Takeoff distance at a hot-and-high runway with slope
You are pilot-in-command planning a departure from runway 15 at an aerodrome with TORA 900 m, elevation 1,400 ft and QNH 1010. Aircraft MTOW is 1,100 kg; actual takeoff mass is 1,050 kg. The AFM gives a sea-level ISA takeoff distance over 50 ft of 520 m at 1,000 kg. OAT is 30°C, wind is 150/12 kt, and the runway slope is 1.2% uphill. Use these corrections: elevation +10% per 1,000 ft; temperature +1.2% per °C above ISA; tailwind +10% per 5 kt; uphill slope +5% per 1%; mass +1.5% per 10 kg above 1,000 kg. Apply a 20% safety margin. Do not take credit for the headwind component in the baseline calculation. You must decide whether to accept the departure.
1. Calculate the corrected takeoff distance over 50 ft. Is the 900 m TORA acceptable with the 20% margin?
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ISA temperature at 1,400 ft is approximately 15 - 2 × 1.4 = 12.2°C. The OAT is 30°C, so the temperature excess is 17.8°C. Apply the corrections to the 520 m base figure: mass +7.5% for 50 kg above 1,000 kg = +39 m; elevation +14% = +72.8 m; temperature +1.2% × 17.8 = +21.4%, giving +111.3 m; slope +5% × 1.2 = +6%, giving +31.2 m. Total corrected distance is about 520 + 39 + 72.8 + 111.3 + 31.2 = 774 m. With the required 20% margin, the required TORA is 774 × 1.2 = 929 m. The available TORA is 900 m, so the departure is not acceptable under these conditions. The headwind is not used to reduce the distance because the instruction says not to take credit for it.
2. If the wind shifts to 330/10 kt, recalculate and state the decision.
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Runway 15 is aligned at 150°; wind from 330° at 10 kt is a direct tailwind of 10 kt. The tailwind correction is +10% per 5 kt, so +20% of the 520 m base = +104 m. Adding this to the previous corrected distance of 774 m gives 878 m. With the 20% margin, the required TORA is 878 × 1.2 = 1,054 m, which exceeds the available 900 m by about 154 m. The decision is clearly no-go for runway 15. A tailwind of 10 kt in already hot-and-high conditions significantly degrades performance, and the calculation shows the margin is not just reduced but eliminated.
3. Recommend two changes that would make the departure acceptable with the same aircraft and runway, showing the effect.
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One option is to reduce takeoff mass to 1,000 kg. That removes the +39 m mass correction, giving about 735 m corrected distance and 735 × 1.2 = 882 m required, which is within the 900 m TORA, though only by 18 m. A second option is to wait for a cooler time of day, for example OAT 22°C. The temperature excess becomes 22 - 12.2 = 9.8°C, so the temperature correction falls to +11.8% of 520 = +61.4 m instead of +111.3 m. The corrected distance becomes about 724 m and the required distance about 869 m, which is acceptable with a better margin. Combining both changes would give a safer result. Neither change should be accepted without recalculating the actual mass, wind and slope at the time of departure.