We’ve covered the journey of forces from the tyre contact patch through the wheels and suspension into the springs and dampers, and now we arrive at their final destination, the chassis.

In this penultimate article of the racecar vehicle dynamics series, tyre dynamics, suspension, kinematics and spring-damper systems all come together and interact with the chassis to complete the puzzle of vehicle performance.

Chassis control is a large part of effective vehicle dynamics. That means keeping all 4 contact patches on track! [Macau Photo Agency]

Chassis Modes

In the vehicle dynamics world, we refer to chassis modes. Modes are combinations of wheel deflections that produce a particular form of chassis displacement. Traditionally these modes are discussed concerning road inputs, but the concept is also used to illustrate chassis displacements caused by longitudinal and lateral forces generated whilst driving.

There are four displacement modes: Heave, Pitch, Roll, and Warp. For brevity, I’ll summarise the modes in the table below.

Chassis Modes; Illustration 1 [Zapletal. (2000) Balanced Suspension]

Heave is an interesting mode in motorsport due to its relationship with ride height and underbody aerodynamics. With huge aerodynamic loads forcing the chassis towards the track surface, spring stiffnesses must be specified very high to maintain the chassis in the optimal window of its aero map; this introduces some significant compromises when those loads aren’t present.

Roll receives a lot of attention in chassis design due to the transient effects on tyre contact patch loads and the dynamic impact on wheel camber.

Excessive roll can do more than just reduce contact patch area. [Macau Photo Agency]

When designing a racecar platform, it’s common to have a roll gradient (°/g of lateral acceleration) target, which is agreed upon by aerodynamicists and the suspension and kinematics team to ensure the car works together as a unit. There’s no magic number to roll or pitching targets. To understand why roll happens, I introduce the much-discussed concept of the roll centre.

The roll centre is the application point of tyre forces to the chassis – its vertical distance from the CoM is the source of roll moment (or roll torque) acting upon the CoM; this is simple leverage.

The roll centre location is important in managing chassis roll torque. The distance h is key. [Jahee Campbell-Brennan]

As you see from the illustration, the resultant tyre forces at the contact patches of a particular axle have both a vertical and horizontal component. The magnitude of each is determined by the roll centre’s vertical height from the track surface. The vertical component of these forces is the jacking force and acts to lift the chassis, which is uncomfortable for a driver and impacts weight transfer by raising the CoM.

It’s desirable to keep the roll centre as low as possible to maximise the horizontal component, but lowering the roll centre too much creates a large moment arm between the CoM, though, so there’s a balance to be made here.

Maintaining a low roll torque also means less roll stiffness is required from the system – returning full circle to the tyre, which finds itself in more favourable conditions. You should now start to see the origins of a vehicle dynamicists desire to keep CoM height low!

There is a direct analogy to this in the side view where the roll centre concept can be applied to the Pitch centre. Here, it’s anti-squat and anti-dive geometry that controls the location of pitch and dive centres, as described in the kinematics article.

Roll and pitch also influence aerodynamic performance by changing the proximity of the underfloor and aerodynamics components to the track surface and introducing the chassis rake angle. Warp is of less significance as it’s not stimulated by any specific chassis accelerations and responds to road inputs. Warp is coupled to the roll mode.

Mode Decoupling

Treatment of these chassis modes is significant in vehicle dynamics because each mode has a different impact on dynamic situations. With different responses, we should manage them separately.

In an ideal situation where freedom to design for optimal chassis control is given, each mode would be controlled by a separate spring-damper system – providing different natural frequencies and different damping rates for each mode. Standard passive suspension systems like those on GT cars are challenging to realise that due to vehicle packaging.

Systems that act to decouple each chassis mode from one another are called mode-decoupling systems. The anti-roll bar contributes towards this by separating spring rates in heave and pitch from a roll in its simplest form. Designers can start to get creative with their approaches on prototype and open-wheel formula cars where there’s more design freedom.

Spring and damping rates suitable to support the heave mode would be way too high in roll, where they will introduce very high variations in contact patch loading and a fall in average grip levels during cornering.

Commonplace in LMP and F1/IndyCar style chassis are suspension designs that tackle this problem by separating heave and pitch damping from roll damping by introducing a heave spring and damper. It provides the proper support for the chassis under high aero loading to maintain the aero map whilst providing a supple enough platform for track compliance in other modes.

Passively decoupling the pitch mode is the tricky one. It usually requires hydraulic linking the front and rear suspension systems to introduce some additional damping to the movement. Porsche had some success with this in their 919 LMP1 car with the FRIC (Front Rear Interconnected Control) system.

The pitch mode has different inertia to heave and thus requires a different set of spring & damping rates. [BMW Team RLL]

Chassis Balance

One of the most critical variables controlling the chassis is the Centre of Mass (CoM) location relative to the contact patches. That can be the difference between a great car and a terrible one.

The chassis balance is often assessed subjectively, but it does have very objective roots. In the most basic terms, chassis balance describes which axle loses grip first and leads to under or oversteer. The physics behind balance forms one of the fundamental equations of cornering, namely the concept of yaw moment equilibrium.

For this article, it’s enough to understand that with all else being equal (i.e. the exact tyre, spring-damper and suspension kinematics on all four wheels), the significant input into chassis balance is the longitudinal CoM location relative to the wheelbase of the racecar.

One can easily deduce the longitudinal CoM position from the static front-to-rear weight distribution of the chassis. With a 50:50 weight distribution, the CoM is precisely between the two axles. Dynamically this is an ideal scenario as it means the tyres on the front and rear axles are operating at the same slip angles and work equally.

With a forward weight distribution, the front tyres are operating at larger slip angles than the rears. From the tyre dynamics article, you’ll remember that once a tyre reaches its optimum slip angle, the lateral force it generates starts to fall, in this case leading to understeer. The opposite is true for oversteer.

As the race car in this situation is grip limited by the overactive axle, it’s harmful for maximum lateral acceleration and tyre wear, so significant efforts are made to package the CoM as centrally as possible during the design phase. One can adjust balance through the springs and dampers, but this addresses the symptom rather than the cause. A fundamentally balanced chassis is always the target.

Weight Transfer

Now that’s understood, we move on to vertical CoM positioning. Starting from the most elementary situations of longitudinal acceleration – a driver applies some throttle, and the car accelerates. 

Due to inertia, the race car’s mass resists acceleration, which the tyres feel as a shift of weight from the front wheels to the rear wheels. The extent of this weight transfer is a function of the vertical location of the chassis CoM from the track surface and the vehicle’s wheelbase. It’s directly proportional to the magnitude of the acceleration.

In a rear-drive car with this simplified scenario, weight transfer is nothing but positive as it will result in an increase of grip at the driven tyres. Still, a high CoM has definite drawbacks in other handling scenarios. 

In cornering, weight transfer is not helpful as it means the inside tyres become unloaded, while the outside tyres become heavily loaded. This time, the extent of the weight transfer is proportional to the vertical CoM height, track width and lateral acceleration.

As you saw in the tyre dynamics article, grip levels increase with vertical loads, but the CoF falls, so in the end, this means that the grip gained by the outside wheels is less than the grip lost by the inside wheels – overall lateral acceleration suffers.

Spring stiffness nor suspension geometry can change this; it’s a hard fact. Weight transfer is undoubtedly something to be minimised, which is why you see and hear such emphasis on keeping the CoM as low as possible during the design process.

Lateral weight transfer can be managed through axle roll stiffness distribution. [Jan Ivo Henze]

Moments of inertia

The inertia of the chassis is crucial in roll and pitch responses, and it’s also an essential influence in the yaw response of the chassis. The idea of considering the vehicle’s mass as concentrated at the CoM is an excellent assumption in many static cases. Still, it doesn’t account for the distribution of that mass within the chassis and dynamic instances.

The closer the mass is located to the CoM (which, for argument’s sake, we will assume to be the axis of rotation), the lower rotational inertia the chassis displays. That ultimately means that the yawing moments generated by the chassis generate higher yaw accelerations and result in a sharper dynamic response.

The chassis moment of inertia is important in defining yaw response. Placing big masses close to the CoM is key. [Jahee Campbell-Brennan]

Generally, on circuit racing cars, locating heavy powertrain components close to the centre of mass is standard practice to keep the yaw inertia as low as possible.

The result is a subjectively sharp response to steering input and positive adjustability at the grip limit for the driver, with an objectively measured improvement in time response to yaw moments for the chassis. That generates more significant yaw accelerations and translates to reduced lap times.

What I hope has been communicated throughout the series thus far is that a holistic approach to racecar performance is required when vehicle dynamics is concerned. Ultimately, the main bulk of the car lays at the chassis, so all other pieces in the puzzle work in symbiosis to accelerate it around the race track as rapidly as possible.

By locating the main masses strategically to optimise balance, weight transfer, and yaw accelerations, interaction with the suspension system provides a platform for all other pieces in the puzzle to create the equation of performance.

The next and final article in the series will focus on data acquisition. Stay close!