Determine speed needed to cause rollover of car hitting ramp

[Trzebs]

Hello,

So my issue is as follows: You have a car going at a constant speed and the right side of the car hits a ramp which causes that side to elevate and cause the car to rotate about its x axis. What I need to figure out is how fast does the car need to hit the ramp to cause a rollover? Assume you know the car's mass (1300 kg), velocity (60. kph), c.g. height( .684 m) and front track width (1.5 m), also you know the length of the ramp (4.5 m) and its height at the take off point (0.9m).

My first tackle at this was to find the time it takes the car to travel the distance of the ramp. Knowing this I could figure out the time it takes for the right side of the car to go from ground level up to the ramp height. With the time and vertical distance of the ramp known I used two of the equations of constant acceleration to determine the vertical velocity of the right side of the vehicle. I treated this vertical velocity as a tangential velocity with the left set of tires as a pivot point. Using v = r*(omega) I was able to find the angular velocity of the vehicle at the top of the ramp. Now at this point I wanted to use either the energy equations of rotation to determine if the car's angular velocity would cause it to reach a tipping point, or the equations of constant acceleration for rotation, but the problem I ran into was not knowing the moment of inertia of the car and also not knowing if the angular acceleration after leaving the ramp is constant which would dictate if I could use the constant acceleration equations again. Is there some aspect I'm failing to consider that would help in this situation?

 

[Trzebs]

Oh and the way I determine a roll is if the car achieves its SSA (static stability angle) which relates a car's c.g. height and track width (track width = the distance from the center of one front tire to the center of the other front tire). SSA is defined as arctan((t/2)/h) where t = vehicle track width, and h is the c.g. height.

 

[CWatters]

Estimate the moment of inertia? Presumably you know the dimensions of the car and perhaps the height of the CoG?

Another possibility is to ignore the rotational aspect and treat it like a ball being thrown up into the air and apply conservation of energy.

 

[Trzebs]

Estimate the moment of inertia? Presumably you know the dimensions of the car and perhaps the height of the CoG?

Another possibility is to ignore the rotational aspect and treat it like a ball being thrown up into the air and apply conservation of energy.

The dimensions are indeed known, as well as the cg

Estimate the moment of inertia? Presumably you know the dimensions of the car and perhaps the height of the CoG?

Another possibility is to ignore the rotational aspect and treat it like a ball being thrown up into the air and apply conservation of energy.

Yes, the dimensions are known as well as the cg height. How would you suggest estimating the moment of inertia? Treat as a known rigid body like maybe a rectangle perhaps?

 

[CWatters]

Yes. I'd suggest a relatively thin rectangular slab.