Vehicle Dynamics 2 - Braking & Accelerating

 In my first Vehicle Dynamics blog we looked at the side to side (lateral) forces a Formula 1 car experiences. 

In this blog, we will be looking at the longitudinal forces F1 cars experience, which come from braking and accelerating. This part of the suspension geometry is calculated by looking at the cars from the side view, rather than the front view which determines the lateral forces geometries.

Intro

The point in looking at side view geometries, as we are about to do now, is so that we can analyse and control the longitudinal forces exerted on the car. As we all know, the acceleration and braking forces in Formula 1 are nothing short of brutal. These extremely harsh forces are transferred through the car and into the suspension systems, which is what makes a car’s nose dive down under braking, and rear end squat under acceleration. Side view geometries let us control things such ‘Anti dive’ and ‘Anti squat’.

We look at these two so that we can control the ride height as the lateral forces take hold of the car. Controlling the ride height means keeping it as constant as possible even when braking into the most demanding of braking zones.

The aim of controlling the ride height is done mainly for aerodynamic purposes; a changing volume of air passing under the car constantly disturbs the pressure balances above and below the car, and therefore starts harming aerodynamic efficiency. Another major reason for controlling the ride height is so that the drivers can comfortably push to their limits. A car that dips down under braking is unstable which means that the driver can’t comfortably decelerate the car to its full potential – increasing lap-times. A car that squats when the driver gets on the throttle at apex could make the front end start understeering at corner exit, as well as making the car unstable mid corner, all resulting in a slower car. This blog will help show you how the engineers cancel these unwanted effects out of an F1 car.

Instant Centre Calculations

I will now demonstrate how to calculate the side view IC’s which can then be used to calculate ‘anti-dive’ and ‘anti-squat’.

Like we looked at before, an Instant Centre needs to be placed. Both the front and rear wheels have an instant centre. The instant centre is a projected, imaginary line which effectively works as a pivot point for that wheel (as it jounces). The instant centre is set by the engineer by angling the upper and lower wishbone together as demonstrated below.
It is common on rear suspensions for the IC to be in front of and above the centreline of the wheel (red line).

G.Piola, 2013, pg 71

The green lines visualise the angles of the wishbones. The point at where these two extrapolated lines (Green) meet is the Instant Centre. In this example, the Ferrari F2012 Technical Officer and Senior rear suspension design engineers decided to place the IC just under the large Ferrari logo on the monocoque. This is a very common area to place the IC, as it is above the rear wheel centreline (Red) and also ahead of the rear wheel.

Another two examples of side view wishbone angles from Piola: (Wishbone lines in red this time)

Piola, 2013, pg 82

G.Piola,2013,Pg 70

Anti-Dive

Anti-Dive is the coupling relationship between a braking force and front suspension vertical movement.

Let’s take T1 at Monza as an example; as a car brakes from 320km/h+. How does that deceleration force couple itself with the vertical movement at the front suspension, due to longitudinal weight transfer onto the front axle?

Choosing a specific Instant Centre can help us decide how much vertical movement is absorbed by the wishbones and linkages, and how much the torsion bars and dampeners react to the deceleration. Ride height change only occurs when the longitudinal force is reacted by the torsion bars and dampeners.

To help show how anti dive is calculated, I have created my own (crude) sketch of an F1 car. 

The IC has been determined by the front suspension wishbone angles, and now a ‘swing arm’ has been drawn from the front tyre contact patch to its IC.  

We have now triangulated the IC with the tyre contact patch and the ground, this allows us to use a short equation to find out our anti dive percentage.
The equation uses factors such as brake balance, swing arm length - 1672mm, (as shown in the diagram above), swing arm height – 416mm and the angle between the contact patch and IC - 14̊.

If an ‘anti’ percentage is calculated to be 100%, then we have a scenario where the longitudinal load transfer is controlled by the wishbones, therefore no dive and no change in ride height at the front. If an ‘anti’ percentage is calculated to be 0% then the longitudinal load transfer is reacted by the torsion bars and dampeners, therefore changing ride height due to dive.

This is where FRIC started to get very expensive. Engineers must’ve had to find solutions where FRIC would work in harmony with the natural reactions of the suspension systems.
For example, in a braking zone, the nose wants to dip down due to the weight transfer, but FRIC was dropping the nose even more as velocity decreased.
You can see how these two systems are counter-intuitive, yet they still made the cars go faster when a compromise was found.

Anti-Squat

Anti-Squat is the relationship between acceleration forces and vertical movement downwards at the rear suspension.

Squat occurs when harsh acceleration forces cause weight transfer to the rear axle. The ride height at the back reduces – squats. This squatting changes the ride height at the rear and therefore affects the airflow coming from under the diffuser. The diffuser is a critical component for downforce, and is very sensitive, so irregular changes in airflow through the diffuser could destroy a car’s aerodynamic efficiency.

This area of suspension geometry is very complex, and with the inclusion of FRIC, it also becomes very expensive to get right. This was the main reason in banning the FRIC systems.
The general design of a Formula 1 car helps to reduce diving and squatting because of the low amounts of weight transfer occurring between the front and rear axles. This is mainly because of the low profile of an F1 car. The Centre of Gravity is very low and this helps to greatly reduce the coupling effects between longitudinal forces and vertical suspension movements.

Thanks for reading,
Ali