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As a theoretical physicist, there is a question that I have been asking myself for a while: I would like to know how bearing and distance are precisely calculated by the GPS.

As a practical one I suggest you chuck that old Garmin over the side. Buy a new one. That one is ancient.

In the set-up menu it has an option to use Great Circle or direct routes.

If more than 100nms you will be using the Great circle Route otherwise your trip from the USA to UK will take you through the centre of the earth, or at least, a long way in the wrong direction.

Mark
 

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Ive flown transport category aircraft for decades using both INS and GPS nav systems. I feel like I should know the answer to the OPs question. Im sure Ive glanced over it in reading the minutia of a particular nav system. Im fairly certain (most?) GPS uses the WGS84 model and will always plot great circle routes for course and heading.
That is also my experience: Great Circle Routes. Every GPS I've seen allows you to select a geodetic model other than WGS84. DON'T! There are still a few areas where the charts aren't based on WGS84, but unless you know what you're doing, never deselect WGS84. Whenever crew have unsupervised access to my GPS, I always check to make sure they didn't change the geodetic system. Bad things can happen if you don't notice that change (the young people these days seem to like to twiddle every setting on everything when they're bored on deck watch.)

If we want to argue minutia, the earth is a "geoid." That's the cartographers way of saying it's a lumpy, irregular, slightly distorted sphere with variable gravity that bulges just a bit around the equator. That's a long description, so they just say "geoid."

Nature seems to hate perfection as much as she hates a vacuum.

(Please don't tell the Flat Earth Society about this thread or we'll be inundated with comical descriptions of how we are all deluded by our conspiratorially-derived beliefs.)
 

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Discussion Starter #24
Think we need someone who knows more about the engineering of gps use to answer this question. It remains a good question. How does the software work? Understand how you get a position from it but don’t understand how the software uses that.
I agree, one should really see how the software works and talk to someone who knows about the GPS engineering. CrispyCringle's answer is along these lines, I like it.
 

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Discussion Starter #25
Ive flown transport category aircraft for decades using both INS and GPS nav systems. I feel like I should know the answer to the OPs question. Im sure Ive glanced over it in reading the minutia of a particular nav system. Im fairly certain (most?) GPS uses the WGS84 model and will always plot great circle routes for course and heading.
Cool answer, thank you.
 

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I see more value in understanding how the math/navigation works. Understand the trigonometry and the software is just a fancy calculator with the hardware providing a visually appealing, easy to understand display.

With higher end chart plotters, you select which read out you want, rhumb line or great circle and the chartplotter performs the calculation for you.

Most people find great circles difficult to steer so the default is generally rhumb line. If you are going longer distance, you switch to great circle and find a way to steer the great circle, traditionally it was done by squaring off the curve, but I am guessing newer autopilts can do it on their own.

The software/hardware will constantly change, but the fundamental math and navigation principles don't.
 

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Most people find great circles difficult to steer so the default is generally rhumb line. If you are going longer distance, you switch to great circle and find a way to steer the great circle, traditionally it was done by squaring off the curve, but I am guessing newer autopilts can do it on their own.
This confuses me...

In the real world... say I am sailing from Montauk to English Harbor.
I determine a waypoint for Antigua enter it into the plotter as I am clearing Montauk. The GPS plotter software tell me what the bearing/heading to that waypoint is. It will report in integer degrees I believe. I can't hand steer to an integer. But I can set that value into the AP and as I make way... assuming I can sail that course.... my GPS will tell me the course I am making (as well as the ship's heading)... course takes leeway etc into account. I choose to then correct the heading so the course is actually the heading I wanted to steer.

I WILL have to alter the AP as conditions changed... and I likely can keep that original heading despite the changing leeway etc. These are not usually momentary changes. I monitor the TRACK like to see that it appears smooth and close to the original heading line.

For sure I can't carry a course without leaving a narrow "cross track road"... a bit. But over the two thousand miles... what is the implication of this? How many extra miles would I likely sail?

And lets not forget that having favorable wind direction for 2000 miles is likely not going to happen.
 

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You don't sound confused to me. That's what I meant by squaring off the curve. You steer a series of straight courses to acheive what is ultimately a curving course on a mercator projection chart, but due to other naturally occuring circumstances and practical considerations, it doesn't matter that much. On a ship or a power boat it can be more noticeable. Unless you are steering the rhumb line on a long offshore passage, in which case, you could potentially be adding hundreds of miles onto a long passage.
 

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Here is an article that explains it. It describes the squaring off I was describing. I was taught the same way the article describes. Change course once daily. So on a 30 day crossing you could make 30 course alterations, once per day. So during a given 24 hour period you are steering a straight line, but the resultant course on a mercator projection chart, is curved.

Some one specifically used the New York to London example because its a higher latitude, long distance run where the difference between the great circle and rhumb line is more pronounced.

https://astrolabesailing.com/2014/10/08/great-circle-sailing/
 

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Here is an article that explains it. It describes the squaring off I was describing. I was taught the same way the article describes. Change course once daily. So on a 30 day crossing you could make 30 course alterations, once per day. So during a given 24 hour period you are steering a straight line, but the resultant course on a mercator projection chart, is curved.

Some one specifically used the New York to London example because its a higher latitude, long distance run where the difference between the great circle and rhumb line is more pronounced.

https://astrolabesailing.com/2014/10/08/great-circle-sailing/
Perfect explanation and completely understand and agree!
 

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It's like masking off a paint line along a curve. The line curves, the masking tape is straight. So use small pieces of straight tape to approximate the curve.

Technically, it's called: a "piecewise smooth" curve.
 

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Why would anyone trying to get someplace sail a rhumb line? Makes no sense. Sure, a great circle will probably have a heading change. But its insignificant. Especially at sailboat speeds. Changing winds, currents, trim changes, will make you adjust the autopilot or helm way more than great circle heading change.

Flying from LA direct to NYC at over 450 kts ground speed may have 10-12 deg heading change on a great circle route. Just guessing from experience. Thats only 2-3 deg/hr (at 450 kts). It would be insignificant sailing a boat 100 NM/Day. Its just not a factor, as far as task load.

Unless you tweak your GPS, its always going to give great circle. There is no "short range" gps solutions and "long range" transitions. Also, GPS is not using a mercator projection. Its using the WGS084 model, which is WAY more accurate that mercator.
 

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Why would anyone trying to get someplace sail a rhumb line? Makes no sense. Sure, a great circle will probably have a heading change. But its insignificant. Especially at sailboat speeds. Changing winds, currents, trim changes, will make you adjust the autopilot or helm way more than great circle heading change.

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Unless you tweak your GPS, its always going to give great circle. There is no "short range" gps solutions and "long range" transitions. Also, GPS is not using a mercator projection. Its using the WGS084 model, which is WAY more accurate that mercator.
Why do people sail rhumb lines? Because they allow for constant compas headings over a distance and and most of us have traditionally used a compas course relative to north to get to where we are going, rhumb lines appear as straight lines on mercator projection charts, which is what a lot of us use a lot of the time. Its simple, its easy.

WGS 84 and mercator projections are not exclusive of one another. WGS 84 is a horizontal reference datum. Mercator is a chart projection. They aren't the same thing.
 

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Even under the windvane have the course plotted. Rarely, if ever, when coastal let the AP follow The quickie course the chart plotter automatically generates. Rather, when with the AP is on sail waypoint to waypoint. Pay attention to how far “off course” we are but also pay attention to point of sail, comfort and especially weather. Have had rare occasion of not touching the sails for days but that’s pretty unusual for me. Paying attention to vmg and dodging bad weather seems more important on a sailboat. Probably not as important in your thinking when on power vessels although even for them headseas aren’t as comfortable and increase fuel consumption.
Think the breadcrumbs are great circle. Still, wonder about what’s under the hood. The software and mechanics of it are of interest to some of us.
Before chart plotters did transfer the great circle to a series of dots on the plotting chart for North Atlantic. Got that concept. Computers can do an infinite number of dots so their curve can be smooth for all practical purposes . Like to hear a software engineers explain how the chart plotter or nav computor does it.
Btw handsteer way less than 5% of the time. So fairly interested in how this works.
 

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If autopilot is talking to a compas, whether magnetic, flux gate or a gyro, its following a rhumb line. If autopilot is programmed to follow a GPS it may be following a great circle.

Bread crumbs are neither great circle nor rhumb line. They are an indication of where you have been and include variables including lee way and manual course alterations for weather.

If you want know whether your gps is following a rhumb line or a great circle and its not described in the owners manual, just look at the course it plots over a long distance. You have recently sailed to the carribean? Was it a straight line on a mercator projection? Thats a rhumb line. Was it curvy? Thats a great circle.
 

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If autopilot is talking to a compas, whether magnetic, flux gate or a gyro, its following a rhumb line. If autopilot is programmed to follow a GPS it may be following a great circle.

Bread crumbs are neither great circle nor rhumb line. They are an indication of where you have been and include variables including lee way and manual course alterations for weather.

If you want know whether your gps is following a rhumb line or a great circle and its not described in the owners manual, just look at the course it plots over a long distance. You have recently sailed to the carribean? Was it a straight line on a mercator projection? Thats a rhumb line. Was it curvy? Thats a great circle.

On a mercator projection chart the great circle would have had you do more easting further north then curved to the south. Rhumb line would have been straight.
Don't APs need a compass? Mine does and does not accept GPS steering info.
 

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There are autopilots capable of following gps. But I agree, a lot of us use them with some kind of a compas.
 

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A shouldn’t have said bread crumbs as that implies what we left behind. Actually it’s a colored line of where we’d like to go. Guess you didn’t pick up on what I was saying. In all my trips back and forth never once did we have the joy of following either a rhumb line nor great circle. Rather you meander around your intended course wanting to keep the boat moving and avoid weather. Often weather router tells you “be at X lat Y lon by such and such a time”. Or “get past such and such a line before such and such a time”. Or you look at weather forecasts and make similar decisions. Deviations from either rhumb or great can be quite large. We use a different color/shape way points-to draw in front lines, lows and other weather details on the chart plotter. Another difference one for interim target waypoints we want to reach or lines we want to cross.
Before starting out you do put in the great circle but it’s theoretical in practice. Never held to it.
Still, want to know when I set a course between two points how does the gps do it?
 

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A shouldn’t have said bread crumbs as that implies what we left behind. Actually it’s a colored line of where we’d like to go. Guess you didn’t pick up on what I was saying.
How could I have? The term bread crumbs comes from Hansel and Gretel leaving a trail of bread crumbs to find their way back out of the forest. In chartplotter terms, that's your track, not your route.

Track is where you have been. Route is where you would like to go. Different things entirely. If one was in New England and dropped a waypoint in Antigua or where ever, a chart plotter, if one is being used, would display a route. Assuming mercator projection, the route would appear straight for a rhumb line or curvy for a great circle. If not using a chart plotter, which I think would be somewhat unusual in 2019, then one would plot it on a paper chart. Same thing. Curvy for great circle on a mercator chart, straight for a rhumb line.

Of course you alter course between new england and the carribean, but you are still plotting a route on some kind of a chart?
 
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