[aerobod]

The calculation of scrub radius is fairly straightforward on a macpherson strut suspension. There are a number of dimensions that stay fixed, a number that move an inconsequential amount and two that cause the primary change in the scrub radius:

The z (vertical) dimension for the top strut bearing relative to the LCA outer ball joint stays nominally the same for a given spring length. The z-dimension from the LCA outer ball joint to the ground also stays nominally the same, assuming camber changes less than about 2 degrees.

The y (lateral) dimension for the LCA outer ball joint stays fixed.

Basically the two variable dimensions are the y-dimension for the strut top bearing and the y-dimension of the extrapolated line that runs through the top strut bearing and the outer LCA ball joint (the virtual pivot line), to where it touches the ground.

If we are just looking at scrub radius, we don't need to look at any x (longitudinal) dimensions, but changes in "x" can have an effect on castor and SIA (steering axis inclination) values, thus affecting steering feel.

One way to calculate the point where the virtual pivot line touches the ground is as follows:Y

- Measure the distance between the top bearings on both front struts and divide it by 2, then add approximately 6mm (the bearing centre is approximately 6mm outboard from the centre of the top of the strut). This dimension is 'Ty'.

- Measure the height ot the top of the strut above the ground, then subtract approximately 25mm (the bearing centre is about 25mm below the centre of the top of the strut). This dimension is 'Tz'.

- Measure the distance between the centre of both LCA outer ball joints and divide it by 2. This dimension is 'By'.

- Measure the height of the centre of the LCA outer ball joint above the ground (car on the ground). This dimension is 'Bz'.

- Measure the distance between the centre of the contact patches of the front tyres where they touch the ground and divide by 2. This dimension is 'Cy'.

The scrub radius (S) is expressed as:

S=Cy-By-(By-Ty)*Bz/(Tz-Bz)
For example, if Cy=0.760m, By=0.700m, Ty=0.600m, Bz=0.225m, Tz=0.675m, then S=0.010m, or 10mm

As the camber is increased by moving the top bearing inwards, a given movement of the top bearing (Dy), will cause a change in the virtual pivot line where it hits the ground (Vy) as follows:

Vy=-Dy*Bz/(Tz-Bz)
For example, if Dy=-0.010m, Bz=0.225m, Tz=0.675m, then Vy=0.005m, or 5mm
In this case, scrub radius will change by 5mm if the centre of the contact patch stays the same.

The relationship between camber F(C) and Dy is nominally:

C=arctan(Dy/Tz)
For example, if Dy=-0.010m, Tz=0.675m, then C=-0.85°, i.e. a 10mm inward movement of the strut would cause a 0.85° degree increase in negative camber.

If a different wheel is used, then the ET difference will directly corelate to the movement of the centreline of the wheel. If the tyre size, pressure and camber stay the same, then the centre of the contact patch will move relative to the change in ET. If the camber and/or pressure changes, then the centre of the contact patch may also move independent of the ET change (think about the outside of the tyre lifting off the ground as negative camber increases, displacing the centre of the contact patch away from the centreline of the wheel).

The overall effect of increasing camber is that the virtual pivot line will move further outward where it touches the ground, making scrub radius more negative, but the contact patch will tend to move somewhat inward especially with a stiffer tyre and/or higher pressure, driving the scrub radius to be even more negative.

As I'm not at home at the moment (travelling for the next 10 days), the above dimensions don't represent the Z4M, but are just used for illustration!!!