Density altitude at Lichinga
You plan a morning departure from Lichinga (FQLG), elevation approximately 4,500 ft AMSL, in a normally aspirated Cessna 172. The aerodrome temperature at 08:00 is 24 °C and the QNH is 1013 hPa. Runway length available is 1,600 m, dry asphalt, with a 1% upslope. Aircraft mass is 1,050 kg (MTOW 1,111 kg). The POH at sea level, ISA, MTOW, gives a take-off ground roll of 290 m and a 50 ft obstacle clearance distance of 520 m. The aircraft has no turbocharger.
1. Estimate the density altitude and explain qualitatively how it affects the take-off run and climb gradient.
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Density altitude. Pressure altitude = 4,500 ft (QNH 1013 ≈ standard). ISA temperature at 4,500 ft = 15 − (2 × 4.5) ≈ 6 °C. The actual temperature is 24 °C, i.e. about 18 °C above ISA.
A useful rule of thumb: density altitude rises roughly 120 ft per °C of ISA deviation. 18 × 120 ≈ 2,160 ft. So density altitude ≈ 6,600 ft.
Effect. At 6,600 ft DA the air density is roughly 80% of sea-level standard. The engine produces less power (normally aspirated, mixture leans but cannot recover full power), the propeller thrust falls, and true airspeed for a given IAS is higher so the ground roll lengthens. Climb gradient and rate of climb both degrade markedly. Expect the POH sea-level figures to be roughly doubled, before applying the upslope and mass corrections.
2. Using the POH figures given, estimate the actual take-off distance to 50 ft and decide whether the 1,600 m runway is adequate with a sensible safety factor.
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Corrections (approximate, typical C172 factors).
- Density altitude 6,600 ft: factor ≈ 1.9–2.0 on both ground roll and 50 ft distance
- 1% upslope: factor ≈ 1.1
- Mass 1,050 kg vs 1,111 kg: factor ≈ 1.05 (lighter, so slightly shorter)
Ground roll. 290 × 1.95 × 1.1 × 0.95 ≈ 590 m. To 50 ft. 520 × 1.95 × 1.1 × 0.95 ≈ 1,060 m.
Judgement. Against 1,600 m the 50 ft distance of ~1,060 m leaves about 540 m, i.e. a factor of only 1.5. That is below the 1.5–2.0 planning margin normally demanded for high-density-altitude operations, and the estimate carries uncertainty (wind, surface, pilot technique, real POH chart vs. rule of thumb). The prudent decision is to delay to a cooler part of the day, reduce mass (fuel to the minimum needed for the sector), or use a longer runway if one exists. If you go, brief a rejected take-off point and accept that a engine failure after rotation at this DA leaves very little climb performance - plan the departure path over the lowest terrain.