GPS and polar navigation . . .

[Xyn_Air]

So, I decided to fly out over the north Atlantic for a bit just for the heck of it.  I took off from Norway (where half of my sweetie's ancestors hale from) and started going north-by-northwest.

Eventually I decided to head to Svalbard Airport, Longyear (ENSB).  As I write this, I am still in the air heading to that airport, or so I hope.  In any case, ENSB is rather far north, and I was wondering how this was affecting navigation.

When I fly manually, I thought about heading direct (roughly 330* magnetic, though I know magnetic compass bearing gets all wonky the further towards the poles you go).  But, as the hours passed, I have also used my GPS to control the autopilot (flying the Grumann flying boat, btw).  Now, the GPS is taking me in a decidely northeastern direction - which seems away from where I want to go.  This has led to two questions:

1) Because it relies on satellite data, is GPS navigation still accurate near or over the poles?

2) Because of the curvature of the Earth at the poles, how can you tell when circumnavigating gets you to your destination more quickly than flying direct?

Anyway, things get strange up here . . . but it is rather pretty out over the ocean.

Darrin

[Brett_Henderson]

I'll take a stab at this...

1) GPS doesn't care about the poles (in the way a compass does). GPS satellites are in multiple, orbits that aren't constant (like geostationary communication satellites). They just care about where you are, relative to them.

[Xyn_Air]

Just to update:

Well, it doesn't seem that the autopilot nav hold using GPS wants to take me to where I want to go.  While on nav hold, it appears as if the A/P would have taken me the long way around, at the very least, and quite possibly off in the wrong direction altogether (I tracked the flight for about an hour-and-a-half, and it was waaay off into nowhere).  I will have to do this flight again a couple of times, because there could be some non-flight issues (i.e. software or hardware issues) affecting this flight (ahem, some earlier multitasking seems to have mucked up a few things, for example, the ability to move through different views, so . . . ?).

I am going to go back to manual flight later when I have the chance to see if I can still make it to the airport . . . or land . . . or something.  Since I have to head off to work, I put the plane down in the middle of the ocean (it's the Grumann flying boat); I guess I am lucky FSX doesn't know how to simulate big ocean waves, chunks of floating ice, and so on (peaceful day on the north Atlantic in the middle of winter!?!?!).

Anyway, hopefully the plane will still be floating there when I get back this afternoon.



Lost way up yonder,
Darrin

[Splinter562]

Brett, you'd be correct. A GPS should give you the great circle route to your destination.

The difficult part when thinking about direct routes is making the jump from a 2D map, which you are used to looking at, to a 3D sphere, which you are actually flying over. As you probably well know, you cannot transfer the surface of a sphere onto a 2D surface without loosing something in the process. The 2D pictures which people are commonly used to looking at is called a Mercator Projection http://mathworld.wolfram.com/MercatorProjection.html. Near the equator it's ok, but as you mentioned before, the lines of longitude actually converge at the poles but in a Mercator they remain parallel. This leads to some pretty hefty distortion in the polar regions. If you were to draw a straight line on this chart, what you'd end up with is a Rhumb Line http://en.wikipedia.org/wiki/Loxodrome. If you were to actually draw this on a globe, you'd find out that the line is actually curved, not straight. An example of a rhumb line is a line of latitude. They cross each meridian at 90 degrees and appear straight on a Mercator projection, but plotted on a globe, they are actually curved lines.

Now, the shortest distance between any two places on the globe is actually the reverse of that. You want a straight line on the globe. This is, as mentioned before, the Great Circle Route http://en.wikipedia.org/wiki/Great_circle. The unfortunate part about a great circle route is that it is difficult to calculate from a chart, especially near the poles. A Lambert Conformal Projection http://mathworld.wolfram.com/LambertConformalConicProjection.html will get you close, but only over a small distance. Luckily, equations work out pretty nicely in math terms, and with GPS and computer technology, calculating great circle routes is a snap. Now, plotting a great circle route on a Mercator projection will look like a curved line (like the rhumb line looks curved on a globe) because it usually crosses each meridian at a different angle. As such, great arcs are not as easy to fly manually because you will be slowly, but constantly changing your  true (or magnetic) course. Again, with the advent of GPS technology and autopilots, this becomes less of an issue.

This little speech does come with a warning though. This is what real GPS units do, including the real Garmin units that are emulated in MSFS, however I've never bothered to check if MSFS's units emulate this behavior correctly, thought I can't imagine why they would not.

[Xyn_Air]

Brett, you'd be correct. A GPS should give you the great circle route to your destination.

The difficult part when thinking about direct routes is making the jump from a 2D map, which you are used to looking at, to a 3D sphere, which you are actually flying over. As you probably well know, you cannot transfer the surface of a sphere onto a 2D surface without loosing something in the process. The 2D pictures which people are commonly used to looking at is called a Mercator Projection http://mathworld.wolfram.com/MercatorProjection.html. Near the equator it's ok, but as you mentioned before, the lines of longitude actually converge at the poles but in a Mercator they remain parallel. This leads to some pretty hefty distortion in the polar regions. If you were to draw a straight line on this chart, what you'd end up with is a Rhumb Line http://en.wikipedia.org/wiki/Loxodrome. If you were to actually draw this on a globe, you'd find out that the line is actually curved, not straight. An example of a rhumb line is a line of latitude. They cross each meridian at 90 degrees and appear straight on a Mercator projection, but plotted on a globe, they are actually curved lines.

Now, the shortest distance between any two places on the globe is actually the reverse of that. You want a straight line on the globe. This is, as mentioned before, the Great Circle Route http://en.wikipedia.org/wiki/Great_circle. The unfortunate part about a great circle route is that it is difficult to calculate from a chart, especially near the poles. A Lambert Conformal Projection http://mathworld.wolfram.com/LambertConformalConicProjection.html will get you close, but only over a small distance. Luckily, equations work out pretty nicely in math terms, and with GPS and computer technology, calculating great circle routes is a snap. Now, plotting a great circle route on a Mercator projection will look like a curved line (like the rhumb line looks curved on a globe) because it usually crosses each meridian at a different angle. As such, great arcs are not as easy to fly manually because you will be slowly, but constantly changing your  true (or magnetic) course. Again, with the advent of GPS technology and autopilots, this becomes less of an issue.

This little speech does come with a warning though. This is what real GPS units do, including the real Garmin units that are emulated in MSFS, however I've never bothered to check if MSFS's units emulate this behavior correctly, thought I can't imagine why they would not.

Thanks for the wonderful post, Splinter.  It sure brought back a lot of memories from doing naval navigation!  OMG, was ever that a headache . . . yet, strangely fun, too!

As for the Garmin's, et al, in MSFS . . . well, I am still checking out how things work, but I am beginning to wonder if something may be a little wonky.

As for really real navigation, could you still use the radio beacons (such as are available in these remote areas)?

Lost but curious none-the-less,
Darrin

EDIT:
Fly far north in FSX and compare where your map thinks you are and where you are heading versus what your GPS says . . .



Anyone know if there is a difficulty in real life for a GPS to display your position near the poles?

[Splinter562]

I've never flown arctic before, but I don't see why you shouldn't be able to use a radio beacon. The catch is that when you're tracking a radio beacon, you're actually flying a Rhumb line because you are maintaining constant course. Though usually over the distances that you can receive the beacon from, the difference between the Rhumb line and the great arc isn't much. The difference will be greater as you get near the poles, but it will still get you to the station.

Now, VORs will fly you the great arc route even if they are sitting on top of a pole. This is because the radials radiate out in straight lines over the globe, which means they are great arcs. The receiver doesn't know anything about magnetic heading, it only know what radial it is on. Now, if you were to have a VOR right near a pole, you would have to continually change your magnetic heading to stay on a specific radial as you flew towards or away from the station.

[Splinter562]

Follow up to edit:

I can't speak for GPS, thought I can't imagine it would have trouble at the poles. As Brett said, you'd probably loose resolution on lat/lon coords, but the distance of a second of longitude near a pole is tiny compared to that at a mid-latitude. The problem would come with the mapping software. The standard Garmin projection seems to be Mercator, which will break down and even become unusable as you approach a pole. I don't know if they change projections if you go too far north, I haven't tried. In fact, I really don't know what any commercially available units do in that situation. Unfortunatly, the most common projections break down at the poles since very few people are interested in it. You could switch over to a polar projection, but that'd be a pretty big jump in the display. I personally have a trick up my sleeve that I use to do away with all my projection woes, including polar and international date line issues, but it's best I keep that to myself for now.  


Edit:

Just checked the Garmin 430 (non WAAS) desktop sim and it's not happy. At N82*, I'm getting a line of text that say "NO MAP". I'm getting some dashed grid lines. It will still draw a course line though, and it appears to still be in Mercator. So I'd imagine the moving map of the 430 isn't going to be a whole lot of help to you in polar regions. Thought you could still use it's functionality to fly great arc routes from point A to B, so long as they were in the database.

[Ivan]

Polar navigation is an odd subject...

Usually, the planes that go there have a special compass onboard, adn fly true headings instead of magnetic ones.

[Splinter562]

Polar navigation is an odd subject...

Agreed. If you wanted to do it without the help of GPS, INS, or NAV aids, the problem gets pretty tricky. In the old days they used to use something called grid navigation for polar flights. Which is a method of overlying a grid of fake parallels and meridians and setting your directional gyro to align with that grid rather than magnetic north.