Let's redraw the world

Great Debates
1

This current thread has me pondering.

You are aware of the Mercator projection of the earth. Differences in latitude are differences in relative distance no matter where you are on the earth. There’s no distortion on the Mercator projection going north or south.

But there obviously is going east and west as we insist on using meridians to grid east and west.

What if we changed the Mercator projection to specify longitude in the same way as latitude. That is distance from the 0 longitude.

Would that make modern GPS navigation simpler ?

Would the great circle paths appear as straight lines given that actual distances are represent on both axes ?
What is the down side?
Is it time to make the switch ?

Oy my head hurts.

2

The problem is that there are no natural east and west poles, and even if you made arbitrary ones, there would still be no way to project the globe onto a map without some distortion.

3

[QUOTE=Great Dave]
The problem is that there are no natural east and west poles, and even if you made arbitrary ones, there would still be no way to project the globe onto a map without some distortion.
[/QUOTE]

Well i can see some distortion given that the diameter of the equator is somewhat larger than the diameter of a meridian, but as a visualize plotting a map utilizing the intersection of latitudes and "east west latitudes’, I can see a method for reasonable relationship of distances and perception that would allow me to scale distances between points on the earth.

4

Do you have any map making experience? Taken a cartography course? There are many projections, and I’ve never seen one with E/W latitudes like you struggle to suggest.

5

[QUOTE=The Flying Dutchman]
Well i can see some distortion given that the diameter of the equator is somewhat larger than the diameter of a meridian, but as a visualize plotting a map utilizing the intersection of latitudes and "east west latitudes’, I can see a method for reasonable relationship of distances and perception that would allow me to scale distances between points on the earth.
[/QUOTE]
I think that the map on this wiki page is approximately what you’re talking about. Note that, due to the fact that latitude lines are ‘somewhat’ smaller as you go towards the poles, there is significant distortion, which increases dramatically as you move towards the edge of the map in any direction.

Suffice to say, this doesn’t make for a map that makes navigation simpler. The simple fact is that we’re projecting an approximately spherical shape onto a flat plane; no matter what you do you’re not going to get all measurements in every direction to be proportionately correct.

6

[QUOTE=begbert2]
I think that the map on this wiki page is approximately what you’re talking about. Note that, due to the fact that latitude lines are ‘somewhat’ smaller as you go towards the poles, there is significant distortion, which increases dramatically as you move towards the edge of the map in any direction.

Suffice to say, this doesn’t make for a map that makes navigation simpler. The simple fact is that we’re projecting an approximately spherical shape onto a flat plane; no matter what you do you’re not going to get all measurements in every direction to be proportionately correct.
[/QUOTE]

Not quite. Those “vertical” lines are longitudinal, and all meet at the north pole.

7

[QUOTE=The Flying Dutchman]
This current thread has me pondering.

You are aware of the Mercator projection of the earth. Differences in latitude are differences in relative distance no matter where you are on the earth. There’s no distortion on the Mercator projection going north or south.

But there obviously is going east and west as we insist on using meridians to grid east and west.

What if we changed the Mercator projection to specify longitude in the same way as latitude. That is distance from the 0 longitude.

Would that make modern GPS navigation simpler ?

Would the great circle paths appear as straight lines given that actual distances are represent on both axes ?
What is the down side?
Is it time to make the switch ?

Oy my head hurts.
[/QUOTE]

Let me make sure I’ve got this right. You’re proposing a system such that the longitude would be drawn like latitude? So, for example, we could use the Prime Meridian as a longitudal equator and draw parallel rings that specify a distance from it?

If this is what you’re proposing, it introduces an enormous number of problems without really fixing anything.

With the current system, at any given point on the globe (except the two poles) the latitude and longitude lines intersect at right angles. This gives us an unambiguous and consistent way to navigate because the four cardinal directions would always be orthogonal.

In this new system, there would be very few points where the Longitude and Latitude would intersect at right angles and, in some cases they would actually be parallel, resulting in no way to unambiguously navigate in those areas. For instance, with this method, when you are on the Great Circle that intersects the current North and South poles, along with the new “East” and “West” poles, if you’re in the North East quarter, North and West wold both point toward the North Pole and South and East would both point toward the “East” Pole, making it impossible to navigate.

Besides the complexities and ambiguities of a non-orthogonal coordinate system, you’d also introduce two more points (the East and West poles), except no matter when you choose the Prime Meridian to be, they would necessarily have to be in a place that has a significant amount more navigation than the current poles.

Worst of all, because it would now be non-orthogonal it would make the new navigation system non-intuitive, location specific. That is, anywhere in the world, if someone tells me where North is, I can find the other directions; with this different system, I’d need to find North and East (or West), and their relative directions (based on everyday observation) would seem to change with distances many people travel regularly.

You have to remember, that there is no way to project the globe to a flat surface without either distortion or discontinuities. For most every day experiences, this distortion is negligible (eg, street maps). The system we have now was chosen (either on purpose or by accident) because orthogonal coordinates are simple, intuitive, and the projection is straight forward. I’m unsure what you’d perceive would be the advantages of this alternate system, so I’d be interested to hear what they would be.

So, to answer your questions, AFAICT, it wouldn’t make navigation simpler; in fact, it would make it enormously more difficult. Of course, if I’m misunderstanding your system, can you take another shot at what you’re describing?

8

[QUOTE=Great Dave]
Not quite. Those “vertical” lines are longitudinal, and all meet at the north pole.
[/QUOTE]
What? I never said they weren’t, or didn’t. I just said that the latitude lines get smaller (as in, a shorter physical distance to circumnavigate the globe) as you approach the poles.

9

[QUOTE=begbert2]
I think that the map on this wiki page is approximately what you’re talking about. Note that, due to the fact that latitude lines are ‘somewhat’ smaller as you go towards the poles, there is significant distortion, which increases dramatically as you move towards the edge of the map in any direction.

Suffice to say, this doesn’t make for a map that makes navigation simpler. The simple fact is that we’re projecting an approximately spherical shape onto a flat plane; no matter what you do you’re not going to get all measurements in every direction to be proportionately correct.
[/QUOTE]

Actually, this is the projection I was visualizing. I would like to know the name of that projection. I’ll bet I can get my compass out, scale the distance between any two points, average my bearing off the longitude and latitude if neccessary at the extremities of the projection and navigate my way forward. Almost like navigating off a local marine chart I won’t be able to find a great circle route though, and I wonder if 19th century navigators bothered with that anyway.

I don’t see any distortion except the prime meridian is curved (I checked with a linked larger map). That shouldn’t happen if the projection is properly centred, I would imagine. I scaled the distance between 0[sup]0[/sup], 30 and 60 longitude and saw no difference. I would have wished the poles weren’t bucked off.

10

[QUOTE=Blaster Master]

So, to answer your questions, AFAICT, it wouldn’t make navigation simpler; in fact, it would make it enormously more difficult. Of course, if I’m misunderstanding your system, can you take another shot at what you’re describing?
[/QUOTE]

Well I’m now inclined to agree with you. i think my system would work well as a plotting device to construct the projection I want, but I definitely would need the longitudes shown for reference.

11

[QUOTE=begbert2]
What? I never said they weren’t, or didn’t. I just said that the latitude lines get smaller (as in, a shorter physical distance to circumnavigate the globe) as you approach the poles.
[/QUOTE]

Sorry, I understood the OP as Blaster Master did, that is, create an East and West poles with concentric circles around them, as if one copied the N/S latitudes and tipped them 90* (okay, so I don’t know the Alt codes). I thought you were suggesting that that map was an example of this, and it is not. I guess this part

threw me off. Latitude lines getting smaller? Shorter, maybe, but duh. I can circumnavigate the globe multiple times a day, even in minutes, if I pick a latitude close enough to the poles. And every single world map has greater distortion at the edges.

12

[QUOTE=Great Dave]
Sorry, I understood the OP as Blaster Master did, that is, create an East and West poles with concentric circles around them, as if one copied the N/S latitudes and tipped them 90* (okay, so I don’t know the Alt codes). I thought you were suggesting that that map was an example of this, and it is not. I guess this part

threw me off. Latitude lines getting smaller? Shorter, maybe, but duh. I can circumnavigate the globe multiple times a day, even in minutes, if I pick a latitude close enough to the poles. And every single world map has greater distortion at the edges.
[/QUOTE]
Hmm, maybe I’m just confused; I didn’t see anything in the OP that led me to think about east and west poles. I figured his main point was that you’d lay out your map east-west based on “distance from the 0 longitude.”

I suppose that, technically, to precisely meet what I’m seeing as being his specifications, you’d have to take the map I pointed at and replace the curved longitude lines with perfectly straight parallel vertical lines tangent to the current longitude lines at the equator…but that’s of course silly because then you’d have longitude lines forming weird nonsensical curves that met and ended in odd places on the opposite side of the globe from the 0 longitude…so I glossed over that part.

(And, not every single world map has greater distortion at the edges, though I admit most do. The point I was trying to make was that the map I showed grew increasingly distorted as you advanced in any direction, whereas several common projections (the cylindrical ones, for example) distort increasingly only as you approach the poles.)

13

[QUOTE=The Flying Dutchman]
Actually, this is the projection I was visualizing. I would like to know the name of that projection. I’ll bet I can get my compass out, scale the distance between any two points, average my bearing off the longitude and latitude if neccessary at the extremities of the projection and navigate my way forward. Almost like navigating off a local marine chart I won’t be able to find a great circle route though, and I wonder if 19th century navigators bothered with that anyway.

I don’t see any distortion except the prime meridian is curved (I checked with a linked larger map). That shouldn’t happen if the projection is properly centred, I would imagine. I scaled the distance between 0[sup]0[/sup], 30 and 60 longitude and saw no difference. I would have wished the poles weren’t bucked off.
[/QUOTE]
Whups; I almost overlooked your post. According to this site, the projection has several names; I think that I prefer “Mercator equal-area” of the ones they’ve given, even though they don’t.

Becasue a straight line on this map clearly isn’t the shortest distance between two points on it (unless that straight line happens to be on a horizontal, or the 0 latitude), I’d say it was pretty certain that distances on it (besides the ones mentioned) don’t scale correctly. If you used this for navigation, any north-south traveling you did would take sweeping curves off from the optimal (straightest) course.