Density Altitude and a Short Runway Departure
You are departing a 900 m grass strip at elevation 3,800 ft. Temperature is +28 C, QNH 1013 hPa, wind calm. Your aircraft's AFM gives, for sea level, ISA, zero wind, dry grass: take-off distance to 50 ft of 480 m and take-off run of 300 m. The AFM provides a density-altitude correction: add 12 percent per 1,000 ft of density altitude above sea level for the take-off distance to 50 ft, and 10 percent per 1,000 ft for the take-off run. There is no grass correction in the AFM, but the flight manual notes that dry grass adds about 15 percent to the take-off run compared with paved surface. Your aircraft is loaded to maximum take-off mass.
1. Calculate the density altitude and the resulting take-off distance to 50 ft.
Read the worked answer
Density altitude. Pressure altitude at QNH 1013 hPa equals elevation = 3,800 ft. ISA temperature at 3,800 ft is 15 - (1.98 x 3.8) = 15 - 7.5 = 7.5 C. The actual temperature is 28 C, so the ISA deviation is +20.5 C. A rough but standard approximation is 120 ft of density altitude per 1 C of ISA deviation: 20.5 x 120 = 2,460 ft. Density altitude is therefore about 3,800 + 2,460 = 6,260 ft, which we can round to 6,300 ft.
Take-off distance to 50 ft. Correction is 12 percent per 1,000 ft: 6.3 x 12 = 75.6 percent. So distance = 480 x 1.756 = 843 m.
Take-off run. 10 percent per 1,000 ft: 6.3 x 10 = 63 percent. Run = 300 x 1.63 = 489 m. Adding the 15 percent dry-grass factor: 489 x 1.15 = 562 m.
Compare with the strip. 843 m to 50 ft against 900 m available. That leaves only 57 m, about 6 percent, and the 900 m is the physical strip length, not a declared TODA with a clearway. The margin is unacceptable for a maximum-mass departure.
2. State your decision and the options available to you.
Read the worked answer
Decision. Do not depart at maximum mass in these conditions. A 6 percent margin on a grass strip at 6,300 ft density altitude is not a safe planning basis. The figures are also based on a new aircraft and a new engine; a real aircraft with a tired engine, long grass or a soft surface will do worse.
Options. First, reduce mass: offload fuel or payload to bring the take-off distance comfortably inside the strip, and recalculate with the actual mass. Second, wait for a cooler part of the day; a 10 C reduction in temperature cuts density altitude by roughly 1,200 ft and removes about 14 percent from the take-off distance. Third, use a longer or paved runway nearby. Fourth, if none of these is possible, do not go.
Judgement point. The AFM figures are minima, not targets. The correct discipline is to plan to a margin, typically at least 15-20 percent on a grass strip, and to treat any departure where the calculated distance is within 10 percent of the available length as a no-go until mass or conditions change.