Which limit actually stops the take-off?
A regional twin-jet has BEM 3,620 kg at 4.10 m. Crew 220 kg at 2.50 m; removable service equipment 80 kg at 3.00 m. Payload is 1,050 kg at an average arm of 5.00 m. Take-off fuel is 780 kg at 4.70 m; trip fuel 520 kg. MTOM 5,700 kg, MZFM 5,050 kg, MLM 5,350 kg. For the day's conditions the runway-limited mass is 5,620 kg, obstacle-limited mass 5,580 kg, and climb-limited mass 5,600 kg. Reserve fuel is 260 kg and must remain on board at landing. The operator wants to keep the payload and reduce fuel if possible. The crew has already checked the runway length and obstacle clearance; the figures are the approved performance-limited masses for the actual temperature, wind and pressure altitude.
1. Calculate DOM, ZFM, TOM and LM, and identify the controlling mass limit.
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DOM = BEM + crew + removable equipment = 3,620 + 220 + 80 = 3,920 kg. ZFM = DOM + payload = 3,920 + 1,050 = 4,970 kg. TOM = ZFM + take-off fuel = 4,970 + 780 = 5,750 kg. LM = TOM − trip fuel = 5,750 − 520 = 5,230 kg. Check: ZFM 4,970 ≤ MZFM 5,050; LM 5,230 ≤ MLM 5,350; TOM 5,750 > MTOM 5,700. Performance: runway 5,620, obstacle 5,580, climb 5,600, so the lowest performance limit is 5,580 kg. The controlling limit is the obstacle-limited mass of 5,580 kg, not MTOM.
2. How much must TOM be reduced, and why can the reduction not be made entirely by reducing fuel?
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Required reduction = 5,750 − 5,580 = 170 kg. Reducing fuel by 170 kg would leave 780 − 170 = 610 kg at take-off. After the 520 kg trip burn only 90 kg would remain, less than the 260 kg reserve, so fuel cannot be used for the whole reduction. Payload must be reduced by at least 170 kg (assuming no other change).
3. If 170 kg of payload is offloaded, calculate the new ZFM, TOM and LM and verify the structural limits.
Read the worked answer
Offload 170 kg payload: new payload 880 kg; ZFM = 3,920 + 880 = 4,800 kg; TOM = 4,800 + 780 = 5,580 kg; LM = 5,580 − 520 = 5,060 kg. Checks: ZFM 4,800 ≤ 5,050; TOM 5,580 ≤ MTOM 5,700 and equals the obstacle limit; LM 5,060 ≤ MLM 5,350. The flight is now limited by obstacle performance, with 250 kg ZFM margin and 290 kg landing margin.