Density altitude and take-off performance
You are departing a 4,200 ft elevation airfield on a day when the QNH is 1003 hPa and the OAT is +28 °C. The runway is 1,400 m long, asphalt, dry, with a 0.8% upslope. Your aircraft's AFM gives, for a sea-level ISA take-off, a ground roll of 380 m and a 50 ft screen distance of 720 m. The AFM provides correction factors: +10% per 1,000 ft of pressure altitude, +8% per 10 °C above ISA, +5% for a 1% upslope, and +15% for a dry grass surface (not applicable here). MTOW is 1,150 kg; you are loaded to 1,120 kg.
1. Estimate the pressure altitude and the ISA deviation, then compute the corrected 50 ft screen distance.
Read the worked answer
Pressure altitude ≈ elevation + 30 × (1013 − QNH) = 4,200 + 30 × 10 = 4,500 ft.
ISA temp at 4,500 ft = 15 − 1.98 × 4.5 ≈ 6.1 °C. ISA deviation = 28 − 6.1 ≈ +22 °C.
Corrections to the 720 m screen distance:
- Altitude: +10% × 4.5 = +45% → ×1.45
- Temperature: +8% × 2.2 = +17.6% → ×1.176
- Upslope: +5% × 0.8 = +4% → ×1.04
720 × 1.45 × 1.176 × 1.04 ≈ 1,277 m. Runway is 1,400 m, so the screen distance uses ~91% of the runway - no meaningful margin.
2. Is the take-off acceptable? What would you do?
Read the worked answer
No. A 1,277 m screen distance on a 1,400 m runway leaves only 123 m (≈9%) - below any sensible safety margin and likely below the operator's minimum (commonly 15–20% for a dry runway). Also, the AFM figures are for MTOW; at 1,120 kg you gain a little, but not enough to change the conclusion.
Options: wait for cooler air (a 10 °C drop saves ~8% ≈ 100 m), depart early morning, reduce fuel/payload, or use a longer runway. Do not simply accept the take-off because the calculated distance is technically less than the runway length.
3. Why is the pressure-altitude correction applied before the temperature correction?
Read the worked answer
Because the temperature correction is expressed as a deviation from ISA at that pressure altitude. You must first establish the pressure altitude (which sets the ISA reference temperature and the base performance), then compare actual OAT to that ISA value. Reversing the order gives the wrong ISA deviation and therefore the wrong temperature penalty. This is why the AFM presents corrections in a defined sequence.