Hot-afternoon departure from Kano with a shortened runway
It is 1500 local time in March at Mallam Aminu Kano International (DNKN), elevation 1,565 ft. ATIS gives QNH 1008 hPa, temperature 42°C, dewpoint 8°C, wind 070/12 kt, visibility 6 km in dust haze. You are captain of a turboprop at maximum certified takeoff mass. Runway 06/24 is normally 3,300 m, but 850 m is closed for resurfacing, leaving 2,450 m available. Slope is negligible. The performance manual gives a takeoff ground roll of 1,180 m at 1,565 ft ISA and 1,650 m at 5,000 ft density altitude. Company requires a 35% margin over ground roll and 500 ft net at the runway end. The first officer sets 1013 hPa on the altimeter for departure. A deadheading engineer asks whether the aircraft will make 500 ft and whether the setting is correct. Fuel is sufficient for a 30-minute delay, but the crew is already at duty limit after 45 minutes.
1. Calculate pressure altitude and density altitude for the departure. State your assumptions and whether the dust haze changes the calculation.
Read the worked answer
- Pressure altitude: use 30 ft per hPa below 1013. PA = 1,565 + 30 x (1013 - 1008) = 1,565 + 150 = 1,715 ft.
- ISA temperature at that height: 15 - 1.98 x 1.715 = about 11.6°C. Actual temperature is 42°C, so ISA deviation is about +30.4°C.
- Density altitude by the common rule of thumb: DA = PA + 120 x ISA deviation = 1,715 + 120 x 30.4 = about 5,360 ft. Using 118 instead of 120 gives about 5,300 ft, so quote 5,300-5,400 ft.
- Assumptions: dry-air approximation, standard lapse rate, and a QNH rounded to 1013 rather than 1013.25 hPa. The error from rounding is negligible.
- Dust haze does not alter pressure altitude or density altitude. It affects visibility, pilot workload, and possibly engine intake contamination and power margin. It is not a correction to the altimetry calculation, but it is a reason to add conservatism to the performance decision.
2. Using the manual figures, assess takeoff distance and the 500 ft net requirement. Would you depart at maximum mass? What would you change?
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- Interpolate ground roll between 1,565 ft and 5,000 ft: rise is 1,650 - 1,180 = 470 m over 3,435 ft, or about 0.137 m per ft of density altitude.
- At about 5,360 ft DA: ground roll = 1,650 + 0.137 x 360 = about 1,700 m.
- Required 35% margin: 1,700 x 1.35 = about 2,295 m. Available runway is 2,450 m, leaving only about 155 m, or 6%.
- That is a thin margin with no allowance for a tailwind, runway contamination, or engine deterioration. More importantly, ground roll does not prove the 500 ft net requirement. Hot, high density altitude reduces excess power and climb gradient, and the manual extract gives no climb data. At maximum mass the net gradient may not meet 500 ft.
- Decision: do not depart at maximum mass on the basis of this calculation. Reduce payload or fuel, wait for the evening temperature fall, or use a performance chart that explicitly shows 500 ft net at 5,360 ft DA and the proposed mass. If a later departure at, say, 35°C reduces DA to roughly 4,500 ft, the margin improves markedly.
3. The first officer has set 1013 hPa while QNH is 1008 hPa. Explain the altimeter error on departure and on a later approach if QNH remains 1008. Would the hot temperature make the error safer or worse?
Read the worked answer
- With 1013 set instead of 1008, the subscale is 5 hPa too high. The altimeter overreads by about 5 x 30 = 150 ft.
- On the ground at Kano the altimeter would indicate about 1,715 ft while the aircraft is at 1,565 ft. In flight, true altitude is about 150 ft lower than indicated. This reduces terrain and obstacle clearance: high to low, look out below.
- On approach the same error is worse because it occurs close to the ground. If the crew flew an indicated altitude based on 1013, they would be about 150 ft low. The correct setting is QNH 1008, or aerodrome elevation when on the ground.
- Temperature effect: in air warmer than ISA, pressure surfaces are higher, so for a given indicated altitude the true altitude is higher than standard. That partially offsets a 150 ft low error, but it is not a correction and varies with height and temperature. Near the surface, QNH is the correct reference. Do not rely on a temperature offset to cancel a wrong subscale setting.