## Center of Gravity

**CENTER OF GRAVITY**

Definiton - Center of Gravity

The center of gravity (CG) 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.

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

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 is Center of Gravity Determined?

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.

Measuring 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 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 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 and SE8913 series of center of gravity measurement instruments.

Accuracy

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)