The scrub radius is the distance in front view between the Steering Axis and the centre of the tyre contact patch where both would theoretically touch the road.
The “steering axis” is the line between the top pivot point of the hub and the lower ball joint of the hub. The inclination of the steering axis is the angle of inclination from vertical and is known as SAI (Steering Axis Inclination) or KPI (King Pin Inclination).
If the steer axis intersection point is outboard of the center of the contact patch it is negative, if inside the contact patch it is positive.
Large positive values of scrub radius, 4 inches or 100 mm or so, were used in cars for many years. The advantage of this is that the tyre rolls as the wheel is steered, which reduces the effort when parking. On a rear-wheel-drive vehicle with positive scrub radius, the vehicle’s forward motion and the friction between the tyre and the road causes a force which tends to move the front wheels back, keeping the vehicle heading straight ahead. This also allows greater width in the engine bay, which is very important in some compact sports cars. During braking, on any type of drive, if braking effort is greater on one side of the vehicle than the other, positive scrub radius will cause the vehicle to veer towards the side with the greater effort. It therefore requires much higher driver involvement and also competence to maintain control and stop the vehicle being tugged into puddles.
Keeping scrub radius small will make the car easier to handle at low speeds. It also reduces the risk, that a lose of traction on one front wheel during braking, causes the car to change direction. 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. However, zero scrub radius, under hard braking, causes the suspension to be skittish because varying road conditions created varying amounts of torque (both positive and negative) around the steering axis. Therefore, some amount of scrub radius, positive or negative, is preferred. Having a small amount of scrub radius, under hard braking, generates a small bit of torque to a predictable side. While this torque isn’t desirable, it’s predictable and relatively not−affected by changes in road conditions, which makes the steering smooth.
An advantage of a negative scrub radius is that the geometry naturally compensates for split braking, or failure in one of the brake circuits. Vehicles with a diagonal-split brake system have negative scrub radius built into the steering geometry. If one half of the brake system fails, then the vehicle will tend to pull up in a straight line. Negative scrub radius also provides centre point steering in the event of a tyre deflation, which provides greater stability and steering control in this emergency situation. If you hit a puddle at speed on one side of the car, with negative scrub radius the torque on the steering will steer you away from the puddle. Which balances the effect of drag on one side of the car.
The goal in DIY suspension design would be minimise but not eliminate scrub radius. Steering sensitivity would be reduced but this could be regained by using a numerically lower steering rack ratio.