# Car's Center of Mass Calculator

If you give the appropriate computations in our tool, the Car Center of Mass Calculator will reveal an object's centre of gravity in a matter of seconds. Use our handy tool to estimate the position of an important vehicle parameter.

### What does it mean to have a centre of gravity?

The Center of Mass, also known as the Center of Gravity, is the one point where an object's mass is concentrated and acts as if the entire mass is concentrated at that point. When force is applied to the centre of a point, the item moves in the direction of the force. The centre of gravity can also be defined as the place where the gravity moments are balanced.

You must examine three different coordinates to find the centre of mass of a three-dimensional object, and they are as follows

- Position on a Longitudinal Scale
- Side Position
- Altitudinal Position

The location where these three coordinates connect in space is known as the centre of mass. To determine a car's centre of gravity, you'll need a few weight data in various geometries.

### How to Calculate a Car's Center of Gravity?

Certain measures must be taken to estimate a car's centre of gravity. Know how to calculate the centre of mass in three different positions, each one explained in detail.

### Longitudinal Position

Assume that both automobile axles are on the same level on a weighing scale. There is an equal and opposite reaction, according to Newton's third law. Three forces are acting on the rear axle: gravity force Fg, response force Fb, and reaction force Fa acting on the front axle.

Around that point, the total torque is zero. If force and arm length are perpendicular to one other, torque is just the product of the two. When we add up the torques around the rear axle, we get Fb * 0 + Fa * L - Fg * b = 0. Following a simple transformation. b = L * (Fa / Fg)

The scale under the front axle measures Fa, which is the weight. Similarly, if we add the torques around the front axle, we get the equation shown below. a = L * (Fb / Fg). The weight measured on the scale beneath the rear axle is referred to as Fb.

### Altitudinal Position

Finding the Center of Mass in an altitudinal position is a little more difficult than in a longitudinal position, but the concept is the same. Three forces are comparable, but the two reaction forces are not. We must add up all of the torques surrounding a specific place and equalise them. Fa' * 0 + Fb' * L*cosθ - Fg * |AC| = 0

The weights Fa' and Fb' are measured on a scale beneath the front and rear wheels, respectively. The angle defines how high the axles have been lifted. Three red triangles can be identified by referring to the diagram. Where h is the height of the centre of mass and r is the radius of the wheel, Distance |AB| = |DE| = (h - r) * sinθ Distance |BC| = |EC| * cosθ = a * cosθ, where an is the predicted longitudinal position from the previous step. As a result, the distance |AC| = |AB| + |BC| = (h - r) * sinθ + a * cosθ. After a few modifications, we have the result in the torques summation equation. h = [(Fb'/Fg)* L - a] * cot(θ) + r

θ = asin(H/L) is an arsin function, while cot() is the cotangent function. We can rewrite it by replacing the value of a with the value of a. We already know that a = L * (Fb / Fg). h becomes h = (Fb' - Fb)/Fg * L * cot(θ) + r

Where Fb'-Fb is the change in weight of the rear axles after the front wheels are raised. The torque summation around the front axle can be calculated using the same method. h = (Fa - Fa')/Fg * L * cot(θ) + r Where Fa - Fa' denotes the change in front axle weights as a result of lifting the front wheels.

### Side Position

It's as easy to calculate side position as it is to calculate longitudinal position. Consider the fact that the left wheels are on one scale and the right wheels are on another.

There are three types of gravitational forces: The gravitational force Fg acts on the centre of mass, whereas the reaction force FL acts on both wheels on the left and the response force FR acts on both wheels on the right. When the torques surrounding the left wheels are added together, we get the following equation.

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

As a result, x = T * (FR / Fg)

Similarly, the equation for right wheels is y = T * (FL / Fg).

For more concepts check out physicscalculatorpro.com to get quick answers by using this free tool.

### FAQs on Car's Centre of Mass

**1. How can you figure out where a car's centre of mass is?**

Our Car Center of Mass Calculator can help you figure out where a car's centre of mass is located.

**2. What is the Car Center of Mass Calculator and how do I use it? **

Provide the appropriate inputs in the calculator's designated input box, then press the calculate button to see how quickly our calculator performs calculations for you.

**3. What is a vehicle's centre of gravity?**

The theoretical place where the total of all the masses of each of a vehicle's constituent components effectively acts is called the centre of gravity, or CG.

**4. What are some vehicles with a high centre of gravity?**

However, larger vehicles with a higher centre of gravity, such as SUVs, vans, and school buses, are more prone to rolling over than vehicles with a lower centre of gravity.

**5. How should a car's weight be distributed? **

The optimal weight distribution is 50/50, which means the vehicle's weight is evenly distributed between the front and back axles. Truth: While most sport-oriented automobiles have weight distributions close to 50/50, proper handling requires far more than that.