Density Altitude at El Alto on a Warm Afternoon
You plan a VFR departure from El Alto (elevation 13,325 ft / 4,061 m) in a normally aspirated Cessna 172. The airfield QNH is 1020 hPa and the outside air temperature is 22 °C. Your aircraft has a maximum takeoff mass of 1,111 kg and a maximum permissible zero-fuel mass of 1,000 kg. The planned fuel load is 120 kg, the pilot and passenger together weigh 160 kg, and baggage is 30 kg. The runway is 4,000 m long but only the first 2,500 m are usable for the takeoff run due to a displaced threshold marking on the opposite end. The aircraft's POH gives an indicated airspeed of 55 kt for rotation and a takeoff ground run of 300 m at sea level, ISA conditions, at maximum mass.
1. Calculate the pressure altitude and estimate the density altitude. What effect does this have on the takeoff run?
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Pressure altitude = field elevation + 30 ft per hPa below 1013.25. QNH is 1020 hPa, which is 6.75 hPa above standard, so pressure altitude ≈ 13,325 − (6.75 × 30) ≈ 13,325 − 203 ≈ 13,122 ft. Using the rule of thumb that density altitude increases about 120 ft per °C above ISA, and ISA temperature at 13,000 ft is roughly −3 °C (15 − 2 × 13), the temperature excess is about 25 °C. Density altitude ≈ 13,122 + (25 × 120) ≈ 16,100 ft. At this density altitude the air density is roughly 60 percent of sea-level value, so the engine produces far less power and the true airspeed for a given IAS is much higher. The takeoff ground run and the distance to 50 ft will both increase dramatically - typically by a factor of three or more compared with the POH sea-level figure. The 300 m sea-level ground run could easily become 900–1,200 m, and the climb gradient will be marginal. The 2,500 m usable runway may physically contain the ground run but leaves little margin for the climb segment, and obstacle clearance must be checked separately.
2. Check the mass and balance against the limits and decide whether the flight can legally depart.
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Zero-fuel mass = empty mass + pilot/passenger + baggage. Empty mass is not given, but maximum takeoff mass is 1,111 kg and maximum zero-fuel mass is 1,000 kg. If we take the empty mass as 750 kg (typical for a 172), then zero-fuel mass = 750 + 160 + 30 = 940 kg, which is below the 1,000 kg limit. Takeoff mass = 940 + 120 = 1,060 kg, which is below 1,111 kg. So the loading is within limits on mass. However, the centre of gravity must also be checked: with two occupants forward and 30 kg in the baggage compartment, the CG may be near the forward limit, which increases rotation speed and takeoff distance. If the CG is forward of the limit, the aircraft may be unable to rotate at 55 kt and the takeoff run will be longer. The pilot should compute the CG from the loading chart and confirm it lies within the envelope. On mass alone the flight is legal, but the combination of high density altitude and a possibly forward CG makes the departure marginal and the pilot should consider offloading fuel or baggage.
3. What operational decision would you make, and what alternate plan would you propose?
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The combination of a density altitude around 16,000 ft, a 1,060 kg takeoff mass, a possibly forward CG and a usable runway of 2,500 m makes the departure unsafe for a normally aspirated 172. The aircraft would be operating near its absolute ceiling for the ambient conditions, and the climb gradient after liftoff would be very shallow. The correct decision is to delay the flight until the cooler early morning hours (when the temperature may be 5–8 °C, cutting density altitude by 1,500–2,000 ft), reduce mass by offloading fuel to the minimum required plus reserve, and move baggage aft within the CG envelope to bring the CG nearer the mid-range. If the departure is still marginal, the pilot should plan a different route from a lower-elevation airfield or accept a lower cruise altitude. The key judgement is that legal mass limits do not guarantee adequate performance; density altitude and CG must be evaluated together before accepting the takeoff.