Definition
An algebraic relationship used in aircraft weight and balance calculations to determine how much weight must be moved between two stations to produce a desired shift in the center of gravity (CG). The formula is expressed as: Weight to be shifted / Total weight = Distance CG moves / Distance between arms. Rearranging this equation allows the pilot to solve for any one unknown when the other three values are known.
Plain English
A simple ratio that tells you how much weight to move from one spot in the aircraft to another to get the balance point where you want it. The fraction of total weight you shift equals the fraction of the distance between the two spots that the balance point will move.
Context Anchor
Used during weight-and-balance calculations when a pilot, instructor, or mechanic needs to predict the effect of moving passengers, baggage, or equipment to a different location in the aircraft.
Derivation
Proportion comes from a Latin idea meaning “according to share.” That fits this formula because it compares two shares: the share of total aircraft weight being moved, and the share of movement passed on to the aircraft's balance point.
Why Pilots Care
Keeps the center of gravity inside certified limits after any weight movement, preserving stability, control feel, and stall recovery margins.
Analogy
Think of a seesaw with two people on it. If you want the balance point to shift halfway toward one end, you move half the total weight that direction. The formula is just the math version of that intuition.
Grounding Statement
If a 100-pound bag is moved 10 inches in a 2,000-pound airplane, the airplane's balance point does not move 10 inches; it moves only a small fraction of that distance.
Intuition Check
Do not assume the aircraft's balance point moves the same distance as the item you move. It moves in proportion to how much of the total aircraft weight was shifted.
Example Sentence 1
Using the shifting weight proportion formula, the pilot calculated that moving 50 pounds of baggage from the aft compartment to the forward compartment would bring the CG back within limits.
Example Sentence 2
Before sliding the cargo pallet forward, the crew used the shifting weight proportion formula to verify the new CG remained within limits.