High Density Altitude Departure from a Desert Strip
You are planning a VFR departure from a 950 m desert strip near Haima at 1500 local time. Aerodrome elevation is 1,500 ft, QNH is 1002 hPa, and OAT is 46°C. The runway is 950 m long, dry, and level, with a 15 m obstacle just beyond the departure end. Wind is calm. The Cessna 172 has a maximum gross weight of 1,111 kg and a current takeoff weight of 1,080 kg. The POH gives a sea-level ISA takeoff ground roll of 300 m and a 50 ft obstacle distance of 550 m. There is no POH data above 40°C. The aircraft has full fuel and two adults, and the next fuel available is 2 hours away.
1. Calculate the pressure altitude, ISA temperature, ISA deviation, and approximate density altitude.
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Pressure altitude = aerodrome elevation + 30 ft per hPa below 1013. With QNH 1002, the difference is 11 hPa, so add about 330 ft. Pressure altitude is about 1,830 ft. ISA temperature at 1,830 ft is 15°C minus about 2°C per 1,000 ft, so about 11.3°C. The ISA deviation is 46°C minus 11.3°C, about 34.7°C. Using the approximation that density altitude increases about 120 ft per 1°C above ISA, the density altitude is about 1,830 + (120 × 34.7) = 1,830 + 4,164 = about 5,994 ft, or roughly 6,000 ft. That is a very high density altitude for a normally aspirated C172 and is the key performance driver.
2. Using a rough rule that takeoff distance increases about 10% per 1,000 ft of density altitude, estimate the ground roll and 50 ft distance. Is the departure within the available runway and obstacle clearance?
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At about 6,000 ft density altitude, the increase over sea-level ISA is approximately 60%, or a factor of 1.6. Estimated ground roll is 300 m × 1.6 = 480 m. Estimated 50 ft obstacle distance is 550 m × 1.6 = 880 m. The runway is 950 m, so the ground roll appears to fit, but the 50 ft distance leaves only 70 m to the 950 m runway end, before considering the 15 m obstacle just beyond it. The rule of thumb is crude, the POH has no data at 46°C, and the aircraft is only 31 kg below maximum weight. There is no margin for a delayed rotation, soft surface, or downdraught. The departure should not be accepted as planned: the obstacle clearance is marginal at best and likely unsafe.
3. What realistic options would you consider before departure?
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The best option is to wait for cooler conditions, such as early morning or after sunset, when density altitude falls substantially. Reducing weight is the other main lever: offload fuel or a passenger, or split the journey, but the next fuel is 2 hours away, so fuel reduction must be planned carefully. A short-field takeoff technique and leaning for maximum power may help, but they do not overcome a 6,000 ft density altitude and a marginal obstacle. Check the actual wind; a headwind component would improve performance, but calm wind is forecast. If neither delay nor weight reduction is possible, do not depart. Use the POH and a performance app if available, but do not extrapolate beyond the chart without a large safety margin. The decision should be made on the ground, not after rotation.