View Full Version : rhumb line placement

07-10-2010, 04:31 PM
I guess I really don't understand cartouche (cartouches?). The navigation lines emanating from them must aid in navigation, but where do you place them in order for them to be useful? I've looked at many maps that use them and, although they look very nice and definitely add flavor to the map, they seem (to me) to be arbitrarily placed purely for aesthetic reasons. For them to be useful, it seems like there must be specific criteria that would dictate their placement. Does anyone know what that criteria might be?
no2 vaporizer (http://vaporizer.org/reviews/no2/)

07-10-2010, 04:56 PM
A line on the surface of the earth that cuts all meridians at the same angle. It appears as a curved line on the surface of a sphere. Only one such line may be drawn through any two points. Although this is not the shortest distance, the direction is constant. Normally, flights of less than 1,000 NM distance follow the rhumb-line track, whereas flights of a longer distance follow the great-circle track. Also called an equiangular spiral, loxodrome, loxodromic curve, or Mercator track.

As far as I can figure out, the origins of the rhumb lines are generally marked by wind roses having the cardinal directions, and are chosen to be easily identifiable navigable points... harbours or points where you could triangulate by line of sight.

-Rob A>

07-10-2010, 05:13 PM
Clarification: A cartouche is a label enclosed by a border, a map's legend and/or title is usually on a cartouche. The rhumb lines may emanate from beneath a compass rose placed in a cartouche.

On some maps, rhumb lines indicate bearing to a particular port or navigation point. The navigator plots the route from the rally point (from which the lines originate) to the destination port by simply aligning the heading along the rhumb line. Or they can run from rally point to rally point. This is an easy method of navigation requiring only a magnetic compass and an accurate chart.

07-10-2010, 05:33 PM
Ah, I see that I had my terms confused as well. But I guess I still don't understand where rhumb lines should originate in order to be useful. My poor understanding leads me to think that they would be most useful if each port had rhumb lines emanating from them. But I don't ever remember seeing a map that incorporated them in that way.
hero honda achiever history (http://www.honda-wiki.org/wiki/Hero_Honda_Achiever)

07-10-2010, 06:20 PM
Maps with many sets of radiating lines are called portolan charts. http://en.wikipedia.org/wiki/Portolan_chart has a reasonable description.

Rhumb lines are hard to do on large-scale maps unless they are in a specific projection. This projection is called the Mercator Projection and it requires relatively advanced mathematics as shown at http://mathworld.wolfram.com/MercatorProjection.html.

07-10-2010, 08:00 PM
Since it's so complicated and I don't know the first thing about placing them properly I just made a large image of radiating lines that I can copy and just plop them down on my ports to fake the look.

07-10-2010, 10:09 PM
Since it's so complicated and I don't know the first thing about placing them properly I just made a large image of radiating lines that I can copy and just plop them down on my ports to fake the look.
All things considered, I think that method will probably work best for me as well.
vapir no2 vaporizer (http://vaporizers.net/no2-vaporizer/)

07-11-2010, 09:45 PM
Yeah, I pretty much go by Ascension's methodology too. I started looking into this issue once and came across a coastal map of Africa that had eight sets of rhumb lines, even though most of the map was land, not sea. Looked completely random to me, so I figured most people who looked at my map wouldn't nitpick too much.

07-12-2010, 05:01 AM
Title edited and moved to 'How To' as others might find this thread useful.

07-12-2010, 10:49 AM
The placement of the origins is not entirely arbitrary. They seem to be arranged in polygonal chains at equidistant intervals from each other. Like this:
Note that rhumb lines are only truly useful as a navigational aid on flat worlds - or a relatively small geographical area if the world is non-flat. The bearings they indicate on those medieval maps become increasingly erroneus the further you plot the course, due to the curvature of the planet's surface.

07-12-2010, 04:15 PM
Just to back up Ghostman's post, one of the maps that inspired me most when trying to figure this out for myself is this one - with the same pattern shown by Ghostman.. Another thing if you want some accuracy to it is to notice the line weights - thick/thin and dashed for particular angles :)

(and i created a PSD with the lines drawn out as well so I could just copy the layer into new files, but the website won't let me upload it - it gets to the end of the file and tells me it's not a valid image file.. grr.)

07-12-2010, 05:01 PM
Yeah, my rhumb line image is 5000 x 5000 so it won't upload either. But for those of you who want one just draw a line on a layer, duplicate the layer, rotate it 90, merge down, duplicate and rotate 45, merge down and duplicate then rotate 22.5.

Bill Hooks
07-16-2010, 08:47 PM
I've just done some quick research and Ghostman is essentially correct, except that there are sixteen points of origin rather than twelve. Each set of parallel lines indicates a wind direction, or rather two wind directions (it might take some Magic Eye-style brain gymnastics to see the chart as overlapping parallels rather than an upended bag of uncooked spaghetti, but once you figure it out it's easy).


EDIT: Oops, didn't notice there was a page two -- this post is probably redundant then.

07-16-2010, 11:11 PM
Looking at those maps I notice that the rhumbs are placed at intersections of a grid. The grids are not set to latitude or longitude (not sure about that first one). So, to me, it looks like a random placement...put your grid anywhere and put rhumbs on top. As far as the parallel lines thing, as soon as you place two sets of radiating lines you'll get a parallel somewhere. Put enough of them on a grid and they'll all be evenly spaced. Interesting to see that the lines use 4 different colors in the one posted by Bill.

Bill Hooks
07-17-2010, 12:26 AM
In fact, in almost every example I can find -- here's another (http://beinecke.library.yale.edu/digitallibrary/portolan.html) -- the basis of the system is a circle whose center is the center of the map, and whose radius touches the top or bottom edge of the map. It's hard not to conclude that the lines are mostly, or even entirely, decorative.

07-17-2010, 12:41 AM
Good eye on that circle thing - wherever the unseen circle hits the grid you place the rhumbs (in these examples). Now to just figure out how the grids are situated, random or reason?

Bill Hooks
07-17-2010, 12:54 AM
The sixteen rhumb line origins are equidistant from each other, spaced by 22.5 degree increments around the circumference of the circle. The grid is drawn after the fact and connects origin points across the circle. Bottom line, it's not random, but nor is it related to actual geographical measurements in any way that I can discern.

07-17-2010, 12:58 AM
The map that Coyotemax posted shows a classic pre-printed base map that navigators would use as the basis for drawing during explorations. The basic layout of a portolan chart included lines from the center out at N, NNE, NE, ENE, E, ESE, SE, SSE, S, SSW, SW, WSW, W, WNW, NW, and NNW. Each of these basic lines has another set out near the edge to allow for simple course changes using a compass at given locations.

Bill Hooks
07-17-2010, 01:56 AM
Okay, with Waldron's post and having read up a little on early navigation I'm starting to get the idea of how these were used. Thanks, Waldron.

07-17-2010, 12:10 PM
Looking at those maps I notice that the rhumbs are placed at intersections of a grid.
The "grid" you're seeing seems to be rather the result of the North-South and East-West going lines, than anything that was put in place before the rhumbs. The rectangular boxes of these grids are of differing sizes and proportions. In a proper grid of square (or even just identically rectangular) boxes it would be impossible to place the rhumbs so that they'd connect to each other forming a circle while at the same time matching the grid intersections.

07-17-2010, 12:22 PM
Haven't been talking, but I have been listening to (and fascinated by) this whole discussion. For any GIMP users, I've spent the morning creating a rhumb diagram according to the rules above -- all of the lines are paths, so you can scale the image, crop it to your map, and then stroke all of the lines however you see fit. Here it is ...

//Edit: Added a .psd version to the zip.

Bill Hooks
07-17-2010, 04:54 PM
Is there any chance that anyone's working on a Photoshop version of one of these things? I've been trying but I'm about ready to tear my hair out.

07-17-2010, 04:59 PM
Ask and ye shall receive :) Actually, I'm an idiot for not including a .psd version in the first place, since gimp will save to psd as easily as xcf. So I did so and added it to the zip in the previous post.

Bill Hooks
07-17-2010, 06:00 PM
Heh, thanks Gidde. Ironically, after I complained I went back to it and made my own anyway. However, that does raise another question . . . how did you get the file size so small on a .psd? Even in grayscale, with smaller pixel dimensions than yours, mine is like 25 megs versus 6 megs for yours. I've checked Image Size and I'm at a loss to figure out what the difference is, except that the headers on your doc say "Gray/8#" whereas mine just say "Gray/8". Is that a clue?

07-17-2010, 08:38 PM
I'm not sure, honestly. It's probably because I made it in gimp compared to one created in PS. That's my best guess, anyhow.

07-17-2010, 11:13 PM
There are a number of factors that affect psd filesize when saving from photoshop. One is "save for compatibility" which is actually quite useless, since the "compatibility" is for one particular outdated format/program from what I remember, and not really necessary at all. Another thing that can impact filesize is the "save with preview", as that will composite the layers into a single layer for image previews and icon thumbnails.

Bill Hooks
07-17-2010, 11:50 PM
Hmm, could be either of those. Unfortunately, "Save As" doesn't seem to give me an option to turn those features off so it's hard to say.

Getting back to maps, I slapped together a try-out inspired that Portuguese chart with tri-color rhumb lines:

07-18-2010, 10:42 AM
You can change that behavior in the Preferences: Edit > Prefereneces… > File Handling

Bill Hooks
07-18-2010, 11:01 PM
Thanks, midgardsormr, I'll play with that and see what I can do.

In the meantime, and I can't believe I didn't think of this before, I saved my tricolor grid as a .GIF with transparency, which hopefully will be of use to somebody:

07-19-2010, 07:30 PM
How about a png. I also just found out that I cannot upload svg. Seems odd.

Wow! That is huge.

07-20-2010, 01:53 AM
Yeah, svg isn't among the allowed file types at this time, but you can zip the file and upload it that way. It just won't show a thumbnail.

07-20-2010, 02:12 PM
Attached is an zip of an inkscape SVG conversion of the gimp paths...

-Rob A>