Loading a Charter Flight to the Last Kilogram
You are preparing the load sheet for a Brunei-registered twin-turboprop (MTOM 7500 kg, MLM 7200 kg, MZFM 6300 kg, MRW 7300 kg) departing a 1600 m runway. Basic empty mass is 4800 kg with an empty CG at 4.20 m aft of datum. The operator's CG envelope limits are 3.90 m to 5.60 m aft of datum at all masses. Planned fuel is 900 kg in two wing tanks with a balance arm of 4.10 m. Six passengers (85 kg each including hand baggage) are to be seated at arm 5.20 m; 400 kg of cargo is booked at arm 2.80 m. The crew (170 kg total) sits at arm 3.60 m. The dispatcher proposes adding a further 300 kg of cargo at arm 2.80 m to use spare capacity, arguing the aircraft is still below MTOM.
1. Compute the zero-fuel mass, take-off mass and take-off CG with the original 400 kg cargo. Is the aircraft inside all mass and CG limits?
Read the worked answer
Masses
- Basic empty: 4800 kg
- Crew: 170 kg
- Passengers: 6 × 85 = 510 kg
- Cargo: 400 kg
- ZFM = 4800 + 170 + 510 + 400 = 5880 kg (limit 6300 kg - clear by 420 kg)
- Fuel: 900 kg
- TOM = 5880 + 900 = 6780 kg (MTOM 7500 kg, MRW 7300 kg - clear)
Moments about datum (kg·m)
- Empty: 4800 × 4.20 = 20 160
- Crew: 170 × 3.60 = 612
- Passengers: 510 × 5.20 = 2652
- Cargo: 400 × 2.80 = 1120
- ZF moment = 24 544; ZF CG = 24 544 / 5880 = 4.174 m
- Fuel: 900 × 4.10 = 3690
- TO moment = 28 234; TO CG = 28 234 / 6780 = 4.164 m
Verdict: ZFM, TOM and CG (4.16 m, inside 3.90–5.60 m) are all within limits. The aircraft is legal, but note the CG is only 0.26 m forward of the forward limit - forward-loading margin is thin.
2. Evaluate the dispatcher's proposal to add 300 kg at arm 2.80 m. State the new masses and CG and explain the operational consequence.
Read the worked answer
New masses
- ZFM = 5880 + 300 = 6180 kg (limit 6300 kg - still legal, 120 kg margin)
- TOM = 6180 + 900 = 7080 kg (below MTOM 7500 kg)
New CG
- New ZF moment = 24 544 + (300 × 2.80) = 24 544 + 840 = 25 384
- ZF CG = 25 384 / 6180 = 4.107 m
- TO moment = 25 384 + 3690 = 29 074; TO CG = 29 074 / 7080 = 4.107 m
Consequence: The CG has moved forward to 4.11 m because the cargo arm (2.80 m) is well ahead of the current CG (4.16 m). It remains inside the 3.90 m forward limit, so the load is legal - but the forward margin is now only 0.21 m. Adding mass ahead of the CG shifts the CG toward the forward limit; if any passenger were later moved aft or fuel burned off, the CG would migrate further forward. The correct judgement is that "below MTOM" does not mean "acceptable": the dispatcher must check the CG trend, not just the total mass. A safer option is to load the extra cargo aft of the CG or confirm the forward limit is not breached after fuel burn.
3. During the flight, 500 kg of fuel is burned. Recalculate the landing mass and landing CG and state whether any limit is threatened.
Read the worked answer
Landing mass (with the 300 kg extra cargo)
- LM = 7080 − 500 = 6580 kg (MLM 7200 kg - clear)
Landing CG
- Fuel remaining = 400 kg at arm 4.10 m = 1640 kg·m
- Landing moment = ZF moment (25 384) + 1640 = 27 024
- Landing CG = 27 024 / 6580 = 4.107 m
Interpretation: Because the fuel arm (4.10 m) is almost identical to the aircraft CG (4.11 m), burning fuel barely moves the CG - it stays at 4.11 m. The forward limit is not threatened by fuel burn here; the risk would arise if fuel were carried in a tank with an arm significantly aft of the CG, in which case burn-off would drive the CG forward. The key exam point: fuel burn moves the CG away from the fuel's arm toward the remaining mass centroid, so the direction of CG travel depends on whether the fuel arm is forward or aft of the current CG. Landing mass and CG are both within limits.