Cold Temperature Altimetry over the Southern Alps
You are at FL140 over the Southern Alps near Aoraki/Mt Cook. The highest terrain in the area is 12,200 ft. OAT is −30°C and QNH is 1013 hPa, so you are using standard pressure. Company procedure requires 2,000 ft terrain clearance. The first officer calculates that 14,000 ft indicated gives 1,800 ft clearance above the 12,200 ft terrain and proposes to continue. You know that cold temperature causes true altitude to be lower than indicated altitude. The aircraft is not equipped with a radio altimeter. You must calculate the true altitude using the 4 ft per 1,000 ft per °C ISA deviation rule, determine the actual terrain clearance, and decide whether to climb, divert, or continue. The next waypoint is 20 nm ahead; terrain rises to 12,200 ft.
1. Calculate the ISA deviation and the true altitude at FL140.
Read the worked answer
ISA temperature at 14,000 ft = 15 − 1.98 × 14 = −12.7°C.
ISA deviation = OAT − ISA temperature = −30 − (−12.7) = −17.3°C.
Using the 4 ft per 1,000 ft per °C rule: Correction = 4 × 14 × (−17.3) = −969 ft.
True altitude = 14,000 − 969 = 13,031 ft.
Because the air is colder than ISA, the aircraft is about 969 ft lower than the indicated altitude suggests.
2. Determine the actual terrain clearance and whether it meets the 2,000 ft requirement.
Read the worked answer
Terrain is 12,200 ft. True altitude is 13,031 ft.
Actual clearance = 13,031 − 12,200 = 831 ft.
The company minimum is 2,000 ft, so the clearance is deficient by 1,169 ft. The first officer's 1,800 ft figure is also incorrect because it uses indicated altitude. The aircraft is not safely clear of terrain under the company standard.
3. What action should the crew take, and why is indicated altitude misleading here?
Read the worked answer
Climb immediately or turn away from the rising terrain. Do not continue at FL140. Indicated altitude is pressure altitude; in air colder than ISA, the true altitude is lower than the indicated altitude. The colder the air and the higher the altitude, the larger the error.
To obtain 2,000 ft clearance over 12,200 ft, the aircraft needs a true altitude of 14,200 ft. With the current correction, the indicated altitude would need to be about 15,169 ft, so a climb to at least FL160 would be needed and the true altitude should be recalculated after the climb. The crew should also consider the missed approach or diversion options if terrain or performance prevents the climb.