Density Altitude on a Hot Afternoon
You are departing a 4200 ft elevation airfield with a 2600 m runway. Temperature is 32 °C, QNH 1013 hPa, wind calm. The pilot's operating handbook gives, for maximum take-off mass at sea level ISA, a take-off ground roll of 320 m and a 15 m obstacle clearance distance of 610 m. The chart correction for 4200 ft pressure altitude at ISA+20 °C is a factor of 1.85 for ground roll and 1.95 for the obstacle distance. The airplane is loaded to 60 kg below maximum take-off mass, which the handbook credits with a 5 % reduction in both figures. A line of trees 12 m high stands 700 m from the brake-release point.
1. Calculate the corrected take-off distance and decide whether the departure is acceptable.
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Pressure altitude equals aerodrome elevation because QNH is 1013 hPa, so 4200 ft. ISA temperature at 4200 ft is about 15 − 2 × 4.2 ≈ 6.6 °C; actual 32 °C means roughly ISA+25, which is worse than the chart's ISA+20 correction - so the published factor is a minimum, not a guarantee. Using the chart: ground roll 320 × 1.85 = 592 m; obstacle distance 610 × 1.95 = 1190 m. Applying the 5 % mass credit: 562 m and 1130 m. The trees at 700 m are cleared only if the airplane is above 15 m by then, which the 1130 m figure says it is not. The departure is not acceptable at this mass and temperature without a demonstrated performance margin.
2. What operational options would you consider, and which would you reject?
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Options: reduce mass (offload fuel or baggage) and recompute; wait for cooler air, since a 10 °C drop materially reduces the correction factor; use a longer runway or a different departure path that avoids the trees. Reject: assuming the wind will help (it is calm), assuming the airplane will 'feel' fine, or using a soft-field technique to shorten the roll - technique cannot create performance. Also reject departing and 'seeing how it goes'; a rejected take-off at high density altitude has its own stopping distance problem, which must be checked against the runway remaining.