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Given:

Altimeter setting: 1013 hPa
Altimeter reading: 5 000 ft
Outside air temperature at 5 000 ft: +5°C
QFE: 958 hPa
QNH: 983 hPa
What is the true height of the aeroplane above the aerodrome?
(Barometric lapse rate: 27 ft/hPa)
  • A
    4 190 ft
  • B
    4 325 ft
  • C
    4 865 ft
  • D
    3 515 ft
Refer to figure.

True altitude calculation from a Flight Level:
In this question, we are given a pressure altitude and are asked for the terrain clearance, therefore we need to determine the corresponding true altitude.

The first step is to compute the pressure correction by considering the deviation from the standard mean sea level pressure of 1013 hPa: 1013 hPa - 983 hPa = 30 hPa. The question provides a barometric lapse rate near the surface of 27 ft/hPa, the pressure correction can be calculated as follows: Pressure correction = 30 hPa x 27 ft/hPa = ­­­810 ft.
This value needs to be subtracted from the pressure altitude as per the rules below:

Indicated altitude = 5 000 ft - 810 ft = 4 190 ft.

To determine the temperature correction, it is necessary to have knowledge of the ISA air temperature for the given altitude (5 000 ft). In the International Standard Atmosphere (ISA), the air temperature at sea level is 15ºC, and the temperature lapse rate is -2ºC/1 000 ft. The formula to calculate the ISA temperature is therefore: ISA temperature = 15ºC - (5 000/1 000) x 2, giving an ISA temperature of ­­­+5ºC. The actual outside air temperature is also +5 ºC, which means OAT = ISA. Therefore, the temperature correction may be disregarded.

Next, we need to calculate the elevation of the aerodrome: QNH - QFE = 983 hPa - 958 hPa = 25 hPa

The question provides a barometric lapse rate near the surface of 27 ft/hPa:
25 hPa x 27 ft/hPa = 675 ft airfield elevation

The true height of the aeroplane below the aerodrome = 4 190 ft – 675 ft = 3 515 ft below the ground of the aerodrome.


RULES. The following rules should be considered for altimetry calculations:
  • All calculations are based on rounded pressure values to the nearest lower hPa.
  • The value for the barometric lapse rate between MSL and 500 hPa to be used is 30 ft/hPa as an acceptable approximation of the barometric lapse rate (if not provided by the question).
  • To determine the true altitude/height, the following rule of thumb, called the ‘4 %-rule’, shall be used: the altitude/height changes by 4% for each 10°C temperature deviation from ISA.
    For simplification: Height correction for the temp = 4 × (ISA DEV) × Indicated alt/1000 = ___ ft
  • If no further information is given, the deviation of the outside-air temperature from ISA is considered to be the same throughout the whole layer.
  • The elevation of the aerodrome has to be taken into account. The temperature correction has to be considered for the layer between the station (usually an aerodrome) and the position of the aircraft.
HIGHER PRESSURE; INDICATED ALTITUDE > PRESSURE ALTITUDE
LOWER PRESSURE; INDICATED ALTITUDE < PRESSURE ALTITUDE
WARMER THAN ISA; TRUE ALTITUDE > INDICATED ALTITUDE
COLDER THAN ISA; TRUE ALTITUDE < INDICATED ALTITUDE
DEFINITIONS.
Pressure Altitude: The altimeter indication with standard pressure (1013.2 hPa) set.
Indicated Altitude: The altimeter indication with local QNH set.

True altitude: The actual altitude of the aircraft above mean sea level.

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