Roll centre

[Tony]

The roll centre is an imaginary point about which the vehicle rolls. The calculation process that’s followed to find the roll centre varies a little according to the suspension design; this diagram shows the approach for double wishbones where one wishbone is angled to the horizontal. The lines of the wishbones are extended until they reach a common point – ‘A’. A line is then drawn that connects ‘A’ to the centre of the tyre’s contact patch – ‘C’. The roll centre is where this line crosses the centreline of the car – ‘R’.

 

The amount of body roll that occurs with a given cornering force largely depends on the relationship between the height of the centre of gravity and the roll centre. Raising the suspension roll centre, or lowering the centre of gravity, will decrease roll.

 

However, while having a high roll centre therefore sounds attractive, it has significant negatives associated with it. In fact, most well set up vehicles run a roll centre at, slightly above, or slightly below ground level.

 

So what does this mean to you?

Effectively, the only thing you are interested in is the centre of gravity of the sprung mass. Imagine attaching a string to this point and pulling - sideways to simulate a cornering load, fore or aft to simulate acceleration or braking, diagonally to simulate a combination. The attitude a car adopts when subject to these forces is dependent upon how stiff the springs and anti roll bars are, and of course these will be different front and rear. Due to differing roll resistances front and rear, and the fact that weight is transferred diagonally, the car will almost always be operating in what Allan Staniforth refers to as 'skewed roll' - ie. a combination of roll and dive/squat.

 

The main implication of the roll centre locations are that they are used to calculate diagonal weight transfer, which in turn can be used to derive suspension deflection and individual tyre loads (which in turn influence understeer/oversteer balance).

 

The traditional rule of thumb was that that the roll centre is lower at lighter end of the car, but many other factors have to be taken into account - spring/roll bar stiffness, tyre sizes, front and rear track, CG location etc., so this rule is by no means hard-and-fast.

 

Probably more important to make sure that your roll centres don't move about much in relation to the sprung mass, as movement changes the diagonal weight transfer and can lead to very uncertain handling characteristics.

 

Roll and dive/squat

Steady state under constant lateral acceleration:

 

The total amount of lateral weight transfer is determined by the CoG position and track width.

 

Some of the lateral weight transfer occurs through the suspension links. This is what I term unsprung weight transfer. The amount for each axle can be determined from the weight on the axle and the position of the roll center for that axle. Obviously the answer can and usually will be different for each axle. It's independent of spring rates etc.

 

The remaining lateral weight transfer i.e. total minus unsprung is what I call the sprung weight transfer. This occurs because the body rolls and deflects the springs, dampers and anti-roll bars etc. The body is usually stiff enough that the front and rear roll can be considered identical. In a steady state the sprung lateral weight transfer is divided between the front and rear axles in proportion to the roll stiffness i.e. front twice as stiff in roll as the rear means the front sprung lateral weight transfer will be twice as much as the rear. There's a slight subtlety - it is actually the roll moment which is divided in this ratio. If the front and rear tracks are different then the weight transfer will be proportional to roll stiffness divided by track, not just proportional to roll stiffness. But to avoid getting a headache let's pretend the front and rear tracks are always the same, in that case the weight transfer is proportional to roll stiffness.

 

If you change the springs and/or anti roll bar stiffness to change the ratio of front versus rear roll stiffness then this will have effect of increasing the sprung lateral weight transfer at the end you are making (relatively) harder, and reducing it at the end you are making (relatively) softer. The total is fixed, so if you take 50 lbs of weight transfer away from one end, you will end up adding 50 lbs to the other.

 

If you want to express this in terms of a percentage of the weight on that axle then it will obviously depend on the weight on the axle. And you need to bear in mind that the car be have longitudinal acceleration as well as lateral, so there will be longitudinal weight transfer too. It's not at all uncommon for the total weight transfer from both effects to reduce the load on a wheel to zero - you'll often see a fwd lifting a rear wheel under cornering plus braking, or a rwd car lifting a front wheel under cornering plus acceleration. If you're going to express lateral weight transfer in percentage terms, you need to be clear whether you talking in terms of the static weight on the axle, or the actual instantaneous weight.

[Jhonno]

Very interesting post.. Came up on a google search. Was it you who posted on the e36coupe forum the other day?

 

Just trying to clarify a few things..

 

By raising the roll centre or lowering the centre of gravity, would you be trying to get them to be at the same point?

 

What are the negative effects of raising the roll centre? I run an BMW e30, which sits pretty low, and see people offering kits to raise the front roll centre.. So having read this, I am confused as to why now.. Is it to try and match the front and rear roll centres?

 

I'm sure I have other questions, but I'll start there

[Jhonno]

Could well be being a little special.. The above diagram is an A arm setup, as opposed to the Mac strut of the e30.. Have to find a diagram of how it works with the e30 setup

[Jhonno]

So continuing to talk to myself, a Mac strut uses the top mount upper arm?

[Tony]

Very interesting post.. Came up on a google search. Was it you who posted on the e36coupe forum the other day?

 

Just trying to clarify a few things..

 

By raising the roll centre or lowering the centre of gravity, would you be trying to get them to be at the same point?

 

What are the negative effects of raising the roll centre? I run an BMW e30, which sits pretty low, and see people offering kits to raise the front roll centre.. So having read this, I am confused as to why now.. Is it to try and match the front and rear roll centres?

 

I'm sure I have other questions, but I'll start there

 

Hello and yes it was.

 

What problems are you having or what are you trying to achieve?...... here's a few more pointers

 

Trailing Arm and Semi-Trailing Arm Suspensions

 

With trailing arm and semi-trailing arm suspensions the wheels are free to bounce independently. Each wheel moves up and down around the axis of a trailing or semi-trailing arm. The difference between the two designs is that the axis of the trailing arm is at right angles to the vehicle centerline whereas the semi-trailing arm axis angle inboard and toward the rear. Both configurations are popular for either powered or non-powered rear suspension systems.

 

If the rear wheels are powered, the final drive is mounted in a fixed location and each wheel is driven by an axle half-shaft. Each half-shaft is equipped with an outboard and inboard universal joint to accommodate angular variations during bounce. Half-shafts also have a telescopic action to accommodate the variation in final drive-to-wheel distance as wheels move up and down. Rear end lift during braking is countered by the downward component at the leading end of the arms.

 

Body roll produces camber and toe changes in the semi-trailing arm design. Consequently, camber thrust and modest slip-angle forces can combine to produce steering inputs as the body rolls to the outside of the turn. Roll-steer effects are at a minimum when the arm axis is parallel to the ground and increase when the inboard end is raised or the outboard end is lowered. The degree of camber change depend primarily on the distance to the instantaneous center. The instantaneous center is normally located no closer than the centerline of the opposite wheel. A closer location will produce wheel movements that emulate the swing-axle, along with the negative attributes of tuck-under and unfavorably large camber change.

[Jhonno]

Well I am trying to understand the concept and apply it to my car as I am in the process of spending a fair amount of time and energy on the chassis, and looking to get it right (coilovers, adjustable front and rear toe, caster and camber)

 

E30 is trailing rear arm like Z3's, or is it semi trailing, I should know this I know the camber increases as you lower the rear..

 

I think with the front macpherson setup, there is limited camber gain however..

 

You are relatively local to me, so I shall try and set it up enough to drive it down to you guys for a full setup I think, inc rolling of arches and balancing of wheels (I think my fronts have been done badly.. Not helped by having to run spacers to clear brakes currently)

[CIH]

how does trailing arm and semi-trailing arm set-ups differ ?

[Tony]

Well I am trying to understand the concept and apply it to my car as I am in the process of spending a fair amount of time and energy on the chassis, and looking to get it right (coilovers, adjustable front and rear toe, caster and camber)

 

E30 is trailing rear arm like Z3's, or is it semi trailing, I should know this I know the camber increases as you lower the rear..

 

I think with the front macpherson setup, there is limited camber gain however..

 

You are relatively local to me, so I shall try and set it up enough to drive it down to you guys for a full setup I think, inc rolling of arches and balancing of wheels (I think my fronts have been done badly.. Not helped by having to run spacers to clear brakes currently)

 

Blimey your my worst nightmare in the "modify/ consequence" department..... I feel you have gone a little to deep in the need to understand the chassis, your kind of looking at the design stage whereas you should be looking at the "calibration stage".

 

We could pants on for days about roll centres/ couples/ transitions and dynamics when all we actually need is an image -V- solution.

[Jhonno]

Well I am trying to understand the concept and apply it to my car as I am in the process of spending a fair amount of time and energy on the chassis, and looking to get it right (coilovers, adjustable front and rear toe, caster and camber)

 

E30 is trailing rear arm like Z3's, or is it semi trailing, I should know this I know the camber increases as you lower the rear..

 

I think with the front macpherson setup, there is limited camber gain however..

 

You are relatively local to me, so I shall try and set it up enough to drive it down to you guys for a full setup I think, inc rolling of arches and balancing of wheels (I think my fronts have been done badly.. Not helped by having to run spacers to clear brakes currently)

 

Blimey your my worst nightmare in the "modify/ consequence" department..... I feel you have gone a little to deep in the need to understand the chassis, your kind of looking at the design stage whereas you should be looking at the "calibration stage".

 

We could pants on for days about roll centres/ couples/ transitions and dynamics when all we actually need is an image -V- solution.

 

 

Well I have too much time on my hands at the minute, so unfortunately the thought processes gather momentum

 

So you are saying, throw it all together then tweak it? Put in a crude way..

 

How will it be evident if the roll centre would need fiddling then? Or am I still missing the mark?

[Jhonno]

how does trailing arm and semi-trailing arm set-ups differ ?

 

 

Rather than try and explain the pics do the talking..

 

http://en.wikipedia.org/wiki/Trailing_arm

[Tony]

Well I am trying to understand the concept and apply it to my car as I am in the process of spending a fair amount of time and energy on the chassis, and looking to get it right (coilovers, adjustable front and rear toe, caster and camber)

 

E30 is trailing rear arm like Z3's, or is it semi trailing, I should know this I know the camber increases as you lower the rear..

 

I think with the front macpherson setup, there is limited camber gain however..

 

You are relatively local to me, so I shall try and set it up enough to drive it down to you guys for a full setup I think, inc rolling of arches and balancing of wheels (I think my fronts have been done badly.. Not helped by having to run spacers to clear brakes currently)

 

Blimey your my worst nightmare in the "modify/ consequence" department..... I feel you have gone a little to deep in the need to understand the chassis, your kind of looking at the design stage whereas you should be looking at the "calibration stage".

 

We could pants on for days about roll centres/ couples/ transitions and dynamics when all we actually need is an image -V- solution.

 

 

Well I have too much time on my hands at the minute, so unfortunately the thought processes gather momentum

 

So you are saying, throw it all together then tweak it? Put in a crude way..

 

How will it be evident if the roll centre would need fiddling then? Or am I still missing the mark?

 

Knowledge and needs are very different things... at this point you don't know what you need to know..... Example this car has very distressed roll centres wouldn't you think?

 

As horrific as it looks the RC is fine since the geometric gains even during transition are very low... Doing the math between the RC, CG is entertaining but misses real world hands on, matter of fact analysis.

[Jhonno]

Right been trying to think it through..

 

Indeed, that pic above, it looks wrong, but evidently isn't

 

So you are saying, as long as the geometry gains remain suitable for the new lowered suspension travel range, there is no need to worry about roll centres?

[Tony]

Right been trying to think it through..

 

Indeed, that pic above, it looks wrong, but evidently isn't

 

So you are saying, as long as the geometry gains remain suitable for the new lowered suspension travel range, there is no need to worry about roll centres?

 

Yes ..... If you have serious track intentions RC would need to be explored as well as CG and corner weight.... Domestically a tuned calibration combined with some dynamic testing is more than enough.