The Temperature Rose at a Hot-and-High Departure
A twin-engine jet is scheduled to depart from an aerodrome at elevation 1 500 ft, runway 2 400 m dry, 0.5 % uphill, wind calm. The obstacle-limited take-off weight table in the operator's airport analysis is published for 1 500 ft pressure altitude and gives 66 800 kg at 29 C, 65 300 kg at 32 C and 63 900 kg at 35 C. The correction for pressure altitude above the table value is about 220 kg per 100 ft. One hour before departure the ATIS gave 29 C and QNH 1013, and the crew computed a planned TOW of 65 900 kg and a reduced-thrust setting. The current ATIS gives 32 C and QNH 1005. The AFM gives a gross second-segment gradient of 3.0 % at 65 900 kg and 32 C; the net-to-gross reduction for a twin is 0.8 %; the departure procedure requires a net 2.4 % to clear an obstacle 1 800 m from the end of TODA.
1. Calculate the current pressure altitude and ISA deviation, determine the maximum take-off weight now available, and state the reduction from the planned 65 900 kg.
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Pressure altitude 30 ft per hPa below 1013: 1 500 + (1013 - 1005) x 30 = 1 500 + 240 = 1 740 ft.
ISA deviation ISA at 1 740 ft = 15 - 1.98 x 1.74 = about 11.6 C; OAT 32 C, so ISA +20.4 C.
Weight
- The table is valid at 1 500 ft pressure altitude, so there are 240 ft to correct for: 2.4 x 220 = about 530 kg penalty.
- At 32 C the table gives 65 300 kg; corrected: 65 300 - 530 = about 64 770 kg.
- Planned TOW 65 900 kg exceeds this by about 1 130 kg.
Reduce the take-off weight by at least 1 150 kg to leave a margin. Because the table is already obstacle-limited, the second-segment check is embedded in it, but the gradient should still be verified at the new weight (next question). The reduced-thrust setting computed for 29 C is now invalid and must be recomputed against 32 C, or full thrust used.
2. Compute the net second-segment gradient and explain what 'net' means and where the segment starts and ends.
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Calculation Net = gross - net-to-gross reduction = 3.0 - 0.8 = 2.2 %, against a required 2.4 %. That is a 0.2 % gradient shortfall, so even before the temperature change the take-off does not clear the obstacle - and the 3.0 % figure was already at 65 900 kg and 32 C, above the corrected limit.
What the numbers mean
- The gross gradient is the AFM demonstrated performance in the certification configuration: gear up, take-off flap, one engine inoperative, V2, and on the flight path.
- The net gradient is the gross gradient reduced by a fixed penalty (typically 0.8 % for twins, 0.9 % for three-engine, 1.0 % for four-engine types) to allow for pilot technique, turbulence and engine deterioration. The net flight path is the one that must clear all obstacles by the required margin.
- The second segment runs from 35 ft above the runway surface at V2 (the end of the first segment) to at least 400 ft above the runway, gear up, take-off flap, one engine inoperative. At 400 ft the aircraft enters the acceleration segment.
The obstacle at 1 800 m may fall in the second or third segment, so the full take-off flight path, not just the second segment, has to be checked after any weight change.
3. Rank the available options for fixing the problem and identify the trap in each.
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Best first option - reduce weight. Reliable and directly improves both the field length and every climb segment. Cost is payload or fuel, and the whole computation (take-off run, accelerate-stop, all segments, obstacle) must be redone, not just the table entry.
Second - wait for a cooler time of day. This is a density-altitude problem: the ISA deviation of +20.4 C is doing most of the damage. The cost is schedule and duty time, and the crew must not simply wait without re-planning fuel and FDP.
Third - different runway or into-wind runway. A headwind improves all segments; a different runway may have a lower obstacle or a downslope. Trap: an apparently 'better' runway may have a different obstacle or a shorter TODA - recompute.
Fourth - bleed configuration, flap setting, thrust.
- Air-conditioning bleeds off gives thrust but must be per the AFM and consistent for the whole flight.
- A smaller take-off flap improves the second segment but lengthens the field length and can worsen the acceleration segment and obstacle clearance; it needs a full new computation, not a gradient-only check.
- Reduced thrust is the trap here: the assumed temperature was computed at 29 C. Using it at 32 C, QNH 1005, with an obstacle-limited case may exceed the permitted thrust reduction. Recompute, or use full thrust.