geography and great circle routes

[xouper]

Now that we have a geography forum, I though I'd pilfer some information from an old thread, consolidate it, repackage it slightly, and start a new thread here.

ceptimus: ... if you wish to sail, or fly the shortest course between two points, a straight line on a Mercator map is not what you want. All things being equal, you'd want to use a great circle route, and these will almost always be curves on the Mercator map.
As in the attached examples. The red curved lines show the shortest flying distance (great circle routes), respectively:

from London to Los Angeles or Atlanta.


from Chicago to Dubai.


from Chicago to Tokyo.

Images courtesy of www.landings.com

[xouper]

If you go here (http://www.landings.com/evird.acgi$pass*69462846!_h-www.landings.com/_landings/pages/search/search_dist_apt.html) and type in the ICAO identifiers for the departure and destination airports, leave the other boxes empty, check "Show area map of flight route", and click the send button, it will give you a map showing the great circle route between the two airports.

Here are some ICAO airport identifiers:

Rome: LIRF
New York: KJFK
London: EGLL
Dubai: OMDB
Chicago: KORD
Tokyo: RJAA

You can also find more ICAO airport identifiers here (http://www.landings.com/evird.acgi$pass*69462846!_h-www.landings.com/_landings/pages/search/search_ap-ident.html).

[xouper]

Here's another great circle route tool: http://gc.kls2.com/

[livius drusus]

Great idea, xoup. Thank you for reviving this discussion to help inaugurate the new forum. :yup:

I have a question. It is a stupid one. It is also a lazy one. But you're here and I'm tired and I just can't resist the urge to make you do my thinking for me: Do all the routes peak higher north as they get longer?

I told you it was stupid. I'm sure it's inherent in the curvature or the whole point or something, but that's the best my poor, strained meninges can do right now.

[viscousmemories]

If you go here and type in the ICAO identifiers for the departure and destination airports, leave the other boxes empty, check "Show area map of flight route", and click the send button, it will give you a map showing the great circle route between the two airports.
That's very cool. It also solves the mystery of why we refueled in Newfoundland when I flew from New York to London once. I couldn't for the life of me figure out what we were doing up there...

[xouper]

More about great circle routes:
http://en.wikipedia.org/wiki/Great_circle

[xouper]

livius drusus: Do all the routes peak higher north as they get longer?
In general, yes.

In extreme cases, when two cities (northern hemisphere) are on opposite sides of the globe, the great circle route crosses near the North Pole, as in the attached images of the route from Seattle to Moscow.

This is also why nuclear missiles from Russia to the U.S. would be coming over the top of the globe across Canada (and vice versa), since that is the shortest route.

[ceptimus]

If you have access to a globe, you can plot the great circle route by using a piece of elastic stretched between the start and end points of your journey. If we consider the northern hemisphere, then any routes that fly directly over the north pole must start and end at longitudes with a difference of 180 degrees. Obviously such routes in the southern hemisphere 'curve south' and go over the south pole in extreme cases.

When the endpoints of the journey are exactly opposite each other on the globe (longitudes differ by 180 degrees, and latitudes add to zero (taking latitudes south of the equator as negative)) then there are an infinity of great circle routes - you can set off in any direction you like, and as long as you maintain a straight course (this does not mean a constant compass bearing, of course), then you will arrive at your destination.

For anyone having trouble imagining that a constant compass heading doesn't result in a straight course, and vice versa, imagine yourself near the north pole. Say you are 20 feet away from the pole, and head due east at all times. You will then walk in a 40 foot diameter circle. Similarly if you start 20 feet from the pole, and walk in a dead straight line, missing the pole by a foot to the right, then you will start out almost due north, be going east as you pass the pole, and more or less due south after another 20 feet or so.

[livius drusus]

This is also why nuclear missiles from Russia to the U.S. would be coming over the top of the globe across Canada (and vice versa), since that is the shortest route.

Thanks xoup; that makes a great deal of sense. It's topical and interesting too, in light of Canada's recent decision to opt out of the US's missile defense (http://www.latimes.com/news/nationworld/world/la-fg-missile25feb25,1,3310433.story?coll=la-headlines-world&ctrack=1&cset=true) plan.

For anyone having trouble imagining that a constant compass heading doesn't result in a straight course, and vice versa, imagine yourself near the north pole. Say you are 20 feet away from the pole, and head due east at all times. You will then walk in a 40 foot diameter circle. Similarly if you start 20 feet from the pole, and walk in a dead straight line, missing the pole by a foot to the right, then you will start out almost due north, be going east as you pass the pole, and more or less due south after another 20 feet or so.

Very helpful image, cep. Thank you.

[xouper]

ceptimus: For anyone having trouble imagining that a constant compass heading doesn't result in a straight course, and vice versa, imagine yourself near the north pole. Say you are 20 feet away from the pole, and head due east at all times. You will then walk in a 40 foot diameter circle. Similarly if you start 20 feet from the pole, and walk in a dead straight line, missing the pole by a foot to the right, then you will start out almost due north, be going east as you pass the pole, and more or less due south after another 20 feet or so.

livius drusus: Very helpful image, cep. Thank you.
Yes, it's a good thought experiment.

In reality, the north magnetic pole cannot be located with that much precision.

Also, it wiggles around too much on a daily basis and has been known to wiggle up to 80 kilometers in a single day.

http://www.geolab.nrcan.gc.ca/geomag/daily_mvt_nmp_e.shtml