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Center of Gravity
The center of gravity (CG) is the point of action of the entire weight (Force) of an object. If the location of the center of gravity is exactly known, then one can balance the object on a pin point at this location. Objects in free flight will rotate about their centers of gravity if an external force is applied at any off centered location. If an external force is applied at the center of gravity, it will not cause the object to rotate.

The center of gravity location is a very important parameter in calculating the stability of an airplane. The airplane can only be stable if its neutral point falls behind the center of gravity. The location of the neutral point of the airplane can be computed using the wing's aerodynamic center location, the tail location and their moment magnitudes.

How to Use the CG Calculator
The center of gravity calculator will estimate the center of gravity of your airplane and other systems using the location and weight of discrete objects. In the calculations, it is assumed that the center of gravity of the discrete items are know and the distance from a reference location and the object's center of gravity is also known. To use the calculator please enter the following data:

Item Name:	This input is for reference only. It does not influence the calculation of the center of mass location.
Weight:	The weight of each specific item. These objects are labeled as W1, W2, W3, ...  as shown in Figure 1 below. There can be a total of ten (10) input items.
Location:	The location of each object measured from an arbitrary reference point. The reference point can conveniently be located at the airplane's nose. There can be a total of ten (10) input items.
Units:	The units of weight can be either Metric or English and can be any magnitude. However, once your units are selected, they must be the same for subsequent weight entries. The total mass of your object will be in the chosen units. Similarly, the units of location can be arbitrary. However, once a unit is chosen, it must be consistent for the entire calculation. The location of the center of gravity will be in your chosen units.

Figure 1. Diagram showing the location and weight of specific objects.

Formulas
The center of gravity can be estimated by summing the product of weights and locations (Moments) of individual masses and then dividing the sum by the sum of the weights. The distance is computed from a reference point which could be either on or off the airplane. A good reference point can be the nose of the airplane or perhaps the pilots location.

Examples

Airplane CG

The center of gravity location is needed to ensure the stability of an airplane. The center of gravity calculator can be used to determine the CG location for pre-flight checks. Here are some suggestions:

1.	Enter the weight and center of gravity location of the empty aircraft. This information is often given by the manufacturer of the airplane.
2.	Enter the weight and location of the fuel.
3.	Enter the weight and location of the pilot and each passenger.
4.	Enter the weight and location of your payload or luggage.
5.	Enter the weight and location of other items not included in the empty weight of the aircraft.
6.	Click the Calculate! button to find the Center of Gravity and flight/takeoff weight of the airplane.

Classroom Example
This example can be done by students of all grades to demonstrate the role of the center of gravity in weights location and balancing. Students will learn concepts in gravity, weights, addition, multiplication, measuring, data recording and the scientific process.

Materials: 1. Yard stick (36 inches);  2. A number of one ounces weights

Procedure:
a. Position the weights along the yard stick as shown in the diagram below. Please be sure to include the weight and center of gravity of the yard stick. Since the stick is uniform, the center of gravity will be located directly at the 18 inches point (mid stick). In the diagram the weights and distances are as follows:

Glossary

Aerodynamic Center: The aerodynamic center of the wing is the location about which the wing's moment coefficient does not vary with a change in angle of attack. The aerodynamics center is determined using MultiSurface Aerodynamics for systems of wings and control surfaces.

English Units: The English units are, pounds for weight, slugs for mass, and feet/inches for length.

External Force: A force acting on an object from the exterior.  An external force will change the linear and angular momentum of an object. In other words, it will change the objects velocity and rate of spin. 

Free Flight: Flight without the aid of onboard or remote pilot control. An example of free flight is tossing a paper airplane or glider across a room.

Gravity: Gravity is the Earth's pull. In the presence of a gravitational field an object will accelerate a towards the Earth's center. If the object is supported, then the support will experience a force known as weight. The object's weight is equal to its mass multiplied to the acceleration due to gravity.

Metric Units: The Metric units are, Newtons for weight, kilograms/grams for mass and millimeters/centimeters/meters for length.

Neutral Point: The airplane neutral point is a point along the airplane about which the rate of change of pitching moment with respect to angle of attack is zero. Therefore, the pitching moment does not vary with angle of attack about this point. The neutral point can be regarded as the aerodynamic center of the entire airplane. MultiSurface Aerodynamics can be used to perform the calculations to find the neutral point.

Stability: An airplane is stable if a nose down motion is counteracted by a nose up moment (rotation force) and a nose up motion is counteracted by a nose down moment.

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