The science behind determining F1 suspension set-ups

We have discussed in this column previously the importance of ride quality even in a stiffly sprung racing car, but the current Formula 1 aerodynamic regulations have led to teams getting maximum performance by running the cars very close to the ground. This very limited ground clearance leads to needing extremely stiff springs to maintain the low ride heights under the immense downforce that’s trying to compress the springs and tyres, and push the plank and the skids into the track.

These very stiff springs lead to a very harsh ride. Now the total vertical stiffness of a car is not just a function of the suspension springs. Any vertical load, whether it comes from the aerodynamic downforce or bumps in the road, also has to pass through the tyre – and the tyre is in itself a spring.

You’ll have noticed in your own cars how, if you park on a kerb, the tyre is compressed. This is because more load is passing through it. There is very little you can do to alter the spring rate of the tyre – in fact the only thing under the control of the teams is the tyre pressure and they want to run this as low as the prescriptions from Pirelli will allow, so they can optimise the contact patch.

So how does a team go about deciding how stiff to make the suspension springs to find the correct compromise between supporting the car close to the ground and yet giving it enough suppleness to absorb at least some of the bumps?

The answer lies first in modelling the suspension system and then in testing it on a sophisticated rig. The modelling is done by using a computer to solve the equations of motion of the system. Many will remember from school physics Newton’s second law of motion: that the acceleration of an object depends on the mass of the object and the force applied to it.

This is an equation of motion, and, for a suspension system, we’re able to write a much more complex equation which sums all the forces and resistances from the inputs to the system and the suspension elements such as the springs and dampers. The equations are slightly complicated by the fact that the stiffness of the suspension is different depending on how much it’s deflected. Engineers call this non-linearity, but computers deal with this relatively easily.

Current aero regulations means teams are aiming to run their cars as close to the ground as possible

Photo by: Zak Mauger / Motorsport Images

As with any computer modelling, it’s no bad thing to back it up with some practical experiments and it’s here the test rigs come into play. One can test just one corner of a car on what’s called a quarter-car rig but, these days, teams have access to rigs that can support the whole car and effectively shake it by moving powerful rams under the tyres to replicate bumps.

In the early days of this testing a simple vibration signal of varying frequency was fed into the rams in what was known as swept-sine testing. This was because the actual ‘bumpiness’ of the tracks couldn’t be measured. These days it can, and track replay is a common test technique.

I started doing this testing when we were developing active suspension in the 1980s. We had to use one of the few rigs available to us and these were always 4-post rigs. In other words, they had one actuator (or post) under each wheel. The one I used had been designed to test armoured vehicles so was rather meaty. We then needed to add something which replicated downforce. This had to be a constant force irrespective of the displacement of the vehicle on the rig.

There’s still something of a skill in deciding how to trade off the wheel-control quality and the chassis control and this is done using a ride-performance index

Our first attempts at this were with constant-force springs of the type you find in the Tensabarriers that control queues at airports. In fact, Tensator – who make those barriers – made us special springs. The biggest problem with these was friction and they had to run in copious amounts of oil. A later development was to use a giant gas spring. This is another non-linear device but, if the volume of the gas chamber is very large relative to the displacement needed, it behaves like a constant-force spring.

As the control systems for the rigs improved, and as more teams started installing custom devices in their own factories, the move was made to seven-post rigs where three additional, carefully controlled, actuators provided a constant load to replicate downforce.

To assess ride quality, accelerometers are placed on the actuators, the wheel hubs and the body. By looking at how the acceleration (and hence force) is transmitted from the actuator to the wheel and body using a mathematical technique known as a transfer function, one can determine the effect of different settings on the vertical wheel control (for tyre grip) and the chassis control (for aerodynamic consistency).

The early four-post rigs then developed into the more advanced seven-post rigs, such as this one used by Toyota in the mid-2000s

Photo by: Toyota

There’s still something of a skill in deciding how to trade off the wheel-control quality and the chassis control and this is done using a ride-performance index. This is another equation that will look at the transfer functions at the front and rear contact patches as well as the transmissibility and damping in the bounce and pitch modes.

The actual weighting applied to each comes from experience and will depend on the required characteristics that nuances of the regulations determine. The current regulations, for example, put much more emphasis on chassis control to maintain downforce than it might on the wheel control, hence the stiff ride we see.

Finally, we mustn’t confuse ride quality in this context with the harsh impacts caused by the plank and skids hitting the ground. This can be damaging to the drivers, and it is this that the FIA regulated for a while when teams were tending to run the cars too low.