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Calculate the mean magnetic track and distance from Bisho (S32°55' E027°16') to Burgersdorp (S30°58' E026°20').

  • A

    181°(M) and 127 NM

  • B

    001°(M) and 100 NM

  • C

    057°(M) and 100 NM

  • D

    338°(M) and 127 NM

Refer to figure.
Based on the coordinates, the aircraft is travelling in a north-westerly direction. However, since both latitude and longitude are changing, we need to calculate both components.
1. 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 together.

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

  • Change in latitude = S32°55' - S30°58'
  • Change in latitude = 1°57'N*

* We are travelling towards ‘North’.

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

  • Distance (NM) = ch.lat (°) x 60 NM
  • Distance = 1°57' x 60 NM
  • Distance = 117 NM

2. 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 together.

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

  • Change in longitude = E027°16' - E026°20'
  • Change in longitude = 0°56'W*

* We are travelling towards ‘West’.

Step 2: Calculate the distance
The change 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 = (S32°55' + S30°58') / 2 = S31°56'30''

  • Departure = ch.long (in minutes) x cos (mean lat)
  • Departure = 56' x cos (31°56'30")
  • Departure = 48 NM

3. ROUTE DISTANCE CALCULATION
Using Pythagoras' Theorem:

  • Hyp2 = Base2 + Perp2
  • (Route distance)2 = (Distance of ch.long)2 + (Distance of ch.lat)2
  • √(Route distance)2 = √[(48 NM)2 + (117)2]
  • Route distance = 127 NM

4. TRACK CALCULATION
From the figure, a right-angled triangle is formed. Therefore,

  • cos (angle) = Base / Hypotenuse
  • cos (angle) = 48 NM / 127 NM
  • cos (angle) = 0.38
  • angle = arccos (0.38)
  • angle = 68°

Since the track is measured clockwise from True North. Therefore,

  • True track: 270° + 68° = 338°

270° is the angle from True North to the base, and the angle between the base and the hypotenuse is 68°.
Since no variation is given in the question, we assume it to be 0°. Therefore,

  • Magnetic Track = True Track → 338°(M)

Therefore, the answer is: 338°(M) and 127 NM

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