Chile - Australia route

[Dercaful]

So, yesterday I was having dinner with my girlfriend and her family and we started discussing about the route an airplane would take when travelling from Chile to Australia.

Her thesis: It would travel from West to East.
Her argument: The plane travel from the Occidental to the Oriental part of the map, so we start at the West and end up in the East.

My thesis: It would travel from East to West.
My argument: As the Earth is spherical, we can just watch a globe and see the route, as shown in the image below (used Google Maps instead of a globe bc it's easier and works anyway).

So, who do you think is right in here?

[tox]

i cant provide a picture from expedia.ca but most flights are 2-4 stops and go from lets say Sydney to Santiago and would first stop in Los Angeles and then in Miami then would go down to Santiago

[Dercaful]

At 12/18/13 01:03 PM, tox wrote: i cant provide a picture from expedia.ca but most flights are 2-4 stops and go from lets say Sydney to Santiago and would first stop in Los Angeles and then in Miami then would go down to Santiago

I wasn't asking that. Please read the whole thing.

[tox]

thenthe plane is going to travel from the south eastern hemisphere to the north western hemisphere to the south western hemispere

[Insateddii]

Ain't that line you drew on the map good enough as a route?

[tox]

At 12/18/13 01:11 PM, tox wrote: thenthe plane is going to travel from the south eastern hemisphere to the north western hemisphere to the south western hemispere

making you both wrong
happy?

[Painbringer]

I actually own a globe.

The plane would fly south, directly over Antarctica.

[Lagerkapo]

At 12/18/13 02:35 PM, Painbringer wrote: I actually own a globe.

The plane would fly south, directly over Antarctica.

In this case it would be south then north.

In the case of the line in OP's post, it would (appear) to be heading east, from the west.

Because the globe is polar, longitudinal travel remains consistently east or west, but if one traverses latitudinally past a pole the direction would switch from south to north or vice-versa.

That said, I, too, own a globe.

If one were departing Cape Horn at the southern tip of Chile, one could, theoretically, pass over the actual landmass of Antarctica if one were to bear straight, and the bearing would be southeast until one passed the Rockefeller Plateau in Antarctica, at which point one's latitude would begin bearing north, and the longitudinal travel would continue being easterly.

That, too, being said, Chile's capital of Santhiago and the city of Sydney in Australia are at almost identical latitudes, within just a few degrees, and given those as the departure and arrival points, respectively, the direction of travel would be a clean east.

[Evark]

You both are right. The problem is that saying that a plane is directionally travelling from the Occident to the Orient does not specify the spatial relationship between the two (though the names imply them). So, you saying that the plane is traveling from the West to the East in the socio-political sense of the terms is ambiguous, one could travel from the West to the East either by taking a plane traveling west or taking a plane travelling east, due to the nature of the globe. Whereas, your girlfriend is technically more accurate in that she recognizes the question is not asking where the origin and destination is (as you are answering), but rather the compass-specific direction in which the plane is more likely to travel.

[i-am-ghey]

You are right. The plane should travel from east to west as shown in the map, although it should not follow a straight path.
The "straight line" on a curved surface is not the shortest path.

Traveling along an arc towards the south pole will minimize distance and flight time.

[stafffighter]

You could always try booking a flight and see what route it gives you. Then presumable you would stop before actually booking the flight.

[ElMagnificoBurro]

How dead is your relationship that your conversations are about geography and directions?

[i-am-ghey]

But to be fair, saying the plane travels from "the" west to "the" east makes sense in everyday language, because people have adopted a convention where chile belongs to the set of western countries and Australia belongs to the eastern countries. You will reach a different conclusion if the convention is reversed.

[Dercaful]

At 12/18/13 08:20 PM, ElMagnificoBurro wrote: How dead is your relationship that your conversations are about geography and directions?

You'd be surprised if you heard all we talk about things like that. The only problem is that she's more of a mathematician and I'm more of a humanist, so she always wins in Maths stuff and I always win in History, Grammar and that stuff.

Wouldn't say it's dead though. You couldn't be more wrong.

[Splats]

At 12/18/13 01:07 PM, Dercaful wrote:

At 12/18/13 01:03 PM, tox wrote: i cant provide a picture from expedia.ca but most flights are 2-4 stops and go from lets say Sydney to Santiago and would first stop in Los Angeles and then in Miami then would go down to Santiago

I wasn't asking that. Please read the whole thing.

This is Newgrounds, don't expect a serious answer
Like, ever
Welcome

[Lagerkapo]

At 12/18/13 08:15 PM, i-am-ghey wrote: You are right. The plane should travel from east to west as shown in the map, although it should not follow a straight path.
The "straight line" on a curved surface is not the shortest path.

Traveling along an arc towards the south pole will minimize distance and flight time.

As I pointed out earlier, after consulting my globe, the two cities of Santhiago, Chile and Sydney, Australia are on nearly exactly the same lines of latitude, therefore a straight (yes, curved, but not latitudinally, just curved because of the spherical nature of the globe) path bearing due west is the fastest route.

The only way passing near (not over, but very near) the south pole is the fastest route is, again, if one is departing from Cape Horn at the southern tip of Chile.

[NuclearInfected]

At 12/18/13 08:20 PM, ElMagnificoBurro wrote: How dead is your relationship that your conversations are about geography and directions?

Deader than Kenny in a razor blade and bazooka factory.

[i-am-ghey]

As I pointed out earlier, after consulting my globe, the two cities of Santhiago, Chile and Sydney, Australia are on nearly exactly the same lines of latitude, therefore a straight (yes, curved, but not latitudinally, just curved because of the spherical nature of the globe) path bearing due west is the fastest route

You should consult a book on differential geometry as well.
The geodesic between two points on a smooth manifold is given by setting the convariant derivative to be zero along the path. Moreover the path does not depend on the choice of coordinates.

The solution may not be unique, however, the line obtained naively by connecting two points on the map with a ruler is certainly not the shortest path.

I think the plane should pass over Antarctica, (or neighboring seas) to minimize distance.

[Lagerkapo]

At 12/19/13 12:53 AM, i-am-ghey wrote: The solution may not be unique, however, the line obtained naively by connecting two points on the map with a ruler is certainly not the shortest path.

I used a globe, not a map, and even if I use a segment of string the difference is obvious: The straight line is shorter.

I think the plane should pass over Antarctica, (or neighboring seas) to minimize distance.

Ok, so I have used this (unfortunately mercator projection) image from the OP and added some lines to demonstrate what I mean.

How is the curved line shorter than the straight one again?

I am failing to see how your differential geometry proves your point: The straight line is invariably shorter.

[Lagerkapo]

Ok, so it seems I truly am failing to understand this.

I googled the flight map from Sydney to Santhiago, and this is the result, an, indeed, curved flight path.

It does not, however, pass over the south pole or Antarctica, but it does follow a south- then northerly trajectory.

I will admit when I am wrong; I simply do not seem to understand this.

[Lagerkapo]

At 12/19/13 01:09 AM, Lagerkapo wrote: I will admit when I am wrong; I simply do not seem to understand this.

ok ok ok, so I did some more research and found out about the concept of the "great circle" formula.

Maths aside (because I'm only going at the concept here and have no need for trigonometrical proofs [Jesus, Chrome's dictionary has the word trigonometrical but not latitudinal...]), the idea is that the circle drawn in two dimensions, in relation to the sphere in three, whose circumference includes both the center point of the sphere and two given points on the surface of the sphere (in this case Sydney and Santhiago) will provide, at the intersection arc of its plane and the surface of the sphere, the most efficient arc of distance between the two points along the surface of the sphere.

Very simple really.

Yes, once again, I will admit that I was wrong.

Cool, you learn something every day. Hopefully.

[i-am-ghey]

Here is a way to look at it.

The earth is round, so, the distance representing 1 degree longitude along the equator, is much greater than 1 degree longitude along, say the 60 degree latitude line. You can imagine that you will travel a shorter distance if you move south a bit first then go westwards.

The map does not seem to represent this fact. That is why you have the illusion that the straight path as seen on the map is shorter.