airplaneguy
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Great Circle Routes

Sat Jul 21, 2012 9:03 pm

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.
 
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ADent
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RE: Great Circle Routes

Sat Jul 21, 2012 9:14 pm

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).
 
26point2
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RE: Great Circle Routes

Sat Jul 21, 2012 10:25 pm

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.
 
tdscanuck
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RE: Great Circle Routes

Sun Jul 22, 2012 12:44 am

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.
 
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zeke
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RE: Great Circle Routes

Sun Jul 22, 2012 6:01 am

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.
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airplaneguy
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RE: Great Circle Routes

Sun Jul 22, 2012 9:14 pm

Thanks for the highly informative responses. You guys definitely shed light on the question.
 
Rara
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RE: Great Circle Routes

Sun Jul 22, 2012 10:25 pm

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.
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September11
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RE: Great Circle Routes

Sun Jul 22, 2012 10:55 pm

Quoting Rara (Reply 6):

Very good example

so the first one is more of "illusion"
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flybaurlax
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RE: Great Circle Routes

Tue Jul 24, 2012 10:28 pm

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.
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PITingres
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RE: Great Circle Routes

Wed Jul 25, 2012 3:48 am

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]
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LH707330
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RE: Great Circle Routes

Wed Jul 25, 2012 2:18 pm

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?
 
26point2
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RE: Great Circle Routes

Wed Jul 25, 2012 4:52 pm

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]
 
timz
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RE: Great Circle Routes

Wed Jul 25, 2012 5:16 pm

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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