Vehicle Dynamics: What Makes a Car ‘Balanced’?

A hot topic. The term ‘chassis balance’ is used loosely in many different circles, from enthusiasts through to top level professionals. But, its quite an ambiguous phrase. With respect to road vehicles, you’ve more than likely heard it used to describe the tendency of a cornering car to oversteer, understeer, or as we’ll learn, neither.

I don’t want this to be a long, technical article, but i did think it would be enjoyable to get into, for the sake of revisiting the fundamentals if nothing else!

I’d like to stay within the realm of steady-state balance and leave transient responses for a later date as it can quickly become quite complex and less of a casual article.

Having both front and rear engine configurations between them, this pair will have a very different approach to balance.

Continuing the existing theme we have introduced, using a tyre centric approach to dynamic behaviour, the first picture to build is the concept of ‘balance’ in terms of the management of lateral forces and yawing moments.

As i’ve mentioned in the tyre dynamics article featured on Racecar Engineering, there are many many variables that dictate the maximum force a tyre can produce; camber angles, roll steer, frictional coefficients, weather.. We could go on.

Let’s start just by looking at it from a high level, with a consideration to the development of simple forces and moments.

If you're not familiar with the concept of cornering stiffness with respect to tyres, it’s important to this discussion so let's clarify.

We define it as the lateral force generated per degree of slip angle, it carries the units of Newtons per degree; N/°.

The force produced by a particular tyre can therefore be defined as

Where α = slip angle.

Cornering stiffness is an inherent property of a tyre and therefore aside for some minor adjustment via inflation pressures and temperatures, it’s not an adjustable quantity.

So, to keep things palatable for discussion, i'll introduce the concept of chassis balance by making some basic assumptions of a vehicle in the simplest case:

1. The Centre of Mass (CoM) of the car is at the centre of the wheelbase, giving a 50:50 weight distribution with identical front and rear roll stiffness.
   

2. We assume that the radius of the turn is large enough that the steering angle of the front wheels is sufficiently small to be approximated as zero - the lateral force generated by the front and rear tyres is therefore acting parallel with one another.
   

3. The car has achieved steady-state cornering.

Case 1: CoM is balanced within the wheelbase; lateral force contribution from each axle is equal.

In this scenario, both front and rear tyres generate the same slip angles and therefore peak force is generated simultaneously on each axle. As the adhesion threshold is passed, the car transitions into a slide with all 4 wheels in unison and is said to have neutral balance.

Staying with our 50:50 weight distribution example, Let’s explore the case of neutral balance a little further - what does this mean in a practical sense?

It means firstly that, the lateral forces generated at both axles are equal in magnitude.

It also means that the yaw rate (alternatively yaw velocity) is constant, in other words the angular velocity of the chassis is constant. For this condition to be true, the yawing moments at the front and rear of the car must also be balanced, or at equilibrium.

Note - Equilibrium in this context is relative to the forces and moments generated at the CoM due to lateral acceleration.

To drive a change the yaw velocity, there has to be an unbalanced yawing moment. Since this configuration doesn’t provide such an opportunity, we get a neutral response. Easy, job done!?

I do want to make clear that an imbalance of yawing moments is necessary in some parts of the cornering phase, this is what steering the front wheels does after all. Where we don't want them however is when we’re trying to get the car into the steady-state phase of the corner approaching the limit of grip.

So let’s step away from an ideal world and consider the real world. How do unbalanced yaw moments come about and give rise to an understeer or oversteer balance?

We look to the conditions at the tyre.

1. Different slip angles at front/rear axle due to CoM positioning: This means unequal lateral forces are generated to maintain moment equilibrium.
   

2. Cornering stiffness is not equal at both axles: In this case, the slip angles may be equal but the magnitude of lateral forces generated at the contact patch is not.

The trouble, or undesirable behaviour results when with high speed cornering regimes. Physics dictates that criteria for equilibrium can't be met as one axle reaches saturation before the other. One end of the car will begin to slip.

Balance really starts and ends with how the vehicle is using the tyres - there’s no escaping it.

Perhaps this is easiest to imagine when picturing a car driving round a fixed radius circle, as speed increases there will be a threshold at which it is unable to maintain the cornering radius. The manner in which it loses grip is what we’re talking about when we mention balance.

As a car with an oversteering balance approaches this threshold, for example due to a rearwards CoM, the rear axle reaches its limit, the lateral force plummets as the tyres begin to slide and the vehicle is unable to generate the required loads to maintain moment equilibrium. This results in a yaw acceleration acting to steer the nose of the car into the corner centre.

Case 2: Rearward CoM - At the moment the rear axle begins to slide, moment equilibrium is lost, initiating a yaw acceleration.

Likewise with an understeering balance, the rear yawing moment exceeds the magnitude of the front, the car yaws ‘out’ of the turn.

Aside from affecting the drivers confidence and ability to control the car in race situations, over or understeer balance is actually detrimental to maximum cornering speed.

As explained prior; the advantage of neutral steer in a chassis is that both axles reach grip saturation simultaneously and maximum cornering forces can be produced. Take an oversteering tendency for example. When one end of the chassis becomes grip saturated before the other, the cornering speed of the car suffers.

Let’s give it some numbers to help drive this home:

As you can see, a change of weight distribution from 50:50 to 70:30 demands very different output from the tyres. In this case, the rear tyres are asked to work 42% harder than the fronts to maintain moment equilibrium. Clearly when this axle reaches peak force, the fronts will still have much more in reserve.

Let’s say the tyres reach a peak lateral force of 9000N, the 50:50 vehicle will be able to produce a cornering force of around 1.8g, while the 70:30 vehicle will only manage 1.28g.

Neutral steering is therefore a crucial target for any vehicle dynamicist, although in practice it's not always a straight forward objective.

Understeer Gradient

So now we’ve established the concept of balance, how it works and why we aim for 50:50, how do we quantify a car's balance?

Common practice is to use a concept we call the Understeer Gradient.

The understeer gradient relates the amount of steering input, away from neutral (Ackermann) steering that the driver must introduce at the wheels for every unit of lateral acceleration. Its clear to see from this that the steering input must also increase as the vehicle speed increases.

Note: This only holds true as the tyre behaviour is linear, up until you approach the limit of grip.

Positive understeer gradient indicates an understeering car, a negative indicates an oversteering car.

In practice, some degree of understeer or oversteer may be desired by a driver as it offers a degree of adjustability at the limit, so what are some of the tools we have available to tune the balance in a finished platform?

While the total lateral weight transfer is fixed by track width and CoM placement, the distribution of weight transfer between front and rear axles can be tweaked by adjusting roll stiffness. Increasing the roll stiffness at the opposite to the saturated axle will increase the load seen by the outside tyre there, increasing it's contribution to lateral force for a given slip angle.

Chart 1: Note the non linear relationship.

You may also use suspension geometry and kinematics to manipulate static and dynamic toe variables, moving the tyres towards to operate at different slip angles. Increasing reaction force also increases the slip angle at which the peak lateral force is generated, so this can further take advantage of this additional capability.

Lastly, but no less importantly we can play around with the cornering stiffness at each axle. Assuming the same tyre compound is used throughout; this can be achieved using wider wheels and/or a greater wheel diameter.

Not only to increase the surface area for adhesion, a larger contact patch reduces the contact pressure, which raises the frictional coefficient also.

With a rear weight bias, the designers of this Leyton House F1 car staggered the wheel sizes to aid chassis balance.

So, that should provide a little insight into the world of chassis balance! I hope i clearly communicated what it is, the physics behind it and also provided some ideas you may use to adjust yours.

I think i’ll also produce a video on this one in the near future so keep your eyes open. As ever i welcome a discussion so if you have any questions or queries please grab me.