Omatako
New member
Would any of the resident pundits like to take a shot at "Understanding Great Circle Distance For Dummies"??
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Great Circle Distance
- Thread starter Omatako
- Start date
Ric
Well-known member
Do you mean "explaining" great circle distance?
"Great circle distance", or orthodromic distance is the "real" shortest distance between two points on the globe. Imagine getting out your toy globe and stretching a piece of string over its surface between (say) London and Tokyo. That is the "great circle" distance.
Loxodromic distance is what you plot on the charts you typically use for sailing (most are mercator projections). To put it in simple terms, the chart distorts reality because the curved surface of the earth has been represented on a flat piece of paper. So if you plot a straight line on a chart, then follow it exactly in your boat, you will actually sail in a very slight curve.
For typical cruising distance, the difference between loxodromic and orthodromic distance is negligible. If you cross the Atlantic, it becomes important though. However most of us now use GPS chartplotters, and they all plot orthodromes, so even a long sail is not the navigational exercise it used to be.
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"Great circle distance", or orthodromic distance is the "real" shortest distance between two points on the globe. Imagine getting out your toy globe and stretching a piece of string over its surface between (say) London and Tokyo. That is the "great circle" distance.
Loxodromic distance is what you plot on the charts you typically use for sailing (most are mercator projections). To put it in simple terms, the chart distorts reality because the curved surface of the earth has been represented on a flat piece of paper. So if you plot a straight line on a chart, then follow it exactly in your boat, you will actually sail in a very slight curve.
For typical cruising distance, the difference between loxodromic and orthodromic distance is negligible. If you cross the Atlantic, it becomes important though. However most of us now use GPS chartplotters, and they all plot orthodromes, so even a long sail is not the navigational exercise it used to be.
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john_morris_uk
Well-known member
Great circle distance is the sortest distance between two points on the surface of the earth. If you got a globe and put two drawing pins in and stretched a string between the two, the string would be the shortest distance and would decribe a 'great circle route'. Its called great circle, because if we approximate the earth's surface to a sphere, all such routes form a part of a circle around the earth.
The complications that confuse arise from the way we make charts. For good reasons, most charts are on a mercator projection, and although all bearings are correct on them, if you have a mercator chart of a large part of the world, a straight line does not always represent a great circle route. You can get a chart where straight lines are great circle routes: they are called gnomonic projections, but you can't use a plotter on it quite as easily. (If you see one its obvious why - all the lines of longiude are not North-South.)
For coastal and channel cruising - and even crossing Biscay - don't worry about it. Its only when you start crossing oceans you have to remember this stuff, and even then I've never managed to sail an exact great circle route - you're always more worried about the best wind etc etc and which is a fast and safe course in about the right direction..
Most GPS's always calculate courses as 'great circle routes'
If you are still with me, you might also be interested to know that GPS does not assume that the earth is a perfect sphere, and allows for the different radii of the earths surface at different points of the earths surface when it calculates your position.
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The complications that confuse arise from the way we make charts. For good reasons, most charts are on a mercator projection, and although all bearings are correct on them, if you have a mercator chart of a large part of the world, a straight line does not always represent a great circle route. You can get a chart where straight lines are great circle routes: they are called gnomonic projections, but you can't use a plotter on it quite as easily. (If you see one its obvious why - all the lines of longiude are not North-South.)
For coastal and channel cruising - and even crossing Biscay - don't worry about it. Its only when you start crossing oceans you have to remember this stuff, and even then I've never managed to sail an exact great circle route - you're always more worried about the best wind etc etc and which is a fast and safe course in about the right direction..
Most GPS's always calculate courses as 'great circle routes'
If you are still with me, you might also be interested to know that GPS does not assume that the earth is a perfect sphere, and allows for the different radii of the earths surface at different points of the earths surface when it calculates your position.
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kimhollamby
Active member
<font size=1>Most GPS's always calculate courses as 'great circle routes'</font size=1>
That in itself is an interesting statement. Did an indepth look at this a few years back. I'll try to dig out the info and perhaps make it available as a PDF if anyone interested.
Kim
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That in itself is an interesting statement. Did an indepth look at this a few years back. I'll try to dig out the info and perhaps make it available as a PDF if anyone interested.
Kim
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Jacket
New member
Any idea how you calculate a great circle route using a mercator chart? Its something I've wondered about for a while, but have never seen an answer.
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30boat
N/A
I am.
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MedMan
New member
Great Circles
The defining property of a 'Great Circle' is that its plane passes through the centre of the earth. The equator is a 'great circle' as are all lines of Longitude when joined onto their reciprocal to form a circle. Lines of latitude (other than the equator) are clearly circles, but they are not 'Great Circles' as their planes do not pass through the centre of the earth.
<hr width=100% size=1><A target="_blank" HREF=http://www.yachtretreat.com>http://www.yachtretreat.com</A>
The defining property of a 'Great Circle' is that its plane passes through the centre of the earth. The equator is a 'great circle' as are all lines of Longitude when joined onto their reciprocal to form a circle. Lines of latitude (other than the equator) are clearly circles, but they are not 'Great Circles' as their planes do not pass through the centre of the earth.
<hr width=100% size=1><A target="_blank" HREF=http://www.yachtretreat.com>http://www.yachtretreat.com</A>
MedMan
New member
Have a look <A target="_blank" HREF=http://www.yachtretreat.com>http://www.yachtretreat.com
B
bob_tyler
Guest
Yes please Kim.
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G
Guest
Guest
???
<<Generally, but not always, this will follow the nationality of the owner.>>
Not strictly true .... its called a Great Circle because the plane of the complete circle, that the line between two points is part of, lies through the centre of the earth ......
<hr width=100% size=1>Nigel ...
So WHAT does the EU really stand for ????/forums/images/icons/cool.gif
<<Generally, but not always, this will follow the nationality of the owner.>>
Not strictly true .... its called a Great Circle because the plane of the complete circle, that the line between two points is part of, lies through the centre of the earth ......
<hr width=100% size=1>Nigel ...
So WHAT does the EU really stand for ????/forums/images/icons/cool.gif
G
Guest
Guest
GC and Mercator chart ...
You don't construct / calculate a GC via a Mercator chart .... you can do it on a polar projection or by strict calculation.
The less efficient way to do it - which tended to prevail before the advent of Computers and Navigation Calculators ... was to compute the initial course based on spherical trig. Steer that course for given time and then compute another initial course to steer etc. This is repeated at regular set intervals ... used to be each noon for pacific trips and possibly 12 hour intervals for some atlantic stuff.
BUt this is actually a poor way to calculate it as the course or GC is not a GC in its true sense and tebnds to get more exagerated at the final stages ... basically getting more hooked in outline.
Later nav calculators worked on setting intermediate latitudes intervals and then calculating the courses between each along with the longitudes ....... this gave a closer approimation to the true curve if sufficient intermedaite points were taken.
Using the polar chart .... a straight line on that is the GC and points can be taken directly of it to form the position points of course change. Simple Mercator / Rhumb line calcs between the two points then would give distnace to travel.
So endeth lesson # 221 verse 6
<hr width=100% size=1>Nigel ...
So WHAT does the EU really stand for ????/forums/images/icons/cool.gif
You don't construct / calculate a GC via a Mercator chart .... you can do it on a polar projection or by strict calculation.
The less efficient way to do it - which tended to prevail before the advent of Computers and Navigation Calculators ... was to compute the initial course based on spherical trig. Steer that course for given time and then compute another initial course to steer etc. This is repeated at regular set intervals ... used to be each noon for pacific trips and possibly 12 hour intervals for some atlantic stuff.
BUt this is actually a poor way to calculate it as the course or GC is not a GC in its true sense and tebnds to get more exagerated at the final stages ... basically getting more hooked in outline.
Later nav calculators worked on setting intermediate latitudes intervals and then calculating the courses between each along with the longitudes ....... this gave a closer approimation to the true curve if sufficient intermedaite points were taken.
Using the polar chart .... a straight line on that is the GC and points can be taken directly of it to form the position points of course change. Simple Mercator / Rhumb line calcs between the two points then would give distnace to travel.
So endeth lesson # 221 verse 6
<hr width=100% size=1>Nigel ...
So WHAT does the EU really stand for ????/forums/images/icons/cool.gif
ongolo
New member
Download from the dutch hydrographer a program called CNAV40, it comes free and is very good.
I did compare the routes for a great circle and not a great circle from here to Rio, but the time difference at constant sped was not enough for me to worry about since I am not racing. If I remember it was only some eight hours, but then it is almost due west.
regards ongolo
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I did compare the routes for a great circle and not a great circle from here to Rio, but the time difference at constant sped was not enough for me to worry about since I am not racing. If I remember it was only some eight hours, but then it is almost due west.
regards ongolo
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Ric
Well-known member
Jacket asked "Any idea how you calculate a great circle route using a mercator chart? Its something I've wondered about for a while, but have never seen an answer"
You can make an approximation by applying what is called the "Givry correction". Basically draw your loxodromic line on your mercator chart. Then you "aim off" northwards (in NH, opposite in SH) from your loxodromic departure bearing by 0.5*(difference in longitude between start and finish)*Sin(average latitude of trajectory). Obviously when you are halfway between A and B your orthodromic and loxodromic bearings are parallel, then they converge again at B. You can get a good stab at an orthodromic route with this approximation.
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You can make an approximation by applying what is called the "Givry correction". Basically draw your loxodromic line on your mercator chart. Then you "aim off" northwards (in NH, opposite in SH) from your loxodromic departure bearing by 0.5*(difference in longitude between start and finish)*Sin(average latitude of trajectory). Obviously when you are halfway between A and B your orthodromic and loxodromic bearings are parallel, then they converge again at B. You can get a good stab at an orthodromic route with this approximation.
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Omatako
New member
Yes please Kim
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Omatako
New member
OK so if I cut the earth in half with the cut going through the centre, any distance from point A to point B along the circumference of the slice would be a GCD. Great. That seems simple enough.
I am plannng to sail from Durban South Africa to Fremantle and have planned a route to drop from about 29 degrees south down to the 37 degree parallel and follow that most of the way and then easing back up to Fremantle which is further north (don't want to bore you with precise detail).
This route is planned for no other reason than the Pilot Chart for that area for that time of year says it is a favourable weather route and we can find no evidence to contradict this assumption. No reason to assume that we won't deviate from the chosen route if weather dictates it. But it is a distance of some 4400 miles and if the % savings are significant, perhaps we should replan.
The way you have explained is that this would not be a GCD. What sort of variation distance-wise would it be from a GCD? Would it be significantly longer? Should I concern myself with the difference?
Thanks to all respondents but as you can see I remain a dummy in this regard.
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I am plannng to sail from Durban South Africa to Fremantle and have planned a route to drop from about 29 degrees south down to the 37 degree parallel and follow that most of the way and then easing back up to Fremantle which is further north (don't want to bore you with precise detail).
This route is planned for no other reason than the Pilot Chart for that area for that time of year says it is a favourable weather route and we can find no evidence to contradict this assumption. No reason to assume that we won't deviate from the chosen route if weather dictates it. But it is a distance of some 4400 miles and if the % savings are significant, perhaps we should replan.
The way you have explained is that this would not be a GCD. What sort of variation distance-wise would it be from a GCD? Would it be significantly longer? Should I concern myself with the difference?
Thanks to all respondents but as you can see I remain a dummy in this regard.
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alant
Active member
Great Circle Distance as follows:
(1) using calculators : cos great circle distance= sin Lat1.sin Lat2 + cos Lat1.cos Lat2.cos diff Long
(2) Using PZX triangle tables - In this method, ZX (normally zenith distance will become Great Circle Distance) :
Diff in Long = LHA
Lat of Start (A) = latitude for tables
Lat of destination (B) = declination
apply to sight reduction tables to obtain Hc, d and Z
Great Circle Distance = Zenith Distance = 90 - Hc (convert from angular distance (degrees & minutes) to Nm
Great Circle Initial Track = Zn = 360 - Z
If Lats (A) & (B) are the same name, use the same tables.
If Lats (A) & (B) are different names, use the contrary tables.
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(1) using calculators : cos great circle distance= sin Lat1.sin Lat2 + cos Lat1.cos Lat2.cos diff Long
(2) Using PZX triangle tables - In this method, ZX (normally zenith distance will become Great Circle Distance) :
Diff in Long = LHA
Lat of Start (A) = latitude for tables
Lat of destination (B) = declination
apply to sight reduction tables to obtain Hc, d and Z
Great Circle Distance = Zenith Distance = 90 - Hc (convert from angular distance (degrees & minutes) to Nm
Great Circle Initial Track = Zn = 360 - Z
If Lats (A) & (B) are the same name, use the same tables.
If Lats (A) & (B) are different names, use the contrary tables.
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G
Guest
Guest
What you have described is limiting latitude or extremis GC route. It is common for N.Atlantic croosings in winter etc. tolimit the northern latitude to avoid ice etc.
Yes this will increase the distance, but you will still retain an advantage over pure Rhumb Line distance.
<hr width=100% size=1>Nigel ...
So WHAT does the EU really stand for ????/forums/images/icons/cool.gif
Yes this will increase the distance, but you will still retain an advantage over pure Rhumb Line distance.
<hr width=100% size=1>Nigel ...
So WHAT does the EU really stand for ????/forums/images/icons/cool.gif
Budgie
New member
Great circle distance Durban - Freemantle is 4240 nm. On this track your maximum latitude would be 39.10S at 75.51E.
Following this track you would cut the 37S parallel at 53.30E and 98.11E. If you were to sail a rhumb line between these longitudes you would increase your track distance by a whopping 21 miles!
Calculations coutesy of http://williams.best.vwh.net/avform.htm
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Following this track you would cut the 37S parallel at 53.30E and 98.11E. If you were to sail a rhumb line between these longitudes you would increase your track distance by a whopping 21 miles!
Calculations coutesy of http://williams.best.vwh.net/avform.htm
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snowleopard
Active member
calculating a great circle on a mercator chart.... if you want to do it as a mathematical excercise, fine. for practical purposes however, go out and buy a gnomonic chart of the ocean in question or get a great circle sailing diagram (pub by admiralty).
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