The Take-off CG Is Fine, So Why Is the Load Sheet Wrong?
Freighter Flight 903: MTOW 76 500 kg, MLW 66 000 kg, MZFW 62 500 kg, MAC 4.53 m. Aft CG limit 33.0 % MAC at all weights; forward limit 12.0 %. MAC leading edge at station 20.50 m; %MAC = (CG station − 20.50) / 4.53 × 100. DOW 38 900 kg at station 21.50 m. Loading: forward lower hold 2 600 kg at station 15.00 m; aft lower hold 3 000 kg at station 25.50 m; main deck positions 1–4 (capacity 6 000 kg) 3 000 kg at station 19.00 m; main deck positions 11–16 (capacity 15 000 kg) 15 000 kg at station 24.50 m. Take-off fuel 9 000 kg at station 21.00 m. Load control has closed the doors, the pallets are secured, and the captain presents a load sheet showing a take-off CG of 30.8 % MAC, inside the limit, and asks you to release the flight.
1. Compute the zero-fuel weight, the ZFW CG and the take-off CG. Is the load sheet correct?
Read the worked answer
Weights: 38 900 + 2 600 + 3 000 + 3 000 + 15 000 = 62 500 kg ZFW - exactly MZFW, zero margin. Take-off weight 62 500 + 9 000 = 71 500 kg.
Moments (kg·m):
| Item | Weight | Station | Moment |
|---|---|---|---|
| DOW | 38 900 | 21.50 | 836 350 |
| Fwd lower hold | 2 600 | 15.00 | 39 000 |
| Aft lower hold | 3 000 | 25.50 | 76 500 |
| Main deck 1–4 | 3 000 | 19.00 | 57 000 |
| Main deck 11–16 | 15 000 | 24.50 | 367 500 |
| ZFW total | 62 500 | 1 376 350 | |
| Fuel | 9 000 | 21.00 | 189 000 |
| TO total | 71 500 | 1 565 350 |
CGs:
- ZFW: 1 376 350 / 62 500 = 22.022 m → (22.022 − 20.50) / 4.53 = 33.6 % MAC
- Take-off: 1 565 350 / 71 500 = 21.893 m → 30.7 % MAC
The take-off figure on the load sheet is right. The ZFW CG is 0.6 % MAC (about 2.7 cm) beyond the 33.0 % aft limit, and the aircraft is simultaneously sitting exactly on MZFW. The load sheet is either wrong or incomplete, and the flight cannot be released as loaded.
2. What is the minimum change that brings the load inside the limits? Verify it, and compare it with offloading cargo.
Read the worked answer
Move, don't offload. Main deck 1–4 has 3 000 kg loaded against a 6 000 kg capacity - there is room.
Move 1 000 kg from main deck 11–16 (24.50 m) to main deck 1–4 (19.00 m):
- Δmoment = 1 000 × (19.00 − 24.50) = −5 500 kg·m
- New ZFW moment = 1 376 350 − 5 500 = 1 370 850 → CG = 21.934 m → 31.7 % MAC ✔
- ZFW unchanged at 62 500 kg (still at MZFW - the move costs no payload)
- New take-off moment = 1 559 850 / 71 500 = 21.816 m → 29.1 % MAC ✔
Compare with offloading 1 000 kg from the aft main deck: ZFW becomes 61 500 kg and the moment 1 351 850 → CG 21.981 m = 32.7 % MAC. Legal, but only 0.3 % of margin, and a tonne of revenue is gone. Offloading is inefficient precisely because it reduces the total weight as well as the moment - the CG moves less per kilogram removed than per kilogram repositioned.
Verification before signing: confirm the pallet weights are actual rather than standard, that floor loading and tie-down limits at the new position are respected, and reissue the load sheet with a fresh signature.
3. The captain argues that the take-off CG is inside the limit and that fuel can be used to trim. Why is that wrong, and what else must you check before accepting the fix?
Read the worked answer
Fuel cannot fix a ZFW CG. Zero-fuel weight and its CG are, by definition, computed with the fuel removed. Adding or burning fuel changes the take-off and in-flight CG but leaves ZFW and its CG untouched, so the violated limit remains violated. The MZFW CG limit is a structural limit - fuselage bending between the wing and the tail, main-deck floor loading - not a handling trim limit that can be traded against fuel.
Secondary points to make to the captain: an aft ZFW CG also reduces the certified static margin and alters the rotation and handling characteristics the performance data was predicated on, so the take-off performance figures and the rotation technique are not guaranteed in the out-of-limit configuration.
Checks before accepting the move:
- Weight as well as CG. ZFW is exactly at MZFW. Any late addition - a jump-seat rider, last-minute freight, catering - breaches MZFW before it breaches MTOW, so re-run both checks together and leave a deliberate margin.
- Position limits at the destination position: floor loading, contour and tie-down pattern for the pallet actually being moved.
- Actual versus standard weights for all pallets, not just the moved one.
- Reissued paperwork - the load sheet with the corrected figures, signed, and the numbers passed verbally to the crew before pushback.