# Vehicle rollover physics

1. Jan 11, 2010

### bitrex

I was watching a a "Mythbusters" rerun where they were experimenting with bus rollovers a la "Speed", and it got me thinking about the physics of vehicle rollovers. Applying my basic physics knowledge my intuitive understanding of the process is that it occurs because the reactive centrifugal force on a vehicle having a high center of gravity causes a net torque on the vehicle that wants to push it over. Is it true that if it were possible to perfectly balance the mass of a vehicle, that it would not roll as the torques would always be perfectly balanced? Does the center of gravity define the axis of the rotation of the vehicle when it does begin to roll?

The countermeasure in the film and in the TV experiment replicating the film was to redistribute the mass to the side of the vehicle that was tipping upwards. This was described as redistributing the center of gravity, but it seems to make more sense in my mind that they were using the mass and gravity to provide a torque counteracting the torque that was causing the roll. Are these two views equivalent, or is my understanding incorrect? Thanks for any insight.

2. Jan 11, 2010

### rcgldr

The rolling torque is related to the height of the center of mass x centripetal acceleration. The equal and opposing torque is related to the difference in downforce at the tires x the distance between the tires. If the difference in downforce results in all of the force going to the outside tires, the vehicle will roll over. Moving the center of mass inwards reduces the difference in downforce between the tires when cornering at maximum grip, which keeps the vehicle from rolling at that rate of cornering.

3. Jan 11, 2010

### Staff: Mentor

The bus isn't supported by anything about its center of gravity, it is supported by the tires, so the axis of rotation has to be where the tires contact the ground.

4. Jan 12, 2010

### Eric McClean

It is tough to tell so quickly. Give me time I will approach you.

5. Jan 12, 2010

### DannoXYZ

Kinda. The contact-patch is where the inward push occurs that turns the vehicle. But the actual roll-centre is a function of suspension geometry. This roll-centre will change in height and location as the suspension compresses on one side and extends on the other.

Roll is different than jacking, which is what you're talking about in rollover examples. Lateral swing-arms move the roll-centre higher and higher as the body rolls (a la VW bug). Multi-link suspensions can maintain a low roll-centre and avoid the jacking effect. The result is the grip of the tyres will be overcome before enough jacking has occurred to cause a rollover.

6. Jan 12, 2010

### xxChrisxx

It's best not to consider the suspension in this at this time, as although it will have a sizable impact its a different problem. Talking about roll centres wll only confuse things. The 'roll' in this case is differnt from the roll in the suspension. This is a vital distrinction between weight ransfer and load transfer.

When tipping the roll axis isn't defined by suspension geometry, its defined by the tipping point/last piont in contact with the ground. As you are appraching the point of 100% weight transfer the roll axis is the centre of the contact patch.

The most basic apprach is from a pure statics point of view, assuming no suspension what so ever.

Weight*Lateral acceleration * CG height vs Weight*1/2 track.
When the LHS > RHS the car will tip. Basically when there is more than 100% weight transfer.

Adding suspensiions and taking into account tyre grip makes this far more tricky.

In reality the tyres will give way long before rollover from static cornering is achieved (they are disgned to do that). There is ususally a dynamic component (hitting a bump, or swinging the car). Buses are slighty different, as they can have very high CG heights, making low lateral G a must.

Last edited: Jan 12, 2010