When taking the exam the most important thing is to select the correct answer.
When preparing to take the exam the most important thing is to learn the correct method.
The great circle track X - Y measured at x is 319°, and Y 325° Consider the following statements:
a Southern hemisphere, Rhumb line track is 322°
b Northern hemisphere, Rhumb line track is 313°
c Southern hemisphere, Rhumb line track is 331°
d Northern hemisphere, Rhumb line track is 322°
The important thing to remember here is because both the rhumb line and the great circle join the two points, the rhumb line track is the average of the great circle track at the two points. So in this question we just need to add the two together and divide by two to get (319 + 325) / 2 = 322.
Great circles are always convex to the nearest pole.
We have a great circle that is changing from 319 to 325, so we must be in the southern hemisphere. Sketch the situation if have difficulty visualising it.
A great circle track joins position A (59°S 141°W) and B (61°S 148°W). What is the difference between the great circle track at A and B?
a It increases by 6°
b It decreases by 6°
c It increases by 3°
d It decreases by 3°
For this one we need to use the conversion angle formula
The conversion angle is the difference between the great circle and the rhumb line.
Conversion angle = 1/2 x Sin mean latitude x difference in longitude.
In this case we have
Mean latitude = (59S + 61S) / 2 = 60S.
So Conversion angle = 1/2 x Sin60S x ( 148W - 141W)
If we use the conventions that
Latitudes North are positive
Latitudes South are negative
Differences in longitude to the West are positive
Differences in longitude East are negative
We get
Conversion angle = 1/2 x Sin -60 x 7W = -3.03 degrees.
The conversion angle is the difference between the great circle and the rhumb line so at position A the great heading is 3.03 degrees less than the rhumb line.
But the great circle and the rhumb line meet at positioon B so the great circle heading must gradually increase until it becomes 3.03 degrees greater than the rhumb line.
Starting 3.03 less and ending up 3.03 more, the great circle must have increased by 6.06 degrees.
If the use of plus and minus values is too confusing, then simply sketch the situation.
Great circles are always convex to the nearest pole.
We are in the southern hemisphere so the great circle initialy heads south of the starting point then gradually curves to the north until it reaches the second position. We are going west so this curving must represent a gradual increase in heading.
So the answer to this question is increasing by 6.06 degrees.