Hot-day take-off performance from a short runway
You are planning a take-off from a 950 m paved runway at elevation 186 ft, QNH 1015 hPa, OAT 32°C, wind 120°/8 kt. Runway heading 140°. Aircraft mass 1,080 kg (MTOW 1,150 kg). POH: take-off distance to 50 ft at ISA sea level, MTOW = 650 m. Corrections: +12% per 1,000 ft pressure altitude; +10% per 10°C above ISA; +15% for wet runway. Use 120 ft per °C ISA deviation for density altitude. The runway has a 1% upslope and a 15 m obstacle 700 m from the start of the take-off run. Your operator's SOP requires a 15% margin over the 50 ft distance for any upslope. The POH does not provide a slope correction. Wind is a 7 kt headwind component. There is no clearway or stopway.
1. Calculate pressure altitude and density altitude.
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Pressure altitude = elevation + 30 ft per hPa below 1013. QNH 1015 is 2 hPa above 1013, so PA = 186 + 30(1013 − 1015) = 186 − 60 = 126 ft. ISA temperature at 126 ft = 15 − 1.98(0.126) = 14.8°C. ISA deviation = 32 − 14.8 = +17.2°C. Density altitude = PA + 120 × ISA deviation = 126 + 120 × 17.2 = 2,190 ft.
2. Calculate the 50 ft take-off distance and compare it with the runway and obstacle.
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Base 50 ft distance is 650 m. Pressure-altitude correction: +12% × (126/1000) = +1.5%, factor 1.015. Temperature correction: +10% × (17.2/10) = +17.2%, factor 1.172. Wet runway: ×1.15. Slope SOP: ×1.15. Distance = 650 × 1.015 × 1.172 × 1.15 × 1.15 ≈ 1,023 m. The available runway is 950 m, so the computed 50 ft distance exceeds the runway by about 73 m. The 15 m obstacle at 700 m cannot be assumed cleared because the aircraft reaches 50 ft only at about 1,023 m. The take-off is not acceptable at 1,080 kg.
3. What action would you take to make the departure legal and safe?
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Options are to reduce mass (payload or fuel), wait for a cooler temperature, or use a longer runway. The operator requires a 15% margin, so the 50 ft distance must be no more than 950/1.15 ≈ 826 m before that margin is applied. Even before the slope margin, the wet distance is about 889 m, so neither the runway nor the margin is met. I would not depart as loaded. I would reduce payload and recompute with the POH, or delay until OAT falls; if neither gives a 50 ft distance plus margin within 950 m and obstacle clearance, I would cancel or use another aerodrome.