Hot-Day Takeoff Limited by Tailwind
You are planning a takeoff from a 3,400 m dry runway at Kuwait International (elevation 63 m) in a twin turboprop. QNH is 998 hPa, OAT 46°C, wind 150°/08 kt, runway 33L, slope zero. MTOM is 5,700 kg. The AFM dry-runway takeoff distances at 1,000 ft pressure altitude and 46°C are: 5,200 kg 2,750 m; 5,400 kg 2,980 m; 5,600 kg 3,240 m. The operator applies a 10% increase in takeoff distance for each 10 kt of tailwind; no credit is taken for headwind. The runway TORA/TODA is 3,400 m. The aircraft is currently loaded to 5,600 kg, and the dispatcher says the takeoff is legal because 3,240 m is less than 3,400 m. The departure requires a 3.3% climb gradient; the AFM net gradient at 5,600 kg and 46°C is 3.6%.
1. Calculate pressure altitude and density altitude, and state why the AFM table at 1,000 ft is or is not conservative.
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Pressure altitude = elevation + (1013 − QNH) × 30 = 63 + (1013 − 998) × 30 = 63 + 450 = 513 ft.
ISA temperature at 513 ft = 15 − 1.98 × 0.513 = 14.0°C. The temperature deviation is 46 − 14.0 = 32.0°C. Density altitude ≈ pressure altitude + 120 × deviation = 513 + 120 × 32.0 = 4,353 ft.
Using the 1,000 ft table is conservative because actual pressure altitude is only 513 ft. The table already includes the 46°C effect, so the density altitude calculation explains the poor performance but the table itself is the correct source for takeoff distance.
2. Apply the tailwind correction and determine the maximum mass that satisfies the 3,400 m TODA. Comment on the dispatcher's statement and on the climb-gradient requirement.
Read the worked answer
Wind 150° on runway 330° is a direct tailwind of 8 kt. At 10% per 10 kt, the correction factor is 1.08.
At 5,600 kg: 3,240 × 1.08 = 3,499 m, which exceeds 3,400 m. The dispatcher's comparison of 3,240 m with 3,400 m is invalid because it ignores the tailwind.
At 5,400 kg: 2,980 × 1.08 = 3,218 m. The zero-wind distance allowed for 3,400 m is 3,400 ÷ 1.08 = 3,148 m. Interpolating between 5,400 kg (2,980 m) and 5,600 kg (3,240 m): fraction = (3,148 − 2,980) ÷ (3,240 − 2,980) = 168 ÷ 260 = 0.646. Mass = 5,400 + 0.646 × 200 = 5,529 kg.
So the takeoff-distance limit is about 5,530 kg, not 5,600 kg. The climb-gradient requirement is satisfied at 5,600 kg because the net gradient 3.6% exceeds 3.3%, but that does not remove the runway-distance limit. Reduce mass by about 70 kg, or wait for the tailwind to decrease.