How does the need for side force increase and decrease in relation to speed?

The side force increases and decreases quadratically in relation to speed. If you double the speed, the need for side force will multiply four times, and if you triple the speed, the need for side force will multiply nine times. In order to reduce the driving side force during cornering, it is very important that you maintain an appropriate speed in the curve.

Side force is the lateral (i.e., parallel to the road surface) force produced by a vehicle tyre when cornering (taking a curve). Without side forces from the road, the front tyres cannot make the car turn. But if the driving side force on the front tyres is greater than the counteracting side force on the rear tyres, the cornering becomes unstable and potentially very dangerous.