CG Shift from Fuel Burn

Find the new center of gravity after burning a mass of fuel located at a known station.

InputCG₁ = (W₀·CG₀ − W_f·CG_f) / (W₀ − W_f)

Initial gross weight (kg)or enter lb — converts to kgInitial CG station (m)or enter in — converts to mFuel burned (kg)or enter lb — converts to kgFuel station (m)or enter in — converts to m

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The engineering

Weight and balance is bookkeeping on moments: every mass contributes weight times its arm from a reference datum, and the CG is the total moment divided by total weight. Burning fuel removes a moment at the fuel's station, so the aircraft CG walks away from that station — burn from a forward tank and the CG moves aft, burn from an aft tank and it moves forward.

The sanity check: if the fuel is burned from a station ahead of the current CG, the CG must move aft, and vice versa. Watch your datum sign convention — stations are usually positive aft of the datum, but keep CG₀ and CG_f in the same frame or the arithmetic silently lies. Real airplanes manage burn sequence specifically to keep the CG inside the certified envelope through the whole flight.

Where this math comes from

Weight-and-balance moment accounting is as old as heavier-than-air flight — the Wrights trimmed with movable ballast — but the tabular station-and-arm method engineers still use was formalized as aircraft grew large enough that a full fuel load could shift the CG by feet, not inches. Daniel Raymer's Aircraft Design: A Conceptual Approach codified the modern conceptual-design treatment of CG travel and fuel-burn effects for a generation of students.

The consequence of ignoring it is unforgiving: an out-of-envelope CG at the end of a long cruise can leave insufficient elevator authority to flare. Fuel management schedules — transferring between tanks or scheduling burn order — exist precisely to keep the moment sum inside limits from takeoff to landing.

1903Wright BrothersTrim the Flyer with movable ballast, an early CG-management practice.
1926U.S. Air Commerce ActIntroduces loading and balance requirements into airworthiness rules.
1992Daniel RaymerPublishes Aircraft Design: A Conceptual Approach, standardizing CG-travel and fuel-burn analysis in design education.

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