Center of Gravity Definition

Center of gravity (CG) is the point within an object where its weight is evenly balanced in all directions. Understanding its significance is important because it helps predict how an object will behave when it’s moved or supported. For example, if a box’s center of gravity is not centered, it may tip over easily. In manufacturing, design and logistics, knowing how to find center of gravity helps to create stable products, design ergonomic tools and optimize transportation for efficiency and safety.

In this article, we explore the significance of center of gravity, explain how to calculate it and discuss its practical applications where the center of gravity formula comes in handy.

Understanding Center of Gravity

Before discussing the application in different industries, we need to look into the definition of center of gravity and the factors affecting it.

What Is Center of Gravity?

The center of gravity location is the average location of all the weight of an object. The center of gravity is the balance point of an object, also expressed as the point where all the mass appears to be located.

How to Calculate Center of Gravity

Mathematically, center of gravity can be defined as the weighted average of all point masses in an object, which satisfies the following:

CG = sum(mi * ri)/sum(mi): Where ri is the position of each point mass and mi is the mass of each point mass.

What Is the Importance of Determining the Center of Gravity Location?

The center of gravity location has several unique properties:

An object in space rotates about its center of gravity.
A force applied to the center of gravity causes pure translation.

Therefore, the location of center of gravity is an essential parameter to determine the flight characteristics of an object. Controlling the flight of an object necessitates good knowledge of its center of gravity location.

For example, aligning the direction of thrust of a rocket motor so that it pushes exactly through the center of gravity of the rocket is essential to achieving a straight flight.

In the automotive industry, the center of gravity height is an essential parameter. The lower the center of gravity is, the more stability the car or truck has. This explains why SUVs have more rollover issues than cars, because they are higher off the road so their center of gravity is higher. Race cars always have a very low center of gravity. Some racing organizations limit the allowable location of the center of gravity height of race cars to keep a fair competition.

How Do You Find Center of Gravity?

Finding the center of gravity of an object is a complex task. Center of gravity is generally calculated first, using CAD models for example. But even modern tools have their limitations. The position of components such as cables cannot be accurately determined by software. The way cables are actually routed inside the object can shift its center of gravity by a significant amount. Manufacturing tolerances also create uncertainties in the location of every component of the payload. All these small errors add up to a large center of gravity uncertainty.

This accumulation of errors explains why the center of gravity of an actual object must often be measured.

How Do You Measure Center of Gravity?

Several concepts have been used to measure the center of gravity of a real object.

The simplest concept is to use a load cell system. This is the technique used in the WCG series and SE90168 production series of center of gravity measurement instruments. The object is placed on a fixed platform connected to three load cells. The weighted average of each load cell reading gives the location of the center of gravity of the object.

A different gravity center calculation concept is used where high accuracy is required. The object is placed on top of a table that is pivoted about a defined axis. The moment due to center of gravity offset of the object from the center axis is measured using a force transducer. The location of center of gravity is derived from the moment measurement by applying the following formula:

M = W x d: Where M is the moment applied, W is the weight of the object, d is the distance from the pivot point to the center of gravity of the object

This moment measurement method is used in the KSR series and SE8913 series of center of gravity measurement instruments.

Accuracy of Center of Gravity Measurement

Depending on what you are trying to do, your requirement for accuracy will vary. For example, if you want to stack books on a table, you only need to know the center of gravity within a few inches. But if you want your model airplane to fly straight, you need to know its center of gravity within a fraction of an inch. Below is a list of examples with typical accuracy requirements:

Human: 2 inches (5 cm)
Golf ball: 0.05 inch (1.25 mm)
Rocket: 0.01 inch (0.25 mm)
Spacecraft: 0.04 inch (1 mm)

Practical Applications of Center of Gravity

Center of gravity has practical applications across various industries. In the context of manufacturing, design, logistics and supply chain management, the center of gravity refers to the point at which the total weight of an object or system is considered to act.

Some examples include:

Automotive industry: In vehicle design, determining the center of gravity is important to achieve optimal balance and stability. It influences handling, cornering performance and the overall safety of vehicles. The center of gravity is normally located near the center of a car.
Aerospace industry: Proper center of gravity positioning ensures aircraft operate safely and efficiently, whether in rest or in motion. The center of gravity maintains stability and control in flight dynamics. For airplanes, the center of gravity is near the wings.
Heavy machinery: Center of gravity influences the stability and performance of equipment. When designing heavy machinery, center of gravity analysis is crucial to prevent tipping accidents and ensure operational safety.
Sports equipment: In sports like cycling, skiing and gymnastics, knowledge of how center of gravity works helps to design equipment that enhances performance and minimizes risks of falls or injuries.
Package design: In packaging industries, getting the center of gravity right in package design ensures they remain stable during handling and transportation, reducing the risk of damage and improving logistics efficiency.
Construction: When building bridges, establishing the center of gravity is crucial to keep the structure stable and prevent it from collapsing.
Supply chain management: Supply chain professionals use knowledge of the center of gravity to enhance warehouse operations, like stacking goods to maximize storage space.

Partner With Raptor Scientific for Expert Solutions

Whether you’re a manufacturing engineer, industrial designer, product developer, logistics manager or supply chain professional, understanding the concept of center of gravity is helpful for product stability, design optimization and risk mitigation. To make the process easier, center-of-measurement tools can help professionals locate products’ balance points.

Raptor Scientific is a global provider of test and measurement solutions. Our mission is to deliver precision and safety to our customers through an array of high-quality instruments and aftermarket services. To learn more, get in touch, and one of our team members will get back to you.