the inertia force acts at the center of gravity, there will be a weight transfer from the inside tires to the outside tires. Once the vertical force acting on the inside tires is equal to 0, then the inside tires are off the ground, leaving the total weight of the vehicle on the outside tires. This is the rollover limit. The maximum load that can be transferred from the inside tires will be half of the total vertical force. Doing the sum of moments, we get:

Rewriting:

Summing up equations (1c) and (1d):