Coordinates
Tuesday 21st August
So when you’re working with global coordinates, there’s a problem. Latitudes are easy… wherever you are, if you travel north/south by one degree of latitude, you travel 69.4 km.
East/west is another matter. At the equator, there are 69.4 km between degrees of longitude, but in the extreme case at the north or south pole, you can travel through 360 degrees of longitude by making, for example, a 1-metre circle.
So calculations of distance are not easy. There’s a latitude factor to be taken into account for all longitude calculations. Messy. I know this because I wrote a web application once to measure the distance between two clicks on a map.
Anyway… I hereby propose, and I’m sure no-one has thought of it before… the isometric sperical coordinate system shown as part 2 of the diagram below. (Part 1 is the current lat/long system)…
I can’t see any possible downside to this scheme. Well, maybe one or two, but I’m in denial. Imagine being able to travel, not only to the north and south pole, but also the the east and west pole - or maybe the front and back pole.
I believe that this system allows simple pythagorean arithmetic to be performed when calculating distances.
The floor is open…
Nothing to do with your new idea, but related to your assertation that 1 degree of latitude being 69.4km. How does this adjust for the squashedness of the planet (i.e. it not being a sphere but a sphere that has been sat on)?
On the idea itself, I don’t think normal pythagorean arithmetic works because of the distance between intersections of your grid changing according to diameter. Might be wrong though.
Rich
21 Aug 07 at 4:27 pm
Hmm.
1) Are you sure delta(latitude)=K delta(distance) ? I can’t remember whether the Earth’s oblacity comes into play here. I have a feeling it doesn’t, because I think they defined latitude such that it compensates for the ellipsoid cross-section of the earth.
2) By the old measurement, you could tell the time by your longitude and the position of the sun over the horizon.
3) Don’t you end up horribly undefined at the east and west poles in the new system like you did in the old?
4) Unlike the north and south poles, the east and west poles will have a giant McStarbucks MegaPlex and a temple of McBuddha, respectively. Also these will be immensely long structures because it will be impossible to survey anything smaller than 500m long near the poles.
Surely a MUCH friendlier system would be to provide your straight-line distance (i.e. a chord inside the earth) from Mecca, Jerusalem, Lourdes, and Somnath. The buddhists are pretty chilled anyway, so there shouldn’t be any trouble from those guys that they weren’t included.
sweavo
21 Aug 07 at 4:31 pm
If the floor’s open, hadn’t you better stop messing about and call a builder?
Omally
21 Aug 07 at 5:26 pm
Imagine all the GPS devices that need to be patched to cope with the new system; my Garmin already has issues when changing map datum and position format!
John
21 Aug 07 at 6:11 pm
The earth isnt flat?
lordhutton
21 Aug 07 at 6:36 pm
I’d suggest that knowing your time by longitude and position of sun on the horizon isn’t so much of an issue as has been previously, but how about this…
We live in a digital age. We can deal with a multitude of formats. Why can’t we all just get along?
*sings “I’d like to teach the world to sing”*
Kouros
21 Aug 07 at 7:28 pm
Rich: Ok… 1 degree of latitude just about equals 69km. Yes, there’s a little squashiness, but not a great deal (about 4% tops). The point of this system _is_ that the intersections are equally spaced if you ignore the squashiness.
Sweavo: 1) No. But it’s not far off. Better than 69km - 0mm for the non-parallel system. 2) You could. Now you can’t. In fact all sort of navigation becomes a complete nightmare. 3) Not undefined, but certainly the accuracy required increases as it does at our current north and south poles. 4) Hehe… yes, I agree.
Straight-line distances sound just fine.
Omally: You have a good point. And I have a blog about that.
John: You’d only have to add a new datum or something. Of course, it’d take a few years before everyone moved over to my _much better_ scheme.
LordHutton: Afraid not. Sorry.
Kouros: Noooo! Anything to stop the singing!
stu
21 Aug 07 at 7:33 pm
Are you sure that this post is not just an excuse to use that Digital Art Software!
Phil
21 Aug 07 at 7:33 pm
Hehe… you spotted it, Phil. I particularly like the ‘curve’ tool. Very nice.
stu
21 Aug 07 at 7:36 pm
If the earth was cuboid, how would you name the poles, assuming each corner of the cube to be a pole? Now my head hurts
max
21 Aug 07 at 8:45 pm
Your head hurts, Max?… I think I’ll join you.
stu
21 Aug 07 at 8:53 pm
This is exactly why I don’t travel any further away than in a fifty mile radius. It’s just TOO SCARY to contemplate!
Debster
21 Aug 07 at 11:31 pm
“If the earth was cuboid, how would you name the poles, assuming each corner of the cube to be a pole? Now my head hurts…”
I’d name them Bob, Betty, Stu, Sue, Larry, Mo, Fran and Stan.
Cuboid? I rather liked “the squashedness of the planet” and I’m already trying to think of ways to steer tomorrow’s water cooler conversation around to the subject JUST so I can drop that into it.
Holly
28 Aug 07 at 4:26 am