Aft CG Exceedance on a Commuter Turboprop
Your company operates a twin turboprop commuter aircraft with a basic empty mass of 4,200 kg at an arm of 5.10 m. The load sheet for a 55-minute sector shows: two flight crew 170 kg at 2.60 m; forward hold 100 kg at 3.00 m; six passengers 510 kg at 7.60 m; aft hold 200 kg at 8.40 m; fuel 800 kg at 5.30 m. MTOW is 6,800 kg, MZFW 6,000 kg and MLW 6,500 kg. The certified CG envelope is 4.95 m to 5.22 m at 5,180 kg and 4.95 m to 5.25 m at 5,980 kg. The forward hold is certified to 250 kg and already contains 100 kg. The dispatcher notices the load sheet was signed without a CG check. The captain wants to depart on time and suggests burning 100 kg of fuel before take-off to solve the problem. No passengers are willing to be offloaded.
1. Calculate the zero-fuel mass, take-off mass and the CG position at both states. State whether the aircraft is within mass and CG limits.
Read the worked answer
ZFW = 4,200 + 170 + 100 + 510 + 200 = 5,180 kg. TOW = 5,180 + 800 = 5,980 kg. Both are below MZFW 6,000 kg and MTOW 6,800 kg.
Moments about the datum:
- BEM: 4,200 × 5.10 = 21,420 kg·m
- Crew: 170 × 2.60 = 442
- Forward hold: 100 × 3.00 = 300
- Passengers: 510 × 7.60 = 3,876
- Aft hold: 200 × 8.40 = 1,680
- Fuel: 800 × 5.30 = 4,240
ZFW moment = 27,718 kg·m, so CG = 27,718 / 5,180 = 5.35 m. TOW moment = 31,958 kg·m, so CG = 31,958 / 5,980 = 5.34 m. The aft limit is 5.22 m at ZFW and 5.25 m at TOW, so both states are outside the envelope by about 0.09–0.13 m. The loading is not legal.
2. The forward hold can accept only another 150 kg. How much aft-hold load can be moved, and what CG results? Is the aircraft then legal?
Read the worked answer
Only 150 kg can be moved from the aft hold (8.40 m) to the forward hold (3.00 m). Moment change = 150 × (3.00 − 8.40) = −810 kg·m.
New TOW moment = 31,958 − 810 = 31,148 kg·m; CG = 31,148 / 5,980 = 5.21 m. New ZFW moment = 27,718 − 810 = 26,908 kg·m; CG = 26,908 / 5,180 = 5.19 m. At these masses the limits are 4.95–5.22 m (ZFW) and 4.95–5.25 m (TOW), so the aircraft is now inside the envelope with about 0.03 m margin at ZFW. The forward hold is at its 250 kg limit, the remaining 50 kg stays aft, and mass limits are unchanged. A fresh load sheet and performance calculation are still required.
3. The captain proposes burning 100 kg of fuel before take-off. Evaluate this as a solution.
Read the worked answer
Fuel is at 5.30 m, forward of the current CG of about 5.34 m. Removing mass ahead of the CG moves the CG aft, not forward: new TOW = 5,880 kg, new moment = 31,958 − (100 × 5.30) = 31,428 kg·m, CG = 5.345 m. The aft-limit exceedance remains and is marginally worse. The method also assumes 100 kg can be burned on the ground without delay, may compromise trip fuel, and does not address the ZFW condition. It is not an acceptable substitute for a correct load distribution. The legal fix is to move the available 150 kg forward, or offload/move the remaining 50 kg, and re-check the CG.