Updated: Oct 30, 2020
I often talk about using a ‘tyre centric’ approach in my vehicle dynamics work which makes perfect sense to me, but could probably do with some further explanation.
As has been repeated endlessly, the tyre is the only component of the race car in contact with the race track, a fact that automatically tells us that all efforts should be made to ensure that the tyre is the most ‘comfortable’ for its particular task at that moment. The tyre is king in vehicle dynamics.
But, what does this actually mean? How exactly do we place the tyre in the best environment at a race weekend?
The ‘best’ environment is not an explicit quantity - Is it a qualifying or race event? Is it an endurance race, or a sprint?
it’s not an easy question to answer, but we can start by looking at some of the important parameters that go into the equation of tyre comfort and how they affect its performance.
I do cover this in some detail in my tyre dynamics article online on the Racecar Engineering Magazine website, but ultimately, we can measure the operating environment of the tyre at any moment using a few important metrics.
Slip angle: Every tyre has a slip angle in which it produces the most grip for a given vertical load. This is controlled through steering/toe angles.
Contact area: Adding negative camber to ensure the outside wheel is oriented to present the most contact area to a track surface as the body rolls.
Input Energy: The point at which the tyre is generating the most grip is the time at which it is dissipating the most energy, this is also when it exhibits maximum hysteresis. As the tyre is a visco-elastic material, this point is dependant on the temperature and the rate of the energy input.
Important parameters here are vertical loading, lateral & longitudinal acceleration, molecular friction through deformation and driver aggressiveness.
Slip angle and contact area considerations are covered in my the tyre dynamics and kinematics articles here.
In this two part article i want to spend some time exploring the formula of tyre ‘comfort’; covering the influence of input energy and its relationship with tyre temperature, exploring how we can utilise it to our advantage for tyre performance in different scenarios.
By the time we’re finished i hope you have a picture of how we can control this energy input by manipulating chassis parameters and driver inputs according to what we need from the tyre in different circumstances.
I want to also touch on the tyre considerations between FWD, 4WD and RWD and how each configuration affects how the race car uses the tyres.
The most logical place to start is from the foundations of the vehicle - the longitudinal position of the Centre of Mass (CoM); this position defines the weight distribution over each axle.
The biggest input to CoM location is, logically, the position of the engine and other heavy powertrain components such as gearboxes, so it’s determined by the basic layout of the racecar and can’t be significantly changed.
The importance of weight distribution becomes clear when you consider the governing equations of cornering:
As usual in my articles i really prefer to stay descriptive rather than dive into equations and derivations etc - there is a time and place, so i’ll try to inflict a minimum of maths on you, but the following should be clear in your mind.
In order for steady state cornering to be achieved, two main conditions need to be met.
Equilibrium must be achieved between the lateral force generated by the tyres and the centripetal force acting on the CoM.
Yaw moment equilibrium must be achieved between the axles.
Lateral force equilibrium is pretty self explanatory; In order for the race car to maintain steady state cornering, the tyres must produce a lateral (centripetal) force matching the lateral acceleration requirement of the particular corner radius.
Yaw moment equilibrium is slightly more complex, but not much.
The mechanical advantage/moment arms between the front and rear axles and the CoM vary depending on the CoM location.
Steady state cornering is true only if there is no yaw acceleration present. In order for the total yawing moment to be balanced (i.e. zero), there is a requirement for differing lateral forces to be generated at each axle. If the yawing moment falls out of balance, the vehicle is understeering or oversteering.
Lets compound this with an example.
A 1000kg race car has wheelbase of 4m and a rear-mid engine layout resulting in a 40:60 weight distribution. It’s cornering with a lateral acceleration of 2g
In this fictitious example, the lateral acceleration acting on the CoM is generating a force of 19,620N, this tells us that to achieve lateral force equilibrium, the tyres need to generate 19,620N, simple (hah!)…
To achieve yaw moment equilibrium, considerations around the CoM come into play. The 40:60 weight distribution indicates that the CoM is located 2.4m behind the front wheels, or 1.6m ahead of the rear wheels, leading to the following lateral force requirements from each axle to maintain a zero yawing moment:
Front = 7848N
Rear = 11772N
As a first insight, this understanding allows us to predict the balance of the car; with equal tyre on each axle, the greater force requirement from the rear is going to mean that the rear tyres are forced to assume a larger slip angle than the fronts to maintain steady state cornering.
Now, let’s look at this graph of lateral force generation vs slip angle.
From this, it’s clear to see that as the cornering speed and slip angles increase, the rear axle is going to its reach peak grip capacity before the front. At further slip angles the lateral force falls off, yaw moment balance is lost and in this specific case the car will begin to oversteer.
This relationship is doubly important as the rate of tyre temperature increase has a strong correlation with lateral force generation. In the case of our example, the rear tyres are likely going to be operating at a higher temperature than the front tyres.
Tyres have a narrow operating window in which they are most effective - perhaps 70 - 80˚C; this has implications for degradation as i’ll elaborate on later.
In the mean-time, with these two observations on unequal lateral force requirements and tyre energy, what can we do to improve the environment for the tyres and restore some balance?
Lateral Load Transfer Distribution & Roll Stiffness
The lateral load transfer distribution is an important thing to understand as it has a quite significant input into tyre energy. While we can’t do anything about the overall lateral load transfer, we can use a number of tools to fine tune the distribution of lateral load transfer between each axle to our benefit.
To get into this, i’ll explain the function of roll stiffness as a key parameter.
Roll stiffness is fairly self explanatory - it’s the resistance provided by the race car in response to roll moments generated through the CoM and roll centre relationship, expressed in (Nm/˚)
Chassis roll stiffness is generated through two methods
The compressive stiffness of the tyre sidewall i.e. tyre pressure
The combined stiffness of the suspension components i.e. road springs, anti-roll bars, dampers
Thus far, the examples we’ve used have assumed an equal roll stiffness front to rear, it gets interesting when you consider the effect of unequal contributions from each axle.
Generally, the stiffer axle takes the larger share of lateral load transfer, so referring back to our example above, increasing the front axle spring rate in roll would serve to increase the proportion of vertical load it receives.
As i’m sure you’ll be able to extrapolate - this also means that the tyre is able to generate more lateral grip for a given slip angle.
This is a tool that can be used to adjust the cornering balance of the car, but importantly as you stiffen the axle, it will also generate more tyre temperature as the increased vertical load allows it to generate more grip.
Besides the increase in vertical load, any increase in spring rate means there is also an increase in the variation of contact pressure at the tyre-road interface.
In some cases (i.e. particularly bumpy tracks) this can move you in the wrong direction and reduce the available grip, but it will also introduce more agitation at the contact patch as it dissipates this additional energy. This means more temperature.
You might be forming a mental picture around how all this fits together by now and how we can manipulate the chassis to alter conditions for the tyre, but how do we define what the tyre wants?
For a start, tyre operating temperature is directly linked to longevity. This is especially important in endurance racing, where relaxing the total chassis roll stiffness can create a more comfortable environment for the tyre.
On the other hand, increasing the roll stiffness may serve better to get the tyres up to temperature quicker and deliver more intense performance in qualifying sessions.
Maintaining the total roll stiffness but shifting the distribution between axles can move some of the cornering load from front to rear and vice versa - useful if specific axles are degrading faster than others or struggling with temperature.
While tyres are below this narrow temperature operating window, they generally experience a lot of sliding as their viscosity is high; this is a condition where they experience relatively high wear rates.
Worn tyres can place you in a tricky situation in which the reduced tread bulk volume undergoes less deformation and therefore experiences less molecular friction to generate heat. As the tyre loses more heat than it generates, all attempts to find temperature in this situation lead to higher wear.
On the other side of the temperature range, an excess of heat can lead to degradation issues such as graining and blistering as the overheated rubber begins to melt and loses its ability to resist shearing forces at the contact patch. The decreased viscosity also reduces the grip it is able to produce as it transitions into this state.
Tyres are very communicative in the sense that through their degradation and relative temperatures, they tell you a lot about how the suspension is using them. This information can be used to implement adjustments to setup or driving styles. The tyre is king in the dynamics world.
Using the freedom of the chassis to get what you want from the tyre is important crucial. Here in part 1 i’ve discussed how roll stiffness can manipulate the lateral load transfer distribution to achieve this. Part 2 will explore the relationship of driver inputs around combined acceleration states and the experience of the stability index. We’ll also touch on the considerations related to FWD, RWD and 4WD configurations.
I welcome comments and discussion! Leave your thoughts below or find us on IG, Linkedin and waveydynamics.com