High-Density-Altitude Departure from a Grass Strip
A Cessna 172S is departing a 750 m dry grass strip at elevation 1200 m. QNH is 1013 hPa; OAT is 28°C. Reported wind is 360° at 5 kt; the runway is 18, upslope 1.5%. The aircraft carries pilot, two passengers and 40 kg of baggage; takeoff mass is 1060 kg, 20 kg below MTOM. The AFM gives sea-level ISA ground roll 290 m and takeoff distance over a 15 m obstacle 520 m. Use these planning factors: ground roll increases 10% per 1000 ft of density altitude, plus 10% for a 5 kt tailwind, 15% for dry grass, and 5% for upslope; obstacle distance increases 10% per 1000 ft density altitude and 5% for a 5 kt tailwind. The pilot must decide whether a full-length departure is acceptable or whether to reduce load or wait for cooler conditions.
1. Calculate pressure altitude, ISA temperature and density altitude for the departure.
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Pressure altitude with QNH 1013 hPa equals elevation: 1200 m = 3937 ft, approximately 3900 ft. ISA temperature at that pressure altitude is 15 - 1.98 x 3.937 = about 7.2°C. The actual OAT is 28°C, so the ISA deviation is about 20.8°C. Density altitude = pressure altitude + 120 x ISA deviation = 3937 + 120 x 20.8 = about 6430 ft, or roughly 6400 ft. This is a high density altitude for a normally aspirated C172S: true airspeed and climb performance are reduced, and the takeoff distance will be much greater than the sea-level ISA book figure.
2. Using the stated factors, compute the adjusted ground roll and obstacle distance. Compare them with the 750 m runway.
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Density altitude factor: 6400 ft = 6.4 thousand ft, so multiply by 1 + 0.10 x 6.4 = 1.64. Ground roll: 290 x 1.64 = 476 m. Tailwind on runway 18 with wind 360 at 5 kt: +10%, giving 523 m. Dry grass: +15%, giving 602 m. Upslope: +5%, giving 632 m. Obstacle distance: 520 x 1.64 = 853 m; tailwind +5% gives 896 m. The ground roll of about 632 m fits within the 750 m runway, leaving only about 118 m. The obstacle distance of about 896 m exceeds the runway length. On these planning figures, a full-length departure as loaded cannot be accepted if the 15 m obstacle must be cleared.
3. What options would you consider, and what is your decision as PIC?
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The departure as loaded is not acceptable on the stated figures because the obstacle distance exceeds the runway. Options are to reduce mass by offloading fuel, baggage or a passenger; wait for a cooler time of day; use a runway with a headwind component; or use a longer runway. Reducing mass lowers both takeoff speed and distance, but the pilot must recompute with the AFM, not assume a small reduction is enough. Waiting for OAT to fall by 10°C would reduce density altitude by about 1200 ft, a meaningful improvement. My decision would be not to depart as loaded. I would offload or wait, then recompute both ground roll and obstacle distance with a safety margin, and only depart when the obstacle clearance is demonstrably adequate.