Great Circle Sailing v Rhumb Line

A very helpful explanation from the ever-authoritative bilbobaggins makes me wonder why I weighed in with my ha'pennyworth. Probably because I swallowed ground bait left by James Jermain, and look forward to hearing more about the facility of displaying rhum line courses on GPS sets.

Mark
 
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Again, just to be pedantic, but mainly because I feel we are going around in circles & I'm still confused,
(1) What is the difference between WGS84 & 'Great Circle', when making an Atlantic crossing.
Is WGS84 waypoint sailing, the same as rhumbline?
(2) Do 'all' GPS sets have 'rhumbline' or 'Great Circle' facilities/datums?

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When you are making a chart you have to have some initial reference point from which to make the measurements. If a chart of the world were being made, the Equator and the Poles are obvious starting points, and by international agreement the Greenwich Meridian is another. If the world were a perfect sphere, and if one could make a continuous theodolite mapping round the world, then charting would be easy. Unfortunately, it's not so. The world has lots of bumps and hollows (not just hills and valleys, even water levels can be non-spherical because of gravitational anomalies). And theodolites can't be used across seas where the width is greater than the horizon distance. So each country used to set up its own reference points, which were then referred back to the basics (Equator and Greenwich) using astro-navigation. The datums you can find on your Garmin are these national ones.

For instance, the UK was surveyed by the Ordnance Survey using a datum called OSGB36. Much of Europe was mapped using European Datum 1950 (ED50). You'll find datums on your Garmin for many different countries. All these worked well while their use was restricted to the countries they were intended for, but were not so good when working between countries.

When satellite navigation (particularly GPS) came along, it gave the chance of unifying the world's various datum systems. It did this by setting up a mathematical representation of the Earth's sea level surface against which everywhere could be charted. This was the World Geodetic Survey 1984, abbreviated to WGS84. All the world's maritime charts are gradually being changed to this datum, but a complete changeover will take time. If you are using your GPS with a chart, then either you should set your GPS to use the same datum as the chart (which will be marked on the chart usually just under the title) or you should set your GPS to WGS84 and apply a correction.

The difference between Great Circle and Rhumb line is quite independent of the datum. If you look at a map of the world you will see that the UK and Vancouver are roughly on the same latitude. If you set out from the UK and flew due west you would arrive somewhere near Vancouver. That would be flying along a rhumb line, a line of constant bearing. But if you took a globe and joined the UK to Vancouver by a tight piece of string, the string would go way up into the Arctic and then down again. The string would be a great circle path, which in general is always shorter than the rhumb line (unless the rhumb line follows either the equator or a meridian of longitude). But the difference in distance is usually negligible unless you are sailing for several hundred miles or more, so usually it won't matter whether your GPS is set to give you rhumb line or great circle distances. Nothing to do with WGS84 or any other datum; just that the shortest distance between any two points on the surface of a sphere lies on the plane joining those points and the center of the sphere, which is the definition of a great circle.

Is waypoint sailing the same as rhumb line? It depends on your GPS set. Some give rhumb line bearings, some give great circle bearings, some can be switched between the two. The manual should tell you which; if not, ask the manufacturer. And no, not all GPSs are the same.

(You see, that's the trouble with being a slow, two-fingered typist (one for the shift key). People like Bilbo can beat me every time. But I have used a GPS which gave either rhumb line or great circle bearings and distances, depending on setting.)

Oh, for any pedants around, I know that the plural of datum is data. It's just that the usage of those two words is forcing them to have different meanings, so that I try to use the one that is easiest to understand.
 
I feel I'm in the middle of a Ph D debate now & still a dimwit.

"If one simply steers only the Initial Course given by the GPS device, then one is quite unlikely to arrive at the destination."

So, a GPS bearing & distance between 2 points, from say Bermuda to Azores, doesn't follow the same line as a 'piece of string' stretched between those two coordinates on a spheroid/globe.

"If one does as has always been 'the ordinary practice of seamen', (and airmen in the Golden Age of Air navigation - i.e. by astro ) and re-calculate the DTG and new Initial Course from a series of fixes at daily - or hourly ( air ) - intervals, then one follows a composite path which approximates to a true Great Circle."

But, this was pre-GPS, so is it still done? Or, does one just keep following the (apparently changing) bearing to the original destination waypoint.

" Then, using your GPS, calculate and plot for each of those ~200-mile legs a series of 4-hour leg-segments ( a composite Great Circle path ) - using DR SOG of, say, 6kts - and Initial Courses re-calculated from each new progressive DR position along the relevant leg."

Bilbo, for those mortals amongst us, could you speak very slowly & explain this bit again please. Would like to try this.
 
Most gps systems will give you the choice. Unless you are doing blue water sailing, it's not really a problem to worry about, other than an interesting intellectual exercise.
 
"But if you took a globe and joined the UK to Vancouver by a tight piece of string, the string would go way up into the Arctic and then down again. The string would be a great circle path,"

Just to repeat a question asked of Bilbo, following his also incredibly knowledgeable thesis (I feel I'm in the presence of God's), would this tight piece of string be the same as my GPS reading (whichever datum, but usually WGS84), or does my GPS give simply an initial bearing, which changes as I move along that string towards my destination?
 
"it's not really a problem to worry about, other than an interesting intellectual exercise."

I'm beginning to wonder if I now have any 'intellect' to exercise.
However, Blue water apart, Bilbo has given evidence that there are benefits even in 'coastal' hops in shortening the distance sailed.

I await more eagerly.
 
a great circle on short coastal hops will have no advantage whatsoever , tides will dominate your route

same as a g.c. crossing oceans, not tides this time but weather /forums/images/graemlins/cool.gif
 
FWIW - I was taught the following 'rule of thumb'

On an E - W (ish) course it is not worth calculating Gt Circle routes for passages less than 300 m.

On a NW (ish) course then 600m and pro rata in between.

I have an ancient Garmin 12 ( the Morris 1000 of the GPS world ?) which does not appear to give any option for Rhumb / Great Circle.

Garmin say that Gt Circle is their default where there is an option and the only one on the 12.

Landaftaf's point about tides should be heeded and I would stir the pot a bit by saying that this concept also applies to the Fastnet route.
 
"I have an ancient Garmin 12 ( the Morris 1000 of the GPS world ?) which does not appear to give any option for Rhumb / Great Circle."

I have inherited one of those.
& was puzzled I couldn't find any option for Great Circle or Rhumb line.

Masses of other datums I'd never heard of.
These presumably only work in conjunction with a chart of the same datum.

Looked at the list, no 'default' found, so how do you reach that option?

Has a 'User' option, but don't understand what DX,DY,DZ,DA & DF mean.
 
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Just to repeat a question asked of Bilbo, following his also incredibly knowledgeable thesis (I feel I'm in the presence of God's), would this tight piece of string be the same as my GPS reading (whichever datum, but usually WGS84), or does my GPS give simply an initial bearing, which changes as I move along that string towards my destination?


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I also use a Garmin 12. The bearing it shows is the great circle route. The tight piece of string points on that bearing only at the start end. (See how it crosses each line of longitude at a different angle.)

To add to the earlier example of Vancouver, the initial bearing from the UK would read just west of north. As you travel along that bearing, the bearing to destination shown on your GPS would change constantly, and and if you kept changing bearing in line with the GPS, as you got nearer Vancouver you would find yourself going just west of south.

You appear to have been puzzled by the statement that following the initial GPS bearing wouldn't get you to your destination. It wouldn't. Keep going just west of north and you'll eventually arrive at the magnetic north pole.

Mark
 
Down load the user manual from Garmins website if you haven't already done so.
And read it - several times, it is not the most coherent piece of writing.

Get it clear in your mind that WGS84 and Great Circle/Rhumb have absolutely nothing whatsoever to do with each other - see peteb above.

Perhaps I used the wrong word - Great Circle bearings on the Garmin 12 is the factory setting and there appears to be no other option. Not a default setting as I previously said.

Now, WGS84 is the default setting for Chart datums and, as you rightly say, the many other datums should only be used with charts with that same datum.
However, there are maps ( and possibly charts) that are not referenced to any datum and the 'User' option with DX, DY etc is for you to personally reference that particular item.
Personally I ignore that bit and all the other chart datums and only use the default WGS84 - very occasionally, these days, one comes across fairly old charts with e.g. WGS72 or whatever and these should be re-referenced.
I only bother to do this in fog, but then I'm rather old fashioned and don't rely on GPS 100%.
Hope this helps.
 
As others have said, the rhumb line / great circle option has nothing to do with chart datum. I think you could set the GPS datum to WGS84, and then choose either rhumb line or great circle for your route planning (or not, if there is no choice).

If you are looking for great circle / rhumb line in the datum part of the menu, you are probably looking in the wrong place.
 
"To add to the earlier example of Vancouver, the initial bearing from the UK would read just west of north. As you travel along that bearing, the bearing to destination shown on your GPS would change constantly, and and if you kept changing bearing in line with the GPS, as you got nearer Vancouver you would find yourself going just west of south."

OK, after this 'masterclass' (this is great stuff, thanks guys), I can accept that my GPS Start bearing (as measured from 000/360 deg going clockwise - as conventionally done) will be a great circle route & as I leave my start meridian & go west, at each subsequent meridian my GPS bearing (measured from 360) will keep changing. So, why if I follow the changing 'goto' bearing shown on my GPS will I not get to Vancouver, but end up "west of south"? Or, will I arrive in Vancouver & am mis-reading your statement.



"If you are looking for great circle / rhumb line in the datum part of the menu, you are probably looking in the wrong place."

I've been looking in 'Setup' then 'Navigation', this gets into datum. Where else do you suggest 'rhumb line/Great Circle could be found?
 
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could you speak very slowly & explain this bit again please. Would like to try this.

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Mucho sorree-o! This rather slow and frequently-outwitted, jaded old 19th Century Navigator falls back on the technical language he was taught at length ( and slowly ), to help explain stuff that is soundly based on a big heap of other slightly-technical stuff. Such as the distortions ( direction, distance, shape, area, etc ) that come with the use of e.g. a Mercator chart, how to deal with them .....and when to bother. It took me a long time to build that up, 'brick-by-brick', and I've met only a few that got it all, right first time. They tended to end up running outfits like Strike Command and Trimble.....

We're most of us agreed that the shortest distance between two points on the surface of the globe is an arc of a Great Circle. While it's often economic to want to steam or fly exactly along the shortest distance, frequently that's not appropriate, due to land or pack-ice getting in the way, or bad weather, or - in the case of the Velux 5 Oceans - the organisers saying 'you will not go further south than a series of Mandatory Waypoints here
'cos we don't want you hitting any icebergs.' So doing Great Circle Sailing into high latitudes often gets truncated, with the 'hi-lats' bit being missed out, and the boat/ship/aircraft just trundling E-W along the limiting parallel of latitude until it meets the true Great Circle path again.

Navigators would calculate, for each Great Circle segment they wanted to use, an Initial Course. They'd set off steering that but, if they continued to steer that day after day, by definition they'd be sailing along a Rhumb Line course ( a course which cuts all meridians at the same angle ). And they wouldn't get to where they wanted.

To steer a true Great Circle course requires steering a constantly-changing course and, while a small nav computer ( e.g. a GPS device ) can do this every second if needed and feed the output to an autopilot, before onboard electrickery the master or navigation officer would update things perhaps once a day on a ship, or once an hour on trans-oceanic aircraft, and make the requisite adjustment.

A number of points along the intended correct Great Circle track would be pre-plotted onto the chart to be used at sea/in the air, and for this, a Mear's Diagram chart ( a form of Gnomonic chart ) was used to determine the lat/longs of these points. Then, for each of these short route-segments, a Course and a Distance would be derived. Heading out across the Atlantic from the Bishop Rock towards Halifax, Nova Scotia - for example - the Initial Course steered would be something like 295º. A day later, it would change to something like 290º, then 285º, and so on until in mid-voyage it would be West. Then it would reduce sequentially down to, perhaps, 245º or less. It is obvious when one looks at the chart that, steering only 295º for days on end, one would eventually bump into Greenland. Not good for the career!

The guys who could reliably turn in a fast ( economic ) trip between ports/airports got the next job/next ship, and those who couldn't, didn't. Of course, there are many other considerations that feed into a pro decision about where to point - but 'the shortest distance' has always been one of them.

A good pro - and a very good amateur - nav would always be aware of the potential for relative gain or loss of distance, when the decision to go 'left or right of line' was being considered....even approaching the 'Varvasi' wreck!

So here's a ( pedantic ) live example.....

One of the Classes in the '03 Fastnet was won by a boat called 'Triohe'..... by 4m55s on corrected time. She consistently held just a little north of the straight line drawn on the Mercator chart, therefore closer to the true Great Circle/shortest distance. The No 2 boat in that Class consistently sailed to the other side of the line - not the shortest distance.

One could argue - and one or two did - that short-tacking errors, slips in reading the strength of a foul tide-stream and needing another board, even a minor calculation error in the Handicap ( although the Ratings Officer was aboard the No 2 boat with his laptop ) made all the difference. Who knows? But 'Triohe' sailed a shorter distance than the other boats......

'Triohe' also won the Class Series that year, with 3 Firsts and a Second, out of 4 Starts. Doing something right, and doing it consistently...... Was it Paul Elvstrom who famously said "The winner of any Race Series is usually s/he who consistently makes the fewest mistakes...."


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Gnomonic charts (long)

I have in front of me Chart 5095B. The last correction on it is dated 1955, so it's not exactly up-to-date, and I don't know whether there is a current version. It shows the route from the UK to the Mona Passage (the passage between Haiti and Puerto Rica.

The interesting thing about this chart is that it is drawn not on Mercator's Projection but on the Gnomonic Projection.

On the Mercator Projection lines of latitude and longitude are straight. Lines of longitude run up and down the chart parallel to each other. Lines of latitude run across the chart also parallel to each other and at right angles to lines of longitude. It's the chart we all know and love, and any straight line drawn on the chart will be a rhumb line, a line of constant bearing. It's called a projection because that's one way of visualising the method by which it changes the curved surface of the Earth into a flat sheet of paper.

Imagine the Earth as a Perspex sphere with a point source of light at its centre. Imagine the paper to be rolled into a cylinder wrapped round the sphere, touching it at the Equator. Any point on the sphere (except the poles) will now throw a shadow onto the paper. If you were to draw the outline of the UK onto the sphere, then a similar outline would be projected as a shadow onto the paper. Mark the projected outline onto the paper, unroll it, and you have a Mercator chart.

To make a chart on the Gnomonic projection, take the same Perspex sphere but, instead of wrapping the paper round the sphere, rest the paper flat (as a tangent plane) against a point on the sphere. Trace out the projected outline and you have a Gnomonic chart.

Now the point of making a Gnomonic chart is that this time rhumb lines are curved, but great circles are straight. Any straight line on a Gnomonic chart is a piece of a great circle.

Also marked on the chart are the lines of latitude and longitude. My chart is a "Polar Gnomonic" chart, i.e. the piece of paper was pressed against the north pole when the projection was made. (It could have been any other point on the sphere, but polar gnomonics have certain advantages) The lines of latitude are shown as circles round the north pole (or would be, if my chart went that far). The lines of longitude (which are great circles) are straight lines; but not parallel, they radiate out from the pole.

So the chart in front of me will show the great circle route from the UK to the Mona Passage as a straight line. As I travel along that line the angle of the line relative to the lines of longitude will change, i.e. my heading will change. This particular chart has an extra refinement; it has a set of curves showing for each point on the chart the course required to follow the great circle route from that point to the Mona Passage. If I lay off the straight line between Lands End and the Mona Passage I can read off immediately my initial course as 260degrees; by the time I've reached halfway I would be steering 242deg and I would finish steering about 215deg.

And this on a chart originally published in 1937, before even the idea of GPS or WGS84 had been dreamt of!

Sorry it's so long, but I hope it's helpful. If you can get hold of that chart (or another similar one) it's very enlightening.
 
Bilbo has done us proud again, but just to clear up this specific point:
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So, why if I follow the changing 'goto' bearing shown on my GPS will I not get to Vancouver, but end up "west of south"? Or, will I arrive in Vancouver & am mis-reading your statement.


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I meant that your heading, as you arrive in Vancouver (by land yacht, of course) would be a little west of south (i.e. somewhere between the bearings 185 and 225).

Mark
 
[quoteOK, after this 'masterclass' (this is great stuff, thanks guys), I can accept that my GPS Start bearing (as measured from 000/360 deg going clockwise - as conventionally done) will be a great circle route & as I leave my start meridian & go west, at each subsequent meridian my GPS bearing (measured from 360) will keep changing. So, why if I follow the changing 'goto' bearing shown on my GPS will I not get to Vancouver, but end up "west of south"? Or, will I arrive in Vancouver & am mis-reading your statement.

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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.

Try it on your GPS or Plotter next time you can, (I'm presuming you have a world map, or can just plug in the coordinates

Manchester 53.20'N 2.15'W

Vancouver 49.07'N 123.12'W

and see what it gives as the bearing, or Course to Steer

You will arrive in Vancouver on a heading west of south if you follow a Great Circle.
 
Re: Gnomonic charts (long)

Why is it that, suddenly, everyone and his uncle wants to go to Vancouver tonight?

My dear 'Concerned of Radlett, Herts'; if only it were that simple. But hang in there, you're nearly, almost, not far off, 'close enough for government work', right. But lay off the Perspex sphere with a lightbulb inside. That's for KeyStage 3 kids, and it's not quite right.

Tell you what, go off and explore the meanings of 'Azimuthal', 'Polar Stereographic', 'Orthomorphic' and 'Conformal'. Factor those into your helpful post about the Mona Passage, then come back with an ever-so-slightly revised perspective.....

This stuff is all contained - in exquisite detail - within the Professional Studies for Master Mariner, under 'The Sailings'. Much of it, indeed most of it, is of less than significance to anyone with a firm grip on the here and now, who is not a practicing hydrographer. Or not writing one of the three hundred and ten near-identical treatises on navigation/chart theory. We really don't need to know all this stuff, unless we're going for professional exams. Even then, it's tedious.

No, not quite true. It's interesting, when one considers it from the perspective of the ancient cartographers who were trying to give us something usable to overcome a problem. And if someone senses I'm a bit acerbic suddenly, please put it down to the dodgy pate and toast my lady gave me earlier in the evening....

Actually, I love poring over old charts when in the mood - especially large scale ones of places I haven't been, or not recently. I've a developed job-skill in visualising in 3D from a 2D chart, so I'm fairly good at peering at, say, Craighouse, Loch na Droma Bhuide, Ile Molene, Les Ecrehous ....and getting the picture about right from various angles, daylight and dark. And deciding I want to go in there, 'cos it looks interesting.

Only a fool like me would go looking for the Hell Rock......

Chart study is only one of the skills a pro navigator employs to keep the 'lower decks' in order. 'Druid seaweed' is helpful in weather forecastery, an ability to see what's actually on the horizon and coming this way is helpful in choosing when to put one's oilies on and call for a reef, and a sudden interest in the inside of the heads compartment is VIP when the harbourmaster's 'Summer Strine' calls for the mooring fees....

But do have a read at 'Ocean Passages For The World' - it brings alive some of the decisions of the RKJ's, the Goldings, the McArthurs, the Bullimores as they play their marketing tunes on our broadband connections. There are usually lots of elderly copies at the Beaulieu Boat Jumble.....


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