# Determine speed needed to cause rollover of car hitting ramp

• Trzebs
In summary, the conversation discusses the calculation of the speed needed for a car to hit a ramp and cause a rollover, taking into account the car's mass, velocity, c.g. height, front track width, and the dimensions of the ramp. The approach involves finding the time and velocity of the right side of the car as it goes up the ramp, then using equations of constant acceleration to determine the angular velocity of the vehicle at the top of the ramp. The main issue is not knowing the moment of inertia of the car, but suggestions are made to estimate it using the dimensions of the car and treating it as a rigid body. Another suggestion is to ignore the rotational aspect and apply conservation of energy.
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?

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.

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.

Last edited:
CWatters said:
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
CWatters said:
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?

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

## 1. How do you calculate the speed needed to cause a car to rollover when hitting a ramp?

The speed needed to cause a car to rollover when hitting a ramp can be calculated using the formula:v = √(rgtanθ), where v is the speed in meters per second, g is the acceleration due to gravity (approximately 9.8 m/s²), r is the radius of the car's wheelbase in meters, and θ is the angle of the ramp in degrees.

## 2. What factors affect the speed needed for a car to rollover when hitting a ramp?

The speed needed for a car to rollover when hitting a ramp is affected by several factors, including the angle and shape of the ramp, the weight and distribution of weight in the car, the suspension and handling of the car, and the speed and direction of the car before hitting the ramp.

## 3. Can a car rollover if it hits a ramp at a slow speed?

Yes, a car can still rollover if it hits a ramp at a slow speed. The speed needed for a car to rollover when hitting a ramp depends on various factors, as mentioned in the previous question. Even at a slow speed, if the weight and distribution of weight in the car are not balanced, it can still cause the car to rollover.

## 4. How can knowing the speed needed for a car to rollover when hitting a ramp be helpful?

Knowing the speed needed for a car to rollover when hitting a ramp can be helpful in designing and testing car safety features, such as anti-rollover systems. It can also help in determining the maximum safe speed for driving on certain ramps, such as highway exit ramps.

## 5. Does the speed needed for a car to rollover differ for different types of vehicles?

Yes, the speed needed for a car to rollover when hitting a ramp can differ for different types of vehicles. Factors such as weight, size, and handling capabilities can affect the speed required for a car to rollover. For example, a larger and heavier vehicle may require a higher speed to rollover compared to a smaller and lighter vehicle.

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