Hot, High, Uphill and Downwind
Departure aerodrome elevation 1,400 ft, QNH 1,003 hPa, OAT 38°C. Runway 27, TORA/TODA 1,050 m, surface upslope 1% along the take-off run, reported tailwind component 8 kt. A 12 m obstacle (trees) stands 250 m beyond the departure end. Aircraft at maximum take-off mass, flaps 10°, paved dry runway. The POH gives, for these conditions: at 2,000 ft pressure altitude and 30°C, ground roll 520 m and 50 ft distance 845 m; at 2,000 ft and 40°C, 610 m and 980 m; at 3,000 ft and 40°C, 700 m and 1,120 m. The POH states: add 10% to take-off distance for each 2 kt of tailwind up to 10 kt; no slope or obstacle correction is included.
1. Compute pressure altitude and density altitude, and explain why both matter here.
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Pressure altitude. 1,400 ft + 30 ft per hPa below 1013: 1013 − 1003 = 10 hPa → +300 ft. PA = 1,700 ft.
Density altitude. ISA temperature at 1,700 ft = 15 − (2 × 1.7) ≈ 11.6°C. The OAT of 38°C is 26.4°C above ISA. DA = PA + 120 × 26.4 ≈ 1,700 + 3,170 ≈ 4,870 ft - call it 4,900 ft.
Why both. PA drives the mixture and the aerodynamics as the altimeter sees them; DA drives the engine power and propeller thrust actually available. A normally aspirated engine at 4,900 ft DA has lost roughly 15% of sea-level power before any temperature effect on the wing is counted, and the wing needs a higher true airspeed for the same lift.
On a 1,050 m strip at 38°C the practical consequences are: longer ground roll, a shallower initial climb gradient, and less obstacle clearance - all at the moment when the aircraft is heaviest. The density altitude is the number that explains why the book figures are what they are, and why a pilot's 'it always gets off here' experience from a 20°C morning is worth nothing today.
2. Using the POH data, estimate the 50 ft distance and decide whether the departure is legal and sensible.
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Interpolate at 1,700 ft / 38°C. At 2,000 ft, 38°C is 80% of the way from 30°C (845 m) to 40°C (980 m): 845 + 0.8 × 135 ≈ 953 m. Then correct 300 ft down from 2,000 ft: between 2,000 and 3,000 ft at 40°C the 50 ft distance grows 140 m, so subtract 0.3 × 140 ≈ 42 m → ≈ 910 m.
Apply wind. 8 kt at 10% per 2 kt = +40% → 910 × 1.40 ≈ 1,274 m to 50 ft.
Compare. TODA is 1,050 m. The requirement is 1,274 m before the upslope, the trees, or any allowance for a pilot technique that is not POH-standard. The take-off is not acceptable - it is not marginal, it is roughly 220 m short.
The hidden margins. The book figure assumes a level runway, no obstacle, and a clean departure; here there is 1% upslope (further lengthening the ground roll) and a 12 m obstacle at 250 m that must be cleared by a net flight path, not by a 50 ft screen height. Both push the same way.
Answer to the examiner's real question: with an 8 kt tailwind there is no technique, no soft-field finesse and no 'rotate early' that recovers 220 m. The departure is rejected on numbers.
3. You must still get the aircraft out today. What are your options and how would you verify the new plan?
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Work the variables you control.
- Wind: the 10%/2 kt rule means TODA of 1,050 m against a 910 m still-air distance allows only a 15% increase - about 3 kt of tailwind. Anything above that fails. Use runway 09 (into wind) if surface wind permits and the strip is available; that converts a 40% penalty into a headwind benefit.
- Temperature/time: delay to the evening. At 2,000 ft PA every 10°C is worth about 135 m, so dropping from 38°C to 25°C saves well over 150 m.
- Mass: offload fuel and baggage to the POH mass actually used for the chart - recalculate, do not guess a percentage.
- Runway/obstacle: accept only if the net take-off flight path clears the trees, not just the 50 ft screen height.
Verification. Re-enter the POH at the new PA, temperature, mass and wind; apply slope and any grass correction the POH specifies; compare the result with TODA, not TORA, and keep a personal margin (e.g. 15%) above the book figure. Do not invent corrections the POH does not provide - if the chart has no slope allowance and the strip is sloping, that margin must come out of your own buffer. If no combination works, the aerodrome and the day are incompatible; that is a legitimate answer.