High density altitude takeoff with tailwind, slope and obstacle
You are planning a takeoff from a 1,300 m asphalt runway at an aerodrome elevation of 3,800 ft. QNH is 1,002 hPa, OAT 33°C, and the runway has a 1% upslope. The wind is 310° at 10 kt; you intend to use runway 13. TORA is 1,300 m, TODA is 1,400 m, and there is a 15 m obstacle 1,200 m from the start of the take-off run. The aircraft weighs 1,050 kg, 50 kg below MTOW. The POH gives a sea-level ISA take-off run of 450 m and a 15 m obstacle clearance distance of 700 m. The POH charts stop at 7,000 ft density altitude. The aircraft is normally aspirated.
1. Calculate pressure altitude and density altitude, and explain what they mean for performance.
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Pressure altitude = 3,800 + 30(1,013 − 1,002) = 3,800 + 330 = 4,130 ft. ISA temperature at 4,130 ft is 15 − 2(4.13) ≈ 6.7°C. Density altitude = 4,130 + 120(33 − 6.7) ≈ 4,130 + 3,156 ≈ 7,290 ft. That means the aircraft and engine perform as if at about 7,300 ft on a standard day: reduced power, higher true airspeed for the same IAS, longer ground roll, and a lower climb gradient.
2. Can the takeoff be legally and safely conducted on the available data? State what is missing.
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The takeoff should not be conducted on the available data. The density altitude is above the 7,000 ft limit of the POH charts, so the operator cannot show compliance with the AFM performance data. A 10 kt tailwind on runway 13, a 1% upslope, and the 15 m obstacle all increase the required distance. The sea-level ISA figures of 450 m and 700 m cannot be extrapolated by guesswork. The missing data are the POH corrections for altitude, temperature, wind, slope, and obstacle, plus the actual runway condition. Without them, the takeoff is not legally performance-limited.
3. If the operator insists on departing, what changes would you make and what abort criteria would you set?
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Reduce weight, wait for a cooler part of the day, and use runway 31 into wind if the runway and obstacle data permit. Recalculate with the correct POH charts or an approved performance tool. Set a clear abort point: if the aircraft is not at the expected speed or has not lifted off by a fixed point, close the throttles and brake. Do not use a “try it and see” takeoff; the upslope and obstacle leave little margin.