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An aircraft flies to PHALABORWA (S23°54’ E031°10’) from a fix located at (S25°30’ E030°10'). What is the distance?

  • A

    120 NM

  • B

    90 NM

  • C

    100 NM

  • D

    110 NM

Refer to figure.
Based on the coordinates, it can be seen that the aircraft is travelling in a north-easterly direction. Since both latitude and longitude are changing, the distance must be calculated by considering both components.

1. Calculate the distance of change in latitude
Step 1: Calculate the change in latitude (ch.lat)

  • For different hemispheres, we add the two latitudes together.
  • For same hemispheres, we subtract the smaller latitude from the larger one.

Since both positions lie in the Southern Hemisphere, we will subtract the latitudes. Therefore,

  • Change in latitude = S25°30' - S23°54'
  • Change in latitude = 1°36'N*

* We are travelling northwards to a lower latitude, which is why ‘North’ is mentioned.

Step 2: Calculate the distance
A change of 1' of latitude corresponds to a distance of 1 NM and a change of 1° of latitude corresponds to 60 NM. Therefore,

  • Distance (NM) = change in latitude (°) x 60 NM
  • Distance = 1°36' x 60 NM
  • Distance = 96 NM

2. Calculate the distance of change in longitude
Step 1: Calculate the change in longitude (ch.long)

  • For different hemispheres, we add the two longitudes together.
  • For same hemispheres, we subtract the smaller longitude from the larger one.

Since both positions lie in the Eastern Hemisphere, we will subtract the longitudes. Therefore,

  • Change in longitude = E031°10' - E030°10'
  • Change in longitude = 01°00'E*

* We are travelling eastwards to a higher longitude, which is why ‘East’ is mentioned.

Step 2: Calculate the distance
The length of 1° of longitude varies with latitude. Therefore, the ‘departure’ formula is used to calculate the east–west distance.
Mean latitude: (Lat 1 + Lat 2) / 2 = (S25°30' + S23°54') / 2 = S24°42'

  • Departure (NM) = ch.long (°) x cos (mean lat) x 60 
  • Departure = 01°00' x cos (24°42') x 60
  • Departure = 55 NM

CALCULATE THE ROUTE DISTANCE
From the figure, a right-angled triangle is formed. Therefore, Pythagoras’ theorem can be used.

  • Hyp2 = Base2 + Perp2
  • (Route distance)2 = (Distance of ch.lat)2 + (Distance of ch.long)2
  • √(Route distance)2 = √[(96 NM)2 + (55 NM)2]
  • Route distance = 110 NM

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