Vehicle Dynamics: Tyre Sizing and Chassis Balance

Running a car with different tyre sizes on each axle is a reaction to address the shortcomings of unequal weight distribution, but to understand the engineering motivations you first have to understand the influence of CoM (Centre of Mass) positioning on chassis dynamics and secondly, you have to understand how tyre physics allow it to make a difference.

In this article i’ll work through the concept of front : rear staggered tyre sizes, to explain why it's done and how it works.

Let's start with the problem and then work through to the solution.

Staggered tyre sizing front to rear has been recognised as a chassis tuning tool for decades.

50:50 Vision

In an ideal world, all race cars would be designed with 50:50 weight distribution. This is a great configuration for vehicle dynamics as in steady-state cornering situations it results in both front and rear axles working equally to generate performance, but of course packaging rarely allows this to be a reality.

Steady-state cornering conditions are observed in the mid-corner phase when yaw acceleration has reduced to zero. The requirement for this condition is that the cornering moments around the CoM generated by each axle are equal and opposite. This is called moment equilibrium.

Balance of forces and moments on a chassis with 50:50 weight distribution

The physics in the 50:50 scenario demand equal lateral forces from the tyres on each axle to achieve equilibrium.

This is what we call a neutral balance. If the same weight, size and compound tyres are on each axle, they must be working at the same slip angles.

Perhaps more importantly though, equal tyres at equal slip angles are also generating the same temperature (neglecting longitudinal forces) and will wear at the same rates. More on that a little later.

So that’s the ideal case - building on this by demonstrating the dynamics of a more typical unequal weight distribution, let’s consider a typical rear-mid engined open wheeler with a 65:35 weight bias.

Balance of forces and moments on a chassis with a rearward weight distribution.

Due to the unequal length moment arms, achieving equilibrium under steady-state cornering means the rear tyres must generate higher lateral forces than the front. This demands a larger slip angle, working the tyre harder and subsequently generating more heat and greater wear than the front.

In this condition, the 65:35 scenario is working the tyres disproportionately; the rear axle reaches saturation whilst the front axle still has plenty to give. Ultimately, the result is a progressively worsening oversteer balance as the tyres wear, which isn’t great for engineer or driver.

An inherent oversteer chassis balance is only going to progress as the tyres wear. [Credit: Alexandria Bates]

So how can we try and correct this behaviour using tyres?

To start with, we need to understand the concept of cornering stiffness as a property of the tyre, so let's spend a little time on that.

The concept of cornering stiffness of a tyre is nothing complex, it’s a measure of its ability to produce lateral force at any particular slip angle - measured in Newtons per Degree: N/°

Cornering stiffness varies due to the operating conditions of the tyre, but generally of most interest to us as vehicle dynamicists is the vertical load (contact pressure), tyre inflation pressures, wheel camber and tyre temperature as those are the variables we have direct control of.

Applying Pressure

For this article we’ll focus on vertical load and manipulation of the contact pressure to gain a performance advantage. By changing the tyre sizes to increase or decrease the contact area, we can influence the coefficient of friction (CoF).

As far as the tyre is concerned, this is effectively the same effect as a change in vertical load. The end result is that the contact pressure between the tyre and the road is changed.

I know i’ll need to expand on that, so stay with me.

Take two tyres of identical rubber compound with the same vertical load of 4000N applied to each of them.

Tyre 1 has a contact area of 0.01 m^2, Tyre 2 has a contact area of 0.02 m^2

This generates a total contact pressure of 400,000 Pa for tyre 1 and 200,000 Pa for tyre 2.

If we view the contact patch as a matrix of discrete elements, for arguments sake let's say each element is 0.001 m^2 (10 elements for tyre 1, 20 elements for tyre 2) then each of the elements in tyre 2 has its contact pressure halved relative to tyre 1.

With the contact patches of both hypothetical tyres broken out into a matrix of discrete elements, the relationship between vertical load and contact pressure becomes clearer to see.

To understand the importance of this, we’ve got to look at tyre characteristics to understand how the CoF relates to the vertical load.

Chart: CoF vs. Reaction Force [Credit: Balkwill, J. (2017) Performance Vehicle Dynamics]

Although it's not a linear relationship, the CoF increases as vertical load (i.e. contact pressure) is reduced.

If you’d like to explore tyres a little further. Here’s an online article i wrote for Racecar Engineering Magazine on Tyre Dynamics.

This fact ultimately gives us the understanding that for a given vertical load, increasing the contact area will increase the cornering stiffness of the tyre.

Increasing the contact area can be done by increasing the width or diameter of a tyre, which directs us to the staggered kind of arrangements which we see on the heavily rear-biased older F1 cars.

The converse is of course true for front weight biased cars, as Audi demonstrated by specifying wider front tyres than the rear on their production model RS3 in efforts to cure the relentless understeer.

Nissan also followed this concept on their front engined Nissan GT-R LM Nismo LMP1 car.

A Balancing Act

So, the benefits..

Perhaps most importantly, staggered tyres allows the chassis balance to be adjusted. In our 65:35 scenario, by increasing the rear tyre sizing (width and diameter) the balance is moved forwards from oversteer towards neutral.

This isn’t only a positive for drivability, but also performance over the tyres life. As mentioned earlier, having the rear axle reaching saturation significantly before the front is a problem that’s only going to get worse as it wears.

Any adjustability and fine tuning further to this can be managed by altering the chassis roll stiffness distribution.

This is something i also explore in more detail in my ‘Performance Through Tyre Management’ article.

Of course in reality, cornering only accounts for a small proportion of a lap, so another justification for using staggered wheel sizes even with 50:50 weight distribution is of course in RWD cars.

On throttle, the driven rear wheels pick up a lot more wear than the fronts due to longitudinal slip, and on average operate at a higher temperature, which can make the issue doubly worse as the rubber starts to melt and 'runaway'!

Even with a relatively neutral weight distribution, there is still a benefit in having staggered tyre sizing front:rear. [Credit: BMW Team RLL]

This kind of thing can be seen in cars such as the M6 GTLM.. With its front-mid mounted engine and transaxle gearbox it has a pretty neutral weight distribution, but has wider rear wheels relative to the fronts for exactly this reason.

Instead of starting a stint with neutral balance which progresses into oversteer as the rear tyres wear, staggered sizing can bring the advantage of beginning with a slight understeer balance on fresh tyres, moving towards an oversteer balance as the rear tyres wear faster. The ‘average’ balance will be more favourable in this configuration.

That point of neutral balance as the chassis transitions is a great place to be in qualifying for example. The key thing for a race engineer is to ensure the duration of that phase is as long as possible!

Reality Bites

in reality of course things are never as cut and dry as theory might initially tell us. Balance is a dynamic quantity and is speed sensitive, so a car will never be perfectly balanced in every corner on track.

We also neglected the concept of the Polar Moment of Inertia for this article, which is independent of weight distribution and influences chassis behaviour at turn-in and exit of a corner.

I will leave those layers of complexity for another article though :-)

I remember having this question in my mind for a long while so i hope it helped some of you. Remember, when you’re approaching things that aren’t so straightforward to understand. Be methodical with your approach and tackle one concept at a time.

Break the bigger question down into a number of smaller obstacles. Find an answer for the first gap in your knowledge. When you understand that bit, you’ll likely realise you have another piece of missing understanding, so do the same.

Piece by piece you’ll move towards your solution, something like peeling the layers of an onion.

As ever, give me a message if you have any questions or need some more clarity on anything.

Be inspired. More soon.