The last suspension characteristic I wanted to analyze was one that is less intuitive than the rest, called "Roll Centre Migration". It's best described by imagining that when the chassis begins to tilt during a turn, it starts out tilting along an axis that runs down the centre of the car from the front to the rear. Once the chassis starts to roll though, that roll axis doesn't remain parallel nor level with the chassis. It starts to spiral outwards away from the centre line of the car and downwards causing the chassis to feel as though it is no longer simply rolling, but spiralling. The driver feels this shift in the manner the car is tilting as an unnatural motion.
To show how this comes about, this is one case where illustrations are essential. The first step is to find the rear roll centre of the chassis at rest. If you followed through on post #25 where I showed how to find the rear swing arm and instantaneous centre, finding the rear roll centre is only one step further. Here's the illustration from post #25 again with one more line added to it: the blue line running from the instantaneous centre to the centre of the tire patch.
The roll centre is located where the blue line from the left wheel intersects a similar line from the right wheel. With the chassis level and at ride height, that point also corresponds to where either blue line intersects the centre line of the car as shown above. On the '88 Fiero that point is 73 mm above the ground. That is the point that the rear of the chassis initially starts to roll about as shown by the red arc in this next drawing here:
The roll centre is located where the blue line from the left wheel intersects a similar line from the right wheel. With the chassis level and at ride height, that point also corresponds to where either blue line intersects the centre line of the car as shown above. On the '88 Fiero that point is 73 mm above the ground. That is the point that the rear of the chassis initially starts to roll about as shown by the red arc in this next drawing here:
Intuitively you would think that the rear of the chassis would simply continue to roll about that point, however that isn't the case. As the chassis rolls, the angles of the lower control arms change, which changes the location of the instantaneous centres for both wheels. That causes the blue lines from each wheel to intersect at a different location, taking the roll centre with it.
To put a number on how much the roll centre moves on the '88 Fiero rear end, I used the Lotus Suspension Analyzer software to plot its migration for every chassis roll angle up to 6 degrees both ways. This is what that graph looks like (each dot represents a 1/2 degree incremental roll angle from zero, at the center line):
To illustrate what the graph above depicts, I've superimposed the graph and the '88 Fiero rear end onto the same scale showing just how much the rear end of the '88 Fiero spirals away from a true roll by the time the chassis has tilted 4 degrees:
As before, the red arc shows the path the rear end will roll once it reaches 4 degrees... no longer centred on centre line of the chassis. In fact, the roll centre is now buried 111 mm below the ground, and located 1.24 metres from the centre line!
For even more dramatic effect, I continued the plot to show the arc the rear end follows by the time the chassis reaches its maximum 6 degrees of tilt. By that point the roll centre is located 398 mm below the ground and a whopping 2.1 metres from the chassis centre line.
Clearly roll centre migration wasn't a top priority in the redesign of the '88 suspension. Ideally, the roll center location shouldn't change at all. I'll have to see if I can do better!
Well, that's the last of the posts on stock suspension analysis. Again, the reason for going through this was to have a baseline against which to compare my own suspension design's performance. I have a tall order to fill... lower the entire chassis on the wheels by several inches for better appearance, AND design a suspension so that it performs at least as well as stock. The next post will be the start of that process.