Kathmandu Departure - High Altitude, Obstacle-Dominated Second Segment
You are planning a departure from Kathmandu (elevation 4,390 ft, QNH 1004 hPa, OAT 24 °C) in a twin jet with MTOW 68,000 kg. Runway 02 TORA is 3,050 m, slope +0.5 % uphill. The departure procedure requires a minimum climb gradient of 5.5 % to 9,500 ft. The AFM gives a second-segment climb gradient of 3.1 % at MTOW, sea level, ISA, and shows the gradient decreasing by 0.35 % per 1,000 ft of pressure altitude and by 0.08 % per °C above ISA. The first segment is limited to 2.7 % and the runway is clear of close obstacles. Wind is calm.
1. Determine the achievable second-segment gradient at the actual conditions and decide whether the SID can be flown at MTOW.
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Pressure altitude = 4,390 ft with QNH 1004 (slightly below 1013, so add about 250 ft) ≈ 4,640 ft. ISA temperature at 4,640 ft is 15 − 1.98 × 4.64 ≈ 5.8 °C. Actual OAT is 24 °C, so ISA deviation is about +18 °C.
Apply the corrections to the 3.1 % sea-level ISA gradient:
- Altitude: 3.1 − (4.64 × 0.35) = 3.1 − 1.62 = 1.48 %.
- Temperature: 1.48 − (18 × 0.08) = 1.48 − 1.44 = 0.04 %.
The achievable gradient is essentially zero, far below the required 5.5 %. Even without the temperature correction the altitude alone reduces the gradient to about 1.5 %. The aeroplane cannot fly this SID at MTOW.
The remedy is to reduce take-off mass until the corrected gradient reaches 5.5 % plus a margin, which will require a substantial weight reduction (the gradient improves roughly 0.1–0.15 % per tonne for a jet of this size, so several tonnes). Alternatively, request a different SID with a lower gradient, or wait for cooler conditions. Departing at MTOW would be a gross performance error.
2. Explain why the uphill runway slope and the high elevation interact to make this departure particularly demanding.
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Uphill slope increases the ground roll because gravity opposes acceleration, typically adding about 5 % to the ground roll per 1 % of uphill slope; a 0.5 % slope adds roughly 2.5 % to the ground roll, which is modest but reduces the margin on a 3,050 m runway.
High elevation reduces air density, which reduces engine thrust and lift at a given IAS, so the true ground speed at rotation is higher and the ground roll is longer. The two effects compound: the aeroplane needs more runway at exactly the airport where the runway is already marginal.
More importantly, high elevation and high temperature reduce the climb gradient, as calculated in the previous task. The interaction is non-linear because thrust falls faster than density at high EGT, and the second-segment gradient is the binding constraint here, not the field length. The correct planning sequence is to check field length, then obstacle/SID gradient, then climb-limited mass, and take the lowest of the three. In this case the SID gradient is clearly the limiting case.