Allan
Well-Known Member
If I put a waypoint into my GPS, 2000miles west of my present position then press GoTo it doesn't say head west, (270deg). How do I predict what bearings the GPS will tell us?
Allan
Allan
Great circle.
- Thread starter Allan
- Start date
sarabande
Well-Known Member
depends on your latitude, N or S of start point and ditto finish point.
Here's a javascipt calculator with start LatLong and finish LatLong, and a wee mappy thing from Mr Google.
http://www.gpsvisualizer.com/calculators
Here's a javascipt calculator with start LatLong and finish LatLong, and a wee mappy thing from Mr Google.
http://www.gpsvisualizer.com/calculators
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Doug_Stormforce
Well-Known Member
Hi Allan
The shortest distance between two points on the same latitude is not necassarily dead East or West, in the N Hemisphere there will be some Northerly component to the bearing (ie North of 270 if the destination is to the west) and in the SH the opposite applies. The further apart the 2 points the more so. the further from the equator the more so.
On many GPS sets you can select whether you want the GPS to compute the great circle route or not.
The shortest distance between two points on the same latitude is not necassarily dead East or West, in the N Hemisphere there will be some Northerly component to the bearing (ie North of 270 if the destination is to the west) and in the SH the opposite applies. The further apart the 2 points the more so. the further from the equator the more so.
On many GPS sets you can select whether you want the GPS to compute the great circle route or not.
Allan
Well-Known Member
Many thanks for that, I'll have a look. I discovered it when crossing the Atlantic, we were heading due west but the GPS said 296 deg.
Allan
Allan
Buck Turgidson
Well-Known Member
Were you heading due west or tracking due west?
Doug_Stormforce
Well-Known Member
You have probably already considered this but there are some quite big Westerley compass variations mid Atlantic, to the order of 20 degrees
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geem
Well-Known Member
When i sailed from Cape Verde to Barbados, about 2000 miles, i simply did a go to on my gps and sailed there on my electric autopilot (apart from a couple of minor variations when the wind didnt allow it for a few hours). We plotted our position every 12 hours and after 15 days we had a nice great circle route on our chart. It was a lovely curve to the north. Our friends who sailed over at the same time using a wind vane had a quite different route as they had simply been following the compass. Their route looked more like a straight line on the chart.
oldvarnish
Well-Known Member
I've got 2 GPSs I regularly look at. One is an A65 Raymarine plotter and the other a Furuno. Coming up the Atlantic recently (on roughly a NE course) I noticed a difference of almost 10 degrees between them when showing the course to the the waypoint (Azores). There was also a difference in distance of about 10 miles at a distance of 7/800 miles. Of course, as I progressed north eastwards the two came into line at about a hundred miles to go.
I assumed one was showing Great Circle and the other Rhumb Line. But nowhere in the menus, or even the manuals, was I able to select one or the other, or find out which I was being shown.
(Nothing like a long ocean passage for reading manuals cover to cover for the first time)
I assumed one was showing Great Circle and the other Rhumb Line. But nowhere in the menus, or even the manuals, was I able to select one or the other, or find out which I was being shown.
(Nothing like a long ocean passage for reading manuals cover to cover for the first time)
jdc
Well-Known Member
It's not too hard to do Gt Circle calcs and I'd always rely on my own rather than the GPS. This is especially because my Raymarine GPS can't cope with distances above ~400 miles! Blowing my own trumpet, but you can download this app to a phone, iPad or laptop - feedback welcome.
http://www.awelina.co.uk/sextant/GreatCircle_latest.html
Screenshot here:
http://www.awelina.co.uk/sextant/GreatCircle_latest.html
Screenshot here:
AntarcticPilot
Well-Known Member
As mentioned, Great Circle Calculations are fairly straightforward - the Cosine Rule of spherical trigonometry is a good starting point, allowing you to solve the entire spherical triangle. There are a few situations where you might have problems, but a yacht's navigator is not very likely to encounter them (they happen when the maths works out that you're taking the diference of two similar large numbers). Of course, the cosine rule assumes the earth is spherical (which it nearly is); for the highest accuracy you need to use an ellipsoidal version of the calculations.
This page http://trac.osgeo.org/proj/wiki/GeodesicCalculations gives a lot of useful information and links.
jrc1983
Well-Known Member
Unless it's all being calculated electronically I wouldn't go near Geodesic's as it's particularly long winded for little gain.
There's an article in every edition of Brown's Nautical Almanac where a Captain Doctor (yes, both!) Tijardovic makes a comparison between a Great Circle and Geodesic distance between 51-46N 055-22W and 55-32N 007-14W. Result are as follows:
Great Circle distance: 6162.377892 nautical miles
Geodesic Curve distance: 6162.377979 nautical miles
A difference in distance of 0.2 metres, but with a major difference in mathematical complexity.
AntarcticPilot
Well-Known Member
Well, a Great Circle is a geodesic - the special case of a geodesic on a sphere. I agree there isn't a lot of difference, though I think that the example quoted is one where the difference wouldn't be expected to be great. You get more difference for N-S tracks than for E-W tracks, as the radius of curvature varies less for a generally E-W geodesic than for a N-S one. But I agree - the difference is small, with a very large increase in complexity.
I just did a test calculation for the distance between 56N,0E to 56S, 15W, and was a bit surprised by the result.
The ellipsoidal computation (using http://geographiclib.sourceforge.net/cgi-bin/GeodSolve) comes out at 12491.002520 km (claimed accuracy to 1mm!); the spherical computation (using http://www.movable-type.co.uk/scripts/latlong.html) gives 12530 km - a much bigger difference than I expected. After all, 40km is several hours sailing! The ellispsoidal computation is from a source I know and trust; the spherical one looks OK, but of course may have bugs in it.
The page I referred to in my previous post suggests that spherical computations can be expected to have errors in the region of 0.5% - 1%. The error above is 0.33% (approximately), so I guess it's int he right ball-park.
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jrc1983
Well-Known Member
Granted N/S will see greater variance due to the oblate spheroid shape of the planet coming into play, but at the same time N/S great circle passages are quite rare (I've certainly never made one) as there's invariably lumps of the solid stuff to dodge in between.
One of the few passages I can think of where practical use may be more likely would be from West Africa to Southern South America, but in reality you'd never manage it anyway due to weather routing and avoiding/utilising ocean currents.
A regular voyage I undertake is Ascension Island-Falklands and whilst the passage plan is a straight line from Ascension to Cape Pembroke, and whilst a GC would shorten the distance by a few miles we never bother as any gain would likely be offset dodging low pressure systems as you get further South.
One of the few passages I can think of where practical use may be more likely would be from West Africa to Southern South America, but in reality you'd never manage it anyway due to weather routing and avoiding/utilising ocean currents.
A regular voyage I undertake is Ascension Island-Falklands and whilst the passage plan is a straight line from Ascension to Cape Pembroke, and whilst a GC would shorten the distance by a few miles we never bother as any gain would likely be offset dodging low pressure systems as you get further South.
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AntarcticPilot
Well-Known Member
Well, I've had to compute these distances from time to time - the Falklands being the "jumping off" point for transit to UK research stations in Antarctica, and having done a fair bit of work concerning South Georgia (I've never been there!)!
My point wasn't that you could save distance, but that the distance calculation using an ellipsodal formula gives a significantly different distance from the spherical one.
I just computed the Great Circle track from Plymouth to Stanley (Falkland Islands) and you can do the entire great circle route without crossing land. As you suggest, I doubt if the rhumb-line distance is much greater, but except for destinations in Antarctica, that must be one of the longest feasible great circle tracks.
Allan
Well-Known Member
Many thanks for all the replies. Can anyone give a simple explanation of why it is shorter to sail in a curve than a straight line? I assume it is due to the way a sphere is plotted on flat charts.
Allan
Allan
oldvarnish
Well-Known Member
Because your are sailing in a straight line and not a curve. Euclid will be along in a moment to explain.
oldbilbo
...
'Great Circle' routes on a globe, one of the oblate spheroids, a geoid - even a geodesic - are by definition the shortest surface distance between two surface points. One of the properties of a Mercator chart, as 'AntarcticPilot' will tell us, is that 'Great Circles are depicted as convex to the nearer pole', and such routes show on such charts as curves. They are 'straight line' on the earth's surface.
On the surface and, more importantly, in the air, following a Great Circle route can save distance/time/fuel. Have a peek at the chartlet in 'Ocean Passages For The World' depicting routes followed by steamships and compare that with the other chartlet showing the sailing ship routes. Consider that transatlantic flights originating at Heathrow/Gatwick, heading far west to e.g. Vancouver, San Francisco, Japan route up past Prestwick, the Faeroe Isles, by Iceland, and many route over Greenland to 'curve' back down to lower destination latitudes. Shortest distance - smallest fuel burn ( other things being equal ).
All charts introduce some distortions. The pro navigator selects those charts, with distortions, that best suit his purposes. So, Mercatorial Projection, Lamberts Conformal with Two Standard Parallels, Transverse Mercator, Polar Stereographic, Gnomonic..... Phew, once upon a time I had to know all this stuff, to avoid career-impacting landing on the wrong continent....
Sybarite
Well-Known Member
Einstein explained it in the General Theory of Relativity. Simples.
Pye_End
Well-Known Member
If you get a ball or a globe and put a piece of string between two points, you will wind that when you tighten it, the line it describes does not follow the easet/west line (unless on the equator), but a curve towards the nearest pole. That is the shortest line, and you can then visualise why you need a set of different compass headings to follow it.
AntarcticPilot
Well-Known Member
'Great Circle' routes on a globe, one of the oblate spheroids, a geoid - even a geodesic - are by definition the shortest surface distance between two surface points. One of the properties of a Mercator chart, as 'AntarcticPilot' will tell us, is that 'Great Circles are depicted as convex to the nearer pole', and such routes show on such charts as curves. They are 'straight line' on the earth's surface.
On the surface and, more importantly, in the air, following a Great Circle route can save distance/time/fuel. Have a peek at the chartlet in 'Ocean Passages For The World' depicting routes followed by steamships and compare that with the other chartlet showing the sailing ship routes. Consider that transatlantic flights originating at Heathrow/Gatwick, heading far west to e.g. Vancouver, San Francisco, Japan route up past Prestwick, the Faeroe Isles, by Iceland, and many route over Greenland to 'curve' back down to lower destination latitudes. Shortest distance - smallest fuel burn ( other things being equal ).
All charts introduce some distortions. The pro navigator selects those charts, with distortions, that best suit his purposes. So, Mercatorial Projection, Lamberts Conformal with Two Standard Parallels, Transverse Mercator, Polar Stereographic, Gnomonic..... Phew, once upon a time I ad to know all this stuff, to avoid career-impacting landing on the wrong continent....
Thanks for the accolade! The Gnomonic projection (which you note) has the useful property that Great Circles are straight lines; sadly it has other less useful properties - mainly that it can only depict one hemisphere on a single map, and that it introduces horrendous scale distortions (the equator is an infinite distance from the pole, in the polar aspect). Mind, Mercator's projection also introduces awful scale distortion and has the same property that the equator is an infinite distance from the pole, but straight rhumb-lines are also a useful property, and is unique to Mercator's projection. I always introduced Mercator projections with a warning triangle when I was teaching about them!
In fact, except for a few special cases (e.g. the plotting chart for Antarctica, which cannot be represented on Mercator projection), navigators are unlikely to find charts published on any projection other than a variant of Mercator's projection (normal aspect usually; occasionally transverse). While I routinely used Polar Stereographic and Lambert Conformal Conic, they are not convenient for plotting positions (longitudes are not parallel lines, nor are latitudes straight); they are well-behaved with regard to scale distortion and conformality, though.