Density Altitude on a Short Strip
A normally aspirated four-seat aeroplane is loaded to 1,090 kg against a 1,100 kg maximum. The departure strip is 620 m of dry grass, sloping 1.5% uphill in the take-off direction, with a 6 kt tailwind component. Field elevation is 1,400 ft, QNH 1013 hPa, and OAT is 28 °C. The POH gives a sea-level, ISA, paved, zero-wind take-off distance to 50 ft of 480 m for this mass. The pilot's rule of thumb is +10% per 1,000 ft, +1% per 1 °C above ISA, +10% for grass, and +10% for a 10 kt tailwind.
1. Estimate the take-off distance to 50 ft and compare it with the available strip.
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Pressure altitude ≈ 1,400 ft. ISA temperature at 1,400 ft ≈ 15 − 2 = 13 °C; actual 28 °C, so ISA+15. Apply corrections: altitude +14%; temperature +15%; grass +10%; tailwind +6% (6/10 of 10%); uphill slope, say +5%. Multiplicative factor ≈ 1.14 × 1.15 × 1.10 × 1.06 × 1.05 ≈ 1.60. Distance ≈ 480 × 1.60 ≈ 768 m, versus 620 m available. The take-off is not viable as loaded - roughly 150 m short, and that is before any allowance for obstacle clearance or pilot technique.
2. What realistic changes would make the departure safe, and how would you verify?
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Reduce mass (each removed passenger or bag cuts both the distance and the climb penalty); wait for cooler air (a 10 °C drop saves ~10%); depart into wind from the other end if the slope then works against you less than the wind helps; or use a longer paved runway nearby. Verify by recomputing with the POH chart using actual pressure altitude and temperature, not the rule of thumb, and confirm the climb gradient clears obstacles in the departure path. If no combination gives a comfortable margin, the correct answer is not to go.
3. Why is the uphill slope a double problem?
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It lengthens the ground roll because gravity opposes acceleration, and it reduces the climb gradient after rotation, since part of the thrust or power is spent climbing the slope. With high density altitude the engine and propeller are already degraded, so the two effects compound. Slope correction is often omitted by pilots using simple rules, which is exactly how marginal strips catch people out.