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Does anyone have a good source, preferably free on-line, simply described to explain "exactly" how GPS co-ords work and relate to each other.

I am thoroughly familiar with planar co-ords and have controlled many construction projects with them; before the advent of AutoCAD on construction sites I had programs that could relate one co-ord to another in any position.

However with GPS I am confused.

I have just used a "Trimble" satellite setting out unit and robotic total station on a large job where I was fed the information.
Everything worked out alright but I was "drawing by numbers"
I was totally reliant on the technology and felt uncomfortable with it as I could not relate one point to another.

I have tried to find fuller explanations of what is happening with GPS but without success.

PLease advise



Not sure what you mean; GPS coordinates are basically Earth latitude, longitude, and altitude, based on the WGS84 geoid model of the Earth. On some receivers, you have the option to convert to different geoids or other coordinate systems.

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Hi IRstuff

Thank-you for your input.

I am confused by GPS coordinates and I have not found a source that will explain exactly what they are and how they
relate to each other.

I go back to the days of theodolite and tape; before electronic instruments were the norm. So I like to get a solid
understanding of what is happening.

If you see the small sketch attached:

If the radius of the earth is 6378.1 km and my sums are correct

Offsets from the tangent:

y= 100m x= 7.9x10-4 m
200m, 3.1mm.......................LEVELS BECOME INPORTANT
300m, 7.1mm
500m, 20mm

Offsets from the chord at mid-point:

CHORD= 100m, MIDPOINT OFF-SET= 2x10-4m
300m, 1.76mm
500m, 4.9mm
1000m, 19.5mm
2000m, 78.4mm
5000m, 490mm
10000m, 1960mm, ARC= 10001m ..............DISTANCES BECOME IMPORTANT

So for most building projects and minor civils works, which I have been involved with all my life, you can set out a project using GPS equipment with a datum and a direction and use planar, or cartesian, co-ordinates in the vicinity of that project: so long as the project is no bigger than about 200m x 200m when levels start to become important; depending on the tolerances and what you are building.

Above 10km then co-ordinate distances start to become important ( ie: major civils works like motorways, railways and service lines)

So most of my career I have not been involved with GPS co-ordinates. I can relate planar co-ordinates with each other quite well but I do not understand how GPS co-ords relate to each other.

If you look up a book it will say things like "....they relate to a transverse mercator...." which does not tell me anything.

They certainly do not relate to the simple trigonometry outlined above.

So if anyone has any reference they can point me to I would be very obliged. If anyone has any comments on the above then please feel free to comment. I am certainly prepared to proved wrong in order to learn; which is what I am trying to do.

Please advise.

Cheers peakpilgrim.


I'm unclear how you came up with 200m; by my calculation assuming a flat earth results in 15.7 um of height error or 65 nm of length error, so even if you are building integrated circuits 200 m across, it would still be negligible.

Again, GPS produces relatively accurate single reading latitude, longitude, altitude (LLA) directly from calculating its time of flight from GPS satellites in extremely accurately characterized orbits. This is ostensibly done in 3D cartesian coordinates on the earth centered earth fixed (ECEF) coordinate system. This then converted to LLA in conjunction with the WGS84 geoid. Some receivers are able to amp into different datum systems, like NAD83 or NAD27. Generally, this only makes sense in the context of using a "real-time kinematic" (RTK) GPS system that uses a base station with a highly accurate, known, GPS position. Since this receiver "knows" its position is absolutely accurate, it therefore "knows" that the error from each real-time GPS position solution is due to errors in emphemeris or ionspheric RF delays, and can therefore "tell" any RTK GPS receiver linked to it what the errors are, resulting in the RTK GPS calculating an extremely accurate GPS position based on what the base station is telling it. This correction can be as good as 1 cm over a 1000 km radius.

This basic process is no different than using theodolites and chains to measure coordinates relative to a survey monument.

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Hi IRstuff,

Again than-you for your interesting and informative input.

You are right to question the 200m building project.

From my simple trigonometric model, assuming the earth is a perfect sphere,(which it isn't),the earth drops off the tangent 3.1mm at 200m; with the earth radius 6378.1 km. You would have to be doing extremely accurate work for this to be an issue.

I have never had to consider using GPS on any building project, apart from set up, even large housing estates, because the errors incurred far outweigh the accuracy required.

When using the Trimble GPS equipment I would often see that the units were plugged into maybe eight to ten satellites; all adjusting the position and producing, as you say, extremely accurate results.

As you say you can set up an extremely accurate known position and datum for a building project, using the equipment; then as long as you have a back-site you can set out your building project using cartesian co-ordinates.

Unfortunately you lost me when you started to talk about WGS84 NAD83 or NAD27. I do not know what these are but I would like to know and find out how one point relates to another so that, if necessary, one can check it with a calculator; like cartesian co-ordinates; without relying on the electronics to do all the hard sums.

When I first started using EDM equipment on site, in the early 1990's, I would always check the distance with a steel tape to make sure that the technology was behaving itself! as I said above I do like to get a solid idea of what is happening

Kind regards,



WGS84 is the currently accepted/acceptable geoid model of the Earth's surface, and so altitudes are calculated relative to that surface. Latitude/longitude are mapped onto that surface. USGS maintains it's own vertical datum system, now called NAD83.

Your GPS most likely can also output in UTM northing/easting coordinates, or at least, with post-processing

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