Departure from La Paz with a Runway Change and Rising Density Altitude
You are the pilot-in-command of a twin-engine turboprop charter with 9 passengers, departing El Alto International Airport, La Paz (elevation about 4,060 m / 13,320 ft). The aircraft has a maximum takeoff mass of 7,500 kg and a maximum landing mass of 7,100 kg. Ramp mass is 7,180 kg; taxi fuel burn is 30 kg. Takeoff fuel is 620 kg. The runway in use has been changed from the longer runway to the shorter one because of a tailwind report on the primary runway, and the new runway is 3,000 m long with a 0.8 percent upslope. Reported conditions: QNH 1022 hPa, OAT +14 C, wind calm, runway dry. The performance charts show that at 4,060 m pressure altitude and +14 C, the accelerate-stop distance is 2,450 m, the takeoff distance to 15 m is 2,620 m, and the second-segment climb gradient is 2.1 percent in the takeoff configuration. The aircraft is not certified for operations above a 2.0 percent second-segment gradient in this configuration at this mass.
1. Compute the actual takeoff mass and determine whether the aircraft can legally and safely use the shorter runway. State every correction you apply and your decision.
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Takeoff mass = ramp mass minus taxi fuel = 7,180 - 30 = 7,150 kg. This is below the 7,500 kg maximum takeoff mass, so the mass structural limit is satisfied. Now compare the 7,150 kg performance figures with the runway. The published takeoff distance to 15 m at 4,060 m pressure altitude and +14 C is 2,620 m, which already exceeds the 3,000 m runway only after slope correction is applied. The upslope of 0.8 percent increases the takeoff distance; a conservative correction of about 8 percent per percent of upslope gives roughly 2,620 x 1.064 = 2,788 m. The accelerate-stop distance of 2,450 m also rises with upslope, to about 2,607 m. Both are now uncomfortably close to the 3,000 m available, leaving less than the 15 percent margin normally required for a dry runway. More decisively, the second-segment climb gradient of 2.1 percent exceeds the aircraft's certified 2.0 percent limit at this mass. The aircraft therefore cannot depart legally at 7,150 kg from this runway under these conditions. The correct action is to reduce mass by offloading payload or fuel, or to wait for cooler conditions, and to recompute before departure.
2. The operator suggests waiting until late afternoon when the temperature drops to +6 C. Estimate qualitatively how this changes the performance and whether it resolves the problem.
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A drop from +14 C to +6 C reduces density altitude by roughly 8 C x 120 ft per degree, or about 960 ft, which is significant at this elevation. Lower temperature increases air density, which improves engine power, propeller thrust, and wing lift. The takeoff distance to 15 m and the accelerate-stop distance both decrease, typically by several percent for each 1,000 ft of density-altitude reduction. The second-segment climb gradient also improves because the engines produce more thrust and the wings produce more lift at the same indicated airspeed. However, the fundamental constraint is the certified 2.0 percent second-segment gradient limit at this mass, which is a mass-and-configuration limit, not purely a temperature limit. Cooling may bring the actual gradient below 2.0 percent, but the pilot must verify with the chart rather than assume. If the chart shows a gradient at or below 2.0 percent at the new temperature and the corrected distances fit within 3,000 m with margin, the departure is acceptable. Otherwise, mass must be reduced. Waiting is a partial mitigation, not a substitute for a mass reduction.
3. What operational and regulatory considerations apply if the pilot decides to depart anyway because the passengers have connecting flights?
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Departing despite an exceedance of a certified performance limit is a violation of the operating limitations in the aircraft flight manual and of the DGAC civil aviation regulations that require compliance with the approved performance data. The pilot-in-command has final authority, but that authority does not permit exceeding certification limits. The second-segment gradient limit exists to guarantee obstacle clearance and controllability after an engine failure; exceeding it exposes passengers and crew to an unacceptable risk. Commercially, the operator may face certificate action, fines, and insurance complications. The correct response is to explain the delay to the passengers, coordinate with the operator for a mass reduction or a later departure, and document the decision. If an alternate airport with lower elevation or a longer runway is available within fuel range, that may be a better solution than waiting. The pilot should record the performance calculations and the reason for the delay in the flight log.