In the first part of this series, i introduced the concepts of CoM position and lateral load transfer distribution as important parameters influencing how the race car demonstrates balance and by extension, uses its tyres.
I also want to take the opportunity to quantify the balance of a chassis. We’re clear that it can usefully be defined in terms of oversteer or understeer tendency, but how do we evaluate a cars balance objectively?
To explore this, i want introduce the concept of the Stability Index (SI).
The Stability Index is a very useful indicator in understanding what is in effect, the relationship between slip angles at the front and rear of the car as lateral acceleration builds. With it, you can predict whether the car has a stable or unstable behaviour and put a number to it.
The SI is approximated as the magnitude of the moment arm between the CoM and the Neutral Steer Point (NSP), normalised by the wheelbase.
This moment arm is denoted as the Static Margin (SM), a concept bought over from aeronautical engineering.
And here's the maths.
The Neutral Steer Point itself is the point along the wheelbase at which you can apply a lateral force to the chassis resulting in pure lateral translation. There is no yaw acceleration resulting as the yawing moments generated by the front and rear axles balance at this point.
Put another way, the NSP can be understood as the effective ‘Centre of Force’ of the tyres on the X Axis; analogous to the aerodynamic Centre of Pressure. When a lateral acceleration is applied to the CoM, the NSP becomes an effective centre of rotation.
As conditions at the contact patch are constantly changing during a manoeuvre, the Neutral Steer Point is always changing position, this should allow you to deduce that it is a dynamic parameter.
So how does the SI allow us to understand balance?
EDIT: The above term is a only a rough approximation to allow demonstration of the concept. There are more detailed analysis of the Stability Index around, in reality it must incorporate a velocity dependant yaw damping term, though this is a relatively small contribution to the overall SI.
If you’re interested in further reading check out Race Car Vehicle Dynamics by Milliken & Milliken, who give the most comprehensive coverage of it i’ve seen.
The first thing to understand is that its sense allows us to understand the how the tyre slip angles are increasing. SI > 0 indicates the NSP is in front of the CoM and that the rear slip angles are greater than the front, giving an oversteering, or ‘unstable’ behaviour.
Likewise a SI < 0 indicates it’s behind the CoM which gives an understeering, or ‘stable’ behaviour as the slip angles follow the opposite pattern.
Where it starts to really give you a lot of information is when you’re looking at its magnitude. A larger SI indicates that the racecar has more of a ‘relaxed character’ at the limit of grip, easy to control and ‘predictable’ - subjective observations, but correct nonetheless.
On the other hand a smaller SI, perhaps < 0.10 would be said to give a response that tends to feel on more of a ‘knife edge’, with a twitchy, unsettled character.
As the NSP defines the effective centre of rotation (from the reference frame of the chassis) of a vehicle, the radius of the CoM from this point (the Static Margin) has influence to the angular acceleration of the body when traction is lost through its effect on rotational inertia.
Smaller inertia = Larger angular acceleration.
From a driver control point of view, as the SI reduces, the effect is a vehicle which requires quicker control input to catch once lateral balance is lost.
On paper, an SI of 0 might look attractive for performance by providing neutral balance, but in reality would appear to be unpredictable. The NSP can even reverse its sense in some scenarios, which creates a stable-unstable behaviour. Yaw accelerations are large and driver confidence would be low.
A range of 0.05 - 0.10 might be said to be comfortable for most drivers.
As experienced drivers are more precise with their input, this also explains how professional drivers can tolerate and even prefer a smaller SI with faster and more precise control responses.
The location of the NSP and therefore the Stability Index is a function of many different inputs; tyre sizing, tyre pressure, wheel kinematics, longitudinal weight transfer, roll stiffness/lateral load distribution, aerodynamic CoP and instantaneous vertical loading are an important few. Not to mention the CoM itself which moves during a run as fuel load changes.
The Static Margin is always changing based on conditions at the tyre.
Keeping with the theme of the article - this is just another tool we can use to manage tyre energy/comfort and find performance!
Up until this point we’ve covered how we can use understandings of vehicle & tyre dynamics to manipulate the cars behaviour and influence how it wears, but there’s also a lot to be said about the drivers approach too.
I’m sure you’re all familiar with the concept of the friction circle. Maximising cornering speed is easy, maximising longitudinal acceleration is easy, but if the transitions between each are not elegant, there is always a time at which the tyres are not saturated and time is lost.
Blending the transition between lateral and longitudinal acceleration is an important driver tool, so i want to spend some time covering that.
The basic premise is to keep the tyres at the limit of the friction circle at all opportunities; the tyres will always give you something, it would be silly not to use it.
From what was discussed in Part 1 of the article, you may now be able to connect the friction circle to the energy input into tyres over a lap and subsequent effects.
Maintaining combined acceleration in the beginning phases of a corner (i.e. trail braking) is a not just a technique for cutting lap times, but a tool which can be used to generate heat in the compound - reaching working temperature in less time. On the other hand, in an endurance event you may need to be a little more considered with regards to wear and drive more conservatively.
In endurance racing or any racing where tyre management is important, there can be a several second difference between qualifying and race lap times, this can be a result of setup or driver techniques.
To drive this home, in this years Le Mans 24h the pole winning LMP2 car, United Autosports, lapped 5.2 seconds faster than its quickest race lap. Much of this is tyre management.
The key takeaway for you is that an understanding of what a driver is doing to the contact patch is a significant component to decision making which will enable them to get what is needed in terms of performance through tyres, this is important for both engineer and driver to know.
To finish this article, i want to step back to fundamentals for a second and talking on the long standing debate around driven wheels and what is best for performance.
I say debate - track based motorsport has almost universally converged to RWD as the chosen format, but why is that?
Yet again, it comes down to tyre mechanics. In terms of FWD vs. RWD it’s a fairly clear argument - where it matters in conditions where traction is needed (i.e. pure longitudinal acceleration), the rearward weight transfer on throttle application will move the weight exactly where it is best used with a RWD application for optimal traction; the rear wheels.
With FWD - the opposite case, the weight moves away from where it is wanted and the potential for acceleration is reduced. This is a simple relationship.
4WD seems like a happy medium, but aside from the additional weight and complexity that it carries, many systems are either fixed in their torque distribution, or work with too much lag in their response.
The result can be a somewhat dynamically clumsy car, but ultimately it means that available friction isn’t managed very efficiently.
This is why the system of Toyota Gazoo Racing with the TS050 LMP car is so great. With the combustion engine and a single electric motor powering the rear wheels and two independent electric motors on the front wheels, the electronic systems can very precisely detect and manage longitudinal wheel torque, allowing them to be at the edge of their friction radius at all times, yet not exceeding its limit.
On paper then, 4WD would come through as a winner - the real precise control in torque vectoring offered by electric motors is a certain way to maximise a powertrains use of the tyres.
Something to think on!
I hope you’ve enjoyed the article. Usual story - i love to discuss and exchange ideas with peers so i welcome your comments.
Until the next one..