Aft CG Limit After Last-Minute Cargo
A twin turboprop is being loaded for a 2-hour sector. Basic empty mass is 9,200 kg at arm 6.80 m. Crew are 2 × 80 kg at 3.50 m. Thirty passengers average 85 kg at 8.00 m. Cargo is 400 kg at 4.00 m and 250 kg at 11.50 m. Fuel is 1,800 kg at 7.30 m. The aft CG limit for take-off is 7.00 m; the forward limit is 6.20 m; maximum take-off mass is 15,000 kg. At the last minute, a courier delivers 120 kg that must travel in the aft hold at 11.50 m. The dispatcher asks whether the load is acceptable and, if not, what to move or offload before departure.
1. Calculate the zero-fuel mass, take-off mass, total moment and CG without the courier cargo, and state whether the aircraft is within limits.
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| Item | Mass kg | Arm m | Moment kg·m |
|---|---|---|---|
| Basic empty | 9,200 | 6.80 | 62,560 |
| Crew | 160 | 3.50 | 560 |
| Passengers | 2,550 | 8.00 | 20,400 |
| Cargo fwd | 400 | 4.00 | 1,600 |
| Cargo aft | 250 | 11.50 | 2,875 |
| Fuel | 1,800 | 7.30 | 13,140 |
| Total | 14,360 | 101,135 |
CG = 101,135 / 14,360 = 7.043 m. Mass is below 15,000 kg, but the CG is 0.043 m aft of the 7.00 m aft limit. The load is not acceptable as loaded.
2. If the 120 kg courier cargo must travel, calculate the effect of putting it in the aft hold at 11.50 m and propose a workable solution.
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Adding 120 kg at 11.50 m gives:
- New mass = 14,360 + 120 = 14,480 kg.
- New moment = 101,135 + (120 × 11.50) = 102,575 kg·m.
- New CG = 102,575 / 14,480 = 7.085 m, worse and still outside the aft limit.
Move 120 kg of existing aft cargo from 11.50 m to the forward hold at 4.00 m. Moment change = −120 × (11.50 − 4.00) = −900 kg·m. New moment = 101,675 kg·m; CG = 101,675 / 14,480 = 7.022 m, still slightly outside. Therefore move more, or offload. Moving about 162 kg from aft to forward gives CG ≈ 7.00 m: solve (102,575 − 7.5x) / 14,480 = 7.00, giving x ≈ 161 kg. Offloading 120 kg from the aft hold alone would leave the CG near 7.005 m, so it is not sufficient.
3. What is the operational decision if the courier cargo cannot be moved to the forward hold?
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If the 120 kg must remain at 11.50 m and no compensating forward load can be moved, the aircraft cannot depart at that CG. Offload at least about 140 kg from the aft hold, or reduce aft cargo and reload forward. Recompute the load sheet after any change and confirm both the mass and CG limits. Do not accept a take-off with the CG 0.085 m aft of limit; the aft limit protects pitch control and stall recovery, and a small exceedance can matter at low speed or with icing. The dispatcher should issue a revised load sheet before departure.