Load Sheet With an Aft CG Exceedance
Your twin-turboprop is being loaded at Kuwait International for a 2 h 15 min flight. MTOM is 5,700 kg, MLM 5,400 kg and MZFM 5,100 kg; the CG envelope is 4.10 m to 4.25 m aft of the datum. Basic empty mass is 3,600 kg at 4.10 m. Two pilots, 80 kg each, occupy seats at 2.40 m. Four passengers are seated: two at 90 kg in seats at 5.20 m and two at 75 kg in seats at 5.60 m. All 120 kg of baggage is in the aft hold at 6.30 m; a nose hold at 1.80 m is available but empty. Fuel is 800 kg at 4.60 m, and planned trip fuel is 450 kg. The load sheet is being signed by the commander. The ground engineer says the aircraft is 'well under MTOM, so the CG must be fine'.
1. Calculate the takeoff mass, takeoff CG, zero-fuel mass and zero-fuel CG. State whether each limit is met.
Read the worked answer
Moment = mass × arm.
| Item | Mass (kg) | Arm (m) | Moment (kg·m) |
|---|---|---|---|
| BEM | 3,600 | 4.10 | 14,760 |
| Pilots | 160 | 2.40 | 384 |
| Passengers | 180 | 5.20 | 936 |
| Passengers | 150 | 5.60 | 840 |
| Baggage | 120 | 6.30 | 756 |
| Fuel | 800 | 4.60 | 3,680 |
| Takeoff | 5,010 | 4.263 | 21,356 |
Takeoff mass 5,010 kg is below MTOM 5,700 kg and MLM 5,400 kg. But takeoff CG 21,356 ÷ 5,010 = 4.263 m, which is 13 mm aft of the 4.25 m aft limit. The aircraft is not within the takeoff CG envelope.
Zero-fuel mass = 5,010 − 800 = 4,210 kg, below MZFM 5,100 kg. Zero-fuel moment = 21,356 − 3,680 = 17,676 kg·m; CG = 17,676 ÷ 4,210 = 4.198 m, inside the forward limit of 4.10 m. So mass limits are satisfied, but the aft CG limit is exceeded at takeoff.
2. Is the engineer's statement correct? If not, propose a practical load change and verify that it brings both takeoff and zero-fuel CG inside the envelope.
Read the worked answer
No. Being under MTOM says nothing about CG. The problem is the 120 kg of baggage all loaded at 6.30 m. Moving 40 kg of baggage to the nose hold at 1.80 m changes the moment by 40 × (1.80 − 6.30) = −180 kg·m.
New takeoff moment = 21,356 − 180 = 21,176 kg·m; CG = 21,176 ÷ 5,010 = 4.227 m, inside 4.10–4.25 m. New zero-fuel moment = 17,676 − 180 = 17,496 kg·m; CG = 17,496 ÷ 4,210 = 4.156 m, also inside. Mass is unchanged at 5,010 kg.
Check landing: 5,010 − 450 = 4,560 kg with 350 kg fuel remaining. Landing moment = 17,496 + 350 × 4.60 = 19,106 kg·m; CG = 19,106 ÷ 4,560 = 4.190 m. The revised load is within all limits. Simply offloading 40 kg from the aft hold is less effective: mass becomes 4,970 kg and CG 21,104 ÷ 4,970 = 4.246 m, only just inside and with less payload.