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# Laterally offset RC

## Laterally offset RC

(OP)
How would one calculate roll stiffness with a RC not in the lateral center. Say with a track of 65in, 400lb/in springs, MR of .7, RC height 3.5in off ground 8in to passenger side.

### RE: Laterally offset RC

The car typically does not roll about the roll centre, so it doesn't matter.

The roll centre would be better named "the single point at which the forces in the suspension arms can be considered to act on the sprung body in front view", but I don't think it will catch on.

However, if it does roll about that axis, then the easy way is to work out the torque resulting from a given small rotation.

Cheers

Greg Locock

### RE: Laterally offset RC

(OP)
But there is a difference in roll stiffness due to offset of the RC? force based or geometrically based

### RE: Laterally offset RC

I suspect there is but I don't know. Hmm, have a look at that WOB link suspension in one of threads further down the page. That has an undeniable roll centre... imagine displacing the roll centre right over to one spring. That spring could no longer participate in the roll stiffness, so yes, it does have an effect.

Let's see, roll axis in the centre, we have 2 springs, restoring couple is 2*(theta*L/2*k)*L/2 so the roll stiffness is kL^2/2

Now put the roll centre at one spring

couple=theta*L*k*L

twice as much!

BUT that is partly because the car now jacks, it does not just roll.

OK well I'm too hung over to figure out how to get round that.

Cheers

Greg Locock

### RE: Laterally offset RC

it has been a long time since this was posted but I keep in in my archives because it has helped me alot

blackbirdblue (Automotive) Jun 10, 2002
Roll Centre (excuse my UK spelling) has to be one of the biggest areas of confusion in suspension design that there is.

First, it isn't any sort of centre of motion, it's really a force centre.  Second, for an independent suspension you can't arbitrarily combine the characteristics of both sides of the vehicle at the centre line.

The reason it matters is that it determines what proportion of suspension forces are transmitted via a "fast" mechanical route and what proportion are transmitted by a "slow" suspension spring/anti-roll bar/damper route.

The only things that matter in vehicle dynamics are forces on the tyres.  A high roll force centre gives more load via the "fast" route and less via the "slow" route.  Thus for a typical vehicle with higher rear roll force centre than front, the rear tyres load up faster during turn-in. This helps reduce the phasing between yaw and lateral acceleration and is generally A Good Thing.

If the roll force centre is below ground it means the suspension is "pro-roll" - the roll moment carried by the
sprung elements is greater than the inertial moment one might calculate using CG height and lateral acceleration.  Motorcycle front suspension forks are similar in pitch.

In fact, the whole subject is better approached using the "anti-dive" logic applied to pitch motions rather than all this roll centre voodoo.  Track down any half decent vehicle dynamics book and look at the anti-dive definitions then imagine them applied to roll.

One thing that isn't so obvious is that limit behaviour is helped by a low roll force centre and so some race cars have a rear roll force centre that plunges from above to below the front one to aid both turn-in and limit behaviour.
So you might find that lifting the rear roll force centre on your friend's car makes it technically faster but much more scary to drive and hence he'll return slower lap times.

As for camber, it has a lot to do with tyre wear but is really quite a small modifier on fundamental vehicle dynamics.  There are a lot of people who will dispute that statement but none of them use any coherent maths to do it, only some very flawed reasoning.

In summary, think of roll-centres like anti-dive, reject any attempts to turn it into voodoo and find a good vehicle dynamics book. And set your static camber to maximise tyre life with the camber change characteristics you have, use tyre temperatures to predict tyre life without actually wearing them out.

### RE: Laterally offset RC

(OP)
More worried about calculating static weight transfers with close to correct roll stiffness values, rather then dynamic movement

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