Weight and Balance Equation (WxA=M)

WAM: Weight and Balance Equations

Weight and balance is major performance consideration because it can significantly change how an airplane flies. Pilots should understand how performance will change with weight and different CG locations, and be able to confidently calculate weight and balance.

Lesson Notes

Weight relates to performance because the heavier an airplane is, the more lift is required to get and keep it airborne. Because accelerating to a faster takeoff speed requires more time and distance, we require more runway when our airplane is heavier. This means we can’t take off as soon, and can’t climb over obstacles as easily.

Balance relates to performance because if our airplane is not balanced it may be completely unstable to the point where a pilot can’t even do anything to keep it flying. Furthermore, as you’ll see in the next lesson, the balance of the airplane can cause the airplane to require aerodynamic forces that effectively make it lighter or heavier.

Weight x Arm = Moment

In plain English, the weight of something (equipment, passenger, baggage) multiplied its distance from a standard reference line tells us how much effect that weight will have.

When we run a weight and balance equation we need to find (1) total weight of the payload and fuel (e.g. people, bags, fuel, oil, etc.) and (2) the total moment of all payload items. Then we can divide the total moment by the total weight to find the average arm, which is also known as the center of gravity (CG).

Generally, weight and balance information will either be displayed in tables or in graphs:

Graphs
When weight and balance information is displayed in a graph, the user starts with the weight of an item and follows the corresponding line on the graph until reaching the corresponding weight on the vertical axis. Then, they go straight down to the horizontal axis which lists the corresponding moment.

Tables
Weight and balance tables usually give the user arm information for a variety of passenger and baggage locations, as well as fuel and oil. Multiplying the arm by the corresponding weight will give the moment for each passenger, bag, and so forth.

Units
Weight is usually measured in pounds (lbs) and moment in inches (in). Moment, remember, is weight multiplied by arm, so moment is measured in lb-inches. In order to make moment numbers seem smaller and more reasonable, many manuals divide moment by 1,000 or 100. When this is done 20,000 lb-inches (the moment of, say, a 200 lb person at 100 inches), is written as 20 lb-inches/1000 or 200 lb-inches/100. Ironically, many people find this more complicated than simply dealing with larger numbers. Find a system that works for you.

Practice Questions

Additional Resources

Performance

W&B Graph

W&B Table 1

W&B Table 2