Wednesday, March 31, 2010

The Basics of Vehicle Rollovers

The latest fad towards ever taller cars is the result of a lack of understanding of the physics of driving. It has been pointed out over and over that tall narrow cars tip over more easily than low wide cars. And yet still people buy high narrow cars and drive them at foolish speeds. Obviously we need a refresher course on basic physics.

There is really only one vehicle that can be tall and still go fast, and that is a motorcycle. And that is because the motorcycle leans into the turns. Cars that sit on four wheels cannot lean into a turn and so are vulnerable to a rollover in case the turn is taken too quickly. I think almost everybody knows this rule about tall narrow cars, so let me just add a few caveats to it.

The first caveat is this. Just because you call your car a truck, or even better, an SUV, does not mean it defies the rules of physics. A lot of people who are in denial about the roadholding capabilities of their vehicle think that this law only applies to cars. Just because SUV has the word "Sport" in it does not make that vehicle competent at high speed. And by high speed, I mean a cruising speed for a "normal" low and wide car.

The second caveat is this. You can roll over even on a perfectly straight road. This can happen in any one of a number of ways. First you may leave the road momentarily, getting the right wheels on the gravel shoulder and over correct coming back. Second, you may be hit from the side by another vehicle either in a T-bone or a sideswipe. Third, you may swerve to miss a raccoon in the road. You don't swerve for raccoons you say? OK then child. Fourth, you may get on black ice and spin. I can think of more, but you get the idea.

So now for the physics lesson. Is there actually a law of physics that says a high narrow car will tip over and roll more easily? And is there any way that a car can be designed to be high and narrow but not tip over?

First, lets deal with the concept of "Centre of gravity". In order to simplify calculations on a car, it is useful to find a point where the average of all the mass converges. You can imagine this if you could balance the car on one finger. If so, the centre of gravity would be somewhere on a line directly up from your finger. In order to find exactly where it is on that line, you turn the car on its side, and balance it again on one finger. Now you have a different line through the car, but amazingly, at some point those two lines will cross each other. Where they meet is called the centre of gravity or centre of mass, and it is very useful in determining how the car will act while in motion. By the way, in case you were wondering, this also applies to boats, planes, trains. It does not apply too much to non rigid objects like people, who can change their CG by bending. There are also some cars that can actually change their CG, like the Citreon DS. Also, remember you can change a CG by loading a car. Also, the CG can change if the load shifts, but let's just go with as simple a model as possible for now.

Now look at the diagram, where CG and the pivot are marked. The car will start to roll by rotating around the pivot, in this case one of the wheels, seen from the front (it does not matter which side if they are symmetrical). If the weight of the car is 1000 kg, there will be a force of 1000 kg directly down from the CG, and that will stay the same through the turn. If you are going straight, the sideways or tipping force is zero. This sideways force is called centrifugal force.

Now let's imagine that the car is turning. I don't want to get into a theoretical argument about whether or not centrifugal force does exist. That argument is only for people who have an understanding of physics. For everybody else, the faster you turn the higher the centrifugal force. If you have a whole bunch of cars racing around the same curve at the same speed, they will all have the same "G force". By G force, I mean that if you have a 1000 kg car, with a centrifugal force of .5 G, the car will have a 500 kg force pushing it sideways. If you have a 2000 Kg car at the same speed on the same corner, it will also have a centrifugal force of .5 G, but a sideways force will work out to 1000 kg. for the heavier the car. So you do not gain any advantage by having a big heavy car in going around corners. While you have a heavier weight to keep you down, you also have a proportionally stronger force pushing you out.

Now let's think about the height of the CG. Imagine a rectangle with one corner the CG and the opposite corner the pivot. The important thing is the difference between the height of the rectangle and the width of that rectangle. If the height and width are the same, the car will be able to corner at up to 1 G but no faster, or it tips over.

For the purpose of simplification, I am not considering the limitations in cornering because of tires which will slide instead of roll over on ice and snow, or even bare pavement.  So, not considering the slipping of tires, if the rectangle is half as high as it is wide, the car can corner at 2 Gs before flipping over. And if the rectangle is twice as high as it is wide, the car can only corner at one half G before it rolls over.

The only real advantage you can have in not rolling over, is to keep the CG low compared to the width of the tires.


  1. There are 'lateral G' numbers available for most vehicles - the ratio of maximum lateral force to the mass of the vehicle before the vehicle breaks loose or rolls.

    These are 'available' but require a bit of digging - because manufacturers don't normally publish this figure. Especially manufacturers of SUVs.

    Lateral-G's of more than 1.00 are rare, except in highly modified or racing cars. Formula One cars, for example run in the 1.30-1.40 G range.

    The $1,000,000 McLaren F1 supercar achieves 0.86 G. But, then, so does the $30,000 MINI Cooper S ... so you can save yourself a couple of bucks there! :-)

    For all those people who bought SUVs 'to be safe in.' The lateral-G figures for things like Ford Explorers are typically in the low to mid .60s. Small wonder that SUVs account disproportionately for rollover fatalities, with 60% of fatal rollover accidents involving SUVs, with 90% of those being single vehicle accidents.

    It's very, very difficult to cheat on the laws of physics.

  2. The G forces you looked up are more for tires than for CG height. Cars rarely if ever exceed 1 G, because tire friction limits the theoretical turning speed more than the height of the CG. (Those Formula 1 tires are like glue) The engineers know the approximate limitation of the tires, and so they always build the CG low enough to not roll over before the tires slip.

    Insurance Institute for Highway Safety

    For several other reasons that I did not write about, a low CG can actually help the tires stick to the road better. There will be less lean going around the corner (keeping the wheel treads flat on the road), also giving better load distribution between left and right tires. But this varies tremendously with the type of suspension.

    Most real-life rollovers result from tripping, where tires hit a curb. But one kind of rollover can be provoked using tire friction alone. This can happen when a driver makes two sudden back-to back steering changes, suddenly swinging the steering one way then the other at just the wrong time. Cars generally lean over the "wrong" way when turning, because of their springs and air filled tires. So by suddenly turning right, the car will tip to the left, compressing the springs and tires on the left. Then as the car reaches maximum lean to the left, if you suddenly turn left, it will force the car to violently return to upright and then lean over to the right. The rotational momentum of this sudden change of angle may be enough to push the CG over to the right far enough to tip the car over. Once again, the laws of physics about height of the CG vs. the wheel width is one of the main determining factors. The lower the CG, the less the car will lean (given the same tires and springs). And the lower the CG, the less the "pendulum" effect of the lean. (imagine an upside down pendulum with the CG as the moving end of the pendulum.)

    Then there are the hundreds of ways that the CG can get raised or moved that the engineers cannot predict. For example, a poorly loaded vehicle (think roof racks), a flat tire on the outside, hitting a big bump on one side or a pothole on the other. Any of those combined with a directional change, can result in the CG moving so far that a tipover might occur before the tire's friction limit.

    There are rare and minor anomalies, cars with a slightly higher CG that actually have better rollover resistance than others with a lower CG and wider wheels in a real world situation. But information like this is only useful to engineers studying vehicle dynamics, and if it ever gets out to the public, will only spread more uncertainty and doubt. My suggestion to those people would be: Get a motorcycle if you want to sit up high. Even a Harley will get you up higher than most car roofs.

  3. At the risk of digressing from your original thesis, The Basics of Vehicle Rollovers ... Admittedly the vast majority (over 90%?) of SUV rollovers appear to be due to tripping. But frictional causes do account for thousands of SUV accidents each year.

    That 'two sudden back-to back steering changes' you describe can most certainly result in CG shifts contributing to rollover. And that was exactly the maneuver was used to illustrate the instability of the Jeep CJ in the notorious 1980 edition of CBS News' 60 Minutes on Jeep instability (from the same 'objective' folks who brought us the Audi SUA exposé).

    The ability of a vehicle to handle 'lateral G' forces is a complex function of CG, tires, suspension and even aerodynamics ... which is why racing cars are built very low, have sticky tires, specialized suspensions and aerodynamics which operate to provide downforce.'

    SUVs, by contrast, have high CGs, unsuitable (semi-offroad or 'all season') or under inflated tires, stiff suspensions and unhelpful aerodynamics. Significant passenger and cargo loads are also common.

    The physics of incipient rollover are actually (with apologies again for digression from the Basics thesis) quite complex. But once the rolling action is initiated, it is self-reinforcing and virtually impossible to recover from.

    Given the physical characteristics of SUVs, it is possible to initiate rollover with sudden maneuvers much simpler than that 'sudden back-to-back steering' action - under the 'right' (i.e. wrong) conditions something as 'simple' as an overaggressive lane change at speed can do it.

    The U.S. NHTSA (National Highway Traffics Safety Agency) uses a 'five star' rating system for probability of rollover by vehicle. A 5-star rating (<10% risk) for passenger cars is quite common, whereas no 2010 SUVs receive that level, most earning a 4-star (10-20% risk) or even a 3-star (20-30% risk) rating (although the situation has improved significantly since 2001 when this rating was introduced ... at which time 1-star (>40%!) and 2-star (30-40%) ratings preponderated).

    But, however we dice these eggs, tripping or frictional, 'lateral g' or static frictional coefficient, the fact remains that SUVs are inherently less stable and drivers who purchase these vehicles in quest of 'safety' continue to delude themselves.

  4. Wow, you found some really good websited that I had not seen about vehicle rollovers. The "quite complex" link made some of the same points I did, but backed it up with scientific formulas.

    I was not aware of cases where a normally loaded, mechanically sound vehicle would roll with a simple yank on the wheel. And I'm not saying it has never happened. However, in the case you gave "an aggressive lane change", wouldn't that actually consist of two back to back opposite steering inputs?

  5. wouldn't that actually consist of two back to back opposite steering inputs?

    Not necessarily ... not if the rollover starts before the 'to back' part of the maneuver ;-)

  6. Point taken. It counts as a lane change even if the driver rolls the car upside down while crossing the dotted line.