# Center of gravity problem

1. May 4, 2014

1. The problem statement, all variables and given/known data
I need to find a vehicles center of gravity

2. Relevant equations
I'm thinking euler's equations but im new to them.

3. The attempt at a solution
I'm designing a rig as part of a project that would allow a race car to be suspended from a lift on 4 ropes and then allow to move in on its x, y and z axis in order to get mesaures for the roll, pitch and yaw angles. I'm having difficulties adding it all together however in order to find the point which all these inertias act through

Last edited by a moderator: May 4, 2014
2. May 4, 2014

### Staff: Mentor

Could you post some sketches/photos? It's kind of hard to help without seeing a lot more about the problem.

3. May 5, 2014

Ok imagine a car is placed on a platform which is suspended from a lift or roof by four ropes attached sypherical bearings, it is to find the centre of gravity which passes through the roll, yaw and pitch axis like on this plane

An accelerometer could be placed in the car

This image shows how the rig could measure the yaw angle

This image shows how the rig could measure the roll angle

This image shows how the rig could measure the pitch angle

Now I need a way to use these three angles which the car moves to find the center of gravoty location, I tried to use trigonometry to no success, my second idea is to model everything using CAD then draw three dotted line which follow the cars movement angles and where they meet will be the COG, would this be accurate?

4. May 5, 2014

### Staff: Mentor

Why can't it just be calculated from the known mass distribution?

Chet

5. May 5, 2014

calculating from the weight distribution dosent get the height of the CoG though or yaw center

6. May 5, 2014

### SteamKing

Staff Emeritus
It's fairly easy to get the car's longitudinal c.g. and transverse c.g. by putting each wheel on a separate scale. Simple statics can be used to calculate l.c.g. and t.c.g. For the location of the vertical center of gravity, I believe the Society of Automotive Engineers has a procedure which places the vehicle on an incline or jacking one side up, and knowing the slope of the incline and the force at each wheel, one can work back and estimate the v.c.g. above the ground. This procedure is used for unusual vehicles like tractors and excavators. It's important that the suspension of the vehicle be locked while tested, to ensure no change in wheel reactions due to the movement of the suspension.

This SAE paper citation also looks at the special problems encountered when trying to measure the c.g. location of racing vehicles:

http://papers.sae.org/2004-01-1076/

Another good reference is Race Car Vehicle Dynamics, by WF Milliken and DL Milliken, SAE 1995.

In any event, the construction of a trapeze is not required to do this test.

7. May 5, 2014

### Staff: Mentor

Of course you can get the height of the CG from knowledge of the mass distribution (I didn't say weight distribution, I said mass distribution).

Chet

8. May 5, 2014