High-elevation departure at 31°C
You are the pilot-in-command of a normally aspirated, four-seat single-engine aeroplane, MTOW 1,150 kg, departing a dry, sealed runway 1,250 m long at an aerodrome elevation of 4,400 ft. The QNH is 1016 hPa and the outside air temperature is 31°C. Wind is calm and the runway has a 1% upslope in the take-off direction. The aircraft is loaded to 1,120 kg. The POH gives a 50 ft take-off distance of 1,180 m at 4,400 ft and 30°C, and 1,480 m at 6,000 ft and 30°C; the climb gradient at 4,400 ft and 30°C is 4.6%, falling by about 0.5% per 1,000 ft of density altitude. The planned departure is at 1400 local, with high terrain 6 nm ahead requiring a 3.3% net climb gradient. There is no longer runway within 100 nm and no cooler time available before the crew duty limit.
1. Estimate the density altitude and explain how you would apply the POH, including the extrapolation beyond 6,000 ft.
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Pressure altitude is 4,400 + 30 × (1016 − 1013) = 4,490 ft, say 4,500 ft. ISA temperature at 4,500 ft is 15 − 1.98 × 4.5 ≈ 6°C, so ISA deviation is 31 − 6 = +25°C. Density altitude ≈ PA + 120 × ISA deviation = 4,500 + 3,000 = 7,500 ft. The POH table stops at 6,000 ft, so interpolate first: between 4,400 ft/30°C (1,180 m) and 6,000 ft/30°C (1,480 m) the increase is 300 m per 1,600 ft, or 0.1875 m/ft. From 6,000 ft to 7,500 ft adds 1,500 × 0.1875 ≈ 281 m, giving about 1,760 m. Treat that as a minimum: extrapolation, upslope, and pilot technique all add error. The operational point is that the aeroplane is performing at 7,500 ft density altitude, not 4,400 ft elevation.
2. Assess the take-off distance and initial climb against the runway and obstacle requirements. Show the numbers.
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Required 50 ft distance is about 1,760 m against 1,250 m available, a shortfall of roughly 510 m before allowing for the 1% upslope, which further reduces acceleration. The climb check is equally unfavourable. The tabulated gradient at 4,400 ft/30°C is 4.6%; density altitude is about 3,100 ft above 4,400 ft, so subtract 3.1 × 0.5 ≈ 1.6%, leaving about 3.0% gross. The obstacle requires 3.3% net, and gross-to-net margin would make the net gradient even lower. A 3.0% gross gradient cannot satisfy a 3.3% net requirement. Therefore the take-off is not acceptable even before considering the high terrain 6 nm ahead. The candidate should state the limiting numbers, not simply say 'high and hot'.
3. What is your decision, and which mitigations would you consider? Explain why offloading alone may not be enough.
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My decision is not to depart as loaded. The most effective mitigations are to wait for a cooler temperature, use a longer runway, or reduce weight enough to bring the required distance below 1,250 m and the net gradient above 3.3%. A small offload is unlikely to close a 500 m gap; the POH would need to be re-entered at the new weight and temperature. Waiting until the temperature falls to about 15°C would reduce density altitude by roughly 2,000 ft and improve both distance and gradient, but the crew duty limit may prevent that. If no cooler departure or longer runway is available, cancel or change aircraft. I would not accept the take-off on the basis of 'calm wind' or 'dry runway' alone.