Performance-limited departure with a forward CG check
A turboprop has MTOW 7,200 kg, MLW 6,800 kg, MZFW 6,200 kg and basic empty mass 4,500 kg at arm 5.0 m. CG limits are 4.7–5.7 m. The load is pilot 85 kg at 3.0 m, two front passengers 170 kg at 3.5 m, four rear passengers 340 kg at 6.0 m, baggage 200 kg at 7.0 m and fuel 1,500 kg at 5.0 m. The departure runway is 1,500 m, pressure altitude 2,000 ft, OAT 30°C, tailwind 10 kt. The performance chart gives a maximum take-off mass of 6,500 kg for these conditions. Required fuel is taxi 60 kg, trip 850 kg, contingency 5% of trip, alternate 250 kg and final reserve 300 kg. The crew wants to know whether the planned load can depart and, if not, what to change.
1. Compute the zero-fuel mass, take-off mass and CG. Are the mass and CG within limits?
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ZFW = 4,500 + 85 + 170 + 340 + 200 = 5,295 kg, below MZFW 6,200 kg. Take-off mass = 5,295 + 1,500 = 6,795 kg, below MTOW 7,200 kg but above the performance-limited mass of 6,500 kg.
Moment = (4,500×5.0) + (85×3.0) + (170×3.5) + (340×6.0) + (200×7.0) + (1,500×5.0) = 22,500 + 255 + 595 + 2,040 + 1,400 + 7,500 = 34,290 kg·m. CG = 34,290 / 6,795 = 5.05 m, inside 4.7–5.7 m. Structurally and in CG terms the load is acceptable, but it is not acceptable for the runway/weather performance limit.
2. Determine the performance-limited maximum fuel and whether the required fuel can be carried. What action is needed?
Read the worked answer
At the performance limit of 6,500 kg, maximum fuel = 6,500 − 5,295 = 1,205 kg. Required fuel = taxi 60 + trip 850 + contingency 42.5 + alternate 250 + final reserve 300 = 1,502.5 kg. The aircraft is short by 1,502.5 − 1,205 = 297.5 kg.
The crew cannot simply reduce fuel below the required figure, because that would breach fuel policy. They must reduce mass by about 298 kg (offload payload) or wait for lower OAT/less tailwind, or use a longer runway. Reducing fuel alone is not a legal option here.
3. If the crew offloads three rear passengers (255 kg) and 43 kg of baggage, compute the new ZFW, take-off mass and CG. Is the result acceptable?
Read the worked answer
New ZFW = 5,295 − 255 − 43 = 4,997 kg. Available fuel at the 6,500 kg limit = 6,500 − 4,997 = 1,503 kg, which covers the required 1,502.5 kg.
New moment = original moment − (255×6.0) − (43×7.0) = 34,290 − 1,530 − 301 = 32,459 kg·m using the original fuel mass; recomputing with 1,503 kg fuel: 32,459 + (3×5.0) ≈ 32,474 kg·m. New mass is 6,500 kg, so CG ≈ 32,474 / 6,500 = 5.00 m. This is within 4.7–5.7 m. The load is acceptable, but the CG has moved forward, so the crew should confirm the forward limit is still satisfied at landing with lower fuel.