Question: Angular 'Rays' on Maps

[ValiantBadger]

Hello! I've been very interested in maps for a while now, and I something I see a lot among them are these angular 'rays' or lines (or whatever they're called), often clustered together and spewing from a certain position.
I'm sure this is probably something to do with coordinating. For the record I do not mean latitude/longitude lines.
I'm talking about lines like the ones in this map:
http://upload.wikimedia.org/wikipedi...d_Thornton.jpg

This one has a cluster in the bottom right, bottom left, one at the top, and two in the upper left- but for what reason?
What I'm asking is, what are these line-clusters called and why are they there?

[Falconius]

They are called Rhumb Lines. Their purpose is to aid in navigation.

As far as I understand, which is to say I'm probably incorrect, navigators would align their ships with that point on a map then steer on that compass point until the next node whereupon they would alter their course accordingly. Note that they probably also used parallel rulers so they didn't actually have to be at the node physically. This would allow them to navigate quite easily without having to account for projections etc.

[ValiantBadger]

They are called Rhumb Lines. Their purpose is to aid in navigation.

As far as I understand, which is to say I'm probably incorrect, navigators would align their ships with that point on a map then steer on that compass point until the next node whereupon they would alter their course accordingly. Note that they probably also used parallel rulers so they didn't actually have to be at the node physically. This would allow them to navigate quite easily without having to account for projections etc.

Oh, thanks for the response!

[Mermaid Shayna]

Just joined the forum (hi!) And I'm falling in love with maps. In this age of technology we don't see maps much anymore and never realize how vomplicated they are, and how cool they look.

[Hai-Etlik]

Rhumb lines are also called "Loxodromes" or "Lines of constant Bearing". That last one should give you a clue as to what they fundamentally are. If you have a perfect compass aligned to true north, and you pick a bearing on it, and then follow that bearing on the compass walking forward, you'll trace out one of these lines.

On the globe, these lines (except in the cardinal directions) are spirals that get tighter and tighter around the poles. (Think about trying to walk northeast when you are only a few metres from the north pole.) On a map which is "Bearing preserving" they will appear as straight lines.

It is important to understand the difference between these lines, and "Great Circles", also known as "Orthodromes" or "Geodesics". An Orthodrome is the line you get by "walking straight" without turning to one side or the other, or by slicing the globe through the centre. The smaller of the two arcs of a great circle through two points is the shortest distance between those two points. That's why a flight from Vancouver to London down around 50 N will go north of Iqaluit in the arctic. The loxodrome between them is almost due east, but the orthodrome goes through the arctic, and that's the best analogue of a "straight line" in spherical geometry.

Maps with clusters of rhumb lines are intended for marine navigation, particularly by a method called "dead reckoning" which is when you use a compass to figure out your direction, and then estimate the distance you've travelled following that bearing. they can also show up on other maps, although it doesn't make sense. They should never appear on a map that is not bearing preserving (the same goes for a compass rose).

So how do you make a map bearing preserving? Method one, make it a large scale map ("zoomed in") in an appropriate projection to its extent. If you only look at a small part of the globe, it's fairly close to flat, so if you use a large scale, you can draw a loxodrome and it will come close to a straight line within the small extent of the map.

Method two, use the Mercator projection. The Mercator projection is designed for dead reckoning navigation, and so it specifically preserves bearings. It has to distort areas a great deal to do this, and the distortion increases toward the poles (That infinite spiral in toward the pole means the Mercator map need to be infinitely tall to contain the poles while also straightening out the line. That's why Mercator maps always chop off the polar regions, and why everything gets "bigger" the further from the pole you get on them.

If neither of those is true of your map, it is not bearing preserving and should not have rhumb lines or compass roses.

[Midgardsormr]

The places where the lines intersect are called rally points.

I notice that we're getting a lot better at answering this question!

Incidentally, that is a lovely sample; thanks for posting it!