How to Calculate CG

By Dianne Christensen

The center of gravity (CG), also referred to as the center of mass, is a point within the object where the weight of an object is concentrated and is the mean location for all the mass in the system. The object remains stable at its gravitational center. Aircraft rotate about the center of gravity, so it is important that the CG is correct so the plane does not crash during flight. Calculating the center of gravity for an object involves a mathematical equation.

Determine how much the object weighs. Make sure to calculate any added weight to the object. For example, assume a seesaw 14 feet long that weighs 40 pounds and has two people sitting on it, one weighing 50 pounds and the other 70 pounds. Both of these people are sitting 1 foot from the edge of the seesaw.

Calculate the center of gravity for each object in the example. The equation for the center of gravity is cg = center of gravity, x = distance from a reference point, and m = mass of an object is: cg = ((m1 * x1) + (m2 * x2))/ (m1 + m2). The reference point in this example is one end of the seesaw, although it can be anywhere on the seesaw. The seesaw's center is 7 feet from the reference point. Person A is 13 feet away from the reference point and Person B is 1 foot away from this point. The center of gravity for each object equals: 40 pounds x 7 feet = 280; 50 pounds x 1 foot = 50 foot-pounds; 70 pounds x 13 feet = 910 foot-pounds.

Add the sum of all the equations in Step 2, and the result is 1,240 foot-pounds. The weights added together: 40 pounds + 50 pounds + 70 pounds = 160. Divide the sum of the centers of gravity by the sum of the weights: 1,240 foot-pounds/ 160 pounds = 7.75 feet. This is the center of gravity of the seesaw from the reference point.