Meridians (lines of longitude) are semi-great circles joining the poles and they converge as they run towards each pole.
The highlighted areas represent change of longitude (Ch. Long) and the Ch. Long is the same value despite the latitude.
The Definition of Convergence is the angle between two Meridians at a given Latitude,
..or the amount by which a great circle track changes from one point to another.
Convergence is maximum at the poles, zero at the Equator, and elsewhere the convergence is dependent upon the latitude.
Convergence Formula can be used for calculations
Convergence = Ch. Long x sin Mean Latitude
You might need to rearrange the formula depending on what information you have been given.
Drawing a sketch will help you solve convergence problems
- Check you are in the right hemisphere.
- Use the given track to decide which point is on the left and which is on the right.
- Draw angles clockwise from North.
- Don’t worry about latitudes as the diagram keeps things simple.
The Initial Great Circle track is the track measured from the Meridien passing through the point of departure.
The Final Great Circle track is the track measured from the Meridien passing through the destination.
Example 1
You are in the Southern Hemisphere.
The initial GC track at A is 257°, Convergence is 38°, what is the GC track at B?
Solution:
Draw a sketch diagram with the known values
By inspection we can see that the track direction at B is greater than at A, so the GC track at B must be 257° plus 38°
Answer: 295°
Example 2
What is the Convergence between A (45°30’S 025°05’E) and B (16°30’S 063°47’E)?
Solution:
Calculate Ch Long and the mean latitude.
- Ch long = 63°47’ minus 25°05’ = 38°42’
- Mean Lat = 45°30’ plus 16°30’ ÷ 2 = 31°S
- Convergence = Ch. Long x sin mean lat
= 38°42’ x sin 31°
= 38.7 x 0.515
Answer: = 19°55’55’’ = 19.93°(20°).