Follow fuel through the balance envelope

Why can burning fuel move CG aft?

Fuel has a location as well as a mass.

Remove fuel at its tank arm

For a tank of approximately fixed arm, burning fuel removes mass and moment at that arm. Burning fuel aft of the current CG moves the remaining CG forward; burning fuel forward of it moves CG aft. The aircraft does not automatically move towards the nose as fuel is consumed.

The tank’s effective arm can itself vary with quantity and attitude. Use the manufacturer’s fuel moment or index tables where supplied; a constant-arm model is a teaching simplification.

Check the path, not just the amount

Tank-use order and transfers determine the CG trajectory. A transfer at constant total mass follows the redistribution equation, while fuel consumption follows removal. Applying one formula to the other gives a wrong result.

Do not replace total fuel with usable fuel inconsistently. Unusable fuel is included in a defined baseline where the aircraft documentation specifies it; the loading calculation must use the same convention.

Understand a changing trajectory

With one constant-arm tank, removing a kilogram always removes the same moment. The CG shift per kilogram is not constant, because the remaining total mass and the separation between tank arm and current CG change. The final mass/CG relationship is a ratio, rather than a straight-line interpolation of CG against fuel quantity.

With two tanks on opposite sides of the dry CG, consuming one tank first can move the CG one way and consuming the other can reverse that movement. An intermediate condition may therefore be more limiting than either endpoint. The laboratory isolates one tank so that this mechanism is visible; a real multi-tank calculation must preserve each tank’s quantity, effective moment and approved use sequence instead of averaging all fuel at one convenient arm.

How can the same uplift volume produce a different loading result?

Fuel volume becomes mass only after applying the correct density and units.

Density connects volume and mass

Mass = volume × density. With 4,000 L and 0.80 kg/L, uplift is 3,200 kg. With a different measured density, the same litres produce a different mass and moment. A constant assumed conversion can hide a mass error even when the fuel gauge volume looks right.

Account for usable capacity, uplift measurement, existing fuel and any prescribed temperature correction. Do not mix US gallons, imperial gallons and litres; the volume units are different.

Transfer versus consumption

Moving 500 kg from a 10 m tank to an 18 m tank adds 4,000 kg·m of moment without changing aircraft mass. At 20,000 kg total, CG moves 0.2 m aft. Fuel pump operation must follow the approved sequence, because a correct final CG does not guarantee a safe intermediate state.

For each phase, update mass and moment from the same tank quantities. A landing mass from one fuel plan and a landing index from another are inconsistent inputs.

Use the delivered mass, not an attractive volume

Litres describe space occupied; kilograms describe inertia and the quantity used in a mass limitation. Density bridges the two. A litre of warmer fuel can have a different mass from a litre of colder fuel of the same grade. Use the measured or otherwise authorised density and the documentation’s temperature convention rather than assuming that every uplift litre has a universal mass.

A transfer changes the balance without making fuel available that was not already on board. In the moment ledger, subtract transferred mass at the source tank arm and add the same mass at the receiving tank arm. The two mass entries cancel, while their moments generally do not. Consumption instead has only the removal entry. Keeping the two operations distinct makes a complex fuel schedule easier to audit.

Can you explain and apply the mechanism?

Four original questions. Work from the stated facts, then compare your reasoning with the explanation.