# Moment of Inertia - center of a rod w/ unequal distribution

1. Dec 5, 2014

### redhatman

Hello everyone!

New member here, as an ME major I always seem to come across very valuable information here, so I figured I would see if possibly someone here could help me.

The problem I am dealing with involves modeling a car through certain motions such as hitting a speed bump, and part of this is finding the moment of inertia.

The vehicle weight distribution is as follows;
Total Weight = 2063.85 kg

Weight Distributions;
Front = 57.9% = 1194.97 kg
Rear = 42.1% = 868.88 kg

I'll try and ask this as clear as possible, please bear with me.

I am confused when it comes to evaluating this. Assume that I am correct in creating a simple model by modeling it as a rod (1/12)(m)(l^2). I am not sure if I should use the center of the overall length, combined with the parallel axis theorem, or if I should be looking more into the radius of gyration. Also, when using these, should I determine first the center of gravity for the weight distribution (making l1 > l2), and then solve with those values?

Any and all input is very much appreciated, I feel as though I am very close but I am definitely missing some key differences between the methods. I have included a simple diagram to aid in visualizing my problem statement.

2. Dec 5, 2014

### SteamKing

Staff Emeritus
Cars are not very rod-like. Their mass is not only distributed longitudinally, but to a certain extent, vertically and transversely as well.

Things like engines and transmissions represent concentrations of mass which are a significant fraction of the total mass of the vehicle. The radius of gyration would be a more appropriate piece of information to use to develop the MOI of a complex machine like a car.

The radius of gyration is typically calculated using the MOI about the c.g., so you should also know where the c.g. of the vehicle is located. The F/R weight distribution will give you one coordinate of the c.g.; you'll have to estimate the other two.

3. Dec 5, 2014

### redhatman

Thank you for your input SteamKing.

I understand that cars are much more complex than just a rod, however this simulation is "basic" simulation which will be created using Simulink.

The parameters I provided were referenced from Jeep handbooks as 56/44 (%, F/R dist.). After accounting for the additional weights, summing forces and moments, I came up with the seemingly reasonable new value of 57.9% and 42.1%.

It sounds like I would want to use the radius of gyration method for this problem, but what do you mean the F/R Distribution will give me one, but I'll have to estimate the other two? I assume you're talking about treating the front and rear of the vehicle as something like a point mass or distributed load, some distance away?

4. Dec 5, 2014

### redhatman

(Attachment in aid to my previous post)

5. Dec 5, 2014

### SteamKing

Staff Emeritus
What I meant was that the F/R weight distribution will give you the longitudinal location of the center of gravity, not the radius of gyration. The gyradius can be different for different cars with the same F/R weight distribution.

The gyradius is either given as a distance (in feet or meters, for example) or as a percentage of length, width,or height of the car, depending on which MOI you are interested in.

6. Dec 5, 2014

### redhatman

Okay, thank you very much!

Would you (or anyone else) be able to steer me in the right direction of finding the MOI about the center of gravity under the conditions I have provided?

Once again, thank you very much for all of your help, I appreciate it immensely.

7. Dec 5, 2014

### SteamKing

Staff Emeritus
Further to your quest for calculating the MOI of anything, there is a class of engineer, formerly called weight engineers, whose specialty it was to do a weight take-off of a vehicle, whether it was an automobile, airplane, spacecraft, ship, whatever, where the total weight, c.g., and inertia properties were critical to the proper design of the machine.

Now, you could make a rough weight take-off estimate of the MOI of your vehicle by looking at the major weight groups, like the engine, transmission, wheels and tires, suspension parts, body & frame, etc. As an ME major, I'm somewhat surprised that you haven't had to do such a calculation as part of your training.