Which way do I go

[Jokodo]

And if we're going to nitpick, there's only one great circle path - the equator. The rest are great ellipses.

 

[Jokodo]

A map is a projection not reality. From the Mercator link. If you have a flat map 'projection' and are at point x and want to go to poiny y you lay your compass on the map, set the compass oriented properly to North and read the bearing in degrees to point y off the compass.

Walking and maintain the compass heading will get you where you want to go.

Eventually, yes. In 99.9% of cases, it won't be The optimal Route though.

 

[bilby]

It seems that it’s not a map one needs but a globe.

Let’s say I walked the 10 meters (marked as point A) and that’s where I find you. Your destination is 31.4/2 m east. I could show you on a globe which way to walk so you could walk straight there. I could point and say “go that way and don’t veer left or right.” The problem is that’s not a typical direction—more like a continuous set of changing directions.

It depends on the map. I lived in the Idaho panhandle in the 90s surrounded by federal and state forests. I bought uSGS topological sectional maps. They covered maybe a section 20x20 miles with altitude curves. The distance scale is linear. It is important to be able to see landmarks on the map in actual local relationships. The section is treated as a flat surface.

Whenever I went out in the back country by foot or jeep I carried a map and compass.

A USA map is a flat projection of a sphere. If you look at the distance scale at the bottom it is not linear, it varies. 12 inches is not 12 x 1 inch. on the map is not twice the distance of one inch on the map. It accounts for curvature of the surface.

To navigate between two points you only need a bearing relative to north to navigate. That is what a compass does. For long distance navigation a map projections allows you to derive a compass bearing to follow, a Great Circle path. It is not a line on a flat surface.

If you are flying from Europe to the USA there are multiple paths you can take.

Constant bearing is going to produce a suboptimal (longer) route in all but 2scenarios:

When you are travelling due North/South

When travelling due East/West at The equator.

A constant bearing is not a feature of great circle paths outside of thise edge cases, and of all the multiple routes between a point in the US and one in Europe, only one is the shortest.

And only very rarely is the shortest track the quickest.

The North Atlantic tracks for airliners are repositioned twice daily, to maximise tailwinds and minimise headwinds; And to account for the differing traffic volumes at different times of day, while maintaining sufficient tracks with adequate separation to ensure that there are no conflicts in the Atlantic gap, where Air Traffic Control radar coverage is lacking.

They are calculated based on Great Circle routes, but then adjusted to move eastbound traffic into the jetstream, and to move westbound traffic out of it, wherever possible. It saves a very large amount of time, aviation fuel, and money. Simply trying to fly a Great Circle route (with vertical separation between east- and west-bound traffic) would be far less efficient, despite the distances traveled being shorter.

Similar tracks, that vary daily or twice daily to account for variations in high altitude winds, are also used between Asia and the Australian east coast (another heavily trafficked set of routes that have little intermediate ATC coverage).

 

[Gun Nut]

A Great Circle is not a curved path.

Say that again. Slowly.

Any straight path that starts on the surface of a sphere leaves that surface (either it's a tangent that heads off into space, or a chord that tunnels into the ground).

All paths that are bound to the surface of a sphere are curved.

Besides that fact that I am a private pilot with an instrument rating, I also am a fan of cartography. I love maps. So I know a little more than a little about this.

AAAA GRRRRREAT CIRRRRRRRRRCLE. There nice and slow for you.
"circle is in the name"... great argument Airplanes fly great circle paths... so how can they ever deliver passengers to any destination??? If they fly a CIRCLE, then they always end up where they started!!!! Air travel is a lie!

Look at a globe. Then look at a map. Compare the size of Greenland between the two. I guess you would be completely shocked to discover that Greenland looks GIGANTIC on the map compared with the globe.... ever wonder why? It's because globes are spherical and maps are flat planes. Well how can you draw a map that can be folded up and put in your pocket or included in a book of flat pages? It's called making a projection... a way of making the "edges" of the map spread out relative to the middle of the map so the scale can be consistent across the entire map. This makes land masses appear larger at the edges than in the middle... that is just geometry.. projecting a curved surface onto a flat plane.
So, how can pilots navigate using flat maps? The solution is called flying a "great circle". It's just a name, they don't really fly in circles. They fly a straight line from point A to point B... when re-drawn on a globe would be a straight line.. but when drawn on a flat map it appears to be a curve (to the north, if located in the northern hemisphere).

That is what a great circle is... don;t let the label confuse you.

edited to add: aren't you a submariner? or am I thinking of another poster? dude, this is very basic Nautics (aero or otherwise). whether you are under, on, or over the water... basic navigational principles are all the same.

 

[Jokodo]

A Great Circle is not a curved path.

Say that again. Slowly.

Any straight path that starts on the surface of a sphere leaves that surface (either it's a tangent that heads off into space, or a chord that tunnels into the ground).

All paths that are bound to the surface of a sphere are curved.

Besides that fact that I am a private pilot with an instrument rating, I also am a fan of cartography. I love maps. So I know a little more than a little about this.

AAAA GRRRRREAT CIRRRRRRRRRCLE. There nice and slow for you.
"circle is in the name"... great argument Airplanes fly great circle paths... so how can they ever deliver passengers to any destination??? If they fly a CIRCLE, then they always end up where they started!!!! Air travel is a lie!

Look at a globe. Then look at a map. Compare the size of Greenland between the two. I guess you would be completely shocked to discover that Greenland looks GIGANTIC on the map compared with the globe.... ever wonder why? It's because globes are spherical and maps are flat planes. Well how can you draw a map that can be folded up and put in your pocket or included in a book of flat pages? It's called making a projection... a way of making the "edges" of the map spread out relative to the middle of the map so the scale can be consistent across the entire map. This makes land masses appear larger at the edges than in the middle... that is just geometry.. projecting a curved surface onto a flat plane.
So, how can pilots navigate using flat maps? The solution is called flying a "great circle". It's just a name, they don't really fly in circles. They fly a straight line from point A to point B... when re-drawn on a globe would be a straight line.. but when drawn on a flat map it appears to be a curve (to the north, if located in the northern hemisphere).

That is what a great circle is... don;t let the label confuse you.

edited to add: aren't you a submariner? or am I thinking of another poster? dude, this is very basic Nautics (aero or otherwise). whether you are under, on, or over the water... basic navigational principles are all the same.

Sorry to blunt, but you are making it Sound as though you haven't fully understood the globe thing. A great circle is called a circle because it is in fact a circle centered at the earth's centre - or more accurately an ellipsis. It is called great because any larger circle/ellipsis larger than it will take you off planet - as will a straight line.

 

[skepticalbip]

Sorry to blunt, but you are making it Sound as though you haven't fully understood the globe thing. A great circle is called a circle because it is in fact a circle centered at the earth's centre - or more accurately an ellipsis. It is called great because any larger circle/ellipsis larger than it will take you off planet - as will a straight line.

I generally describe a great circle a bit differently. Any two points on a sphere (usually one point being where someone is, the other where they want to be) and the center of the Earth define a plane. Where that plane intersects the surface of the sphere is the shortest distance between those two points along the surface of the sphere and is an arc of the great circle. The full great circle will bisect the Earth and is the largest diameter circle (great circle) around the Earth that will pass through those two points - e.g. if the two points are at the same latitude then the latitude line will describe a smaller circle around the Earth but a longer arc between those two points.

 

[Gun Nut]

Besides that fact that I am a private pilot with an instrument rating, I also am a fan of cartography. I love maps. So I know a little more than a little about this.

AAAA GRRRRREAT CIRRRRRRRRRCLE. There nice and slow for you.
"circle is in the name"... great argument Airplanes fly great circle paths... so how can they ever deliver passengers to any destination??? If they fly a CIRCLE, then they always end up where they started!!!! Air travel is a lie!

Look at a globe. Then look at a map. Compare the size of Greenland between the two. I guess you would be completely shocked to discover that Greenland looks GIGANTIC on the map compared with the globe.... ever wonder why? It's because globes are spherical and maps are flat planes. Well how can you draw a map that can be folded up and put in your pocket or included in a book of flat pages? It's called making a projection... a way of making the "edges" of the map spread out relative to the middle of the map so the scale can be consistent across the entire map. This makes land masses appear larger at the edges than in the middle... that is just geometry.. projecting a curved surface onto a flat plane.
So, how can pilots navigate using flat maps? The solution is called flying a "great circle". It's just a name, they don't really fly in circles. They fly a straight line from point A to point B... when re-drawn on a globe would be a straight line.. but when drawn on a flat map it appears to be a curve (to the north, if located in the northern hemisphere).

That is what a great circle is... don;t let the label confuse you.

edited to add: aren't you a submariner? or am I thinking of another poster? dude, this is very basic Nautics (aero or otherwise). whether you are under, on, or over the water... basic navigational principles are all the same.

Sorry to blunt, but you are making it Sound as though you haven't fully understood the globe thing. A great circle is called a circle because it is in fact a circle centered at the earth's centre - or more accurately an ellipsis. It is called great because any larger circle/ellipsis larger than it will take you off planet - as will a straight line.

..on a globe. You don't need a great circle on a globe... every shortest path between two points on a globe is a great circle, by definition. no one talks about "great circles" on a globe... just like you don't talk about what great resolution the scenery is in when you are looking at it in real life (not an image on a screen). "resolution" refers to the level of detail of a projection of an image onto a flat screen. when you are not talking about viewing it on a screen, "resolution" is nonsense... just like great circles on a globe.... on a flat map a great circle is simply what the shortest path between two points looks like, and is curved because flat maps are deformed representations of the surface of the earth. that's it.. it's not so complicated.

 

[skepticalbip]

..on a globe. You don't need a great circle on a globe... every shortest path between two points on a globe is a great circle, by definition. no one talks about "great circles" on a globe... just like you don't talk about what great resolution the scenery is in when you are looking at it in real life (not an image on a screen). "resolution" refers to the level of detail of a projection of an image onto a flat screen. when you are not talking about viewing it on a screen, "resolution" is nonsense... just like great circles on a globe.... on a flat map a great circle is simply what the shortest path between two points looks like, and is curved because flat maps are deformed representations of the surface of the earth. that's it.. it's not so complicated.

I think you are taking the term 'great circle' a bit too literally. A great circle is just a mathematical technique used to determine what route is necessary to travel that shortest distance and that shortest route will not be by following a constant bearing. Not to say a constant bearing will not get you there, it will, but it will be a bit longer trip.

 

[Jokodo]

Besides that fact that I am a private pilot with an instrument rating, I also am a fan of cartography. I love maps. So I know a little more than a little about this.

AAAA GRRRRREAT CIRRRRRRRRRCLE. There nice and slow for you.
"circle is in the name"... great argument Airplanes fly great circle paths... so how can they ever deliver passengers to any destination??? If they fly a CIRCLE, then they always end up where they started!!!! Air travel is a lie!

Look at a globe. Then look at a map. Compare the size of Greenland between the two. I guess you would be completely shocked to discover that Greenland looks GIGANTIC on the map compared with the globe.... ever wonder why? It's because globes are spherical and maps are flat planes. Well how can you draw a map that can be folded up and put in your pocket or included in a book of flat pages? It's called making a projection... a way of making the "edges" of the map spread out relative to the middle of the map so the scale can be consistent across the entire map. This makes land masses appear larger at the edges than in the middle... that is just geometry.. projecting a curved surface onto a flat plane.
So, how can pilots navigate using flat maps? The solution is called flying a "great circle". It's just a name, they don't really fly in circles. They fly a straight line from point A to point B... when re-drawn on a globe would be a straight line.. but when drawn on a flat map it appears to be a curve (to the north, if located in the northern hemisphere).

That is what a great circle is... don;t let the label confuse you.

edited to add: aren't you a submariner? or am I thinking of another poster? dude, this is very basic Nautics (aero or otherwise). whether you are under, on, or over the water... basic navigational principles are all the same.

Sorry to blunt, but you are making it Sound as though you haven't fully understood the globe thing. A great circle is called a circle because it is in fact a circle centered at the earth's centre - or more accurately an ellipsis. It is called great because any larger circle/ellipsis larger than it will take you off planet - as will a straight line.

..on a globe. You don't need a great circle on a globe... every shortest path between two points on a globe is a great circle, by definition.

Not "by definition", but because it is a great circle.

no one talks about "great circles" on a globe... just like you don't talk about what great resolution the scenery is in when you are looking at it in real life (not an image on a screen). "resolution" refers to the level of detail of a projection of an image onto a flat screen. when you are not talking about viewing it on a screen, "resolution" is nonsense... just like great circles on a globe....

Literally the opposite is true. ONLY on a globe does talking of great circles make sense.

on a flat map a great circle is simply what the shortest path between two points looks like, and is curved because flat maps are deformed representations of the surface of the earth. that's it.. it's not so complicated.

It's actually much less complicated than you make it to be, but you still got it wrong. Whether a great circle path (or any other path, for that matter) between two points on a map looks straight or crooked depends on the projection and the points involved. Some great circle paths can turn out straight on some, many or most projections, given the right parameters, e. g. the equator is a great circle (strictly speaking the only one because the others are ellipses only conventially referred to as great circles).

In 3-dimensional reality however, all great circle paths are curved in bending around around the centre of the earth, though without veering left or right - the ones that appear curved for all the wrong reasons on your Mercator map, and the ones that appear straight for all the wrong reasons alike.

Also, not everyone even uses Mercator maps. You seem to be under the impression that it is the only map projection there is.

 

[steve_bank]

Mount Rainer can be seen far into a gnarly flat central Washington. If I start walking words Mt Rainer form 100s of miles away I maintain a constant bearing relative to magnetic north. To me as I walk it seems like I am walking in a starlight line but I am not. Relative to the center of the earth I am walking a circular arc.

If it is at night I look at a map and orient it to north. From a compass circle on the map I derive a bearuingnto the mountain ans start walking. No different than visual.

Bearing is relative to magnetic north.

I start 200 miles away at night and take a bearing based on map and compass. If I walked straight at 100 miles I get the same bearing from the map and compass. If I did not walk straight then I'd get another bearing and I would change course. That is navigation.

Fast's conundrum is not realizing a map of the USA is like cutting around the borders and flattening the USA. It is impossible to have a linear scale on the flat projection. Cities on the map are reference points from which to measure distance on the map. They do not represent physical locations. The scales at the bottom of a large map of the USA are not linear.

If 1 inch = 50 miles 2 inches

 

[bilby]

A Great Circle is not a curved path.

Say that again. Slowly.

Any straight path that starts on the surface of a sphere leaves that surface (either it's a tangent that heads off into space, or a chord that tunnels into the ground).

All paths that are bound to the surface of a sphere are curved.

Besides that fact that I am a private pilot with an instrument rating, I also am a fan of cartography. I love maps. So I know a little more than a little about this.

AAAA GRRRRREAT CIRRRRRRRRRCLE. There nice and slow for you.
"circle is in the name"... great argument Airplanes fly great circle paths... so how can they ever deliver passengers to any destination??? If they fly a CIRCLE, then they always end up where they started!!!! Air travel is a lie!

Look at a globe. Then look at a map. Compare the size of Greenland between the two. I guess you would be completely shocked to discover that Greenland looks GIGANTIC on the map compared with the globe.... ever wonder why? It's because globes are spherical and maps are flat planes. Well how can you draw a map that can be folded up and put in your pocket or included in a book of flat pages? It's called making a projection... a way of making the "edges" of the map spread out relative to the middle of the map so the scale can be consistent across the entire map. This makes land masses appear larger at the edges than in the middle... that is just geometry.. projecting a curved surface onto a flat plane.
So, how can pilots navigate using flat maps? The solution is called flying a "great circle". It's just a name, they don't really fly in circles. They fly a straight line from point A to point B... when re-drawn on a globe would be a straight line.. but when drawn on a flat map it appears to be a curve (to the north, if located in the northern hemisphere).

That is what a great circle is... don;t let the label confuse you.

edited to add: aren't you a submariner? or am I thinking of another poster? dude, this is very basic Nautics (aero or otherwise). whether you are under, on, or over the water... basic navigational principles are all the same.

Your condescension is unwarranted. A great circle is a circle centred on the centre of the Earth, and is very definitely a circle. A great circle route is the shorter of the two arcs of a great circle that passes through both origin and destination.

And a straight line route between two points on the surface of a sphere requires a tunnel. If you don't know what a straight line is, then you have no business discussing geometry.

And I have already, in this thread, explained both that fact, and in detail what Mercator's projection is, what it's good for, why it's shit for understanding anything else about geography (including but not limited to the relative areas of various land masses), and how it can be used for simplifying navigation but doesn't provide optimal shortest routes (instead giving constant bearing routes).

In summary, your post pointing out my errors is erroneous in every detail, and a simple reading of my other posts in this thread would have provided you with that information, and could have saved you from making a collosal tit of yourself.

You are also wrong about me being a submariner. But at least that error's correction would have required reading more than just my posts in this thread alone.

 

[bilby]

Besides that fact that I am a private pilot with an instrument rating, I also am a fan of cartography. I love maps. So I know a little more than a little about this.

AAAA GRRRRREAT CIRRRRRRRRRCLE. There nice and slow for you.
"circle is in the name"... great argument Airplanes fly great circle paths... so how can they ever deliver passengers to any destination??? If they fly a CIRCLE, then they always end up where they started!!!! Air travel is a lie!

Look at a globe. Then look at a map. Compare the size of Greenland between the two. I guess you would be completely shocked to discover that Greenland looks GIGANTIC on the map compared with the globe.... ever wonder why? It's because globes are spherical and maps are flat planes. Well how can you draw a map that can be folded up and put in your pocket or included in a book of flat pages? It's called making a projection... a way of making the "edges" of the map spread out relative to the middle of the map so the scale can be consistent across the entire map. This makes land masses appear larger at the edges than in the middle... that is just geometry.. projecting a curved surface onto a flat plane.
So, how can pilots navigate using flat maps? The solution is called flying a "great circle". It's just a name, they don't really fly in circles. They fly a straight line from point A to point B... when re-drawn on a globe would be a straight line.. but when drawn on a flat map it appears to be a curve (to the north, if located in the northern hemisphere).

That is what a great circle is... don;t let the label confuse you.

edited to add: aren't you a submariner? or am I thinking of another poster? dude, this is very basic Nautics (aero or otherwise). whether you are under, on, or over the water... basic navigational principles are all the same.

Sorry to blunt, but you are making it Sound as though you haven't fully understood the globe thing. A great circle is called a circle because it is in fact a circle centered at the earth's centre - or more accurately an ellipsis. It is called great because any larger circle/ellipsis larger than it will take you off planet - as will a straight line.

..on a globe. You don't need a great circle on a globe... every shortest path between two points on a globe is a great circle, by definition. no one talks about "great circles" on a globe... just like you don't talk about what great resolution the scenery is in when you are looking at it in real life (not an image on a screen). "resolution" refers to the level of detail of a projection of an image onto a flat screen. when you are not talking about viewing it on a screen, "resolution" is nonsense... just like great circles on a globe.... on a flat map a great circle is simply what the shortest path between two points looks like, and is curved because flat maps are deformed representations of the surface of the earth. that's it.. it's not so complicated.

When you are in a hole, stop digging.

 

[Elixir]

... every shortest path between two points on a globe is a great circle, by definition.

When you are in a hole, stop digging.

Heh, what an appropriate admonition, given that the shortest distance between any two points on the surface of a sphere is through the sphere itself. Yes, kids of America, the shortest route to China is to dig a hole. It's a little more difficult than transiting an arc on the surface of the almost-a-sphere of earth, but it's SHORTER!

ETA: Projections are interesting

 

[bilby]

... every shortest path between two points on a globe is a great circle, by definition.

When you are in a hole, stop digging.

Heh, what an appropriate admonition, given that the shortest distance between any two points on the surface of a sphere is through the sphere itself. Yes, kids of America, the shortest route to China is to dig a hole. It's a little more difficult than transiting an arc on the surface of the almost-a-sphere of earth, but it's SHORTER!

It's better than that; It's fast and (almost) free!

A straight line tunnel between any two points on the surface of the Earth, evacuated and made frictionless (maglev? superconductors?) can get you from one end to the other in about 90 minutes, purely on gravitational acceleration.

That's a pretty good journey time for most trips - cf. over 20 hours from Sydney to London by subsonic jet.

Of course, drilling and maintaining an airtight and evacuated tunnel in a completely straight line through the mantle (and for some trips, the core) of the Earth may prove to be a little tricky from an engineering perspective. Some kind of Unobtanium tunnel lining may be needed to keep the magma out. And unless you want 90 minute char-broiled passengers, some thermal insulation may also be in order.

 

[fast]

I do have a better appreciation for this than before.

For example, if I mark two points on a map (‘a’ and ‘b’ for a beginning point and ending point) and draw a straight line between the two, and then, mark the half way point as ‘c’, and then, do the same on a globe, then although points ‘a’ and ‘b’ will be the same for both the map and the globe, point ‘c’ (the half way point) will be different.

 

[steve_bank]

It is apparent from the discourse 'you can't get there from here'. As the saying goes.



GPS is a good thing for some people. For any ex boy Scouts, which side of a tree does moss grow on typically?

 

[bilby]

It is apparent from the discourse 'you can't get there from here'. As the saying goes.



GPS is a good thing for some people. For any ex boy Scouts, which side of a tree does moss grow on typically?

The south side - because that side never gets the full sun on it.

Of course, I was never a boy scout; And I live in the Southern Hemisphere - in the Northern Hemisphere the moss would predominantly grow on the north side of trees.

 

[skepticalbip]

Even though I have always heard all my life the "survival tip" of navigating by tree moss' preference for the north side of trees, I have found it useless in the area of the country I live in. The forests are dense so no side of trees get regular sunlight. Also humidity isn't that high so few trees have moss on the trunks and the ones that do have some sparse moss have it on all sides. A compus or even the sun's position would be more useful but only if the best direction to go to get out of the forest is first known.

 

[bilby]

Even though I have always heard all my life the "survival tip" of navigating by tree moss' preference for the north side of trees, I have found it useless in the area of the country I live in. The forests are dense so no side of trees get regular sunlight. Also humidity isn't that high so few trees have moss on the trunks and the ones that do have some sparse moss have it on all sides. A compus or even the sun's position would be more useful but only if the best direction to go to get out of the forest is first known.

Yeah, if you want to know which way is north, the position and length of shadows is likely your best indicator.

But frankly, if you are lost, there's more to be said for topology than orientation. Who cares whether you are facing north or south, if you don't know where anything else is in relation to your position?

If you're lost, you are best off making yourself visible to those who are not lost, rather than moving - any significant movement most likely gets you further from your last known position, and just increases the search radius for rescuers.

But the best strategy really does depend on your situation. If you are stranded in the outback, staying with your vehicle is almost always the best bet. It's a LONG way to the nearest tree, or water source, or anything else, in many places. And your car is much easier to locate from a rescue aircraft than your body is.

 

[Jokodo]

I do have a better appreciation for this than before.

For example, if I mark two points on a map (‘a’ and ‘b’ for a beginning point and ending point) and draw a straight line between the two, and then, mark the half way point as ‘c’, and then, do the same on a globe, then although points ‘a’ and ‘b’ will be the same for both the map and the globe, point ‘c’ (the half way point) will be different.

And in many cases, c will be different for two different maps