I think I understand the whole rhumb line and great circle idea but I can't seem to find an answer on this question. Suppose I am driving a car (i don't use ship because I don't want to put the constant compass bearing idea on the table) and that I can move for quite a long distance on land (across Russia for example) without any obstacles. If I keep the steer fixed so that the car moves dead ahead will I be following a rhumb line, a great circle or none of these.

I've found this on wikipedia:

If you were to drive a car along a great circle you would hold the steering wheel fixed, but to follow a rhumb line you would have to turn the wheel, turning it more sharply as the poles are approached

but everything else I've found seems to contradict this. And yet I'm not sure if keeping the steer fixed means fixed dead ahead or fixed turned at 30 degrees left for example.

EDIT After a request to give some examples of contradicting information found on the internet I edit my question to quote an example:

http://www.maritimeprofessional.com/Blogs/Maritime-Musings/February-2011/Rhumb-line.aspx

The problem for navigation is that sailing a true great circle would require constant changes in the course steered

I now understand that what the writer of this text probably refers to when writing course steered is holding the compass indication unchanged. But this way of phrasing it is (at least to a not native english speaker like me) very confusing. In my mind "sailing a true great circle would require constant changes in the course steered" means that i have to constantly turn the ship's steering wheel in order to reach my destination.

I had found some similar examples which I can't find again now. But the greatest problem was I couldn't find any other source stating clearly that moving dead ahead equals following a great circle.

However, stating that "everything else I've found seems to contradict this" was a bit of an exaggeration and I apologize for it.

• Welcome to GIS SE. Could you expand upon "everything else I've found" with an example or two, via the edit button? Commented Dec 28, 2014 at 0:00
• Well done with the follow-up. Yes, course and heading are some of the many synonyms for azimuth or bearing -- all to do with "direction from north". Commented Dec 29, 2014 at 1:50

If the wheels are pointing straight ahead, you are taking the shortest route toward some point directly ahead and thus following a great circle (or geodesic).

If you wish to cross each meridian at exactly the same azimuth each time (and thus follow a rhumb line), you would have to gradually steer slightly more towards the meridian as you progress. Generally, rhumb lines that head between 0° and 90° spiral toward a pole. Parallels of latitude are special cases, with azimuth staying at 90° or 270°.

More special cases to the above are if you happen to be driving straight along a meridian or the equator, which are both great circles and rhumb lines.

• Recommended reading for these elementary properties of geodesics: D. Hilbert & S. Cohn-Stossen, Geometry and the Imagination (Chelsea, NY, 1952), pp. 220-224.
– cffk
Commented Dec 29, 2014 at 10:23
• @MartinF aren't latitude circles also rhumb lines ?
– user36959
Commented Jan 20, 2016 at 14:52
• @gansub -- Correct. And I've added more notes to the answer. Commented Jan 21, 2016 at 1:10

I know the question has answered already, but allow me to show you something cool for future use: A live Google map where you can move the edge markers affecting the great circle and rhumb line same time. Here is the link: Great circle article!

So I found this question in a search for why the great circle route requires course corrections, and this post got me to my answer but didn't answer it directly.

As what @gansub says, latitude circles are also rhumb lines that are 90 degrees from longitude. So, we can look at a real-world example of Venice, Italy and Montreal, Canada- both at 45 degrees N. Now, if we travel on the line of latitude from one to the other we are traveling on the rhumb line between the two, as all meridian crossing are at 90 degrees, so our heading is always due west or east. You can see this easily on a mercator projection, where it literally is the 45th parallel. What you can't see is that there is a significant amount of curvature that has to be "climbed" and then "descended" as compared to a direct through-earth line between the points. I'll later refer to that as a "bulge", and this is where the two lines differ.

When we calculate the great circle route, the line on the sphere isn't in the same plane as our navigation lines, so navigating by it means constantly adjusting our heading, moving northward for half the trip, then southward for the other. You can experience this yourself on Google Earth if you plot a line (which will be a great circle) between the two cities the corresponding line will move north (compared to the 45th parallel) for half the trip, then south for the other half.

This reduces the "bulge" of the sphere to its absolute minimum, and thus the distance between the cities.