Cargo Hold Loading and the Balance Arm Error
A freighter-configured aircraft (MTOM 5700 kg, MZFM 4900 kg) is being loaded. Basic empty mass 3300 kg at arm 3.00 m. Crew 150 kg at arm 2.80 m. The forward hold is at arm 2.20 m and the aft hold at arm 4.60 m. The loadmaster has 900 kg of cargo to distribute. He proposes 600 kg forward and 300 kg aft. The CG envelope is 2.60 m to 4.20 m aft of datum. Fuel of 500 kg is at arm 3.40 m. During loading, a cargo pallet is found to be 100 kg heavier than its manifest mass.
1. Compute ZFM, TOM and CG with the proposed distribution. Is the aircraft within limits?
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Masses
- ZFM = 3300 + 150 + 900 = 4350 kg (MZFM 4900 kg - clear)
- TOM = 4350 + 500 = 4850 kg (MTOM 5700 kg - clear)
Moments
- Empty: 3300 × 3.00 = 9900
- Crew: 150 × 2.80 = 420
- Cargo fwd: 600 × 2.20 = 1320
- Cargo aft: 300 × 4.60 = 1380
- ZF moment = 13 020; ZF CG = 13 020 / 4350 = 2.993 m
- Fuel: 500 × 3.40 = 1700
- TO moment = 14 720; TO CG = 14 720 / 4850 = 3.035 m
Verdict: ZFM, TOM and CG (3.04 m) are all inside limits (CG envelope 2.60–4.20 m). The load is legal. The forward-biased distribution keeps the CG near the middle of the envelope, which is a stable loading.
2. The 100 kg discrepancy is in a forward-hold pallet. Recompute the CG and assess the effect on the forward limit.
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Revised load
- Forward cargo = 600 + 100 = 700 kg at 2.20 m; aft cargo 300 kg at 4.60 m
- ZFM = 3300 + 150 + 700 + 300 = 4450 kg (MZFM 4900 kg - clear)
- TOM = 4450 + 500 = 4950 kg (MTOM 5700 kg - clear)
Moments
- Empty: 9900
- Crew: 420
- Cargo fwd: 700 × 2.20 = 1540
- Cargo aft: 300 × 4.60 = 1380
- ZF moment = 13 240; ZF CG = 13 240 / 4450 = 2.975 m
- Fuel: 1700
- TO moment = 14 940; TO CG = 14 940 / 4950 = 3.018 m
Assessment: The extra 100 kg forward moves the CG forward from 2.99 m to 2.98 m - a small change because the extra mass is close to the CG. The forward limit (2.60 m) is still clear by 0.38 m. The lesson: a manifest error near the CG has little effect, but the same 100 kg error in a hold far from the CG (e.g. the aft hold at 4.60 m) would move the CG much more. Always recompute after a discrepancy rather than assuming it is negligible.
3. Explain how the loadmaster should redistribute cargo to move the CG toward the envelope centre, and give the resulting CG.
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Objective: Move the CG toward the envelope midpoint (3.40 m) from the current 3.02 m - i.e. move cargo aft.
Proposal: Move 200 kg from the forward hold (2.20 m) to the aft hold (4.60 m). Total cargo and masses unchanged, so ZFM and TOM stay the same.
New moments
- Forward cargo: 500 × 2.20 = 1100
- Aft cargo: 500 × 4.60 = 2300
- ZF moment = 9900 + 420 + 1100 + 2300 = 13 720; ZF CG = 13 720 / 4450 = 3.083 m
- Fuel: 1700
- TO moment = 15 420; TO CG = 15 420 / 4950 = 3.115 m
Assessment: The CG moves aft to 3.12 m, closer to the midpoint, improving the stability margin in both directions. Moving a further 200 kg aft would push the CG to about 3.21 m - still well inside the 4.20 m aft limit. The loadmaster should balance the holds so the CG sits near the centre, giving equal margin to both limits and making the aircraft tolerant of last-minute changes.