We ended our previous entry showing why the instant centre is so important both for suspension kinematics but also to understand how the contact patch forces are transferred to the car. In particular, we have seen how the only way for a contact patch force not to cause a movement of a (2D simplified) suspension (corner) is that the force act on the line defined connecting the contact patch and the instant centre.
Anyway, generally the force applied by the road to a tyre in a pure cornering situation acts in a different direction than the one of the above-mentioned line. Our 2D suspension will normally experience a resultant force at the contact patch that can be decomposed in two components: a lateral one, which we named already in several occasions Fy and a vertical one, Fz.
Let’s focus for a moment only on the lateral component, Fy. We immediately recognize how the lateral components of the forces acting at the contact patches generate a moment about the relative IC and, hence, an effect that tends to rotate our “idealized swing arms”.
What the reader should keep in mind is that, if the IC seats as shown in the picture, these moments will move the suspension in the opposite direction than the one in which the body would roll, under the action of the centrifugal force (acting at the CG). De facto, as long as the IC seats as in the picture, the two moments generated by each side cornering force will tend to unroll the car, extending the outer suspension and compressing the inner. This is why, if the IC seats as in the above picture we can assume their effect to be a kind of antiroll action. If the IC seats below the ground or outboard with respect to the wheel, on the other hand, the cornering forces moments will have an opposite sign and a kind of pro-roll effect. As we will see, these are the basics to understand a mythical vehicle dynamic concept, namely the roll centre. More about this later.
Looking at the complete picture of the forces acting on the vehicle in a pure cornering situation, we will find, beside the already mentioned tyres contact patch forces also the centrifugal force, acting on car CG (we ignore for a moment the separation between sprung and unsprung mass) and any aerodynamic action. For the sake of simplicity, we will focus only on the vertical component of the resultant aerodynamic force (downforce). This will couple together with the weight/gravity action, to compose a resultant vertical force, acting at the CG.
As we saw, the centrifugal force, acting at the CG (or the portion of this force taken one of the two axle) and coupling with the contact patches lateral forces, rolls the car, compressing the outer springs and tyres, extending the inner ones and twisting the antiroll bars, while leading to a load transfer that will increase the vertical load acting on the outer tyres and lower inner tyres one.
At each contact patch, we will have a resultant force with a generic direction, generally different than the one of our idealized swing arm. As we said, this force can be decomposed in a lateral (Fy) and a vertical (Fz) component. Anyway, we can also decompose it differently, considering the component lying on the line connecting the contact patch and the IC.
This approach allows us to consider not only the magnitude of the resultant force transmitted directly to the control arms (FCA), whose lateral component (FCAy) is equal to Fy, but also to separate the vertical force Fz in two summing elements, FCAz and Fs: the first one is the vertical component of FCA and is often referred as Jacking Force, because it tends to lift the car (at least if the IC seats as in our previous pictures); the second one is the portion of Fz that cannot be transmitted through the control arms and will be reacted by suspension elastic elements (see the springs and anti-roll bars).
It is easy to see how the relative magnitude of FCAz and Fs depends strictly on the position of IC or, in other terms, on the inclination of the line connecting the contact patch to IC. Some call this line “n-line”. Anyway, what is really important is that, given an Fz, the bigger the inclination of the n-line, the bigger the magnitude of FCAz and the smaller the magnitude of Fs. This means, the bigger the inclination of the n-line, the smaller will be the force that the elastic elements of car suspensions have to react and, hence, the smaller will be the roll angle of the car for a given stiffness of these elastic elements.
This point can be now linked to what we previously analyzed when we described the antiroll torque created by the Fy with respect to the IC. The bigger the inclination of the n-line, the bigger will be the antiroll torque generated by the Fy, which will play against the car rolling under the influence of the centrifugal force.
FCAz points upward if we consider the outer side (suspension) of the car and downward on the inner side; anyway, since on the outer side its magnitude is bigger than on the inner side (mainly because of the bigger vertical load acting at tyre contact patch, but sometimes also because of suspension movement in roll, leading to a movement of the IC), we will have a net effect pushing the car upward, in a case with the ICs seating as in our picture.
For a given amount of lateral load transfer experienced by the car and a given roll stiffness, the steeper are suspensions n-lines, the smaller the roll angle, because there will be a bigger antiroll action generated by the lateral forces acting at the contact patches. Similarly, the total lateral load transfer distribution (TLLTD) will be influenced both by the relative roll stiffness distribution of an axle with respect to the other (see, how stiff are front springs and antiroll bar compared to their rear counterparts) and by the relative magnitude of the antiroll torque generated by an axle with respect to the other (see, how big is the inclination of the n-lines of one axle with respect to the other, assuming the IC seats as shown in the picture).
As readers who are more familiar with vehicle dynamics topics have already probably recognized, this whole discussion simply shows a different approach to what many experts and books identify with the term roll centre (s).
The roll centre of a suspension is defined as the point where the resultant lateral force of an axle can be applied without causing any roll of the body. This point is nothing less than the intersection of the n-lines relative to the left suspension and the right suspension of an axle. If the car doesn’t roll and the suspensions have a symmetric design (the left side is a mirrored version of the right side), the roll centre lies on the car centerline/plane (longitudinal middle plane).
It is worth to come back shortly to a case we had seen in our previous entry, namely a situation where the two control arms are parallel to each other and to the ground. In that case, the instant centre IC is undefined and the roll centre lies on the ground.
Actually, it is more correct to talk about a roll axis, is defined as the line connecting the front and rear roll centres. In simple terms, this axis should be considered as the axis around which the body rolls, when cornering.
The logic behind roll centres definition can be understood if we imagine sliding our FCA along the n-line till we meet the middle plane of the car. Assuming that both left and right FCA have the same magnitude (hence a situation where the car negotiates a corner with very low centripetal acceleration, thus experiencing very low load transfer), we will have a resultant force with a lateral component two times the magnitude of FCay and a vertical component given by the vector sum of the left and right FCAz (that normally have opposite signs). This latest force is normally identified as Jacking Force, as we mentioned.
The roll centre concept works very well as long as we assume a symmetrical case, meaning we consider the car having the same suspension design (only mirrored) on both sides, not rolling and having contact patches lateral forces with the same magnitude on both sides. This is, of course, a simplification that proves to produce bigger errors as soon as lateral acceleration (and, hence, the lateral load transfer and roll angle) grows, because we move away from the symmetric case we initially assumed. Moreover, the reader has to keep in mind that the roll centre is a point that moves in space depending on suspension position, for example in roll. With certain design the roll centre could migrate meters (if not kilometres) away from its initial position, thus losing its significance. On the other hand, the inclination of n-lines is something that always remains easily definable and measurable.
Nonetheless, roll centers can be successfully used to get a picture (at least statically) of what to expect in terms of load transfer (and hence, of handling), because under the correct assumptions they are an indicator of how much suspension geometry influences load transfer at the front axle, with respect to the rear.
In our next article, we will put all together and define the final lateral load transfer distribution.