Afternoon departure from an 800 m grass strip on the Jos Plateau
You are rostered for a charter lift out of a 750 m licensed grass strip on the Jos Plateau, elevation 4,300 ft. Departure is planned for 14:30 local. The 14:00 observation gives OAT 32 °C and QNH 1010 hPa. Your Cessna 172 is loaded to 2,280 lb, 20 lb below maximum take-off weight. The strip slopes uphill at about 1.5 per cent towards the departure end, and there is a line of trees that you must clear by 50 ft. The wind is 080/05 kt; the only usable departure direction gives you a 3 kt tailwind component. The pilot who flew the aircraft in yesterday says it 'came off quickly and climbed fine' - he departed at 07:00 with two people on board and half fuel. The POH quotes a take-off distance to 50 ft of 960 ft at sea level, ISA, MTOW, on a paved level runway.
1. Calculate the pressure altitude and density altitude, then estimate what the 960 ft POH figure becomes in today's conditions. Show every step and state your assumptions.
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Pressure altitude. Elevation 4,300 ft; QNH 1010 hPa is 3 hPa below 1013, and 1 hPa ≈ 30 ft, so PA ≈ 4,300 + (3 × 30) = 4,390 ft.
ISA temperature at that level. 15 − (1.98 × 4.39) ≈ 6.3 °C.
ISA deviation. 32 − 6.3 = +25.7 °C.
Density altitude. Using 120 ft per °C of deviation: 4,390 + (25.7 × 120) ≈ 7,470 ft.
Take-off distance. The 960 ft assumes sea level, ISA, MTOW, paved, level, still air. Apply the corrections cumulatively (the POH chart is authoritative; these factors are for reasoning):
- density altitude ≈ 7,500 ft: roughly +75 % → 1,680 ft
- dry grass: roughly +15 % → 1,930 ft
- 1.5 % upslope: roughly +10 % → 2,120 ft
- 3 kt tailwind: roughly +10 % → ≈ 2,330 ft
Against 750 m (2,460 ft) of strip, that leaves about 130 ft - around 5 % - before allowing for the 50 ft screen, technique, or the wind dropping to calm.
2. Is yesterday's 07:00 report useful evidence for today's decision? Explain what changed between the two departures.
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It is close to meaningless as evidence, and treating it as reassurance is the trap. Three variables changed at once:
- Temperature. At 07:00 the OAT was perhaps 20 °C, giving a deviation near +14 °C and a density altitude around 6,100 ft - roughly 1,400 ft lower than now. Every 1 °C of temperature is worth about 120 ft of density altitude, and density altitude drives both the ground roll and the climb gradient.
- Weight. Two people and half fuel is perhaps 400–450 lb lighter than today's 2,280 lb. Take-off distance falls roughly in proportion to the square of the weight ratio, and climb gradient improves markedly.
- Wind. A morning departure on the same strip probably had a headwind or calm, not a 3 kt tailwind, which is a double penalty: less airspeed for the same groundspeed and a longer ground run.
A report of 'it came off quickly' from a lighter aircraft in cooler, still air says nothing about a near-MTOW departure at 7,500 ft density altitude on uphill grass.
3. The party refuses to be split and asks you to 'just go, it is a short flight'. State your decision and list the specific alternatives you can offer them.
Read the worked answer
Decision: do not depart as loaded and configured at 14:30. A 5 % margin on a calculated distance is not a margin - the POH figures assume a new engine, a proficient pilot and a smooth technique, and the calculation excludes the climb gradient needed to clear the trees at the 50 ft screen with a tailwind and rising ground.
Alternatives to offer:
- Wait for the evening. Departing at 18:30 with OAT around 24 °C cuts density altitude by roughly 1,000 ft and removes most of the performance problem.
- Reduce weight. Offload 150 lb of baggage or one passenger; this shortens the ground roll and steepens the climb gradient.
- Reduce fuel to the minimum for the sector plus a fixed reserve, if a fuel stop is acceptable; 20 US gal saved is about 120 lb.
- Use a different departure surface. A nearby paved airport with a longer runway removes the grass and upslope penalties.
- Use the downhill direction if the wind and obstacle situation genuinely permit it, verified against the POH rather than by feel.
If none is acceptable, the answer is still no.