Mass and Balance and Take-off Performance at a Hot, High Aerodrome
A light twin is scheduled from a 1,400 m asphalt runway at elevation 4,500 ft, OAT +30 °C, QNH 1005 hPa, slope 1% uphill, wind 180°/10 kt, runway 18. The AFM gives a sea-level ISA take-off distance of 850 m, with a 12% increase per 1,000 ft of pressure altitude, 1% per 1 °C above ISA, and a 10% increase for a 1% uphill slope. Zero-fuel mass is 2,900 kg, fuel 300 kg, maximum take-off mass 3,400 kg. The CG is at the forward limit.
1. Compute the pressure altitude and the corrected take-off distance, and decide whether the runway is adequate with a 1.15 factor.
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Pressure altitude = elevation + 30 × (1013 − QNH) = 4,500 + 30 × 8 = 4,740 ft. ISA temperature at 4,740 ft ≈ 15 − 2 × 4.74 ≈ 5.5 °C; OAT 30 °C is 24.5 °C above ISA. Corrections: altitude 4.74 × 12% ≈ 56.9%; temperature 24.5 × 1% ≈ 24.5%; slope 1% × 10% = 10%. Total factor ≈ 1 + 0.569 + 0.245 + 0.10 = 1.914. Corrected distance ≈ 850 × 1.914 ≈ 1,627 m. With the 1.15 factor, required ≈ 1,871 m. The 1,400 m runway is not adequate; even without the factor, 1,627 m exceeds the runway. The uphill slope and hot/high conditions combine to make this departure unsafe; reduce mass, wait for cooler conditions, or use a longer runway.
2. Check the mass and balance and identify the effect of the forward CG on performance.
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Zero-fuel mass 2,900 kg + fuel 300 kg = 3,200 kg, below MTOM 3,400 kg, so mass is legal. However, the forward CG increases the elevator downforce required, raising stall speed and increasing take-off distance and reducing climb gradient. With the already marginal runway, the forward CG worsens the situation. Consider moving load aft within limits (e.g., ballast or baggage) to bring the CG toward the mid-range, but never aft of the limit. Recompute the take-off distance with the actual CG; the AFM corrections may add another 5–10%, making the departure even less viable.