Car Center of Mass Calculator

Center of Mass or Center of Gravity is defined as the unique point in which the mass of an object is located and behaves as if the entire mass is concentrated at that point. On applying force in the center of point the object will move in the direction in which force is applied. We can also state the definition of center of gravity as the point in which the gravity moments are balanced.

In order to determine the center of mass of a three dimensional object you need to consider three different coordinates and they are as follows

• Longitudinal Position
• Altitudinal Position
• Side Position

All these three coordinates will intersect in space and the point is known as center of mass. In order to calculate the center of gravity of car you need to know few weight measurements in different geometries.

In order to estimate the center of gravity of a car you need to perform certain measurements. Know calculation of center of mass in three different positions explained clearly one by one.

Longitudinal Position

Let us consider both the car axles lie on a weighing scale on a same level. As per netwon's third law there is an equal and opposite reaction. There are different forces namely gravitational force Fg, reaction force Fb acting on rear axle, reaction force Fa acting on frot axle.

Total torque around that point is zero. Torque is nothing but the product of force and arm length if force and arm length are perpendicular to each other.

Summing up torques around rear axle we will get the equation as Fb * 0 + Fa * L - Fg * b = 0

After trivial transformation

b = L * (Fa / Fg)

Fa is the weigt measured by the scale under the front axle. In the Same way, if we sum up the torques around front axle we will get the equation as under

a = L * (Fb / Fg)

Fb is the weight measured on the scale under the rear axle.

Altitudinal Position

Finding Center of Mass in case of altitudinal position is a bit complicated compared to longitudinal position however the idea remains the same. There are three forces similarly however the two reaction forces are a bit different. We need to sum up every torque around a certain point and equate it zero.

Fa' * 0 + Fb' * L*cosθ - Fg * |AC| = 0

Fa' and Fb' are weights measured on scale under front and rear wheels respectively. Angle θ determines how high we have raised the axles.

By referring to the figure we can identify three triangles in red.

Distance |AB| = |DE| = (h - r) * sinθ where h is the height of center of mass and r is the radius of the wheel.

Distance |BC| = |EC| * cosθ = a * cosθ in which a is the logitudinal position estimated in earlier step.

Thus distance |AC| = |AB| + |BC| = (h - r) * sinθ + a * cosθ

Placing the result in the torques summation equation after few transformations we have

h = [(Fb'/Fg)* L - a] * cot(θ) + r

In which cot(θ) is the cotangent function and angle θ = asin(H/L) an arsin function. We can rewrite it by substituting the value of a

We know a = L * (Fb / Fg)

h becomes h = (Fb' - Fb)/Fg * L * cot(θ) + r

Where Fb'- Fb is the change in weight of rear axles after raising up the front wheels. We can use the same technique to find the torque summation around front axle.

h = (Fa - Fa')/Fg * L * cot(θ) + r

Where Fa - Fa' is the Change in weights of front axle after raising the front wheels.

Side Position

Estimating the Calculations of Side Position is as simple as finding for Longitudinal Position. Consider left wheels lie on one scale and the right wheels are on other scale. There are three different forces gravitational force Fg gravitational force acting on center of mass, reaction force FL acting on both wheels on the left, reaction force FR acting on both the right wheels.

On summing the torques around the left wheels we have the following equation

FL * 0 + FR * T - Fg * x = 0

Thus x = T * (FR / Fg)

Similarly for right wheels we have the equation as y = T * (FL / Fg)

Physicscalc.Com has got concepts like friction, acceleration due to gravity, water pressure, gravity, and many more along with their relevant calculators all one under one roof.

1. What is a Cars Center of Gravity?

A Car Center of Gravity is a theoretical point in which sum of all masses of each of its individual components effectively act.

2. How to determine the location of the center of mass of a car?

You can determine the location of center of mass of a car using our Car Center of Mass Calculator.

3. How to use Car Center of Mass Calculator?

Provide the respective inputs in the specified input section of the calculator and then click on the calculate button to know how quickly our calculator does calculations for you.