An imprtant question for Loony BoB (and others, perhaps)

[DocFrance]

Is it quicker to reach Scotland from New Zealand by flying north, or by flying south? And what exactly was your route when making this voyage? This has been bugging me all evening, and I fear I won't get any sleep tonight unless I know the answer.

Now what do you, the member who is not Loony BoB think about this? This is a question of the utmost urgency!

[Kirobaito]

North. Duh. This would be different if Scotland was in the Southern Hemisphere or something, but it's in the northern hemisphere. In the issue of going east or west, I'm not sure. It's probably a toss-up. It would probably be safer going east, so you can make a stop in the US, instead of a Middle Eastern country.

[Dr Unne]

In Euclidean geometry, the shortest distance between two points is a straight line. However Euclidean geometry doesn't apply when dealing with the surface of a sphere; Spherical geometry is non-Euclidean. The shortest distance between two points on a sphere is actually a portion of a circle called a "great circle". A great circle is the circle which results from the intersection of a sphere with a plane which passes through the sphere's center. It seems strange, but for example the shortest line between Florida and the Phillipines takes you through Alaska, even though the Phillipines is south of Florida, and Alaska is far north of both. You can thank Euclid's Fifth Postulate for this.

I don't know whether any of this applies to the question at hand in this thread, but I wouldn't be too quick to jump to conclusions without checking a globe (not a map) for yourself.

[Kirobaito]

It seems strange, but for example the shortest line between Florida and the Phillipines takes you through Alaska, even though the Phillipines is south of Florida, and Alaska is far north of both. You can thank Euclid's Fifth Postulate for this. - Dr Unne

I know it's been 2 years since I've taken Geometry, but this statement makes my head hurt...

[eestlinc]

the fastest way is on a double canoe with a piano.

[Baloki]

The best way is not to go somewhere so cold and northern.

Try France or Antartica, either are warmer!

[Flying Mullet]

Unless it's a direct flight I'd imagine that you'd have to fly south, and either accross North America or Asia, as that's where people live and that's where the planes go.

[Loony BoB]

Who gives a crap, it's over 24 hours stuck in a plane and you're going to have a stopover. Best to just go with the cheapest option, which is generally via South-East Asia. I went via Kuala Lumpur, although I never got out of the airport there. Bloody nice airport, though. xD I just did my best to stretch out at that point. So many hours tucked into a seat in a 747 is not good. In fact, it's awful.

Hmm. More direct... Well, if I remember correctly, Spain is the actual opposite end of Earth from New Zealand... hmm. North? I dunno for sure.

[Meat Puppet]

You'll probably stop in Thailand.

[fire_of_avalon]

Haha, I like the first part of BoB's answer. And I don't like geometry. DocFrance, are you going from New Zealand to Scotland or vice versa?

[Big D]

Usually, there's a stopover in Southeast Asia, as BoB said, or in North America, I believe. Going South, in a direct line over Antarctica, would probably cause problems with unfavourable jetstreams and such, as well as the inevitable lack of fuel. However, NASA claims that their new SCRAMjet technology could cut the trip down to 90 minutes or so, given time to develop it.

[DocFrance]

Originally posted by Loony BoB
Kuala Lumpur I've seen things, I've seen them with my eyes... [/obscure reference]

FoA: No, just very, very curious.

[Peegee]

Dr Unne's post sounds weird, because if you think 2 dimensionally, flying to Alaska, then to the Philiphines is very long (you transverse the diagonal length of N. America). However if you realise that the earth's rotation forces the "height" of the earth down, you'll realise that N. America stretches very far to the side while N/S wise it is much shorter.

And if you look at the map from Alaska to the Philipines you will see that it is shorter to reach there than from, say, California.

--

Anyway, I don't have ANY idea how far the north and south poles are from each other, or how the earth "bends" so the relative location of Austrailia/NZ and Russia is completely confusing me at this moment.

Perhaps the best course of action is to forgo spherical geometry and get a subterrainean man-driven drill. That way you can go in a straight line for Scotland and forget all this math mumbo jumbo.

[Jack]

West :D

You love me really

[TasteyPies]

Our planet is an oblate spheriod if noone has pointed that out already, its egg shaped so one way is definitely closer, north or south that is

[Thunday Man]

Dont forget about JET STREAMS. Going with these high altitude high speed winds will help alot.

[Flying Mullet]

Originally posted by Thunder God Cid
Dont forget about JET STREAMS. Going with these high altitude high speed winds will help alot.

Originally posted by Big D
Usually, there's a stopover in Southeast Asia, as BoB said, or in North America, I believe. Going South, in a direct line over Antarctica, would probably cause problems with unfavourable jetstreams and such, as well as the inevitable lack of fuel. However, NASA claims that their new SCRAMjet technology could cut the trip down to 90 minutes or so, given time to develop it.

[Peegee]

Which reminds me that the fastest way to do anything is using a rocket or shuttle (except when the distance is short enough that the time spent flying up and falling down is longer than the speed it takes to drive/train there). Failing that just take a jet.

[gokufusionss1]

In Euclidean geometry, the shortest distance between two points is a straight line. However Euclidean geometry doesn't apply when dealing with the surface of a sphere; Spherical geometry is non-Euclidean. The shortest distance between two points on a sphere is actually a portion of a circle called a "great circle". A great circle is the circle which results from the intersection of a sphere with a plane which passes through the sphere's center. It seems strange, but for example the shortest line between Florida and the Phillipines takes you through Alaska, even though the Phillipines is south of Florida, and Alaska is far north of both. You can thank Euclid's Fifth Postulate for this.

Dr Unne why do you allways over-complicate the inital question, is it some need to use this weeks newly learnt word?

I would guess south is actually shorter, but north is used because you can stop off and refuel ect

[Loony BoB]

Okay, this is all done by pretending the world is spherical...

Auckland: 36° 51' S / 174° 46' E
Edinburgh: 55° 55' N / 3° 11' W

As you can see, they're not exactly opposite ends. West and East won't really make too much of a difference, either... I don't think. Anyway, the way to figure it out is this - should you be taking off from 36° 51' S, the opposite end of the world should be at some point on latitude 36° 51' N. Should the location you are heading to be above this, it would be more direct to travel North. Should it be below this, it would be more direct to travel South - provided it's on the opposite longitude. Obviously if it was on the same longitude, it would always be more direct to travel North. Okay... keeping in mind 90° is the maximun latitude (ie, the poles) and that the longitudes should add to 180 to be exact opposites, you have to figure out the difference in latitude and longitude. That's 177° 57' - so we're about 2° out longitude wise. Latitude is 19° or so, which is a bit more noticable. Going by the fact that Edinburgh is approximately 19° further North than Aucland is South along with the fact that it is only an approximately 3° difference longitude-wise (aka, they're very close to bein on the opposite longitudes), I think it's safe to say that the plane would be going on a Northern trip. Both of these factors work in the favour of a Northern trip. If, however, you were going to somewhere such as Northern Africa, that would be a little more difficult to figure out, as it is below the opposite end of the world (which would indicate a Southern trip would be more direct), yet the difference in longitude could change that.

However, with all that info, you have to then keep in mind that the world is not spherical, so who knows!? =] I don't think it would be too much different, though, as either way you're going to cross the equator.

[-N-]

Isn't Euclid's Fifth considered incomplete or something? Or empirically determined rather than theoretically so? I remember some arguments against it... oh well.

[Kirobaito]

Originally posted by Loony BoB
Okay, this is all done by pretending the world is spherical...

Auckland: 36° 51' S / 174° 46' E
Edinburgh: 55° 55' N / 3° 11' W

As you can see, they're not exactly opposite ends. West and East won't really make too much of a difference, either... I don't think. Anyway, the way to figure it out is this - should you be taking off from 36° 51' S, the opposite end of the world should be at some point on latitude 36° 51' N. Should the location you are heading to be above this, it would be more direct to travel North. Should it be below this, it would be more direct to travel South - provided it's on the opposite longitude. Obviously if it was on the same longitude, it would always be more direct to travel North. Okay... keeping in mind 90° is the maximun latitude (ie, the poles) and that the longitudes should add to 180 to be exact opposites, you have to figure out the difference in latitude and longitude. That's 177° 57' - so we're about 2° out longitude wise. Latitude is 19° or so, which is a bit more noticable. Going by the fact that Edinburgh is approximately 19° further North than Aucland is South along with the fact that it is only an approximately 3° difference longitude-wise (aka, they're very close to bein on the opposite longitudes), I think it's safe to say that the plane would be going on a Northern trip. Both of these factors work in the favour of a Northern trip. If, however, you were going to somewhere such as Northern Africa, that would be a little more difficult to figure out, as it is below the opposite end of the world (which would indicate a Southern trip would be more direct), yet the difference in longitude could change that.

However, with all that info, you have to then keep in mind that the world is not spherical, so who knows!? =] I don't think it would be too much different, though, as either way you're going to cross the equator.

So I was right. North.

[Maxico]

Originally posted by DocFrance
I've seen things, I've seen them with my eyes... [/obscure reference]


Man, that thing made me laugh for about a half hour.

Anyway, I would say the shortest route would be whichever one was the cheapest route.

[Dr Unne]

<i>Our planet is an oblate spheriod if noone has pointed that out already, its egg shaped so one way is definitely closer, north or south that is</i> --TasteyPies

It's so nearly spherical that it can be treated as a sphere for most things, so far as I know. The difference between the north-south and equatorial diameters is less than 30 miles. The difference between a sphere and the shape of the earth is 1/3 of 1 percent.

<i>Dr Unne why do you allways over-complicate the inital question, is it some need to use this weeks newly learnt word? </i> --gokufusionss1

How is my post an overcomplication? If you think a straight line on a map is the shortest distance between two points on earth, then you'd be wrong, and oversimplifying the problem.

If anything, my post oversimplified the problem as well. There aren't airports at every point on a globe, only in specific places. Planes have limited fuel supplies. National borders have to be taken into account.

<i>Isn't Euclid's Fifth considered incomplete or something?</i> --princeofdarknez

Yes, Euclid's Fifth isn't provable, which is what allows non-Euclidean geometries (Spherical, Hyperbolic etc.) to be consistent.

[Loony BoB]

National borders have to be taken into account.

Yeah, that'd have a big effect. I remember watching our flight path duck under Iraq and bump over Israel. Or something like that.