Moment Arm and Center of Gravity

Key Definitions

• Datum: A fixed reference point chosen by the manufacturer, from which all horizontal distances (arms) are measured.
• Moment Arm (Arm): The horizontal distance from the datum to the center of gravity of a mass or item.
• Moment: The product of mass and its arm (Moment = Mass × Arm), representing the turning effect about the datum.
• Center of Gravity (CG): The point along the aircraft’s longitudinal axis where the total weight is considered to act.

Moment and Arm Explained

Each item loaded onto the aircraft creates a moment, depending on its mass and how far it is from the datum. Moments forward of the datum are negative; moments aft are positive. The sum of all moments (taking their signs into account) determines the aircraft’s overall balance.

CG Calculation

To find the center of gravity position:

1. List all masses and their arms (distances from the datum).
2. Calculate each moment (mass × arm).
3. Add all moments (positive and negative).
4. Add all masses.
5. Divide the total moment by the total mass: CG position = Total Moment / Total Mass.

Practical Example

If an aircraft has several items loaded at different arms, calculate each moment, sum them, and divide by the total mass to find the CG’s position relative to the datum. This ensures the aircraft is loaded within safe CG limits.

Operational Consequences

• CG Forward of Forward Limit: Aircraft may become nose-heavy, making rotation and flare difficult and increasing stall speed.
• CG Aft of Aft Limit: Aircraft becomes tail-heavy, reducing stability and making recovery from stalls or spins more difficult.

Where to Find Data

The aircraft's weight and balance manual provides the datum location and standard arms for all stations and compartments.