Density altitude and runway performance on a hot mountain strip
You plan to depart a 4200 ft elevation strip with a 2600 m runway. The outside air temperature is 28 degrees Celsius, QNH 1013 hPa, and the wind is calm. Your aeroplane's pilot operating handbook gives a sea-level, ISA take-off ground roll of 350 m and a 50 ft obstacle clearance distance of 620 m at maximum take-off mass. The chart correction is 10 percent per 1000 ft of density altitude and 1 percent per 10 degrees Celsius above ISA, applied to the ground roll. Your actual take-off mass is 95 percent of maximum. The strip has a 1.5 percent upslope in the take-off direction.
1. Estimate the density altitude and the corrected take-off distance over the 50 ft obstacle.
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Pressure altitude is essentially 4200 ft because QNH equals 1013 hPa. ISA temperature at 4200 ft is 15 minus (1.98 x 4.2) = about 6.7 degrees Celsius. The actual temperature is 28 degrees, so the ISA deviation is about +21 degrees.
Density altitude is approximately pressure altitude plus 120 ft per degree of ISA deviation: 4200 + (120 x 21) = 4200 + 2520 = about 6720 ft.
Correction for density altitude: 10 percent per 1000 ft gives about 67 percent, so the 620 m obstacle distance becomes 620 x 1.67 = about 1035 m. The 1 percent per 10 degrees above ISA correction is already largely captured by the density-altitude term; if the handbook applies both independently, add roughly another 2 percent, giving about 1056 m. Mass at 95 percent of maximum reduces the distance, but the handbook factor must be read from the chart rather than assumed. The upslope adds a further penalty. A conservative planning figure is well over 1100 m.
2. The runway is 2600 m. What other factors must you check before deciding the departure is safe, and what would make you reject it?
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A 2600 m runway appears generous against a 1100 m obstacle distance, but the relevant comparison is the take-off distance available against the required distance including the failure case. For a single-engine aeroplane, you must consider the distance to a safe forced-landing area after an engine failure on the ground roll or just after rotation, and whether the climb gradient clears obstacles beyond the strip.
Check the wind (calm here, so no credit), the upslope effect on acceleration, the surface condition (dry grass or gravel increases the roll substantially), and the obstacle profile beyond the departure end. Reject the departure if the corrected obstacle distance plus a sensible margin exceeds the available distance, if the climb gradient at the expected mass and temperature cannot clear terrain, or if the density altitude pushes the aeroplane outside the handbook envelope. Also verify the tyre and brake limits and the engine's maximum take-off power at this temperature.
3. How would you change the plan to reduce risk without cancelling the flight?
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The most effective lever is mass: reduce fuel and payload to the minimum consistent with the flight, which lowers the stall speed, shortens the ground roll and improves the climb gradient. Second, depart in the coolest part of the day, early morning, which can cut the ISA deviation by 10 degrees or more and reduce density altitude by over 1000 ft.
Third, use the full runway and select a rotation point that maximises the margin over the obstacles, and brief a rejected take-off point. Fourth, confirm the wind; even a few knots of headwind improve both the roll and the gradient. Finally, plan the departure path over the least hostile terrain and identify forced-landing areas in advance. If none of these produces a comfortable margin, the correct action is to wait or to depart from a lower, longer strip.