Density Altitude and Take-Off Dispatch Decision
An operator plans a departure from a runway 1,200 ft above sea level. The QNH is 1003 hPa and the outside air temperature is 32°C. The runway is 1,400 m long and dry. The aircraft flight manual gives a take-off distance to 50 ft of 1,180 m at 4,000 ft pressure altitude and 30°C, and 1,320 m at 5,000 ft and 30°C. Company procedure requires the AFM distance to be multiplied by 1.15 for the actual conditions. The crew wants to depart at maximum passenger load. The dispatcher asks you to verify the pressure altitude, estimate the density altitude using 120 ft per °C of ISA deviation, decide whether the available runway is acceptable, and explain what operational action is appropriate if the margin is inadequate. No wind or slope correction is given.
1. Calculate pressure altitude, ISA temperature at that altitude, ISA deviation and estimated density altitude.
Read the worked answer
Pressure altitude = field elevation + 30 ft per hPa below 1013 hPa.
PA = 1,200 + 30 × (1013 − 1003) = 1,200 + 300 = 1,500 ft.
ISA temperature at 1,500 ft = 15 − 1.98 × 1.5 = 12.0°C (about 12°C).
ISA deviation = OAT − ISA temperature = 32 − 12 = +20°C.
Density altitude estimate = PA + 120 × ISA deviation
= 1,500 + 120 × 20 = 3,900 ft.
The air is therefore about 2,400 ft denser-altitude equivalent above the pressure altitude. That reduces engine power and lift for a given IAS, and increases true airspeed and take-off distance. The 120 ft/°C figure is an approximation, so final dispatch must use the AFM chart, not the estimate alone.
2. Using the AFM data, determine the factored take-off distance and decide whether the 1,400 m runway is acceptable.
Read the worked answer
At 4,000 ft and 30°C the AFM distance is 1,180 m. The calculated density altitude is 3,900 ft, but the actual temperature is 32°C, which is above the 30°C chart line. A conservative first check uses the 4,000 ft/30°C value: 1,180 × 1.15 = 1,357 m.
A linear interpolation down to 3,900 ft would give 1,180 − 14 = 1,166 m, and 1,166 × 1.15 = 1,341 m. Both figures are below 1,400 m, but the margin is only about 43 m to 59 m, roughly 3% to 4%. Because the temperature is above the charted value and no wind or slope correction is given, this is a thin margin.
The runway is acceptable only if the actual AFM chart at 32°C, 4,000 ft and the actual aircraft weight confirms a factored distance below 1,400 m. If the chart value exceeds 1,400 ÷ 1.15 = 1,217 m, the departure must be changed.
3. If the margin is inadequate, what operational action should be taken and why?
Read the worked answer
Reduce take-off weight, for example by offloading passengers, baggage or fuel, or wait for a cooler part of the day. A lower weight reduces both the lift required and the take-off distance; a lower temperature reduces density altitude. Other options include using a longer runway or a runway with a clear take-off path, but only if the AFM and performance software confirm the change.
The decision should not be based on the sea-level or 4,000 ft figure alone. Density altitude affects engine acceleration, propeller or fan thrust, lift at rotation and climb gradient. A 1,400 m runway with a calculated 43 m margin can be lost through late rotation, runway contamination, or a small QNH change. Record the actual AFM figures used and the final weight so the release is traceable.