Hot-and-high take-off with a slot delay
A twin turboprop with MTOM 22,000 kg, MLM 21,300 kg and MZFM 20,400 kg is planned from a 2,300 m runway at an elevation of 5,900 ft. QNH is 1022 hPa, OAT is 32°C and the wind is calm. Basic operating mass is 13,600 kg and the booked traffic load is 6,900 kg. Fuel planned is taxi 60 kg, trip 1,450 kg, contingency 90 kg, alternate 320 kg and final reserve 400 kg, so take-off fuel will be 2,260 kg. The AFM data (masses in kg) give a field-length-limited take-off mass of 22,100, an obstacle-limited mass of 22,050 and a WAT (climb-limited) mass of 21,900 at 32°C, decreasing by 105 kg for each 1°C above 32°C. Pressure altitude may be taken as elevation plus 30 ft for each hPa by which QNH exceeds 1013.
1. Determine the pressure altitude and the limiting take-off mass, and show how each limit was checked.
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Pressure altitude: QNH is 9 hPa above 1013, so pressure altitude is higher than elevation:
PA = 5,900 + (30 × 9) = 5,900 + 270 = 6,170 ft.
That is a useful sanity check: a high QNH costs performance here, and the AFM figures quoted are for this pressure altitude.
Limiting take-off mass - take the lowest of every applicable limit:
| Limit | Mass (kg) |
|---|---|
| Structural MTOM | 22,000 |
| Field length | 22,100 |
| Obstacle | 22,050 |
| WAT (climb) at 32°C | 21,900 |
So the limiting take-off mass is 21,900 kg, set by climb performance, not by the runway.
Now test the planned figures: ZFW = 13,600 + 6,900 = 20,500 kg, which already exceeds the MZFM of 20,400 kg by 100 kg; TOW = 20,500 + 2,260 = 22,760 kg, which exceeds MTOM by 760 kg and the WAT limit by 860 kg. So the flight as loaded is illegal on two counts, and the WAT limit is the binding one.
2. Calculate the maximum traffic load that may be carried and state exactly what you would offload.
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Work backwards from the limiting mass:
- Maximum take-off mass = 21,900 kg.
- Take-off fuel = 2,260 kg, so maximum zero-fuel mass permitted by performance = 21,900 − 2,260 = 19,640 kg.
- This is below the MZFM of 20,400 kg, so the performance limit governs.
- Maximum traffic load = 19,640 − 13,600 = 6,040 kg.
- Planned traffic load is 6,900 kg, so 860 kg must come off.
Check the landing mass: fuel at landing = 2,260 − 60 (taxi) − 1,450 (trip) = 750 kg, so landing mass = 19,640 + 750 = 20,390 kg, comfortably inside the MLM of 21,300 kg.
What to offload: payload, not fuel. The fuel already includes only trip, 5%-style contingency, alternate and final reserve - reducing it means eating into a regulatory reserve. The correct action is to offload 860 kg of passengers/cargo (or split the load), re-issue the load sheet, recompute the CG (a large aft or forward shift must be rechecked), and confirm the figures with the commander's own calculation rather than accepting the load sheet.
3. Temperature rises to 36°C and ATC imposes a 40-minute delay before departure. How does the picture change, and what would you refuse to do?
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New WAT limit: 4°C above 32°C × 105 kg/°C = 420 kg reduction, so WAT mass = 21,900 − 420 = 21,480 kg.
- Maximum zero-fuel mass = 21,480 − 2,260 = 19,220 kg.
- Maximum traffic load = 19,220 − 13,600 = 5,620 kg.
- Total offload now 1,280 kg against the original 6,900 kg booking.
The 40-minute delay matters twice. First, the aircraft will burn fuel on the ground (APU/engine) beyond the 60 kg taxi allowance; if that fuel has to be replaced, TOW rises and eats further into payload. Second, a delay pushes the departure into the hottest part of the day, with the temperature still rising, so the WAT mass may fall again before brake release.
What I would refuse:
- Departing above the WAT mass on the argument that the aircraft "will burn it off in the climb" - the limit applies at brake release.
- Reducing the final reserve or the alternate fuel to preserve payload.
- Using an assumed lower temperature or an earlier QNH to "recover" performance.
Legitimate options: offload 1,280 kg, split the load or send it by road, wait for the evening temperature to fall and recompute, or make a technical stop. The performance calculation is redone and re-signed each time the temperature or fuel changes.