SUV Center of Gravity

I heard a broadcast of the show this past Sunday, December 30, 2008 in which the brothers make the claim that the suspensions of SUVs are somehow compliant enough to enable the vehicle’s center of gravity to move outside the rectangle defined by the four wheels. Does anyone know where I can find a transcript of the show? I’d like to confirm that I heard it correctly before I waste anyone’s time trying to correct this misconception. I believe I’ve heard this from them before, but I don’t know if it was just a rerun.

That is December 30, 2007, of course.

This can happen with any vehicle, if it tilts up enough to roll over. It just can happen more easily with an SUV because the center of gravity is higher off the ground.

All they meant is that it could tip over. You don’t have to be an engineer to speak so badly that people can’t understand you, but it helps in Tom’s case.

I heard it last weekend as well, just download their most recent podcast.

They did give a convoluted explanation, but they were simply saying it’s pretty easy to tip over in a SUV. If the center of gravity ends up outside the “footprint” of the four wheels, you are going to be upside-down. I’m not sure what misconception you heard, but they gave a very simplistic (static) explanation of a process that is actually very dynamic. In reality, you can generate enough (angular) momentum to make tipping inevitable before the center of gravity is actually outboard of the wheels (although it will end up there eventually). Don’t try this at home.

All “science” aside, I see about 5 times more SUVs/trucks/mini-vans than sedans on their roofs every-time we have a snowy day in CO. I own an old jeep, and I’ve come close a couple of times.

You don’t have to be an engineer to speak poorly either.

Not angular momentum, but centripetal acceleration. Acting as if it were on the center of mass. Which is more of a problem when the center of mass is high off the ground.

Thanks for the podcast suggestion. I found it right away: show 0752, segment 5.

I completely agree with their assertion that it is easier to tip over in an SUV, but I disagree with their explanation. It is not about getting the center of gravity outside of some box. That is the misconception. The problem would still exist even if the suspension were perfectly rigid. You are on the right track with angular momentum.

I also get a kick out of counting the SUVs stuck on the side of the road during a snow storm. They are always in the majority.

Perhaps both. One way to analyze the situation and predict tipping over is to calculate the angular momentum about the axis made by the two wheels on the outside of the curve. The rate of change of angular momentum will be the centripetal acceleration times the total mass times the moment arm, which in this case will be the height of the center of mass; minus the acceleration of gravity times the total mass times the moment arm, which in this case will be about half the track width. This will be the net moment about that axis: a positive number means you’re going over. The center of mass never needs to move relative to the wheels. It isn’t necessarily a suspension problem. A driver should not be reassured by noticing that the center of mass remains squarely centered between the wheels.

No, but it helps.

They are basically correct that once the center of gravity is no longer above the rectangle formed by the four points where the wheels contact the round, it will become (statically) unstable and will tip over (assuming there are no dynamic forces at work).

This is a first semester engineering type exercise. In the static case, you draw a little sketch of the vehicle (called a free body diagram) and you include force vectors pointing up into the bottoms of the tires (representing the magnitude and direction of the force being exerted on the tires by the road); you also draw a vector from the center of gravity of the vehicle straight towards the center of the earth (to represent the force exerted by gravity). Now, the hapless freshman is asked to determine the direction and magnitude of each of these vectors if the vehicle is in static equilibrium. The magnitude and direction of the “gravity” vector is know (it is a function of the mass and orientation of the vehicle). The student now writes a bunch of equations including all five vectors to determine the magnitude and direction of each. When he is done, the total forces and moments in all three directions have to equal 0 (i.e., the forces on the four wheels have to be distributed to cancel out both the downward force and and the tipping (moment) caused by gravity. In the simplest case (the vehicle is sitting still on level ground), the force due to it’s mass is pointing straight down through from the center of gravity to the center of the earth and all the vectors at each wheel are pointing straight up; all out poor student has to do is determine the magnitude of each force (pretty simple).

Now, consider the more complex case where the vehicle is parked at an angle on a steep hill; the student must do the same thing but not all the force vectors are straight up or down. The direction of the vectors at the wheels will potentially have three components (x,y,z; or up/down, front/back, right/left). After lots of math (and pizza) the student will still be able to get a result; however, if the hill is steep enough he might find that the required force on one or two of the wheels is in the wrong direction (the wheel needs to held down to the ground). In that case, the wheel will lift up and the vehicle will tip over. If you drew a diagram of the case, you would find that the “gravity” vector from the center of gravity passes “outside” of the box draw between the four wheels. That is all they were trying to say. That was just the static case.

In the dynamic case, the problem is messier. In addition to the “gravity” vector passing trough the center of gravity, the vehicle may have both linear and angular accelerations in all three directions (six total “accelerations” to worry about). Also, the magnitude and direction of these force vectors will be constantly changing, as will the corresponding forces at the four wheels. After lots more pizza, the student can analyze a single point in time by calculation the forces resulting from all these linear and angular accelerations (F=ma type equations) and determining the forces at the wheels. If he has a computer (and lots more pizza), he can calculate a series of cases and model the response of the vehicle over time. This is harder than it sounds because he has to consider the dynamic response of the vehicle suspension as well as the capability of the tires to transmit lateral force (i.e., will they grip or slide) and a bunch of other factors. By the time he’s a grad student (with a grant) he can fully analyze the response of a vehicle to this transient condition (maybe).

Because the radio show isn’t 3 weeks long, they tried to explain the simple static case only.

There is more than one way to model this problem, I was trying to give the simplest explanation (most folks know what angular momentum means). See my post below, fully calculating this problem for a real dynamic condition would require more than a little effort, and it may get pretty non-linear if you consider the actual suspension response of the vehicle (a real factor in most SUVs, unfortunately). How much free time do you have?

“They are basically correct that once the center of gravity is no longer above the rectangle formed by the four points where the wheels contact the round, it will become (statically) unstable and will tip over (assuming there are no dynamic forces at work).”

Except that they explicitly state “because the suspension has the ability to move the body around in relation to the wheels it’s possible on turns, especially quick abrupt turns, to have the center of gravity somehow wind up outside the box.” They then go on to attribute this to the compromises made in suspension design of SUVs to “allow them to go off road.” The amount that the center of gravity moves due to suspension compliance is nowhere near enough. This part of their statement is completely false, and I think they are doing a disservice by explaining it this way. To make it easy to understand, all they have to do is mention the centrifugal force passengers feel inside a vehicle as it goes around a curve, and then explain that the higher the center of gravity, the longer the moment arm this force has to tip the vehicle over. No imaginary boxes or bogus center of gravity movement is necessary.

I agree they could have explained it much better, and they did inappropriately combine up the static and dynamic cases. I think they were trying to say that soft, long travel SUV suspension contributes to their lack of dynamic stability (I.e., it allows the vehicle to develop more angular movement/momentum during transients than would not occur with stiffer suspension). Obviously, we know what they meant and about 99.9% of there audience probably zoned out anyway. Trying to explain anything technical to a general american audience is a little like trying to teach algebra to your cat.

None of the previous posts mentions the case where a vehicle slides sideways and hits a curb or some other low but immovable obstacle. Vehicles with high a CG will flip easier than vehicles with a low CG. Seems very simple to me and not much math or dynamics required.

And we won’t even venture into the scenerio where the vehicle slides onto an embankment. With a nice firm snowbank on the leading edge to stop the wheels from sliding sideways while the body continues doing so. We have lots of those situations here in NH.

Very true, that will get you upside-down in a hurry in most SUVs/trucks/mini-vans too. I suspect that is what usually happens to the dozens of these things that litter the sides of the roads in bad weather.

I drive a SUV (4 runner). It’s NOT one of the HUGH SUV’s but it is more prone to tip then my wifes Lexus. With that…all it means to me…is to drive my SUV within it’s limits (and mine). I don’t drive my wifes Lexus like I do my 4runner. Those SUV’s you see on their roof were driven by someone who was NOT driving the vehicle within it’s limits…They were probably use to driving a car and tried to manuver the SUV the same as the car…

I also have an old jeep, and I agree that it would take a pretty bonehead move to flip it on dry pavement (although it could be done). However, try sliding an SUV into a curb or snow bank at 30 or 40 mph. I understand that these things can be driven safely, but there is certainly less margin for error. Occasionally, I do hop in the jeep and forget that I’m not driving a real car for a second, very scary at the first corner.

And when it’s all said and done, it’s STILL the drivers fault for winding up up-side-down, not the vehicles’. Regardless of type.