Mass and Balance with a Late Cargo Change
You are loading a twin-engine turboprop freighter for a 2-hour flight. The aircraft has a maximum takeoff mass of 6,800 kg, a maximum zero-fuel mass of 6,000 kg, and a maximum landing mass of 6,400 kg. The basic empty mass is 4,300 kg, and the basic empty moment places the centre of gravity at 25 percent of mean aerodynamic chord. The forward CG limit is 15 percent and the aft limit is 35 percent. The load sheet shows 800 kg of cargo in the forward hold at 2.5 m from the datum and 600 kg in the aft hold at 8.5 m from the datum. Fuel is 900 kg at 5.0 m from the datum. At the last minute, the shipper asks to move 200 kg of cargo from the forward hold to the aft hold.
1. Compute the takeoff mass, zero-fuel mass, and the CG position before and after the cargo move.
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Before the move: zero-fuel mass = basic empty mass + cargo = 4,300 + 800 + 600 = 5,700 kg, below the 6,000 kg limit. Takeoff mass = 5,700 + 900 = 6,600 kg, below the 6,800 kg limit. Landing mass is not directly given but is less than takeoff mass, so it is below 6,400 kg. Moments: basic empty moment = 4,300 x 0.25 MAC, but the datum moment is not given in metres, so work in relative terms. Cargo moment = 800 x 2.5 + 600 x 8.5 = 2,000 + 5,100 = 7,100 kg-m. Fuel moment = 900 x 5.0 = 4,500 kg-m. Total moment excluding basic empty = 11,600 kg-m. Total mass excluding basic empty = 2,300 kg. The combined CG of the load is 11,600 / 2,300 = 5.04 m. To include the basic empty, the basic empty moment must be added, but since the basic empty CG is at 25 percent MAC, the final CG must be computed with the basic empty moment. Without the basic empty moment in metres, the change can be evaluated by the shift caused by the move. After moving 200 kg from forward to aft: forward cargo = 600 kg, aft cargo = 800 kg. New cargo moment = 600 x 2.5 + 800 x 8.5 = 1,500 + 6,800 = 8,300 kg-m. The moment increases by 1,200 kg-m, and the mass is unchanged at 6,600 kg. The CG shift is 1,200 / 6,600 = 0.18 m aft. If the original CG was near the middle of the envelope, this shift is acceptable; if it was near the aft limit, it may not be.
2. Determine whether the move is acceptable and what the pilot should do if the CG moves beyond the aft limit.
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The move adds 1,200 kg-m of moment and shifts the CG aft by about 0.18 m. Whether this is acceptable depends on where the original CG sat within the 15 to 35 percent MAC envelope. If the original CG was at 25 percent MAC and the MAC is about 2 m, the shift is about 9 percent MAC, placing the CG at about 34 percent, which is just inside the aft limit but with almost no margin. If the original CG was already at 30 percent, the shift would place it at 39 percent, beyond the aft limit. An aft CG reduces static stability and can cause difficulty in stall recovery, so the pilot must not accept it. The pilot should recompute the CG precisely using the basic empty moment from the mass and balance report, and if the result exceeds the aft limit, refuse the move or redistribute cargo. The pilot may also reduce aft cargo or add forward ballast. The load sheet must be amended and signed before departure.
3. What documentation and regulatory requirements apply to the last-minute change?
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The load sheet and trim sheet must be revised to reflect the new cargo distribution, and the pilot-in-command must review and sign the revised documents before departure. The DGAC regulations require that the aircraft be loaded in accordance with the approved mass and balance manual and that the pilot verify the CG is within limits. The operator must retain the load sheet for the required period. If the cargo move changes the declared mass and balance, the pilot should also verify that the takeoff performance calculations remain valid, since an aft CG can affect rotation and takeoff distance. The shipper should be informed of the change and any delay. If the move cannot be accommodated within limits, the pilot has the authority to refuse it, and the operator should support that decision.