This article was first published in 2009.
If you're talking suspension design and use the the phrase ‘virtual swing-arm length’, it’s very likely that people will immediately assume glazed-eye expressions. Start talking about ‘virtual centres’ and the conversation is likely to immediately switch to some topic that sounds much more friendly!
But these ‘virtual’ parts of suspension geometries are actually not at all hard to understand. Furthermore, they can be extremely useful in picturing (and predicting) suspension behaviour. Finally, they are an important ingredient in understanding roll centres – another topic for eye glazing!
One of the problems is that most textbooks start off with complex, real-world suspension systems – and then apply the concepts to those systems. I think it’s a lot easier to start off with the absolute simplest suspensions, where these ideas are far more self-evident.
Virtual Swing-Arm Length
Let’s start off with a swing-arm suspension system. This is where the arms are pivoted at or near the centre of the car.
When the wheel passes over an obstacle on the road (like this red rock), the wheel rises, pivoting around the inner point. You can see that the camber of the wheel (the angle it makes to the vertical) changes a great deal - that’s one of the negatives of this type of suspension system when being used on most (but not all) types of vehicles.
The length of the arm around which the wheel is pivoting (shown here in purple, and drawn to the centre of the wheel) is, as you’d expect, called the ‘swing-arm length’. The longer the swing-arm, the less the camber of the wheel changes for a given size of bump.
In fact, to minimise camber change, this 1960s Honda 1300 front-wheel drive used a rear suspension comprising swing-axles pivoted from the opposite sides of the car.
However, in many cases, less camber change is desired than can be achieved even with very long swing-arms. The trick is to swap to a different design of suspension, like the double wishbones shown here. The disadvantage is that the number of pivots has risen from one to four, and the number of arms has doubled (both significant deficiencies in, for example, ultra light-weight vehicles). But one benefit is that the wheel can remain vertical during its suspension movement – that is, the camber doesn’t change with up/down suspension movement.
However, in the real world, some camber change is actually usually desirable, primarily to keep the wheel vertical, even when the car is leaning in a corner. One way to achieve this slight increase in negative camber in bump is to angle the wishbones – one or both of them. Now this looks like a pretty minor change – but it isn’t. So why isn’t it? Because we’ve turned the suspension into the equivalent of a long swing-arm design! Let’s take a look.
What we’ve done here is to use red lines to extend the length of the wishbones until the lines intersect. The point where they join is called a ‘virtual centre’– that is, it’s an imaginary pivot point. The suspension acts as if the there is a single swing arm that connects to this ‘virtual pivot’.
As you’d then expect, the distance between the centre of the wheel and this virtual pivot point is called the ‘virtual swing-arm length’. This is shown here in purple.
So if you mentally draw a line from the virtual pivot point to the centre of the wheel, and imagine the wheel acting as if it was suspended by a solid swing-arm of this length, you’ve just got your head around some pretty important ideas.
But hold on! What about the ‘virtual centre’ and ‘virtual swing-arm length’ of the wishbone system with parallel wishbones?
If you extend the wishbones (red lines) you can see that they will never come together – the swing-arm is infinitely long, thus the wheel moves up and down vertically (when the wishbones are parallel to the road, anyway).
From the foregoing, it now becomes clear that all suspension systems can be said to have either:
- An infinitely long virtual swing-arm
- Or a virtual swing-arm of a specific length, pivoting around a virtual centre.
Virtual Swing Arms and Roll Centres
We’ve seen that the idea of virtual swing arms and virtual centres is very useful for determining the camber change that will occur as the wheel moves through its suspension travel. But it’s even more useful in working out another aspect of suspension design, called the ‘roll centre’.
Let’s take a look at the idea of roll centres, starting again with our simplest swing-arm suspension design.
The roll centre is found by drawing a line from the contact patch of the tyre through the pivot point of the swing arm. That line is shown here in green.
Another line is then drawn vertically on the centreline of the car (blue). The roll centre is where the two lines cross (purple arrow).
The roll centre is of a lot more than academic interest. All the cornering forces being developed by the tyre act through the roll centre. Therefore, as can be seen here by the red arrow, in a simple swing arm design of suspension, the force has both sideways (lateral) and vertical components. The latter tries to lift the car’s body, causing the problem of ‘jacking’ that afflicts this suspension design.
Looking at those two force components in more detail, here the red arrow shows the jacking (lifting) component and the brown arrow shows the sideways component of the force.
Let’s go back to our angled double wishbone system. To find the roll centre we again draw a line (green) from the tyre contact patch through the pivot point of the suspension system – but in the case of the double wishbone system, it’s the virtual pivot point (ie virtual centre) that we use. Again the centreline of the car is shown by the vertical blue line.
The roll centre is again where the green and blue lines cross, as shown here by the purple dot. You can see that the roll centre of this suspension design is much lower in height (ie it’s closer to the ground) than the roll centre in the swing-arm suspension system.
And what about when the wishbones are parallel to each other and to the ground? Because the virtual swing arm is infinitely long, the green line in this case goes to a point infinitely far away, therefore it runs along the road. The result is that the roll centre is at ground level. Roll centres can be located above ground level, at ground level or below ground level.
The common McPherson strut is one design where it can be initially difficult to work out where the roll centre is. This diagram shows how it’s done – the top line is drawn at right angles from the strut axis, starting from the upper mount.
Another way of defining the roll centre is to say it is the point in space around which the car rolls. Therefore, it can also be found by directly measuring the way the body of a car behaves. Mark vertical lines of different colours on screens attached at each end of the car. Roll the car (eg by applying external forces) and photograph the end views of the car at different roll angles in each direction. As this diagram shows, the roll centre will be revealed.
Dispending on the suspension system being used, roll centres can migrate during suspension deflection. Therefore, drawing of the roll centre should occur at static ride height, maximum bump and maximum droop. Note also that the roll centre for the front and rear suspension systems can be at different heights.
Roll Centre and Centre of Gravity
There’s one final concept that ties these ideas together. A car’s centre of gravity is another ‘virtual’ point. If you imagine all the car’s mass concentrated at one point, you have the idea of the centre of gravity.
In different cars the centre of gravity can be at different heights above the ground (if the heavy objects in a car are low, so will be the centre of gravity), and it can be closer to the front or to the rear of the car. (For example, a rear engine car will have a centre of gravity that is often rearwards.) In most cars, the centre of gravity is aligned on the central longitudinal axis of the car.
So what has the centre of gravity got to do with suspension? If the centre of gravity is higher than the roll centre, the car will lean outwards when being cornered. In fact, the higher the centre of gravity is compared with the roll centre, the greater will be the lean for a given cornering acceleration. Therefore, lowering the roll centre increases body roll! If the roll centre is at the same height as the centre of gravity, no roll will occur. If the roll centre is above the centre of gravity, the car will actually lean into the corner.
Let’s have a look at why these characteristics occur. We know that the cornering forces all get fed through the roll centre, and that the centre of gravity can be thought of as being the point where all the car’s weight is concentrated. If in this diagram there’s a force pushing towards the left at the roll centre, the car body will roll to the right. That’s because the vertical distance between the roll centre and the centre of gravity creates a virtual lever arm (red).
If the roll centre and the centre of gravity are at the same point, no lever arm is developed and so no roll occurs.
Finally, if the centre of gravity is below the roll centre, a lever arm will develop that causes the car to lean the opposite way – into the corner. Now of course this sounds very attractive, but it comes at the cost of having a high roll centre – which in turn causes the jacking (and other) problems we referred to earlier.
It’s very easy to get lost in suspension design, especially when obscure terms are thrown about freely. However, by starting with simple suspension systems, where the ‘virtual’ ingredients can often be actually seen, understanding what the ideas mean becomes a much simpler process.
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