Path used to compute bearing and distance by GPS? - SailNet Community
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post #1 of 49 Old 4 Weeks Ago Thread Starter
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Cool Path used to compute bearing and distance by GPS?

Dear all,
I have been sailing on a cruiser which has a basic GPS: one can enter the WGS 84 coordinates of a waypoint, and the GPS displays in real time the distance and bearing of the waypoint, something like the one in the image attached.

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. In particular, given a curve on the WGS84 ellipsoid that joins the current location of the boat (A) to the waypoint (B), one may choose this curve in different ways. For instance, a loxodrome (i) or a geodesic curve on the ellipsoid (ii), i.e., the shortest path between A and B, which would coincide with a great circle in the case where the ellipsoid reduces to a sphere.

In either case, the angle between the curve and the local meridian at A yields a bearing, and the length of the curve a distance. Does the bearing displayed on the GPS screen correspond to choice (i) or (ii), or something else? Or does it depend on the GPS settings, or on the GPS model?

Thank you very much for your help!


PS I am aware that there is little discrepancy between the twos if the distance between the two points is small. Also, I found a related question on a forum years ago, but there seems to be no definite answer there...
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post #2 of 49 Old 4 Weeks Ago
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Re: Path used to compute bearing and distance by GPS?

For practical purposes I believe GPS plotters assumes that the earth is flat. I believe when distance exceed some threshold the computations are great circle... and so the heading will change as you proceed on the path to the destination.

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Re: Path used to compute bearing and distance by GPS?

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.
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post #4 of 49 Old 4 Weeks Ago
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Re: Path used to compute bearing and distance by GPS?

Excellent question. I thought gps determines your position by simple triangulation. More satellites above the horizon more opportunities for triangulation so position circle of uncertainty improves. That circle is really a sphere.
I thought the base map was projected as 2 dimensional but includes elevations. Therefore it’s really 3 dimensional. So each pixel has 3 variables. For navigational use on water (boat) additional variables such as depth, POIs etc. are added and on land (car) other variables are added. Using old school terms all courses on a boat, even short one, are great circle. However, this isn’t calculated as a great circle but rather as the shortest distance on a surface of varying height. Base map determines what’s permissible. Roads on land, water surface for us. Gps doesn’t care if you’re on water, land or flying.

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Re: Path used to compute bearing and distance by GPS?

It's simply voodoo magic. Sorta like the multiverse.
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Re: Path used to compute bearing and distance by GPS?

Until accurate clocks that would function at sea were invented folks sailed fixed latitudes. No need for changing course while following a fixed latitude. Given they were using magnetic compasses not a true shortest great circle but due to magnetic variation not a rhumb line great circle issue. Earth isn’t a perfect sphere mildly flattened not apple so you’re right rhumb and great circle will vary some depending upon what latitude. True even with a fluxgate compass. 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. Question remains how to get to the shortest great circle.

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Re: Path used to compute bearing and distance by GPS?

Earth isn’t a sphere
Definition of great circle
: a circle formed on the surface of a sphere by the intersection of a plane that passes through the center of the sphere
specifically : such a circle on the surface of the earth an arc of which connecting two terrestrial points constitutes the shortest distance on the earth's surface between them
Strange but True: Earth Is Not Round
Credit: Gary S. Chapman Getty Images
As countless photos from space can attest, Earth is round—the "Blue Marble," as astronauts have affectionately dubbed it. Appearances, however, can be deceiving. Planet Earth is not, in fact, perfectly round.
This is not to say Earth is flat. Well before Columbus sailed the ocean blue, Aristotle and other ancient Greek scholars proposed that Earth was round. This was based on a number of observations, such as the fact that departing ships not only appeared smaller as they sailed away but also seemed to sink into the horizon, as one might expect if sailing across a ball says geographer Bill Carstensen of Virginia Tech in Blacksburg.
Isaac Newton first proposed that Earth was not perfectly round. Instead, he suggested it was an oblate spheroid—a sphere that is squashed at its poles and swollen at the equator. He was correct and, because of this bulge, the distance from Earth's center to sea level is roughly 21 kilometers (13 miles) greater at the equator than at the poles.

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Re: Path used to compute bearing and distance by GPS?

Quote:
Originally Posted by outbound View Post
Until accurate clocks that would function at sea were invented folks sailed fixed latitudes. No need for changing course while following a fixed latitude. Given they were using magnetic compasses not a true shortest great circle but due to magnetic variation not a rhumb line great circle issue. Earth isn’t a perfect sphere mildly pear not apple so you’re right rhumb and great circle will vary some depending upon what latitude. True even with a fluxgate compass. 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. Question remains how to get to the shortest great circle.
I suspect that the computation considers the earth a sphere... and updates the computation based on current fix if the vessel is moving.

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Re: Path used to compute bearing and distance by GPS?

Misspoke above shouldn’t have said great circle in post #6. Rather just circle.

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Re: Path used to compute bearing and distance by GPS?

Think you’re correct but OPs original question remains. How?

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