Roll Center, Center of Gravity & Weight Transfer

From a discussion on regarding Suspension Geometry.

The other thing is, you want to get your roll centre RC and centre of gravity COG as close as you can to the same point. Don’t get these two confused. The RC is axis the suspension causes the body to rotate on. The COG is the centre of the mass of the car, doesn’t even matter if the car is on its wheels or not.
This is only correct for a very special case not associated with normal passenger or competition vehicles.

The amount of body roll is proportional to:
(cornering force) x (height difference between the RC and the COG)

If the roll centre is below the COG (as is usually the case), the body leans away from the corner.

If the roll centre is above the COG, the body leans into the corner.

If the roll centre is at the same height as the COG, there will be zero roll.

It would be easy to assume the last condition is optimum because the body would remain dead flat during a turn; however with suspension design there is always a trade off.

The height of the COG is determined by the distribution of mass within the vehicle, and can only be altered by adding or removing weight, so for practical purposes the position of the COG should be viewed as fixed. This means the only way to bring the COG and RC closer is by adjusting the height of the roll centre.

The position of the roll centre can be readily shuffled by altering the suspension geometry and without too much effort can be made the same height as the COG.

Now comes the trade off. If we view the vehicle from the front with the eye at ground level then bounce the car up and down we see the point where the tread contacts the pavement moves sideways. The higher the roll centre the larger the horizontal movement.

Now visualise the vehicle in a high speed turn. The tyres are just holding on, then a wheel rolls over a bump forcing the contact point sideways and to skid across the pavement. This causes to the tyre lose grip, and as they say, the rest is history. Even in sedate driving the passengers feel an uncomfortable sideways jerk as a single wheel negotiates a bump.

If the roll centre is at ground level, this sideways movement is just about eliminated -which is desirable, but the large difference between the height of RC and COG leads to severe body roll unless the suspension is very stiff or substantial anti-roll bars are fitted.

Heavy anti-roll bars cause the vehicle to heave in response to single wheel bumps and this induces an uncomfortable sideways jerk in the passengers head. As a general guide the roll stiffness contribution should not exceed 50% of the corresponding wheel stiffness.

For competition vehicles a roll centre height of about 100mm has traditionally been considered a sensible compromise, while it is generally higher for passenger vehicles to improve comfort albeit at the expense of performance.

Now we should consider weight transfer from inner to outer wheel during a turn.
Weight transfer is proportional to:
(cornering force)x(height of COG above pavement)/(vehicle track width)

(Note the height of the roll centre does not affect the transfer of weight from inside to outside wheel during a turn.)

The amount of grip the tyre generates is affected by the vertical force between the tread and pavement. While the vehicle is moving in a straight line the left and right wheels on the same axle line will have close to equal weight so are capable of developing the same sideways force. As the car sweeps into a corner, weight transfers from the inner to outer wheels reducing the grip of the inner wheels and increasing the grip of the outer wheels. It would be easy to conclude the total grip remains the same, by applying the logic the grip lost by the inner wheel is made up by the additional grip gained by the more heavily loaded outer wheel, however that is not the case.

The problem here is that the weight to grip relationship is not linear. In other words, if the tyre load is progressively increased in even steps, the extra grip does not go up in even steps, instead the increase in grip tapers off. This means the grip lost by the more lightly loaded wheel is not made up by the increased grip of the more heavily loaded outer wheel and as a consequence their combined grip diminishes.

Can anti-roll bars solve this dilemma? Anti-roll bars do not affect the total weight change from inner to outer wheels, only how much is swapped between the front wheels, and how much is swapped between the rear wheels. Imagine a really stiff anti-roll bar on the front and nothing at the rear. During a turn the vehicle goes into roll, the front roll bar dramatically transfers weight from the front inner to front outer, almost lifting the inner wheel off the ground. The total weight change across the car can not alter, so there must be a smaller weight change between the rear wheels than experienced by the same car without the front anti-roll bar.

We already know that when weight transfers from the inner wheel to the outer wheel on the same axle line their combined grip reduces. This means on this car with the stiff anti-roll bar at the front, there will be a significant reduction in front wheel grip, and a much smaller reduction in the rear wheel grip. So, an anti-roll bar worsens the loss of grip at the end of the car it is fitted, and improves the grip of the wheels at the other end of the car.