Loading calculations

031 Mass & BalanceChapter 6

Loading problems reduce to moments and the load shift formula. Master one method and apply it to shift, transfer, add, and remove scenarios.

Moment method

Formula — New total moment

New total moment = Old total moment ± load moment change

Load moment = Mass × Arm (sign per datum convention)

Key fact

After updating total mass and total moment, recalculate CG = total moment ÷ total mass. For index-based load sheets, apply the same logic with scaled indexes.

Load shift / transfer

When mass m moves distance D between compartments, the CG shifts by d:

Formula — Load shift (transfer between compartments)

d ÷ D = m ÷ M

M = total aircraft mass (before or after — use consistently)
m = mass moved
D = distance between compartment stations
d = distance CG moves (same direction as mass movement)

Key fact

CG moves toward the added mass and away from removed mass. If 100 kg moves aft 5 m, CG moves aft by d = (m/M) × D.

Load addition / removal

Formula — Load addition or removal

d ÷ D = m ÷ M

Addition:  M = new total mass (old mass + m)
Removal:   M = old total mass (before removal)
m = mass added or removed
D = distance from compartment station to CG (old or new — see scenario)
d = CG shift

Key fact

Addition — use new mass as M if known; D from load station to old CG (or as specified in manual). Removal — use old mass as M; D from station to old CG.

Worked logic (no numbers)

Key fact

1. Identify m, M, and D from the load sheet stations.
2. Calculate d = (m/M) × D.
3. Apply d in the direction of mass movement (add aft → CG moves aft).
4. Verify CG remains within envelope at current mass.

Load sheet distribution

Key fact

To distribute mass using a load sheet: measure CG change from old to new position; compare arm lengths to cargo compartment stations; add compartment values and divide as per manual procedure (often averaging four corner loads for pallets).

Cargo types

Definition — Palletised cargo

Individual or multiple items on standard pallets, secured with nets and straps.

Definition — Containerised cargo

Standard-size containers lock into cargo bays — each has its own manifest. Normal checked baggage often containerised.

Definition — Bulk cargo

Loose items: late/rush baggage, last-minute bags, cabin crew baggage — held in bulk compartments without containers.

Key fact

Passenger personal belongings should be placed as baggage in approved containers where required. Floor load and running load limits must be checked for all cargo.

Last-minute changes

Key fact

Acceptable last-minute changes must be documented on the load sheet and within LMC limits. Exceeded baggage mass must be determined by actual weighing or additional mass increments — not standard masses alone.

Exam trap

d/D = m/M — students invert it. CG shift d is proportional to mass moved m and inversely proportional to total mass M. Double the aircraft mass → half the CG shift for the same load move.

Exam trap

For load transfer, D is the distance between compartments, not to the CG. For add/remove, D is from the load station to the CG (old or new depending on case).

Exam trap

When fuel index is not given, use the next highest index — conservative, keeps CG within limits.