The scrub radius is the distance in front view between the king pin axis and the center of the contact patch of the wheel, where both would theoretically touch the road.
The kingpin axis is the line between the upper and lower ball joints of the hub. On a MacPherson strut, the top pivot point is the strut bearing, and the bottom point is the lower ball joint. The inclination of the steering axis is measured as the angle between the steering axis and the centerline of the wheel. This means that if the camber angle is adjustable within the pivot points the scrub radius can be changed, this alters the width and offset of the tires on a vehicle.
If the kingpin axis intersection point is outboard of the center of the contact patch it is negative, if inside the contact patch it is positive. The term scrub radius derives from the fact that either in the positive or negative mode, the tire does not turn on its centerline (it scrubs the road in a turn) and due to the increased friction, more effort is needed to turn the wheel.
Large positive values of scrub radius, 4 inches/100 mm or so, were used in cars for many years. The advantage of this is that the tire rolls as the wheel is steered, which reduces the effort when parking. This also allows greater width in the engine bay, which is very important in some compact sports cars.
If the scrub radius is small then the contact patch is spun in place when parking, which takes a lot more effort. The advantage of a small scrub radius is that the steering becomes less sensitive to braking inputs, in particular.
An advantage of a negative scrub radius is that the geometry naturally compensates for split µ (mu) braking, or failure in one of the brake circuits. It also provides center point steering in the event of a tire deflation, which provides greater stability and steering control in this emergency.
The steering axis inclination (SAI) is the angle between the centerline of the steering axis and vertical line from center contact area of the tire (as viewed from the front).
SAI urges the wheels to a straight ahead position after a turn. By inclining the steering axis inward (away from the wheel), it causes the spindle to rise and fall as the wheels are turned in one direction or the other. Because the tire cannot be forced into the ground as the spindle travels in an arc, the tire/wheel assembly raises the suspension and thus causes the tire/wheel assembly to seek the low (center) return point when it is allowed to return. Thus, since it has a tendency to maintain or seek a straight ahead position, less positive caster is needed to maintain directional stability. A vehicle provides stable handling without any of the drawbacks of high positive caster because of SAI.