How are great circle tracks and rhumb lines drawn when not on a chart?

[Alex Whittingham]

A great circle track is the one you would get if you stretch a rubber band across the globe from point to point. A rhumb line would lie on the equatorial side of that and be a longer (constant direction) track.

These lines exist on a spherical surface. You can't represent them totally accurately on a piece of paper, only approximate to them. The purpose of the sketch diagrams we draw is only to get the sense of the question right, and to determine whether perhaps convergency is added or subtracted, or conversion angle.

For this reason I would suggest you lay out your diagrams in a standard style, and make no attempt to get them looking exactly like the lines would look on the earth's surface, because if you do you are going to fail anyway. The style I use follows these rules:

1. Determine which hemisphere you are in, draw in the meridians as straight lines with an easily discernible slope that reflects the hemisphere.
2. Draw in a representation of the great circle track as a straight horizontal line between the two meridians. Make sure it extends beyond the meridians.
3. Look at the question. Decide whether the track is generally Easterly or generally Westerly. If Easterly your start point is on the left and your end point on the right, vice versa if Westerly. Label points 'A' and 'B' or whatever.
4. Look at the question. If there is a rhumb line involved draw it in as a curved track on the equatorial side of the straight line great circle track between points A and B. Make sure it extends out beyond points A and B.

There are two possible reasons why someone would draw the rhumb line as a straight line and the great circle as a curve. The first and most common one is that they are confused and under confident about exactly what great circles and rhumb lines are (and who isn't when they first meet them??) and the second is when someone is trying to represent how the lines appear on a Mercator chart, which is a very particular archaic chart projection which does actually show rhumb lines as straight lines and great circles as curves. If you are asked questions on a Mercator you can draw the diagram out as it would be on the chart but the question will work just as well if you stick to a 'standard diagram' format as above.

I will try to add an example question with a diagram to this thread later today. Red, if you could provide the full text of your first example I will do that one for you.