Weight and balance with a last-minute load change
A turboprop is being loaded for a 3 h sector. Basic empty mass is 9 800 kg at a moment of 24 500 kg m. The forward and aft CG limits at take-off mass are 4.2 m and 5.0 m from the datum. Load: 12 passengers at 84 kg each in rows 2 to 5 (arm 5.6 m), 400 kg of freight in the forward hold (arm 3.1 m) and 250 kg in the aft hold (arm 8.4 m). Fuel is 1 200 kg at an arm of 5.0 m. At the last minute, 200 kg of freight is moved from the forward hold to the aft hold, and two passengers are moved from row 2 to the last row (arm 7.2 m).
1. Compute the take-off CG before and after the change and state whether the aircraft remains within limits.
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Before change: passengers 12 x 84 = 1 008 kg at 5.6 m gives 5 645 kg m; forward freight 400 x 3.1 = 1 240; aft freight 250 x 8.4 = 2 100; fuel 1 200 x 5.0 = 6 000. Total mass = 9 800 + 1 008 + 400 + 250 + 1 200 = 12 658 kg. Total moment = 24 500 + 5 645 + 1 240 + 2 100 + 6 000 = 39 485 kg m. CG = 39 485 / 12 658 = 3.12 m, which is forward of the 4.2 m limit.
After change: 200 kg moves from 3.1 m to 8.4 m, adding 200 x 5.3 = 1 060 kg m; two passengers (168 kg) move from 5.6 m to 7.2 m, adding 168 x 1.6 = 269 kg m. New moment = 39 485 + 1 060 + 269 = 40 814 kg m; mass unchanged at 12 658 kg; CG = 3.22 m. Still forward of the limit. The aircraft is not within limits; ballast or a load redistribution is needed.
2. What operational action resolves the forward CG, and what checks confirm it?
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Move freight aft or add ballast in the aft hold, then recompute. Moving 300 kg from the forward hold to the aft hold adds 300 x 5.3 = 1 590 kg m, giving CG = (40 814 + 1 590) / 12 658 = 3.35 m, still short. A larger redistribution or ballast is needed, and the load sheet must be reissued. Confirm the zero-fuel mass and CG, the take-off mass and CG, and the landing mass and CG against the envelope; check that the aft limit is not exceeded. The commander signs the final load sheet, and any change after signing requires a new sheet.