High-Altitude Takeoff Performance and Density Altitude at Almaty
You are planning a takeoff from Almaty aerodrome, elevation 2,230 ft, runway 05, length 1,500 m, dry asphalt, 1% uphill slope. Temperature is 32 °C, QNH 1005 hPa, wind calm. The aircraft weighs 3,750 kg, and the POH table gives a total takeoff distance to 50 ft of 1,650 m at 5,000 ft pressure altitude and 30 °C. The obstacle clearance requirement after takeoff is 2,250 m from the runway end, and the aircraft's scheduled climb gradient at this weight is 3.0%, while the required obstacle gradient is 3.3%. The next cooler period is expected after 18:00 local, when the temperature should fall to 22 °C. You must decide whether the takeoff can be made now, and if not, what change is required.
1. Calculate the pressure altitude and density altitude, and explain what they mean for takeoff.
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Pressure altitude = aerodrome elevation + 30 ft per hPa below 1013. Here 1013 - 1005 = 8 hPa, so PA = 2,230 + 240 = 2,470 ft. ISA temperature at 2,470 ft is about 15 - 2 × 2.47 = 10.1 °C. The actual temperature is 32 °C, so the ISA deviation is about +21.9 °C. Density altitude = PA + 120 × ISA deviation = 2,470 + 120 × 21.9 ≈ 5,100 ft. That is the altitude at which the aircraft behaves as if it were at 5,100 ft on a standard day. Because the POH table is given at 5,000 ft and 30 °C, the actual condition is slightly worse than the table: the air is less dense, so the engine produces less power, the propeller thrust is lower, and the true airspeed for the same IAS is higher. Takeoff roll and distance to 50 ft both increase, as does the time to reach obstacle height.
2. Using the given figures, can the takeoff be made at 3,750 kg now? Show the limiting factor.
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No. The POH total takeoff distance to 50 ft at 5,000 ft and 30 °C is 1,650 m, and the actual density altitude is about 5,100 ft, so the real distance is at least 1,650 m. The available runway is 1,500 m, so the aircraft cannot reach 50 ft before the runway end even before considering the obstacle. In addition, the required obstacle clearance is 2,250 m from the runway end, while the aircraft's scheduled climb gradient is 3.0% versus the required 3.3%. At 3,750 kg the aircraft cannot meet the obstacle gradient, so obstacle clearance is the second limiting factor. The 1% uphill slope further increases the ground roll. The takeoff is therefore not permissible at this weight and temperature, regardless of the fact that the runway is dry and the wind is calm.
3. What realistic change would make the takeoff acceptable, and how would you verify it?
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The most practical change is to wait until the temperature falls to about 22 °C after 18:00, or to reduce weight. With 22 °C, the ISA deviation is about +12 °C, so density altitude falls to roughly 2,470 + 120 × 12 ≈ 3,900 ft. Using the rule that takeoff distance increases about 10% per 1,000 ft of density altitude, the distance would fall from about 1,650 m at 5,100 ft to roughly 1,650 × (1 - 0.12) ≈ 1,450 m, which is within the 1,500 m runway but with little margin. Reducing weight by, for example, 200 kg would also shorten the takeoff and improve the climb gradient. Verify by recalculating density altitude, using the actual POH chart for the new weight and temperature, checking the obstacle gradient is at least 3.3%, and applying a safety margin of at least 15% on the runway distance. Do not depart on the basis of the sea-level figures.