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Center of Gravity 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 formula

  • 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 

Related Formulas

Adj formula    

Tangent formula

Circumference formula


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 q = opposite / adjacent

Pythagorean Theorem   Pythagorean theorem

 

Triangle

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:

Adj formula

Level wheelbase

Figure 2

Once we know the value of the adjacent side of our triangle we solve for the tangent of q using:

Tangent formula

Raised wheelbase

Figure 3

Ok, 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:

CGH formula

  • WB is the wheelbase
  • FWc is the change in front wheel weights
  • TW is the total weight
  • Tan q 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.

Circumference formula

  • C is the average circumference found by adding the LF and RF sizes and dividing by 2.
  • p 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).

  Wheelbase CG 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)

 

  Track width CG
 

 

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.

 

 

 

Is it possible to raise the car too much?

 

  You don't want to raise the car any more than 45º. This approximates to 70.7% of your wheelbase. (Based on more rules for right triangles.) For example: If your wheelbase is 104", you would not want to raise the rear of the car any higher than 73.5".  This would not really be a consideration for a stock car, but could come into play for a kart or other vehicle with a shorter wheelbase.

 

 
 
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