With the importance of center of gravity (CG) location and some of the attached myths explained (Pacific Flyer March and April, 2007), it is time to unravel the calculations used to determine this vital statistic. As I stated in the opening article, the calculation is often performed more through rote memory than active understanding.
The CG is the fulcrum of the aircraft, its balance point, so one avenue would be to take a car jack out on the ramp and experiment until the precise teeter-totter location is found. It is best to do this with someone else’s plane.
A slightly less direct approach would be to weigh the airplane on a set of three scales, one for each wheel, then compute where the total weight is concentrated. This nuts-and-bolts process is the starting point of all weight and balance data.
As you add and subtract weight after that initial measurement, it is more common to use math rather than direct experimentation to keep track of CG location. This process must begin with a definition of terms.
WEIGHT is fairly obvious: the downward force created by the attraction of gravity, usually measured in pounds.
ARM: the distance of an object, or weight, from a pivot point, usually measured in inches.
MOMENT: a twisting or rotational force exerted around a pivot point. Unlike weight and arm, which are simple measurements, moment requires a computation: weight multiplied by arm. The product is usually expressed in inch/pounds or foot/pounds.
BALANCE: the concept of equal moments on either side of a pivot point.
MOMENT—THE CONCEPT
Of all of these, “moment” is the least intuitively understood. To start with, it is tied to “leverage” and “torque” and other commonly misunderstood words. Then there is the fact that moment is a mathematic abstraction: what exactly is an inch/pound?
Finally, and most important: moment, unlike weight, is not a constant.
The moment exerted by a given weight changes with its distance (“arm”) from the point around which it is trying to pivot. You can demonstrate this reality with a simple experiment.
Start by stretching out your right arm, parallel to the ground. Next, continuing to hold your arm level, press down gently on your right elbow with your left hand, trying to twist your arm around its pivot point, your right shoulder. As you do this, pay some attention to the amount of pressure you exert on your elbow.
Next, press down with the same pressure on your right wrist. It will be obvious that it is harder to resist the same downward pressure: the moment (twisting force) has increased as the “arm” lengthened.
MOMENT—THE NUMBER
It is convenient that moment, can be expressed mathematically by multiplying “arm” times “weight.” Using this formula, we can determine that a five pound weight placed one foot from your shoulder has a downward twisting force of five foot/pounds. After that, the progression is quite basic: as you double the distance, the moment also doubles, so that the same five pounds placed near your wrist has double the twisting force: two feet multiplied by five pounds, or a moment of ten foot/pounds.
Objects balance at the point (CG) where the moments on each side are equal. Without the use of scales, the ability to assign a numeric value to moment provides an essential tool for computing that location. As an example, if two objects, one ten pounds and the other five, are placed on a three foot long board, the board can be predicted to balance one foot from the center of the ten pound weight, or two feet from the five pounder. In both cases, computation of moment around that point produces the same value: ten foot/pounds. For convenience, this example assumes the board weighs nothing.
This ability to compute the balance point is crucial. You should look at the problem this way: we started with two separate objects whose combined weight was fifteen pounds. We now know where a single “phantom” object with the same mass would have to be located to create the same balance point.
Next month, the rest of the puzzle: how the concept of “datum” resolves the trickiest part of balance computations.
