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How It Works
The weight shift formula calculates how an aircraft's center of gravity (CG) moves when cargo or passengers are repositioned. It divides the moment created by the moved weight (weight times arm distance) by total airplane weight. If the CG drifts outside the aircraft's approved envelope, the plane becomes dangerously unstable.
Example Problem
A light aircraft weighs 2,400 lbs. A 150 lb bag is moved from arm station 40 to arm station 100. How far does the CG shift?
- Distance between arms: d = 100 − 40 = 60 in
- ΔCG = 150 lb × 60 in / 2,400 lb = 3.75 in aft
A shift of 3.75 inches may sound small, but it can move the CG outside the approved envelope on a small trainer.
Frequently Asked Questions
What is a weight shift calculation in aviation?
It determines how far the center of gravity moves when weight is relocated inside an aircraft. Pilots use ΔCG = Wₘ × d / Wₐ before every flight to confirm the CG stays within the manufacturer's approved limits.
Why does center of gravity matter for flight safety?
A CG that is too far forward makes the nose heavy and increases fuel consumption. A CG that is too far aft can make the aircraft uncontrollable. Most light aircraft have an allowable CG range of only a few inches, so even small weight shifts matter.
How do you calculate weight and balance for a Cessna 172?
List every item (empty weight, fuel, pilot, passengers, baggage) with its weight and arm station. Multiply each weight by its arm to get a moment, sum all moments, then divide by total weight. For a typical Cessna 172 at 2,300 lbs gross weight, the CG must fall between about 35 and 47 inches aft of datum.
What units are used in weight shift calculations?
In the US, weight is in pounds and arm distances are in inches. Internationally, newtons and meters or centimeters are common. The calculator above supports both systems with automatic unit conversion.
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