Great Circle Sailing v Rhumb Line

Sorry, should have used a smiley.

I think Kermudjon's point is that in the unlikely event that the boat is really a point then it will only sail in ever-decreasing circles without actually reaching the pole. I think.
 
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I've thought about this a bit,

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You may be right, but I was reliably informed by someone that you end up going in a neverending spiral. My brain is aching badly & it may be someone owes me a drink
 
The path described will certainly be a spiral, but it's one with a constant speed of advance northwards, so the time of arrival at the Pole can be readily calculated. What you do once you're there - stop, spin on the spot, or go somewhere else - is another issue!

I think the "infinity" confusion comes from incorrectly treating increasingly small increments. I have heard an early example of this sort of "paradox" quoted from ancient Greece. IIRC the argument goes as follows:

Heracles is set the task of racing against a tortoise and, to make the competition fairer, the tortoise is allowed to start a mile in front. The starting signal is given and they both set off. After a few minutes Heracles reaches the tortoise's starting point, but by now it is some yards ahead. In a few seconds more Heracles reaches that position, but by now the tortoise has moved a bit further ahead. Repeat ad nauseum. Conclusion: Heracles cannot overtake the tortoise.
 
From The Caribbean to UK, we used to alter course at noon everyday if we were following a great circle, (pre-GPS), i.e. a series of Rhumb lines."
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"Usual way of demonstrating this is to stretch a string between two points on ball. It will follow a curve."

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I think its getting clearer!

Apart from the dangers of dis-appearing up my own firmament if I sail at 45degrees, toward the North Pole, it seems to be simply a problem with 'flat' chart projections of a spherical body then?

What about -

"What does my GPS read?
Is a waypoint such as Azores, a Great Circle sailing from say Bermuda?

I have seen suggestions that a GPS datum can be changed from eg WGS 84 to 'Great Circle Sailing', but can't seem to find that on my Garmin handheld."
 
It's easier to understand if you think of looking vertically down at the pole where the Long. lines radiate out and the Lat. lines are circles. Keeping at 45 deg to the Lat. lines traces out a spiral that approaches the Pole reasonably quickly. I've just spent a few minutes sketching this out on an atlas and, starting at 70 degN I get to within a pencil thickness of the Pole after 1 revolution.

OK the last bit gets a bit more complicated, because it's a spiral that gets tighter and tighter but always with the same geometry - like a snail shell - and the more you zoomed in, the more turns you'd see. You could argue that since there is no limit to the level of convolution the path length must also be infinite, but that's fallacious. Since most of the complicated bit is actually quite small it would in practical terms be transitted quite quickly - leaving aside theoretical arguments about just how fast you would be rotating on your own axis at the instant of reaching the Pole - or indeed how many angels could dance there.
 
Friday

I've a problem with Friday, in that I've a conflicting social engagement. It's the mountaineering club dinner in Kirkcaldy that night, which herself and I are currently signed up for. So, unless there's a last minute hitch with that, I'm afraid I'll have to tender my apologies. Bit of a shame after making the practice session not to make the main event! (Somehow that last statement reminds me vaguely of an unsuitable joke I used to know...)
 
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"What does my GPS read?
Is a waypoint such as Azores, a Great Circle sailing from say Bermuda?

I have seen suggestions that a GPS datum can be changed from eg WGS 84 to 'Great Circle Sailing', but can't seem to find that on my Garmin handheld."

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If the GPS is set to Great Circle then the Course to Steer will be Great Circle, and will change form something like 045T setting off from Bermuda, and gradually change to something like 100T arriving at The Azores. (I havent calculated it, so the courses are guesses and could be wildly wrong).

If set to WGS84, the course will be 078T all the way.

This assumes that the plotter has a Great Circle facility... I cant find one on SOB>

Cheers

Richard
 
"Your question on GPS datum vs great circle sailing interested me - I have always believed that GPS gave the great circle course. I will now have to go and check... "
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Yes, me too, hence my question.
(how do you check?)

Certainly was unaware of a GPS Great Circle Datum, whatever that is.

Been looking at my handheld GPS & have pages of them from A-Z. Whats the difference?
 
How do you steer using your compass to an accuracy of one degree? Particularly since most compasses are only graduated in units of five deg? /forums/images/graemlins/confused.gif
 
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Yes, me too, hence my question.
(how do you check?)


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Easy. Enter a waypoint on the other side of the world at approx the same latitude (e.g. Ust-Kamchatsk 56 N 163 W), then press Go to <UST-K> or whatever. If it tells you to head off at 012 degrees or so it is giving you the Great Circle route. Is GPS capable of doing it any other way?

Mark
 
You won't be able to change from WGS84 to Great Circle (two different things altogether) but all GPS sets have the ability to navigate by rhumb line or great circle. It is quite an interesting exercise to put in a waypoint and then switch modes. Over short distances, as has been said, there is very little difference and rhumb lines, which have constant courses, are to be prefered. Over a long passage in high latitudes, the difference is significant but, as others have said, the weather and currents are often a bigger determinant than the difference between rhumb line and great circle courses.
 
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but all GPS sets have the ability to navigate by rhumb line or great circle. It is quite an interesting exercise to put in a waypoint and then switch modes.

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Are you saying there should be a setting (which I cannot find on my brand new Garmin 278C) for this? /forums/images/graemlins/confused.gif
 
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How do you steer using your compass to an accuracy of one degree? Particularly since most compasses are only graduated in units of five deg? /forums/images/graemlins/confused.gif

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I reached the dizzy heights of 3rd officer with Blue Star Ship Management, and sailed on larger ships where the compass was graduated in degrees.

having said that.... We can all, (most of us), set our autopilots to increment in degrees.

Hand steering with any kind of sea, I tend to keep within about 10 degrees either side of the course.
 
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Are you saying there should be a setting (which I cannot find on my brand new Garmin 278C) for this? /forums/images/graemlins/confused.gif

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I always thought that my old Garmin 45 had such a facility, but now I can't find it. But if you go to the Menu page, then Navigation Setup, then you may find a toggle between Great Circle and Rhumb Line. We've certainly got that on the fixed set on the boat. Maybe they reckon that people with just hand-held GPS sets are unlikely to be doing Great Circle sailing.
 
"Easy. Enter a waypoint on the other side of the world at approx the same latitude (e.g. Ust-Kamchatsk 56 N 163 W), then press Go to <UST-K> or whatever. If it tells you to head off at 012 degrees or so it is giving you the Great Circle route. Is GPS capable of doing it any other way?"
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Obviously from some of the answers, YES (see below).

"You won't be able to change from WGS84 to Great Circle (two different things altogether) but all GPS sets have the ability to navigate by rhumb line or great circle."

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?

What are the differences in all the datums I have discovered on my handheld GPS? /forums/images/graemlins/confused.gif
 
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Your question on GPS datum vs great circle sailing interested me - I have always believed that GPS gave the great circle course. I will now have to go and check...

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All the GPS devices I've seen ( and that's a few ) when required to calculate a Course between two waypoints, calculate the Distance and the Initial Course based on a Great Circle calculation/algorithm.

The model of the spheroid used - ED50, WGS84, whatever - refers to the mapping datum the machine uses, and will give small differences if one switches between them, which are insignificant for shipping ( large and small ) purposes, but quite significant in the terminal guidance of a US cruise missile - which is what the system was designed for.

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

The problems generated by the distortions of an Erect Mercator projection ( the type we commonly use ) are addressed in professional navigation training, such that one may select charts based on other projections with differing advantages and distortions, such as a Transverse Mercator, A Lamberts Comformal, an Azimuthal, and a Gnomonic..... A straight line drawn between two points on a Mercator chart does NOT represent a Great Circle. Nor does it accurately represent a Rhumb Line path - although it is often closer to that. One would certainly not use an Erect Mercator chart for trans-polar flight, for example, much above about 80º of latitude.

As for practical on-the-water yottie use, on could usefully re-visit 'Ocean Passages for the World' for guidance on how best to calculate what's needed.

There is a difference between a true Great Circle path ( the shortest distance ) and that described on a Hydrographic Office Mercator chart by a drawn straight line. Whether that is significant or not depends on what you're doing. So here's a tip for budding Fastnet Race '07 navigators....

Go to the trouble of marking in and measuring, on your passage planning Mercator chart, the straight-line distances between the Needles Bridge Buoy ( mark of the course ? ) and a chosen point off The Lizard; then the same between a chosen point south of the Pendeen Light and the Fastnet Rock; then the same between the Special Mark set SW of the Fastnet Rock and a chosen point off the Bishop Rock. Three longish legs......

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. Tedious, but when you compare, you will see there is a difference of several miles to be 'gained' by following the composite Great Circle path..... other tactical considerations permitting, of course.

So, you will find that the 'whitebait' will be trying to follow the straight line on the chart, while the better-informed will be sailing closer to the true Great Circle and saving several miles.

Is that not worth a beer next time you trip over me in the Royal Western? Maybe I'll see you there.....

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