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post #11 of 49 Old 11-11-2019
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Re: Path used to compute bearing and distance by GPS?

I dont understand the problem. If the question is "How does GPS compute course and heading" thats pretty simple. Spherical geometry is how one computes angles on a sphere. Smart guys worked that out a long time ago. Geographic models such as the WGS84 are used to translate the earth surface into a 2d image that we use on our charts. I thought the OP was asking what model is used to model the earth surface, but maybe he needs to clarify.

Google Spherical Geometry and WGS 84.



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post #12 of 49 Old 11-11-2019
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Re: Path used to compute bearing and distance by GPS?

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I dont understand the problem. If the question is "How does GPS compute course and heading" thats pretty simple. Spherical geometry is how one computes angles on a sphere. Smart guys worked that out a long time ago. Geographic models such as the WGS84 are used to translate a spherical surface into a 2d image that we use on our charts. I thought the OP was asking what model is used to model the earth surface, but maybe he needs to clarify.

Google Spherical Geometry and WGS 84.
Bot we all realize that for a waypoit/destination thousands of miles away... the ship's heading for the shortest path... will be changing as it proceeds. That is if you entered a waypoint 2,000 miles away that is not on the same lattitude... and your plotter told you to steer Xį at the get go and you held THAT Xį heading you would miss the mark!

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post #13 of 49 Old 11-11-2019
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Re: Path used to compute bearing and distance by GPS?

Thanks but thought it was a more basic question. Sure spherical geometry is used and perhaps modified to account for the earth being a spheroid rather than a sphere but whatís the mechanism? How is it done? Are all calculations off of a base map thatís spherical? Or off various Mercator projections? In some places due to tides and currents thereís significant perturbations with mounding of the sea so the surface isnít spherical in that local area. Is that accounted for? Most chart plotters give you tides/currents/ depth at low tide but also current expected depth is in there. Perhaps of no concern at smaller latitudes near the equator but in NB, PEI or even Maine variation would impact on shortest course. The fastest course is a separate calculation and more important to us sailors but the question remains and is a good one.

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post #14 of 49 Old 11-11-2019
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Re: Path used to compute bearing and distance by GPS?

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Thanks but thought it was a more basic question. Sure spherical geometry is used and perhaps modified to account for the earth being a spheroid rather than a sphere but whatís the mechanism? How is it done? Are all calculations off of a base map thatís spherical? Or off various Mercator projections? In some places due to tides and currents thereís significant perturbations with mounding of the sea so the surface isnít spherical in that local area. Is that accounted for? Most chart plotters give you tides/currents/ depth at low tide but also current expected depth is in there. Perhaps of no concern at smaller latitudes near the equator but in NB, PEI or even Maine variation would impact on shortest course. The fastest course is a separate calculation and more important to us sailors but the question remains and is a good one.
I don't think any of your concerns are part of short distance calculations. I don't know what would define short distance. They simply don't matter. The precisions would have to be to many more decimal places! and no helmsmen or AP will work with that level of precision. No GPS plotter reports accuracies of more than 0.X places if that. Does your plotter tell you a course is 38.1į or it is 38į. What is the precision of the speed probably the same.

GPS can be very precise for fixes I believe... but that level of precision is not required for commercial and recreational navigation.

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post #15 of 49 Old 11-11-2019
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Re: Path used to compute bearing and distance by GPS?

Hello,

I really depends on your particular GPS.

This is from the user guide of my B&G Vulcan:

Navigation method:
Different methods are available for calculating the distance and bearing between any two points on a chart.
The Great circle route is the shortest path between two points. However, if you are to travel along such a route, it would be difficult to steer manually as the heading would constantly be changing (except in the case of due north, south, or along the equator).
Rhumb lines are tracks of constant bearing. It is possible to travel between two locations using Rhumb line computation, but the distance would usually be greater than if Great circle is used.

I get to select Great Circle or Rhumb Line.

I don't know if or how Garmin allows you to select any options.

Barry
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post #16 of 49 Old 11-11-2019
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Re: Path used to compute bearing and distance by GPS?

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Hello,

The Great circle route is the shortest path between two points. However, if you are to travel along such a route, it would be difficult to steer manually as the heading would constantly be changing (except in the case of due north, south, or along the equator).
.

Barry
Good post Barry.

I think the heading on any lattitude... due east of west would be accurate as well as the equator. Once the heading crosses a lattitude the computations need to be great circle.

The distance does need spherical geometry because all paths are over a curved surface... assumed to be a sphere.

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post #17 of 49 Old 11-11-2019
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Re: Path used to compute bearing and distance by GPS?

As far as I know, the only line of latitude that is a great circle is the equator. All other lines of latitude are small circles. All meridians of longitude are great circles. The plane of the circle has to pass through the centre of the sphere for it to constitite a great circle.
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post #18 of 49 Old 11-11-2019
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Re: Path used to compute bearing and distance by GPS?

A gots it. Was asking a software question in a clumsy way. Oh well...

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post #19 of 49 Old 11-11-2019
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Re: Path used to compute bearing and distance by GPS?

As I understand the question, the OP is asking whether calculated bearing and distance consider that the earth is not perfectly round. Clearly, the GPS knows where the destination is located. The question is one of accuracy and efficiency of the route to get there, but only on a theoretical basis. Of the roughly 25,000 mile circumference of the globe I think the equator and the longitudinal distances are only off by about 40 or 50 miles. Theoretical it is. You are going to arrive at the proper destination, you simply may be a short distance to the side of the most efficient course.

I believe the WGS84 datum considers the distance from the center of the earth, as well as it's two dimensional location on the surface. Therefore, it would stand to reason, it calculates distance and bearing, using this out of round shape. I can't say for sure, it does.
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post #20 of 49 Old 11-12-2019
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Re: Path used to compute bearing and distance by GPS?

So thatís the answer. All are great circle. Probably no compensation for 13 nm spheroid compression at the poles nor local anomalies due to local phenomena.

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