Great Circle Sailing v Rhumb Line

Not replying to anyone in particular, but you can in fact try this, if you have Google Earth.

Open up Google Earth and place yourself above London. Then tilt the screen so you can see the horizon in the middle of the screen, or a little above - sort of the view out of the cockpit of an airplane.

Then zoom out so you are maybe 100 to 200 miles above the surface. Rotate the screen so "head up" is about NNW. Then press the arrow that moves you forward.

As you move forward, look at the compass in the bottom left of the screen. As you move north, the compass swings, so you are no longer going NNW. Eventually it will show due West, and then show that you are moving South of West.

If you put your initial heading in correctly (it needs a little luck to get it exactly right) you will end up in Vancouver. If not, you will end up in Alaska, northern BC or perhaps California.

I don't know if this will help - but it is kind of fun!
 
"Dont be too sure that your GPS will give a Great Circle... I've just plotted a route from Manchester to Vancouver on SOB plotter software, and the course is 267T x 4533Nm... it's a straight line on a Mercator Chart."

Richard, up until then, with all the excellent explanations, I thought I'd got it cracked.

Now you bowl a googly, by saying that the shortest distance between 2 points, seems to be a straight line, not a Great Circle. Suggesting it has now become a rhumbline. Also that a GPS will give a continuous bearing all the way to destination!

Is it something to do with both latitudes being similar?

Is it a straight line if plotted on a Gnomic chart?

Its also a bit late & my brains gone numb.

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No, that GPS is not giving him the shortest distance, it is giving him a rhumb line course.

You don't seem to be getting this, so maybe I will try a different way. Assume for a moment that London and Vancouver are on the same latitude. Not quite true, but just assume it for a second.

A rhumb line course would pass along a single line of latitude. If you took a knife the the earth and sliced all the way through the earth along that course, you would cut off the top of the earth along that line of latitude. Note you would cut off the top of the earth - not cut through the center.

In order to find the great circle route, you would have to cut the earth perfectly in half, with both the origin and the destination on the "edge" of the cut. In this case you have to start cutting the earth well to the north of the two places, continue cutting through them, then continue straight on to the center of the earth and through.

Again, don't know if that helps, but it is another way of looking at it.

I'm off to bed.
 
Re: Gnomonic charts (long)

Surprisingly enough, I do know about the meanings of 'Azimuthal', 'Polar Stereographic', 'Orthomorphic', 'Conformal' and more. I got taught about them in the course of an honours maths degree, nearly 60 years ago. It's not only sailors that get taught such things. And I know that the sphere with the lamp inside isn't quite right, but it is sufficiently right to illustrate the essential differences between the two projections. Incidentally, I suspect that that was the way that Mercator thought about it, rather than the mathematical way, and he should know!

The problem about much of this stuff is that it requires a lot of background knowledge to understand it properly. When I'm teaching on a boat, one of the first questions I ask is what jobs people do in their lives ashore. If everyone has a technical background then teaching is going to be a lot easier. The crunch usually comes with vector triangles; if everyone understands them then we're OK, if not, then we've got a bit more teaching to do.

I have a book in front of me at the moment called "Charts: their use and meaning". It was written in 1931 for the Challenger Society 'for the promotion of the study of oceanography'. It uses exactly the same analogies of projections as I've suggested, except that being written before the invention of Perspex it uses glass. I notice that the acknowledgements include both the Superintendant of Charts and the Senior Chief Hydrographer "without whose constant help and searching criticism the book would not have been written". I suspect that had the analogies been as poor as you suggest, then those two gentlemen would have commented on it.
 
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Is it a straight line if plotted on a Gnomic chart

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I suspect you are a troll /forums/images/graemlins/cool.gif
 
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"Dont be too sure that your GPS will give a Great Circle... I've just plotted a route from Manchester to Vancouver on SOB plotter software, and the course is 267T x 4533Nm... it's a straight line on a Mercator Chart."

Richard, up until then, with all the excellent explanations, I thought I'd got it cracked.

Now you bowl a googly, by saying that the shortest distance between 2 points, seems to be a straight line, not a Great Circle. Suggesting it has now become a rhumbline. Also that a GPS will give a continuous bearing all the way to destination!

Is it something to do with both latitudes being similar?

Is it a straight line if plotted on a Gnomic chart?

Its also a bit late & my brains gone numb.

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I have an (elderly) version of Tsunamis 99. If I use it to plot a route, then I can choose either rhumb line or great circle.

If I choose rhumb line then it will give me a route which keeps the same heading at all points along its length. For a route from Lands End (or thereabouts) it quotes a course of 271 deg and gives me a distance of 4701 nm. Plotted on the Mercator chart used by the plotter it shows as a straight line, but if I were to plot it on a Gnomonic chart it would show as curved.

If I choose great circle, then it quotes a course of 325 deg and a distance of 4087 nm. The route looks curved on the Mercator chart (for interest, it crosses Greenland and Baffin Island), but if plotted on a Gnomonic chart it shows as a straight line. The course of 325 deg is only the initial course; as I move along the route the course needed to stay on the great circle will change. Slightly awkward, perhaps, but you'll notice that it's saved me more than 600 miles.
 
Haarumph!

At times like these, I reach for my copy of 'Bowditch' - and my aspirins.

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'Bowditch' or 'American Practical Navigator'.....

'This epitome of navigation has been maintained since its original publication in 1802..... a total of over 900,000 copies have been printed in about 85 editions during the more than two centuries since the book was first published.... It has lived because it has combined the best thoughts of each generation of navigators, who have looked to it as their final authority.'

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'Nuff said.

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Entered those Lat/Longs into my Garmin 12 via 'Distance/Sun'.

This gave a bearing of 326 & 3980 Nm, which presumably suggests that it is reading a Great Circle.

Quickly did the same on an Encarta Chart of the Globe & it seemed to be very slightly curved toward North (Gnomic Chart)- optical illusion?

Placing a potter on the screen, gave an approximate start bearing, leaving the UK, of 318 deg & arrival bearing of about 215 deg.

My Encarta, also suggested that the Lat/Long of N 53deg20min & W 02deg15min, was actually Alderley Edge (Isn't that where all the WAGS live?) /forums/images/graemlins/tongue.gif
 
I don't know which projection Encarta uses. At the moment I'm in our local library; I've been looking at the Reader's Digest world atlas. It uses neither Mercator nor Gnomonic projection, instead some peculiar equal-area projection with neither rhumb lines nor great circles showing as straight lines.

You can't trust no-one nowadays!
 
"It uses neither Mercator nor Gnomonic projection, instead some peculiar equal-area projection with neither rhumb lines nor great circles showing as straight lines."

I seem to remeber an episode of West Wing, in which the POTUS, was being solicited by an organisation who wanted all Maps to be changed to a projection which was more realistic than those in common usage.

Their argument, was that most maps, showed 2nd World Countries (Africa, etc) as much smaller than they really were. With 1st World Countries (all Europe, etc) as much larger than they were.

Their projection redressed this anomaly.
 
Please feel free to borrow my copy - http://www.irbs.com/bowditch/
Relevant para's are 2 and 24, though I think they might be even more confusing. Ever the pedant, I must point out your use of the term "composite sailing" is misleading. I understand your intention in describing the series of rhumb lines used to approximate a Great Circle, but a "composite" route is quite a different kettle of fish - landaftaft alluded to it, and it's explained in chap 24. No disrespect meant, as other than that, it was a first-rate dissertation.
 
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If I compare the Earth to an orange, is a Great Circle Route a line joining start & finish?

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Yes - a Great Circle makes a ring, but so do Small Circles. If you accept that the equator is a great circle, then travelling E or W along it you will end where you start. If you travel E or W along any other parallel of latitude, you will also arrive at your starting point, but you will have travelled a small circle.
 
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If I compare the Earth to an orange, is a Great Circle Route a line joining start & finish?
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Yes - a Great Circle makes a ring, but so do Small Circles. If you accept that the equator is a great circle, then travelling E or W along it you will end where you start. If you travel E or W along any other parallel of latitude, you will also arrive at your starting point, but you will have travelled a small circle.
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So, from the above, can we assume that a Great Circle, is a line joining any 2 points on the Earth, OTHER than those of the same Latitude, except when at the Equator.

Effectively, the plane of any line which is N/S or S/N, MUST cut through the centre of the Earth, thus making it a Great Circle. Is this correct?

Also, getting back to my GPS, depending upon the Latitudes of the points involved, as above, could be giving me both small & great circles, while measuring the shortest route at all times.
 
Correct, a GC is any plane, N-S meridian, Equator, or oblique which passes through the centre of the Earth.
 
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use of the term "composite sailing" is misleading

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"First, define your terms."

Yes, well, I understand the potential for ambiguity, as do you. I reasoned that anyone who understood Composite Great Circle would also understand the semantic difficulty - as you did - and that's why I chose to use a 'small c' in my post.

The truly superb quality in 'Bowditch' is the clarity of language in explanation of complex and difficult topics, which was of course, Nathaniel Bowditchs' objective. A quality I can only aspire to, I'm afraid.

Nonetheless, after decades of being unable to afford/justify my own copy, I came across a dated one in Plymouth some years ago which graces my bookshelf - and am delighted that the web gives me access to ( one of ) the latest versions, as you indicated.

Perhaps when someone comes on the forum with a navigation query, we should just refer him to the relevant section of our Electronic Bowditch..... but that would only answer the question, and remove the potential for another 1000-plus thread!

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So, from the above, can we assume that a Great Circle, is a line joining any 2 points on the Earth, OTHER than those of the same Latitude, except when at the Equator.

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Yes and no. It is the shortest line joining any 2 points on Earth without drilling through the Earth. A rhumb line could also fit your description above.

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Effectively, the plane of any line which is N/S or S/N, MUST cut through the centre of the Earth, thus making it a Great Circle. Is this correct?

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Yes, and with deference to skysail, the plane of any Great Circle will bisect the Earth. Cut your orange in half, whether through the poles, the equator, or from one tropic to the other and you will have a Great Circle.

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Also, getting back to my GPS, depending upon the Latitudes of the points involved, as above, could be giving me both small & great circles, while measuring the shortest route at all times.

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A small circle is, in essence, a rhumb line. As said before, your particular unit is probably set-up to default to either RL or GC, and may or may not be reset. If your owner's manual doesn't tell you, perhaps you can query the company directly. Or you could plot waypoints on the same lat at ever increasing distances and see what course it suggests - obviously a 090/270 course would be a small circle rhumb, whereas a NE/NW course (in the N hemisphere; SE/SW in S hemisphere) would indicate the initial course of a Great Circle route. Contrary to the other answers you've received, I believe there could be a correlation between the selected datum and navigation defaults of your unit. For instance the 1936 GB Ordnance datum probably doesn't extend much beyond the British isles, so conceivably your unit would default to rhumb lines while set on that datum, whereas WGS84 being truly worldwide, might default to a Great Circle. Not saying this is the case, just raising the possibility. Most of the units I've worked with have the ability to toggle between RL and GC (as others have indicated) - this is usually done from the set-up page. btw - I think user-defined datums are only useful for cartographers. I would not underestimate the importance of using the correct datum; if the GPS set is using a local datum like Tokyo27 or GBOD36 halfway around the world from its centre, the positional information could be several miles off.
 
"Yes and no. It is the shortest line joining any 2 points on Earth without drilling through the Earth. A rhumb line could also fit your description above."

Doesn't
"OTHER than those of the same Latitude, except when at the Equator."
mean the same thing?

Isn't a rhumbline a line on a small circle, which can only be achieved by connecting points of the same Latidude (but with different Longitudes).
 
A rhumb line is any line that crosses the meridians of longitude at the same angle. Not all small circles will scribe rhumb lines, but parallels of latitude are. Sorry if this muddies matters.
 
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Isn't a rhumbline a line on a small circle, which can only be achieved by connecting points of the same Latidude (but with different Longitudes).

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A rhumb line IS an arc of a Small Circle i.e. a circle on the surface of the spheroid, the plane of which does NOT intersect with the centre of the spheroid.

Examples are: arcs of all the parallels of latitude EXCEPT the Equator, 'cos in that special case, the plane also passes through the centre.

However, Small Circles are not confined to parallels of latitude. They can be oriented at any angle to the Equator, except in the 180º/360º orientation, because that plane also passes through the centre.

But what do I know.....
 
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