# Ground impact force of a vehicle rolling over

1. Apr 15, 2012

### Louis_nutter

Hi all, this is my first post on Physics forums so I apologise in advance if I have posted in the wrong section etc. This is something that I have been trying to figure out for nearly a week now! I have modeled a vehicle in Solidworks, specifically an external roll cage, and hope to conduct a stress analysis for the vehicle rolling over. What I am trying to obtain is a suitable force to apply to the edges of the roof corners that make contact with the ground. After fumbling through more equations than I have space for on here and utterly confusing myself reading books on vehicle crash mechanics, I have reached the conclusion that I need help!

Some information I can give;

Vehicle turning circle = 11.58m,
Track width = 1.308m,
Total width = 1.628m,
Vehicle height = 1.969m,
Center of gravity height = 0.665m,
Curb weight = 1315kg,

If there is anymore information needed I will do my best to provide it.

I know for this subject there is a multitude of different variables, for this particular application however I am looking for the highest value of force to obtain a 'worst case' scenario. For simplicity I have been assuming the vehicle to be a solid model, taking the compression of suspension as negligible. I can appreciate that this post is vague at best, but I would certainly appreciate any help out of this mess that I am in.

Thanks, Louis.

2. Apr 15, 2012

### Louis_nutter

I probably should have added that the rollover in question is likely to occur at a slow speed as it is for an off-road scenario. Using a roll over velocity formula;

v = sqrt (r * g * RT)

where -

RT - rollover threshold = Trackwidth / 2 x center of gravity height,

r = 1/2 vehicle turning circle (assuming full lock),

I have calculated a speed of 16.72mph, not at all sure if this is correct or even useful :-/

3. Apr 15, 2012

### haruspex

Seems to be my daily task to explain the difference between force and impulse.

In an impact, there is no simple limit to the forces involved. It will depend on the materials.
You can compute the kinetic energy and the total impulse (momentum). The momentum change is the integral of the force over the time the impact lasts, and if all comes to rest then it equals the speed times mass of the projectile. When two rigid bodies collide - concrete blocks say - the impact lasts a very short time, so the forces are enormous.

In the present case, I think what you care about is the total energy. Because you might land on a very hard surface, it's probably too much to expect that the cage will survive undamaged. In fact a protective cage is more usually considered sacrificial - you want it to buckle a bit to absorb energy.
So you want to know how far it will buckle.
In general this is quite tricky because you have to consider the buckling mode - which bars and angles will flex. The more the better to absorb all that energy.
Once you've solved that, and decided how far it is safe for the members to flex, you can just apply the energy equation: kinetic energy = sum(force * distance).
So this should tell you how much force it needs to be able to take before buckling.

The other side of the coin is the poor occupants. If the cage is too stiff then they suffer a huge force. So this puts an upper limit on the buckle strength.
If that conflicts with the calculated lower limit, it means the cage is too close and needs more room to buckle without damaging the vehicle.