An aircraft is flying over a mountainous region at flight level 290. The highest peak in the flight path is approximately 25 400 feet high. Given that the temperature at FL290 is -60°C and the local QNH reported by nearby station close to sea level is 981 hPa, what is the approximate minimum ground clearance of the aircraft over the highest peak? Assume the pressure altitude is affected by the non-standard temperature and pressure.
Refer to figure.
This question gives us a planned Flight Level of 290 (pressure altitude 29 000 ft) and some meteorological conditions, which we must use to calculate our true altitude, and then compare to the local highest terrain to find our terrain clearance at this altitude.
To start with, we must make a barometric correction to turn pressure altitude into indicated altitude.
The QNH is quoted as 981 hPa, which is 1013 - 981 = 32 hPa less than standard pressure. Because we are in low pressure, our indicated altitude is lower than our pressure altitude. Each hPa is 30 ft of height (unless otherwise specified), so the indicated altitude is 32 x 30 = 960 ft lower than the pressure altitude.
Indicated Altitude = 29 000 - 960 = 28 040 ft
To make this into a true altitude, we must do a temperature correction for any ISA deviation, which we must first calculate.
ISA at 29 000 ft should be 15 - 2(29) = -43°C, but our OAT is 17°C colder than this at -60°C, therefore our OAT is ISA -17°C.
As our temperature is lower than ISA, our true altitude will be even lower than our indicated altitude.
Temperature correction = 4 x ISA Deviation x Height above QNH station (in thousands of feet).
In this case, the QNH station is near sea level, so our temperature correction is 4 x -17 x (28 040/1000) = (-)1907 ft
Therefore, true altitude = 28 040 - 1907 = 26 133 ft
This makes our terrain clearance 26 133 - 25 400 = 733 ft, closest answer 750 ft
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