Density Altitude and Runway Length on a Hot Mountain Departure
You are departing a 4,200 ft elevation runway, 1,450 m long, asphalt, dry, with a 1% upslope in the takeoff direction. OAT is 30 °C, QNH 1010 hPa. Your airplane's AFM gives, for 4,200 ft pressure altitude and 30 °C: ground roll 520 m, total to 50 ft 980 m. The AFM figures assume zero wind, zero slope, dry paved runway, and maximum takeoff weight. You are 40 kg below MTOW. A 6 kt tailwind component is reported. Density altitude computed from the chart is approximately 6,300 ft.
1. Apply the corrections and judge whether the departure is acceptable with a 15% safety margin over the 50 ft distance.
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Start from 980 m to 50 ft. Tailwind of 6 kt: a common AFM correction is about +10% per 2 kt of tailwind, i.e. +30%, or roughly +150 m per 5 kt depending on the chart - using the conservative 10%/2 kt gives 980 × 1.30 ≈ 1,274 m. Upslope 1%: about +5% to +10%; at +10% → ≈ 1,401 m. Being 40 kg below MTOW gives a small decrement, perhaps −3% to −5% → ≈ 1,330–1,360 m. Required with 15% margin = 1,360 × 1.15 ≈ 1,564 m. Available = 1,450 m. Decision: departure is not acceptable - the corrected distance plus margin exceeds the runway. Remove the tailwind by waiting or using the opposite runway, reduce weight, or depart in cooler conditions.
2. Explain why the chart's density altitude (6,300 ft) differs from the pressure altitude and what that means for climb performance.
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Pressure altitude = elevation + 30 × (1013 − QNH) = 4,200 + 30 × 3 = 4,290 ft. The 30 °C temperature at that pressure altitude is far above ISA (ISA at 4,290 ft ≈ 15 − 2 × 4.29 ≈ 6.4 °C), so the air is much less dense: density altitude ≈ 6,300 ft. The engine produces less power and the propeller/thrust is reduced, while true airspeed for a given IAS is higher and the climb gradient is shallower. Expect a significantly reduced rate of climb and a longer takeoff run. Obstacle clearance after liftoff must be judged on the reduced gradient, not on sea-level experience.
3. What pre-takeoff and en-route actions follow from this analysis?
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Lean the mixture for maximum power at this density altitude before takeoff (per AFM procedure), use the full available runway, and brief a rejected-takeoff point. Verify V-speeds for the actual weight and density altitude. Plan a departure path clear of obstacles, since the climb gradient is degraded; if terrain requires a steeper gradient than the airplane can achieve, the departure must not be attempted. En route, expect reduced climb to cruise altitude and higher fuel burn during the extended climb; recalculate the fuel plan. Monitor CHT and oil temperature on the long climb.