Takeoff Distance at Density Altitude
A grass strip 480 m long, elevation 1400 ft, temperature 30 °C, QNH 1002 hPa. The POH gives a sea-level, ISA, paved takeoff roll of 180 m and a 50 ft distance of 320 m at MTOW. The grass surface adds 15% and a 1% upslope adds 10%. Your actual weight is 520 kg against a 560 kg MTOW. Wind is calm. The strip has a 4 m tree line 60 m beyond the departure end. You have a 95 kg passenger and full tanks.
1. Estimate the density altitude and the likely takeoff distance, then decide whether to depart.
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Density altitude. Pressure altitude ≈ 1400 + (1013 − 1002) × 30 ≈ 1400 + 330 = 1730 ft. ISA temperature at 1730 ft is about 15 − 2 × 1.73 ≈ 11.5 °C. The actual 30 °C is about 18.5 °C above ISA, which adds roughly 18.5 × 120 ≈ 2220 ft. Density altitude ≈ 1730 + 2220 ≈ 3950 ft.
Distance. Density altitude of ~3950 ft increases takeoff distance by roughly 1.15–1.2× compared with sea level (rule of thumb ~10% per 1000 ft above sea level for normally aspirated engines, less at partial power). Apply 1.45× for density, 1.15× for grass, 1.10× for slope: 320 × 1.45 × 1.15 × 1.10 ≈ 587 m. Even the takeoff roll scales similarly: 180 × 1.45 × 1.15 × 1.10 ≈ 330 m.
Judgement. 587 m required against 480 m available means the aircraft cannot clear 50 ft within the strip. The 4 m tree line 60 m past the end makes the margin worse. Do not depart. Options: wait for cooler air, reduce fuel and passenger load, or use a longer paved strip.
2. What weight reduction would be needed to make the departure viable, and what else would you verify?
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Required distance must fall to ≤480 m, i.e. a factor of 480/587 ≈ 0.82 on the current figure. Takeoff distance scales roughly with the square of weight, so weight must fall by about √0.82 ≈ 0.90, i.e. to ~470 kg - a reduction of ~50 kg. That means offloading most of the fuel (about 65 kg at 0.72 kg/L) or the passenger, neither of which is attractive.
A better path is to combine a modest weight reduction with cooler conditions or a headwind component. A 10 kt headwind can reduce ground roll by 15–20%, which combined with 30 kg off would bring the 50 ft distance near 470 m - still tight against a 480 m strip with trees.
Also verify: CG with the revised load, tyre and brake condition on grass, obstacle clearance gradient to 50 ft (the trees demand a steeper than normal climb), and the POH's grass/slope corrections rather than generic rules of thumb. If any figure is uncertain, the correct answer is not to go.