Determine Your Jeep's Center of Gravity & Rollover Angles

[Daless2]

(I will post eight separate posts on this thread as I have no clue how to post a document anywhere. Please forgive my ignorance in this matter.)

1. How To Determine The Center of Gravity and Roll Over Angles of “Your Jeep”

So often in our trail side conversations we talk about the CG (Center of Gravity) of one Jeep being higher or lower then the CG of another Jeep, and we relate this not only to the ability to get up or down a slope, but also to the dreaded thought of rolling over.

Yet most of us have never really figured out where the Center of Gravity is actually located on our own Jeep and similarly what the Rollover Angles are.

Why haven’t we done this? Well to be honest, probably because it isn’t so easy to do.

This write-up is an effort to provide a process that most folks can follow to determine the Center of Gravity and Rollover Angles for their own Jeep.

There is some mathematics involved here, Algebra, Geometry and Trigonometry.

However, if you are like me and not a math wiz kid, don’t let that scare you away. I have automated all the math via an Excel spreadsheet.

All that is really required is that you follow some simple directions, take some accurate weight and distance measurements, and then just plug the numbers into the spreadsheet.

If you hang in here with me and follow this process through you will be rewarded with the actual physical locations of the following values for your Jeep.

The 3-Demensional Single Point Center of Gravity of your Jeep as well as the:

* Wheelbase Center of Gravity
* Wheel Track Center of Gravity
* Height of the Center of Gravity


Rollover Angles in the directions of: (incomplete at this time)

* Driver Side
* Passenger Side
* Front
* Rear

If you can use a tape measure, and can get a few minutes access to a truck “weighing scale” like you find at truck stops or a roadside weigh station you can do this.


Frank

[Daless2]

2. Capturing Weights and Measures

In this section you will take some specific measurements of your Jeep following these three process steps.

1 Preparing your Jeep for off-road use
2 Measuring lengths and heights in your driveway
3 Measuring weights at a truck stop scale


Tools Needed:

You will need the following tools.

- Measuring tape (12-feet long)
- Access to a truck weighing scale for approximately 5 minutes
- A means to elevate the front tires of your Jeep at least 24 inches off the ground (Ramps, blocks, a trailer with car ramps on it, etc.)
- A Helper


Measured Values:

During this process you will be measuring and recording the values shown in the table below. Each will be explained in detail within this document.

(Please note I have put fictitious numbers in this table to use in the examples to follow. You must record your own numbers in this table and then in the formulas or spreadsheet.)




As you make each measurement record the value in the chart above.


Calculated Values:

Using the values you recorded above, the following values will be calculated and used in your efforts to determine the Center of Gravity and Rollover angles.




If you would like, you can calculate these values yourself, however the Excel spreadsheet will perform this for you auto-magically!

Jeep Setup

Before you begin to make any measurements you will need to set your Jeep up just as if you were ready to take it off road. This step is vital in determining the Off-Road Center of Gravity and Rollover Angles.

However you prepare for an off road trip, do the same now. Pack that toolbox, spare parts, Hi-Lift Jack and anything else that you would normally bring. Please make sure everything is safely anchored down.

If you have two sets of tires, one for the street and another set for off road, put the off road tires on and air them down to the level you would use off road.

Fill your gas tank.

If you would normally off road with a person in the passenger seat, or any other seats for that matter, make sure that person is available to sit in that seat for you.

I cannot overemphasize the importance of weight and weight distribution in and on your Jeep to accurately determine the Center of Gravity. Your efforts in setting your Jeep up now will be rewarded in accuracy later.


Frank

[Daless2]

3. Off-Scale Measurements

These measurements should be taken away from the weight scale so the scale is not tied up when it isn’t necessary.

With your friend, measure and record the following values.


LWB – Length of Wheelbase

You want to measure your Jeep’s wheelbase length while it is sitting on level ground and fully prepared for an off road trip.

Your Jeeps wheelbase is the distance between the center of the front tire footprint on the ground and the rear tire footprint on the ground. This is a bit difficult to measure accurately, however we can get it by measuring the distance between the axle hubs.

With your friend measure the distance between the center of the front axle hub and the center of the rear axle hub. This will be equal to the wheelbase.

All measurements should be accurate to 1/16-inch.

Here is a drawing of what you will need to measure to capture the wheelbase length.



Convert any fractions to decimal values and record the wheelbase measurement in inches for the value of LWB. (For example, 92 and 5/16-inchs would be converted to 92.3125 inches. LWB = 92.3125)

Here is a table to assist in converting fractions to decimal format.




LTB – Width of Wheel Track Base

Measure the distance between the outer edges of your rear tires. This is the Track Width of your Jeep. Convert any fractions to decimal values and record this measurement in inches as LTB.

Here is a drawing of the measurement you need to take.
(LTB.jpg)



HF1 – Front Axle Height

Measure the distance from the center of your front hub to the ground and record this as HF1. Be sure your Jeep is sitting on level ground when you do this.




Frank

[Daless2]

4. Weighing Your Jeep

Drive your Jeep over to the local friendly neighborhood weigh station.

Be sure to bring whatever means you will use to elevate the front axle with you. (Please remember to take whatever it is out of your Jeep before you weigh your Jeep.)


Potential Scale Locations

* Major Truck Stops
* Highway Roadside Weigh Stations
* Agricultural Centers (Bulk Grain Sales)
* Salvage Yards
* Recycling Centers

The scale you choose should be accurate to at least 5 lbs. (1 lb would be better.)

Once you have identified the scale you would like to use, I have found it helpful to pay a visit to the friendly scale operator ahead of time. Explain what you want to do and how you will do it. Be nice and be friendly! Maybe even entice the operator with a seat in your Jeep for next weekends trail ride.

If all else fails try $10 !

The objective is to get five to ten minutes on that scale!!!

OK, now that you have the politics out of the way here’s what you need to do.

Weigh the front axles of your Jeep and record it as WF. Simply pull your front axle onto the scale plate.




Weigh your entire Jeep by pulling all four wheels onto the scale plate and record this as WT.



Weigh the rear axle of your Jeep by pulling the front tires off the scale plate and record this at WR1.



Next, you must come up with a means to lift the front axle of your Jeep, by the tire patches, at least 24-inches higher than on level ground.

DO NOT USE A JACK to do this. You MUST elevate your front axle BY THE TIRE PATCHES or the geometry will be thrown completely off and your calculation will be flawed. This is truly vital to success.

The first time I did this I used a set of 13-inch tall car ramps bolted to 12-inch square railroad ties. Yes this was a pain to carry there and back but it allowed me to lift the front, by the tire patches, a little more than 24 inches.

The second time a friend volunteered the use of a flat bed trailer.

I pulled the trailer in front of the scale plate, put the trailer ramps down and my car ramps on top of the trailer bed. I drove my Jeep up and managed to get more than 30 inches of lift above level.

OK, figured out how you’re going to elevate the front of your Jeep BY THE TIRE PATCHES yet?

Good, now weigh the rear axle with the front elevated (at least 24 inches) and record this as WR2.

Measure the distance from the ground to the center of the elevated front hub and record this as HF2.




Weigh the passenger side of your Jeep by pulling only the passenger side tires on the scale plate. Record this weight as WP.



You have now finished collecting all the data you will need to determine your Jeep’s Center of Gravity and Rollover Angles. All that is left is to calculate a few formulas.


Frank

[Daless2]

5. Calculating “X” The Wheelbase Center of Gravity (WB-CG)

The easiest CG (Center of Gravity) to find is where the CG lies relative to your Jeep’s wheelbase.

The weight on your Jeep’s front and rear axles is directly proportional to the location of the CG along the wheelbase. In fact, it is a direct inverse ratio.

Think about it. If 100% of the weight of your Jeep was located on the front axle, the CG would be located ZERO inches, or 0% of the wheelbase distance from the front axle.

If the weight were distributed 60% on the front axle, then the CG would be located 40% of the wheelbase distance from the front axle.

To calculate your Jeep’s WB-CG (Wheelbase Center of Gravity) you will use the values that you measured and recorded earlier.

(Please Note. In these examples I am using fictitious numbers. You will need to plug your own numbers in, or type them into the spreadsheet.)

LWB = 95 inches = Wheelbase in Inches
WF = 2,600 lbs = Weight on Front Axle
WT = 4,800 lbs = Total weight of Jeep


The following formula will enable you to determine in inches where the WB-CG (Wheelbase Center of Gravity) is located behind the front axle.


(1 - (WF / WT)) * LWB = WB-CG location, in inches, behind the front axle


(1 - (2,600 / 4,800)) * 95 =

(1 - 0.541667) * 95 =

0.46 * 95 = 43.54 Inches behind the front axle

Frank

[Daless2]

6. Calculating “Y” The Wheel Track Center of Gravity (WT-CG)

The location of your Jeep’s WT-CG (Wheel Track Center of Gravity) is calculated in much the same way as you just calculated the WB-CG.

The WT-CG is a direct inverse ratio of the weight on each side of your Jeep to the wheel track.

Here are the data elements you will need to use for this formula. Once again I have assigned fictitious numbers.

LTB = 65 inches - Width of your wheel track
WP = 2,100 lbs – Weight on passenger side of your Jeep
WT = 4,800 lbs – Total weight of your Jeep


The following formula will enable you to determine in inches where the WT-CG is located from the outer tire edge on the passenger side of your Jeep.


(1 - (WP / WT)) * LTB = WT-CG in inches, from the passenger side outer tire edge


Substitute the values with what you measured and recorded and then simplify and solve the formula as in this example.


(1 - (2,100 / 4,800)) * 65 =

(1 - 0.4375) * 65 =

0.5625 * 65 = 36.56 Inches from the passenger side outer tire edge


Frank

[Daless2]

7. Calculating “Z” The Center of Gravity Height (HT-CG)

The Height of your Jeep’s Center of Gravity (HT-CG) is not quite as easy to determine.

Calculating the HT-CG is a bit more difficult to accomplish. Its difficult for some people to even visualize, and difficult for me to explain.

Let me give it a shot.

When you went about measuring and weighing your Jeep, one of the things you did was lift the front axle (at least 24 inches higher than it would be on level ground) and then you weighed the rear axle.

When you lifted the front, you in effect shortened the wheelbase as it relates to gravity. In other words, the horizontal distance between the front and rear tire patches became shorter than what it is on level ground.

Here is a picture that might help in understanding this.





Now, if we can measure how high we lifted the front axle, calculate the length of this shortened wheelbase, and determine how much weight was added to the rear axle when we lifted the front, we will be able to calculate the Height of your Jeep’s Center of Gravity.

Here are three formulas we must solve before we can get to the HT-CG. Plug in your numbers. I am using the fictitious numbers from the table above.

HFd = HF2 - HF1 = Height difference between front axle Level and Elevated


HFd = 42.7 – 17.4

HFd = 25.3 inches


LWBn=SQRT (LWB^2 - HFd^2) = Length of the shortened wheelbase when elevated


LWBn=SQRT (95^2 – 25.3^2)

LWBn=SQRT ((95 * 95) – (25.3 * 25.3))

LWBn=SQRT (9025 – 640.09)

LWBn=SQRT (8384.91)

LWBn=91.57 inches


WRd = WR2 – WR1 = Weight added to rear axle


WRd = 2,415 – 2,200

WRd = 215 lbs.

OK, now we have all the data needed to find the Height of your Jeep’s Center of Gravity above your tire patches.

Plug your numbers into this formula.

HT-CG = HF1 + ((WRd * LWB * LWBn) / (WT * HFd)) = Your Jeep’s CG Height


HT-CG = 17.4 + ((215 * 95 * 91.57) / (4,800 * 25.3))

HT-CG = 17.4 + (1,870,317.2 / 121,440)

HT-CG = 17.4 + 15.40

HT-CG = 32.80 Inches above the tire patches


Frank

[Daless2]

8. So where are we?

We now know the X, Y, and Z coordinates of the single point 3D Center of Gravity of your Jeep.

For the fictitious numbers that I used in the examples the Center of Gravity for the Jeep is located at a point:

43.54 Inches behind the front axle,
36.56 Inches from the passenger side outer tire edge, and
32.80 Inches above the Jeep’s tire patches.

Can you see it?

Good cause I have no clue how to draw it in 3D.

Next on the agenda will be using this data to determine minimum roll over angle in four directions, forward, backward, driver side and passenger side.


I still need to do the write-up on rollover angles and have the more complex formulas validated. I also need to complete the spreadsheet.

Hope you find this info of some use.

Merry Christmas to all,
To all a Good Night.


Frank

[This message was edited by Daless2 on December 23, 2001 at 09:25 PM.]

[JeepKat]

[Jeff Weston]

<BLOCKQUOTE><font size="-1">quote:</font><HR>Originally posted by JeepKat:
[/quote]

That made me laugh Kat!

Jeff