The procedure for solving this type of question has been explained by previous posters, so I will confine my post to answering the original question:
How are great circle tracks and rhumb lines drawn when not on a chart?
The two most obvious reasons for making a drawing are:
1. To solve the problem by measuring angles directly from the drawing.
2. To assist in visualize the situation.
Reason 1 applies to a number of exam questions mainly those relate to Polar Stereographic charts.
Reason 2 applies to all other exam questions with the exception of those which refer to a specific type of chart.
The sketch provided by Alex has the following advantages:
1. By showing the meridians as converging lines it makes it obvious which hemisphere (Northern or Southern) is involved.
2. It correctly shows that the Great Circle is a straight line and is shorter than the Rhumb Line.
But it has the disadvantage that it shows parallels of latitude as curved lines, which is contrary to most people’s intuitive vision.
An alternative sketch also shows the meridians as converging lines but shows the Rhumb Lines as straight lines, Great Circles are shown as curved lines. This has the following advantages:
1. By showing the meridians as converging lines it makes it obvious which hemisphere (Northern or Southern) is involved.
2. It shows the parallels of latitude as straight lines, which complies with most people’s intuitive vision.
3. It shows Great Circles as lines which curve up towards the nearest pole and then back towards the Equator. This is how a Great Circle would appear when looking at a side view of a model of the Earth.
Each of the two methods have their advantages, so the choice of which to use is one of personal preference. Both methods will achieve the aim of assisting in visualizing the situation.
The question of whether a Great Circle or a Rhumb Line is a straight line is a curious one. The Equator is a straight line and is a Great Circle because its centre is at the centre of the Earth. But it is also a Rhumb Line because it crosses all meridians at the same angle.
The most commonly used definition of a Rhumb Line is one which crosses all meridians in its path at the same angle. Using this definition, all parallels of latitude and meridians are Rhumb Lines. The meridians are straight-line Rhumb Lines and when coupled with their anti-meridians form great circles. But if we were to draw any Rhumb Line which was not the Equator or a meridian/anti-meridian, it would not produce a circle, but would spiral towards the poles. So those Rhumb Lines which are the Equator or meridians are straight lines, but all other Rhumb lines are curves.
So in attempting to distinguish between Great Circles and Rhumb Lines by testing the straightness, all that can be really said is that all Great Circles are straight lines but some Rhumb Lines are not.
Last edited by keith williams; 28th November 2014 at 19:29.
Reason: Deletion of incorrect statements.