Density Altitude on a Hot Plateau Departure
You are captain of a normally aspirated light twin at a plateau airfield, elevation 1,850 m (6,070 ft), on a summer afternoon. Aerodrome temperature is 32 °C, QNH 1013 hPa, and the runway is 1,400 m long with rising terrain beyond the departure end. The aircraft manual gives a sea-level, ISA take-off ground roll of 520 m and a 50 ft screen distance of 900 m. The manual's correction chart states: add 10 % to ground roll per 1,000 ft of pressure altitude and 10 % per 10 °C above ISA. A pilot colleague argues that because QNH is exactly 1013, the altimeter reads correctly and pressure altitude equals elevation, so density effects are minor. The aircraft is loaded 60 kg below maximum take-off mass.
1. Calculate the pressure altitude, ISA temperature at that level, and the temperature deviation, then estimate the corrected ground roll and 50 ft screen distance.
Read the worked answer
Pressure altitude with QNH 1013 hPa equals indicated altitude, so PA ≈ 6,070 ft. ISA temperature at 6,070 ft = 15 − (1.98 × 6.07) ≈ 15 − 12.0 = 3.0 °C. Deviation = 32 − 3 = +29 °C, i.e. about 2.9 × 10 °C above ISA.
Corrections: altitude factor 1 + (10 % × 6.07) = 1.607. Temperature factor 1 + (10 % × 2.9) = 1.29.
Ground roll ≈ 520 × 1.607 × 1.29 ≈ 1,078 m. Screen distance ≈ 900 × 1.607 × 1.29 ≈ 1,866 m.
Both exceed the 1,400 m runway. The colleague's reasoning is wrong: QNH = 1013 makes the altimeter correct in the static-pressure sense but says nothing about density. High temperature at high elevation gives low density, long take-off runs and degraded climb gradient toward rising terrain - the limiting factor is the obstacle, not just the runway length.
2. The aircraft is 60 kg below maximum mass. Explain how you would use this margin and what other operational decisions follow from the numbers.
Read the worked answer
The 60 kg margin reduces mass, which lowers stall speed and improves acceleration and climb, but the manual corrections are given for maximum mass; without a mass-correction table you cannot claim credit quantitatively. Treat any improvement as a bonus, not as a planning allowance, and plan on the maximum-mass figures.
Operational decisions: the computed screen distance exceeds the runway, so a full-length departure at 32 °C is not acceptable. Options include waiting for cooler evening temperatures (recompute with the actual temperature), reducing fuel or payload to a mass for which a documented short-field technique exists, or selecting a longer runway or a departure path clear of obstacles. Also verify climb gradient in the second segment and single-engine case, because high density altitude degrades both, and check tyre speed limits and brake energy. If no combination works, the departure must be delayed or cancelled.