great circle
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The shortest distance between 2 points on the sphere is "orthodromy" and is a part of a great circle . Distance given between 2 navaids 
.
The longest distance is "loxodromy" . It's a path crossing the meridians at a constant angle .
.The longest distance is "loxodromy" . It's a path crossing the meridians at a constant angle .
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Dude... forget drawing lines, imagine a plane that passes from the 2 points and the center of the earth. There is only one such plane (3 points define a plane). The section of that plane with the surface of the earth is the 'great circle' between those two points.
Check google earth (not google maps) and click 'measure'. The distances and routes it gives you are great circles. Even at same latitude it doesn't follow a line of latitude (unless both points are on equator)
Alternatively:
Take an orange. Mark 2 points. Then imagine cutting with a knife that passes from the two points and the centre of the orange. The cut is a 'great circle'.
Geometry...
Check google earth (not google maps) and click 'measure'. The distances and routes it gives you are great circles. Even at same latitude it doesn't follow a line of latitude (unless both points are on equator)
Alternatively:
Take an orange. Mark 2 points. Then imagine cutting with a knife that passes from the two points and the centre of the orange. The cut is a 'great circle'.
Geometry...
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@Keith
Amazing way of explaination..sliced 7 tomatoes..got it..thnx
Another basic question which has been troubling me is the fact that meridians of longitude are rhumb lines.By definition rhumb lines are lines which cut all the meridians at equal angle.So how come a meridian becomes a rhumb line.
Looking forward to another great explaination.Thnx.
Amazing way of explaination..sliced 7 tomatoes..got it..thnx
Another basic question which has been troubling me is the fact that meridians of longitude are rhumb lines.By definition rhumb lines are lines which cut all the meridians at equal angle.So how come a meridian becomes a rhumb line.
Looking forward to another great explaination.Thnx.
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You do not draw any track or great circle on any globe .
Either you draw it on a Jepp Chart or any other chart with similar globe projection.
Or Calculate
Dist= asin ( sin Lat1 x sin Lat 2 + cos Lat 1 x cos Lat 2 x cos ( Long 2- Long 1))
Track Heading will constantly change with the distance....
even if both Lat1 and Lat 2 are on the same paralel....unless they are on equator.
(That is why it was not possible to use it while flying constant heading, before the time of INS etc)
P.S.
Or just use your RNAV computer
Either you draw it on a Jepp Chart or any other chart with similar globe projection.
Or Calculate
Dist= asin ( sin Lat1 x sin Lat 2 + cos Lat 1 x cos Lat 2 x cos ( Long 2- Long 1))
Track Heading will constantly change with the distance....
even if both Lat1 and Lat 2 are on the same paralel....unless they are on equator.
(That is why it was not possible to use it while flying constant heading, before the time of INS etc)
P.S.
Or just use your RNAV computer
I'm not 100% sure what projection a Jeppesen chart uses- sounds as if it is a Lambert projection.
On a Lambert, the great circle track between any two points on the chart is straight line on that chart. If you check such a line, you will see the angle at which it cuts each successive line of longitude changes progressively, showing that mapped onto the surface of the earth the track will be curved.
Does that help?
You can spot a Lambert projection because all the lines of longitude are straight lines pointing to (& meeting if projected to) the apex at the Pole. Lines of latitude will be arcs of a circle.
On a Lambert, the great circle track between any two points on the chart is straight line on that chart. If you check such a line, you will see the angle at which it cuts each successive line of longitude changes progressively, showing that mapped onto the surface of the earth the track will be curved.
Does that help?
You can spot a Lambert projection because all the lines of longitude are straight lines pointing to (& meeting if projected to) the apex at the Pole. Lines of latitude will be arcs of a circle.
The confusion occurs as a result of the way navigation, as an art and science developed.
Drawing lines of Longitude around the globe from the two poles was obvious - and easy to see that it simplified the definition of how far West or East a point is. Segment lines that make the chocolate orange possible.
The lines of latitude are not so obvious, it's one way of doing it, but it could be argued that adding another pair of poles on the equator could generate a second set of segment lines that would intersect at points to give relative coordinate.
The former method looks good on a map, but what it doesn't show is that it is not a straight line in any sense.
We're brought up on maps that have nice straight lines on them. Nobody tells us until we're older that it's all an enormous fudge. Not only are lines of latitude not straight, but the type of projection means that not much actually looks like a map from a satellite. The only viewpoint that would see a line of latitude as straight is from a satellite sitting in the same plane as that line. From there, every other line of latitude would not be straight.
All lines of longitude are great circles.
The only line of latitude that is a great circle is the equator.
A Rhumb line is a quick and dirty way to get a heading from A to B. It needs no finessing if you're going North or South, but the closer to East West you head, and the farther up or down the globe you go the more a Great Circle will save you distance. You'll also need to factor in crosswinds/tides (aircraft/ship), but that's obvious.
Drawing lines of Longitude around the globe from the two poles was obvious - and easy to see that it simplified the definition of how far West or East a point is. Segment lines that make the chocolate orange possible.
The lines of latitude are not so obvious, it's one way of doing it, but it could be argued that adding another pair of poles on the equator could generate a second set of segment lines that would intersect at points to give relative coordinate.
The former method looks good on a map, but what it doesn't show is that it is not a straight line in any sense.
We're brought up on maps that have nice straight lines on them. Nobody tells us until we're older that it's all an enormous fudge. Not only are lines of latitude not straight, but the type of projection means that not much actually looks like a map from a satellite. The only viewpoint that would see a line of latitude as straight is from a satellite sitting in the same plane as that line. From there, every other line of latitude would not be straight.
All lines of longitude are great circles.
The only line of latitude that is a great circle is the equator.
A Rhumb line is a quick and dirty way to get a heading from A to B. It needs no finessing if you're going North or South, but the closer to East West you head, and the farther up or down the globe you go the more a Great Circle will save you distance. You'll also need to factor in crosswinds/tides (aircraft/ship), but that's obvious.
Last edited by boguing; 3rd Mar 2011 at 12:00. Reason: Glaring mistake that nobody seemed to spot!
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FBTW - you will need to stretch your mind a little! All meridians of longitude are both Rhumb and great circle. Brace yourself - they do cut meridians at the same angle = 0.
Thinks - that might be 180
Thinks - that might be 180
Many references define a Rhumb Line as a line that crosses all of the meridians at the same angle. This definition leads to a second characteristic, which is that a Rhumb Line is a line of constant heading.
Historically the radial lines on a compass rose were called Rhumb Lines. So sailing a rhumb line course simply meant sailing a constant heading course.
The meridians are clearly lines of constant heading, (True North or True South), so they satisfy this condition for being rhumb lines.
Now let’s look again at the statement that “A Rhumb Line is a line that crosses all of the meridians at the same angle.”
The first point to note is that a line cannot cross any meridian that is not in its path. So we could refine our definition a little bit to become “A Rhumb Line is a line that crosses all of the meridians in its path at the same angle.”
The meridians of longitude are not circles, but are semi-circles. They start at one pole and end at the other. Where one meridian ends, its anti-meridian begins. And where the anti-meridian ends, its meridian begins. This means that the meridians and anti-meridians meet at the poles, but never actually cross each other. So between the poles the meridians of longitude are rhumb lines, which never cross any other meridians.
For a track which goes directly over one of the poles there will be a constant heading followed by an abrupt reversal of heading at that pole, after which the heading will again be constant. So we could argue that this track is made up of two rhumb lines.
Historically the radial lines on a compass rose were called Rhumb Lines. So sailing a rhumb line course simply meant sailing a constant heading course.
The meridians are clearly lines of constant heading, (True North or True South), so they satisfy this condition for being rhumb lines.
Now let’s look again at the statement that “A Rhumb Line is a line that crosses all of the meridians at the same angle.”
The first point to note is that a line cannot cross any meridian that is not in its path. So we could refine our definition a little bit to become “A Rhumb Line is a line that crosses all of the meridians in its path at the same angle.”
The meridians of longitude are not circles, but are semi-circles. They start at one pole and end at the other. Where one meridian ends, its anti-meridian begins. And where the anti-meridian ends, its meridian begins. This means that the meridians and anti-meridians meet at the poles, but never actually cross each other. So between the poles the meridians of longitude are rhumb lines, which never cross any other meridians.
For a track which goes directly over one of the poles there will be a constant heading followed by an abrupt reversal of heading at that pole, after which the heading will again be constant. So we could argue that this track is made up of two rhumb lines.
Last edited by keith williams; 2nd Mar 2011 at 22:46.
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From Wikipedia:
I suppose one can reverse that statement, so that any line that maintains a constant heading to true north is a rhumb line?
So the equator and the parallels are also rhumb lines?
regards,
HN39
In navigation, a rhumb line (or loxodrome) is a line crossing all meridians of longitude at the same angle, i.e. a path derived from a defined initial bearing. That is, upon taking an initial bearing, one proceeds along the same bearing, without changing the direction as measured relative to true north.
So the equator and the parallels are also rhumb lines?
regards,
HN39
Psychophysiological entity
I claim the prize for the shortest answer in post 10. However, I omitted to say one has to hold the two halves of the world together before walking along the cut line. Oh, and I also omitted to say the world is an oblate spheroid, so all the rules get twisted a tad.
Not much though. 12,756 / 12,714 km
Not much though. 12,756 / 12,714 km
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Keith Williams;
I assume you didn't intend what you wrote?
EDIT :: OK folks, Keith has now fixed the original.
So between the poles the meridians of latitude are rhumb lines, which never cross any other meridians.
EDIT :: OK folks, Keith has now fixed the original.
Last edited by mm43; 2nd Mar 2011 at 23:06.
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Basics!!
Green Guard
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You do not draw any track or great circle on any globe .
Either you draw it on a Jepp Chart or any other chart with similar globe projection.
Or Calculate
Dist= asin ( sin Lat1 x sin Lat 2 + cos Lat 1 x cos Lat 2 x cos ( Long 2- Long 1))
Track Heading will constantly change with the distance....
even if both Lat1 and Lat 2 are on the same paralel....unless they are on equator.
(That is why it was not possible to use it while flying constant heading, before the time of INS etc)
P.S.
Or just use your RNAV computer
Join Date: Aug 2000
Location: RedIndia
Age: 96
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You do not draw any track or great circle on any globe .
Either you draw it on a Jepp Chart or any other chart with similar globe projection.
Or Calculate
Dist= asin ( sin Lat1 x sin Lat 2 + cos Lat 1 x cos Lat 2 x cos ( Long 2- Long 1))
Track Heading will constantly change with the distance....
even if both Lat1 and Lat 2 are on the same paralel....unless they are on equator.
(That is why it was not possible to use it while flying constant heading, before the time of INS etc)
P.S.
Or just use your RNAV computer
Keep going like that and soon there will be Unmanned Airliners flying cause if its ok to use the RNAV cause you don't understand what a 'sphere' and a 'plane' are (geometrical plane, not the flying one), then it will be ok not to understand what 'lift' and 'glideslope' is cuase you can use the 'green dot'... I'd trust as a passenger more a computer than a 'RNAV user' or a 'green dot follower'. At least computers are deterministic.
delete if offending
cheers
(SLF)
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If you have i tunes installed, you could follow this link.
Connecting to the iTunes Store.
Then under categories on the right hand side, click mathematics. Then click on the the picture with the hot air baloon, then start with the the video at line 5 titled "spherical geometry", followed by "looking for theta" and "great circle distance"
Connecting to the iTunes Store.
Then under categories on the right hand side, click mathematics. Then click on the the picture with the hot air baloon, then start with the the video at line 5 titled "spherical geometry", followed by "looking for theta" and "great circle distance"
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Rhumb lad
No, the Equator strangely enough is in fact a Great Circle. One of the reasons being is that is does not `concave` to the nearer pole - like rhumb lines do. As the most lear-ned chaps and chapessess have said - if you put an elestic band round a large orange around the middle, with the pip bit at the top . . . now, if you move the elastic band up to say . . half way up the orange towards the top . . and it stays on . . then, then the track the elastic band is forming over the surface of the orange is now, is now, concave to the nearer pole - the North Pole of the orange.
In other words your EASTerly track will follow the curve of the Earth - you will always be heading EAST but you will not be TRACKING to your EASTerly DESTINATION you will be following the curvature of the Earth.
So, Inertial Navigation Systems can calculate a DIRECT GREAT CIRCLE TRACK - = A STRAIGHT LINE to the destination WITHOUT GOING AROUND THE CURVATURE OF THE EARTH. In other words it cuts the corner or in this case the bend.
So, say you are in Western Europe France, Paris say and you want to go to Eastern China. If you go due East South East you may eventually arrive there but it would take a long time and a lot of fuel.
So, you may wish to head North East from Paris ! Yep, North East and go East over the North Siberian coast all the way round through Mogolia or wherever your "DIRECT" Great Circle Track Takes you to your destination.
So, your initial heading is North East! and your subsequesnt headings will be East and South East respectively.
There are formulae for working all this out, which you will get on your ATPL course and the INS/IRS systems do it all using accellerometers and different types of gyro systems and flux things and well it gets very involved but enough to say it maintains the Heading of the aircraft to co-incide with the Track required instead of basing the heading (as you correctly said) on Magnetic North.
Just to completely freak you out - it does in fact calculate from Mag North in order to ascertain which way it is pointing, how far it is from the Pole as a waypoint etc., if only to inform the pilot, so it does "have a reference" to Mag North but will or will not use it to calc this TRACK - as it will effectively just look at the destination co-ordinates and draw a stright line to it (Great Circle Track) and maintain THAT line to Destination.
Hope that helps.
In other words your EASTerly track will follow the curve of the Earth - you will always be heading EAST but you will not be TRACKING to your EASTerly DESTINATION you will be following the curvature of the Earth.
So, Inertial Navigation Systems can calculate a DIRECT GREAT CIRCLE TRACK - = A STRAIGHT LINE to the destination WITHOUT GOING AROUND THE CURVATURE OF THE EARTH. In other words it cuts the corner or in this case the bend.
So, say you are in Western Europe France, Paris say and you want to go to Eastern China. If you go due East South East you may eventually arrive there but it would take a long time and a lot of fuel.
So, you may wish to head North East from Paris ! Yep, North East and go East over the North Siberian coast all the way round through Mogolia or wherever your "DIRECT" Great Circle Track Takes you to your destination.
So, your initial heading is North East! and your subsequesnt headings will be East and South East respectively.
There are formulae for working all this out, which you will get on your ATPL course and the INS/IRS systems do it all using accellerometers and different types of gyro systems and flux things and well it gets very involved but enough to say it maintains the Heading of the aircraft to co-incide with the Track required instead of basing the heading (as you correctly said) on Magnetic North.
Just to completely freak you out - it does in fact calculate from Mag North in order to ascertain which way it is pointing, how far it is from the Pole as a waypoint etc., if only to inform the pilot, so it does "have a reference" to Mag North but will or will not use it to calc this TRACK - as it will effectively just look at the destination co-ordinates and draw a stright line to it (Great Circle Track) and maintain THAT line to Destination.
Hope that helps.
