Takeoff from a short grass strip at high density altitude
You plan a departure in a Cessna 172S from a 600 m grass strip. Elevation 1,400 ft, QNH 1013 hPa, OAT 27°C, wind calm, upslope 1.5%. Aircraft weight 1,100 kg (MTOW 1,157 kg). The POH sea-level ISA figures for this weight are: ground roll 280 m, distance over 50 ft 520 m. The POH supplement states: increase distances by 12% per 1,000 ft of density altitude; grass adds 15%; 1.5% upslope adds 10%. No wind correction. You have a 1,200 m alternative runway 20 minutes away, but it is 200 ft lower and has the same temperature. Your passenger is anxious to leave. You must decide whether to take off from the strip, and if not, what change would make it acceptable.
1. Calculate density altitude and explain its effect on takeoff performance.
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Pressure altitude is 1,400 ft because QNH is 1013 hPa. ISA temperature at 1,400 ft is about 15 - 1.98 x 1.4 = 12.2°C. The actual OAT is 27°C, so the ISA deviation is +14.8°C. Using the standard approximation, density altitude = pressure altitude + 120 x ISA deviation = 1,400 + 120 x 14.8 = 3,176 ft, about 3,200 ft.
At higher density altitude the air is less dense: the engine produces less power, the propeller produces less thrust, and the true airspeed for a given indicated airspeed is higher. All of these increase ground roll, takeoff distance to 50 ft, and initial climb distance. The effect is significant here: about 3,200 ft DA is well above the strip elevation.
2. Apply the corrections and compare with runway length; decide.
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Use the POH supplement corrections as multiplicative factors:
- DA factor: 1 + 0.12 x 3.176 = 1.381.
- Ground roll: 280 x 1.381 = 387 m; grass +15% = 445 m; upslope +10% = 490 m.
- Over 50 ft: 520 x 1.381 = 718 m; grass +15% = 826 m; upslope +10% = 909 m.
The runway is 600 m. The ground roll might fit, but the distance to 50 ft (909 m) exceeds the runway by a wide margin. There is no wind correction and no extra margin for soft ground, pilot technique, or engine abnormality. On a 600 m grass strip with a 1.5% upslope, this takeoff is not acceptable. The pilot should reject the takeoff from this strip.
3. What change would make the takeoff acceptable?
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Acceptable options, in order of practicality:
- Use the 1,200 m alternative runway. It is 200 ft lower, so density altitude is lower; even allowing for the same temperature, the longer runway gives a real margin. Verify the alternative runway surface, slope, and obstacles before using it.
- Wait for a cooler part of the day. A lower OAT reduces density altitude and takeoff distance; recalculate before departure.
- Reduce weight by offloading fuel or payload, then recalculate. The required reduction is large: to bring the 909 m over-50-ft distance down to 600 m needs a factor of about 0.66, i.e. about a 34% reduction, which may not be achievable without leaving inadequate fuel. Do not simply hope the ground roll fits; the 50 ft obstacle distance is the limiting figure.