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Great Circle Routes  
User currently offlineairplaneguy From United States of America, joined Dec 2009, 52 posts, RR: 0
Posted (2 years 5 months 4 days 2 hours ago) and read 5991 times:

Given that most routes between destinations are great circle routes, and that great circle routes are curves rather than straight lines, does that mean the aircraft is in a slight bank while flying the route?

What about when the routing calls for various waypoints/legs on a single journey?

This question came to me having recently flown YYZ-TPA and while watching the in-flight map.

Thanks in advance.

Airplaneguy.

12 replies: All unread, jump to last
 
User currently offlineADent From United States of America, joined exactly 8 years ago today! , 1406 posts, RR: 2
Reply 1, posted (2 years 5 months 4 days 2 hours ago) and read 5938 times:

If you look at a globe great circle routes are straight. It is an artifact of the map projection if it isn't straight on the map.

Most parts of the world have air routes of some kind or other, so typically a flight will not fly a true great circle route.

Also winds will change the least fuel used route from a GCR to something else. And you must avoid severe weather and no-fly zones (like an air force fighter test range).


User currently offline26point2 From United States of America, joined Mar 2010, 856 posts, RR: 0
Reply 2, posted (2 years 5 months 4 days 1 hour ago) and read 5893 times:

The great circle track is in fact a straight line but the heading will change as the flight progresses. A flight from KSFO-KLHR begins at about a 040 degree course to end on a 150 degree course. Wings stay level.

N. Atlantic crossing routes are roughly a great circle route but made of pt. to pt. segments 10 degrees of longitude wide. There is a slight turn every 10 degrees.


User currently offlinetdscanuck From Canada, joined Jan 2006, 12709 posts, RR: 80
Reply 3, posted (2 years 5 months 3 days 22 hours ago) and read 5828 times:

Quoting airplaneguy (Thread starter):
Given that most routes between destinations are great circle routes

As noted, very few routes are actually true great circles. Most areas have defined tracks and airways that deviate; good dispatches will match you up to the shortest path after taking winds, weather, restrictions, diversions, etc. all into account.

Quoting airplaneguy (Thread starter):
that great circle routes are curves rather than straight lines

They're only curved relative to lattitude/longitude lines, or equivalent on flat projections. Great circle routes are "straight" with respect geometry.

Quoting airplaneguy (Thread starter):
does that mean the aircraft is in a slight bank while flying the route?

No. Even on routes that are curved, they're flown as a series of straight line segments except in a few rare circumstances, like DME arcs.

Quoting airplaneguy (Thread starter):
What about when the routing calls for various waypoints/legs on a single journey

That's the normal state of things. The FMC will connect the points so you'll have a slight turn as you pass each point. On the nicer predictive FMC's they'll actually start the turn slightly early to give you a nice smooth curve between the segments.

Tom.


User currently offlinezeke From Hong Kong, joined Dec 2006, 9230 posts, RR: 76
Reply 4, posted (2 years 5 months 3 days 17 hours ago) and read 5747 times:

Quoting airplaneguy (Thread starter):

What about when the routing calls for various waypoints/legs on a single journey?

Published routes are great circles, just a combination of lots of small segments. The tracks that are defined by radio navigation aids are great circles as the wave propagation from a transmitter is generally a great circle (some terrain and equipments effects can bend this a little).

Flying between way-points is done on a great circle. When flying VFR, if one flies the route on the map, the actual flight path will depend on the projection of the chart that is used, on shorter VFR flights, the difference between a great circle and a rhumb line is negligible, it is easier to use a flat chart, rather than a curved one. GPS equipment normally navigate great circles over a mathematical representation of earth called an ellipsoid.The great circle flown on the GPS ellipsoid (commonly WGS84) can also differ from the real earth a little as well. Sometimes a GPS track will slightly vary from a track based upon ground based navigation aids.



We are addicted to our thoughts. We cannot change anything if we cannot change our thinking – Santosh Kalwar
User currently offlineairplaneguy From United States of America, joined Dec 2009, 52 posts, RR: 0
Reply 5, posted (2 years 5 months 3 days 2 hours ago) and read 5528 times:

Thanks for the highly informative responses. You guys definitely shed light on the question.

User currently onlineRara From Germany, joined Jan 2007, 2169 posts, RR: 2
Reply 6, posted (2 years 5 months 3 days 1 hour ago) and read 5504 times:

London-New York on a great circle:



http://img6.imagebanana.com/img/fktlie1m/Unbenannt2.JPG

Appears as a curve....




... but is straight as can be.

Note how the route goes right across Newfoundland on both images.



Samson was a biblical tough guy, but his dad Samsonite was even more of a hard case.
User currently offlineSeptember11 From United States of America, joined May 2004, 3623 posts, RR: 21
Reply 7, posted (2 years 5 months 3 days ago) and read 5493 times:

Quoting Rara (Reply 6):

Very good example

so the first one is more of "illusion"



Airliners.net of the Future
User currently offlineflybaurlax From United States of America, joined Oct 2008, 638 posts, RR: 0
Reply 8, posted (2 years 5 months 1 day ago) and read 5173 times:

Quoting September11 (Reply 7):
so the first one is more of "illusion"

It's not an "illusion." It's a projection of a straight line from a curved surface to a flat surface.



Boilerup! Go Purdue!
User currently offlinePITingres From United States of America, joined Dec 2007, 1163 posts, RR: 13
Reply 9, posted (2 years 5 months 19 hours ago) and read 5109 times:

Quoting airplaneguy (Thread starter):
Given that most routes between destinations are great circle routes, and that great circle routes are curves rather than straight lines, does that mean the aircraft is in a slight bank while flying the route?

"Curves" only when looking at the track from the point of straight line Euclidian geometry.

In a spherical geometry such as is used for navigating around the earth, one might properly say that a great circle route is the straight line, nonaccelerated, non-curved route, with anything else being curved. The "curved" track is the geodesic, ie the shortest distance between two points. So no, the aircraft is not banking, because it's flying a locally straight line.

[Edited 2012-07-24 20:50:14]


Fly, you fools! Fly!
User currently offlineLH707330 From United States of America, joined Jun 2012, 848 posts, RR: 0
Reply 10, posted (2 years 5 months 9 hours ago) and read 5019 times:

Quoting 26point2 (Reply 2):

N. Atlantic crossing routes are roughly a great circle route but made of pt. to pt. segments 10 degrees of longitude wide. There is a slight turn every 10 degrees.

Does this mean that you hold a given heading (rhumbline) between these points and then have little course changes? If so, your track over a globe projection would look like a series of gentle left curves with angled right turns (crossing N Atl west to east), no?


User currently offline26point2 From United States of America, joined Mar 2010, 856 posts, RR: 0
Reply 11, posted (2 years 5 months 6 hours ago) and read 4980 times:

Sort of. You navigate from point to point and the aircraft "heading" will change along this straight line as discussed but you will not change course until the next point. Usually these points are at 10 degree latitude and longitude intervals but not always.

Typical segment would be something like flying from 60N x 30W to 60N x 20W. You are not "on" the 60N parallel but will be close. At the 20W fix you might then make a slight turn to fly next to 50N x 10W as the next fix. These routes or "tracks", are changed twice per day by Oceanic ATC to take advantage or to avoid the jet stream depending on direction of flight.

Today's flight from CYQX-EINN would run KOBEV 5050N 5340N 5430N 5320N MALOT. (5340N = 53N 40W for example). If you plot this on a chart you will see.

[Edited 2012-07-25 09:54:48]

User currently offlinetimz From United States of America, joined Sep 1999, 6902 posts, RR: 7
Reply 12, posted (2 years 5 months 6 hours ago) and read 4966 times:

Quoting PITingres (Reply 9):
one might properly say that a great circle route is the straight line, nonaccelerated, non-curved route, with anything else being curved.

Or to be more proper, a great circle is curved like any other line on the surface of a sphere. It has the largest radius, so it's the shortest surface route between any two points.


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