In our previous entries, we analyzed a simplified vehicle model and this proved to be helpful to understand the basics of cornering physics and to isolate some of the fundamental metrics about handling.
Let’s now move a further step forward and try to understand what should we look at, in a vehicle with four wheels and the centre of mass seating above the ground.
The basics we have discussed regarding the bicycle model and how it handles are of course still valid. The most important differences, anyway, lies in the higher complexity of a vehicle with four wheels and in the consequences of having the vertical load acting on each wheel changing in time, because of the load transfer associated with the CG seating above the ground. We will also consider the effects of the aerodynamic forces and, as we know, in some cars they have a very important influence on the final load that each tyre experiences at the contact patch.
Anyway, not too make things too complicated, we will still consider a simplified vehicle, where the wheels will not move exactly as the suspension kinematics would dictate (other than assuming the front wheels will steer) but always remain perfectly vertical with respect to the ground, although experiencing the effect of suspensions and their stiffness on the vertical loads.
As we have seen dealing with tyres, in our first series of technical articles, if we ignore the effects of camber, temperature and pressure, the main driver to define how big the friction ellipse of each tyre will be is the vertical load.
For a car traveling in straight line, with no aerodynamic forces acting on it (either because the car has no significant downforce or is moving at such a lower speed that these actions can be neglected), the dimension of the friction circle (ellipse) of each tyre will depend directly on the static vertical load acting on it, which will be linked to CG location, longitudinally and laterally and on overall vehicle mass.
In the previous picture, we assume the CG is located on the middle line of the car and slightly behind the half of the wheelbase l.
Each of the four circles (two blue ones at the front and two green one at the rear) identifies a tyre friction circle (assuming, for the sake of simplicity, that the grip envelope of each tyre can be represented with a circle).
If we now imagine a certain downforce acting on the car, with a centre of pressure located at the same position of the CG, we will see all four friction circles increasing their dimensions (as we described in our tyre articles), although the rear in a slightly bigger extent than the front ones, because the centre of pressure (as the CG) is closer to the rear axle and there is a bigger portion of the overall downforce acting on the rear tyres.
As we already know, this happens because, if the vertical load acting on a tyre grows, also the planar resultant force (hence, the radius of the friction circle) that the tyre can exchange with the road gets bigger, although at slower and slower rate as the load increases.
This suggests a first extremely important conclusion: not only, the higher the downforce, generally the bigger is the grip that the tyres can produce and hence the accelerations that the car can sustain, for example travelling in a corner or braking. This is a crucial point about downforce effects, something we have described already in our articles about tyres and aerodynamics, but that is worth to mention again here. Downforce makes a car faster, because it increases the dimensions of the friction circle (thus increasing the maximum force the road can exert on the car) without any of the associated penalties we would have when a tyre would experience a higher vertical load because of more weight or of load transfer (we will come to this in a while).
Also, equally important, we can influence how a car handle by loading the front or the rear tyres more by moving the CoP forward or backwards: a bigger downforce acting on the front wheels, will mean that the front tyres will be able to exchange a bigger force with the road, for example. More grip at the front, means, on one side, more overall grip for the whole car, but also less understeer or more oversteer.
Since downforce depends on the square of the speed, its effects will be weaker in very slow corners but will be extremely important in high-speed turns.
Beside the aerodynamics, another fundamental element influencing handling is how the load is transferred from a wheel to the others during cornering, braking and accelerating. We already dealt with the basics of load transfer in some of the previous entries and we have seen how, basically, it happens because of the CG seat above the ground. During, for example, a cornering manoeuvre, the road will apply to the tyres forces with a lateral component that will accelerate the car toward the centre of its (circular) path. At the same time, the car will also feel the action of an inertial (centrifugal) force that will try to bring it back to a straight trajectory.
Since the two lateral tyre forces (Fyf and Fyr in the previous picture) will act at the ground and the centrifugal force (-mAy in the previous picture) at CG location (above the ground), the car will experience a moment trying to rotate its body toward the outside of the corner and loading the outer wheels more than in static conditions, while equally unloading the inner wheels.
This hurts the overall cornering potential of the car, because the coefficient of grip decreases as the vertical load increases; this means that the increase of maximum lateral force achievable by the outer tyre because of the bigger vertical load will be smaller (in absolute value) than the decrease of the maximum lateral force achievable by the inner tyre because of the smaller vertical load.
In other words, if we look at the previous picture, what happens is that for a certain ΔFz with respect to each tyre static load, the reduction of the maximum inner tyre force (ΔFin) will be bigger than the growth of the maximum outer tyre force (ΔFout).
The sum of the two new maximum tyre forces of an axle, Fin and Fout will be smaller than two times the force that each tyre could exchange with the road when only the static was acting on it (Fstatic).
All these words basically to say that the bigger is the load transfer that the car or, more important for us right now, a single axle will experience, the bigger the grip lost that the car or the axle will suffer.
Jumping too quickly to conclusions, we could then say that load transfer is bad. Well, this is actually true, because it indeed hurts grip (and that is why it is important to have the CG seating as low as possible in a racecar). Anyway, since there are ways to influence how much load transfer takes place at the front axle and how much at the rear one, it turns it can be used as an extremely powerful tool to influence how the car handle, which basically means how much understeer or oversteer the car has. In particular, having a bigger portion of the overall vehicle load transfer happening at the front axle will mean less grip at the front and, in general, more understeer. On the other hand, if the portion of load transfer happening at the rear will grow, we will move toward a less understeering/more oversteering behaviour.
Before we dig into more details about this topic, we must stress an extremely important concept, that is sometimes subject to misunderstanding. If we consider a car moving on a circular path with radius R at a constant speed V, hence with a centripetal acceleration given by:
the car will experience a load transfer that only depends on CG height above ground, track widths of the car and vehicle overall mass.
For a given Ay, we can consider the overall load transfer more or less as a given term. The engineer cannot change it. Anyway, working on the car, he can change the portion of this phenomenon happening on the front and on the rear axle.
In particular, a parameter called Total Lateral Load Transfer Distribution (TLLTD) is often used to define, for a given overall amount of load transfer (and, hence, for a given Ay), how big is the portion of it that interests the front axle.
As we will see in another entry, the most effective tool that a race engineer has to tune the TLLTD are the suspensions. In particular, some of the most important parameters influencing which portion of TLLTD will be taken by an axle are suspension stiffness (in roll) and suspension geometry.