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From a visual fix at S26°20', E021°15' at 0925 UTC, an aircraft flies directly to Keetmanshoop (S26°32' E018°07') with a TAS of 120 kt and a tailwind of 12 kt. Calculate the ETA for Keetmanshoop.

  • A

    1042 UTC

  • B

    1053 UTC

  • C

    1103 UTC

  • D

    1033 UTC

Refer to figure.
To find the ETA for Keetmanshoop, we first need to calculate the distance and groundspeed (using TAS and the tailwind component) between the two locations to determine the time. From the coordinates, the aircraft is traveling in a south-westerly direction. However, since both latitude and longitude are changing, we must calculate the distance of both components.

1. LONGITUDE CALCULATION
Step 1: Calculate the change in longitude (ch.long)

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

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

  • Change in longitude = E021°15' - E018°07'
  • Change in longitude = 03°08'W*

* We are travelling towards ‘West’.

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 = (S26°20' + S26°32') / 2 = S26°26'

  • Departure (NM) = ch.long (°) x cos (mean lat) x 60
  • Departure = 03°08' x cos (26°26') x 60
  • Departure = 168 NM

2. LATITUDE CALCULATION
Step 1: Calculate the change in latitude (ch.lat)

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

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

  • Change in latitude = S26°32' - S26°20'
  • Change in latitude = 0°12'S*

* We are travelling towards ‘South’.

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

  • Distance (NM) = ch.lat (in minutes) x 1 NM
  • Distance = 0°12' x 1 NM
  • Distance = 12 NM

3. ROUTE DISTANCE CALCULATION
From the figure, a right-angled triangle is formed. Therefore, we can use Pythagoras' Theorem.

  • Hypotenuse2 = Base2 + Perpendicular2 
  • (Route distance)2 = (Distance of ch.lat)2 + (Distance of ch.long)2
  • √(Route distance)2 = √[(12 NM)2 + (168 NM)2]
  • Route distance = 168 NM

3. GROUNDSPEED CALCULATION
Since we have the TAS and the tailwind component, we can calculate the groundspeed (GS). Therefore,

  • Groundspeed (kt) = TAS (kt) + tailwind component (kt)
  • Groundspeed = 120 kt + 12 kt
  • Groundspeed = 132 kt

4. ETA CALCULATION
With the groundspeed and distance known, we can now apply the formula to calculate the flight time to Keetmanshoop.

  • Time (hr) = Distance (NM) / Groundspeed (kt)
  • Time = 168 NM / 132 kt
  • Time = 1.27 hr or 1 hr 17 min

Therefore, the ETA is: Time overhead fix + flight time to Keetmanshoop = 0925 UTC + 01:17 = 1042 UTC

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