How to calculate rollover based on angle of turn, velocity, and wheel distance

[yw917]

This is for my senior design project for which we are constructing a luggage propulsion system.

One of the things I have to do is calculate what is the sharpest turn possible for a given speed with a given wheel distance without it rolling over. I do not have the actual numbers yet as we are trying to decide on an optimal wheel distance. I guess what I am looking for are the formulas you would use to calculate such things and maybe an example.

The dimensions of our product are 18''w x 12'' l x 30''h, for the purpose of calculations we are assuming the center of gravity is right in the middle even though in actuality it is not.

Thanks.

 

[haruspex]

Please post your own attempt.

 

[yw917]

This isn't a homework problem, I took physics 1 four years ago and don't remember much, don't have a textbook either.

I'm trying to get pointed in the right direction like which formulas you would use to calculate such a thing.

I understand the concept of needing the center of gravity to be supported but what I don't know is how to calculate if you turn at a certain angle at a certain speed how far the device will be tilted.

 

[haruspex]

You start by drawing a 'free body diagram'. This takes one rigid component of the system (the vehicle) and marks all the forces on it with arrows. These should show the approximate direction of the force, a label (like 'N' for the directly upward force from the road), and the line through which the force acts (gravity acts through the centre of gravity). Where friction is involved, it's usual to separate the normal force (the one perpendicular to the surfaces) from the frictional force (parallel to the surfaces). Since the vehicle is not skidding, the friction will be static friction.
Next, you consider the acceleration which the vehicle undergoes. Generally this will involve both linear and rotational acceleration. Since forces are vectors, it helps to consider linear forces in two or three directions separately. This is called 'resolving'. In the present case, horizontal and vertical. (If the surface is banked, it might be better to resolve parallel and perpendicular to the surface.) For the rotation, you need to pick a point to take moments about.
You should get three equations, something like:
- resultant acceleration vertically * mass = net upwards force
- resultant acceleration horizontally * mass = net sideways force
- resultant angular acceleration * moment of inertia = net torque
For your problem, the first and third of those should equate to zero. The middle one is nonzero: the centripetal acceleration required to negotiate the bend = v²/r.
There's plenty of stuff on the net which you can follow up from those pointers. Forgive me for not taking the time to provide a complete introductory course on dynamics.

 

[Nickie]

Calculating the rollover potential for your luggage propulsion system is an important step in ensuring its safety and stability. To do so, you will need to consider the angle of turn, velocity, and wheel distance of your system. The following formulas can help you calculate the maximum angle of turn before rollover occurs:

1. Calculate the maximum lateral acceleration (a) based on the velocity (v) and wheel distance (d) using the formula:

a = v^2 / d

2. Calculate the maximum lateral force (F) that can be applied to the system before rollover occurs using the formula:

F = m * a

Where m is the mass of your system.

3. Calculate the lateral force (FL) applied to the system due to the angle of turn (θ) using the formula:

FL = m * g * tan(θ)

Where g is the acceleration due to gravity (9.8 m/s^2).

4. Set the maximum lateral force (F) equal to the lateral force (FL) and solve for the angle of turn (θ). This will give you the maximum angle of turn before rollover occurs.

Example:

Let's say your system has a mass of 20 kg and a wheel distance of 0.5 meters. You want to know the maximum angle of turn at a velocity of 5 m/s.

1. Calculate the maximum lateral acceleration:

a = (5 m/s)^2 / 0.5 m = 50 m/s^2

2. Calculate the maximum lateral force:

F = 20 kg * 50 m/s^2 = 1000 N

3. Calculate the lateral force due to the angle of turn:

FL = 20 kg * 9.8 m/s^2 * tan(θ)

4. Set F = FL and solve for θ:

1000 N = 20 kg * 9.8 m/s^2 * tan(θ)

θ = arctan(1000 N / (20 kg * 9.8 m/s^2)) = 26.6 degrees

Therefore, the maximum angle of turn at a velocity of 5 m/s with a wheel distance of 0.5 meters is 26.6 degrees before rollover occurs.

Please note that these calculations assume a perfectly balanced and symmetrical system. As you mentioned, the actual center of gravity may not be in the exact middle, so it is important to consider