Load-sheet last-minute change and fuel density
A twin-jet has DOW 42,300 kg at arm 17.90 m. MZFW is 62,700 kg, MTOW 79,000 kg, MLW 68,000 kg, and the certified CG range is 16.60 m to 18.20 m. The load sheet shows 120 passengers at 84 kg in the forward cabin (arm 16.80 m), 56 passengers at 84 kg in the aft cabin (arm 22.20 m), 2,000 kg in the forward cargo hold (arm 12.50 m), 1,200 kg in the aft hold (arm 24.50 m), and 11,500 kg of fuel at arm 17.80 m. After the sheet is signed, the load controller moves 30 passengers from the forward to the aft cabin and moves 800 kg of cargo from the forward to the aft hold. The refueller's slip shows 14,500 litres at density 0.79 kg/L. The crew must decide whether to accept the load sheet, what correction is needed, and whether the fuel figure is acceptable.
1. Calculate the CG before and after the last-minute change and determine whether the load sheet is acceptable.
Read the worked answer
Before the last-minute change: total mass = 42,300 + 10,080 + 4,704 + 2,000 + 1,200 + 11,500 = 71,784 kg. Moment = 757,170 + 169,344 + 104,429 + 25,000 + 29,400 + 204,700 = 1,290,043 kg·m. CG = 1,290,043 / 71,784 = 17.97 m, inside 16.60–18.20 m. ZFW = 60,284 kg, below MZFW 62,700 kg; TOW is below MTOW.
After the move: 30 passengers = 2,520 kg shifted aft by 5.40 m = +13,608 kg·m; 800 kg cargo shifted aft by 12.00 m = +9,600 kg·m. Total moment = 1,313,251 kg·m. CG = 1,313,251 / 71,784 = 18.29 m. That is 0.09 m beyond the aft limit, so the load sheet is not acceptable.
2. What correction would you make, and how should it be controlled?
Read the worked answer
Move 600 kg of cargo from the aft hold back to the forward hold: 600 × 12.00 = 7,200 kg·m forward, giving moment 1,306,051 kg·m and CG 18.19 m, inside the limit. Moving four passengers forward would shift only 4 × 84 × 5.40 = 1,814 kg·m, not enough. The correction must be reflected in a new load sheet or an approved last-minute-change entry, with the CG rechecked; the ZFW and TOW do not change because only mass is moved. An aft CG beyond the limit reduces static stability and can affect rotation, stall recovery and trim, so “close enough” is not acceptable. If the cargo cannot be moved, offload or add forward ballast.
3. The fuel slip shows 14,500 litres at 0.79 kg/L. Is the fuel figure acceptable, and how should it be reconciled?
Read the worked answer
14,500 L × 0.79 kg/L = 11,455 kg, which is 45 kg less than the 11,500 kg on the load sheet. The mass change is small (about 0.06% of TOW) and the CG change is negligible, but the load sheet and endurance figures should use the actual fuel mass. If the density were 0.785, the fuel would be 11,383 kg, 117 kg less. Using a standard 0.80 density would give 11,600 kg and overstate the fuel by 145 kg. Check the refueller's density against the operator's procedure and the aircraft fuel-quantity indication; if the difference is outside tolerance, correct the load sheet. Do not simply accept the litre figure as a mass figure.