Is it possible to fly to any destination on a rhumb line track?

Question

If we follow a constant rhumb line track, it would eventually lead to the pole (depending on your hemisphere) , so then it may not be possible to fly between any two points on a rhumb line track?

Looking at the picture it gives the impression that I would reach the north pole before I would be able to reach my destination

I do not think a Rhumb line that follows a Latitude will ever lead to a Pole. The most basic example is circling the equator by going Due East/West. — abelenky, Dec 09 '21 at 21:42
Sure you could. You could even fly a Fibonacci spiral to your destination if you like, but why? — Michael Hall, Dec 10 '21 at 02:04
To all asking, please look at the picture to know why I have this confusion — Sachin Chaudhary, Dec 10 '21 at 06:19
@SachinChaudhary I'm not sure how that picture helps. It doesn't show the destination you want to fly to! The fact that most rhumb lines eventually lead to a pole seems to have nothing to do with your actual question. — Bianfable, Dec 10 '21 at 09:07
This question is effectively asking that if you keep moving towards the edge of a table, will you eventually fall off? Well, yes, because the path you describe by definition keeps moving towards a pole at a constant rate. — Flater, Dec 10 '21 at 14:11
What the picture demonstrates is that if you choose a direction to fly without regard to where you want to go, you will likely not reach your desired destination. — David K, Dec 10 '21 at 14:31
If you flew the rhumb line you depicted, you would fly through each and every point along the track. So why do you say it isn't possible to fly through two points along it? And if you are talking about two different points not on this particularly rhumb line, then simply draw a new rhumb line that connects them. You haven't done a very good job at explaining the basis of your confusion, and I don't know why this question has 6 upvotes... — Michael Hall, Dec 10 '21 at 15:51

mins · Accepted Answer · 2021-12-10T15:58:27.967

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A rhumb line is a line which crosses all meridians at the same angle. Such a route is of constant true heading. This property is the reason rhumb line navigation was invented, and Mercator maps created.

On a Mercator map you just draw the straight line between the two points. This means you can always draw a route between two arbitrary places. E.g. let's connect:

Rio de Janeiro
Nome, a small city in Alaska
An abitrary point at coordinates lat = 85°, lon = 0°.
Hawaii
Stonehenge

Dotted lines show how the route completes pole-to-pole (full rhumb lines)

On most projections, rhumb lines appear as curves spiraling between poles, e.g. on this orthographic projection:

Why rhumb line navigation in the first place?

16th century navigators knew perfectly the shortest route was a great circle. But following a great circle requires constant and precise heading adjustments.

To simplify navigation, they split a great circle route into segments, and navigated each segment as a rhumb line, that is a route within the same rhumb, a rhumb being 1/32th of compass rose (a 32-point rose was often part of the map). They adjusted the heading only at the beginning of the next segment, possibly after they confirmed their position using a sextant.

They used maps just invented by Gerardus Mercator for the purpose of facilitating drawing rhumb lines and determining headings.

Aircraft with computerized navigation systems and autopilots are able to adjust the heading as required. They restored the interest in pure great circle navigation.

edited Dec 10 '21 at 15:58

answered Dec 09 '21 at 22:10

mins

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Please look at the photo in my edit. Looking at the picture it gives the impression that I would reach the north pole before I would be able to reach my destination. Or is the case that the rhumb line atleast first would lead me to my destination, and after that if I continue on that track I would go to north pole? – Sachin Chaudhary Dec 10 '21 at 06:20
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@SachinChaudhary The latter. If you start close to the equator and head nearly due east (say, 89°), you will circle the Earth multiple times before getting close to the pole. (Drawn on a map in the Mercator projection, your route will comprise multiple parallel lines stretching all the way across the map). – TooTea Dec 10 '21 at 07:26
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As long as your points of departure and destination are on the same hemisphere, you can connect any such points with a rhumb line. It's just a matter of selecting a suitable angle with regard to the longitudes. – Jpe61 Dec 10 '21 at 13:31
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@Jpe61 -- all the posted answers seem to show that the departure and destination do not need to be in the same hemisphere – quiet flyer Dec 10 '21 at 15:01
@quietflyer: Actually any rhumb line goes from one pole to the other, and connect any pair of intermediate points regardless of their latitudes. – mins Dec 10 '21 at 16:49
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@mins Except for rhumb lines going straight east ($\beta=90^\circ$) or west ($\beta=-90^\circ$). They'll never reach a pole since they maintain latitude. The term loxodrome explicitly excludes these special cases. – Bianfable Dec 10 '21 at 18:58
@Bianfable: Yes, "any" except these cases. – mins Dec 10 '21 at 18:59
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@SachinChaudhary: “Looking at the picture it gives the impression that I would reach the north pole before I would be able to reach my destination”. Why do you say so? Which is your destination? The curve in your image touches a lot of points (infinitely many!). If your destination isn't among them, you have chosen a wrong angle beta; just chose the correct one, according to what this answer explains. – DaG Dec 10 '21 at 23:18
Holy crap you are right @mins, of course. Now that I actually think about it, it's obvious. Not always wise to go by memory... – Jpe61 Dec 11 '21 at 18:27

HiddenWindshield · Answer 2 · 2021-12-09T21:22:16.477

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Yes, it's possible to fly from any point on the Earth from any other point on the Earth via a Rhumb line. The destination pole depends on the course you select, not the hemisphere you happen to start in. Just because a Rhumb Line leads to a pole doesn't mean it leads to the nearest pole. A track of, say, 135 is always going to terminate at the South pole, even if you start in the Northern hemisphere.

edited Dec 09 '21 at 21:22

answered Dec 09 '21 at 20:42

HiddenWindshield

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xxavier · Answer 3 · 2021-12-09T22:01:21.203

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If you fly an orthodromic course, the rhumb changes continuously during the flight unless the points of departure and arrival are in the equator or in any great circle that passes through the poles...

It is, however, always possible to fly a constant-rhumb course –a loxodrome– between any two points on the planet.

edited Dec 09 '21 at 22:01

answered Dec 09 '21 at 21:55

xxavier

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Is it possible to fly to any destination on a rhumb line track?

3 Answers3