Spring into Action.

(c) Tony Foale 1988-1998

This article was originally written for "Performance Tuning &Sports Car"

and appeared in the March 1988 issue.

The recent development of the Lotus active suspension system has proved that car body movements such as pitch and roll can be precisely controlled. Unfortunately it will take some time before we can all take advantage of these developments, and in the meantime we are stuck with the conventional springs and suspension that seems to have changed little since the days of the horse drawn carriage.
Every enthusiast knows that the roll characteristics of a car have considerable influence on its dynamic behaviour as well as the comfort of its occupants. The parameters that control these characteristics are numerous, terms such as roll centre, roll stiffness, roll axis and roll couple are often bandied about but seldom adequately explained. I have often seen, in books and magazine articles, geometric constructions that can be used to determine roll centres and axis for different suspension layouts, but I have never seen an explanation of why these methods actually provide this information. It seems to be taken for granted that the reader will just accept it on face value, or is it because the writer is unsure himself and is just repeating that which he has read elsewhere. Anyway let's break with tradition and see if we can untangle the subject.
Firstly, we must understand the terminology. The roll axis is an imaginary line running through the car from end to end; when the car rolls, whilst cornering on a smooth road, it rotates about this axis. Any part of the vehicle not on this axis bodily moves, either up or down, side to side or both. Fig 1 shows the motion, as well as the longitudinal position of the roll centres, these usually being points on the roll axis in line with the wheels. Note that there's no theoretical reason why the roll centre heights should be at the same level at each end, and indeed they rarely are.

Now before going into the details of determining the roll centre and axis location, it must be understood that these parameters are not fixed in relation to the car's chassis, but move about depending on the deflection of the suspension and therefore vary depending on the roll angle which is influenced by the cornering force. When the car rolls the suspension on one side is compressed and on the other it becomes extended, for the purposes of analysis it matters not whether we consider the wheels as fixed and the body as capable of movement relative to them, or the body as fixed with wheels capable of moving. But as it is easier to visualise the motion with a fixed chassis we will go with that.
Let's now consider the case of a double wishbone suspension system as in Fig 2. If we allow a very small vertical wheel displacement to take place, then the path of this movement (at the wheel end of the wish- bones) is at right angles to the wishbones, therefore the length of the wishbone does not affect the geometry of movement of the upright and wheel (for small displacements). So if the wishbones were extended in length until their inner pivots coincide then the motion of the wheel would be unaffected, but as the two wishbones now pivot around the same axis, we could replace them with a single arm fixed to the wheel axle, thus in effect creating an equivalent swing axle suspension system.
Because this new swing axle is only a figment of our imagination, let's call it a 'virtual swing axle' and its pivot a 'virtual pivot'.
Now, we need to consider the motion of the wheel at the tyre contact patch because this is our only connection with terra-firma, the reference from which we measure the roll. The diagram shows that this motion is at right angles to the line connecting the virtual pivot and the contact patch. Again for small deflections, this motion is unchanged as long as the effective pivot is located anywhere along this line. A mirror image of this applies to the wheel at the other side also. Thus the only common pivot point that satisfies both sides is the one at the junction of these lines, through the contact patches to the respective virtual pivots.
So if there is one pivot point that can relate the motion of both tyre contact patches relative to the chassis, then that same point locates the chassis relative to the wheels. It is the point about which the body will pivot should the suspension on one side be compressed by the same amount as the suspension on the other side be extended, in other words it is the roll centre.
I have emphasised the point about small wheel displacements, this is very important because the roll centre may vary its position enormously throughout the range of normal wheel movement. As the car rolls, its roll centres may change not only in height but also from side to side, as Fig 3, demonstrates.
Even though we have used a double wishbone system to explain the method of determining the roll centre position, it is very easy to apply the method to any other suspension configuration. It is only necessary to determine the directions of movement of the contact patches, and draw lines at right angles to these through the contact patches, the point at which these last two lines cross is the roll centre. Fig 4, shows the method for several different systems.

All of the above makes one big assumption (anyone spot it?) that the effective spring rates at the wheels are equal side to side. But aren't they, I hear you ask. No, not always: what if you have progressive rate springing? The effective spring rate will be increasing on the side that is compressing and will be reducing on the other. To understand the effect that this may have, let's look at the extreme case of a car with a rigid suspension on one side only and with a normal spring on the other. The chassis is thus completely tied to one contact patch and so this is the only point about which it can roll. Thus the roll centre is at ground level directly under the wheel with the infinitely stiff springing. Obviously this situation is unreal but demonstrates how the actual roll centre moves away from the geometrically constructed one, if the springing is not symmetrical.
It is all very well knowing where the roll centres and thus the roll axis are but what use is that knowledge, how can we use it and where should they be anyway? To answer this, we need to look at the superficially obvious question, 'Just what causes roll?'.
As we negotiate a curve the car is subject to centrifugal force, which is equal to the lateral acceleration multiplied by the mass of the machine (for a 1000Kg car cornering at 0.5g. The centrifugal force is 500Kg). This force is distributed throughout the car but for most analysis purposes can be considered to be acting only through the centre of gravity (C of G). Fig 5, shows that unless the C of G is level with the roll axis, a torque or couple (the roll couple) will be created, tending to make the machine roll about the roll axis.
There is another equally valid way of considering the roll mechanism. The centrifugal force acting through the C of G produces a torque about ground level and is resisted by weight transfer to the outside wheels, that is, the outside wheels support a greater proportion of the car's weight and the inside wheels a lesser proportion.
This change of load on each wheel normally causes the suspension to adopt a new position, or to put it another way the car rolls.
It may have occurred to some of you that if the roll axis is made to coincide with the C of G then there will be no roll couple and hence no roll or, to take things a step further, if the roll axis is above the C of G then the roll couple will be in a direction which makes the car lean inward like a motorbike. Indeed it is quite possible to design the suspension layout to achieve these effects. If this is so, why do we need active suspension to do it for us? Well, because if we use the high roll axis necessary, then the suspension layout will cause a jacking up effect under cornering conditions, a phenomenon experienced with some swing axle designs in the past.
One important point to note, one which is often misunderstood, is that regardless of the amount of roll allowed by the suspension design, the actual degree of weight transfer remains unchanged. This is only affected by the track, C of G height and cornering acceleration.
So, as with most design features in anything mechanical, the selection of roll axis position is a compromise: too low and we get excessive roll, too high and other undesirable handling traits surface. In practice, the com- promise varies with different types of car but always such that some roll occurs. Lowering the C of G is another technically possible way of reducing the roll couple, but this can only be done to a certain extent, due to the boring necessity of leaving comfortable space for the occupants.
The roll couple that such compromise leaves must be resisted by the car's springs, which leads us to roll stiffness. This term is defined such that the degree of roll is equal to the roll couple divided by the roll stiffness. Stiff springing obviously reduces roll and hence increases the roll stiffness, but if this is the criterion for selecting spring rates we will usually end up with an uncomfortable ride over normal road irregularities, so the anti-roll bar was developed to ease the situation.
The anti-roll bar is a torsion bar (torsion spring) connecting the suspension systems on each side of the vehicle in such a way as to allow both wheels to respond unhindered to two-wheel bumps, such as a ridge across the road. But if the wheels try to move independently, as with a single-wheel bump, or in opposite directions when the car rolls then the anti-roll bar resists this tendency. Roll is reduced as intended but comfort suffers as the effective spring rate of each wheel is increased in the individual single-wheel bumps, although the combined spring rate of the two wheels is unchanged over joint disturbances.
Again a compromise must be reached between the requirements of minimum roll and good response to road shocks. Roll bars, unlike the springs, are undamped (theoretically damping could be incorporated, although the manufacturers have generally concluded that it is not worthwhile). This is another reason for limiting the influence of the anti-roll bar, as oscillations might occur if the undamped bar is too stiff.
It is well known that the under/over steering characteristics of a car can be substantially modified by tuning the springing and anti-roll bar stiffnesses, altering the roll stiffnesses of each end.
While the vehicle as a whole has a certain roll stiffness, this is made up of the separate roll stiffnesses at the front and back, which may be quite different. For example, let's consider the case of a beam axle pivotted on the chassis at its mid point, and devoid of any form of springing. As unlikely as this layout seems, you may see it fitted to the front of some tractors, because it has good terrain-following properties. Now, because the chassis is completely free to rotate about the pivot point of this beam axle, then no roll stiffness is provided at this end of the machine and so all the stiffness needed must be available from the other end.
This lack of any roll stiffness means that body roll cannot cause any weight transfer to the outside wheel, and hence as the total weight transfer must be the same anyway, the other end must obviously be subjected to proportionally more.
Tyres have the interesting property that although they are capable of supporting higher cornering forces when subject to higher vertical loading, this does not go up in proportion. In other words, the co-efficient of friction is reduced as more weight is placed on them. In practice this means that weight transfer reduces the combined cornering force capable of being developed by the pair of tyres at one end of the car. Now as we have seen, the weight transfer at either end of the vehicle can be controlled to some extent by altering the roll stiffnesses of one or other, or both ends. Therefore, the tyre slip angles needed to produce the required cornering forces can be adjusted by modifications to the wheel springing, thus giving us the means to alter the under/over steering properties.
Dampers, too, have their part to play in the extremely complex interrelations between the various forces acting on the car. During the transitional period between initiating a turn and it becoming fully established, the dampers will affect the dynamic roll stiffnesses. Because the dampers only contribute whilst the suspension is actually moving, however, they have no effect once the car has settled down to a steady state turn.
So now you know why racers spend so much time setting up the suspension rates on their machines, when at first sight it would appear that the suspension is there only to cushion the bumps. Many competition cars have facilities for altering roll bar stiffness whilst on the move, making it quicker to achieve the desired performance but also allowing adjustments during a race as tyres wear and fuel weight reduces.
So how will active suspension improve the situation? The computer program controlling the system could, for example, be set to apportion the front/rear roll stiffness.
Assuming, that the system is set to give zero roll (this is by no means certain to be the aim of future manufacturers) then it is very interesting to follow through the implications for geometric roll centres, etc. Basically if we have no roll then the term roll axis becomes irrelevant, as does the need to have suspension link layouts that try to keep the outside wheels upright under cornering roll rather than under all conditions. Perhaps active suspension means a return to parallel equal length wishbones or perhaps better still, true trailing or leading arm systems. Normally, these designs suffer because of vast changes in roll centre positions, and because the camber angle varies with the roll angle of the body, the wheels always being held parallel to it. Straight line stability would be improved as bump induced wheel deflections would not cause any of the bump steer which comes from changing wheel camber. That's a desirable state of affairs that is hard, if not impossible to achieve with conventional springs and dampers as we have seen.