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Hi, hope someone can help. I need to find the centre of gravity of a car (x,y and Z). I know the length of the car (108 inch) the distance between the axils and the height of the car (1.515m) I also no the loading on the fronat axil and the rear axil and the total mass of the car is (400 kg). Any suggestions?
Avinash Jha
Ok, now once you have the actual forces, do a moment calculation about the centre of mass. ie Load on front axle*distance from front axle to cm=load on rear axle*distance from rear axle to cm. Here you have two unknowns and one equation, so you need another equation: you know that distance from front axle to cm + distance from rear axle to cm = distance between axles. Solve simulataneously and voila, cm position in terms of front or rear axle. It is true that there is not enough info to calculate the z co-ordinate of your cm, actually, you can only calculate the x co-ordinate (and the y co-ordinate, if you assume symmetry about the z axis.)
Center of Gravity (CG) is defined as that point about which, if the body were suspended from it, all parts of the body would have equilibrium ..i.e.. without
tendency to rotate. it is the 3D balance point of the race car. all acceleration forces acting on a body can be considered to act through the CG of that body..we have the cg to be as low as we can get it.
Mass Centroid- is related to Cg ..sort of...ifin we slice the car into a series of sections, like a loaf of bread, each slice would have its own CG...if, in a side view, we draw a line connecting each sliced CG..we have the Mass Centroid Axis..not really a straight line but close to it.it gives an indication of the distribution of the vehicles mass in the vertical plane.
Roll Center of the suspension is that point , in the traverse plane of the axles, about which sprung mass of that tend of the vehicle will roll under influence of centrifugal force. It is determined by drawing a line from the tire contact patch to a point in space that is the intersection of the upper and lower suspension arm linkage angles.
The CG and RC are located at different points. Usully the CG is many inches above the RC. CG can be change by moving " weight " around on the chassis.. The RC is changed by modifying how the upper and lower control arms mount to the chassis. Correct changes will improve the weight transfer to the rear tires thus improving traction.lot of other stuff goin on here.. race car math of some is on my post in General Physics post " Race Car Physics" 31 Dec 2008
Finding the center of gravity height can be done in several ways, none of which are accomplished very easily and without some work. Presented here is the easiest method. The center of gravity height is calculated by weighing the car when level and then raising the car at least 10 inches at the rear and weighing the front again. Replace each shock absorber with a solid link to eliminate suspension travel
You need a set of electronic scales. You also need a set of blocks o eight inches tall. 10 inch is better.
First, weigh the car normally, then record the total weight (T) and the total number of pounds on the front tires-nose weight (N).
Jack up the rear of the car..CAREFULLY!! Then carefully place the blocks under the rear scales (you may find it useful to lock your rear axle). Now record your new nose weight (NI). Next, subtract your original nose weight (N) from your new, lifted nose weight (NI) and you will have the difference (Nd).
Figure it out using your calculator…
a. Multiply the nose difference (Nd) x 1660= (A)
b. Multiply the total weight (T) x 8 (the height of the blocks)=(B)
c. Divide your previous numbers, A by B, and this equals (C)
d. Add this number, C, to your axle centerline height or spindle center, and the number you obtain is your vertical center of gravity.
CGH= WB x FWc / TW x Tan of angle
Center of Gravity Height Formula
Definition of Variables
CGH - Center of Gravity Height WB - Wheelbase (inches) TW - Total weight FW1 - Front weight LEVEL FW2 - Front weight RAISED FWc - FW2 - FW1 (change in weights) HT - Height raised (inches) Adj - Adjacent side (see below) Tan q - Tangent of angle (see below) CLF - Left Front tire circumference CRF - Right Front tire circumference C - (CLF + CRF) / 2 (average circumference) r - Axle Height
CENTER OF GRAVITY HEIGHT
Finding the center of gravity height can be done in several ways, none of which are
accomplished very easily and without some work. Presented here is the easiest method. The
center of gravity height is calculated by weighing the car when level and then raising the car
at least 10 inches at the rear and weighing the front again. Enter the data into the
program below to calculate your center of gravity height.
Before you begin:
Be sure that all fluids are full
Replace each shock absorber with a solid link to eliminate suspension travel
Make sure the tires are inflated to the maximum pressure as specified by the
manufacturer to eliminate any sidewall flex
Note: If these steps are not taken, the calculations will be inaccurate
Center of Gravity Height Formula
Definition of Variables
CGH - Center of Gravity Height
WB - Wheelbase (inches)
TW - Total weight
FW1 - Front weight LEVEL
FW2 - Front weight RAISED
FWc - FW2 - FW1 (change in weights)
HT - Height raised (inches)
Adj - Adjacent side (see below)
Tan Tangent of angle (see below)
CLF - Left Front tire circumference
CRF - Right Front tire circumference
C - (CLF + CRF) / 2 (average circumference)
r - Axle Height
Related Formulas
This program is used to calculate center of gravity height. Enter the data in the boxes below,
then click the "Calculate" button.
Wheelbase (inches)
Total Weight (lbs)
Front Wheel Weight - Level (lbs )
Front Wheel Weight - Raised (lbs )
Raised Height (inches)
Left Front Tire Size (circumference in inches)
Right Front Tire Size (circumference in inches)
Center of Gravity Height from Axle Height
Center of Gravity Height from Ground
How does all this work?
The center of gravity height is found using the rules of trigonometry and right triangles. Specifically, we are using the Law of Tangents, and the Pythagorean Theorem. The following diagrams are greatly exaggerated for illustration purposes.
Tan = opposite / adjacent
Pythagorean Theorem
Figure 1
So, in our exercise, when we raise the car 10" we are creating a right triangle with the following properties:
Hypotenuse = Wheelbase = c Opposite = Height = b Adjacent = a
Therefore using the Pythagorean Theorem:Figure 2
Once we know the value of the adjacent side of our triangle we solve for the tangent of using:
Figure 3Ok, now that we know the tangent of the angle we can calculate the center of gravity height based on our weight measurements using the following formula:
WB is the wheelbase FWc is the change in front wheel weights TW is the total weight Tan is the tangent calculated above
This calculates the Center of Gravity Height from the axle height.
To find the CGH from the ground, you must add your axle height to the above calculation. You can measure your axle height or calculate it using the average of your two front tire sizes and the formula for the circumference of a circle.
C is the average circumference found by adding the LF and RF sizes and dividing by 2. approximately equals 3.1416 r is your axle height
For example: Your LF is 85.5" and your RF is 87". Your average circumference is (85.5 + 87) / 2 = 86.25". Your axle height is (86.25 / 2) / 3.1416 = 13.727". Add this number to the CGH to find the center of gravity height in relation to the ground.
Frequently Asked Questions
Why do I have to raise the car and re-weigh it to find Center of Gravity?
We are not just looking for the center of gravity (CG), but the center of gravity height (CGH).
The true center of gravity is actually a 3 dimensional point in space. You need to know the CG along the wheelbase, the CG for the track width of the car, and the CGH. Where these 3 coordinates intersect in space is the actual center of gravity. The following formulas will calculate the Wheelbase CG (CGwb) and the Track Width CG (CGtrw).
Definition of Variables
CGwb - Center of Gravity from behind the front wheels
CGtrw - Center of Gravity from left side of track width
RW - Total Rear Weight TW - Total Weight WB - Wheelbase (in inches) RtW - Total Right Side Weight TrW - Track Width (in inches)
Why do I have to raise the car a minimum of 10"?
The Center of Gravity Height calculation is based on the change in the front wheel weights in relation to the angle at which the car is raised. The higher you can raise the rear of the car (higher angle), the greater the weight shift will be, thus creating a greater change in front wheel weights. The more change in the weights that you can create, the more accurate the measurement will be. Ideally, you would want the raise the car at least 20", however, this can be very difficult to do. The minimum of 10" creates just enough weight change to get a relatively accurate result.
inding the Center of Gravity (CG)
~Method 1~
Here is the procedure for mesuring the weight distribution of the vehicle to locate the position of the Center of Gravity (CG):
This first method is for people who have access to 4-wheel scales.
Method 1:1. For best results the car should be "race ready" with Fuel, Driver, N2O bottles, Proper air pressures, etc.2. Take a measurement of the front and rear weights. (No need to measure the total weight of the car for these calculations).3. Measure the wheel base. I measure from the Front Edge of the Front rim to the Front Edge of the Rear rim.
Example:Weight of front end: 2000lbsWeight of rear end: 1800lbsWheel Base: 105"
2000 + 1800 = 3800lbs (This may not be the same as the measured vehicle weight because of unlevel ground or scale accuracy, etc)
2000 / 3800 = .526 ~ Front end distribution = 53%1800 / 3800 = .473 ~ Rear end distribution = 47%
05" x .53 = 55.65" The Center of Gravity is located 55.65" in front of the rear axle.OR105" x .47 = 49.35" The Center of Gravity is located 49.35" behind the front axle.
*Both of the above measurements locate the CG in the same place.
This second method is for people who do not have access to a 4-wheel scale.
~Method 2~
Method 2:1. For best results the car should be "race ready" with Fuel, Driver, N2O bottles, Proper air pressures, etc.2. If you do not have access to a 4-wheel scale then you can use a drive-on scale like at the race track, a farmers COOP, Truck stops, etc. The scale needs to be level/flat with the ground.3. Make a mark with a piece of tape (or chalk or ??) somewhere on the drivers side rocker panel. This doesn't have to be exactly in the middle just somewhere in the middle.4. Drive the car onto the the scale so the tape is on the edge of the scale. Only the front tires will be on the scale. The rear tires will be OFF the scale.5. Take a mesurment of the weight.6. Now drive off the scale until the tape is aligned with the back edge of the scale. Only the rear tires will be on the scale. The front tires will be OFF the scale.7. Take a measurement of the weight.8. Measure the wheel base. I measure from the Front Edge of the Front rim to the Front
Edge of the Rear rim.
Example:Weight of front end: 2000lbsWeight of rear end: 1800lbsWheel Base: 105"
2000 + 1800 = 3800lbs (This may not be the same as the measured vehicle weight because of unlevel ground or scale accuracy, etc)
2000 / 3800 = .526 ~ Front end distribution = 53%1800 / 3800 = .473 ~ Rear end distribution = 47%
105" x .53 = 55.65" The Center of Gravity is located 55.65" in front of the rear axle.OR105" x .47 = 49.35" The Center of Gravity is located 49.35" behind the front axle.
*Both of the above measurements locate the CG in the same place.
Height of the Center of Gravity:There is a procedure that allows you to measure the height but this includes raising the car 2-3 feet off the ground while on scales and replacing the shocks with solid bars, etc.BUT for most doorslammers in order to find the Height of the Center of Gravity (CG) just measure the distance from the ground to the centerline of the camshaft.
