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Old 02-05-2018, 14:30   #16
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Re: Longest Navigable Route with out hitting land

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Originally Posted by Kelkara View Post
Do you have to define "straight" as the shortest distance between two points?
You don't have to, but that is a generally (if not universally) accepted axiom for a straight line in any geometry.

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In Euclidean space it could equally well be defined as a line with constant bearing along its length ... which would be a rhumb-line on a spherical surface.
In "Euclidean space", your Rhumb line is not on a "constant bearing" It is only constant in one plane. In 3 dimensional space, the bearing on the other two planes is constantly changing.

When talking about a sea voyage on the surface of the earth, Euclidean geometry is inappropriate. It only works as an approximation over very small arcs.
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Old 02-05-2018, 14:39   #17
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Re: Longest Navigable Route with out hitting land

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Originally Posted by Cpt Pat View Post
The Earth is, technically, not a sphere. It's an ellipsoid, and a lumpy one at that. It's a little bigger around the equator than around at the poles.
That's why I referred to Reimannian frames of reference rather than the more restrictive spherical the last time this one came up.
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Old 02-05-2018, 15:01   #18
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Re: Longest Navigable Route with out hitting land

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Originally Posted by StuM View Post
But that's not a "straight line". And it's debatable whether it qualifies as a "route".
Sure it is straight. Follow any longitude or latitude and you are on a “straight” line (on a sphere).

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Originally Posted by StuM View Post
In "Euclidean space", your Rhumb line is not on a "constant bearing"
It is if you follow any longitude or latitude, in other words if you go straight east, west, north, or south.

Or correct me if I’m wrong.

Edit: Self correcting - I’m wrong, it’s only straight for longitudes, i.e. north-south.

Or correct me if I’m wrong again. ;-p
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Old 02-05-2018, 15:02   #19
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Re: Longest Navigable Route with out hitting land

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Originally Posted by JPA Cate View Post
We all remember being taught that "the shortest distance between two points is a straight line", Euclidian geometry, plane geometry.

Then, amazement at the simple fact that the shortest distance between two points is a great circle route!

Take that, Flat Earth Society!

Ann
Just so you know, the flat earth society has members around the globe. ;^)
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Old 02-05-2018, 15:21   #20
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Re: Longest Navigable Route with out hitting land

And that took a scientist to figure this out!
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Old 02-05-2018, 16:19   #21
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Re: Longest Navigable Route with out hitting land

Baja Ha Ha. ARC. Looks like a new cruiser's rally route to me.

Let's Go! (somebody start a new thread for sign ups! )
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Old 02-05-2018, 16:19   #22
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Re: Longest Navigable Route with out hitting land

About Jon Sanders' Triple Circumnavigation of the World


Sanders received many accolades following his amazing journey.
The Guinness Book of Records recognised him as the first person to single-handedly complete five circumnavigations, and as the first person to single-handedly complete three non-stop circumnavigations. The triple-circumnavigation was the longest distance sailed continuously by any vessel (131,535 km). 90


john sanders found a pretty good track 3 times around the world non stop
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Old 02-05-2018, 16:59   #23
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Re: Longest Navigable Route with out hitting land

The longest distance is between the first and last letters of the word "smiles".


However, to be really pernickety, considering that the planet is actually an oblate spheroid, then maybe not all great circles are equal. I understand that the "oblateness" is not even uniform.
But why on earth (?) would anyone want to do such a trip? The only rationale I can comprehend is that the wife told the captain to get lost for as long as possible. I have some experience here.
This fits nicely with the implication that such a route would be one where the winds are mainly useless.
Anyway, what do we make of all this when our political leaders open with the line "Getting straight to the point ......." and then show that they are hell bent on avoiding the point. What chance do mere sailors have? To a politician a "great circle" presumably means going around in, as large as possible, circles.
There. The issue is not resolved but I am not sure what the issue really was.


Please do not offer to put me on the right path.
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Old 03-05-2018, 00:10   #24
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Re: Longest Navigable Route with out hitting land

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Originally Posted by StuM View Post
Again, it depends on your frame of reference. When discussing two dimensional spherical geometry, a great circle is a straight line since it is the shortest distance between two points. IF you start at one of those locations facing in a certain direction and sail "straight ahead" or "follow your nose", you will end up at the other location.

Your stance is similar to saying that "line of sight" between the Sun and Alpha Centauri isn't the shortest distance between them because there is a shorter fourth dimensional wormhole between them

According to your definition, there is no such thing as a straight line route of any length, anywhere on the surface of the planet.
Spherical geometry is not two dimensional, so you can't claim it's a straight line. It has nothing to do with your frame of reference. A straight line by definition has no curvature.

This is nothing but a math problem as no one is going to actually run any of these routes, so if we are just doing a math problem, we should use correct terminology and it does not meet the definition of straight line.

When you describe the working methodology for traversing worm holes, we can look into 4th dimensional aspects. Until then the problem is base on Newtonian Physics and Euclidean Geometry.

I think a lot of people are confusing map projections with actual real physical geometry. It's like saying Greenland is nearly the size of South America because in certain map projections, it is drawn roughly the size of South America but by any logical method, no one will claim they are the same size.
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Old 03-05-2018, 00:13   #25
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Re: Longest Navigable Route with out hitting land

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Originally Posted by Cpt Pat View Post
Correct! But the Flat Earthers will certainly disagree.

The Earth is, technically, not a sphere. It's an ellipsoid, and a lumpy one at that. It's a little bigger around the equator than around at the poles.
Good point. I wonder if the original article accounted for this. It would make the math much more difficult.
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Old 03-05-2018, 00:21   #26
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Re: Longest Navigable Route with out hitting land

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Originally Posted by StuM View Post
You don't have to, but that is a generally (if not universally) accepted axiom for a straight line in any geometry.

In "Euclidean space", your Rhumb line is not on a "constant bearing" It is only constant in one plane. In 3 dimensional space, the bearing on the other two planes is constantly changing.

When talking about a sea voyage on the surface of the earth, Euclidean geometry is inappropriate. It only works as an approximation over very small arcs.
What people have been claiming is if you can show a map projection where the line "appears" to be straight, it is a straight line. Common map projections are available that show a lines of latitude as a straight line. Since you are arguing a curved line is actually straight, it is certainly valid to claim that lines of latitude are actually straight lines since they show up that way in certain map projections.

Thus there are an infinite number of infinitely long straight line routes(Every possible circle that forms around the north pole that doesn't hit land).

In fact if you do a projection where the pond in my brother-in-laws backyard is placed where the north pole would usually sit, you could do circles in his pond and it would qualify as an infinitely long straight line by your definition of "straight".
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Old 03-05-2018, 00:26   #27
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Re: Longest Navigable Route with out hitting land

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See also earlier discussion in http://www.cruisersforum.com/forums/...th-157265.html.

If you want a straight line, the winner could be a roughly 400 nm route for submarines in the Mariana Trench.
This is probably closest to a legitimate answer that doesn't require extra dimensions or a definition of a straight line as being curved.

If you drill thru the seafloor are you really at sea anymore?
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Old 03-05-2018, 04:28   #28
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Re: Longest Navigable Route with out hitting land

The shortest route between 2 points on the earth (which is an oblate spheroid) is the minor arc of the great circle on which they both lie.


A great circle route is not a course of constant bearing, it is convex to the nearer pole and the heading keeps changing, crossing each meridian at a different angle so in navigational practicalities it is broken into a series of Rhumb lines ( lines of constant bearing).

The origin and the destination are plotted on a Gnomic Chart , the co-ordinates for where the course crosses selected meridians noted and transferred to a mercator chart, and the course to be followed broken down to a series of Rhumb lines - well that's the theory, but somewhat impractical on a yacht.

Great circle navigation is only used over long passages, such as Sydney to Panama, to reduce the distance steamed, and save on fuel burned, and then it is probably marginal.
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Old 03-05-2018, 05:19   #29
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Re: Longest Navigable Route with out hitting land

Realistic rhumb line: Reykjavik to Antarctica
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Old 03-05-2018, 07:06   #30
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Re: Longest Navigable Route with out hitting land

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Originally Posted by Divevac View Post
Realistic rhumb line: Reykjavik to Antarctica
Maybe also: Japan to Cape Horn.
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