Projection Maps for Alien World Navigation

[DaveC426913]

An ocean world navigational map will not have any reason to chop up its navigational maps into artificial pieces to accommodate continents. That disqualifies several projections to start.

I want to figure out what kind of a projection they would use.

Since they would be doing all their traveling as-the-crow-flies they'll want a map that simplifies measurements and calculations for headings and distances, so that courses could be plotted by hand as simply as possible. (Theoretically, airplanes on Earth could do this, if they didn't use flight paths between major air spaces).

Being a sailor, I know a little about plotting, but it is done on scale maps small enough so as to be considered flat. Headings and distances are consistent anywhere on a given map, making chart-plotting easy.

How could you maximize this on a world map? Or at least on a small set of large-scale quadrant-like maps?

 

[DaveC426913]

Alternately, I wonder if there's a way to make a rigid globe that can fold into a compact shape. With such a device, a simple world line would show every desired heading and distance perfectly...Note: must be manual function. No electronics allowed.

 

[DaveC426913]

Furthermore, is there any reason, other than tradition, to use 360 degrees on a map of a new world?

What if it were metric? One hundred "degrees" from equator to pole, 400 "degrees" of longitude around the equator.

Would problems crop up in the math?

 

[anorlunda]

If it was truly an ocean world with no land, no ice , why have a map? Why travel at all? There would be nothing particularly different about where you're going compared to where you came from.

A possible exception might be the poles.

On the other hand, if it does have land, then maps are needed and why should map making be any different than on Earth. After all, Earth is 70% of the way there to being an ocean world.

So, I think you need to ask the question. What is the purpose of a map on an ocean world?

 

[DaveC426913]

If it was truly an ocean world with no land, no ice , why have a map? Why travel at all? There would be nothing particularly different about where you're going compared to where you came from.

An ocean world doesn't mean zero land.

The Pacific Ocean has uncountable islands yet is still an ocean.

On the other hand, if it does have land, then maps are needed and why should map making be any different than on Earth. After all, Earth is 70% of the way there to being an ocean world.

Why should it be the same? Because 'this is the way we always dun it'?

I repeat:

• many Earth projections try to accommodate continents by splitting the parts up artificially
• projections that don't keep continents together, still have broad distortions in distances and/or directions that make them unsuitable for plotting a course
• on Earth, world-scale maps are not usually used for plotting and navigation - which is why we've never had any reason to have world maps that optimize plotting
• if, OTOH, we went with a book of map sections that are small scale enough to be rendered as effectively flat - then 99% of their pages would be full of empty sea - not much use for navigating long distances
• (BTW, computerized plotting hasn't been suggested yet, but a premise of the story is no electronics - so no computers. A map system needs to be simple enough that a human can make the necessary calculations.)
• ultimately, since several of the factors governing Earth maps need not be prioritized, a map system that optimizes navigation based on the priorities and conditions of a non-Earthlike world will be more efficient

So, I think you need to ask the question. What is the purpose of a map on an ocean world?

This question is based on the faulty premise you made above. An ocean world can be peppered with inhabitable islands.

 

[anorlunda]

By all the criteria in your bullet list, Earth is already an ocean world. That is unless you consider a continent as different than an archipelago for map purposes.

I also think that you have a misconception about marine navigation. A world-scale map projection is no help in plotting a great circle course. Marine charts are useful for local navigation, not for plotting a course from San Francisco to Tokyo, regardless of the projection. Latitude, longitude and celestial navigation would be the tools needed to plot a course to Tokyo, not a map projection. However, you can read the latitude/longitude of Tokyo from a map regardless of the projection or look it up in a table, and that's what is important to the navigator.

Distortions at high latitudes are the only case where projections matter. On ancient Earth, nearly all marine navigation was a lower latitudes. On a world where there was a lot of traffic near the poles, my guess is that they would move to 3D globes rather than 2D maps early on, thus sidestepping the projection problem.

So in a SF story where you're trying to depict a world where many things are different than on Earth, why presume that they use 2D maps?

A more interesting SF case would be an ocean world that did not rotate on its own axis. No poles. No day/night except perhaps on an annual cycle. Really different weather patterns. That would challenge readers to stretch their minds trying to imagine that. If I remember right, Phillip Jose Farmer wrote some stories about worlds like Mercury that are tidally locked to the star with the same side always facing the star.

 

[DaveC426913]

By all the criteria in your bullet list, Earth is already an ocean world. That is unless you consider a continent as different than an archipelago for map purposes.

It certainly is different.

You don't do this on a world without continents:

I also think that you have a misconception about marine navigation. A world-scale map projection is no help in plotting a great circle course. Marine charts are useful for local navigation, not for plotting a course from San Francisco to Tokyo, regardless of the projection.

OK, there is definitely a communication problem here, since that is exactly what I've said, more than once.

I'm at a loss as to how you and I can say the same thing, but when I say it, you call it a misconception.

 

[DaveC426913]

So in a SF story where you're trying to depict a world where many things are different than on Earth, why presume that they use 2D maps?

It might help if I made it clear that these are humans. They're on a colony world. So they bring their historical science and math with them.

Still, I had the same stroke of lateral thinking as you. A small globe - one that stores compactly but unfolds like the petals of an orange peel - would make an excellent map for such a world.

It's possible to make a worldline straightedge that can be rotated to any position to show as-the-crow-flies courses (and if it's constructed right, it won't fall off).

I whipped this up in 90 minutes or so. Needs a little refining but it serves for the story.

 

[Vanadium 50]

You don't do this on a world without continents.

But you do with archipelagos that are shaped like continents.

I think @anorlunda made a very relevant comment. Nobody navigates based on a world map. World maps exist to be hung in classrooms.

 

[DaveC426913]

I think @anorlunda made a very relevant comment. Nobody navigates based on a world map. World maps exist to be hung in classrooms.

It was me that pointed that out :

on Earth, world-scale maps are not usually used for plotting and navigation - which is why we've never had any reason to have world maps that optimize plotting

(How am I not getting this message across?? Earth projections won't work here. Agreed all around!)

But on an ocean world, that's how you'd be navigating all the time. Journeys can routinely be thousands of miles straight line between islands.Now, I did not mention in this thread that, based on a little bit of research, it seems that ocean worlds have a max size limit before atmo, ocean and solid core blend into one from compressive forces. This means that even a trip of a thousand miles would involve more curvature than Earth, exacerbating the projection problem.

 

[Fred Wright]

I would bring an astrolabe and an accurate clock.

 

[anorlunda]

But on an ocean world, that's how you'd be navigating all the time. Journeys can routinely be thousands of miles straight line between islands.

Therein is your misconception about marine navigation. The shortest distance between two islands is not a straight line, it is a great circle. There is no 2D projection that can make a great circle into a straight line. Navigators can not use those projections for long distance navigation.

 

[DaveC426913]

Therein is your misconception about marine navigation. The shortest distance between two islands is not a straight line, it is a great circle.

I know that. (Please stop telling me what my misconceptions are; you're being unnecessarily combative.)

That's why I was alluding to Earth's smaller maps, which are effectively flat such that a course over a short distance is straight - yet over a thousand miles they are not - because they ultimately form a great circle. Which is why Earth maps and navigation are insufficient for such long journeys. (I guess I didn't make that logic explicit enough in my bullets).

There is no 2D projection that can make a great circle into a straight line. Navigators can not use those projections for long distance navigation.

Correct. I'm looking for an optimal solution - it wouldn't be perfect. Naturally, you'd have to do some trig.But yes, I ultimately agree - it's an intractible problem on a 2D map.

A collapsible pocket globe with a wraparound straight edge - as pictured in post 8 - looks like a good solution.

Only downside to it is the scale - which is about 1:68,000,000. Of course it can be supplemented by larger scale flat maps near locations of interest.

Thank you everyone for your input.

 

[DaveC426913]

I would bring an astrolabe and an accurate clock.

Sure, but those are only part of the set of nav tools.
How will you know where your destinations are - without a record of its lat/long, like,say, a map?
I suppose you could get by with a log book with all significant destinations marked with lat/long. That could number in the thousands, even on an ocean world.

EDIT: Ah. I just realized you don't need a map that's undistorted. You only need a undistorted map if you're taking measurements and angles from the map itself - which is what we do on Earth because it eliminates any need for trig and spherical coords.

But as long as you have lat and long of your destination (no matter how it's displayed) you can calculate a direct path from your coords to your destination via spherical coords. It's just a lot more work.

 

[sandy stone]

I believe a Gnomonic projection shows a great circle as a straight line, but you are limited to less than a hemisphere.

 

[DaveC426913]

Gnomonic projection

Indeed. This is exactly what I was hoping for as a contribution. Thanks.
Although distances on such a map are drastically affected, the calculations could factor that in.

But, after some thought and discussion, I think I'm going to stick with my pocket globe.

 

[Fred Wright]

Sure, but those are only part of the set of nav tools.
How will you know where your destinations are - without a record of its lat/long, like,say, a map?

I saw on a tv show (Nova) that the ancient Polynesians navigated thousands of miles without maps, sectants, clocks, etc. I would bring a Polynesian (if he had knowledge of his ancient culture).

 

[anorlunda]

Sorry. I wan't trying to be combative. But I just reread all your posts, and your point is still not apparent. I see no reason why the map projection problem on this planet is any different than on Earth. The archipelago versus continent difference is not a reason.

But with the following, I think we are almost in agreement.

EDIT: Ah. I just realized you don't need a map that's undistorted. You only need a undistorted map if you're taking measurements and angles from the map itself - which is what we do on Earth because it eliminates any need for trig and spherical coords.

I say almost because we don't take distances and angles from a chart for long distance navigation, and neither did the ancients IMO. Short distance navigation is different. There, we print a compass rose on the chart, and you can use parallel rulers to mark headings.

What we do see on some charts are sailing routes with reciprocal magnetic headings marked. (See below.) In those cases, the useful navigational data is printed on the map as numbers, not measured as angles on the chart. Distortion doesn't matter. I'm sure that the ancients did likewise. On your SF world, it would be far superior to print the magnetic headings between every pair of neighbor islands on the chart, than to try to take distances and angles off the chart graphics.

Does your SF world have magnetic poles? If not, then there's more to navigating than just charts. Note the difference between course and heading on the above picture. If they had advanced technology, then surely they would have apps that resemble GPS, instead of paper maps. Even without satellites, the apps could use inertial, celestial, radio, or other means of navigation.

By the way, modern circumnavigators who want a paper backup to GPS must carry a set of about 1300 paper charts to cover the popular circumnavigation routes. Large scale, or world maps are used only to locate which small scale chart to look at, not for navigation.

 

[DaveC426913]

Sorry. I wan't trying to be combative. But I just reread all your posts, and your point is still not apparent. I see no reason why the map projection problem on this planet is any different than on Earth. The archipelago versus continent difference is not a reason.

Many of our projections are split to accommodate the continents. See post 1. It was a simple matter of ruling out all those projections in one swell foop.

@sandy stone provided what I was seeking - there are projections that might be better suited to long-page plotting. The Gnomonic projection he mentions seems to be one - great circle paths are straight, and therefore easy to plot. It's not a full solution, but it's on the right track.

However, I'm abandoning 2D maps in favour of the pocket globe.

If they had advanced technology, then surely they would have apps that resemble GPS, instead of paper maps. Even without satellites, the apps could use inertial, celestial, radio, or other means of navigation.

This is getting little into the technical details of the story, but OK.

Technology is state-of-the-art for 22nd century**. Like 21st century sports, who have the latest, strongest, lightest materials available, so do 22nd century colony tourists. They even have "smart" skinsuits that mold to one's body, etc.

Here's the catch: a core element of the story is that no electronic devices are allowed outside populated areas. No exceptions. And that's 99% of the planet. (The first colonists found - to their detriment - that indigenous wildlife is sensitive in the radio range, and beat themselves to death attacking any radio devices. ) Although self-contained devices - such as personal computers - can be shielded, the planetary government made the ruling unilateral anyway. Too many people flouting the rules. So 99% of the planet is effectively a nature preserve - at least for now.They do have geostat satellites, but without any devices to receive radio signals, they don't have GPS - at least, not out in the wilderness.

Instead, the satellites broadcast in the visible spectrum. Four satellites, at the ... apeces of a tetrahedron mean that three satellites are always visible from anywhere on the surface. A sextant is used to find their positions in the sky, and thus your position on the surface.

(This may be a bit of overkill: the satellites' beacons are colour-coded. The sextant has glass filters that allow one to identify a satellite from other stars and from each other. It's overkill, because it's not like you can't make the satellites stand out in the sky - a simple unique blinking pattern would do. I may have to drop the colour-coding. Pity.)

By the way, modern circumnavigators who want a paper backup to GPS must carry a set of about 1300 paper charts to cover the popular circumnavigation routes. Large scale, or world maps are used only to locate which small scale chart to look at, not for navigation.

I know. I have a set on my boat. It's a regulation requirement.

 

[BillTre]

Here are some non-electronic collapsible globes I googled up.

The future might have better ones based on advanced origami techniques.

 

[DaveC426913]

**on an unrelated note about 22nd century technology.

To have a colony world that is still in active communication with other planets, you have to have some sort of ftl drive. Otherwise, relativistic effects cut the world off - certainly from Earth.

The main character is new to this world - a necessary writing element to provide a narrative for discovering all the new and strange wonders about it. He is Alice-in-Wonderland, so the reader can see these wonders through eyes we can relate to. So he has to come from a world that is as like our own as possible.

I just wish I didn't have to use ftl drive. It's like the Enterprise transporters - several tech levels beyond anything else in the story. But Einsteinian relativity is a harsh mistress.

 

[DaveC426913]

Here are some non-electronic collapsible globes I googled up.
View attachment 266631

The future might have better ones based on advanced origami techniques.

Heh.
I like the Chinese lantern one. Collapses nice and flat.
And the huggable one could - with sufficient technology - blow up to a perfect sphere. Hmm. That's even better than my grapefruit-peel segmented globe.

 

[stefan r]

All maps have flaws. I really enjoy equidistant azimuthal projections. They may be more useful when there are no coastlines. I enjoy contemplating where orbital rings could be placed. A few orbital rings creates a geopolitical crises. The leaders in a city have much to gain if the ring passes through. This makes them allies with cities that are far away but in conflict with nearby cities. So if, for example, we pin New York as a location NASA would choose for an orbital ring elevator then the mayor of Houston Texas is going to suddenly have friends in Barcelona and Cairo but a Senator for Alabama will argue London, Munich, and Dubai make much more sense.

Furthermore, is there any reason, other than tradition, to use 360 degrees on a map of a new world?

What if it were metric? One hundred "degrees" from equator to pole, 400 "degrees" of longitude around the equator.

Would problems crop up in the math?

I thought 360 degrees came from the length of Earth's year. Obviously wrong but not exceptionally obvious. The stars sort of move close to a degree every day and 365 does not break up into nice round numbers(5,73). 364 and 366 don't factor out into anything friendly either (6,61, and 4, 7, 13). It is better to use a simple system like 360 and wait for someone to call you out for being 5 and a quarter days off. Then you know who the radical dissidents are and you can burn them for heresy.

 

[BillTre]

I was told in something like grade school or Jr high that the 360 was used because it was divisible by many useful numbers, like: 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 20
The argument was that it simplified some of the pre-calculator math.

 

[DaveC426913]

I was told in something like grade school or Jr high that the 360 was used because it was divisible by many useful numbers, like: 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 20
The argument was that it simplified some of the pre-calculator math.

A usefulness that ought to have extended to rulers. Instead we adopted base 10.

 

[anorlunda]

Wikipedia has a very interesting take on 360.
https://en.wikipedia.org/wiki/Degree_(angle)#History

The original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year.[6] Ancient astronomers noticed that the sun, which follows through the ecliptic path over the course of the year, seems to advance in its path by approximately one degree each day. Some ancient calendars, such as the Persian calendar, used 360 days for a year.[citation needed] The use of a calendar with 360 days may be related to the use of sexagesimal numbers.

Another theory is that the Babylonians subdivided the circle using the angle of an equilateral triangle as the basic unit and further subdivided the latter into 60 parts following their sexagesimal numeric system.[7][8] The earliest trigonometry, used by the Babylonian astronomers and their Greek successors, was based on chords of a circle. A chord of length equal to the radius made a natural base quantity. One sixtieth of this, using their standard sexagesimal divisions, was a degree.

Aristarchus of Samos and Hipparchus seem to have been among the first Greek scientists to exploit Babylonian astronomical knowledge and techniques systematically.[9][10] Timocharis, Aristarchus, Aristillus, Archimedes, and Hipparchus were the first Greeks known to divide the circle in 360 degrees of 60 arc minutes.[11] Eratosthenes used a simpler sexagesimal system dividing a circle into 60 parts.

The division of the circle into 360 parts also occurred in ancient India, as evidenced in the Rigveda:[12]

Twelve spokes, one wheel, navels three.
Who can comprehend this?
On it are placed together
three hundred and sixty like pegs.
They shake not in the least.
— Dirghatamas, Rigveda 1.164.48

Another motivation for choosing the number 360 may have been that it is readily divisible: 360 has 24 divisors,[note 1] making it one of only 7 numbers such that no number less than twice as much has more divisors (sequence A072938 in the OEIS).[13][14] Furthermore, it is divisible by every number from 1 to 10 except 7.[note 2] This property has many useful applications, such as dividing the world into 24 time zones, each of which is nominally 15° of longitude, to correlate with the established 24-hour day convention.

Finally, it may be the case that more than one of these factors has come into play. According to that theory, the number is approximately 365 because of the apparent movement of the sun against the celestial sphere and that it was rounded to 360 for some of the mathematical reasons cited above.

But @DaveC426913 , you never answered about magnetic poles on this world. The problem of navigating there could be much more interesting than just paper maps.

On an alien world, I would consider the possibility of multiple pairs of N-S poles or zero pairs. I think it's just coincidence that Earth has exactly 1 pair.

If the people there have advanced technology but can't transmit any EM, can they use electronics to passively do celestial navigation? Perhaps using the IR spectrum to penetrate clouds. If we didn't have so many other attractive ways to navigate on Earth, I wager that we could have refined celestial navigation to a highly efficient method. That could be a fun plot twist, as the Earthlings are forced to do new R&D to adapt their methods to this environment.

I think the plot also needs an explanation of why the Earthlings want to travel at all on this planet. If it is just exploration, then they are creating maps, not reading maps. I presume there are not so many Earthlings that they will populate every island. A small colony would stay on one island and have little incentive to visit other islands.

By the way, the natives who don't like EM presumably don't object to light, correct? I presume their planet obits a star. So the natives are allergic to only some frequency bands. The Earthlings could use photonic circuits that don't emit radio band EM. They could also use DC circuits that don't emit much radiation at a distance. If the natives are allergic to DC, what is their physics to sense it? I think someone else already pointed out that the human nervous system uses electricity. What biology would the natives have to avoid that?

 

[DaveC426913]

But @DaveC426913 , you never answered about magnetic poles on this world. The problem of navigating there could be much more interesting than just paper maps.

Yes. It's still up in the air. If there are magnetic poles, like Earth, that may make a lot of my carefully constructed ocean-world navigation tricks just go away. Which is no fun.

On an alien world, I would consider the possibility of multiple pairs of N-S poles or zero pairs. I think it's just coincidence that Earth has exactly 1 pair.

Now that's an interesting tidbit!

Having multiple poles could explain why it's not their go-to navigation aide - while at the same time, not eliminating a planetary magnetosphere necessary to protect life.

Thanks! Gonna add that in.

If the people there have advanced technology but can't transmit any EM, can they use electronics to passively do celestial navigation? Perhaps using the IR spectrum to penetrate clouds.

“So, in a fit of eco-conscious panic, they banned all radio communications from wilderness areas, effectively turning 99% of Brine into a planet-wide nature preserve.

"And that would have been fine, except colonists like their gadgets, and found ways to circumvent the ban, packing what they considered essential safety items such as datapads and comms equipment.

“Brine government reacted by banning all electronic devices unilaterally. If you're caught packing anything even as small as a phone outside civilized areas, it's a hefty fine and prison sentence.

I think the plot also needs an explanation of why the Earthlings want to travel at all on this planet. If it is just exploration, then they are creating maps, not reading maps. I presume there are not so many Earthlings that they will populate every island. A small colony would stay on one island and have little incentive to visit other islands.

I could wax creative on how they're going to populate the thousands of smaller islands, or build out into - or -under - the water.

This is outside the scope of the short story. It is simply a given. Some parts of a story you want to leave to the imagination.

By the way, the natives who don't like EM presumably don't object to light, correct? I presume their planet obits a star. So the natives are allergic to only some frequency bands.

Indeed. Like humans who see visible light but not radio. (Or like humans, who are allergic to UV.)

The Earthlings could use photonic circuits that don't emit radio band EM. They could also use DC circuits that don't emit much radiation at a distance. If the natives are allergic to DC, what is their physics to sense it?

Yeah, I've addressed this broadly, thus:

“They manage on [the great island called] 'Land'. There are devices that can perform a combination of shielding and 'cleaning' the RF signals that are emitted from farming and industrial equipment. And before you ask: no, the cleaners are too bulky to transport on most vessels – so no powered boats or airplanes. At least until the technology matures and can be miniaturized. We're still waiting.”

The colony is only 50 years old.

I think someone else already pointed out that the human nervous system uses electricity. What biology would the natives have to avoid that?

This alien life is built on the same principles as Earth life. They share amino acids. So they too have a bio-electric nervous system.

Not exactly novel: most fish can sense the electrical signals of other fish.

 

[anorlunda]

Here's a depiction of Earth's poles during pole flipping period. The flipping event takes about 7000 years.

 

[jim mcnamara]

Instead of maps per se, how about rhumb lines?

https://en.wikipedia.org/wiki/Rhumb_line

 

[DaveC426913]

Here's a depiction of Earth's poles during pole flipping period. The flipping event takes about 7000 years.

View attachment 267097

Thanks. Even better.
If the planet is in the middle of a pole reversal, then it can have been protected by a magnetosphere for all but the last few millennia.

 

[DaveC426913]

Instead of maps per se, how about rhumb lines?
https://en.wikipedia.org/wiki/Rhumb_line

I am not sure what purpose these would serve.

 

[jim mcnamara]

It is an old method of navigation. Edit: if @anorlunda is a sailor he can explain their use.

 

[BrassOctopus]

Is a holographic solution out of the question?

 

[berkeman]

Is a holographic solution out of the question?

Welcome to PhysicsForums. Could you post a couple links to what you are asking about? That would help us to respond to your question. Thank you.

 

[BrassOctopus]

DaveC426913 was wondering "if there's a way to make a rigid globe that can fold into a compact shape."