Vehicle Dynamics - Suspension & Geometries

The suspension system is critical to an F1 car because it is the link between how the tyres work with the chassis. In recent races, we’ve been hearing how the teams have been struggling to turn the tyres on, or it is taking a while for the drivers to get the tyre in an optimum operating window.  The problem is that teams are trying to balance extracting the maximum amount of friction from the tyres whilst also attempting to keep wear rates as low as possible.  Another factor may be that teams are being too conservative with geometry so that they don’t wear their tyres too quickly during races, but because of this, the car isn’t putting as much load and forces into the tyre and therefore, it is taking the driver a lot longer to get the tyre into its operating window. This area is very complex and there is no set ‘perfect’ geometry.

Suspension geometries are an important branch of vehicle dynamics. Suspension geometries determine how the sprung mass (car chassis) and un-sprung mass (wheel/hub/brake discs etc) connect to each other. The angles and positions of the suspension members dictate how the body of the car behaves as the car corners and the suspension systems are loaded up.

Degrees of Freedom:

The wheels of an F1 car need to be restrained in some way so that the contact patch of the tyre is maintained at a maximum. There are various suspension design layouts that can be chosen to restrict wheel movement, but for open-wheeled F1 car, we can only use a double wishbone system.

The double wishbone system consists of an upper and lower A shaped arm (wishbone) that connects the wheel to the chassis / car body and a push or pull rod to dampen the vertical motion of the wheel.

Camber:

Camber is one of the geometry settings most mentioned on TV. The point of camber adjustment is to maximise the contact patch of the tyre as it corners. Taking a front view of an F1 car (looking at the front wing), camber is the vertical angle of the tyre relative to the floor. Therefore, a tyre sat perpendicularly to the floor has 0 camber. When the tops of the two front tyres (or the two rear tyres respectively) are a closer distance to each other than the bottoms of the tyres, this is called negative camber.

The front tyres are always set to negative camber. A few degrees of negative camber counter acts the body roll and tyre sidewall flex during high down-force cornering. This means that mid corner, the car’s motion will have rolled the negative cambered outside tyre into a neutral camber therefore maximising the contact patch and maximising grip mid corner.

Instant Centre:

In this example, I will only be looking at the front view instant centre. There is also a side view instant centre which is just as important, but for this blog we’ll only look at front view.  Front view instant centre determines important things such as: the roll centre height of the car, change of camber rate and lateral tyre scrub.

This example looks at a simple rear end of an opened wheel car. In the image you can see the two tyres on the left and right, with wishbones connecting the wheels to a ‘body’ of some sort in the middle. (It looks messy, but this is a simple example!)

The instant centre is a point where lines are drawn from one side’s suspension linkages until they intersect each other at some point. The engineer decides to place the IC wherever they want it to be.

As I was the engineer in this example, I had decided to place my instant centres in the middle of the outside wall of the opposite tyre.

For example:

Starting from the left tyre and wishbones, extrapolated lines are drawn from the upper and lower wishbones across to the right hand side until they intersect each other. Where these two lines intersect is the instant Centre, and as said earlier, the instant centre was deliberately placed. Using some simple trigonometry, the angles of the two left hand side wishbones were found to be 3.55° from the horizontal axis. (Both upper and lower have equal angles for simplicity, but in real life they will probably be different)

As the car is symmetrical, both IC’s have been identified and now we can find the roll centre height.

Roll Centre Height:

Roll centre determines where the rolling moment of the cornering car will be and what effects that will bring. (A moment is a ‘Twisting’ force, Moment = Force x Distance)

Roll centre height is found by drawing a straight line from the centre of the tyre’s contact patch to its respective instant centre. Drawing two lines from the contact patch of each to their IC’s makes the lines intersect each other, where the lines intersect shows where the roll centre is. The distance between the floor (bottom of the tyres) to the roll centre is the roll centre height.

In this example, the RCH is 11.5cm from the floor.

When a car is cornering, the lateral force at the centre of gravity can determine the moment about the roll centre. The higher the roll centre height, the smaller the moment about the moment about the roll centre.

The high nosed 2013 F1 cars naturally bought with them a high roll centre height. The steep front wishbones of the cars meant that high instant centres were necessary and therefore, the consequence was a high roll centre. This high roll centre bought with it relatively low moments about the RC. This low moment means that the car isn’t rolling about laterally so it is very stable.

In contrast, this year’s 2014 cars have much lower angled wishbones due to the lower nose/bulkhead height. These smaller angles mean that the roll centre height must be lower on this year’s cars. Although corner speeds are lower this year due to lower amounts of down-force, the rolling moment about the RC is higher because the roll centre height is lower down than in 2013.

The higher moment about the roll centre means the cars aren't as laterally stable as they were last year, and this is most evident in medium speed direction changes where down-force isn't available to plant the car into the floor.

For example, this weekend in Canada we have seen: Gutierrez crash between turns three and four, Ericsson crash between 8 and 9, and Chilton causing a crash by drifting across turn three into his team-mate Bianchi. The leading constructor Mercedes also saw lateral instability, during the race we saw Rosberg make an incredible catch coming out of turn 4 to save his race. This shows that it isn't just the smaller teams struggling with suspension and geometries.

This is a very brief insight into suspension geometries, I hope that you enjoyed reading about it and would like to learn more like I do! Keep an eye out on future vehicle dynamic blogs of mine.

Ali