roktoy84

What is the RIGHT way to figure the center of gravity on my truck. Not just guessing, or, this is usually the place type stuff. I want to know so I can start to designing a good 4 link for the rear of my truck. I know that there is a math formula for this. Just haven't found it yet.

BruceTS

The easiest Center of Gravity coordinate to find is where the Center of Gravity lies relative to your 4Runner’s wheelbase.

The weight on your 4Runner’s front and rear axles is directly proportional to the location of the Center of Gravity along your 4Runner’s wheelbase. In fact, it is a direct inverse ratio.

If 100% of the weight of your 4Runner was located on the front axle, the Center of Gravity 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 Center of Gravity would be located 40% of the wheelbase distance from the front axle.

To calculate your 4Runner’ss WBCG (Wheelbase Center of Gravity) you will use the data values you measured and recorded earlier.

Once again, please remember I am using fictitious data in these examples. You will need to substitute your measurements, 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 your 4Runner

The following formula will enable you to determine in inches where the WBCG is located behind your 4Runner’s front axle.

(1 - (WF / Wt)) * LWB = WBCG 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


“Y” The Wheel Track Center of Gravity (WTCG)

The location of your 4Runner’s WTCG (Wheel Track Center of Gravity) is calculated in much the same way as you just calculated the WBCG.

The WTCG coordinate location is a direct inverse ratio of the weight on each side of your 4Runner to the wheel track.

Here are the data elements you will need to use for this formula.

LTB = 65 inches - Width of your wheel track

WP = 2,100 lbs – Weight on passenger side of your 4Runner

Wt = 4,800 lbs – Total weight of your 4Runner


The following formula will enable you to determine in inches where the WTCG is located from the outer tire edge on the passenger side of your 4Runner.

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

(1 - (WP / Wt)) * LTB = WTCG in inches, from the passenger side tire edge

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

(1 - 0.4375) * 65 =

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


“Z” The Center of Gravity Height (HTCG)

The Height of your 4Runner’s Center of Gravity (HTCG) is not quite as easy to determine.
Calculating the HTCG is a bit more difficult to accomplish. It’s 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 4Runner, 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.

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 4Runner’s Center of Gravity (HTCG).

Here are three formulas you must solve before you can get to the HTCG.

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 you have all the data needed to find the Height of your 4Runner’s Center of Gravity (HTCG).

Here’s the formula.

HTCG = HF1 + ((WRd * LWB * LWBn) / (Wt * HFd)) = Your 4Runner’s CG Height

HTCG = 17.4 + ((215 * 95 * 91.57) / (4,800 * 25.3))

HTCG = 17.4 + (1,870,317.2 / 121,440)

HTCG = 17.4 + 15.40

HTCG = 32.80 Inches above the tire patches

Rugby10

OMG Bruce, best damn reply I've read in a long time...


GOT SHOP MATH?

roktoy84

thank you Bruce. That was exactly what I was looking for. All I can say is you

Jeff the marmot

Hey Bruce,
Since when do you have a 95" wheelbase?

I think he copied it from http://www.jeepaholics.com/tech/cog/#_Toc535118730

But I just wanted to say that if anyone actually does those measurements with a 3rd gen 4Runner I'd be very interested in knowing the results. I haven't yet done it.

BruceTS

It's called 2 second of using a search engine, but I didn't want to say like everybody else " do a search" it was faster for me to copy paste the relevant information......


the concept is exactly the same, I used to do it with our race cars all the time, having 4 scales made the process quite easy, just weight the car on all 4 corners then lift the front up a foot, weigh again and do the math....

Unfortunately each rig will have different results, just depends on the extent of their modifications, once I get the time to go up to my friends shop, i'll weigh my rig for exact numbers....

BTW I did have to edit out "jeep" and replace it with "4Runner" of course